id	sid	tid	token	lemma	pos
cana-943	1	1	communications	communication	NOUN
cana-943	1	2	on	on	ADP
cana-943	1	3	applied	apply	VERB
cana-943	1	4	nonlinear	nonlinear	ADJ
cana-943	1	5	analysis	analysis	NOUN
cana-943	1	6	issn	issn	NOUN
cana-943	1	7	:	:	PUNCT
cana-943	1	8	1074	1074	NUM
cana-943	1	9	-	-	PUNCT
cana-943	1	10	133x	133x	NUM
cana-943	1	11	vol	vol	NOUN
cana-943	1	12	31	31	NUM
cana-943	1	13	no	no	NOUN
cana-943	1	14	.	.	PUNCT
cana-943	2	1	4s	4s	NUM
cana-943	2	2	(	(	PUNCT
cana-943	2	3	2024	2024	NUM
cana-943	2	4	)	)	PUNCT
cana-943	2	5	466	466	NUM
cana-943	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	2	7	the	the	DET
cana-943	2	8	intersection	intersection	NOUN
cana-943	2	9	of	of	ADP
cana-943	2	10	algebra	algebra	NOUN
cana-943	2	11	and	and	CCONJ
cana-943	2	12	cryptography	cryptography	NOUN
cana-943	2	13	:	:	PUNCT
cana-943	2	14	enhancing	enhance	VERB
cana-943	2	15	information	information	NOUN
cana-943	2	16	security	security	NOUN
cana-943	2	17	through	through	ADP
cana-943	2	18	mathematical	mathematical	ADJ
cana-943	2	19	foundations	foundations	PROPN
cana-943	2	20	shashi	shashi	PROPN
cana-943	2	21	raj	raj	PROPN
cana-943	2	22	k1	k1	PROPN
cana-943	2	23	,	,	PUNCT
cana-943	2	24	dr	dr	PROPN
cana-943	2	25	.	.	PROPN
cana-943	2	26	m.	m.	PROPN
cana-943	2	27	manicka	manicka	PROPN
cana-943	2	28	raja2	raja2	PROPN
cana-943	2	29	,	,	PUNCT
cana-943	2	30	dr	dr	PROPN
cana-943	2	31	vijay	vijay	PROPN
cana-943	2	32	more3	more3	PROPN
cana-943	2	33	,	,	PUNCT
cana-943	2	34	dr	dr	PROPN
cana-943	2	35	ch	ch	PROPN
cana-943	2	36	madhava	madhava	PROPN
cana-943	2	37	rao4	rao4	PROPN
cana-943	2	38	,	,	PUNCT
cana-943	2	39	dr	dr	PROPN
cana-943	2	40	.	.	PROPN
cana-943	2	41	m.	m.	PROPN
cana-943	2	42	kavitha5	kavitha5	PROPN
cana-943	2	43	,	,	PUNCT
cana-943	2	44	dr	dr	PROPN
cana-943	2	45	.	.	PROPN
cana-943	2	46	gurwinder	gurwinder	PROPN
cana-943	2	47	singh6	singh6	NOUN
cana-943	2	48	1	1	NUM
cana-943	2	49	assistant	assistant	NOUN
cana-943	2	50	professor	professor	NOUN
cana-943	2	51	,	,	PUNCT
cana-943	2	52	department	department	NOUN
cana-943	2	53	of	of	ADP
cana-943	2	54	electronics	electronic	NOUN
cana-943	2	55	and	and	CCONJ
cana-943	2	56	communication	communication	NOUN
cana-943	2	57	engineering	engineering	NOUN
cana-943	2	58	,	,	PUNCT
cana-943	2	59	dayananda	dayananda	PROPN
cana-943	2	60	sagar	sagar	PROPN
cana-943	2	61	college	college	PROPN
cana-943	2	62	of	of	ADP
cana-943	2	63	engineering	engineering	PROPN
cana-943	2	64	bengaluru	bengaluru	PROPN
cana-943	2	65	,	,	PUNCT
cana-943	2	66	2	2	NUM
cana-943	2	67	assistant	assistant	NOUN
cana-943	2	68	professor	professor	NOUN
cana-943	2	69	,	,	PUNCT
cana-943	2	70	division	division	NOUN
cana-943	2	71	of	of	ADP
cana-943	2	72	computer	computer	NOUN
cana-943	2	73	science	science	NOUN
cana-943	2	74	and	and	CCONJ
cana-943	2	75	engineering	engineering	NOUN
cana-943	2	76	,	,	PUNCT
cana-943	2	77	karunya	karunya	PROPN
cana-943	2	78	institute	institute	PROPN
cana-943	2	79	of	of	ADP
cana-943	2	80	technology	technology	PROPN
cana-943	2	81	and	and	CCONJ
cana-943	2	82	sciences	science	NOUN
cana-943	2	83	,	,	PUNCT
cana-943	2	84	coimbatore	coimbatore	NOUN
cana-943	2	85	,	,	PUNCT
cana-943	2	86	3	3	NUM
cana-943	2	87	associate	associate	NOUN
cana-943	2	88	professor	professor	NOUN
cana-943	2	89	,	,	PUNCT
cana-943	2	90	department	department	NOUN
cana-943	2	91	of	of	ADP
cana-943	2	92	computer	computer	NOUN
cana-943	2	93	engineering	engineering	NOUN
cana-943	2	94	,	,	PUNCT
cana-943	2	95	met	meet	VERB
cana-943	2	96	's	's	PART
cana-943	2	97	institute	institute	NOUN
cana-943	2	98	of	of	ADP
cana-943	2	99	engineering	engineering	PROPN
cana-943	2	100	,	,	PUNCT
cana-943	2	101	bhujbal	bhujbal	ADJ
cana-943	2	102	knowledge	knowledge	NOUN
cana-943	2	103	city	city	PROPN
cana-943	2	104	,	,	PUNCT
cana-943	2	105	nashik	nashik	PROPN
cana-943	2	106	,	,	PUNCT
cana-943	2	107	maharashtra	maharashtra	PROPN
cana-943	2	108	,	,	PUNCT
cana-943	2	109	4	4	NUM
cana-943	2	110	associate	associate	NOUN
cana-943	2	111	professor	professor	NOUN
cana-943	2	112	,	,	PUNCT
cana-943	2	113	koneru	koneru	PROPN
cana-943	2	114	lakshmaiah	lakshmaiah	PROPN
cana-943	2	115	education	education	PROPN
cana-943	2	116	foundation	foundation	PROPN
cana-943	2	117	,	,	PUNCT
cana-943	2	118	vaddeswaram	vaddeswaram	NOUN
cana-943	2	119	,	,	PUNCT
cana-943	2	120	5	5	NUM
cana-943	2	121	associate	associate	NOUN
cana-943	2	122	professor	professor	NOUN
cana-943	2	123	,	,	PUNCT
cana-943	2	124	velalar	velalar	ADJ
cana-943	2	125	college	college	NOUN
cana-943	2	126	of	of	ADP
cana-943	2	127	engineering	engineering	NOUN
cana-943	2	128	and	and	CCONJ
cana-943	2	129	technology	technology	NOUN
cana-943	2	130	,	,	PUNCT
cana-943	2	131	thindal	thindal	ADJ
cana-943	2	132	,	,	PUNCT
cana-943	2	133	tamilnadu	tamilnadu	NOUN
cana-943	2	134	,	,	PUNCT
cana-943	2	135	6	6	NUM
cana-943	2	136	associate	associate	NOUN
cana-943	2	137	professor	professor	NOUN
cana-943	2	138	,	,	PUNCT
cana-943	2	139	chandigarh	chandigarh	PROPN
cana-943	2	140	university	university	PROPN
cana-943	2	141	,	,	PUNCT
cana-943	2	142	mohali	mohali	PROPN
cana-943	2	143	,	,	PUNCT
cana-943	2	144	punjab	punjab	PROPN
cana-943	2	145	.	.	PUNCT
cana-943	3	1	shashiraj18@gmail.com	shashiraj18@gmail.com	X
cana-943	3	2	,	,	PUNCT
cana-943	3	3	manickaraja89@gmail.com	manickaraja89@gmail.com	PROPN
cana-943	3	4	,	,	PUNCT
cana-943	3	5	vbmore2005@rediffmail.com	vbmore2005@rediffmail.com	NOUN
cana-943	3	6	,	,	PUNCT
cana-943	3	7	cmadhavarao@kluniversity.in	cmadhavarao@kluniversity.in	NOUN
cana-943	3	8	,	,	PUNCT
cana-943	3	9	misskavi84@gmail.com	misskavi84@gmail.com	X
cana-943	3	10	,	,	PUNCT
cana-943	3	11	singh1001maths@gmail.com	singh1001maths@gmail.com	X
cana-943	3	12	article	article	PROPN
cana-943	3	13	history	history	NOUN
cana-943	3	14	:	:	PUNCT
cana-943	3	15	received	receive	VERB
cana-943	3	16	:	:	PUNCT
cana-943	3	17	22	22	NUM
cana-943	3	18	-	-	PUNCT
cana-943	3	19	04	04	NUM
cana-943	3	20	-	-	PUNCT
cana-943	3	21	2024	2024	NUM
cana-943	3	22	revised	revise	VERB
cana-943	3	23	:	:	PUNCT
cana-943	3	24	14	14	NUM
cana-943	3	25	-	-	SYM
cana-943	3	26	06	06	NUM
cana-943	3	27	-	-	PUNCT
cana-943	3	28	2024	2024	NUM
cana-943	3	29	accepted	accept	VERB
cana-943	3	30	:	:	PUNCT
cana-943	3	31	23	23	NUM
cana-943	3	32	-	-	SYM
cana-943	3	33	06	06	NUM
cana-943	3	34	-	-	PUNCT
cana-943	3	35	2024	2024	NUM
cana-943	3	36	abstract	abstract	NOUN
cana-943	3	37	:	:	PUNCT
cana-943	3	38	the	the	DET
cana-943	3	39	rapid	rapid	ADJ
cana-943	3	40	advancements	advancement	NOUN
cana-943	3	41	in	in	ADP
cana-943	3	42	digital	digital	ADJ
cana-943	3	43	technologies	technology	NOUN
cana-943	3	44	have	have	AUX
cana-943	3	45	necessitated	necessitate	VERB
cana-943	3	46	the	the	DET
cana-943	3	47	development	development	NOUN
cana-943	3	48	of	of	ADP
cana-943	3	49	robust	robust	ADJ
cana-943	3	50	information	information	NOUN
cana-943	3	51	security	security	NOUN
cana-943	3	52	measures	measure	NOUN
cana-943	3	53	.	.	PUNCT
cana-943	4	1	this	this	DET
cana-943	4	2	paper	paper	NOUN
cana-943	4	3	explores	explore	VERB
cana-943	4	4	the	the	DET
cana-943	4	5	intersection	intersection	NOUN
cana-943	4	6	of	of	ADP
cana-943	4	7	algebra	algebra	NOUN
cana-943	4	8	and	and	CCONJ
cana-943	4	9	cryptography	cryptography	NOUN
cana-943	4	10	,	,	PUNCT
cana-943	4	11	focusing	focus	VERB
cana-943	4	12	on	on	ADP
cana-943	4	13	how	how	SCONJ
cana-943	4	14	algebraic	algebraic	ADJ
cana-943	4	15	principles	principle	NOUN
cana-943	4	16	can	can	AUX
cana-943	4	17	enhance	enhance	VERB
cana-943	4	18	cryptographic	cryptographic	ADJ
cana-943	4	19	techniques	technique	NOUN
cana-943	4	20	to	to	PART
cana-943	4	21	provide	provide	VERB
cana-943	4	22	stronger	strong	ADJ
cana-943	4	23	security	security	NOUN
cana-943	4	24	foundations	foundation	NOUN
cana-943	4	25	.	.	PUNCT
cana-943	5	1	by	by	ADP
cana-943	5	2	leveraging	leverage	VERB
cana-943	5	3	mathematical	mathematical	ADJ
cana-943	5	4	structures	structure	NOUN
cana-943	5	5	such	such	ADJ
cana-943	5	6	as	as	ADP
cana-943	5	7	groups	group	NOUN
cana-943	5	8	,	,	PUNCT
cana-943	5	9	rings	ring	NOUN
cana-943	5	10	,	,	PUNCT
cana-943	5	11	and	and	CCONJ
cana-943	5	12	fields	field	NOUN
cana-943	5	13	,	,	PUNCT
cana-943	5	14	we	we	PRON
cana-943	5	15	can	can	AUX
cana-943	5	16	address	address	VERB
cana-943	5	17	critical	critical	ADJ
cana-943	5	18	challenges	challenge	NOUN
cana-943	5	19	in	in	ADP
cana-943	5	20	encryption	encryption	NOUN
cana-943	5	21	,	,	PUNCT
cana-943	5	22	secure	secure	ADJ
cana-943	5	23	communications	communication	NOUN
cana-943	5	24	,	,	PUNCT
cana-943	5	25	and	and	CCONJ
cana-943	5	26	data	datum	NOUN
cana-943	5	27	privacy	privacy	NOUN
cana-943	5	28	.	.	PUNCT
cana-943	6	1	this	this	DET
cana-943	6	2	study	study	NOUN
cana-943	6	3	reviews	review	VERB
cana-943	6	4	key	key	ADJ
cana-943	6	5	algebraic	algebraic	ADJ
cana-943	6	6	methods	method	NOUN
cana-943	6	7	used	use	VERB
cana-943	6	8	in	in	ADP
cana-943	6	9	contemporary	contemporary	ADJ
cana-943	6	10	cryptographic	cryptographic	ADJ
cana-943	6	11	protocols	protocol	NOUN
cana-943	6	12	,	,	PUNCT
cana-943	6	13	including	include	VERB
cana-943	6	14	elliptic	elliptic	ADJ
cana-943	6	15	curve	curve	NOUN
cana-943	6	16	cryptography	cryptography	NOUN
cana-943	6	17	,	,	PUNCT
cana-943	6	18	homomorphic	homomorphic	ADJ
cana-943	6	19	encryption	encryption	NOUN
cana-943	6	20	,	,	PUNCT
cana-943	6	21	and	and	CCONJ
cana-943	6	22	lattice	lattice	NOUN
cana-943	6	23	-	-	PUNCT
cana-943	6	24	based	base	VERB
cana-943	6	25	cryptography	cryptography	NOUN
cana-943	6	26	,	,	PUNCT
cana-943	6	27	and	and	CCONJ
cana-943	6	28	demonstrates	demonstrate	VERB
cana-943	6	29	their	their	PRON
cana-943	6	30	practical	practical	ADJ
cana-943	6	31	applications	application	NOUN
cana-943	6	32	through	through	ADP
cana-943	6	33	detailed	detailed	ADJ
cana-943	6	34	case	case	NOUN
cana-943	6	35	studies	study	NOUN
cana-943	6	36	.	.	PUNCT
cana-943	7	1	our	our	PRON
cana-943	7	2	comparative	comparative	ADJ
cana-943	7	3	analysis	analysis	NOUN
cana-943	7	4	highlights	highlight	NOUN
cana-943	7	5	the	the	DET
cana-943	7	6	superior	superior	ADJ
cana-943	7	7	performance	performance	NOUN
cana-943	7	8	and	and	CCONJ
cana-943	7	9	security	security	NOUN
cana-943	7	10	of	of	ADP
cana-943	7	11	algebra	algebra	NOUN
cana-943	7	12	-	-	PUNCT
cana-943	7	13	based	base	VERB
cana-943	7	14	cryptographic	cryptographic	ADJ
cana-943	7	15	solutions	solution	NOUN
cana-943	7	16	compared	compare	VERB
cana-943	7	17	to	to	ADP
cana-943	7	18	traditional	traditional	ADJ
cana-943	7	19	methods	method	NOUN
cana-943	7	20	.	.	PUNCT
cana-943	8	1	finally	finally	ADV
cana-943	8	2	,	,	PUNCT
cana-943	8	3	we	we	PRON
cana-943	8	4	discuss	discuss	VERB
cana-943	8	5	the	the	DET
cana-943	8	6	emerging	emerge	VERB
cana-943	8	7	trends	trend	NOUN
cana-943	8	8	and	and	CCONJ
cana-943	8	9	future	future	ADJ
cana-943	8	10	directions	direction	NOUN
cana-943	8	11	in	in	ADP
cana-943	8	12	algebraic	algebraic	ADJ
cana-943	8	13	cryptography	cryptography	NOUN
cana-943	8	14	,	,	PUNCT
cana-943	8	15	emphasizing	emphasize	VERB
cana-943	8	16	the	the	DET
cana-943	8	17	potential	potential	NOUN
cana-943	8	18	of	of	ADP
cana-943	8	19	these	these	DET
cana-943	8	20	mathematical	mathematical	ADJ
cana-943	8	21	foundations	foundation	NOUN
cana-943	8	22	to	to	PART
cana-943	8	23	address	address	VERB
cana-943	8	24	the	the	DET
cana-943	8	25	evolving	evolve	VERB
cana-943	8	26	threats	threat	NOUN
cana-943	8	27	in	in	ADP
cana-943	8	28	information	information	NOUN
cana-943	8	29	security	security	NOUN
cana-943	8	30	.	.	PUNCT
cana-943	9	1	keywords	keyword	NOUN
cana-943	9	2	:	:	PUNCT
cana-943	9	3	algebra	algebra	NOUN
cana-943	9	4	,	,	PUNCT
cana-943	9	5	cryptography	cryptography	NOUN
cana-943	9	6	,	,	PUNCT
cana-943	9	7	information	information	NOUN
cana-943	9	8	security	security	NOUN
cana-943	9	9	,	,	PUNCT
cana-943	9	10	elliptic	elliptic	ADJ
cana-943	9	11	curve	curve	NOUN
cana-943	9	12	cryptography	cryptography	NOUN
cana-943	9	13	,	,	PUNCT
cana-943	9	14	homomorphic	homomorphic	ADJ
cana-943	9	15	encryption	encryption	NOUN
cana-943	9	16	,	,	PUNCT
cana-943	9	17	lattice	lattice	NOUN
cana-943	9	18	-	-	PUNCT
cana-943	9	19	based	base	VERB
cana-943	9	20	cryptography	cryptography	NOUN
cana-943	9	21	,	,	PUNCT
cana-943	9	22	finite	finite	ADJ
cana-943	9	23	fields	field	NOUN
cana-943	9	24	,	,	PUNCT
cana-943	9	25	group	group	NOUN
cana-943	9	26	theory	theory	NOUN
cana-943	9	27	,	,	PUNCT
cana-943	9	28	ring	ring	NOUN
cana-943	9	29	theory	theory	NOUN
cana-943	9	30	,	,	PUNCT
cana-943	9	31	data	data	NOUN
cana-943	9	32	privacy	privacy	NOUN
cana-943	9	33	,	,	PUNCT
cana-943	9	34	quantum	quantum	NOUN
cana-943	9	35	computing	computing	NOUN
cana-943	9	36	,	,	PUNCT
cana-943	9	37	secure	secure	ADJ
cana-943	9	38	communications	communication	NOUN
cana-943	9	39	,	,	PUNCT
cana-943	9	40	blockchain	blockchain	PROPN
cana-943	9	41	,	,	PUNCT
cana-943	9	42	zeroknowledge	zeroknowledge	PROPN
cana-943	9	43	proofs	proof	NOUN
cana-943	9	44	,	,	PUNCT
cana-943	9	45	post	post	ADJ
cana-943	9	46	-	-	ADJ
cana-943	9	47	quantum	quantum	ADJ
cana-943	9	48	cryptography	cryptography	NOUN
cana-943	9	49	.	.	PUNCT
cana-943	10	1	1	1	X
cana-943	10	2	.	.	X
cana-943	10	3	introduction	introduction	NOUN
cana-943	10	4	in	in	ADP
cana-943	10	5	the	the	DET
cana-943	10	6	modern	modern	ADJ
cana-943	10	7	digital	digital	ADJ
cana-943	10	8	era	era	NOUN
cana-943	10	9	,	,	PUNCT
cana-943	10	10	the	the	DET
cana-943	10	11	security	security	NOUN
cana-943	10	12	of	of	ADP
cana-943	10	13	information	information	NOUN
cana-943	10	14	has	have	AUX
cana-943	10	15	become	become	VERB
cana-943	10	16	a	a	DET
cana-943	10	17	paramount	paramount	ADJ
cana-943	10	18	concern	concern	NOUN
cana-943	10	19	.	.	PUNCT
cana-943	11	1	with	with	ADP
cana-943	11	2	the	the	DET
cana-943	11	3	proliferation	proliferation	NOUN
cana-943	11	4	of	of	ADP
cana-943	11	5	internet	internet	NOUN
cana-943	11	6	-	-	PUNCT
cana-943	11	7	enabled	enable	VERB
cana-943	11	8	devices	device	NOUN
cana-943	11	9	,	,	PUNCT
cana-943	11	10	the	the	DET
cana-943	11	11	volume	volume	NOUN
cana-943	11	12	of	of	ADP
cana-943	11	13	data	datum	NOUN
cana-943	11	14	being	be	AUX
cana-943	11	15	transmitted	transmit	VERB
cana-943	11	16	and	and	CCONJ
cana-943	11	17	stored	store	VERB
cana-943	11	18	electronically	electronically	ADV
cana-943	11	19	has	have	AUX
cana-943	11	20	surged	surge	VERB
cana-943	11	21	,	,	PUNCT
cana-943	11	22	necessitating	necessitate	VERB
cana-943	11	23	robust	robust	ADJ
cana-943	11	24	methods	method	NOUN
cana-943	11	25	to	to	PART
cana-943	11	26	safeguard	safeguard	VERB
cana-943	11	27	sensitive	sensitive	ADJ
cana-943	11	28	information	information	NOUN
cana-943	11	29	.	.	PUNCT
cana-943	12	1	cryptography	cryptography	NOUN
cana-943	12	2	,	,	PUNCT
cana-943	12	3	the	the	DET
cana-943	12	4	science	science	NOUN
cana-943	12	5	of	of	ADP
cana-943	12	6	encrypting	encrypt	VERB
cana-943	12	7	and	and	CCONJ
cana-943	12	8	decrypting	decrypt	VERB
cana-943	12	9	information	information	NOUN
cana-943	12	10	,	,	PUNCT
cana-943	12	11	plays	play	VERB
cana-943	12	12	a	a	DET
cana-943	12	13	crucial	crucial	ADJ
cana-943	12	14	role	role	NOUN
cana-943	12	15	in	in	ADP
cana-943	12	16	ensuring	ensure	VERB
cana-943	12	17	data	datum	NOUN
cana-943	12	18	security	security	NOUN
cana-943	12	19	and	and	CCONJ
cana-943	12	20	privacy	privacy	NOUN
cana-943	12	21	.	.	PUNCT
cana-943	13	1	from	from	ADP
cana-943	13	2	securing	secure	VERB
cana-943	13	3	online	online	ADJ
cana-943	13	4	transactions	transaction	NOUN
cana-943	13	5	to	to	ADP
cana-943	13	6	protecting	protect	VERB
cana-943	13	7	confidential	confidential	ADJ
cana-943	13	8	communications	communication	NOUN
cana-943	13	9	,	,	PUNCT
cana-943	13	10	cryptography	cryptography	NOUN
cana-943	13	11	is	be	AUX
cana-943	13	12	the	the	DET
cana-943	13	13	backbone	backbone	NOUN
cana-943	13	14	of	of	ADP
cana-943	13	15	contemporary	contemporary	ADJ
cana-943	13	16	information	information	NOUN
cana-943	13	17	security	security	NOUN
cana-943	13	18	systems	system	NOUN
cana-943	13	19	.	.	PUNCT
cana-943	14	1	communications	communication	NOUN
cana-943	14	2	on	on	ADP
cana-943	14	3	applied	apply	VERB
cana-943	14	4	nonlinear	nonlinear	ADJ
cana-943	14	5	analysis	analysis	NOUN
cana-943	14	6	issn	issn	NOUN
cana-943	14	7	:	:	PUNCT
cana-943	14	8	1074	1074	NUM
cana-943	14	9	-	-	PUNCT
cana-943	14	10	133x	133x	NUM
cana-943	14	11	vol	vol	NOUN
cana-943	14	12	31	31	NUM
cana-943	14	13	no	no	NOUN
cana-943	14	14	.	.	PUNCT
cana-943	15	1	4s	4s	NUM
cana-943	15	2	(	(	PUNCT
cana-943	15	3	2024	2024	NUM
cana-943	15	4	)	)	PUNCT
cana-943	15	5	467	467	NUM
cana-943	15	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	15	7	the	the	DET
cana-943	15	8	foundational	foundational	ADJ
cana-943	15	9	work	work	NOUN
cana-943	15	10	by	by	ADP
cana-943	15	11	diffie	diffie	PROPN
cana-943	15	12	and	and	CCONJ
cana-943	15	13	hellman	hellman	NOUN
cana-943	15	14	in	in	ADP
cana-943	15	15	1976	1976	NUM
cana-943	15	16	introduced	introduce	VERB
cana-943	15	17	the	the	DET
cana-943	15	18	concept	concept	NOUN
cana-943	15	19	of	of	ADP
cana-943	15	20	public	public	ADJ
cana-943	15	21	-	-	PUNCT
cana-943	15	22	key	key	NOUN
cana-943	15	23	cryptography	cryptography	NOUN
cana-943	15	24	,	,	PUNCT
cana-943	15	25	revolutionizing	revolutionize	VERB
cana-943	15	26	the	the	DET
cana-943	15	27	field	field	NOUN
cana-943	15	28	by	by	ADP
cana-943	15	29	enabling	enable	VERB
cana-943	15	30	secure	secure	ADJ
cana-943	15	31	communications	communication	NOUN
cana-943	15	32	over	over	ADP
cana-943	15	33	insecure	insecure	ADJ
cana-943	15	34	channels	channel	NOUN
cana-943	15	35	[	[	X
cana-943	15	36	1	1	NUM
cana-943	15	37	]	]	PUNCT
cana-943	15	38	.	.	PUNCT
cana-943	16	1	subsequent	subsequent	ADJ
cana-943	16	2	advancements	advancement	NOUN
cana-943	16	3	,	,	PUNCT
cana-943	16	4	such	such	ADJ
cana-943	16	5	as	as	ADP
cana-943	16	6	the	the	DET
cana-943	16	7	rsa	rsa	PROPN
cana-943	16	8	algorithm	algorithm	NOUN
cana-943	16	9	by	by	ADP
cana-943	16	10	rivest	riv	ADJ
cana-943	16	11	,	,	PUNCT
cana-943	16	12	shamir	shamir	ADJ
cana-943	16	13	,	,	PUNCT
cana-943	16	14	and	and	CCONJ
cana-943	16	15	adleman	adleman	NOUN
cana-943	16	16	,	,	PUNCT
cana-943	16	17	further	far	ADV
cana-943	16	18	cemented	cement	VERB
cana-943	16	19	the	the	DET
cana-943	16	20	importance	importance	NOUN
cana-943	16	21	of	of	ADP
cana-943	16	22	cryptographic	cryptographic	ADJ
cana-943	16	23	techniques	technique	NOUN
cana-943	16	24	in	in	ADP
cana-943	16	25	digital	digital	ADJ
cana-943	16	26	security	security	NOUN
cana-943	16	27	[	[	X
cana-943	16	28	2	2	NUM
cana-943	16	29	]	]	PUNCT
cana-943	16	30	.	.	PUNCT
cana-943	17	1	however	however	ADV
cana-943	17	2	,	,	PUNCT
cana-943	17	3	as	as	SCONJ
cana-943	17	4	technology	technology	NOUN
cana-943	17	5	evolves	evolve	VERB
cana-943	17	6	,	,	PUNCT
cana-943	17	7	so	so	ADV
cana-943	17	8	do	do	VERB
cana-943	17	9	the	the	DET
cana-943	17	10	threats	threat	NOUN
cana-943	17	11	.	.	PUNCT
cana-943	18	1	modern	modern	ADJ
cana-943	18	2	adversaries	adversary	NOUN
cana-943	18	3	leverage	leverage	VERB
cana-943	18	4	sophisticated	sophisticated	ADJ
cana-943	18	5	methods	method	NOUN
cana-943	18	6	,	,	PUNCT
cana-943	18	7	including	include	VERB
cana-943	18	8	quantum	quantum	NOUN
cana-943	18	9	computing	computing	NOUN
cana-943	18	10	,	,	PUNCT
cana-943	18	11	to	to	PART
cana-943	18	12	break	break	VERB
cana-943	18	13	traditional	traditional	ADJ
cana-943	18	14	cryptographic	cryptographic	ADJ
cana-943	18	15	systems	system	NOUN
cana-943	18	16	.	.	PUNCT
cana-943	19	1	this	this	DET
cana-943	19	2	ongoing	ongoing	ADJ
cana-943	19	3	arms	arm	NOUN
cana-943	19	4	race	race	NOUN
cana-943	19	5	between	between	ADP
cana-943	19	6	security	security	NOUN
cana-943	19	7	measures	measure	NOUN
cana-943	19	8	and	and	CCONJ
cana-943	19	9	attack	attack	NOUN
cana-943	19	10	strategies	strategy	NOUN
cana-943	19	11	underscores	underscore	VERB
cana-943	19	12	the	the	DET
cana-943	19	13	need	need	NOUN
cana-943	19	14	for	for	ADP
cana-943	19	15	continually	continually	ADV
cana-943	19	16	evolving	evolve	VERB
cana-943	19	17	cryptographic	cryptographic	ADJ
cana-943	19	18	techniques	technique	NOUN
cana-943	19	19	.	.	PUNCT
cana-943	20	1	algebra	algebra	NOUN
cana-943	20	2	,	,	PUNCT
cana-943	20	3	a	a	DET
cana-943	20	4	branch	branch	NOUN
cana-943	20	5	of	of	ADP
cana-943	20	6	mathematics	mathematic	NOUN
cana-943	20	7	dealing	deal	VERB
cana-943	20	8	with	with	ADP
cana-943	20	9	symbols	symbol	NOUN
cana-943	20	10	and	and	CCONJ
cana-943	20	11	the	the	DET
cana-943	20	12	rules	rule	NOUN
cana-943	20	13	for	for	ADP
cana-943	20	14	manipulating	manipulate	VERB
cana-943	20	15	these	these	DET
cana-943	20	16	symbols	symbol	NOUN
cana-943	20	17	,	,	PUNCT
cana-943	20	18	provides	provide	VERB
cana-943	20	19	a	a	DET
cana-943	20	20	fundamental	fundamental	ADJ
cana-943	20	21	framework	framework	NOUN
cana-943	20	22	for	for	ADP
cana-943	20	23	modern	modern	ADJ
cana-943	20	24	cryptography	cryptography	NOUN
cana-943	20	25	.	.	PUNCT
cana-943	21	1	algebraic	algebraic	ADJ
cana-943	21	2	structures	structure	NOUN
cana-943	21	3	such	such	ADJ
cana-943	21	4	as	as	ADP
cana-943	21	5	groups	group	NOUN
cana-943	21	6	,	,	PUNCT
cana-943	21	7	rings	ring	NOUN
cana-943	21	8	,	,	PUNCT
cana-943	21	9	and	and	CCONJ
cana-943	21	10	fields	field	NOUN
cana-943	21	11	underpin	underpin	VERB
cana-943	21	12	many	many	ADJ
cana-943	21	13	cryptographic	cryptographic	ADJ
cana-943	21	14	algorithms	algorithm	NOUN
cana-943	21	15	and	and	CCONJ
cana-943	21	16	protocols	protocol	NOUN
cana-943	21	17	.	.	PUNCT
cana-943	22	1	for	for	ADP
cana-943	22	2	instance	instance	NOUN
cana-943	22	3	,	,	PUNCT
cana-943	22	4	elliptic	elliptic	ADJ
cana-943	22	5	curve	curve	NOUN
cana-943	22	6	cryptography	cryptography	NOUN
cana-943	22	7	(	(	PUNCT
cana-943	22	8	ecc	ecc	PROPN
cana-943	22	9	)	)	PUNCT
cana-943	22	10	,	,	PUNCT
cana-943	22	11	which	which	PRON
cana-943	22	12	offers	offer	VERB
cana-943	22	13	higher	high	ADJ
cana-943	22	14	security	security	NOUN
cana-943	22	15	with	with	ADP
cana-943	22	16	smaller	small	ADJ
cana-943	22	17	key	key	ADJ
cana-943	22	18	sizes	size	NOUN
cana-943	22	19	compared	compare	VERB
cana-943	22	20	to	to	ADP
cana-943	22	21	traditional	traditional	ADJ
cana-943	22	22	methods	method	NOUN
cana-943	22	23	,	,	PUNCT
cana-943	22	24	relies	rely	VERB
cana-943	22	25	heavily	heavily	ADV
cana-943	22	26	on	on	ADP
cana-943	22	27	the	the	DET
cana-943	22	28	properties	property	NOUN
cana-943	22	29	of	of	ADP
cana-943	22	30	elliptic	elliptic	ADJ
cana-943	22	31	curves	curve	NOUN
cana-943	22	32	over	over	ADP
cana-943	22	33	finite	finite	ADJ
cana-943	22	34	fields	field	NOUN
cana-943	22	35	[	[	X
cana-943	22	36	3	3	NUM
cana-943	22	37	]	]	PUNCT
cana-943	22	38	.	.	PUNCT
cana-943	23	1	the	the	DET
cana-943	23	2	significance	significance	NOUN
cana-943	23	3	of	of	ADP
cana-943	23	4	algebra	algebra	NOUN
cana-943	23	5	in	in	ADP
cana-943	23	6	cryptography	cryptography	NOUN
cana-943	23	7	extends	extend	VERB
cana-943	23	8	beyond	beyond	ADP
cana-943	23	9	ecc	ecc	PROPN
cana-943	23	10	.	.	PROPN
cana-943	23	11	homomorphic	homomorphic	ADJ
cana-943	23	12	encryption	encryption	NOUN
cana-943	23	13	,	,	PUNCT
cana-943	23	14	a	a	DET
cana-943	23	15	breakthrough	breakthrough	NOUN
cana-943	23	16	allowing	allow	VERB
cana-943	23	17	computations	computation	NOUN
cana-943	23	18	on	on	ADP
cana-943	23	19	encrypted	encrypt	VERB
cana-943	23	20	data	datum	NOUN
cana-943	23	21	without	without	ADP
cana-943	23	22	decryption	decryption	NOUN
cana-943	23	23	,	,	PUNCT
cana-943	23	24	utilizes	utilize	VERB
cana-943	23	25	algebraic	algebraic	ADJ
cana-943	23	26	structures	structure	NOUN
cana-943	23	27	to	to	PART
cana-943	23	28	maintain	maintain	VERB
cana-943	23	29	data	data	NOUN
cana-943	23	30	privacy	privacy	NOUN
cana-943	23	31	and	and	CCONJ
cana-943	23	32	integrity	integrity	NOUN
cana-943	23	33	during	during	ADP
cana-943	23	34	processing	process	VERB
cana-943	23	35	[	[	X
cana-943	23	36	6	6	NUM
cana-943	23	37	]	]	PUNCT
cana-943	23	38	.	.	PUNCT
cana-943	24	1	similarly	similarly	ADV
cana-943	24	2	,	,	PUNCT
cana-943	24	3	lattice	lattice	NOUN
cana-943	24	4	-	-	PUNCT
cana-943	24	5	based	base	VERB
cana-943	24	6	cryptography	cryptography	NOUN
cana-943	24	7	,	,	PUNCT
cana-943	24	8	which	which	PRON
cana-943	24	9	promises	promise	VERB
cana-943	24	10	security	security	NOUN
cana-943	24	11	even	even	ADV
cana-943	24	12	against	against	ADP
cana-943	24	13	quantum	quantum	ADJ
cana-943	24	14	attacks	attack	NOUN
cana-943	24	15	,	,	PUNCT
cana-943	24	16	is	be	AUX
cana-943	24	17	grounded	ground	VERB
cana-943	24	18	in	in	ADP
cana-943	24	19	complex	complex	ADJ
cana-943	24	20	algebraic	algebraic	ADJ
cana-943	24	21	problems	problem	NOUN
cana-943	24	22	[	[	X
cana-943	24	23	12	12	NUM
cana-943	24	24	]	]	PUNCT
cana-943	24	25	.	.	PUNCT
cana-943	25	1	these	these	DET
cana-943	25	2	algebraic	algebraic	ADJ
cana-943	25	3	foundations	foundation	NOUN
cana-943	25	4	not	not	PART
cana-943	25	5	only	only	ADV
cana-943	25	6	enhance	enhance	VERB
cana-943	25	7	the	the	DET
cana-943	25	8	robustness	robustness	NOUN
cana-943	25	9	of	of	ADP
cana-943	25	10	cryptographic	cryptographic	ADJ
cana-943	25	11	systems	system	NOUN
cana-943	25	12	but	but	CCONJ
cana-943	25	13	also	also	ADV
cana-943	25	14	enable	enable	VERB
cana-943	25	15	innovative	innovative	ADJ
cana-943	25	16	approaches	approach	NOUN
cana-943	25	17	to	to	ADP
cana-943	25	18	solving	solve	VERB
cana-943	25	19	emerging	emerge	VERB
cana-943	25	20	security	security	NOUN
cana-943	25	21	challenges	challenge	NOUN
cana-943	25	22	.	.	PUNCT
cana-943	26	1	this	this	DET
cana-943	26	2	paper	paper	NOUN
cana-943	26	3	aims	aim	VERB
cana-943	26	4	to	to	PART
cana-943	26	5	explore	explore	VERB
cana-943	26	6	the	the	DET
cana-943	26	7	intricate	intricate	ADJ
cana-943	26	8	relationship	relationship	NOUN
cana-943	26	9	between	between	ADP
cana-943	26	10	algebra	algebra	NOUN
cana-943	26	11	and	and	CCONJ
cana-943	26	12	cryptography	cryptography	NOUN
cana-943	26	13	,	,	PUNCT
cana-943	26	14	highlighting	highlight	VERB
cana-943	26	15	how	how	SCONJ
cana-943	26	16	algebraic	algebraic	ADJ
cana-943	26	17	principles	principle	NOUN
cana-943	26	18	can	can	AUX
cana-943	26	19	enhance	enhance	VERB
cana-943	26	20	information	information	NOUN
cana-943	26	21	security	security	NOUN
cana-943	26	22	.	.	PUNCT
cana-943	27	1	the	the	DET
cana-943	27	2	primary	primary	ADJ
cana-943	27	3	objectives	objective	NOUN
cana-943	27	4	are	be	AUX
cana-943	27	5	:	:	PUNCT
cana-943	27	6	1	1	X
cana-943	27	7	.	.	PUNCT
cana-943	27	8	to	to	PART
cana-943	27	9	review	review	VERB
cana-943	27	10	the	the	DET
cana-943	27	11	key	key	ADJ
cana-943	27	12	algebraic	algebraic	ADJ
cana-943	27	13	methods	method	NOUN
cana-943	27	14	used	use	VERB
cana-943	27	15	in	in	ADP
cana-943	27	16	contemporary	contemporary	ADJ
cana-943	27	17	cryptographic	cryptographic	ADJ
cana-943	27	18	protocols	protocol	NOUN
cana-943	27	19	.	.	PUNCT
cana-943	28	1	2	2	X
cana-943	28	2	.	.	X
cana-943	28	3	to	to	PART
cana-943	28	4	demonstrate	demonstrate	VERB
cana-943	28	5	the	the	DET
cana-943	28	6	practical	practical	ADJ
cana-943	28	7	applications	application	NOUN
cana-943	28	8	of	of	ADP
cana-943	28	9	these	these	DET
cana-943	28	10	methods	method	NOUN
cana-943	28	11	through	through	ADP
cana-943	28	12	detailed	detailed	ADJ
cana-943	28	13	case	case	NOUN
cana-943	28	14	studies	study	NOUN
cana-943	28	15	.	.	PUNCT
cana-943	29	1	3	3	X
cana-943	29	2	.	.	PUNCT
cana-943	29	3	to	to	PART
cana-943	29	4	provide	provide	VERB
cana-943	29	5	a	a	DET
cana-943	29	6	comparative	comparative	ADJ
cana-943	29	7	analysis	analysis	NOUN
cana-943	29	8	of	of	ADP
cana-943	29	9	algebra	algebra	NOUN
cana-943	29	10	-	-	PUNCT
cana-943	29	11	based	base	VERB
cana-943	29	12	cryptographic	cryptographic	ADJ
cana-943	29	13	solutions	solution	NOUN
cana-943	29	14	versus	versus	ADP
cana-943	29	15	traditional	traditional	ADJ
cana-943	29	16	methods	method	NOUN
cana-943	29	17	.	.	PUNCT
cana-943	30	1	4	4	X
cana-943	30	2	.	.	PUNCT
cana-943	30	3	to	to	PART
cana-943	30	4	discuss	discuss	VERB
cana-943	30	5	emerging	emerge	VERB
cana-943	30	6	trends	trend	NOUN
cana-943	30	7	and	and	CCONJ
cana-943	30	8	future	future	ADJ
cana-943	30	9	directions	direction	NOUN
cana-943	30	10	in	in	ADP
cana-943	30	11	algebraic	algebraic	ADJ
cana-943	30	12	cryptography	cryptography	NOUN
cana-943	30	13	.	.	PUNCT
cana-943	31	1	by	by	ADP
cana-943	31	2	achieving	achieve	VERB
cana-943	31	3	these	these	DET
cana-943	31	4	objectives	objective	NOUN
cana-943	31	5	,	,	PUNCT
cana-943	31	6	the	the	DET
cana-943	31	7	paper	paper	NOUN
cana-943	31	8	seeks	seek	VERB
cana-943	31	9	to	to	PART
cana-943	31	10	underscore	underscore	VERB
cana-943	31	11	the	the	DET
cana-943	31	12	critical	critical	ADJ
cana-943	31	13	role	role	NOUN
cana-943	31	14	of	of	ADP
cana-943	31	15	algebra	algebra	NOUN
cana-943	31	16	in	in	ADP
cana-943	31	17	advancing	advance	VERB
cana-943	31	18	cryptographic	cryptographic	ADJ
cana-943	31	19	techniques	technique	NOUN
cana-943	31	20	and	and	CCONJ
cana-943	31	21	addressing	address	VERB
cana-943	31	22	the	the	DET
cana-943	31	23	evolving	evolve	VERB
cana-943	31	24	threats	threat	NOUN
cana-943	31	25	in	in	ADP
cana-943	31	26	information	information	NOUN
cana-943	31	27	security	security	NOUN
cana-943	31	28	.	.	PUNCT
cana-943	32	1	the	the	DET
cana-943	32	2	paper	paper	NOUN
cana-943	32	3	is	be	AUX
cana-943	32	4	organized	organize	VERB
cana-943	32	5	as	as	SCONJ
cana-943	32	6	follows	follow	VERB
cana-943	32	7	:	:	PUNCT
cana-943	32	8	•	•	NUM
cana-943	32	9	fundamental	fundamental	ADJ
cana-943	32	10	concepts	concept	NOUN
cana-943	32	11	:	:	PUNCT
cana-943	32	12	this	this	DET
cana-943	32	13	section	section	NOUN
cana-943	32	14	provides	provide	VERB
cana-943	32	15	an	an	DET
cana-943	32	16	overview	overview	NOUN
cana-943	32	17	of	of	ADP
cana-943	32	18	algebraic	algebraic	ADJ
cana-943	32	19	structures	structure	NOUN
cana-943	32	20	and	and	CCONJ
cana-943	32	21	cryptographic	cryptographic	ADJ
cana-943	32	22	fundamentals	fundamental	NOUN
cana-943	32	23	,	,	PUNCT
cana-943	32	24	laying	lay	VERB
cana-943	32	25	the	the	DET
cana-943	32	26	groundwork	groundwork	NOUN
cana-943	32	27	for	for	ADP
cana-943	32	28	subsequent	subsequent	ADJ
cana-943	32	29	discussions	discussion	NOUN
cana-943	32	30	.	.	PUNCT
cana-943	33	1	•	•	NUM
cana-943	33	2	literature	literature	PROPN
cana-943	33	3	review	review	PROPN
cana-943	33	4	:	:	PUNCT
cana-943	33	5	a	a	DET
cana-943	33	6	comprehensive	comprehensive	ADJ
cana-943	33	7	review	review	NOUN
cana-943	33	8	of	of	ADP
cana-943	33	9	historical	historical	ADJ
cana-943	33	10	and	and	CCONJ
cana-943	33	11	recent	recent	ADJ
cana-943	33	12	advancements	advancement	NOUN
cana-943	33	13	in	in	ADP
cana-943	33	14	algebraic	algebraic	ADJ
cana-943	33	15	cryptography	cryptography	NOUN
cana-943	33	16	,	,	PUNCT
cana-943	33	17	identifying	identify	VERB
cana-943	33	18	gaps	gap	NOUN
cana-943	33	19	and	and	CCONJ
cana-943	33	20	research	research	NOUN
cana-943	33	21	questions	question	NOUN
cana-943	33	22	.	.	PUNCT
cana-943	34	1	•	•	NUM
cana-943	34	2	algebraic	algebraic	ADJ
cana-943	34	3	techniques	technique	NOUN
cana-943	34	4	in	in	ADP
cana-943	34	5	cryptography	cryptography	NOUN
cana-943	34	6	:	:	PUNCT
cana-943	34	7	detailed	detailed	ADJ
cana-943	34	8	exploration	exploration	NOUN
cana-943	34	9	of	of	ADP
cana-943	34	10	how	how	SCONJ
cana-943	34	11	various	various	ADJ
cana-943	34	12	algebraic	algebraic	ADJ
cana-943	34	13	structures	structure	NOUN
cana-943	34	14	are	be	AUX
cana-943	34	15	applied	apply	VERB
cana-943	34	16	in	in	ADP
cana-943	34	17	cryptographic	cryptographic	ADJ
cana-943	34	18	protocols	protocol	NOUN
cana-943	34	19	.	.	PUNCT
cana-943	35	1	•	•	NUM
cana-943	35	2	implementation	implementation	NOUN
cana-943	35	3	of	of	ADP
cana-943	35	4	cryptographic	cryptographic	ADJ
cana-943	35	5	protocols	protocol	NOUN
cana-943	35	6	:	:	PUNCT
cana-943	35	7	examination	examination	NOUN
cana-943	35	8	of	of	ADP
cana-943	35	9	specific	specific	ADJ
cana-943	35	10	cryptographic	cryptographic	ADJ
cana-943	35	11	protocols	protocol	NOUN
cana-943	35	12	,	,	PUNCT
cana-943	35	13	focusing	focus	VERB
cana-943	35	14	on	on	ADP
cana-943	35	15	practical	practical	ADJ
cana-943	35	16	implementation	implementation	NOUN
cana-943	35	17	and	and	CCONJ
cana-943	35	18	real	real	ADJ
cana-943	35	19	-	-	PUNCT
cana-943	35	20	world	world	NOUN
cana-943	35	21	applications	application	NOUN
cana-943	35	22	.	.	PUNCT
cana-943	36	1	communications	communication	NOUN
cana-943	36	2	on	on	ADP
cana-943	36	3	applied	apply	VERB
cana-943	36	4	nonlinear	nonlinear	ADJ
cana-943	36	5	analysis	analysis	NOUN
cana-943	36	6	issn	issn	NOUN
cana-943	36	7	:	:	PUNCT
cana-943	36	8	1074	1074	NUM
cana-943	36	9	-	-	PUNCT
cana-943	36	10	133x	133x	NUM
cana-943	36	11	vol	vol	NOUN
cana-943	36	12	31	31	NUM
cana-943	36	13	no	no	NOUN
cana-943	36	14	.	.	PUNCT
cana-943	37	1	4s	4s	NUM
cana-943	37	2	(	(	PUNCT
cana-943	37	3	2024	2024	NUM
cana-943	37	4	)	)	PUNCT
cana-943	37	5	468	468	NUM
cana-943	37	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-943	37	7	•	•	NOUN
cana-943	37	8	case	case	NOUN
cana-943	37	9	studies	study	NOUN
cana-943	37	10	and	and	CCONJ
cana-943	37	11	practical	practical	ADJ
cana-943	37	12	applications	application	NOUN
cana-943	37	13	:	:	PUNCT
cana-943	37	14	analysis	analysis	NOUN
cana-943	37	15	of	of	ADP
cana-943	37	16	case	case	NOUN
cana-943	37	17	studies	study	NOUN
cana-943	37	18	showcasing	showcase	VERB
cana-943	37	19	the	the	DET
cana-943	37	20	application	application	NOUN
cana-943	37	21	of	of	ADP
cana-943	37	22	algebraic	algebraic	ADJ
cana-943	37	23	cryptography	cryptography	NOUN
cana-943	37	24	in	in	ADP
cana-943	37	25	secure	secure	ADJ
cana-943	37	26	communications	communication	NOUN
cana-943	37	27	,	,	PUNCT
cana-943	37	28	blockchain	blockchain	NOUN
cana-943	37	29	,	,	PUNCT
cana-943	37	30	and	and	CCONJ
cana-943	37	31	data	datum	NOUN
cana-943	37	32	privacy	privacy	NOUN
cana-943	37	33	.	.	PUNCT
cana-943	38	1	•	•	NUM
cana-943	38	2	comparative	comparative	ADJ
cana-943	38	3	analysis	analysis	NOUN
cana-943	38	4	and	and	CCONJ
cana-943	38	5	evaluation	evaluation	NOUN
cana-943	38	6	:	:	PUNCT
cana-943	38	7	comparative	comparative	ADJ
cana-943	38	8	study	study	NOUN
cana-943	38	9	of	of	ADP
cana-943	38	10	the	the	DET
cana-943	38	11	performance	performance	NOUN
cana-943	38	12	and	and	CCONJ
cana-943	38	13	security	security	NOUN
cana-943	38	14	of	of	ADP
cana-943	38	15	algebraic	algebraic	ADJ
cana-943	38	16	cryptographic	cryptographic	ADJ
cana-943	38	17	techniques	technique	NOUN
cana-943	38	18	versus	versus	ADP
cana-943	38	19	traditional	traditional	ADJ
cana-943	38	20	methods	method	NOUN
cana-943	38	21	.	.	PUNCT
cana-943	39	1	•	•	NUM
cana-943	39	2	enhancing	enhance	VERB
cana-943	39	3	information	information	NOUN
cana-943	39	4	security	security	NOUN
cana-943	39	5	through	through	ADP
cana-943	39	6	mathematical	mathematical	ADJ
cana-943	39	7	foundations	foundation	NOUN
cana-943	39	8	:	:	PUNCT
cana-943	39	9	discussion	discussion	NOUN
cana-943	39	10	on	on	ADP
cana-943	39	11	the	the	DET
cana-943	39	12	role	role	NOUN
cana-943	39	13	of	of	ADP
cana-943	39	14	algebra	algebra	NOUN
cana-943	39	15	in	in	ADP
cana-943	39	16	strengthening	strengthen	VERB
cana-943	39	17	cryptographic	cryptographic	ADJ
cana-943	39	18	protocols	protocol	NOUN
cana-943	39	19	and	and	CCONJ
cana-943	39	20	future	future	ADJ
cana-943	39	21	research	research	NOUN
cana-943	39	22	directions	direction	NOUN
cana-943	39	23	.	.	PUNCT
cana-943	40	1	•	•	ADJ
cana-943	40	2	challenges	challenge	NOUN
cana-943	40	3	and	and	CCONJ
cana-943	40	4	future	future	ADJ
cana-943	40	5	directions	direction	NOUN
cana-943	40	6	:	:	PUNCT
cana-943	40	7	identification	identification	NOUN
cana-943	40	8	of	of	ADP
cana-943	40	9	challenges	challenge	NOUN
cana-943	40	10	in	in	ADP
cana-943	40	11	the	the	DET
cana-943	40	12	field	field	NOUN
cana-943	40	13	and	and	CCONJ
cana-943	40	14	potential	potential	ADJ
cana-943	40	15	future	future	ADJ
cana-943	40	16	developments	development	NOUN
cana-943	40	17	in	in	ADP
cana-943	40	18	algebraic	algebraic	ADJ
cana-943	40	19	cryptography	cryptography	NOUN
cana-943	40	20	.	.	PUNCT
cana-943	41	1	•	•	NUM
cana-943	41	2	conclusion	conclusion	NOUN
cana-943	41	3	:	:	PUNCT
cana-943	41	4	summary	summary	NOUN
cana-943	41	5	of	of	ADP
cana-943	41	6	key	key	ADJ
cana-943	41	7	findings	finding	NOUN
cana-943	41	8	,	,	PUNCT
cana-943	41	9	implications	implication	NOUN
cana-943	41	10	for	for	ADP
cana-943	41	11	information	information	NOUN
cana-943	41	12	security	security	NOUN
cana-943	41	13	,	,	PUNCT
cana-943	41	14	and	and	CCONJ
cana-943	41	15	recommendations	recommendation	NOUN
cana-943	41	16	for	for	ADP
cana-943	41	17	future	future	ADJ
cana-943	41	18	research	research	NOUN
cana-943	41	19	.	.	PUNCT
cana-943	42	1	this	this	DET
cana-943	42	2	structured	structured	ADJ
cana-943	42	3	approach	approach	NOUN
cana-943	42	4	ensures	ensure	VERB
cana-943	42	5	a	a	DET
cana-943	42	6	coherent	coherent	ADJ
cana-943	42	7	and	and	CCONJ
cana-943	42	8	comprehensive	comprehensive	ADJ
cana-943	42	9	examination	examination	NOUN
cana-943	42	10	of	of	ADP
cana-943	42	11	the	the	DET
cana-943	42	12	intersection	intersection	NOUN
cana-943	42	13	between	between	ADP
cana-943	42	14	algebra	algebra	NOUN
cana-943	42	15	and	and	CCONJ
cana-943	42	16	cryptography	cryptography	NOUN
cana-943	42	17	,	,	PUNCT
cana-943	42	18	providing	provide	VERB
cana-943	42	19	valuable	valuable	ADJ
cana-943	42	20	insights	insight	NOUN
cana-943	42	21	into	into	ADP
cana-943	42	22	how	how	SCONJ
cana-943	42	23	mathematical	mathematical	ADJ
cana-943	42	24	foundations	foundation	NOUN
cana-943	42	25	can	can	AUX
cana-943	42	26	enhance	enhance	VERB
cana-943	42	27	information	information	NOUN
cana-943	42	28	security	security	NOUN
cana-943	42	29	.	.	PUNCT
cana-943	43	1	2	2	X
cana-943	43	2	.	.	X
cana-943	43	3	literature	literature	NOUN
cana-943	43	4	review	review	VERB
cana-943	43	5	2.1	2.1	NUM
cana-943	43	6	.	.	PUNCT
cana-943	44	1	historical	historical	ADJ
cana-943	44	2	context	context	NOUN
cana-943	44	3	and	and	CCONJ
cana-943	44	4	development	development	VERB
cana-943	44	5	the	the	DET
cana-943	44	6	field	field	NOUN
cana-943	44	7	of	of	ADP
cana-943	44	8	cryptography	cryptography	NOUN
cana-943	44	9	has	have	VERB
cana-943	44	10	a	a	DET
cana-943	44	11	rich	rich	ADJ
cana-943	44	12	history	history	NOUN
cana-943	44	13	,	,	PUNCT
cana-943	44	14	dating	date	VERB
cana-943	44	15	back	back	ADV
cana-943	44	16	to	to	ADP
cana-943	44	17	ancient	ancient	ADJ
cana-943	44	18	civilizations	civilization	NOUN
cana-943	44	19	that	that	PRON
cana-943	44	20	used	use	VERB
cana-943	44	21	simple	simple	ADJ
cana-943	44	22	ciphers	cipher	NOUN
cana-943	44	23	to	to	PART
cana-943	44	24	secure	secure	VERB
cana-943	44	25	messages	message	NOUN
cana-943	44	26	.	.	PUNCT
cana-943	45	1	the	the	DET
cana-943	45	2	advent	advent	NOUN
cana-943	45	3	of	of	ADP
cana-943	45	4	modern	modern	ADJ
cana-943	45	5	cryptography	cryptography	NOUN
cana-943	45	6	began	begin	VERB
cana-943	45	7	with	with	ADP
cana-943	45	8	the	the	DET
cana-943	45	9	seminal	seminal	ADJ
cana-943	45	10	work	work	NOUN
cana-943	45	11	of	of	ADP
cana-943	45	12	diffie	diffie	PROPN
cana-943	45	13	and	and	CCONJ
cana-943	45	14	hellman	hellman	NOUN
cana-943	45	15	in	in	ADP
cana-943	45	16	1976	1976	NUM
cana-943	45	17	,	,	PUNCT
cana-943	45	18	which	which	PRON
cana-943	45	19	introduced	introduce	VERB
cana-943	45	20	the	the	DET
cana-943	45	21	concept	concept	NOUN
cana-943	45	22	of	of	ADP
cana-943	45	23	public	public	ADJ
cana-943	45	24	-	-	PUNCT
cana-943	45	25	key	key	NOUN
cana-943	45	26	cryptography	cryptography	NOUN
cana-943	45	27	.	.	PUNCT
cana-943	46	1	this	this	DET
cana-943	46	2	groundbreaking	groundbreake	VERB
cana-943	46	3	idea	idea	NOUN
cana-943	46	4	allowed	allow	VERB
cana-943	46	5	secure	secure	ADJ
cana-943	46	6	communication	communication	NOUN
cana-943	46	7	between	between	ADP
cana-943	46	8	parties	party	NOUN
cana-943	46	9	without	without	ADP
cana-943	46	10	the	the	DET
cana-943	46	11	need	need	NOUN
cana-943	46	12	for	for	ADP
cana-943	46	13	a	a	DET
cana-943	46	14	shared	share	VERB
cana-943	46	15	secret	secret	ADJ
cana-943	46	16	key	key	NOUN
cana-943	46	17	,	,	PUNCT
cana-943	46	18	revolutionizing	revolutionize	VERB
cana-943	46	19	digital	digital	ADJ
cana-943	46	20	security	security	NOUN
cana-943	46	21	[	[	X
cana-943	46	22	1	1	NUM
cana-943	46	23	]	]	PUNCT
cana-943	46	24	.	.	PUNCT
cana-943	47	1	following	follow	VERB
cana-943	47	2	this	this	PRON
cana-943	47	3	,	,	PUNCT
cana-943	47	4	rivest	riv	ADJ
cana-943	47	5	,	,	PUNCT
cana-943	47	6	shamir	shamir	ADJ
cana-943	47	7	,	,	PUNCT
cana-943	47	8	and	and	CCONJ
cana-943	47	9	adleman	adleman	PROPN
cana-943	47	10	developed	develop	VERB
cana-943	47	11	the	the	DET
cana-943	47	12	rsa	rsa	PROPN
cana-943	47	13	algorithm	algorithm	NOUN
cana-943	47	14	in	in	ADP
cana-943	47	15	1978	1978	NUM
cana-943	47	16	,	,	PUNCT
cana-943	47	17	which	which	PRON
cana-943	47	18	became	become	VERB
cana-943	47	19	one	one	NUM
cana-943	47	20	of	of	ADP
cana-943	47	21	the	the	DET
cana-943	47	22	first	first	ADJ
cana-943	47	23	practical	practical	ADJ
cana-943	47	24	implementations	implementation	NOUN
cana-943	47	25	of	of	ADP
cana-943	47	26	public	public	ADJ
cana-943	47	27	-	-	PUNCT
cana-943	47	28	key	key	NOUN
cana-943	47	29	cryptography	cryptography	NOUN
cana-943	47	30	and	and	CCONJ
cana-943	47	31	remains	remain	VERB
cana-943	47	32	widely	widely	ADV
cana-943	47	33	used	use	VERB
cana-943	47	34	today	today	NOUN
cana-943	47	35	[	[	X
cana-943	47	36	2	2	NUM
cana-943	47	37	]	]	PUNCT
cana-943	47	38	.	.	PUNCT
cana-943	48	1	throughout	throughout	ADP
cana-943	48	2	the	the	DET
cana-943	48	3	1980s	1980	NOUN
cana-943	48	4	and	and	CCONJ
cana-943	48	5	1990s	1990s	NUM
cana-943	48	6	,	,	PUNCT
cana-943	48	7	the	the	DET
cana-943	48	8	field	field	NOUN
cana-943	48	9	continued	continue	VERB
cana-943	48	10	to	to	PART
cana-943	48	11	evolve	evolve	VERB
cana-943	48	12	with	with	ADP
cana-943	48	13	significant	significant	ADJ
cana-943	48	14	contributions	contribution	NOUN
cana-943	48	15	from	from	ADP
cana-943	48	16	various	various	ADJ
cana-943	48	17	researchers	researcher	NOUN
cana-943	48	18	.	.	PUNCT
cana-943	49	1	notably	notably	ADV
cana-943	49	2	,	,	PUNCT
cana-943	49	3	elliptic	elliptic	ADJ
cana-943	49	4	curve	curve	NOUN
cana-943	49	5	cryptography	cryptography	NOUN
cana-943	49	6	(	(	PUNCT
cana-943	49	7	ecc	ecc	PROPN
cana-943	49	8	)	)	PUNCT
cana-943	49	9	emerged	emerge	VERB
cana-943	49	10	in	in	ADP
cana-943	49	11	the	the	DET
cana-943	49	12	late	late	ADJ
cana-943	49	13	1980s	1980	NOUN
cana-943	49	14	,	,	PUNCT
cana-943	49	15	thanks	thank	NOUN
cana-943	49	16	to	to	ADP
cana-943	49	17	the	the	DET
cana-943	49	18	work	work	NOUN
cana-943	49	19	of	of	ADP
cana-943	49	20	koblitz	koblitz	NOUN
cana-943	49	21	and	and	CCONJ
cana-943	49	22	miller	miller	PROPN
cana-943	49	23	,	,	PUNCT
cana-943	49	24	who	who	PRON
cana-943	49	25	independently	independently	ADV
cana-943	49	26	introduced	introduce	VERB
cana-943	49	27	the	the	DET
cana-943	49	28	use	use	NOUN
cana-943	49	29	of	of	ADP
cana-943	49	30	elliptic	elliptic	ADJ
cana-943	49	31	curves	curve	NOUN
cana-943	49	32	in	in	ADP
cana-943	49	33	cryptographic	cryptographic	ADJ
cana-943	49	34	systems	system	NOUN
cana-943	49	35	[	[	X
cana-943	49	36	3	3	NUM
cana-943	49	37	]	]	PUNCT
cana-943	49	38	.	.	PUNCT
cana-943	50	1	ecc	ecc	PROPN
cana-943	50	2	provided	provide	VERB
cana-943	50	3	enhanced	enhanced	ADJ
cana-943	50	4	security	security	NOUN
cana-943	50	5	with	with	ADP
cana-943	50	6	smaller	small	ADJ
cana-943	50	7	key	key	ADJ
cana-943	50	8	sizes	size	NOUN
cana-943	50	9	compared	compare	VERB
cana-943	50	10	to	to	ADP
cana-943	50	11	traditional	traditional	ADJ
cana-943	50	12	methods	method	NOUN
cana-943	50	13	like	like	ADP
cana-943	50	14	rsa	rsa	PROPN
cana-943	50	15	,	,	PUNCT
cana-943	50	16	making	make	VERB
cana-943	50	17	it	it	PRON
cana-943	50	18	particularly	particularly	ADV
cana-943	50	19	valuable	valuable	ADJ
cana-943	50	20	for	for	ADP
cana-943	50	21	constrained	constrained	ADJ
cana-943	50	22	environments	environment	NOUN
cana-943	50	23	.	.	PUNCT
cana-943	51	1	2.2	2.2	NUM
cana-943	51	2	.	.	PUNCT
cana-943	52	1	key	key	ADJ
cana-943	52	2	theoretical	theoretical	ADJ
cana-943	52	3	foundations	foundation	NOUN
cana-943	52	4	cryptography	cryptography	NOUN
cana-943	52	5	relies	rely	VERB
cana-943	52	6	heavily	heavily	ADV
cana-943	52	7	on	on	ADP
cana-943	52	8	mathematical	mathematical	ADJ
cana-943	52	9	principles	principle	NOUN
cana-943	52	10	,	,	PUNCT
cana-943	52	11	particularly	particularly	ADV
cana-943	52	12	those	those	PRON
cana-943	52	13	from	from	ADP
cana-943	52	14	algebra	algebra	NOUN
cana-943	52	15	.	.	PUNCT
cana-943	53	1	the	the	DET
cana-943	53	2	key	key	ADJ
cana-943	53	3	theoretical	theoretical	ADJ
cana-943	53	4	foundations	foundation	NOUN
cana-943	53	5	of	of	ADP
cana-943	53	6	modern	modern	ADJ
cana-943	53	7	cryptography	cryptography	NOUN
cana-943	53	8	include	include	VERB
cana-943	53	9	the	the	DET
cana-943	53	10	discrete	discrete	ADJ
cana-943	53	11	logarithm	logarithm	NOUN
cana-943	53	12	problem	problem	NOUN
cana-943	53	13	,	,	PUNCT
cana-943	53	14	the	the	DET
cana-943	53	15	rsa	rsa	PROPN
cana-943	53	16	problem	problem	NOUN
cana-943	53	17	,	,	PUNCT
cana-943	53	18	and	and	CCONJ
cana-943	53	19	elliptic	elliptic	ADJ
cana-943	53	20	curve	curve	NOUN
cana-943	53	21	theory	theory	NOUN
cana-943	53	22	.	.	PUNCT
cana-943	54	1	1	1	X
cana-943	54	2	.	.	X
cana-943	54	3	discrete	discrete	ADJ
cana-943	54	4	logarithm	logarithm	PROPN
cana-943	54	5	problem	problem	NOUN
cana-943	54	6	:	:	PUNCT
cana-943	54	7	this	this	DET
cana-943	54	8	problem	problem	NOUN
cana-943	54	9	underpins	underpin	VERB
cana-943	54	10	many	many	ADJ
cana-943	54	11	cryptographic	cryptographic	ADJ
cana-943	54	12	protocols	protocol	NOUN
cana-943	54	13	,	,	PUNCT
cana-943	54	14	including	include	VERB
cana-943	54	15	the	the	DET
cana-943	54	16	diffie	diffie	PROPN
cana-943	54	17	-	-	PUNCT
cana-943	54	18	hellman	hellman	PROPN
cana-943	54	19	key	key	PROPN
cana-943	54	20	exchange	exchange	NOUN
cana-943	54	21	and	and	CCONJ
cana-943	54	22	certain	certain	ADJ
cana-943	54	23	digital	digital	ADJ
cana-943	54	24	signature	signature	NOUN
cana-943	54	25	algorithms	algorithm	NOUN
cana-943	54	26	.	.	PUNCT
cana-943	55	1	its	its	PRON
cana-943	55	2	computational	computational	ADJ
cana-943	55	3	difficulty	difficulty	NOUN
cana-943	55	4	ensures	ensure	VERB
cana-943	55	5	the	the	DET
cana-943	55	6	security	security	NOUN
cana-943	55	7	of	of	ADP
cana-943	55	8	these	these	DET
cana-943	55	9	systems	system	NOUN
cana-943	55	10	.	.	PUNCT
cana-943	56	1	2	2	X
cana-943	56	2	.	.	X
cana-943	56	3	rsa	rsa	PROPN
cana-943	56	4	problem	problem	NOUN
cana-943	56	5	:	:	PUNCT
cana-943	56	6	based	base	VERB
cana-943	56	7	on	on	ADP
cana-943	56	8	the	the	DET
cana-943	56	9	difficulty	difficulty	NOUN
cana-943	56	10	of	of	ADP
cana-943	56	11	factorizing	factorize	VERB
cana-943	56	12	large	large	ADJ
cana-943	56	13	prime	prime	ADJ
cana-943	56	14	numbers	number	NOUN
cana-943	56	15	,	,	PUNCT
cana-943	56	16	the	the	DET
cana-943	56	17	rsa	rsa	PROPN
cana-943	56	18	algorithm	algorithm	NOUN
cana-943	56	19	is	be	AUX
cana-943	56	20	a	a	DET
cana-943	56	21	cornerstone	cornerstone	NOUN
cana-943	56	22	of	of	ADP
cana-943	56	23	public	public	ADJ
cana-943	56	24	-	-	PUNCT
cana-943	56	25	key	key	NOUN
cana-943	56	26	cryptography	cryptography	NOUN
cana-943	56	27	.	.	PUNCT
cana-943	57	1	the	the	DET
cana-943	57	2	security	security	NOUN
cana-943	57	3	of	of	ADP
cana-943	57	4	rsa	rsa	PROPN
cana-943	57	5	is	be	AUX
cana-943	57	6	predicated	predicate	VERB
cana-943	57	7	on	on	ADP
cana-943	57	8	the	the	DET
cana-943	57	9	infeasibility	infeasibility	NOUN
cana-943	57	10	of	of	ADP
cana-943	57	11	factorizing	factorize	VERB
cana-943	57	12	the	the	DET
cana-943	57	13	product	product	NOUN
cana-943	57	14	of	of	ADP
cana-943	57	15	two	two	NUM
cana-943	57	16	large	large	ADJ
cana-943	57	17	primes	prime	NOUN
cana-943	58	1	[	[	X
cana-943	58	2	2	2	NUM
cana-943	58	3	]	]	PUNCT
cana-943	58	4	.	.	PUNCT
cana-943	59	1	communications	communication	NOUN
cana-943	59	2	on	on	ADP
cana-943	59	3	applied	apply	VERB
cana-943	59	4	nonlinear	nonlinear	ADJ
cana-943	59	5	analysis	analysis	NOUN
cana-943	59	6	issn	issn	NOUN
cana-943	59	7	:	:	PUNCT
cana-943	59	8	1074	1074	NUM
cana-943	59	9	-	-	PUNCT
cana-943	59	10	133x	133x	NUM
cana-943	59	11	vol	vol	NOUN
cana-943	59	12	31	31	NUM
cana-943	59	13	no	no	NOUN
cana-943	59	14	.	.	PUNCT
cana-943	60	1	4s	4s	NUM
cana-943	60	2	(	(	PUNCT
cana-943	60	3	2024	2024	NUM
cana-943	60	4	)	)	PUNCT
cana-943	60	5	469	469	NUM
cana-943	60	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	60	7	3	3	X
cana-943	60	8	.	.	PUNCT
cana-943	60	9	elliptic	elliptic	ADJ
cana-943	60	10	curve	curve	NOUN
cana-943	60	11	theory	theory	NOUN
cana-943	60	12	:	:	PUNCT
cana-943	60	13	elliptic	elliptic	ADJ
cana-943	60	14	curves	curve	NOUN
cana-943	60	15	provide	provide	VERB
cana-943	60	16	a	a	DET
cana-943	60	17	group	group	NOUN
cana-943	60	18	structure	structure	NOUN
cana-943	60	19	that	that	PRON
cana-943	60	20	is	be	AUX
cana-943	60	21	utilized	utilize	VERB
cana-943	60	22	in	in	ADP
cana-943	60	23	various	various	ADJ
cana-943	60	24	cryptographic	cryptographic	ADJ
cana-943	60	25	algorithms	algorithm	NOUN
cana-943	60	26	.	.	PUNCT
cana-943	61	1	the	the	DET
cana-943	61	2	elliptic	elliptic	ADJ
cana-943	61	3	curve	curve	NOUN
cana-943	61	4	digital	digital	ADJ
cana-943	61	5	signature	signature	NOUN
cana-943	61	6	algorithm	algorithm	NOUN
cana-943	61	7	(	(	PUNCT
cana-943	61	8	ecdsa	ecdsa	PROPN
cana-943	61	9	)	)	PUNCT
cana-943	61	10	and	and	CCONJ
cana-943	61	11	elliptic	elliptic	ADJ
cana-943	61	12	curve	curve	NOUN
cana-943	61	13	diffie	diffie	PROPN
cana-943	61	14	-	-	PUNCT
cana-943	61	15	hellman	hellman	PROPN
cana-943	61	16	(	(	PUNCT
cana-943	61	17	ecdh	ecdh	PROPN
cana-943	61	18	)	)	PUNCT
cana-943	61	19	are	be	AUX
cana-943	61	20	prominent	prominent	ADJ
cana-943	61	21	examples	example	NOUN
cana-943	61	22	[	[	X
cana-943	61	23	3	3	NUM
cana-943	61	24	]	]	PUNCT
cana-943	61	25	.	.	PUNCT
cana-943	62	1	2.3	2.3	NUM
cana-943	62	2	.	.	PUNCT
cana-943	63	1	review	review	NOUN
cana-943	63	2	of	of	ADP
cana-943	63	3	recent	recent	ADJ
cana-943	63	4	advances	advance	NOUN
cana-943	63	5	in	in	ADP
cana-943	63	6	algebraic	algebraic	ADJ
cana-943	63	7	cryptography	cryptography	NOUN
cana-943	63	8	recent	recent	ADJ
cana-943	63	9	years	year	NOUN
cana-943	63	10	have	have	AUX
cana-943	63	11	witnessed	witness	VERB
cana-943	63	12	significant	significant	ADJ
cana-943	63	13	advancements	advancement	NOUN
cana-943	63	14	in	in	ADP
cana-943	63	15	the	the	DET
cana-943	63	16	field	field	NOUN
cana-943	63	17	of	of	ADP
cana-943	63	18	algebraic	algebraic	ADJ
cana-943	63	19	cryptography	cryptography	NOUN
cana-943	63	20	,	,	PUNCT
cana-943	63	21	driven	drive	VERB
cana-943	63	22	by	by	ADP
cana-943	63	23	the	the	DET
cana-943	63	24	need	need	NOUN
cana-943	63	25	for	for	ADP
cana-943	63	26	more	more	ADV
cana-943	63	27	robust	robust	ADJ
cana-943	63	28	and	and	CCONJ
cana-943	63	29	efficient	efficient	ADJ
cana-943	63	30	cryptographic	cryptographic	ADJ
cana-943	63	31	systems	system	NOUN
cana-943	63	32	.	.	PUNCT
cana-943	64	1	notable	notable	ADJ
cana-943	64	2	developments	development	NOUN
cana-943	64	3	include	include	VERB
cana-943	64	4	:	:	PUNCT
cana-943	64	5	1	1	X
cana-943	64	6	.	.	X
cana-943	64	7	homomorphic	homomorphic	ADJ
cana-943	64	8	encryption	encryption	NOUN
cana-943	64	9	:	:	PUNCT
cana-943	64	10	proposed	propose	VERB
cana-943	64	11	by	by	ADP
cana-943	64	12	gentry	gentry	NOUN
cana-943	64	13	in	in	ADP
cana-943	64	14	2009	2009	NUM
cana-943	64	15	,	,	PUNCT
cana-943	64	16	fully	fully	ADV
cana-943	64	17	homomorphic	homomorphic	ADJ
cana-943	64	18	encryption	encryption	NOUN
cana-943	64	19	allows	allow	VERB
cana-943	64	20	computations	computation	NOUN
cana-943	64	21	on	on	ADP
cana-943	64	22	encrypted	encrypt	VERB
cana-943	64	23	data	datum	NOUN
cana-943	64	24	without	without	ADP
cana-943	64	25	decryption	decryption	NOUN
cana-943	64	26	,	,	PUNCT
cana-943	64	27	preserving	preserve	VERB
cana-943	64	28	data	datum	NOUN
cana-943	64	29	privacy	privacy	NOUN
cana-943	64	30	and	and	CCONJ
cana-943	64	31	enabling	enable	VERB
cana-943	64	32	secure	secure	ADJ
cana-943	64	33	cloud	cloud	NOUN
cana-943	64	34	computing	computing	NOUN
cana-943	64	35	[	[	X
cana-943	64	36	6	6	NUM
cana-943	64	37	]	]	PUNCT
cana-943	64	38	.	.	PUNCT
cana-943	65	1	this	this	DET
cana-943	65	2	breakthrough	breakthrough	NOUN
cana-943	65	3	has	have	AUX
cana-943	65	4	spurred	spur	VERB
cana-943	65	5	extensive	extensive	ADJ
cana-943	65	6	research	research	NOUN
cana-943	65	7	into	into	ADP
cana-943	65	8	optimizing	optimize	VERB
cana-943	65	9	these	these	DET
cana-943	65	10	schemes	scheme	NOUN
cana-943	65	11	for	for	ADP
cana-943	65	12	practical	practical	ADJ
cana-943	65	13	use	use	NOUN
cana-943	65	14	.	.	PUNCT
cana-943	66	1	2	2	X
cana-943	66	2	.	.	X
cana-943	66	3	lattice	lattice	NOUN
cana-943	66	4	-	-	PUNCT
cana-943	66	5	based	base	VERB
cana-943	66	6	cryptography	cryptography	NOUN
cana-943	66	7	:	:	PUNCT
cana-943	66	8	lattice	lattice	NOUN
cana-943	66	9	-	-	PUNCT
cana-943	66	10	based	base	VERB
cana-943	66	11	schemes	scheme	NOUN
cana-943	66	12	,	,	PUNCT
cana-943	66	13	such	such	ADJ
cana-943	66	14	as	as	ADP
cana-943	66	15	those	those	PRON
cana-943	66	16	based	base	VERB
cana-943	66	17	on	on	ADP
cana-943	66	18	the	the	DET
cana-943	66	19	learning	learning	NOUN
cana-943	66	20	with	with	ADP
cana-943	66	21	errors	error	NOUN
cana-943	66	22	(	(	PUNCT
cana-943	66	23	lwe	lwe	PROPN
cana-943	66	24	)	)	PUNCT
cana-943	66	25	problem	problem	NOUN
cana-943	66	26	,	,	PUNCT
cana-943	66	27	have	have	AUX
cana-943	66	28	gained	gain	VERB
cana-943	66	29	prominence	prominence	NOUN
cana-943	66	30	due	due	ADP
cana-943	66	31	to	to	ADP
cana-943	66	32	their	their	PRON
cana-943	66	33	resistance	resistance	NOUN
cana-943	66	34	to	to	ADP
cana-943	66	35	quantum	quantum	NOUN
cana-943	66	36	attacks	attack	NOUN
cana-943	66	37	.	.	PUNCT
cana-943	67	1	regev	regev	PROPN
cana-943	67	2	's	's	PART
cana-943	67	3	work	work	NOUN
cana-943	67	4	in	in	ADP
cana-943	67	5	2005	2005	NUM
cana-943	67	6	laid	lay	VERB
cana-943	67	7	the	the	DET
cana-943	67	8	groundwork	groundwork	NOUN
cana-943	67	9	for	for	ADP
cana-943	67	10	this	this	DET
cana-943	67	11	area	area	NOUN
cana-943	67	12	,	,	PUNCT
cana-943	67	13	leading	lead	VERB
cana-943	67	14	to	to	ADP
cana-943	67	15	the	the	DET
cana-943	67	16	development	development	NOUN
cana-943	67	17	of	of	ADP
cana-943	67	18	practical	practical	ADJ
cana-943	67	19	algorithms	algorithm	NOUN
cana-943	67	20	and	and	CCONJ
cana-943	67	21	implementations	implementation	NOUN
cana-943	67	22	[	[	X
cana-943	67	23	12	12	NUM
cana-943	67	24	]	]	PUNCT
cana-943	67	25	.	.	PUNCT
cana-943	68	1	3	3	X
cana-943	68	2	.	.	X
cana-943	68	3	post	post	ADJ
cana-943	68	4	-	-	ADJ
cana-943	68	5	quantum	quantum	ADJ
cana-943	68	6	cryptography	cryptography	NOUN
cana-943	68	7	:	:	PUNCT
cana-943	68	8	with	with	ADP
cana-943	68	9	the	the	DET
cana-943	68	10	advent	advent	NOUN
cana-943	68	11	of	of	ADP
cana-943	68	12	quantum	quantum	NOUN
cana-943	68	13	computing	computing	NOUN
cana-943	68	14	,	,	PUNCT
cana-943	68	15	traditional	traditional	ADJ
cana-943	68	16	cryptographic	cryptographic	ADJ
cana-943	68	17	systems	system	NOUN
cana-943	68	18	face	face	VERB
cana-943	68	19	potential	potential	ADJ
cana-943	68	20	threats	threat	NOUN
cana-943	68	21	.	.	PUNCT
cana-943	69	1	nist	nist	PROPN
cana-943	69	2	has	have	AUX
cana-943	69	3	initiated	initiate	VERB
cana-943	69	4	efforts	effort	NOUN
cana-943	69	5	to	to	PART
cana-943	69	6	standardize	standardize	VERB
cana-943	69	7	postquantum	postquantum	NOUN
cana-943	69	8	cryptographic	cryptographic	ADJ
cana-943	69	9	algorithms	algorithm	NOUN
cana-943	69	10	,	,	PUNCT
cana-943	69	11	with	with	ADP
cana-943	69	12	lattice	lattice	NOUN
cana-943	69	13	-	-	PUNCT
cana-943	69	14	based	base	VERB
cana-943	69	15	and	and	CCONJ
cana-943	69	16	hash	hash	NOUN
cana-943	69	17	-	-	PUNCT
cana-943	69	18	based	base	VERB
cana-943	69	19	schemes	scheme	NOUN
cana-943	69	20	being	be	AUX
cana-943	69	21	frontrunners	frontrunner	NOUN
cana-943	69	22	in	in	ADP
cana-943	69	23	this	this	DET
cana-943	69	24	domain	domain	NOUN
cana-943	69	25	[	[	X
cana-943	69	26	13	13	NUM
cana-943	69	27	]	]	PUNCT
cana-943	69	28	.	.	PUNCT
cana-943	70	1	recent	recent	ADJ
cana-943	70	2	research	research	NOUN
cana-943	70	3	has	have	AUX
cana-943	70	4	also	also	ADV
cana-943	70	5	focused	focus	VERB
cana-943	70	6	on	on	ADP
cana-943	70	7	improving	improve	VERB
cana-943	70	8	the	the	DET
cana-943	70	9	efficiency	efficiency	NOUN
cana-943	70	10	and	and	CCONJ
cana-943	70	11	security	security	NOUN
cana-943	70	12	of	of	ADP
cana-943	70	13	elliptic	elliptic	ADJ
cana-943	70	14	curve	curve	NOUN
cana-943	70	15	cryptography	cryptography	NOUN
cana-943	70	16	,	,	PUNCT
cana-943	70	17	as	as	ADV
cana-943	70	18	well	well	ADV
cana-943	70	19	as	as	ADP
cana-943	70	20	exploring	explore	VERB
cana-943	70	21	new	new	ADJ
cana-943	70	22	algebraic	algebraic	ADJ
cana-943	70	23	structures	structure	NOUN
cana-943	70	24	for	for	ADP
cana-943	70	25	cryptographic	cryptographic	ADJ
cana-943	70	26	applications	application	NOUN
cana-943	70	27	.	.	PUNCT
cana-943	71	1	for	for	ADP
cana-943	71	2	example	example	NOUN
cana-943	71	3	,	,	PUNCT
cana-943	71	4	liu	liu	PROPN
cana-943	71	5	and	and	CCONJ
cana-943	71	6	wang	wang	PROPN
cana-943	71	7	(	(	PUNCT
cana-943	71	8	2023	2023	NUM
cana-943	71	9	)	)	PUNCT
cana-943	71	10	examined	examine	VERB
cana-943	71	11	advanced	advanced	ADJ
cana-943	71	12	cryptographic	cryptographic	ADJ
cana-943	71	13	techniques	technique	NOUN
cana-943	71	14	for	for	ADP
cana-943	71	15	securing	secure	VERB
cana-943	71	16	communications	communication	NOUN
cana-943	71	17	in	in	ADP
cana-943	71	18	the	the	DET
cana-943	71	19	internet	internet	NOUN
cana-943	71	20	of	of	ADP
cana-943	71	21	things	thing	NOUN
cana-943	71	22	(	(	PUNCT
cana-943	71	23	iot	iot	NOUN
cana-943	71	24	)	)	PUNCT
cana-943	71	25	,	,	PUNCT
cana-943	71	26	highlighting	highlight	VERB
cana-943	71	27	the	the	DET
cana-943	71	28	need	need	NOUN
cana-943	71	29	for	for	ADP
cana-943	71	30	lightweight	lightweight	ADJ
cana-943	71	31	and	and	CCONJ
cana-943	71	32	scalable	scalable	ADJ
cana-943	71	33	solutions	solution	NOUN
cana-943	71	34	[	[	X
cana-943	71	35	20	20	NUM
cana-943	71	36	]	]	PUNCT
cana-943	71	37	.	.	PUNCT
cana-943	72	1	2.4	2.4	NUM
cana-943	72	2	.	.	NUM
cana-943	72	3	identified	identify	VERB
cana-943	72	4	gaps	gap	NOUN
cana-943	72	5	and	and	CCONJ
cana-943	72	6	research	research	NOUN
cana-943	72	7	questions	question	NOUN
cana-943	72	8	despite	despite	SCONJ
cana-943	72	9	these	these	DET
cana-943	72	10	advancements	advancement	NOUN
cana-943	72	11	,	,	PUNCT
cana-943	72	12	several	several	ADJ
cana-943	72	13	gaps	gap	NOUN
cana-943	72	14	remain	remain	VERB
cana-943	72	15	in	in	ADP
cana-943	72	16	the	the	DET
cana-943	72	17	current	current	ADJ
cana-943	72	18	state	state	NOUN
cana-943	72	19	of	of	ADP
cana-943	72	20	algebraic	algebraic	ADJ
cana-943	72	21	cryptography	cryptography	NOUN
cana-943	72	22	,	,	PUNCT
cana-943	72	23	presenting	present	VERB
cana-943	72	24	opportunities	opportunity	NOUN
cana-943	72	25	for	for	ADP
cana-943	72	26	further	further	ADJ
cana-943	72	27	research	research	NOUN
cana-943	72	28	:	:	PUNCT
cana-943	72	29	1	1	X
cana-943	72	30	.	.	X
cana-943	72	31	scalability	scalability	NOUN
cana-943	72	32	and	and	CCONJ
cana-943	72	33	efficiency	efficiency	NOUN
cana-943	72	34	:	:	PUNCT
cana-943	72	35	many	many	ADJ
cana-943	72	36	advanced	advanced	ADJ
cana-943	72	37	cryptographic	cryptographic	ADJ
cana-943	72	38	techniques	technique	NOUN
cana-943	72	39	,	,	PUNCT
cana-943	72	40	such	such	ADJ
cana-943	72	41	as	as	ADP
cana-943	72	42	fully	fully	ADV
cana-943	72	43	homomorphic	homomorphic	ADJ
cana-943	72	44	encryption	encryption	NOUN
cana-943	72	45	and	and	CCONJ
cana-943	72	46	lattice	lattice	NOUN
cana-943	72	47	-	-	PUNCT
cana-943	72	48	based	base	VERB
cana-943	72	49	cryptography	cryptography	NOUN
cana-943	72	50	,	,	PUNCT
cana-943	72	51	are	be	AUX
cana-943	72	52	computationally	computationally	ADV
cana-943	72	53	intensive	intensive	ADJ
cana-943	72	54	.	.	PUNCT
cana-943	73	1	research	research	NOUN
cana-943	73	2	is	be	AUX
cana-943	73	3	needed	need	VERB
cana-943	73	4	to	to	PART
cana-943	73	5	develop	develop	VERB
cana-943	73	6	more	more	ADV
cana-943	73	7	efficient	efficient	ADJ
cana-943	73	8	algorithms	algorithm	NOUN
cana-943	73	9	that	that	PRON
cana-943	73	10	can	can	AUX
cana-943	73	11	be	be	AUX
cana-943	73	12	implemented	implement	VERB
cana-943	73	13	in	in	ADP
cana-943	73	14	real	real	ADJ
cana-943	73	15	-	-	PUNCT
cana-943	73	16	world	world	NOUN
cana-943	73	17	applications	application	NOUN
cana-943	73	18	without	without	ADP
cana-943	73	19	significant	significant	ADJ
cana-943	73	20	performance	performance	NOUN
cana-943	73	21	overhead	overhead	ADV
cana-943	73	22	.	.	PUNCT
cana-943	74	1	2	2	X
cana-943	74	2	.	.	X
cana-943	74	3	quantum	quantum	ADJ
cana-943	74	4	resistance	resistance	NOUN
cana-943	74	5	:	:	PUNCT
cana-943	74	6	while	while	SCONJ
cana-943	74	7	lattice	lattice	NOUN
cana-943	74	8	-	-	PUNCT
cana-943	74	9	based	base	VERB
cana-943	74	10	cryptography	cryptography	NOUN
cana-943	74	11	shows	show	NOUN
cana-943	74	12	promise	promise	VERB
cana-943	74	13	,	,	PUNCT
cana-943	74	14	the	the	DET
cana-943	74	15	development	development	NOUN
cana-943	74	16	of	of	ADP
cana-943	74	17	robust	robust	ADJ
cana-943	74	18	and	and	CCONJ
cana-943	74	19	practical	practical	ADJ
cana-943	74	20	post	post	ADJ
cana-943	74	21	-	-	ADJ
cana-943	74	22	quantum	quantum	ADJ
cana-943	74	23	cryptographic	cryptographic	ADJ
cana-943	74	24	algorithms	algorithms	NOUN
cana-943	74	25	is	be	AUX
cana-943	74	26	still	still	ADV
cana-943	74	27	in	in	ADP
cana-943	74	28	its	its	PRON
cana-943	74	29	early	early	ADJ
cana-943	74	30	stages	stage	NOUN
cana-943	74	31	.	.	PUNCT
cana-943	75	1	more	more	ADJ
cana-943	75	2	work	work	NOUN
cana-943	75	3	is	be	AUX
cana-943	75	4	required	require	VERB
cana-943	75	5	to	to	PART
cana-943	75	6	identify	identify	VERB
cana-943	75	7	and	and	CCONJ
cana-943	75	8	standardize	standardize	VERB
cana-943	75	9	secure	secure	ADJ
cana-943	75	10	algorithms	algorithm	NOUN
cana-943	75	11	that	that	PRON
cana-943	75	12	can	can	AUX
cana-943	75	13	withstand	withstand	VERB
cana-943	75	14	quantum	quantum	NOUN
cana-943	75	15	attacks	attack	NOUN
cana-943	75	16	.	.	PUNCT
cana-943	76	1	3	3	X
cana-943	76	2	.	.	X
cana-943	76	3	interoperability	interoperability	NOUN
cana-943	76	4	and	and	CCONJ
cana-943	76	5	integration	integration	NOUN
cana-943	76	6	:	:	PUNCT
cana-943	76	7	integrating	integrate	VERB
cana-943	76	8	advanced	advanced	ADJ
cana-943	76	9	cryptographic	cryptographic	ADJ
cana-943	76	10	methods	method	NOUN
cana-943	76	11	into	into	ADP
cana-943	76	12	existing	exist	VERB
cana-943	76	13	systems	system	NOUN
cana-943	76	14	poses	pose	NOUN
cana-943	76	15	challenges	challenge	NOUN
cana-943	76	16	related	relate	VERB
cana-943	76	17	to	to	ADP
cana-943	76	18	interoperability	interoperability	NOUN
cana-943	76	19	and	and	CCONJ
cana-943	76	20	backward	backward	ADJ
cana-943	76	21	compatibility	compatibility	NOUN
cana-943	76	22	.	.	PUNCT
cana-943	77	1	developing	develop	VERB
cana-943	77	2	standards	standard	NOUN
cana-943	77	3	and	and	CCONJ
cana-943	77	4	frameworks	framework	NOUN
cana-943	77	5	to	to	PART
cana-943	77	6	facilitate	facilitate	VERB
cana-943	77	7	seamless	seamless	ADJ
cana-943	77	8	integration	integration	NOUN
cana-943	77	9	is	be	AUX
cana-943	77	10	a	a	DET
cana-943	77	11	critical	critical	ADJ
cana-943	77	12	area	area	NOUN
cana-943	77	13	for	for	ADP
cana-943	77	14	future	future	ADJ
cana-943	77	15	research	research	NOUN
cana-943	77	16	.	.	PUNCT
cana-943	78	1	communications	communication	NOUN
cana-943	78	2	on	on	ADP
cana-943	78	3	applied	apply	VERB
cana-943	78	4	nonlinear	nonlinear	ADJ
cana-943	78	5	analysis	analysis	NOUN
cana-943	78	6	issn	issn	NOUN
cana-943	78	7	:	:	PUNCT
cana-943	78	8	1074	1074	NUM
cana-943	78	9	-	-	PUNCT
cana-943	78	10	133x	133x	NUM
cana-943	78	11	vol	vol	NOUN
cana-943	78	12	31	31	NUM
cana-943	78	13	no	no	NOUN
cana-943	78	14	.	.	PUNCT
cana-943	79	1	4s	4s	NUM
cana-943	79	2	(	(	PUNCT
cana-943	79	3	2024	2024	NUM
cana-943	79	4	)	)	PUNCT
cana-943	79	5	470	470	NUM
cana-943	79	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	79	7	research	research	NOUN
cana-943	79	8	questions	question	NOUN
cana-943	79	9	that	that	PRON
cana-943	79	10	arise	arise	VERB
cana-943	79	11	from	from	ADP
cana-943	79	12	these	these	DET
cana-943	79	13	gaps	gap	NOUN
cana-943	79	14	include	include	VERB
cana-943	79	15	:	:	PUNCT
cana-943	79	16	•	•	ADP
cana-943	79	17	how	how	SCONJ
cana-943	79	18	can	can	AUX
cana-943	79	19	the	the	DET
cana-943	79	20	efficiency	efficiency	NOUN
cana-943	79	21	of	of	ADP
cana-943	79	22	fully	fully	ADV
cana-943	79	23	homomorphic	homomorphic	ADJ
cana-943	79	24	encryption	encryption	NOUN
cana-943	79	25	be	be	AUX
cana-943	79	26	improved	improve	VERB
cana-943	79	27	to	to	PART
cana-943	79	28	enable	enable	VERB
cana-943	79	29	practical	practical	ADJ
cana-943	79	30	applications	application	NOUN
cana-943	79	31	in	in	ADP
cana-943	79	32	cloud	cloud	NOUN
cana-943	79	33	computing	computing	NOUN
cana-943	79	34	and	and	CCONJ
cana-943	79	35	data	datum	NOUN
cana-943	79	36	privacy	privacy	NOUN
cana-943	79	37	?	?	PUNCT
cana-943	80	1	•	•	NUM
cana-943	80	2	what	what	PRON
cana-943	80	3	are	be	AUX
cana-943	80	4	the	the	DET
cana-943	80	5	most	most	ADV
cana-943	80	6	effective	effective	ADJ
cana-943	80	7	post	post	ADJ
cana-943	80	8	-	-	ADJ
cana-943	80	9	quantum	quantum	ADJ
cana-943	80	10	cryptographic	cryptographic	ADJ
cana-943	80	11	algorithms	algorithm	NOUN
cana-943	80	12	for	for	ADP
cana-943	80	13	ensuring	ensure	VERB
cana-943	80	14	long	long	ADJ
cana-943	80	15	-	-	PUNCT
cana-943	80	16	term	term	NOUN
cana-943	80	17	security	security	NOUN
cana-943	80	18	against	against	ADP
cana-943	80	19	quantum	quantum	ADJ
cana-943	80	20	adversaries	adversary	NOUN
cana-943	80	21	?	?	PUNCT
cana-943	81	1	•	•	NUM
cana-943	81	2	how	how	SCONJ
cana-943	81	3	can	can	AUX
cana-943	81	4	new	new	ADJ
cana-943	81	5	algebraic	algebraic	ADJ
cana-943	81	6	structures	structure	NOUN
cana-943	81	7	be	be	AUX
cana-943	81	8	leveraged	leverage	VERB
cana-943	81	9	to	to	PART
cana-943	81	10	develop	develop	VERB
cana-943	81	11	innovative	innovative	ADJ
cana-943	81	12	cryptographic	cryptographic	ADJ
cana-943	81	13	protocols	protocol	NOUN
cana-943	81	14	that	that	PRON
cana-943	81	15	balance	balance	VERB
cana-943	81	16	security	security	NOUN
cana-943	81	17	and	and	CCONJ
cana-943	81	18	performance	performance	NOUN
cana-943	81	19	?	?	PUNCT
cana-943	82	1	3	3	X
cana-943	82	2	.	.	X
cana-943	82	3	fundamental	fundamental	ADJ
cana-943	82	4	concepts	concept	NOUN
cana-943	82	5	3.1	3.1	NUM
cana-943	82	6	.	.	PUNCT
cana-943	83	1	overview	overview	NOUN
cana-943	83	2	of	of	ADP
cana-943	83	3	algebraic	algebraic	ADJ
cana-943	83	4	structures	structure	NOUN
cana-943	83	5	algebraic	algebraic	ADJ
cana-943	83	6	structures	structure	NOUN
cana-943	83	7	form	form	VERB
cana-943	83	8	the	the	DET
cana-943	83	9	bedrock	bedrock	NOUN
cana-943	83	10	of	of	ADP
cana-943	83	11	modern	modern	ADJ
cana-943	83	12	cryptographic	cryptographic	ADJ
cana-943	83	13	algorithms	algorithm	NOUN
cana-943	83	14	.	.	PUNCT
cana-943	84	1	understanding	understand	VERB
cana-943	84	2	these	these	DET
cana-943	84	3	structures	structure	NOUN
cana-943	84	4	—	—	PUNCT
cana-943	84	5	groups	group	NOUN
cana-943	84	6	,	,	PUNCT
cana-943	84	7	rings	ring	NOUN
cana-943	84	8	,	,	PUNCT
cana-943	84	9	and	and	CCONJ
cana-943	84	10	fields	field	NOUN
cana-943	84	11	—	—	PUNCT
cana-943	84	12	is	be	AUX
cana-943	84	13	essential	essential	ADJ
cana-943	84	14	for	for	ADP
cana-943	84	15	comprehending	comprehend	VERB
cana-943	84	16	how	how	SCONJ
cana-943	84	17	cryptographic	cryptographic	ADJ
cana-943	84	18	systems	system	NOUN
cana-943	84	19	operate	operate	VERB
cana-943	84	20	and	and	CCONJ
cana-943	84	21	how	how	SCONJ
cana-943	84	22	they	they	PRON
cana-943	84	23	achieve	achieve	VERB
cana-943	84	24	their	their	PRON
cana-943	84	25	security	security	NOUN
cana-943	84	26	properties	property	NOUN
cana-943	84	27	.	.	PUNCT
cana-943	85	1	3.1.1	3.1.1	X
cana-943	85	2	.	.	PUNCT
cana-943	86	1	groups	group	NOUN
cana-943	86	2	a	a	DET
cana-943	86	3	group	group	NOUN
cana-943	86	4	is	be	AUX
cana-943	86	5	a	a	DET
cana-943	86	6	set	set	NOUN
cana-943	86	7	equipped	equip	VERB
cana-943	86	8	with	with	ADP
cana-943	86	9	a	a	DET
cana-943	86	10	single	single	ADJ
cana-943	86	11	binary	binary	ADJ
cana-943	86	12	operation	operation	NOUN
cana-943	86	13	that	that	PRON
cana-943	86	14	satisfies	satisfy	VERB
cana-943	86	15	four	four	NUM
cana-943	86	16	fundamental	fundamental	ADJ
cana-943	86	17	properties	property	NOUN
cana-943	86	18	:	:	PUNCT
cana-943	86	19	closure	closure	NOUN
cana-943	86	20	,	,	PUNCT
cana-943	86	21	associativity	associativity	NOUN
cana-943	86	22	,	,	PUNCT
cana-943	86	23	the	the	DET
cana-943	86	24	existence	existence	NOUN
cana-943	86	25	of	of	ADP
cana-943	86	26	an	an	DET
cana-943	86	27	identity	identity	NOUN
cana-943	86	28	element	element	NOUN
cana-943	86	29	,	,	PUNCT
cana-943	86	30	and	and	CCONJ
cana-943	86	31	the	the	DET
cana-943	86	32	existence	existence	NOUN
cana-943	86	33	of	of	ADP
cana-943	86	34	inverse	inverse	ADJ
cana-943	86	35	elements	element	NOUN
cana-943	86	36	for	for	ADP
cana-943	86	37	every	every	DET
cana-943	86	38	element	element	NOUN
cana-943	86	39	in	in	ADP
cana-943	86	40	the	the	DET
cana-943	86	41	set	set	NOUN
cana-943	86	42	.	.	PUNCT
cana-943	87	1	formally	formally	ADV
cana-943	87	2	,	,	PUNCT
cana-943	87	3	a	a	DET
cana-943	87	4	group	group	NOUN
cana-943	87	5	(	(	PUNCT
cana-943	87	6	g	g	NOUN
cana-943	87	7	,	,	PUNCT
cana-943	87	8	*	*	PUNCT
cana-943	87	9	)	)	PUNCT
cana-943	87	10	consists	consist	VERB
cana-943	87	11	of	of	ADP
cana-943	87	12	a	a	DET
cana-943	87	13	set	set	NOUN
cana-943	87	14	g	g	NOUN
cana-943	87	15	and	and	CCONJ
cana-943	87	16	a	a	DET
cana-943	87	17	binary	binary	ADJ
cana-943	87	18	operation	operation	NOUN
cana-943	87	19	*	*	PUNCT
cana-943	87	20	such	such	ADJ
cana-943	87	21	that	that	SCONJ
cana-943	87	22	:	:	PUNCT
cana-943	87	23	1	1	X
cana-943	87	24	.	.	X
cana-943	88	1	closure	closure	NOUN
cana-943	88	2	:	:	PUNCT
cana-943	88	3	for	for	ADP
cana-943	88	4	every	every	DET
cana-943	88	5	a	a	PROPN
cana-943	88	6	,	,	PUNCT
cana-943	88	7	b	b	NOUN
cana-943	88	8	in	in	ADP
cana-943	88	9	g	g	PROPN
cana-943	88	10	,	,	PUNCT
cana-943	88	11	the	the	DET
cana-943	88	12	result	result	NOUN
cana-943	88	13	of	of	ADP
cana-943	88	14	the	the	DET
cana-943	88	15	operation	operation	NOUN
cana-943	88	16	a	a	DET
cana-943	88	17	*	*	X
cana-943	88	18	b	b	NOUN
cana-943	88	19	is	be	AUX
cana-943	88	20	also	also	ADV
cana-943	88	21	in	in	ADP
cana-943	88	22	g.	g.	PROPN
cana-943	88	23	2	2	NUM
cana-943	88	24	.	.	PUNCT
cana-943	88	25	associativity	associativity	NOUN
cana-943	88	26	:	:	PUNCT
cana-943	88	27	for	for	ADP
cana-943	88	28	every	every	DET
cana-943	88	29	a	a	DET
cana-943	88	30	,	,	PUNCT
cana-943	88	31	b	b	NOUN
cana-943	88	32	,	,	PUNCT
cana-943	88	33	and	and	CCONJ
cana-943	88	34	c	c	X
cana-943	88	35	in	in	ADP
cana-943	88	36	g	g	PROPN
cana-943	88	37	,	,	PUNCT
cana-943	88	38	(	(	PUNCT
cana-943	88	39	a	a	DET
cana-943	88	40	*	*	ADJ
cana-943	88	41	b	b	NOUN
cana-943	88	42	)	)	PUNCT
cana-943	88	43	*	*	PUNCT
cana-943	89	1	c	c	X
cana-943	89	2	=	=	PUNCT
cana-943	89	3	a	a	X
cana-943	89	4	*	*	X
cana-943	89	5	(	(	PUNCT
cana-943	89	6	b	b	X
cana-943	89	7	*	*	PUNCT
cana-943	89	8	c	c	NOUN
cana-943	89	9	)	)	PUNCT
cana-943	89	10	.	.	PUNCT
cana-943	90	1	3	3	X
cana-943	90	2	.	.	X
cana-943	90	3	identity	identity	NOUN
cana-943	90	4	element	element	NOUN
cana-943	90	5	:	:	PUNCT
cana-943	90	6	there	there	PRON
cana-943	90	7	exists	exist	VERB
cana-943	90	8	an	an	DET
cana-943	90	9	element	element	NOUN
cana-943	90	10	e	e	NOUN
cana-943	90	11	in	in	ADP
cana-943	90	12	g	g	PROPN
cana-943	90	13	such	such	ADJ
cana-943	90	14	that	that	PRON
cana-943	90	15	for	for	ADP
cana-943	90	16	every	every	DET
cana-943	90	17	a	a	PRON
cana-943	90	18	in	in	ADP
cana-943	90	19	g	g	NOUN
cana-943	90	20	,	,	PUNCT
cana-943	90	21	e	e	X
cana-943	90	22	*	*	PUNCT
cana-943	90	23	a	a	PRON
cana-943	90	24	=	=	X
cana-943	90	25	a	a	NOUN
cana-943	90	26	*	*	PUNCT
cana-943	90	27	e	e	NOUN
cana-943	90	28	=	=	NOUN
cana-943	90	29	a.	a.	NOUN
cana-943	90	30	4	4	NUM
cana-943	90	31	.	.	PUNCT
cana-943	91	1	inverse	inverse	NOUN
cana-943	91	2	element	element	NOUN
cana-943	91	3	:	:	PUNCT
cana-943	92	1	for	for	ADP
cana-943	92	2	every	every	DET
cana-943	92	3	a	a	PRON
cana-943	92	4	in	in	ADP
cana-943	92	5	g	g	NOUN
cana-943	92	6	,	,	PUNCT
cana-943	92	7	there	there	PRON
cana-943	92	8	exists	exist	VERB
cana-943	92	9	an	an	DET
cana-943	92	10	element	element	NOUN
cana-943	92	11	b	b	NOUN
cana-943	92	12	in	in	ADP
cana-943	92	13	g	g	PROPN
cana-943	92	14	such	such	DET
cana-943	92	15	that	that	SCONJ
cana-943	92	16	a	a	PRON
cana-943	92	17	*	*	X
cana-943	92	18	b	b	PROPN
cana-943	92	19	=	=	SYM
cana-943	92	20	b	b	PROPN
cana-943	92	21	*	*	PUNCT
cana-943	92	22	a	a	PRON
cana-943	92	23	=	=	X
cana-943	92	24	e.	e.	PROPN
cana-943	92	25	groups	group	NOUN
cana-943	92	26	are	be	AUX
cana-943	92	27	pivotal	pivotal	ADJ
cana-943	92	28	in	in	ADP
cana-943	92	29	cryptography	cryptography	NOUN
cana-943	92	30	,	,	PUNCT
cana-943	92	31	particularly	particularly	ADV
cana-943	92	32	in	in	ADP
cana-943	92	33	the	the	DET
cana-943	92	34	construction	construction	NOUN
cana-943	92	35	of	of	ADP
cana-943	92	36	public	public	ADJ
cana-943	92	37	-	-	PUNCT
cana-943	92	38	key	key	NOUN
cana-943	92	39	algorithms	algorithm	NOUN
cana-943	92	40	.	.	PUNCT
cana-943	93	1	for	for	ADP
cana-943	93	2	example	example	NOUN
cana-943	93	3	,	,	PUNCT
cana-943	93	4	the	the	DET
cana-943	93	5	discrete	discrete	ADJ
cana-943	93	6	logarithm	logarithm	NOUN
cana-943	93	7	problem	problem	NOUN
cana-943	93	8	in	in	ADP
cana-943	93	9	cyclic	cyclic	ADJ
cana-943	93	10	groups	group	NOUN
cana-943	93	11	is	be	AUX
cana-943	93	12	the	the	DET
cana-943	93	13	basis	basis	NOUN
cana-943	93	14	of	of	ADP
cana-943	93	15	the	the	DET
cana-943	93	16	diffie	diffie	PROPN
cana-943	93	17	-	-	PUNCT
cana-943	93	18	hellman	hellman	PROPN
cana-943	93	19	key	key	ADJ
cana-943	93	20	exchange	exchange	NOUN
cana-943	93	21	and	and	CCONJ
cana-943	93	22	elgamal	elgamal	ADJ
cana-943	93	23	encryption	encryption	NOUN
cana-943	93	24	[	[	X
cana-943	93	25	1	1	NUM
cana-943	93	26	]	]	PUNCT
cana-943	93	27	.	.	PUNCT
cana-943	94	1	3.1.2	3.1.2	X
cana-943	94	2	.	.	PUNCT
cana-943	94	3	rings	ring	NOUN
cana-943	94	4	a	a	DET
cana-943	94	5	ring	ring	NOUN
cana-943	94	6	is	be	AUX
cana-943	94	7	a	a	DET
cana-943	94	8	set	set	NOUN
cana-943	94	9	equipped	equip	VERB
cana-943	94	10	with	with	ADP
cana-943	94	11	two	two	NUM
cana-943	94	12	binary	binary	ADJ
cana-943	94	13	operations	operation	NOUN
cana-943	94	14	,	,	PUNCT
cana-943	94	15	usually	usually	ADV
cana-943	94	16	referred	refer	VERB
cana-943	94	17	to	to	ADP
cana-943	94	18	as	as	ADP
cana-943	94	19	addition	addition	NOUN
cana-943	94	20	and	and	CCONJ
cana-943	94	21	multiplication	multiplication	NOUN
cana-943	94	22	,	,	PUNCT
cana-943	94	23	that	that	PRON
cana-943	94	24	generalize	generalize	VERB
cana-943	94	25	the	the	DET
cana-943	94	26	arithmetic	arithmetic	NOUN
cana-943	94	27	of	of	ADP
cana-943	94	28	integers	integer	NOUN
cana-943	94	29	.	.	PUNCT
cana-943	95	1	a	a	DET
cana-943	95	2	ring	ring	NOUN
cana-943	95	3	(	(	PUNCT
cana-943	95	4	r	r	NOUN
cana-943	95	5	,	,	PUNCT
cana-943	95	6	+	+	ADJ
cana-943	95	7	,	,	PUNCT
cana-943	95	8	*	*	PUNCT
cana-943	95	9	)	)	PUNCT
cana-943	95	10	must	must	AUX
cana-943	95	11	satisfy	satisfy	VERB
cana-943	95	12	the	the	DET
cana-943	95	13	following	follow	VERB
cana-943	95	14	properties	property	NOUN
cana-943	95	15	:	:	PUNCT
cana-943	95	16	1	1	X
cana-943	95	17	.	.	X
cana-943	95	18	additive	additive	ADJ
cana-943	95	19	closure	closure	NOUN
cana-943	95	20	:	:	PUNCT
cana-943	95	21	for	for	ADP
cana-943	95	22	every	every	DET
cana-943	95	23	a	a	PROPN
cana-943	95	24	,	,	PUNCT
cana-943	95	25	b	b	NOUN
cana-943	95	26	in	in	ADP
cana-943	95	27	r	r	NOUN
cana-943	95	28	,	,	PUNCT
cana-943	95	29	a	a	PRON
cana-943	95	30	+	+	NOUN
cana-943	95	31	b	b	NOUN
cana-943	95	32	is	be	AUX
cana-943	95	33	in	in	ADP
cana-943	95	34	r.	r.	PROPN
cana-943	95	35	2	2	NUM
cana-943	95	36	.	.	PUNCT
cana-943	95	37	additive	additive	ADJ
cana-943	95	38	associativity	associativity	NOUN
cana-943	95	39	:	:	PUNCT
cana-943	95	40	for	for	ADP
cana-943	95	41	every	every	DET
cana-943	95	42	a	a	DET
cana-943	95	43	,	,	PUNCT
cana-943	95	44	b	b	NOUN
cana-943	95	45	,	,	PUNCT
cana-943	95	46	and	and	CCONJ
cana-943	95	47	c	c	X
cana-943	95	48	in	in	ADP
cana-943	95	49	r	r	PROPN
cana-943	95	50	,	,	PUNCT
cana-943	95	51	(	(	PUNCT
cana-943	95	52	a	a	DET
cana-943	95	53	+	+	NOUN
cana-943	95	54	b	b	NOUN
cana-943	95	55	)	)	PUNCT
cana-943	96	1	+	+	NOUN
cana-943	96	2	c	c	X
cana-943	96	3	=	=	PUNCT
cana-943	96	4	a	a	DET
cana-943	96	5	+	+	X
cana-943	96	6	(	(	PUNCT
cana-943	96	7	b	b	NOUN
cana-943	96	8	+	+	CCONJ
cana-943	96	9	c	c	NOUN
cana-943	96	10	)	)	PUNCT
cana-943	96	11	.	.	PUNCT
cana-943	97	1	3	3	X
cana-943	97	2	.	.	X
cana-943	97	3	additive	additive	ADJ
cana-943	97	4	identity	identity	NOUN
cana-943	97	5	:	:	PUNCT
cana-943	97	6	there	there	PRON
cana-943	97	7	exists	exist	VERB
cana-943	97	8	an	an	DET
cana-943	97	9	element	element	NOUN
cana-943	97	10	0	0	NUM
cana-943	97	11	in	in	ADP
cana-943	97	12	r	r	NOUN
cana-943	97	13	such	such	ADJ
cana-943	97	14	that	that	PRON
cana-943	97	15	for	for	ADP
cana-943	97	16	every	every	DET
cana-943	97	17	a	a	PRON
cana-943	97	18	in	in	ADP
cana-943	97	19	r	r	NOUN
cana-943	97	20	,	,	PUNCT
cana-943	97	21	0	0	NUM
cana-943	98	1	+	+	CCONJ
cana-943	98	2	a	a	DET
cana-943	98	3	=	=	NOUN
cana-943	98	4	a.	a.	NOUN
cana-943	98	5	4	4	NUM
cana-943	98	6	.	.	PUNCT
cana-943	98	7	additive	additive	ADJ
cana-943	98	8	inverse	inverse	NOUN
cana-943	98	9	:	:	PUNCT
cana-943	98	10	for	for	ADP
cana-943	98	11	every	every	DET
cana-943	98	12	a	a	PRON
cana-943	98	13	in	in	ADP
cana-943	98	14	r	r	NOUN
cana-943	98	15	,	,	PUNCT
cana-943	98	16	there	there	PRON
cana-943	98	17	exists	exist	VERB
cana-943	98	18	an	an	DET
cana-943	98	19	element	element	NOUN
cana-943	98	20	-a	-a	PUNCT
cana-943	98	21	in	in	ADP
cana-943	98	22	r	r	NOUN
cana-943	98	23	such	such	DET
cana-943	98	24	that	that	SCONJ
cana-943	98	25	a	a	DET
cana-943	98	26	+	+	X
cana-943	98	27	(	(	PUNCT
cana-943	98	28	-a	-a	NUM
cana-943	98	29	)	)	PUNCT
cana-943	98	30	=	=	SYM
cana-943	98	31	0	0	NUM
cana-943	98	32	.	.	NOUN
cana-943	98	33	5	5	NUM
cana-943	98	34	.	.	X
cana-943	98	35	multiplicative	multiplicative	ADJ
cana-943	98	36	closure	closure	NOUN
cana-943	98	37	:	:	PUNCT
cana-943	98	38	for	for	ADP
cana-943	98	39	every	every	DET
cana-943	98	40	a	a	PROPN
cana-943	98	41	,	,	PUNCT
cana-943	98	42	b	b	NOUN
cana-943	98	43	in	in	ADP
cana-943	98	44	r	r	NOUN
cana-943	98	45	,	,	PUNCT
cana-943	98	46	a	a	DET
cana-943	98	47	*	*	X
cana-943	98	48	b	b	NOUN
cana-943	98	49	is	be	AUX
cana-943	98	50	in	in	ADP
cana-943	98	51	r.	r.	PROPN
cana-943	98	52	6	6	NUM
cana-943	98	53	.	.	PUNCT
cana-943	98	54	multiplicative	multiplicative	ADJ
cana-943	98	55	associativity	associativity	NOUN
cana-943	98	56	:	:	PUNCT
cana-943	98	57	for	for	ADP
cana-943	98	58	every	every	DET
cana-943	98	59	a	a	DET
cana-943	98	60	,	,	PUNCT
cana-943	98	61	b	b	NOUN
cana-943	98	62	,	,	PUNCT
cana-943	98	63	and	and	CCONJ
cana-943	98	64	c	c	X
cana-943	98	65	in	in	ADP
cana-943	98	66	r	r	PROPN
cana-943	98	67	,	,	PUNCT
cana-943	98	68	(	(	PUNCT
cana-943	98	69	a	a	DET
cana-943	98	70	*	*	ADJ
cana-943	98	71	b	b	NOUN
cana-943	98	72	)	)	PUNCT
cana-943	98	73	*	*	PUNCT
cana-943	99	1	c	c	X
cana-943	99	2	=	=	PUNCT
cana-943	99	3	a	a	X
cana-943	99	4	*	*	X
cana-943	99	5	(	(	PUNCT
cana-943	99	6	b	b	X
cana-943	99	7	*	*	PUNCT
cana-943	99	8	c	c	NOUN
cana-943	99	9	)	)	PUNCT
cana-943	99	10	.	.	PUNCT
cana-943	100	1	communications	communication	NOUN
cana-943	100	2	on	on	ADP
cana-943	100	3	applied	apply	VERB
cana-943	100	4	nonlinear	nonlinear	ADJ
cana-943	100	5	analysis	analysis	NOUN
cana-943	100	6	issn	issn	NOUN
cana-943	100	7	:	:	PUNCT
cana-943	100	8	1074	1074	NUM
cana-943	100	9	-	-	PUNCT
cana-943	100	10	133x	133x	NUM
cana-943	100	11	vol	vol	NOUN
cana-943	100	12	31	31	NUM
cana-943	100	13	no	no	NOUN
cana-943	100	14	.	.	PUNCT
cana-943	101	1	4s	4s	NUM
cana-943	101	2	(	(	PUNCT
cana-943	101	3	2024	2024	NUM
cana-943	101	4	)	)	PUNCT
cana-943	101	5	471	471	NUM
cana-943	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	101	7	7	7	X
cana-943	101	8	.	.	PUNCT
cana-943	101	9	distributive	distributive	ADJ
cana-943	101	10	properties	property	NOUN
cana-943	101	11	:	:	PUNCT
cana-943	101	12	for	for	ADP
cana-943	101	13	every	every	DET
cana-943	101	14	a	a	DET
cana-943	101	15	,	,	PUNCT
cana-943	101	16	b	b	NOUN
cana-943	101	17	,	,	PUNCT
cana-943	101	18	and	and	CCONJ
cana-943	101	19	c	c	X
cana-943	101	20	in	in	ADP
cana-943	101	21	r	r	NOUN
cana-943	101	22	,	,	PUNCT
cana-943	101	23	a	a	PRON
cana-943	101	24	*	*	X
cana-943	101	25	(	(	PUNCT
cana-943	101	26	b	b	NOUN
cana-943	101	27	+	+	CCONJ
cana-943	101	28	c	c	X
cana-943	101	29	)	)	PUNCT
cana-943	101	30	=	=	NOUN
cana-943	101	31	(	(	PUNCT
cana-943	101	32	a	a	DET
cana-943	101	33	*	*	ADJ
cana-943	101	34	b	b	NOUN
cana-943	101	35	)	)	PUNCT
cana-943	101	36	+	+	CCONJ
cana-943	101	37	(	(	PUNCT
cana-943	101	38	a	a	DET
cana-943	101	39	*	*	ADJ
cana-943	101	40	c	c	NOUN
cana-943	101	41	)	)	PUNCT
cana-943	101	42	and	and	CCONJ
cana-943	101	43	(	(	PUNCT
cana-943	101	44	a	a	DET
cana-943	101	45	+	+	NOUN
cana-943	101	46	b	b	NOUN
cana-943	101	47	)	)	PUNCT
cana-943	101	48	*	*	PUNCT
cana-943	102	1	c	c	X
cana-943	102	2	=	=	PUNCT
cana-943	102	3	(	(	PUNCT
cana-943	102	4	a	a	DET
cana-943	102	5	*	*	ADJ
cana-943	102	6	c	c	NOUN
cana-943	102	7	)	)	PUNCT
cana-943	103	1	+	+	CCONJ
cana-943	103	2	(	(	PUNCT
cana-943	103	3	b	b	X
cana-943	103	4	*	*	PUNCT
cana-943	103	5	c	c	NOUN
cana-943	103	6	)	)	PUNCT
cana-943	103	7	.	.	PUNCT
cana-943	104	1	rings	ring	NOUN
cana-943	104	2	are	be	AUX
cana-943	104	3	used	use	VERB
cana-943	104	4	in	in	ADP
cana-943	104	5	various	various	ADJ
cana-943	104	6	cryptographic	cryptographic	ADJ
cana-943	104	7	constructions	construction	NOUN
cana-943	104	8	,	,	PUNCT
cana-943	104	9	including	include	VERB
cana-943	104	10	the	the	DET
cana-943	104	11	design	design	NOUN
cana-943	104	12	of	of	ADP
cana-943	104	13	certain	certain	ADJ
cana-943	104	14	encryption	encryption	NOUN
cana-943	104	15	schemes	scheme	NOUN
cana-943	104	16	and	and	CCONJ
cana-943	104	17	error	error	NOUN
cana-943	104	18	-	-	PUNCT
cana-943	104	19	correcting	correct	VERB
cana-943	104	20	codes	code	NOUN
cana-943	104	21	.	.	PUNCT
cana-943	105	1	for	for	ADP
cana-943	105	2	instance	instance	NOUN
cana-943	105	3	,	,	PUNCT
cana-943	105	4	polynomial	polynomial	ADJ
cana-943	105	5	rings	ring	NOUN
cana-943	105	6	are	be	AUX
cana-943	105	7	employed	employ	VERB
cana-943	105	8	in	in	ADP
cana-943	105	9	lattice	lattice	NOUN
cana-943	105	10	-	-	PUNCT
cana-943	105	11	based	base	VERB
cana-943	105	12	cryptography	cryptography	NOUN
cana-943	105	13	[	[	X
cana-943	105	14	12	12	NUM
cana-943	105	15	]	]	PUNCT
cana-943	105	16	.	.	PUNCT
cana-943	106	1	3.1.3	3.1.3	X
cana-943	106	2	.	.	PUNCT
cana-943	106	3	fields	field	VERB
cana-943	106	4	a	a	DET
cana-943	106	5	field	field	NOUN
cana-943	106	6	is	be	AUX
cana-943	106	7	a	a	DET
cana-943	106	8	ring	ring	NOUN
cana-943	106	9	in	in	ADP
cana-943	106	10	which	which	PRON
cana-943	106	11	division	division	NOUN
cana-943	106	12	is	be	AUX
cana-943	106	13	possible	possible	ADJ
cana-943	106	14	(	(	PUNCT
cana-943	106	15	except	except	SCONJ
cana-943	106	16	by	by	ADP
cana-943	106	17	zero	zero	NUM
cana-943	106	18	)	)	PUNCT
cana-943	106	19	.	.	PUNCT
cana-943	107	1	formally	formally	ADV
cana-943	107	2	,	,	PUNCT
cana-943	107	3	a	a	DET
cana-943	107	4	field	field	NOUN
cana-943	107	5	(	(	PUNCT
cana-943	107	6	f	f	X
cana-943	107	7	,	,	PUNCT
cana-943	107	8	+	+	ADJ
cana-943	107	9	,	,	PUNCT
cana-943	107	10	*	*	PUNCT
cana-943	107	11	)	)	PUNCT
cana-943	107	12	is	be	AUX
cana-943	107	13	a	a	DET
cana-943	107	14	set	set	NOUN
cana-943	107	15	f	f	NOUN
cana-943	107	16	with	with	ADP
cana-943	107	17	two	two	NUM
cana-943	107	18	operations	operation	NOUN
cana-943	107	19	,	,	PUNCT
cana-943	107	20	addition	addition	NOUN
cana-943	107	21	and	and	CCONJ
cana-943	107	22	multiplication	multiplication	NOUN
cana-943	107	23	,	,	PUNCT
cana-943	107	24	that	that	PRON
cana-943	107	25	satisfy	satisfy	VERB
cana-943	107	26	the	the	DET
cana-943	107	27	following	follow	VERB
cana-943	107	28	properties	property	NOUN
cana-943	107	29	:	:	PUNCT
cana-943	107	30	1	1	X
cana-943	107	31	.	.	X
cana-943	107	32	field	field	NOUN
cana-943	107	33	properties	property	NOUN
cana-943	107	34	:	:	PUNCT
cana-943	107	35	all	all	DET
cana-943	107	36	properties	property	NOUN
cana-943	107	37	of	of	ADP
cana-943	107	38	a	a	DET
cana-943	107	39	ring	ring	NOUN
cana-943	107	40	apply	apply	VERB
cana-943	107	41	.	.	PUNCT
cana-943	108	1	2	2	X
cana-943	108	2	.	.	X
cana-943	108	3	multiplicative	multiplicative	ADJ
cana-943	108	4	identity	identity	NOUN
cana-943	108	5	:	:	PUNCT
cana-943	108	6	there	there	PRON
cana-943	108	7	exists	exist	VERB
cana-943	108	8	an	an	DET
cana-943	108	9	element	element	NOUN
cana-943	108	10	1	1	NUM
cana-943	108	11	in	in	ADP
cana-943	108	12	f	f	PROPN
cana-943	108	13	such	such	ADJ
cana-943	108	14	that	that	PRON
cana-943	108	15	for	for	ADP
cana-943	108	16	every	every	DET
cana-943	108	17	a	a	PRON
cana-943	108	18	in	in	ADP
cana-943	108	19	f	f	PROPN
cana-943	108	20	,	,	PUNCT
cana-943	108	21	1	1	NUM
cana-943	108	22	*	*	PUNCT
cana-943	108	23	a	a	DET
cana-943	108	24	=	=	NOUN
cana-943	108	25	a.	a.	NOUN
cana-943	108	26	3	3	NUM
cana-943	108	27	.	.	PUNCT
cana-943	108	28	multiplicative	multiplicative	ADJ
cana-943	108	29	inverse	inverse	NOUN
cana-943	108	30	:	:	PUNCT
cana-943	108	31	for	for	ADP
cana-943	108	32	every	every	DET
cana-943	108	33	a	a	PRON
cana-943	108	34	in	in	ADP
cana-943	108	35	f	f	PROPN
cana-943	108	36	,	,	PUNCT
cana-943	108	37	except	except	SCONJ
cana-943	108	38	0	0	NUM
cana-943	108	39	,	,	PUNCT
cana-943	108	40	there	there	PRON
cana-943	108	41	exists	exist	VERB
cana-943	108	42	an	an	DET
cana-943	108	43	element	element	NOUN
cana-943	108	44	a^(-1	a^(-1	VERB
cana-943	108	45	)	)	PUNCT
cana-943	108	46	in	in	ADP
cana-943	108	47	f	f	PROPN
cana-943	108	48	such	such	ADJ
cana-943	108	49	that	that	SCONJ
cana-943	108	50	a	a	DET
cana-943	108	51	*	*	PUNCT
cana-943	108	52	a^(-1	a^(-1	ADJ
cana-943	108	53	)	)	PUNCT
cana-943	108	54	=	=	SYM
cana-943	108	55	1	1	X
cana-943	108	56	.	.	X
cana-943	108	57	finite	finite	PROPN
cana-943	108	58	fields	field	NOUN
cana-943	108	59	,	,	PUNCT
cana-943	108	60	or	or	CCONJ
cana-943	108	61	galois	galois	PROPN
cana-943	108	62	fields	field	NOUN
cana-943	108	63	,	,	PUNCT
cana-943	108	64	are	be	AUX
cana-943	108	65	particularly	particularly	ADV
cana-943	108	66	important	important	ADJ
cana-943	108	67	in	in	ADP
cana-943	108	68	cryptography	cryptography	NOUN
cana-943	108	69	.	.	PUNCT
cana-943	109	1	the	the	DET
cana-943	109	2	advanced	advanced	ADJ
cana-943	109	3	encryption	encryption	NOUN
cana-943	109	4	standard	standard	NOUN
cana-943	109	5	(	(	PUNCT
cana-943	109	6	aes	aes	PROPN
cana-943	109	7	)	)	PUNCT
cana-943	109	8	,	,	PUNCT
cana-943	109	9	for	for	ADP
cana-943	109	10	example	example	NOUN
cana-943	109	11	,	,	PUNCT
cana-943	109	12	operates	operate	VERB
cana-943	109	13	in	in	ADP
cana-943	109	14	the	the	DET
cana-943	109	15	finite	finite	ADJ
cana-943	109	16	field	field	NOUN
cana-943	109	17	gf(2	gf(2	PROPN
cana-943	109	18	^	^	NOUN
cana-943	109	19	8)	8)	NOUN
cana-943	109	20	[	[	X
cana-943	109	21	13	13	NUM
cana-943	109	22	]	]	SYM
cana-943	109	23	.	.	PUNCT
cana-943	110	1	3.2	3.2	NUM
cana-943	110	2	.	.	PUNCT
cana-943	110	3	cryptographic	cryptographic	ADJ
cana-943	110	4	fundamentals	fundamental	NOUN
cana-943	110	5	3.2.1	3.2.1	NUM
cana-943	110	6	.	.	PUNCT
cana-943	110	7	encryption	encryption	NOUN
cana-943	110	8	and	and	CCONJ
cana-943	110	9	decryption	decryption	NOUN
cana-943	110	10	encryption	encryption	NOUN
cana-943	110	11	is	be	AUX
cana-943	110	12	the	the	DET
cana-943	110	13	process	process	NOUN
cana-943	110	14	of	of	ADP
cana-943	110	15	converting	convert	VERB
cana-943	110	16	plaintext	plaintext	NOUN
cana-943	110	17	into	into	ADP
cana-943	110	18	ciphertext	ciphertext	NOUN
cana-943	110	19	using	use	VERB
cana-943	110	20	an	an	DET
cana-943	110	21	algorithm	algorithm	NOUN
cana-943	110	22	and	and	CCONJ
cana-943	110	23	a	a	DET
cana-943	110	24	key	key	NOUN
cana-943	110	25	.	.	PUNCT
cana-943	111	1	decryption	decryption	NOUN
cana-943	111	2	is	be	AUX
cana-943	111	3	the	the	DET
cana-943	111	4	reverse	reverse	ADJ
cana-943	111	5	process	process	NOUN
cana-943	111	6	,	,	PUNCT
cana-943	111	7	converting	convert	VERB
cana-943	111	8	ciphertext	ciphertext	NOUN
cana-943	111	9	back	back	ADV
cana-943	111	10	to	to	ADP
cana-943	111	11	plaintext	plaintext	NOUN
cana-943	111	12	using	use	VERB
cana-943	111	13	a	a	DET
cana-943	111	14	key	key	NOUN
cana-943	111	15	.	.	PUNCT
cana-943	112	1	the	the	DET
cana-943	112	2	primary	primary	ADJ
cana-943	112	3	goal	goal	NOUN
cana-943	112	4	of	of	ADP
cana-943	112	5	encryption	encryption	NOUN
cana-943	112	6	is	be	AUX
cana-943	112	7	to	to	PART
cana-943	112	8	ensure	ensure	VERB
cana-943	112	9	that	that	SCONJ
cana-943	112	10	information	information	NOUN
cana-943	112	11	remains	remain	VERB
cana-943	112	12	confidential	confidential	ADJ
cana-943	112	13	,	,	PUNCT
cana-943	112	14	even	even	ADV
cana-943	112	15	if	if	SCONJ
cana-943	112	16	intercepted	intercept	VERB
cana-943	112	17	by	by	ADP
cana-943	112	18	unauthorized	unauthorized	ADJ
cana-943	112	19	parties	party	NOUN
cana-943	112	20	.	.	PUNCT
cana-943	113	1	the	the	DET
cana-943	113	2	two	two	NUM
cana-943	113	3	main	main	ADJ
cana-943	113	4	types	type	NOUN
cana-943	113	5	of	of	ADP
cana-943	113	6	encryption	encryption	NOUN
cana-943	113	7	are	be	AUX
cana-943	113	8	:	:	PUNCT
cana-943	113	9	•	•	NUM
cana-943	113	10	symmetric	symmetric	ADJ
cana-943	113	11	encryption	encryption	NOUN
cana-943	113	12	:	:	PUNCT
cana-943	113	13	the	the	DET
cana-943	113	14	same	same	ADJ
cana-943	113	15	key	key	NOUN
cana-943	113	16	is	be	AUX
cana-943	113	17	used	use	VERB
cana-943	113	18	for	for	ADP
cana-943	113	19	both	both	DET
cana-943	113	20	encryption	encryption	NOUN
cana-943	113	21	and	and	CCONJ
cana-943	113	22	decryption	decryption	NOUN
cana-943	113	23	.	.	PUNCT
cana-943	114	1	examples	example	NOUN
cana-943	114	2	include	include	VERB
cana-943	114	3	aes	aes	PROPN
cana-943	114	4	and	and	CCONJ
cana-943	114	5	des	des	PROPN
cana-943	114	6	.	.	PROPN
cana-943	114	7	symmetric	symmetric	ADJ
cana-943	114	8	encryption	encryption	NOUN
cana-943	114	9	is	be	AUX
cana-943	114	10	generally	generally	ADV
cana-943	114	11	faster	fast	ADJ
cana-943	114	12	and	and	CCONJ
cana-943	114	13	suitable	suitable	ADJ
cana-943	114	14	for	for	ADP
cana-943	114	15	encrypting	encrypt	VERB
cana-943	114	16	large	large	ADJ
cana-943	114	17	amounts	amount	NOUN
cana-943	114	18	of	of	ADP
cana-943	114	19	data	datum	NOUN
cana-943	114	20	[	[	X
cana-943	114	21	13	13	NUM
cana-943	114	22	]	]	PUNCT
cana-943	114	23	.	.	PUNCT
cana-943	115	1	•	•	NUM
cana-943	115	2	asymmetric	asymmetric	ADJ
cana-943	115	3	encryption	encryption	NOUN
cana-943	115	4	:	:	PUNCT
cana-943	115	5	uses	use	VERB
cana-943	115	6	a	a	DET
cana-943	115	7	pair	pair	NOUN
cana-943	115	8	of	of	ADP
cana-943	115	9	keys	key	NOUN
cana-943	115	10	,	,	PUNCT
cana-943	115	11	a	a	DET
cana-943	115	12	public	public	ADJ
cana-943	115	13	key	key	NOUN
cana-943	115	14	for	for	ADP
cana-943	115	15	encryption	encryption	NOUN
cana-943	115	16	and	and	CCONJ
cana-943	115	17	a	a	DET
cana-943	115	18	private	private	ADJ
cana-943	115	19	key	key	NOUN
cana-943	115	20	for	for	ADP
cana-943	115	21	decryption	decryption	NOUN
cana-943	115	22	.	.	PUNCT
cana-943	116	1	rsa	rsa	PROPN
cana-943	116	2	and	and	CCONJ
cana-943	116	3	ecc	ecc	PROPN
cana-943	116	4	are	be	AUX
cana-943	116	5	prominent	prominent	ADJ
cana-943	116	6	examples	example	NOUN
cana-943	116	7	.	.	PUNCT
cana-943	117	1	asymmetric	asymmetric	ADJ
cana-943	117	2	encryption	encryption	NOUN
cana-943	117	3	is	be	AUX
cana-943	117	4	crucial	crucial	ADJ
cana-943	117	5	for	for	ADP
cana-943	117	6	secure	secure	ADJ
cana-943	117	7	key	key	ADJ
cana-943	117	8	exchange	exchange	NOUN
cana-943	117	9	and	and	CCONJ
cana-943	117	10	digital	digital	ADJ
cana-943	117	11	signatures	signature	NOUN
cana-943	117	12	,	,	PUNCT
cana-943	117	13	where	where	SCONJ
cana-943	117	14	the	the	DET
cana-943	117	15	security	security	NOUN
cana-943	117	16	of	of	ADP
cana-943	117	17	private	private	ADJ
cana-943	117	18	keys	key	NOUN
cana-943	117	19	is	be	AUX
cana-943	117	20	paramount	paramount	ADJ
cana-943	117	21	[	[	X
cana-943	117	22	2	2	NUM
cana-943	117	23	]	]	PUNCT
cana-943	117	24	.	.	PUNCT
cana-943	118	1	3.2.2	3.2.2	NUM
cana-943	118	2	.	.	PUNCT
cana-943	119	1	symmetric	symmetric	ADJ
cana-943	119	2	vs	vs	ADP
cana-943	119	3	asymmetric	asymmetric	ADJ
cana-943	119	4	cryptography	cryptography	NOUN
cana-943	119	5	symmetric	symmetric	ADJ
cana-943	119	6	and	and	CCONJ
cana-943	119	7	asymmetric	asymmetric	ADJ
cana-943	119	8	cryptography	cryptography	NOUN
cana-943	119	9	serve	serve	VERB
cana-943	119	10	different	different	ADJ
cana-943	119	11	purposes	purpose	NOUN
cana-943	119	12	and	and	CCONJ
cana-943	119	13	are	be	AUX
cana-943	119	14	often	often	ADV
cana-943	119	15	used	use	VERB
cana-943	119	16	together	together	ADV
cana-943	119	17	to	to	PART
cana-943	119	18	create	create	VERB
cana-943	119	19	a	a	DET
cana-943	119	20	secure	secure	ADJ
cana-943	119	21	and	and	CCONJ
cana-943	119	22	efficient	efficient	ADJ
cana-943	119	23	cryptographic	cryptographic	ADJ
cana-943	119	24	system	system	NOUN
cana-943	119	25	.	.	PUNCT
cana-943	120	1	•	•	NUM
cana-943	120	2	symmetric	symmetric	ADJ
cana-943	120	3	cryptography	cryptography	NOUN
cana-943	120	4	:	:	PUNCT
cana-943	120	5	◦	◦	NOUN
cana-943	120	6	advantages	advantage	NOUN
cana-943	120	7	:	:	PUNCT
cana-943	120	8	faster	fast	ADJ
cana-943	120	9	and	and	CCONJ
cana-943	120	10	more	more	ADV
cana-943	120	11	efficient	efficient	ADJ
cana-943	120	12	for	for	ADP
cana-943	120	13	bulk	bulk	ADJ
cana-943	120	14	data	datum	NOUN
cana-943	120	15	encryption	encryption	NOUN
cana-943	120	16	.	.	PUNCT
cana-943	121	1	◦	◦	NOUN
cana-943	121	2	disadvantages	disadvantage	VERB
cana-943	121	3	:	:	PUNCT
cana-943	121	4	key	key	ADJ
cana-943	121	5	distribution	distribution	NOUN
cana-943	121	6	is	be	AUX
cana-943	121	7	challenging	challenge	VERB
cana-943	121	8	because	because	SCONJ
cana-943	121	9	the	the	DET
cana-943	121	10	same	same	ADJ
cana-943	121	11	key	key	NOUN
cana-943	121	12	must	must	AUX
cana-943	121	13	be	be	AUX
cana-943	121	14	securely	securely	ADV
cana-943	121	15	shared	share	VERB
cana-943	121	16	between	between	ADP
cana-943	121	17	parties	party	NOUN
cana-943	121	18	.	.	PUNCT
cana-943	122	1	communications	communication	NOUN
cana-943	122	2	on	on	ADP
cana-943	122	3	applied	apply	VERB
cana-943	122	4	nonlinear	nonlinear	ADJ
cana-943	122	5	analysis	analysis	NOUN
cana-943	122	6	issn	issn	NOUN
cana-943	122	7	:	:	PUNCT
cana-943	122	8	1074	1074	NUM
cana-943	122	9	-	-	PUNCT
cana-943	122	10	133x	133x	NUM
cana-943	122	11	vol	vol	NOUN
cana-943	122	12	31	31	NUM
cana-943	122	13	no	no	NOUN
cana-943	122	14	.	.	PUNCT
cana-943	123	1	4s	4s	NUM
cana-943	123	2	(	(	PUNCT
cana-943	123	3	2024	2024	NUM
cana-943	123	4	)	)	PUNCT
cana-943	123	5	472	472	NUM
cana-943	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	123	7	◦	◦	NOUN
cana-943	123	8	applications	application	NOUN
cana-943	123	9	:	:	PUNCT
cana-943	123	10	used	use	VERB
cana-943	123	11	for	for	ADP
cana-943	123	12	encrypting	encrypt	VERB
cana-943	123	13	data	datum	NOUN
cana-943	123	14	at	at	ADP
cana-943	123	15	rest	rest	NOUN
cana-943	123	16	,	,	PUNCT
cana-943	123	17	securing	secure	VERB
cana-943	123	18	communication	communication	NOUN
cana-943	123	19	channels	channel	NOUN
cana-943	123	20	(	(	PUNCT
cana-943	123	21	e.g.	e.g.	ADV
cana-943	123	22	,	,	PUNCT
cana-943	123	23	ssl	ssl	PROPN
cana-943	123	24	/	/	SYM
cana-943	123	25	tls	tls	PROPN
cana-943	123	26	)	)	PUNCT
cana-943	123	27	,	,	PUNCT
cana-943	123	28	and	and	CCONJ
cana-943	123	29	in	in	ADP
cana-943	123	30	hardware	hardware	NOUN
cana-943	123	31	encryption	encryption	NOUN
cana-943	123	32	.	.	PUNCT
cana-943	124	1	•	•	NUM
cana-943	124	2	asymmetric	asymmetric	ADJ
cana-943	124	3	cryptography	cryptography	NOUN
cana-943	124	4	:	:	PUNCT
cana-943	124	5	◦	◦	NOUN
cana-943	124	6	advantages	advantage	NOUN
cana-943	124	7	:	:	PUNCT
cana-943	124	8	solves	solve	VERB
cana-943	124	9	the	the	DET
cana-943	124	10	key	key	ADJ
cana-943	124	11	distribution	distribution	NOUN
cana-943	124	12	problem	problem	NOUN
cana-943	124	13	since	since	SCONJ
cana-943	124	14	the	the	DET
cana-943	124	15	public	public	ADJ
cana-943	124	16	key	key	NOUN
cana-943	124	17	can	can	AUX
cana-943	124	18	be	be	AUX
cana-943	124	19	freely	freely	ADV
cana-943	124	20	distributed	distribute	VERB
cana-943	124	21	.	.	PUNCT
cana-943	125	1	◦	◦	NOUN
cana-943	125	2	disadvantages	disadvantage	VERB
cana-943	125	3	:	:	PUNCT
cana-943	125	4	slower	slow	ADJ
cana-943	125	5	and	and	CCONJ
cana-943	125	6	computationally	computationally	ADV
cana-943	125	7	more	more	ADV
cana-943	125	8	intensive	intensive	ADJ
cana-943	125	9	than	than	ADP
cana-943	125	10	symmetric	symmetric	ADJ
cana-943	125	11	cryptography	cryptography	NOUN
cana-943	125	12	.	.	PUNCT
cana-943	126	1	◦	◦	NOUN
cana-943	126	2	applications	application	NOUN
cana-943	126	3	:	:	PUNCT
cana-943	126	4	used	use	VERB
cana-943	126	5	for	for	ADP
cana-943	126	6	digital	digital	ADJ
cana-943	126	7	signatures	signature	NOUN
cana-943	126	8	,	,	PUNCT
cana-943	126	9	secure	secure	VERB
cana-943	126	10	key	key	ADJ
cana-943	126	11	exchange	exchange	NOUN
cana-943	126	12	,	,	PUNCT
cana-943	126	13	and	and	CCONJ
cana-943	126	14	encrypting	encrypt	VERB
cana-943	126	15	small	small	ADJ
cana-943	126	16	amounts	amount	NOUN
cana-943	126	17	of	of	ADP
cana-943	126	18	data	datum	NOUN
cana-943	126	19	,	,	PUNCT
cana-943	126	20	such	such	ADJ
cana-943	126	21	as	as	ADP
cana-943	126	22	keys	key	NOUN
cana-943	126	23	for	for	ADP
cana-943	126	24	symmetric	symmetric	ADJ
cana-943	126	25	algorithms	algorithm	NOUN
cana-943	126	26	.	.	PUNCT
cana-943	127	1	by	by	ADP
cana-943	127	2	combining	combine	VERB
cana-943	127	3	symmetric	symmetric	ADJ
cana-943	127	4	and	and	CCONJ
cana-943	127	5	asymmetric	asymmetric	ADJ
cana-943	127	6	cryptography	cryptography	NOUN
cana-943	127	7	,	,	PUNCT
cana-943	127	8	systems	system	NOUN
cana-943	127	9	can	can	AUX
cana-943	127	10	leverage	leverage	VERB
cana-943	127	11	the	the	DET
cana-943	127	12	strengths	strength	NOUN
cana-943	127	13	of	of	ADP
cana-943	127	14	both	both	DET
cana-943	127	15	approaches	approach	NOUN
cana-943	127	16	.	.	PUNCT
cana-943	128	1	for	for	ADP
cana-943	128	2	instance	instance	NOUN
cana-943	128	3	,	,	PUNCT
cana-943	128	4	in	in	ADP
cana-943	128	5	a	a	DET
cana-943	128	6	typical	typical	ADJ
cana-943	128	7	ssl	ssl	ADJ
cana-943	128	8	/	/	SYM
cana-943	128	9	tls	tls	PROPN
cana-943	128	10	session	session	NOUN
cana-943	128	11	,	,	PUNCT
cana-943	128	12	asymmetric	asymmetric	ADJ
cana-943	128	13	cryptography	cryptography	NOUN
cana-943	128	14	is	be	AUX
cana-943	128	15	used	use	VERB
cana-943	128	16	to	to	PART
cana-943	128	17	exchange	exchange	VERB
cana-943	128	18	a	a	DET
cana-943	128	19	symmetric	symmetric	ADJ
cana-943	128	20	session	session	NOUN
cana-943	128	21	key	key	NOUN
cana-943	128	22	,	,	PUNCT
cana-943	128	23	which	which	PRON
cana-943	128	24	is	be	AUX
cana-943	128	25	then	then	ADV
cana-943	128	26	used	use	VERB
cana-943	128	27	for	for	ADP
cana-943	128	28	the	the	DET
cana-943	128	29	fast	fast	ADJ
cana-943	128	30	encryption	encryption	NOUN
cana-943	128	31	of	of	ADP
cana-943	128	32	the	the	DET
cana-943	128	33	actual	actual	ADJ
cana-943	128	34	data	datum	NOUN
cana-943	128	35	transmitted	transmit	VERB
cana-943	128	36	.	.	PUNCT
cana-943	129	1	4	4	X
cana-943	129	2	.	.	X
cana-943	129	3	algebraic	algebraic	ADJ
cana-943	129	4	techniques	technique	NOUN
cana-943	129	5	in	in	ADP
cana-943	129	6	cryptography	cryptography	NOUN
cana-943	129	7	4.1	4.1	NUM
cana-943	129	8	.	.	PUNCT
cana-943	130	1	group	group	NOUN
cana-943	130	2	theory	theory	NOUN
cana-943	130	3	applications	application	NOUN
cana-943	130	4	4.1.1	4.1.1	NUM
cana-943	130	5	.	.	PUNCT
cana-943	131	1	discrete	discrete	ADJ
cana-943	131	2	logarithm	logarithm	PROPN
cana-943	131	3	problem	problem	NOUN
cana-943	131	4	the	the	DET
cana-943	131	5	discrete	discrete	ADJ
cana-943	131	6	logarithm	logarithm	NOUN
cana-943	131	7	problem	problem	NOUN
cana-943	131	8	(	(	PUNCT
cana-943	131	9	dlp	dlp	NOUN
cana-943	131	10	)	)	PUNCT
cana-943	131	11	is	be	AUX
cana-943	131	12	a	a	DET
cana-943	131	13	cornerstone	cornerstone	NOUN
cana-943	131	14	of	of	ADP
cana-943	131	15	several	several	ADJ
cana-943	131	16	cryptographic	cryptographic	ADJ
cana-943	131	17	protocols	protocol	NOUN
cana-943	131	18	.	.	PUNCT
cana-943	132	1	in	in	ADP
cana-943	132	2	the	the	DET
cana-943	132	3	context	context	NOUN
cana-943	132	4	of	of	ADP
cana-943	132	5	a	a	DET
cana-943	132	6	cyclic	cyclic	ADJ
cana-943	132	7	group	group	NOUN
cana-943	132	8	\	\	PROPN
cana-943	132	9	(	(	PUNCT
cana-943	132	10	g	g	PROPN
cana-943	132	11	\	\	PROPN
cana-943	132	12	)	)	PUNCT
cana-943	132	13	with	with	ADP
cana-943	132	14	generator	generator	NOUN
cana-943	132	15	\	\	PROPN
cana-943	132	16	(	(	PUNCT
cana-943	132	17	g	g	PROPN
cana-943	132	18	\	\	PROPN
cana-943	132	19	)	)	PUNCT
cana-943	132	20	,	,	PUNCT
cana-943	132	21	the	the	DET
cana-943	132	22	dlp	dlp	NOUN
cana-943	132	23	is	be	AUX
cana-943	132	24	the	the	DET
cana-943	132	25	challenge	challenge	NOUN
cana-943	132	26	of	of	ADP
cana-943	132	27	finding	find	VERB
cana-943	132	28	the	the	DET
cana-943	132	29	integer	integer	NOUN
cana-943	132	30	\	\	PROPN
cana-943	132	31	(	(	PUNCT
cana-943	132	32	x	x	SYM
cana-943	132	33	\	\	ADJ
cana-943	132	34	)	)	PUNCT
cana-943	132	35	given	give	VERB
cana-943	132	36	\	\	PROPN
cana-943	132	37	(	(	PUNCT
cana-943	132	38	g	g	PROPN
cana-943	132	39	\	\	PROPN
cana-943	132	40	)	)	PUNCT
cana-943	132	41	and	and	CCONJ
cana-943	132	42	\	\	PROPN
cana-943	132	43	(	(	PUNCT
cana-943	132	44	g^x	g^x	NOUN
cana-943	132	45	\	\	PROPN
cana-943	132	46	)	)	PUNCT
cana-943	132	47	.	.	PUNCT
cana-943	133	1	formally	formally	ADV
cana-943	133	2	,	,	PUNCT
cana-943	133	3	if	if	SCONJ
cana-943	133	4	\	\	PROPN
cana-943	133	5	(	(	PUNCT
cana-943	133	6	y	y	PROPN
cana-943	133	7	=	=	PUNCT
cana-943	133	8	g^x	g^x	PROPN
cana-943	133	9	\	\	NOUN
cana-943	133	10	)	)	PUNCT
cana-943	133	11	in	in	ADP
cana-943	133	12	\	\	PROPN
cana-943	133	13	(	(	PUNCT
cana-943	133	14	g	g	PROPN
cana-943	133	15	\	\	PROPN
cana-943	133	16	)	)	PUNCT
cana-943	133	17	,	,	PUNCT
cana-943	133	18	then	then	ADV
cana-943	133	19	\	\	PROPN
cana-943	133	20	(	(	PUNCT
cana-943	133	21	x	x	SYM
cana-943	133	22	\	\	PROPN
cana-943	133	23	)	)	PUNCT
cana-943	133	24	is	be	AUX
cana-943	133	25	the	the	DET
cana-943	133	26	discrete	discrete	ADJ
cana-943	133	27	logarithm	logarithm	NOUN
cana-943	133	28	of	of	ADP
cana-943	133	29	\	\	PROPN
cana-943	133	30	(	(	PUNCT
cana-943	133	31	y	y	PROPN
cana-943	133	32	\	\	PROPN
cana-943	133	33	)	)	PUNCT
cana-943	133	34	to	to	ADP
cana-943	133	35	the	the	DET
cana-943	133	36	base	base	NOUN
cana-943	133	37	\	\	PROPN
cana-943	133	38	(	(	PUNCT
cana-943	133	39	g	g	PROPN
cana-943	133	40	\	\	PROPN
cana-943	133	41	)	)	PUNCT
cana-943	133	42	.	.	PUNCT
cana-943	134	1	this	this	DET
cana-943	134	2	problem	problem	NOUN
cana-943	134	3	is	be	AUX
cana-943	134	4	computationally	computationally	ADV
cana-943	134	5	hard	hard	ADJ
cana-943	134	6	,	,	PUNCT
cana-943	134	7	which	which	PRON
cana-943	134	8	makes	make	VERB
cana-943	134	9	it	it	PRON
cana-943	134	10	a	a	DET
cana-943	134	11	robust	robust	ADJ
cana-943	134	12	foundation	foundation	NOUN
cana-943	134	13	for	for	ADP
cana-943	134	14	cryptographic	cryptographic	ADJ
cana-943	134	15	systems	system	NOUN
cana-943	134	16	.	.	PUNCT
cana-943	135	1	key	key	ADJ
cana-943	135	2	applications	application	NOUN
cana-943	135	3	of	of	ADP
cana-943	135	4	the	the	DET
cana-943	135	5	dlp	dlp	NOUN
cana-943	135	6	include	include	VERB
cana-943	135	7	the	the	DET
cana-943	135	8	diffie	diffie	PROPN
cana-943	135	9	-	-	PUNCT
cana-943	135	10	hellman	hellman	PROPN
cana-943	135	11	key	key	PROPN
cana-943	135	12	exchange	exchange	NOUN
cana-943	135	13	,	,	PUNCT
cana-943	135	14	where	where	SCONJ
cana-943	135	15	two	two	NUM
cana-943	135	16	parties	party	NOUN
cana-943	135	17	can	can	AUX
cana-943	135	18	securely	securely	ADV
cana-943	135	19	share	share	VERB
cana-943	135	20	a	a	DET
cana-943	135	21	secret	secret	ADJ
cana-943	135	22	key	key	NOUN
cana-943	135	23	over	over	ADP
cana-943	135	24	an	an	DET
cana-943	135	25	insecure	insecure	ADJ
cana-943	135	26	channel	channel	NOUN
cana-943	135	27	by	by	ADP
cana-943	135	28	leveraging	leverage	VERB
cana-943	135	29	the	the	DET
cana-943	135	30	difficulty	difficulty	NOUN
cana-943	135	31	of	of	ADP
cana-943	135	32	solving	solve	VERB
cana-943	135	33	the	the	DET
cana-943	135	34	dlp	dlp	NOUN
cana-943	136	1	[	[	X
cana-943	136	2	1	1	NUM
cana-943	136	3	]	]	PUNCT
cana-943	136	4	.	.	PUNCT
cana-943	137	1	additionally	additionally	ADV
cana-943	137	2	,	,	PUNCT
cana-943	137	3	the	the	DET
cana-943	137	4	elgamal	elgamal	ADJ
cana-943	137	5	encryption	encryption	NOUN
cana-943	137	6	system	system	NOUN
cana-943	137	7	and	and	CCONJ
cana-943	137	8	digital	digital	ADJ
cana-943	137	9	signature	signature	NOUN
cana-943	137	10	algorithms	algorithm	NOUN
cana-943	137	11	like	like	ADP
cana-943	137	12	the	the	DET
cana-943	137	13	digital	digital	ADJ
cana-943	137	14	signature	signature	NOUN
cana-943	137	15	algorithm	algorithm	NOUN
cana-943	137	16	(	(	PUNCT
cana-943	137	17	dsa	dsa	NOUN
cana-943	137	18	)	)	PUNCT
cana-943	137	19	are	be	AUX
cana-943	137	20	built	build	VERB
cana-943	137	21	on	on	ADP
cana-943	137	22	the	the	DET
cana-943	137	23	security	security	NOUN
cana-943	137	24	of	of	ADP
cana-943	137	25	the	the	DET
cana-943	137	26	dlp	dlp	NOUN
cana-943	137	27	[	[	X
cana-943	137	28	4	4	NUM
cana-943	137	29	]	]	PUNCT
cana-943	137	30	.	.	PUNCT
cana-943	138	1	elliptic	elliptic	ADJ
cana-943	138	2	curve	curve	NOUN
cana-943	138	3	cryptography	cryptography	NOUN
cana-943	138	4	(	(	PUNCT
cana-943	138	5	ecc	ecc	PROPN
cana-943	138	6	)	)	PUNCT
cana-943	138	7	elliptic	elliptic	ADJ
cana-943	138	8	curve	curve	NOUN
cana-943	138	9	cryptography	cryptography	NOUN
cana-943	138	10	(	(	PUNCT
cana-943	138	11	ecc	ecc	PROPN
cana-943	138	12	)	)	PUNCT
cana-943	138	13	uses	use	VERB
cana-943	138	14	the	the	DET
cana-943	138	15	algebraic	algebraic	ADJ
cana-943	138	16	structure	structure	NOUN
cana-943	138	17	of	of	ADP
cana-943	138	18	elliptic	elliptic	ADJ
cana-943	138	19	curves	curve	NOUN
cana-943	138	20	over	over	ADP
cana-943	138	21	finite	finite	ADJ
cana-943	138	22	fields	field	NOUN
cana-943	138	23	.	.	PUNCT
cana-943	139	1	an	an	DET
cana-943	139	2	elliptic	elliptic	ADJ
cana-943	139	3	curve	curve	NOUN
cana-943	139	4	is	be	AUX
cana-943	139	5	defined	define	VERB
cana-943	139	6	by	by	ADP
cana-943	139	7	an	an	DET
cana-943	139	8	equation	equation	NOUN
cana-943	139	9	of	of	ADP
cana-943	139	10	the	the	DET
cana-943	139	11	form	form	NOUN
cana-943	139	12	\	\	PROPN
cana-943	139	13	(	(	PUNCT
cana-943	139	14	y^2	y^2	PROPN
cana-943	139	15	=	=	PUNCT
cana-943	139	16	x^3	x^3	PROPN
cana-943	140	1	+	+	PUNCT
cana-943	140	2	ax	ax	NOUN
cana-943	140	3	+	+	CCONJ
cana-943	140	4	b	b	X
cana-943	140	5	\	\	NOUN
cana-943	140	6	)	)	PUNCT
cana-943	140	7	over	over	ADP
cana-943	140	8	a	a	DET
cana-943	140	9	field	field	NOUN
cana-943	140	10	\	\	PROPN
cana-943	140	11	(	(	PUNCT
cana-943	140	12	f	f	PROPN
cana-943	140	13	\	\	PROPN
cana-943	140	14	)	)	PUNCT
cana-943	140	15	.	.	PUNCT
cana-943	141	1	the	the	DET
cana-943	141	2	points	point	NOUN
cana-943	141	3	on	on	ADP
cana-943	141	4	the	the	DET
cana-943	141	5	curve	curve	NOUN
cana-943	141	6	,	,	PUNCT
cana-943	141	7	along	along	ADP
cana-943	141	8	with	with	ADP
cana-943	141	9	a	a	DET
cana-943	141	10	point	point	NOUN
cana-943	141	11	at	at	ADP
cana-943	141	12	infinity	infinity	NOUN
cana-943	141	13	,	,	PUNCT
cana-943	141	14	form	form	VERB
cana-943	141	15	a	a	DET
cana-943	141	16	group	group	NOUN
cana-943	141	17	under	under	ADP
cana-943	141	18	a	a	DET
cana-943	141	19	well	well	ADV
cana-943	141	20	-	-	PUNCT
cana-943	141	21	defined	define	VERB
cana-943	141	22	addition	addition	NOUN
cana-943	141	23	operation	operation	NOUN
cana-943	141	24	.	.	PUNCT
cana-943	142	1	ecc	ecc	PROPN
cana-943	142	2	provides	provide	VERB
cana-943	142	3	the	the	DET
cana-943	142	4	same	same	ADJ
cana-943	142	5	level	level	NOUN
cana-943	142	6	of	of	ADP
cana-943	142	7	security	security	NOUN
cana-943	142	8	as	as	ADP
cana-943	142	9	traditional	traditional	ADJ
cana-943	142	10	systems	system	NOUN
cana-943	142	11	like	like	ADP
cana-943	142	12	rsa	rsa	PROPN
cana-943	142	13	but	but	CCONJ
cana-943	142	14	with	with	ADP
cana-943	142	15	much	much	ADV
cana-943	142	16	smaller	small	ADJ
cana-943	142	17	key	key	ADJ
cana-943	142	18	sizes	size	NOUN
cana-943	142	19	,	,	PUNCT
cana-943	142	20	resulting	result	VERB
cana-943	142	21	in	in	ADP
cana-943	142	22	faster	fast	ADJ
cana-943	142	23	computations	computation	NOUN
cana-943	142	24	and	and	CCONJ
cana-943	142	25	reduced	reduce	VERB
cana-943	142	26	storage	storage	NOUN
cana-943	142	27	requirements	requirement	NOUN
cana-943	142	28	.	.	PUNCT
cana-943	143	1	for	for	ADP
cana-943	143	2	instance	instance	NOUN
cana-943	143	3	,	,	PUNCT
cana-943	143	4	a	a	DET
cana-943	143	5	256	256	NUM
cana-943	143	6	-	-	PUNCT
cana-943	143	7	bit	bit	NOUN
cana-943	143	8	key	key	NOUN
cana-943	143	9	in	in	ADP
cana-943	143	10	ecc	ecc	PROPN
cana-943	143	11	is	be	AUX
cana-943	143	12	considered	consider	VERB
cana-943	143	13	equivalent	equivalent	ADJ
cana-943	143	14	in	in	ADP
cana-943	143	15	security	security	NOUN
cana-943	143	16	to	to	ADP
cana-943	143	17	a	a	DET
cana-943	143	18	3072	3072	NUM
cana-943	143	19	-	-	PUNCT
cana-943	143	20	bit	bit	NOUN
cana-943	143	21	key	key	NOUN
cana-943	143	22	in	in	ADP
cana-943	143	23	rsa	rsa	PROPN
cana-943	144	1	[	[	X
cana-943	144	2	3	3	NUM
cana-943	144	3	]	]	PUNCT
cana-943	144	4	.	.	PUNCT
cana-943	145	1	this	this	DET
cana-943	145	2	efficiency	efficiency	NOUN
cana-943	145	3	makes	make	VERB
cana-943	145	4	ecc	ecc	PROPN
cana-943	145	5	particularly	particularly	ADV
cana-943	145	6	suitable	suitable	ADJ
cana-943	145	7	for	for	ADP
cana-943	145	8	environments	environment	NOUN
cana-943	145	9	with	with	ADP
cana-943	145	10	limited	limited	ADJ
cana-943	145	11	computational	computational	ADJ
cana-943	145	12	power	power	NOUN
cana-943	145	13	and	and	CCONJ
cana-943	145	14	memory	memory	NOUN
cana-943	145	15	,	,	PUNCT
cana-943	145	16	such	such	ADJ
cana-943	145	17	as	as	ADP
cana-943	145	18	mobile	mobile	ADJ
cana-943	145	19	devices	device	NOUN
cana-943	145	20	and	and	CCONJ
cana-943	145	21	smart	smart	ADJ
cana-943	145	22	cards	card	NOUN
cana-943	145	23	.	.	PUNCT
cana-943	146	1	4.2	4.2	NUM
cana-943	146	2	.	.	PUNCT
cana-943	147	1	ring	ring	NOUN
cana-943	147	2	theory	theory	NOUN
cana-943	147	3	applications	application	NOUN
cana-943	147	4	4.2.1	4.2.1	NOUN
cana-943	147	5	.	.	PUNCT
cana-943	148	1	polynomial	polynomial	ADJ
cana-943	148	2	rings	ring	NOUN
cana-943	148	3	and	and	CCONJ
cana-943	148	4	cryptographic	cryptographic	ADJ
cana-943	148	5	uses	use	VERB
cana-943	148	6	polynomial	polynomial	ADJ
cana-943	148	7	rings	ring	NOUN
cana-943	148	8	are	be	AUX
cana-943	148	9	algebraic	algebraic	ADJ
cana-943	148	10	structures	structure	NOUN
cana-943	148	11	where	where	SCONJ
cana-943	148	12	the	the	DET
cana-943	148	13	elements	element	NOUN
cana-943	148	14	are	be	AUX
cana-943	148	15	polynomials	polynomial	NOUN
cana-943	148	16	,	,	PUNCT
cana-943	148	17	and	and	CCONJ
cana-943	148	18	the	the	DET
cana-943	148	19	operations	operation	NOUN
cana-943	148	20	are	be	AUX
cana-943	148	21	polynomial	polynomial	ADJ
cana-943	148	22	addition	addition	NOUN
cana-943	148	23	and	and	CCONJ
cana-943	148	24	multiplication	multiplication	NOUN
cana-943	148	25	.	.	PUNCT
cana-943	149	1	polynomial	polynomial	ADJ
cana-943	149	2	rings	ring	NOUN
cana-943	149	3	find	find	VERB
cana-943	149	4	extensive	extensive	ADJ
cana-943	149	5	applications	application	NOUN
cana-943	149	6	in	in	ADP
cana-943	149	7	cryptographic	cryptographic	ADJ
cana-943	149	8	algorithms	algorithm	NOUN
cana-943	149	9	,	,	PUNCT
cana-943	149	10	particularly	particularly	ADV
cana-943	149	11	in	in	ADP
cana-943	149	12	coding	code	VERB
cana-943	149	13	theory	theory	NOUN
cana-943	149	14	and	and	CCONJ
cana-943	149	15	lattice	lattice	NOUN
cana-943	149	16	-	-	PUNCT
cana-943	149	17	based	base	VERB
cana-943	149	18	cryptography	cryptography	NOUN
cana-943	149	19	.	.	PUNCT
cana-943	150	1	communications	communication	NOUN
cana-943	150	2	on	on	ADP
cana-943	150	3	applied	apply	VERB
cana-943	150	4	nonlinear	nonlinear	ADJ
cana-943	150	5	analysis	analysis	NOUN
cana-943	150	6	issn	issn	NOUN
cana-943	150	7	:	:	PUNCT
cana-943	150	8	1074	1074	NUM
cana-943	150	9	-	-	PUNCT
cana-943	150	10	133x	133x	NUM
cana-943	150	11	vol	vol	NOUN
cana-943	150	12	31	31	NUM
cana-943	150	13	no	no	NOUN
cana-943	150	14	.	.	PUNCT
cana-943	151	1	4s	4s	NUM
cana-943	151	2	(	(	PUNCT
cana-943	151	3	2024	2024	NUM
cana-943	151	4	)	)	PUNCT
cana-943	151	5	473	473	NUM
cana-943	151	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	151	7	in	in	ADP
cana-943	151	8	the	the	DET
cana-943	151	9	context	context	NOUN
cana-943	151	10	of	of	ADP
cana-943	151	11	error	error	NOUN
cana-943	151	12	-	-	PUNCT
cana-943	151	13	correcting	correct	VERB
cana-943	151	14	codes	code	NOUN
cana-943	151	15	,	,	PUNCT
cana-943	151	16	polynomial	polynomial	ADJ
cana-943	151	17	rings	ring	NOUN
cana-943	151	18	are	be	AUX
cana-943	151	19	used	use	VERB
cana-943	151	20	to	to	PART
cana-943	151	21	construct	construct	VERB
cana-943	151	22	codes	code	NOUN
cana-943	151	23	that	that	PRON
cana-943	151	24	can	can	AUX
cana-943	151	25	detect	detect	VERB
cana-943	151	26	and	and	CCONJ
cana-943	151	27	correct	correct	ADJ
cana-943	151	28	errors	error	NOUN
cana-943	151	29	in	in	ADP
cana-943	151	30	transmitted	transmit	VERB
cana-943	151	31	data	datum	NOUN
cana-943	151	32	.	.	PUNCT
cana-943	152	1	reed	reed	PROPN
cana-943	152	2	-	-	PUNCT
cana-943	152	3	solomon	solomon	PROPN
cana-943	152	4	codes	code	NOUN
cana-943	152	5	,	,	PUNCT
cana-943	152	6	widely	widely	ADV
cana-943	152	7	used	use	VERB
cana-943	152	8	in	in	ADP
cana-943	152	9	cds	cd	NOUN
cana-943	152	10	,	,	PUNCT
cana-943	152	11	dvds	dvds	NOUN
cana-943	152	12	,	,	PUNCT
cana-943	152	13	and	and	CCONJ
cana-943	152	14	qr	qr	PROPN
cana-943	152	15	codes	code	NOUN
cana-943	152	16	,	,	PUNCT
cana-943	152	17	are	be	AUX
cana-943	152	18	a	a	DET
cana-943	152	19	prime	prime	ADJ
cana-943	152	20	example	example	NOUN
cana-943	152	21	of	of	ADP
cana-943	152	22	such	such	ADJ
cana-943	152	23	applications	application	NOUN
cana-943	152	24	[	[	X
cana-943	152	25	15	15	NUM
cana-943	152	26	]	]	PUNCT
cana-943	152	27	.	.	PUNCT
cana-943	153	1	4.2.2	4.2.2	X
cana-943	153	2	.	.	PUNCT
cana-943	154	1	ring	ring	NOUN
cana-943	154	2	-	-	PUNCT
cana-943	154	3	lwe	lwe	PROPN
cana-943	154	4	(	(	PUNCT
cana-943	154	5	learning	learn	VERB
cana-943	154	6	with	with	ADP
cana-943	154	7	errors	error	NOUN
cana-943	154	8	)	)	PUNCT
cana-943	154	9	the	the	DET
cana-943	154	10	learning	learning	NOUN
cana-943	154	11	with	with	ADP
cana-943	154	12	errors	error	NOUN
cana-943	154	13	(	(	PUNCT
cana-943	154	14	lwe	lwe	PROPN
cana-943	154	15	)	)	PUNCT
cana-943	154	16	problem	problem	NOUN
cana-943	154	17	,	,	PUNCT
cana-943	154	18	when	when	SCONJ
cana-943	154	19	adapted	adapt	VERB
cana-943	154	20	to	to	ADP
cana-943	154	21	polynomial	polynomial	ADJ
cana-943	154	22	rings	ring	NOUN
cana-943	154	23	,	,	PUNCT
cana-943	154	24	forms	form	VERB
cana-943	154	25	the	the	DET
cana-943	154	26	basis	basis	NOUN
cana-943	154	27	of	of	ADP
cana-943	154	28	ringlwe	ringlwe	NOUN
cana-943	154	29	,	,	PUNCT
cana-943	154	30	a	a	DET
cana-943	154	31	hard	hard	ADJ
cana-943	154	32	problem	problem	NOUN
cana-943	154	33	that	that	PRON
cana-943	154	34	underpins	underpin	VERB
cana-943	154	35	many	many	ADJ
cana-943	154	36	lattice	lattice	NOUN
cana-943	154	37	-	-	PUNCT
cana-943	154	38	based	base	VERB
cana-943	154	39	cryptographic	cryptographic	ADJ
cana-943	154	40	schemes	scheme	NOUN
cana-943	154	41	.	.	PUNCT
cana-943	155	1	the	the	DET
cana-943	155	2	security	security	NOUN
cana-943	155	3	of	of	ADP
cana-943	155	4	ringlwe	ringlwe	PROPN
cana-943	155	5	relies	rely	VERB
cana-943	155	6	on	on	ADP
cana-943	155	7	the	the	DET
cana-943	155	8	difficulty	difficulty	NOUN
cana-943	155	9	of	of	ADP
cana-943	155	10	solving	solve	VERB
cana-943	155	11	noisy	noisy	ADJ
cana-943	155	12	linear	linear	ADJ
cana-943	155	13	equations	equation	NOUN
cana-943	155	14	over	over	ADP
cana-943	155	15	polynomial	polynomial	ADJ
cana-943	155	16	rings	ring	NOUN
cana-943	155	17	[	[	X
cana-943	155	18	12	12	NUM
cana-943	155	19	]	]	PUNCT
cana-943	155	20	.	.	PUNCT
cana-943	156	1	ring	ring	NOUN
cana-943	156	2	-	-	PUNCT
cana-943	156	3	lwe	lwe	PROPN
cana-943	156	4	is	be	AUX
cana-943	156	5	crucial	crucial	ADJ
cana-943	156	6	in	in	ADP
cana-943	156	7	the	the	DET
cana-943	156	8	development	development	NOUN
cana-943	156	9	of	of	ADP
cana-943	156	10	post	post	ADJ
cana-943	156	11	-	-	ADJ
cana-943	156	12	quantum	quantum	ADJ
cana-943	156	13	cryptographic	cryptographic	ADJ
cana-943	156	14	algorithms	algorithm	NOUN
cana-943	156	15	,	,	PUNCT
cana-943	156	16	which	which	PRON
cana-943	156	17	aim	aim	VERB
cana-943	156	18	to	to	PART
cana-943	156	19	be	be	AUX
cana-943	156	20	secure	secure	ADJ
cana-943	156	21	against	against	ADP
cana-943	156	22	quantum	quantum	ADJ
cana-943	156	23	computers	computer	NOUN
cana-943	156	24	.	.	PUNCT
cana-943	157	1	the	the	DET
cana-943	157	2	polynomial	polynomial	ADJ
cana-943	157	3	structure	structure	NOUN
cana-943	157	4	in	in	ADP
cana-943	157	5	ring	ring	NOUN
cana-943	157	6	-	-	PUNCT
cana-943	157	7	lwe	lwe	PROPN
cana-943	157	8	allows	allow	VERB
cana-943	157	9	for	for	ADP
cana-943	157	10	more	more	ADV
cana-943	157	11	efficient	efficient	ADJ
cana-943	157	12	implementations	implementation	NOUN
cana-943	157	13	compared	compare	VERB
cana-943	157	14	to	to	ADP
cana-943	157	15	standard	standard	PROPN
cana-943	157	16	lwe	lwe	PROPN
cana-943	157	17	,	,	PUNCT
cana-943	157	18	making	make	VERB
cana-943	157	19	it	it	PRON
cana-943	157	20	a	a	DET
cana-943	157	21	practical	practical	ADJ
cana-943	157	22	choice	choice	NOUN
cana-943	157	23	for	for	ADP
cana-943	157	24	real	real	ADJ
cana-943	157	25	-	-	PUNCT
cana-943	157	26	world	world	NOUN
cana-943	157	27	applications	application	NOUN
cana-943	157	28	.	.	PUNCT
cana-943	158	1	4.3	4.3	NUM
cana-943	158	2	.	.	PUNCT
cana-943	158	3	field	field	NOUN
cana-943	158	4	theory	theory	NOUN
cana-943	158	5	applications	application	NOUN
cana-943	158	6	4.3.1	4.3.1	VERB
cana-943	158	7	.	.	PUNCT
cana-943	158	8	finite	finite	PROPN
cana-943	158	9	fields	field	NOUN
cana-943	158	10	and	and	CCONJ
cana-943	158	11	galois	galois	PROPN
cana-943	158	12	fields	field	NOUN
cana-943	158	13	finite	finite	VERB
cana-943	158	14	fields	field	NOUN
cana-943	158	15	,	,	PUNCT
cana-943	158	16	also	also	ADV
cana-943	158	17	known	know	VERB
cana-943	158	18	as	as	ADP
cana-943	158	19	galois	galois	PROPN
cana-943	158	20	fields	field	NOUN
cana-943	158	21	,	,	PUNCT
cana-943	158	22	are	be	AUX
cana-943	158	23	fields	field	NOUN
cana-943	158	24	with	with	ADP
cana-943	158	25	a	a	DET
cana-943	158	26	finite	finite	ADJ
cana-943	158	27	number	number	NOUN
cana-943	158	28	of	of	ADP
cana-943	158	29	elements	element	NOUN
cana-943	158	30	.	.	PUNCT
cana-943	159	1	these	these	DET
cana-943	159	2	fields	field	NOUN
cana-943	159	3	,	,	PUNCT
cana-943	159	4	denoted	denote	VERB
cana-943	159	5	as	as	ADP
cana-943	159	6	\	\	PROPN
cana-943	159	7	(	(	PUNCT
cana-943	159	8	gf(p^n	gf(p^n	NOUN
cana-943	159	9	)	)	PUNCT
cana-943	159	10	\	\	NOUN
cana-943	159	11	)	)	PUNCT
cana-943	159	12	,	,	PUNCT
cana-943	159	13	where	where	SCONJ
cana-943	159	14	\	\	PROPN
cana-943	159	15	(	(	PUNCT
cana-943	159	16	p	p	PROPN
cana-943	159	17	\	\	PROPN
cana-943	159	18	)	)	PUNCT
cana-943	159	19	is	be	AUX
cana-943	159	20	a	a	DET
cana-943	159	21	prime	prime	ADJ
cana-943	159	22	number	number	NOUN
cana-943	159	23	and	and	CCONJ
cana-943	159	24	\	\	PROPN
cana-943	159	25	(	(	PUNCT
cana-943	159	26	n	n	PRON
cana-943	159	27	\	\	NOUN
cana-943	159	28	)	)	PUNCT
cana-943	159	29	is	be	AUX
cana-943	159	30	a	a	DET
cana-943	159	31	positive	positive	ADJ
cana-943	159	32	integer	integer	NOUN
cana-943	159	33	,	,	PUNCT
cana-943	159	34	are	be	AUX
cana-943	159	35	fundamental	fundamental	ADJ
cana-943	159	36	to	to	ADP
cana-943	159	37	many	many	ADJ
cana-943	159	38	cryptographic	cryptographic	ADJ
cana-943	159	39	algorithms	algorithm	NOUN
cana-943	159	40	.	.	PUNCT
cana-943	160	1	finite	finite	PROPN
cana-943	160	2	fields	field	NOUN
cana-943	160	3	are	be	AUX
cana-943	160	4	used	use	VERB
cana-943	160	5	extensively	extensively	ADV
cana-943	160	6	in	in	ADP
cana-943	160	7	symmetric	symmetric	ADJ
cana-943	160	8	cryptography	cryptography	NOUN
cana-943	160	9	,	,	PUNCT
cana-943	160	10	error	error	NOUN
cana-943	160	11	-	-	PUNCT
cana-943	160	12	correcting	correct	VERB
cana-943	160	13	codes	code	NOUN
cana-943	160	14	,	,	PUNCT
cana-943	160	15	and	and	CCONJ
cana-943	160	16	pseudorandom	pseudorandom	PROPN
cana-943	160	17	number	number	NOUN
cana-943	160	18	generation	generation	NOUN
cana-943	160	19	.	.	PUNCT
cana-943	161	1	their	their	PRON
cana-943	161	2	algebraic	algebraic	ADJ
cana-943	161	3	properties	property	NOUN
cana-943	161	4	provide	provide	VERB
cana-943	161	5	a	a	DET
cana-943	161	6	robust	robust	ADJ
cana-943	161	7	framework	framework	NOUN
cana-943	161	8	for	for	ADP
cana-943	161	9	constructing	construct	VERB
cana-943	161	10	secure	secure	ADJ
cana-943	161	11	cryptographic	cryptographic	ADJ
cana-943	161	12	protocols	protocol	NOUN
cana-943	161	13	.	.	PUNCT
cana-943	162	1	4.3.2	4.3.2	X
cana-943	162	2	.	.	PUNCT
cana-943	163	1	aes	aes	NOUN
cana-943	163	2	(	(	PUNCT
cana-943	163	3	advanced	advanced	ADJ
cana-943	163	4	encryption	encryption	NOUN
cana-943	163	5	standard	standard	NOUN
cana-943	163	6	)	)	PUNCT
cana-943	163	7	and	and	CCONJ
cana-943	163	8	its	its	PRON
cana-943	163	9	algebraic	algebraic	ADJ
cana-943	163	10	basis	basis	NOUN
cana-943	163	11	the	the	DET
cana-943	163	12	advanced	advanced	ADJ
cana-943	163	13	encryption	encryption	NOUN
cana-943	163	14	standard	standard	NOUN
cana-943	163	15	(	(	PUNCT
cana-943	163	16	aes	aes	PROPN
cana-943	163	17	)	)	PUNCT
cana-943	163	18	is	be	AUX
cana-943	163	19	a	a	DET
cana-943	163	20	symmetric	symmetric	ADJ
cana-943	163	21	encryption	encryption	NOUN
cana-943	163	22	algorithm	algorithm	NOUN
cana-943	163	23	widely	widely	ADV
cana-943	163	24	used	use	VERB
cana-943	163	25	for	for	ADP
cana-943	163	26	securing	secure	VERB
cana-943	163	27	data	datum	NOUN
cana-943	163	28	.	.	PUNCT
cana-943	164	1	aes	aes	PROPN
cana-943	164	2	operates	operate	VERB
cana-943	164	3	on	on	ADP
cana-943	164	4	a	a	DET
cana-943	164	5	4x4	4x4	NUM
cana-943	164	6	column	column	NOUN
cana-943	164	7	-	-	PUNCT
cana-943	164	8	major	major	ADJ
cana-943	164	9	order	order	NOUN
cana-943	164	10	matrix	matrix	NOUN
cana-943	164	11	of	of	ADP
cana-943	164	12	bytes	byte	NOUN
cana-943	164	13	,	,	PUNCT
cana-943	164	14	called	call	VERB
cana-943	164	15	the	the	DET
cana-943	164	16	state	state	NOUN
cana-943	164	17	.	.	PUNCT
cana-943	165	1	the	the	DET
cana-943	165	2	algorithm	algorithm	NOUN
cana-943	165	3	consists	consist	VERB
cana-943	165	4	of	of	ADP
cana-943	165	5	several	several	ADJ
cana-943	165	6	rounds	round	NOUN
cana-943	165	7	of	of	ADP
cana-943	165	8	transformation	transformation	NOUN
cana-943	165	9	,	,	PUNCT
cana-943	165	10	including	include	VERB
cana-943	165	11	substitution	substitution	NOUN
cana-943	165	12	,	,	PUNCT
cana-943	165	13	permutation	permutation	NOUN
cana-943	165	14	,	,	PUNCT
cana-943	165	15	and	and	CCONJ
cana-943	165	16	mixing	mix	VERB
cana-943	165	17	operations	operation	NOUN
cana-943	165	18	,	,	PUNCT
cana-943	165	19	all	all	PRON
cana-943	165	20	based	base	VERB
cana-943	165	21	on	on	ADP
cana-943	165	22	the	the	DET
cana-943	165	23	arithmetic	arithmetic	NOUN
cana-943	165	24	of	of	ADP
cana-943	165	25	finite	finite	ADJ
cana-943	165	26	fields	field	NOUN
cana-943	165	27	,	,	PUNCT
cana-943	165	28	specifically	specifically	ADV
cana-943	165	29	\	\	PROPN
cana-943	165	30	(	(	PUNCT
cana-943	165	31	gf(2	gf(2	PROPN
cana-943	165	32	^	^	SYM
cana-943	165	33	8)	8)	NUM
cana-943	165	34	\	\	NOUN
cana-943	165	35	)	)	PUNCT
cana-943	166	1	[	[	X
cana-943	166	2	13	13	NUM
cana-943	166	3	]	]	PUNCT
cana-943	166	4	.	.	PUNCT
cana-943	167	1	in	in	ADP
cana-943	167	2	aes	aes	PROPN
cana-943	167	3	,	,	PUNCT
cana-943	167	4	bytes	byte	NOUN
cana-943	167	5	are	be	AUX
cana-943	167	6	treated	treat	VERB
cana-943	167	7	as	as	ADP
cana-943	167	8	elements	element	NOUN
cana-943	167	9	of	of	ADP
cana-943	167	10	the	the	DET
cana-943	167	11	finite	finite	ADJ
cana-943	167	12	field	field	NOUN
cana-943	167	13	\	\	PROPN
cana-943	167	14	(	(	PUNCT
cana-943	167	15	gf(2	gf(2	PROPN
cana-943	167	16	^	^	SYM
cana-943	167	17	8)	8)	NUM
cana-943	167	18	\	\	NOUN
cana-943	167	19	)	)	PUNCT
cana-943	167	20	,	,	PUNCT
cana-943	167	21	and	and	CCONJ
cana-943	167	22	the	the	DET
cana-943	167	23	mixcolumns	mixcolumns	PROPN
cana-943	167	24	operation	operation	NOUN
cana-943	167	25	,	,	PUNCT
cana-943	167	26	one	one	NUM
cana-943	167	27	of	of	ADP
cana-943	167	28	the	the	DET
cana-943	167	29	core	core	NOUN
cana-943	167	30	transformations	transformation	NOUN
cana-943	167	31	in	in	ADP
cana-943	167	32	aes	aes	PROPN
cana-943	167	33	,	,	PUNCT
cana-943	167	34	is	be	AUX
cana-943	167	35	performed	perform	VERB
cana-943	167	36	using	use	VERB
cana-943	167	37	polynomial	polynomial	ADJ
cana-943	167	38	multiplication	multiplication	NOUN
cana-943	167	39	in	in	ADP
cana-943	167	40	this	this	DET
cana-943	167	41	field	field	NOUN
cana-943	167	42	.	.	PUNCT
cana-943	168	1	the	the	DET
cana-943	168	2	robust	robust	ADJ
cana-943	168	3	algebraic	algebraic	ADJ
cana-943	168	4	structure	structure	NOUN
cana-943	168	5	of	of	ADP
cana-943	168	6	finite	finite	ADJ
cana-943	168	7	fields	field	NOUN
cana-943	168	8	ensures	ensure	VERB
cana-943	168	9	that	that	SCONJ
cana-943	168	10	aes	aes	PROPN
cana-943	168	11	is	be	AUX
cana-943	168	12	both	both	CCONJ
cana-943	168	13	secure	secure	ADJ
cana-943	168	14	and	and	CCONJ
cana-943	168	15	efficient	efficient	ADJ
cana-943	168	16	,	,	PUNCT
cana-943	168	17	capable	capable	ADJ
cana-943	168	18	of	of	ADP
cana-943	168	19	withstanding	withstand	VERB
cana-943	168	20	various	various	ADJ
cana-943	168	21	cryptographic	cryptographic	ADJ
cana-943	168	22	attacks	attack	NOUN
cana-943	168	23	.	.	PUNCT
cana-943	169	1	5	5	X
cana-943	169	2	.	.	X
cana-943	169	3	implementation	implementation	NOUN
cana-943	169	4	of	of	ADP
cana-943	169	5	cryptographic	cryptographic	ADJ
cana-943	169	6	protocols	protocol	NOUN
cana-943	169	7	5.1	5.1	NUM
cana-943	169	8	.	.	PUNCT
cana-943	170	1	homomorphic	homomorphic	ADJ
cana-943	170	2	encryption	encryption	NOUN
cana-943	170	3	5.1.1	5.1.1	NOUN
cana-943	170	4	.	.	PUNCT
cana-943	171	1	partially	partially	ADV
cana-943	171	2	and	and	CCONJ
cana-943	171	3	fully	fully	ADV
cana-943	171	4	homomorphic	homomorphic	ADJ
cana-943	171	5	encryption	encryption	NOUN
cana-943	171	6	homomorphic	homomorphic	ADJ
cana-943	171	7	encryption	encryption	NOUN
cana-943	171	8	is	be	AUX
cana-943	171	9	a	a	DET
cana-943	171	10	form	form	NOUN
cana-943	171	11	of	of	ADP
cana-943	171	12	encryption	encryption	NOUN
cana-943	171	13	that	that	PRON
cana-943	171	14	allows	allow	VERB
cana-943	171	15	computations	computation	NOUN
cana-943	171	16	to	to	PART
cana-943	171	17	be	be	AUX
cana-943	171	18	performed	perform	VERB
cana-943	171	19	on	on	ADP
cana-943	171	20	ciphertexts	ciphertext	NOUN
cana-943	171	21	,	,	PUNCT
cana-943	171	22	producing	produce	VERB
cana-943	171	23	an	an	DET
cana-943	171	24	encrypted	encrypt	VERB
cana-943	171	25	result	result	NOUN
cana-943	171	26	that	that	SCONJ
cana-943	171	27	,	,	PUNCT
cana-943	171	28	when	when	SCONJ
cana-943	171	29	decrypted	decrypt	VERB
cana-943	171	30	,	,	PUNCT
cana-943	171	31	matches	match	VERB
cana-943	171	32	the	the	DET
cana-943	171	33	result	result	NOUN
cana-943	171	34	of	of	ADP
cana-943	171	35	operations	operation	NOUN
cana-943	171	36	performed	perform	VERB
cana-943	171	37	on	on	ADP
cana-943	171	38	the	the	DET
cana-943	171	39	plaintext	plaintext	NOUN
cana-943	171	40	.	.	PUNCT
cana-943	172	1	this	this	DET
cana-943	172	2	property	property	NOUN
cana-943	172	3	is	be	AUX
cana-943	172	4	highly	highly	ADV
cana-943	172	5	beneficial	beneficial	ADJ
cana-943	172	6	for	for	ADP
cana-943	172	7	applications	application	NOUN
cana-943	172	8	requiring	require	VERB
cana-943	172	9	secure	secure	ADJ
cana-943	172	10	data	datum	NOUN
cana-943	172	11	processing	processing	NOUN
cana-943	172	12	,	,	PUNCT
cana-943	172	13	such	such	ADJ
cana-943	172	14	as	as	ADP
cana-943	172	15	cloud	cloud	NOUN
cana-943	172	16	computing	computing	NOUN
cana-943	172	17	and	and	CCONJ
cana-943	172	18	privacy	privacy	NOUN
cana-943	172	19	-	-	PUNCT
cana-943	172	20	preserving	preserve	VERB
cana-943	172	21	data	datum	NOUN
cana-943	172	22	analysis	analysis	NOUN
cana-943	172	23	.	.	PUNCT
cana-943	173	1	communications	communication	NOUN
cana-943	173	2	on	on	ADP
cana-943	173	3	applied	apply	VERB
cana-943	173	4	nonlinear	nonlinear	ADJ
cana-943	173	5	analysis	analysis	NOUN
cana-943	173	6	issn	issn	NOUN
cana-943	173	7	:	:	PUNCT
cana-943	173	8	1074	1074	NUM
cana-943	173	9	-	-	PUNCT
cana-943	173	10	133x	133x	NUM
cana-943	173	11	vol	vol	NOUN
cana-943	173	12	31	31	NUM
cana-943	173	13	no	no	NOUN
cana-943	173	14	.	.	PUNCT
cana-943	174	1	4s	4s	NUM
cana-943	174	2	(	(	PUNCT
cana-943	174	3	2024	2024	NUM
cana-943	174	4	)	)	PUNCT
cana-943	174	5	474	474	NUM
cana-943	174	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	174	7	partially	partially	ADV
cana-943	174	8	homomorphic	homomorphic	ADJ
cana-943	174	9	encryption	encryption	NOUN
cana-943	174	10	(	(	PUNCT
cana-943	174	11	phe	phe	PROPN
cana-943	174	12	)	)	PUNCT
cana-943	174	13	allows	allow	VERB
cana-943	174	14	only	only	ADV
cana-943	174	15	specific	specific	ADJ
cana-943	174	16	types	type	NOUN
cana-943	174	17	of	of	ADP
cana-943	174	18	operations	operation	NOUN
cana-943	174	19	(	(	PUNCT
cana-943	174	20	e.g.	e.g.	ADV
cana-943	174	21	,	,	PUNCT
cana-943	174	22	addition	addition	NOUN
cana-943	174	23	or	or	CCONJ
cana-943	174	24	multiplication	multiplication	NOUN
cana-943	174	25	,	,	PUNCT
cana-943	174	26	but	but	CCONJ
cana-943	174	27	not	not	PART
cana-943	174	28	both	both	PRON
cana-943	174	29	)	)	PUNCT
cana-943	174	30	to	to	PART
cana-943	174	31	be	be	AUX
cana-943	174	32	performed	perform	VERB
cana-943	174	33	on	on	ADP
cana-943	174	34	ciphertexts	ciphertext	NOUN
cana-943	174	35	.	.	PUNCT
cana-943	175	1	rsa	rsa	PROPN
cana-943	175	2	is	be	AUX
cana-943	175	3	an	an	DET
cana-943	175	4	example	example	NOUN
cana-943	175	5	of	of	ADP
cana-943	175	6	a	a	DET
cana-943	175	7	partially	partially	ADV
cana-943	175	8	homomorphic	homomorphic	ADJ
cana-943	175	9	encryption	encryption	NOUN
cana-943	175	10	scheme	scheme	NOUN
cana-943	175	11	,	,	PUNCT
cana-943	175	12	as	as	SCONJ
cana-943	175	13	it	it	PRON
cana-943	175	14	supports	support	VERB
cana-943	175	15	multiplicative	multiplicative	ADJ
cana-943	175	16	homomorphism	homomorphism	NOUN
cana-943	175	17	:	:	PUNCT
cana-943	175	18	\	\	PROPN
cana-943	175	19	(	(	PUNCT
cana-943	175	20	e(m_1	e(m_1	PROPN
cana-943	175	21	)	)	PUNCT
cana-943	175	22	\cdot	\cdot	NOUN
cana-943	175	23	e(m_2	e(m_2	PROPN
cana-943	175	24	)	)	PUNCT
cana-943	175	25	=	=	SYM
cana-943	175	26	e(m_1	e(m_1	PROPN
cana-943	175	27	\cdot	\cdot	NOUN
cana-943	175	28	m_2	m_2	PROPN
cana-943	175	29	)	)	PUNCT
cana-943	175	30	\	\	NOUN
cana-943	175	31	)	)	PUNCT
cana-943	176	1	[	[	X
cana-943	176	2	1	1	NUM
cana-943	176	3	]	]	PUNCT
cana-943	176	4	.	.	PUNCT
cana-943	177	1	fully	fully	ADV
cana-943	177	2	homomorphic	homomorphic	ADJ
cana-943	177	3	encryption	encryption	NOUN
cana-943	177	4	(	(	PUNCT
cana-943	177	5	fhe	fhe	PROPN
cana-943	177	6	)	)	PUNCT
cana-943	177	7	,	,	PUNCT
cana-943	177	8	on	on	ADP
cana-943	177	9	the	the	DET
cana-943	177	10	other	other	ADJ
cana-943	177	11	hand	hand	NOUN
cana-943	177	12	,	,	PUNCT
cana-943	177	13	supports	support	VERB
cana-943	177	14	arbitrary	arbitrary	ADJ
cana-943	177	15	computations	computation	NOUN
cana-943	177	16	on	on	ADP
cana-943	177	17	encrypted	encrypt	VERB
cana-943	177	18	data	datum	NOUN
cana-943	177	19	.	.	PUNCT
cana-943	178	1	gentry	gentry	NOUN
cana-943	178	2	's	's	PART
cana-943	178	3	groundbreaking	groundbreake	VERB
cana-943	178	4	work	work	NOUN
cana-943	178	5	in	in	ADP
cana-943	178	6	2009	2009	NUM
cana-943	178	7	introduced	introduce	VERB
cana-943	178	8	the	the	DET
cana-943	178	9	first	first	ADJ
cana-943	178	10	viable	viable	ADJ
cana-943	178	11	fhe	fhe	NOUN
cana-943	178	12	scheme	scheme	NOUN
cana-943	178	13	,	,	PUNCT
cana-943	178	14	which	which	PRON
cana-943	178	15	relies	rely	VERB
cana-943	178	16	on	on	ADP
cana-943	178	17	lattice	lattice	NOUN
cana-943	178	18	-	-	PUNCT
cana-943	178	19	based	base	VERB
cana-943	178	20	cryptography	cryptography	NOUN
cana-943	179	1	[	[	X
cana-943	179	2	6	6	NUM
cana-943	179	3	]	]	PUNCT
cana-943	179	4	.	.	PUNCT
cana-943	180	1	this	this	DET
cana-943	180	2	advancement	advancement	NOUN
cana-943	180	3	has	have	AUX
cana-943	180	4	opened	open	VERB
cana-943	180	5	the	the	DET
cana-943	180	6	door	door	NOUN
cana-943	180	7	to	to	ADP
cana-943	180	8	numerous	numerous	ADJ
cana-943	180	9	applications	application	NOUN
cana-943	180	10	where	where	SCONJ
cana-943	180	11	data	datum	NOUN
cana-943	180	12	privacy	privacy	NOUN
cana-943	180	13	is	be	AUX
cana-943	180	14	paramount	paramount	ADJ
cana-943	180	15	,	,	PUNCT
cana-943	180	16	although	although	SCONJ
cana-943	180	17	practical	practical	ADJ
cana-943	180	18	implementations	implementation	NOUN
cana-943	180	19	remain	remain	VERB
cana-943	180	20	a	a	DET
cana-943	180	21	significant	significant	ADJ
cana-943	180	22	challenge	challenge	NOUN
cana-943	180	23	due	due	ADP
cana-943	180	24	to	to	ADP
cana-943	180	25	the	the	DET
cana-943	180	26	high	high	ADJ
cana-943	180	27	computational	computational	ADJ
cana-943	180	28	overhead	overhead	NOUN
cana-943	180	29	.	.	PUNCT
cana-943	181	1	5.1.2	5.1.2	X
cana-943	181	2	.	.	NOUN
cana-943	181	3	practical	practical	ADJ
cana-943	181	4	implementations	implementation	NOUN
cana-943	181	5	and	and	CCONJ
cana-943	181	6	use	use	VERB
cana-943	181	7	cases	case	NOUN
cana-943	181	8	practical	practical	ADJ
cana-943	181	9	implementations	implementation	NOUN
cana-943	181	10	of	of	ADP
cana-943	181	11	homomorphic	homomorphic	ADJ
cana-943	181	12	encryption	encryption	NOUN
cana-943	181	13	are	be	AUX
cana-943	181	14	still	still	ADV
cana-943	181	15	evolving	evolve	VERB
cana-943	181	16	.	.	PUNCT
cana-943	182	1	ibm	ibm	PROPN
cana-943	182	2	's	's	PART
cana-943	182	3	helib	helib	PROPN
cana-943	182	4	and	and	CCONJ
cana-943	182	5	microsoft	microsoft	PROPN
cana-943	182	6	's	's	PART
cana-943	182	7	seal	seal	NOUN
cana-943	182	8	are	be	AUX
cana-943	182	9	two	two	NUM
cana-943	182	10	notable	notable	ADJ
cana-943	182	11	libraries	library	NOUN
cana-943	182	12	that	that	PRON
cana-943	182	13	offer	offer	VERB
cana-943	182	14	implementations	implementation	NOUN
cana-943	182	15	of	of	ADP
cana-943	182	16	homomorphic	homomorphic	ADJ
cana-943	182	17	encryption	encryption	NOUN
cana-943	182	18	.	.	PUNCT
cana-943	183	1	these	these	DET
cana-943	183	2	libraries	library	NOUN
cana-943	183	3	support	support	VERB
cana-943	183	4	both	both	PRON
cana-943	183	5	academic	academic	ADJ
cana-943	183	6	research	research	NOUN
cana-943	183	7	and	and	CCONJ
cana-943	183	8	practical	practical	ADJ
cana-943	183	9	applications	application	NOUN
cana-943	183	10	,	,	PUNCT
cana-943	183	11	providing	provide	VERB
cana-943	183	12	tools	tool	NOUN
cana-943	183	13	for	for	ADP
cana-943	183	14	performing	perform	VERB
cana-943	183	15	encrypted	encrypt	VERB
cana-943	183	16	computations	computation	NOUN
cana-943	183	17	efficiently	efficiently	ADV
cana-943	183	18	.	.	PUNCT
cana-943	184	1	use	use	VERB
cana-943	184	2	cases	case	NOUN
cana-943	184	3	:	:	PUNCT
cana-943	184	4	1.cloud	1.cloud	NUM
cana-943	184	5	computing	computing	NOUN
cana-943	184	6	:	:	PUNCT
cana-943	184	7	homomorphic	homomorphic	ADJ
cana-943	184	8	encryption	encryption	NOUN
cana-943	184	9	enables	enable	VERB
cana-943	184	10	secure	secure	ADJ
cana-943	184	11	data	datum	NOUN
cana-943	184	12	processing	processing	NOUN
cana-943	184	13	in	in	ADP
cana-943	184	14	the	the	DET
cana-943	184	15	cloud	cloud	NOUN
cana-943	184	16	without	without	ADP
cana-943	184	17	exposing	expose	VERB
cana-943	184	18	sensitive	sensitive	ADJ
cana-943	184	19	information	information	NOUN
cana-943	184	20	to	to	ADP
cana-943	184	21	cloud	cloud	NOUN
cana-943	184	22	service	service	NOUN
cana-943	184	23	providers	provider	NOUN
cana-943	184	24	.	.	PUNCT
cana-943	185	1	this	this	PRON
cana-943	185	2	is	be	AUX
cana-943	185	3	particularly	particularly	ADV
cana-943	185	4	useful	useful	ADJ
cana-943	185	5	for	for	ADP
cana-943	185	6	medical	medical	ADJ
cana-943	185	7	data	datum	NOUN
cana-943	185	8	analysis	analysis	NOUN
cana-943	185	9	and	and	CCONJ
cana-943	185	10	financial	financial	ADJ
cana-943	185	11	computations	computation	NOUN
cana-943	185	12	.	.	PUNCT
cana-943	186	1	2.secure	2.secure	NUM
cana-943	186	2	voting	voting	NOUN
cana-943	186	3	systems	system	NOUN
cana-943	186	4	:	:	PUNCT
cana-943	186	5	homomorphic	homomorphic	ADJ
cana-943	186	6	encryption	encryption	NOUN
cana-943	186	7	can	can	AUX
cana-943	186	8	be	be	AUX
cana-943	186	9	used	use	VERB
cana-943	186	10	to	to	PART
cana-943	186	11	design	design	VERB
cana-943	186	12	secure	secure	ADJ
cana-943	186	13	electronic	electronic	ADJ
cana-943	186	14	voting	voting	NOUN
cana-943	186	15	systems	system	NOUN
cana-943	186	16	where	where	SCONJ
cana-943	186	17	votes	vote	NOUN
cana-943	186	18	are	be	AUX
cana-943	186	19	encrypted	encrypt	VERB
cana-943	186	20	,	,	PUNCT
cana-943	186	21	and	and	CCONJ
cana-943	186	22	the	the	DET
cana-943	186	23	tallying	tally	VERB
cana-943	186	24	process	process	NOUN
cana-943	186	25	can	can	AUX
cana-943	186	26	be	be	AUX
cana-943	186	27	performed	perform	VERB
cana-943	186	28	on	on	ADP
cana-943	186	29	encrypted	encrypt	VERB
cana-943	186	30	votes	vote	NOUN
cana-943	186	31	,	,	PUNCT
cana-943	186	32	ensuring	ensure	VERB
cana-943	186	33	voter	voter	NOUN
cana-943	186	34	privacy	privacy	NOUN
cana-943	186	35	and	and	CCONJ
cana-943	186	36	integrity	integrity	NOUN
cana-943	187	1	[	[	X
cana-943	187	2	21	21	NUM
cana-943	187	3	]	]	PUNCT
cana-943	187	4	.	.	PUNCT
cana-943	188	1	3	3	X
cana-943	188	2	.	.	X
cana-943	188	3	privacy	privacy	NOUN
cana-943	188	4	-	-	PUNCT
cana-943	188	5	preserving	preserve	VERB
cana-943	188	6	machine	machine	NOUN
cana-943	188	7	learning	learning	NOUN
cana-943	188	8	:	:	PUNCT
cana-943	188	9	homomorphic	homomorphic	ADJ
cana-943	188	10	encryption	encryption	NOUN
cana-943	188	11	allows	allow	VERB
cana-943	188	12	machine	machine	NOUN
cana-943	188	13	learning	learning	NOUN
cana-943	188	14	models	model	NOUN
cana-943	188	15	to	to	PART
cana-943	188	16	be	be	AUX
cana-943	188	17	trained	train	VERB
cana-943	188	18	on	on	ADP
cana-943	188	19	encrypted	encrypt	VERB
cana-943	188	20	datasets	dataset	NOUN
cana-943	188	21	,	,	PUNCT
cana-943	188	22	ensuring	ensure	VERB
cana-943	188	23	data	datum	NOUN
cana-943	188	24	privacy	privacy	NOUN
cana-943	188	25	while	while	SCONJ
cana-943	188	26	leveraging	leverage	VERB
cana-943	188	27	the	the	DET
cana-943	188	28	power	power	NOUN
cana-943	188	29	of	of	ADP
cana-943	188	30	machine	machine	NOUN
cana-943	188	31	learning	learn	VERB
cana-943	188	32	[	[	X
cana-943	188	33	13	13	NUM
cana-943	188	34	]	]	PUNCT
cana-943	188	35	.	.	PUNCT
cana-943	189	1	5.2	5.2	NUM
cana-943	189	2	.	.	X
cana-943	189	3	zero	zero	NUM
cana-943	189	4	-	-	PUNCT
cana-943	189	5	knowledge	knowledge	NOUN
cana-943	189	6	proofs	proof	NOUN
cana-943	189	7	5.2	5.2	NUM
cana-943	189	8	.	.	PUNCT
cana-943	190	1	1	1	NUM
cana-943	190	2	.	.	NUM
cana-943	190	3	basic	basic	ADJ
cana-943	190	4	concepts	concept	NOUN
cana-943	190	5	and	and	CCONJ
cana-943	190	6	protocols	protocol	NOUN
cana-943	190	7	zero	zero	NUM
cana-943	190	8	-	-	PUNCT
cana-943	190	9	knowledge	knowledge	NOUN
cana-943	190	10	proofs	proof	NOUN
cana-943	190	11	(	(	PUNCT
cana-943	190	12	zkps	zkps	PROPN
cana-943	190	13	)	)	PUNCT
cana-943	190	14	are	be	AUX
cana-943	190	15	cryptographic	cryptographic	ADJ
cana-943	190	16	protocols	protocol	NOUN
cana-943	190	17	that	that	PRON
cana-943	190	18	enable	enable	VERB
cana-943	190	19	one	one	NUM
cana-943	190	20	party	party	NOUN
cana-943	190	21	(	(	PUNCT
cana-943	190	22	the	the	DET
cana-943	190	23	prover	prover	NOUN
cana-943	190	24	)	)	PUNCT
cana-943	190	25	to	to	PART
cana-943	190	26	prove	prove	VERB
cana-943	190	27	to	to	ADP
cana-943	190	28	another	another	DET
cana-943	190	29	party	party	NOUN
cana-943	190	30	(	(	PUNCT
cana-943	190	31	the	the	DET
cana-943	190	32	verifier	verifier	NOUN
cana-943	190	33	)	)	PUNCT
cana-943	190	34	that	that	SCONJ
cana-943	190	35	they	they	PRON
cana-943	190	36	know	know	VERB
cana-943	190	37	a	a	DET
cana-943	190	38	value	value	NOUN
cana-943	190	39	\	\	PROPN
cana-943	190	40	(	(	PUNCT
cana-943	190	41	x	x	SYM
cana-943	190	42	\	\	PROPN
cana-943	190	43	)	)	PUNCT
cana-943	190	44	,	,	PUNCT
cana-943	190	45	without	without	ADP
cana-943	190	46	revealing	reveal	VERB
cana-943	190	47	any	any	DET
cana-943	190	48	information	information	NOUN
cana-943	190	49	about	about	ADP
cana-943	190	50	\	\	PROPN
cana-943	190	51	(	(	PUNCT
cana-943	190	52	x	x	SYM
cana-943	190	53	\	\	PROPN
cana-943	190	54	)	)	PUNCT
cana-943	190	55	itself	itself	PRON
cana-943	190	56	.	.	PUNCT
cana-943	191	1	this	this	DET
cana-943	191	2	concept	concept	NOUN
cana-943	191	3	is	be	AUX
cana-943	191	4	crucial	crucial	ADJ
cana-943	191	5	for	for	ADP
cana-943	191	6	enhancing	enhance	VERB
cana-943	191	7	privacy	privacy	NOUN
cana-943	191	8	and	and	CCONJ
cana-943	191	9	security	security	NOUN
cana-943	191	10	in	in	ADP
cana-943	191	11	various	various	ADJ
cana-943	191	12	applications	application	NOUN
cana-943	191	13	.	.	PUNCT
cana-943	192	1	5.2.2.the	5.2.2.the	DET
cana-943	192	2	fundamental	fundamental	ADJ
cana-943	192	3	properties	property	NOUN
cana-943	192	4	of	of	ADP
cana-943	192	5	zkps	zkps	PROPN
cana-943	192	6	are	be	AUX
cana-943	192	7	:	:	PUNCT
cana-943	192	8	1	1	X
cana-943	192	9	.	.	X
cana-943	193	1	completeness	completeness	NOUN
cana-943	193	2	:	:	PUNCT
cana-943	193	3	if	if	SCONJ
cana-943	193	4	the	the	DET
cana-943	193	5	statement	statement	NOUN
cana-943	193	6	is	be	AUX
cana-943	193	7	true	true	ADJ
cana-943	193	8	,	,	PUNCT
cana-943	193	9	an	an	DET
cana-943	193	10	honest	honest	ADJ
cana-943	193	11	verifier	verifier	NOUN
cana-943	193	12	will	will	AUX
cana-943	193	13	be	be	AUX
cana-943	193	14	convinced	convince	VERB
cana-943	193	15	by	by	ADP
cana-943	193	16	an	an	DET
cana-943	193	17	honest	honest	ADJ
cana-943	193	18	prover	prover	NOUN
cana-943	193	19	.	.	PUNCT
cana-943	194	1	2	2	X
cana-943	194	2	.	.	X
cana-943	194	3	soundness	soundness	NOUN
cana-943	194	4	:	:	PUNCT
cana-943	194	5	if	if	SCONJ
cana-943	194	6	the	the	DET
cana-943	194	7	statement	statement	NOUN
cana-943	194	8	is	be	AUX
cana-943	194	9	false	false	ADJ
cana-943	194	10	,	,	PUNCT
cana-943	194	11	no	no	DET
cana-943	194	12	cheating	cheat	VERB
cana-943	194	13	prover	prover	NOUN
cana-943	194	14	can	can	AUX
cana-943	194	15	convince	convince	VERB
cana-943	194	16	the	the	DET
cana-943	194	17	honest	honest	ADJ
cana-943	194	18	verifier	verifier	NOUN
cana-943	194	19	that	that	SCONJ
cana-943	194	20	it	it	PRON
cana-943	194	21	is	be	AUX
cana-943	194	22	true	true	ADJ
cana-943	194	23	,	,	PUNCT
cana-943	194	24	except	except	SCONJ
cana-943	194	25	with	with	ADP
cana-943	194	26	a	a	DET
cana-943	194	27	small	small	ADJ
cana-943	194	28	probability	probability	NOUN
cana-943	194	29	.	.	PUNCT
cana-943	195	1	3	3	X
cana-943	195	2	.	.	X
cana-943	195	3	zero	zero	NUM
cana-943	195	4	-	-	PUNCT
cana-943	195	5	knowledge	knowledge	NOUN
cana-943	195	6	:	:	PUNCT
cana-943	195	7	if	if	SCONJ
cana-943	195	8	the	the	DET
cana-943	195	9	statement	statement	NOUN
cana-943	195	10	is	be	AUX
cana-943	195	11	true	true	ADJ
cana-943	195	12	,	,	PUNCT
cana-943	195	13	the	the	DET
cana-943	195	14	verifier	verifier	NOUN
cana-943	195	15	learns	learn	VERB
cana-943	195	16	nothing	nothing	PRON
cana-943	195	17	other	other	ADJ
cana-943	195	18	than	than	ADP
cana-943	195	19	the	the	DET
cana-943	195	20	fact	fact	NOUN
cana-943	195	21	that	that	SCONJ
cana-943	195	22	the	the	DET
cana-943	195	23	statement	statement	NOUN
cana-943	195	24	is	be	AUX
cana-943	195	25	true	true	ADJ
cana-943	195	26	.	.	PUNCT
cana-943	196	1	communications	communication	NOUN
cana-943	196	2	on	on	ADP
cana-943	196	3	applied	apply	VERB
cana-943	196	4	nonlinear	nonlinear	ADJ
cana-943	196	5	analysis	analysis	NOUN
cana-943	196	6	issn	issn	NOUN
cana-943	196	7	:	:	PUNCT
cana-943	196	8	1074	1074	NUM
cana-943	196	9	-	-	PUNCT
cana-943	196	10	133x	133x	NUM
cana-943	196	11	vol	vol	NOUN
cana-943	196	12	31	31	NUM
cana-943	196	13	no	no	NOUN
cana-943	196	14	.	.	PUNCT
cana-943	197	1	4s	4s	NUM
cana-943	197	2	(	(	PUNCT
cana-943	197	3	2024	2024	NUM
cana-943	197	4	)	)	PUNCT
cana-943	197	5	475	475	NUM
cana-943	197	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	197	7	5.2.3	5.2.3	NUM
cana-943	197	8	.	.	PUNCT
cana-943	198	1	protocols	protocol	NOUN
cana-943	198	2	:	:	PUNCT
cana-943	198	3	1	1	X
cana-943	198	4	.	.	X
cana-943	198	5	interactive	interactive	ADJ
cana-943	198	6	zero	zero	NUM
cana-943	198	7	-	-	PUNCT
cana-943	198	8	knowledge	knowledge	NOUN
cana-943	198	9	proofs	proof	NOUN
cana-943	198	10	:	:	PUNCT
cana-943	198	11	involve	involve	VERB
cana-943	198	12	multiple	multiple	ADJ
cana-943	198	13	rounds	round	NOUN
cana-943	198	14	of	of	ADP
cana-943	198	15	interaction	interaction	NOUN
cana-943	198	16	between	between	ADP
cana-943	198	17	the	the	DET
cana-943	198	18	prover	prover	NOUN
cana-943	198	19	and	and	CCONJ
cana-943	198	20	the	the	DET
cana-943	198	21	verifier	verifier	NOUN
cana-943	198	22	.	.	PUNCT
cana-943	199	1	a	a	DET
cana-943	199	2	classic	classic	ADJ
cana-943	199	3	example	example	NOUN
cana-943	199	4	is	be	AUX
cana-943	199	5	the	the	DET
cana-943	199	6	fiat	fiat	NOUN
cana-943	199	7	-	-	PUNCT
cana-943	199	8	shamir	shamir	NOUN
cana-943	199	9	heuristic	heuristic	NOUN
cana-943	199	10	,	,	PUNCT
cana-943	199	11	which	which	PRON
cana-943	199	12	transforms	transform	VERB
cana-943	199	13	an	an	DET
cana-943	199	14	interactive	interactive	ADJ
cana-943	199	15	proof	proof	NOUN
cana-943	199	16	into	into	ADP
cana-943	199	17	a	a	DET
cana-943	199	18	non	non	ADJ
cana-943	199	19	-	-	ADJ
cana-943	199	20	interactive	interactive	ADJ
cana-943	199	21	one	one	NOUN
cana-943	199	22	using	use	VERB
cana-943	199	23	a	a	DET
cana-943	199	24	hash	hash	NOUN
cana-943	199	25	function	function	NOUN
cana-943	199	26	[	[	X
cana-943	199	27	9	9	NUM
cana-943	199	28	]	]	SYM
cana-943	199	29	.	.	PUNCT
cana-943	200	1	2	2	X
cana-943	200	2	.	.	X
cana-943	200	3	non	non	ADJ
cana-943	200	4	-	-	ADJ
cana-943	200	5	interactive	interactive	ADJ
cana-943	200	6	zero	zero	NUM
cana-943	200	7	-	-	PUNCT
cana-943	200	8	knowledge	knowledge	NOUN
cana-943	200	9	proofs	proof	NOUN
cana-943	200	10	(	(	PUNCT
cana-943	200	11	nizk	nizk	PROPN
cana-943	200	12	):	):	PUNCT
cana-943	200	13	do	do	AUX
cana-943	200	14	not	not	PART
cana-943	200	15	require	require	VERB
cana-943	200	16	interaction	interaction	NOUN
cana-943	200	17	between	between	ADP
cana-943	200	18	the	the	DET
cana-943	200	19	prover	prover	NOUN
cana-943	200	20	and	and	CCONJ
cana-943	200	21	the	the	DET
cana-943	200	22	verifier	verifier	NOUN
cana-943	200	23	.	.	PUNCT
cana-943	201	1	zk	zk	PROPN
cana-943	201	2	-	-	PUNCT
cana-943	201	3	snarks	snarks	PROPN
cana-943	201	4	(	(	PUNCT
cana-943	201	5	zero	zero	NUM
cana-943	201	6	-	-	PUNCT
cana-943	201	7	knowledge	knowledge	NOUN
cana-943	201	8	succinct	succinct	ADJ
cana-943	201	9	non	non	ADJ
cana-943	201	10	-	-	ADJ
cana-943	201	11	interactive	interactive	ADJ
cana-943	201	12	arguments	argument	NOUN
cana-943	201	13	of	of	ADP
cana-943	201	14	knowledge	knowledge	NOUN
cana-943	201	15	)	)	PUNCT
cana-943	201	16	are	be	AUX
cana-943	201	17	a	a	DET
cana-943	201	18	prominent	prominent	ADJ
cana-943	201	19	example	example	NOUN
cana-943	201	20	,	,	PUNCT
cana-943	201	21	used	use	VERB
cana-943	201	22	in	in	ADP
cana-943	201	23	cryptocurrencies	cryptocurrencie	NOUN
cana-943	201	24	like	like	ADP
cana-943	201	25	zcash	zcash	NOUN
cana-943	201	26	for	for	ADP
cana-943	201	27	anonymous	anonymous	ADJ
cana-943	201	28	transactions	transaction	NOUN
cana-943	201	29	[	[	X
cana-943	201	30	14	14	NUM
cana-943	201	31	]	]	SYM
cana-943	201	32	.	.	PUNCT
cana-943	202	1	5.2.4	5.2.4	NUM
cana-943	202	2	.	.	PUNCT
cana-943	202	3	implementation	implementation	NOUN
cana-943	202	4	challenges	challenge	NOUN
cana-943	202	5	and	and	CCONJ
cana-943	202	6	solutions	solution	NOUN
cana-943	202	7	implementing	implement	VERB
cana-943	202	8	zkps	zkps	PROPN
cana-943	202	9	poses	pose	VERB
cana-943	202	10	several	several	ADJ
cana-943	202	11	challenges	challenge	NOUN
cana-943	202	12	,	,	PUNCT
cana-943	202	13	including	include	VERB
cana-943	202	14	computational	computational	ADJ
cana-943	202	15	complexity	complexity	NOUN
cana-943	202	16	and	and	CCONJ
cana-943	202	17	ensuring	ensure	VERB
cana-943	202	18	soundness	soundness	NOUN
cana-943	202	19	and	and	CCONJ
cana-943	202	20	zero	zero	NUM
cana-943	202	21	-	-	PUNCT
cana-943	202	22	knowledge	knowledge	NOUN
cana-943	202	23	properties	property	NOUN
cana-943	202	24	.	.	PUNCT
cana-943	203	1	advances	advance	NOUN
cana-943	203	2	in	in	ADP
cana-943	203	3	cryptographic	cryptographic	ADJ
cana-943	203	4	research	research	NOUN
cana-943	203	5	have	have	AUX
cana-943	203	6	led	lead	VERB
cana-943	203	7	to	to	ADP
cana-943	203	8	more	more	ADV
cana-943	203	9	efficient	efficient	ADJ
cana-943	203	10	zkp	zkp	NOUN
cana-943	203	11	protocols	protocol	NOUN
cana-943	203	12	,	,	PUNCT
cana-943	203	13	but	but	CCONJ
cana-943	203	14	practical	practical	ADJ
cana-943	203	15	deployment	deployment	NOUN
cana-943	203	16	still	still	ADV
cana-943	203	17	requires	require	VERB
cana-943	203	18	careful	careful	ADJ
cana-943	203	19	consideration	consideration	NOUN
cana-943	203	20	of	of	ADP
cana-943	203	21	performance	performance	NOUN
cana-943	203	22	trade	trade	NOUN
cana-943	203	23	-	-	PUNCT
cana-943	203	24	offs	off	NOUN
cana-943	203	25	.	.	PUNCT
cana-943	204	1	5.2.5	5.2.5	X
cana-943	204	2	.	.	PUNCT
cana-943	205	1	solutions	solution	NOUN
cana-943	205	2	:	:	PUNCT
cana-943	206	1	1	1	X
cana-943	206	2	.	.	X
cana-943	206	3	efficient	efficient	ADJ
cana-943	206	4	protocols	protocol	NOUN
cana-943	206	5	:	:	PUNCT
cana-943	206	6	research	research	NOUN
cana-943	206	7	into	into	ADP
cana-943	206	8	more	more	ADV
cana-943	206	9	efficient	efficient	ADJ
cana-943	206	10	zkp	zkp	NOUN
cana-943	206	11	protocols	protocol	NOUN
cana-943	206	12	,	,	PUNCT
cana-943	206	13	such	such	ADJ
cana-943	206	14	as	as	ADP
cana-943	206	15	bulletproofs	bulletproof	NOUN
cana-943	206	16	and	and	CCONJ
cana-943	206	17	starks	stark	NOUN
cana-943	206	18	,	,	PUNCT
cana-943	206	19	aims	aim	VERB
cana-943	206	20	to	to	PART
cana-943	206	21	reduce	reduce	VERB
cana-943	206	22	computational	computational	ADJ
cana-943	206	23	overhead	overhead	NOUN
cana-943	206	24	and	and	CCONJ
cana-943	206	25	improve	improve	VERB
cana-943	206	26	scalability	scalability	NOUN
cana-943	206	27	[	[	X
cana-943	206	28	20	20	NUM
cana-943	206	29	]	]	PUNCT
cana-943	206	30	.	.	PUNCT
cana-943	207	1	2	2	X
cana-943	207	2	.	.	X
cana-943	207	3	cryptographic	cryptographic	ADJ
cana-943	207	4	libraries	library	NOUN
cana-943	207	5	:	:	PUNCT
cana-943	207	6	libraries	library	NOUN
cana-943	207	7	such	such	ADJ
cana-943	207	8	as	as	ADP
cana-943	207	9	libsnark	libsnark	NOUN
cana-943	207	10	and	and	CCONJ
cana-943	207	11	zk	zk	PROPN
cana-943	207	12	-	-	PUNCT
cana-943	207	13	snarks	snark	NOUN
cana-943	207	14	provide	provide	VERB
cana-943	207	15	tools	tool	NOUN
cana-943	207	16	for	for	ADP
cana-943	207	17	implementing	implement	VERB
cana-943	207	18	zero	zero	NUM
cana-943	207	19	-	-	PUNCT
cana-943	207	20	knowledge	knowledge	NOUN
cana-943	207	21	proofs	proof	NOUN
cana-943	207	22	in	in	ADP
cana-943	207	23	real	real	ADJ
cana-943	207	24	-	-	PUNCT
cana-943	207	25	world	world	NOUN
cana-943	207	26	applications	application	NOUN
cana-943	207	27	,	,	PUNCT
cana-943	207	28	helping	help	VERB
cana-943	207	29	developers	developer	NOUN
cana-943	207	30	integrate	integrate	VERB
cana-943	207	31	zkp	zkp	NOUN
cana-943	207	32	into	into	ADP
cana-943	207	33	systems	system	NOUN
cana-943	207	34	while	while	SCONJ
cana-943	207	35	maintaining	maintain	VERB
cana-943	207	36	performance	performance	NOUN
cana-943	207	37	[	[	X
cana-943	207	38	14	14	NUM
cana-943	207	39	]	]	SYM
cana-943	207	40	.	.	PUNCT
cana-943	208	1	5.3	5.3	NUM
cana-943	208	2	.	.	PUNCT
cana-943	208	3	lattice	lattice	NOUN
cana-943	208	4	-	-	PUNCT
cana-943	208	5	based	base	VERB
cana-943	208	6	cryptography	cryptography	NOUN
cana-943	208	7	5.3.1	5.3.1	PROPN
cana-943	208	8	.	.	PUNCT
cana-943	209	1	lattices	lattice	NOUN
cana-943	209	2	in	in	ADP
cana-943	209	3	cryptographic	cryptographic	ADJ
cana-943	209	4	algorithms	algorithm	NOUN
cana-943	209	5	lattice	lattice	NOUN
cana-943	209	6	-	-	PUNCT
cana-943	209	7	based	base	VERB
cana-943	209	8	cryptography	cryptography	NOUN
cana-943	209	9	leverages	leverage	NOUN
cana-943	209	10	the	the	DET
cana-943	209	11	hardness	hardness	NOUN
cana-943	209	12	of	of	ADP
cana-943	209	13	lattice	lattice	NOUN
cana-943	209	14	problems	problem	NOUN
cana-943	209	15	,	,	PUNCT
cana-943	209	16	such	such	ADJ
cana-943	209	17	as	as	ADP
cana-943	209	18	the	the	DET
cana-943	209	19	shortest	short	ADJ
cana-943	209	20	vector	vector	NOUN
cana-943	209	21	problem	problem	NOUN
cana-943	209	22	(	(	PUNCT
cana-943	209	23	svp	svp	NOUN
cana-943	209	24	)	)	PUNCT
cana-943	209	25	and	and	CCONJ
cana-943	209	26	the	the	DET
cana-943	209	27	learning	learning	NOUN
cana-943	209	28	with	with	ADP
cana-943	209	29	errors	error	NOUN
cana-943	209	30	(	(	PUNCT
cana-943	209	31	lwe	lwe	PROPN
cana-943	209	32	)	)	PUNCT
cana-943	209	33	problem	problem	NOUN
cana-943	209	34	,	,	PUNCT
cana-943	209	35	to	to	PART
cana-943	209	36	build	build	VERB
cana-943	209	37	cryptographic	cryptographic	ADJ
cana-943	209	38	schemes	scheme	NOUN
cana-943	209	39	.	.	PUNCT
cana-943	210	1	these	these	DET
cana-943	210	2	problems	problem	NOUN
cana-943	210	3	are	be	AUX
cana-943	210	4	believed	believe	VERB
cana-943	210	5	to	to	PART
cana-943	210	6	be	be	AUX
cana-943	210	7	resistant	resistant	ADJ
cana-943	210	8	to	to	ADP
cana-943	210	9	quantum	quantum	ADJ
cana-943	210	10	attacks	attack	NOUN
cana-943	210	11	,	,	PUNCT
cana-943	210	12	making	make	VERB
cana-943	210	13	lattice	lattice	NOUN
cana-943	210	14	-	-	PUNCT
cana-943	210	15	based	base	VERB
cana-943	210	16	cryptography	cryptography	NOUN
cana-943	210	17	a	a	DET
cana-943	210	18	promising	promising	ADJ
cana-943	210	19	candidate	candidate	NOUN
cana-943	210	20	for	for	ADP
cana-943	210	21	post	post	ADJ
cana-943	210	22	-	-	ADJ
cana-943	210	23	quantum	quantum	ADJ
cana-943	210	24	security	security	NOUN
cana-943	210	25	.	.	PUNCT
cana-943	211	1	key	key	ADJ
cana-943	211	2	algorithms	algorithm	NOUN
cana-943	211	3	:	:	PUNCT
cana-943	211	4	1	1	X
cana-943	211	5	.	.	X
cana-943	211	6	ntruencrypt	ntruencrypt	PROPN
cana-943	211	7	:	:	PUNCT
cana-943	211	8	a	a	DET
cana-943	211	9	public	public	ADJ
cana-943	211	10	-	-	PUNCT
cana-943	211	11	key	key	NOUN
cana-943	211	12	encryption	encryption	NOUN
cana-943	211	13	scheme	scheme	NOUN
cana-943	211	14	based	base	VERB
cana-943	211	15	on	on	ADP
cana-943	211	16	lattice	lattice	NOUN
cana-943	211	17	problems	problem	NOUN
cana-943	211	18	,	,	PUNCT
cana-943	211	19	providing	provide	VERB
cana-943	211	20	efficient	efficient	ADJ
cana-943	211	21	encryption	encryption	NOUN
cana-943	211	22	and	and	CCONJ
cana-943	211	23	decryption	decryption	NOUN
cana-943	211	24	operations	operation	NOUN
cana-943	211	25	[	[	X
cana-943	211	26	7	7	NUM
cana-943	211	27	]	]	SYM
cana-943	211	28	.	.	PUNCT
cana-943	212	1	2	2	X
cana-943	212	2	.	.	X
cana-943	212	3	ring	ring	NOUN
cana-943	212	4	-	-	PUNCT
cana-943	212	5	lwe	lwe	PROPN
cana-943	212	6	:	:	PUNCT
cana-943	212	7	utilizes	utilize	VERB
cana-943	212	8	the	the	DET
cana-943	212	9	hardness	hardness	NOUN
cana-943	212	10	of	of	ADP
cana-943	212	11	the	the	DET
cana-943	212	12	lwe	lwe	PROPN
cana-943	212	13	problem	problem	NOUN
cana-943	212	14	in	in	ADP
cana-943	212	15	the	the	DET
cana-943	212	16	context	context	NOUN
cana-943	212	17	of	of	ADP
cana-943	212	18	polynomial	polynomial	ADJ
cana-943	212	19	rings	ring	NOUN
cana-943	212	20	,	,	PUNCT
cana-943	212	21	enabling	enable	VERB
cana-943	212	22	efficient	efficient	ADJ
cana-943	212	23	implementations	implementation	NOUN
cana-943	212	24	of	of	ADP
cana-943	212	25	encryption	encryption	NOUN
cana-943	212	26	schemes	scheme	NOUN
cana-943	212	27	and	and	CCONJ
cana-943	212	28	digital	digital	ADJ
cana-943	212	29	signatures	signature	NOUN
cana-943	212	30	[	[	X
cana-943	212	31	12	12	NUM
cana-943	212	32	]	]	PUNCT
cana-943	212	33	.	.	PUNCT
cana-943	213	1	5.3.2	5.3.2	X
cana-943	213	2	.	.	X
cana-943	214	1	post	post	ADJ
cana-943	214	2	-	-	ADJ
cana-943	214	3	quantum	quantum	ADJ
cana-943	214	4	cryptographic	cryptographic	ADJ
cana-943	214	5	implementations	implementation	NOUN
cana-943	214	6	post	post	ADJ
cana-943	214	7	-	-	ADJ
cana-943	214	8	quantum	quantum	ADJ
cana-943	214	9	cryptography	cryptography	NOUN
cana-943	214	10	aims	aim	VERB
cana-943	214	11	to	to	PART
cana-943	214	12	develop	develop	VERB
cana-943	214	13	cryptographic	cryptographic	ADJ
cana-943	214	14	algorithms	algorithm	NOUN
cana-943	214	15	that	that	PRON
cana-943	214	16	are	be	AUX
cana-943	214	17	secure	secure	ADJ
cana-943	214	18	against	against	ADP
cana-943	214	19	quantum	quantum	NOUN
cana-943	214	20	attacks	attack	NOUN
cana-943	214	21	.	.	PUNCT
cana-943	215	1	lattice	lattice	NOUN
cana-943	215	2	-	-	PUNCT
cana-943	215	3	based	base	VERB
cana-943	215	4	cryptography	cryptography	NOUN
cana-943	215	5	is	be	AUX
cana-943	215	6	at	at	ADP
cana-943	215	7	the	the	DET
cana-943	215	8	forefront	forefront	NOUN
cana-943	215	9	of	of	ADP
cana-943	215	10	this	this	DET
cana-943	215	11	effort	effort	NOUN
cana-943	215	12	,	,	PUNCT
cana-943	215	13	with	with	SCONJ
cana-943	215	14	several	several	ADJ
cana-943	215	15	practical	practical	ADJ
cana-943	215	16	implementations	implementation	NOUN
cana-943	215	17	being	be	AUX
cana-943	215	18	developed	develop	VERB
cana-943	215	19	and	and	CCONJ
cana-943	215	20	standardized	standardize	VERB
cana-943	215	21	.	.	PUNCT
cana-943	216	1	implementations	implementation	NOUN
cana-943	216	2	:	:	PUNCT
cana-943	216	3	1	1	X
cana-943	216	4	.	.	X
cana-943	216	5	kyber	kyber	NOUN
cana-943	216	6	:	:	PUNCT
cana-943	216	7	a	a	DET
cana-943	216	8	lattice	lattice	NOUN
cana-943	216	9	-	-	PUNCT
cana-943	216	10	based	base	VERB
cana-943	216	11	key	key	ADJ
cana-943	216	12	encapsulation	encapsulation	NOUN
cana-943	216	13	mechanism	mechanism	NOUN
cana-943	216	14	(	(	PUNCT
cana-943	216	15	kem	kem	PROPN
cana-943	216	16	)	)	PUNCT
cana-943	216	17	that	that	PRON
cana-943	216	18	is	be	AUX
cana-943	216	19	part	part	NOUN
cana-943	216	20	of	of	ADP
cana-943	216	21	the	the	DET
cana-943	216	22	nist	nist	NOUN
cana-943	216	23	post	post	ADJ
cana-943	216	24	-	-	ADJ
cana-943	216	25	quantum	quantum	ADJ
cana-943	216	26	cryptography	cryptography	NOUN
cana-943	216	27	standardization	standardization	NOUN
cana-943	216	28	project	project	NOUN
cana-943	216	29	[	[	X
cana-943	216	30	13	13	NUM
cana-943	216	31	]	]	PUNCT
cana-943	216	32	.	.	PUNCT
cana-943	217	1	communications	communication	NOUN
cana-943	217	2	on	on	ADP
cana-943	217	3	applied	apply	VERB
cana-943	217	4	nonlinear	nonlinear	ADJ
cana-943	217	5	analysis	analysis	NOUN
cana-943	217	6	issn	issn	NOUN
cana-943	217	7	:	:	PUNCT
cana-943	217	8	1074	1074	NUM
cana-943	217	9	-	-	PUNCT
cana-943	217	10	133x	133x	NUM
cana-943	217	11	vol	vol	NOUN
cana-943	217	12	31	31	NUM
cana-943	217	13	no	no	NOUN
cana-943	217	14	.	.	PUNCT
cana-943	218	1	4s	4s	NUM
cana-943	218	2	(	(	PUNCT
cana-943	218	3	2024	2024	NUM
cana-943	218	4	)	)	PUNCT
cana-943	218	5	476	476	NUM
cana-943	218	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	218	7	2	2	X
cana-943	218	8	.	.	X
cana-943	218	9	dilithium	dilithium	NOUN
cana-943	218	10	:	:	PUNCT
cana-943	218	11	a	a	DET
cana-943	218	12	lattice	lattice	NOUN
cana-943	218	13	-	-	PUNCT
cana-943	218	14	based	base	VERB
cana-943	218	15	digital	digital	ADJ
cana-943	218	16	signature	signature	NOUN
cana-943	218	17	scheme	scheme	NOUN
cana-943	218	18	,	,	PUNCT
cana-943	218	19	also	also	ADV
cana-943	218	20	being	be	AUX
cana-943	218	21	considered	consider	VERB
cana-943	218	22	by	by	ADP
cana-943	218	23	nist	nist	NOUN
cana-943	218	24	for	for	ADP
cana-943	218	25	standardization	standardization	NOUN
cana-943	218	26	[	[	X
cana-943	218	27	13	13	NUM
cana-943	218	28	]	]	PUNCT
cana-943	218	29	.	.	PUNCT
cana-943	219	1	use	use	NOUN
cana-943	219	2	cases	case	NOUN
cana-943	219	3	:	:	PUNCT
cana-943	219	4	1	1	X
cana-943	219	5	.	.	X
cana-943	219	6	secure	secure	ADJ
cana-943	219	7	communications	communication	NOUN
cana-943	219	8	:	:	PUNCT
cana-943	219	9	ensuring	ensure	VERB
cana-943	219	10	the	the	DET
cana-943	219	11	security	security	NOUN
cana-943	219	12	of	of	ADP
cana-943	219	13	communications	communication	NOUN
cana-943	219	14	in	in	ADP
cana-943	219	15	a	a	DET
cana-943	219	16	post	post	ADJ
cana-943	219	17	-	-	ADJ
cana-943	219	18	quantum	quantum	ADJ
cana-943	219	19	world	world	NOUN
cana-943	219	20	by	by	ADP
cana-943	219	21	replacing	replace	VERB
cana-943	219	22	traditional	traditional	ADJ
cana-943	219	23	algorithms	algorithm	NOUN
cana-943	219	24	with	with	ADP
cana-943	219	25	lattice	lattice	NOUN
cana-943	219	26	-	-	PUNCT
cana-943	219	27	based	base	VERB
cana-943	219	28	alternatives	alternative	NOUN
cana-943	219	29	.	.	PUNCT
cana-943	220	1	2	2	X
cana-943	220	2	.	.	X
cana-943	220	3	data	datum	NOUN
cana-943	220	4	integrity	integrity	NOUN
cana-943	220	5	:	:	PUNCT
cana-943	220	6	using	use	VERB
cana-943	220	7	lattice	lattice	NOUN
cana-943	220	8	-	-	PUNCT
cana-943	220	9	based	base	VERB
cana-943	220	10	digital	digital	ADJ
cana-943	220	11	signatures	signature	NOUN
cana-943	220	12	to	to	PART
cana-943	220	13	guarantee	guarantee	VERB
cana-943	220	14	the	the	DET
cana-943	220	15	authenticity	authenticity	NOUN
cana-943	220	16	and	and	CCONJ
cana-943	220	17	integrity	integrity	NOUN
cana-943	220	18	of	of	ADP
cana-943	220	19	data	datum	NOUN
cana-943	220	20	,	,	PUNCT
cana-943	220	21	even	even	ADV
cana-943	220	22	in	in	ADP
cana-943	220	23	the	the	DET
cana-943	220	24	presence	presence	NOUN
cana-943	220	25	of	of	ADP
cana-943	220	26	quantum	quantum	ADJ
cana-943	220	27	adversaries	adversary	NOUN
cana-943	220	28	.	.	PUNCT
cana-943	221	1	6	6	NUM
cana-943	221	2	.	.	X
cana-943	221	3	case	case	NOUN
cana-943	221	4	studies	study	NOUN
cana-943	221	5	and	and	CCONJ
cana-943	221	6	practical	practical	ADJ
cana-943	221	7	applications	application	NOUN
cana-943	221	8	6.1	6.1	NUM
cana-943	221	9	.	.	PUNCT
cana-943	222	1	secure	secure	ADJ
cana-943	222	2	communications	communication	NOUN
cana-943	222	3	6.1.1	6.1.1	NUM
cana-943	222	4	.	.	PUNCT
cana-943	223	1	implementation	implementation	NOUN
cana-943	223	2	of	of	ADP
cana-943	223	3	ssl	ssl	PROPN
cana-943	223	4	/	/	SYM
cana-943	223	5	tls	tls	PROPN
cana-943	223	6	protocols	protocol	NOUN
cana-943	223	7	ssl	ssl	PROPN
cana-943	223	8	(	(	PUNCT
cana-943	223	9	secure	secure	ADJ
cana-943	223	10	sockets	socket	NOUN
cana-943	223	11	layer	layer	NOUN
cana-943	223	12	)	)	PUNCT
cana-943	223	13	and	and	CCONJ
cana-943	223	14	tls	tls	PROPN
cana-943	223	15	(	(	PUNCT
cana-943	223	16	transport	transport	NOUN
cana-943	223	17	layer	layer	NOUN
cana-943	223	18	security	security	NOUN
cana-943	223	19	)	)	PUNCT
cana-943	223	20	protocols	protocol	NOUN
cana-943	223	21	are	be	AUX
cana-943	223	22	the	the	DET
cana-943	223	23	cornerstone	cornerstone	NOUN
cana-943	223	24	of	of	ADP
cana-943	223	25	secure	secure	ADJ
cana-943	223	26	communications	communication	NOUN
cana-943	223	27	over	over	ADP
cana-943	223	28	the	the	DET
cana-943	223	29	internet	internet	NOUN
cana-943	223	30	.	.	PUNCT
cana-943	224	1	these	these	DET
cana-943	224	2	protocols	protocol	NOUN
cana-943	224	3	ensure	ensure	VERB
cana-943	224	4	data	datum	NOUN
cana-943	224	5	privacy	privacy	NOUN
cana-943	224	6	and	and	CCONJ
cana-943	224	7	integrity	integrity	NOUN
cana-943	224	8	between	between	ADP
cana-943	224	9	clients	client	NOUN
cana-943	224	10	and	and	CCONJ
cana-943	224	11	servers	server	NOUN
cana-943	224	12	.	.	PUNCT
cana-943	225	1	the	the	DET
cana-943	225	2	security	security	NOUN
cana-943	225	3	of	of	ADP
cana-943	225	4	ssl	ssl	PROPN
cana-943	225	5	/	/	SYM
cana-943	225	6	tls	tls	PROPN
cana-943	225	7	is	be	AUX
cana-943	225	8	built	build	VERB
cana-943	225	9	upon	upon	SCONJ
cana-943	225	10	several	several	ADJ
cana-943	225	11	algebraic	algebraic	ADJ
cana-943	225	12	structures	structure	NOUN
cana-943	225	13	and	and	CCONJ
cana-943	225	14	cryptographic	cryptographic	ADJ
cana-943	225	15	techniques	technique	NOUN
cana-943	225	16	.	.	PUNCT
cana-943	226	1	ssl	ssl	PROPN
cana-943	226	2	/	/	SYM
cana-943	226	3	tls	tls	PROPN
cana-943	226	4	protocols	protocol	NOUN
cana-943	226	5	use	use	VERB
cana-943	226	6	asymmetric	asymmetric	ADJ
cana-943	226	7	cryptography	cryptography	NOUN
cana-943	226	8	for	for	ADP
cana-943	226	9	key	key	ADJ
cana-943	226	10	exchange	exchange	NOUN
cana-943	226	11	,	,	PUNCT
cana-943	226	12	symmetric	symmetric	ADJ
cana-943	226	13	encryption	encryption	NOUN
cana-943	226	14	for	for	ADP
cana-943	226	15	data	data	NOUN
cana-943	226	16	transmission	transmission	NOUN
cana-943	226	17	,	,	PUNCT
cana-943	226	18	and	and	CCONJ
cana-943	226	19	hash	hash	NOUN
cana-943	226	20	functions	function	NOUN
cana-943	226	21	for	for	ADP
cana-943	226	22	message	message	NOUN
cana-943	226	23	integrity	integrity	NOUN
cana-943	226	24	.	.	PUNCT
cana-943	227	1	the	the	DET
cana-943	227	2	diffie	diffie	PROPN
cana-943	227	3	-	-	PUNCT
cana-943	227	4	hellman	hellman	PROPN
cana-943	227	5	key	key	PROPN
cana-943	227	6	exchange	exchange	NOUN
cana-943	227	7	,	,	PUNCT
cana-943	227	8	based	base	VERB
cana-943	227	9	on	on	ADP
cana-943	227	10	group	group	NOUN
cana-943	227	11	theory	theory	NOUN
cana-943	227	12	,	,	PUNCT
cana-943	227	13	allows	allow	VERB
cana-943	227	14	two	two	NUM
cana-943	227	15	parties	party	NOUN
cana-943	227	16	to	to	PART
cana-943	227	17	establish	establish	VERB
cana-943	227	18	a	a	DET
cana-943	227	19	shared	share	VERB
cana-943	227	20	secret	secret	NOUN
cana-943	227	21	over	over	ADP
cana-943	227	22	an	an	DET
cana-943	227	23	insecure	insecure	ADJ
cana-943	227	24	channel	channel	NOUN
cana-943	228	1	[	[	X
cana-943	228	2	1	1	NUM
cana-943	228	3	]	]	PUNCT
cana-943	228	4	.	.	PUNCT
cana-943	229	1	modern	modern	ADJ
cana-943	229	2	implementations	implementation	NOUN
cana-943	229	3	often	often	ADV
cana-943	229	4	use	use	VERB
cana-943	229	5	elliptic	elliptic	ADJ
cana-943	229	6	curve	curve	NOUN
cana-943	229	7	diffie	diffie	PROPN
cana-943	229	8	-	-	PUNCT
cana-943	229	9	hellman	hellman	PROPN
cana-943	229	10	(	(	PUNCT
cana-943	229	11	ecdh	ecdh	PROPN
cana-943	229	12	)	)	PUNCT
cana-943	229	13	to	to	PART
cana-943	229	14	enhance	enhance	VERB
cana-943	229	15	security	security	NOUN
cana-943	229	16	and	and	CCONJ
cana-943	229	17	performance	performance	NOUN
cana-943	229	18	[	[	X
cana-943	229	19	3	3	NUM
cana-943	229	20	]	]	PUNCT
cana-943	229	21	.	.	PUNCT
cana-943	230	1	example	example	NOUN
cana-943	230	2	implementation	implementation	NOUN
cana-943	230	3	:	:	PUNCT
cana-943	230	4	1	1	X
cana-943	230	5	.	.	X
cana-943	230	6	initialization	initialization	NOUN
cana-943	230	7	:	:	PUNCT
cana-943	230	8	the	the	DET
cana-943	230	9	client	client	NOUN
cana-943	230	10	sends	send	VERB
cana-943	230	11	a	a	DET
cana-943	230	12	"	"	PUNCT
cana-943	230	13	clienthello	clienthello	NOUN
cana-943	230	14	"	"	PUNCT
cana-943	230	15	message	message	NOUN
cana-943	230	16	to	to	ADP
cana-943	230	17	the	the	DET
cana-943	230	18	server	server	NOUN
cana-943	230	19	,	,	PUNCT
cana-943	230	20	initiating	initiate	VERB
cana-943	230	21	the	the	DET
cana-943	230	22	ssl	ssl	PROPN
cana-943	230	23	/	/	SYM
cana-943	230	24	tls	tls	PROPN
cana-943	230	25	handshake	handshake	NOUN
cana-943	230	26	.	.	PUNCT
cana-943	231	1	2	2	X
cana-943	231	2	.	.	X
cana-943	231	3	certificate	certificate	NOUN
cana-943	231	4	exchange	exchange	PROPN
cana-943	231	5	:	:	PUNCT
cana-943	231	6	the	the	DET
cana-943	231	7	server	server	NOUN
cana-943	231	8	responds	respond	VERB
cana-943	231	9	with	with	ADP
cana-943	231	10	a	a	DET
cana-943	231	11	"	"	PUNCT
cana-943	231	12	serverhello	serverhello	NOUN
cana-943	231	13	"	"	PUNCT
cana-943	231	14	message	message	NOUN
cana-943	231	15	and	and	CCONJ
cana-943	231	16	provides	provide	VERB
cana-943	231	17	its	its	PRON
cana-943	231	18	certificate	certificate	NOUN
cana-943	231	19	,	,	PUNCT
cana-943	231	20	which	which	PRON
cana-943	231	21	contains	contain	VERB
cana-943	231	22	its	its	PRON
cana-943	231	23	public	public	ADJ
cana-943	231	24	key	key	NOUN
cana-943	231	25	.	.	PUNCT
cana-943	232	1	3	3	X
cana-943	232	2	.	.	X
cana-943	232	3	key	key	ADJ
cana-943	232	4	exchange	exchange	NOUN
cana-943	232	5	:	:	PUNCT
cana-943	232	6	the	the	DET
cana-943	232	7	client	client	NOUN
cana-943	232	8	and	and	CCONJ
cana-943	232	9	server	server	NOUN
cana-943	232	10	use	use	NOUN
cana-943	232	11	the	the	DET
cana-943	232	12	diffie	diffie	PROPN
cana-943	232	13	-	-	PUNCT
cana-943	232	14	hellman	hellman	PROPN
cana-943	232	15	algorithm	algorithm	PROPN
cana-943	232	16	to	to	PART
cana-943	232	17	generate	generate	VERB
cana-943	232	18	a	a	DET
cana-943	232	19	shared	share	VERB
cana-943	232	20	secret	secret	ADJ
cana-943	232	21	key	key	NOUN
cana-943	232	22	.	.	PUNCT
cana-943	233	1	4	4	X
cana-943	233	2	.	.	NOUN
cana-943	233	3	session	session	NOUN
cana-943	233	4	encryption	encryption	NOUN
cana-943	233	5	:	:	PUNCT
cana-943	233	6	both	both	DET
cana-943	233	7	parties	party	NOUN
cana-943	233	8	use	use	VERB
cana-943	233	9	the	the	DET
cana-943	233	10	shared	share	VERB
cana-943	233	11	secret	secret	ADJ
cana-943	233	12	key	key	NOUN
cana-943	233	13	to	to	PART
cana-943	233	14	encrypt	encrypt	VERB
cana-943	233	15	and	and	CCONJ
cana-943	233	16	decrypt	decrypt	VERB
cana-943	233	17	the	the	DET
cana-943	233	18	data	datum	NOUN
cana-943	233	19	exchanged	exchange	VERB
cana-943	233	20	during	during	ADP
cana-943	233	21	the	the	DET
cana-943	233	22	session	session	NOUN
cana-943	233	23	.	.	PUNCT
cana-943	234	1	6.1.2	6.1.2	NUM
cana-943	234	2	.	.	PUNCT
cana-943	234	3	end	end	NOUN
cana-943	234	4	-	-	PUNCT
cana-943	234	5	to	to	ADP
cana-943	234	6	-	-	PUNCT
cana-943	234	7	end	end	NOUN
cana-943	234	8	encryption	encryption	NOUN
cana-943	234	9	techniques	technique	NOUN
cana-943	234	10	end	end	VERB
cana-943	234	11	-	-	PUNCT
cana-943	234	12	to	to	ADP
cana-943	234	13	-	-	PUNCT
cana-943	234	14	end	end	NOUN
cana-943	234	15	encryption	encryption	NOUN
cana-943	234	16	(	(	PUNCT
cana-943	234	17	e2ee	e2ee	NOUN
cana-943	234	18	)	)	PUNCT
cana-943	234	19	ensures	ensure	VERB
cana-943	234	20	that	that	SCONJ
cana-943	234	21	data	datum	NOUN
cana-943	234	22	is	be	AUX
cana-943	234	23	encrypted	encrypt	VERB
cana-943	234	24	on	on	ADP
cana-943	234	25	the	the	DET
cana-943	234	26	sender	sender	NOUN
cana-943	234	27	's	's	PART
cana-943	234	28	device	device	NOUN
cana-943	234	29	and	and	CCONJ
cana-943	234	30	only	only	ADV
cana-943	234	31	decrypted	decrypt	VERB
cana-943	234	32	on	on	ADP
cana-943	234	33	the	the	DET
cana-943	234	34	recipient	recipient	NOUN
cana-943	234	35	's	's	PART
cana-943	234	36	device	device	NOUN
cana-943	234	37	,	,	PUNCT
cana-943	234	38	preventing	prevent	VERB
cana-943	234	39	intermediaries	intermediary	NOUN
cana-943	234	40	from	from	ADP
cana-943	234	41	accessing	access	VERB
cana-943	234	42	the	the	DET
cana-943	234	43	plaintext	plaintext	NOUN
cana-943	234	44	.	.	PUNCT
cana-943	235	1	popular	popular	ADJ
cana-943	235	2	applications	application	NOUN
cana-943	235	3	of	of	ADP
cana-943	235	4	e2ee	e2ee	NOUN
cana-943	235	5	include	include	VERB
cana-943	235	6	messaging	message	VERB
cana-943	235	7	apps	app	NOUN
cana-943	235	8	like	like	ADP
cana-943	235	9	whatsapp	whatsapp	NOUN
cana-943	235	10	and	and	CCONJ
cana-943	235	11	signal	signal	NOUN
cana-943	235	12	.	.	PUNCT
cana-943	236	1	techniques	technique	NOUN
cana-943	236	2	:	:	PUNCT
cana-943	236	3	1	1	X
cana-943	236	4	.	.	X
cana-943	236	5	public	public	ADJ
cana-943	236	6	key	key	ADJ
cana-943	236	7	infrastructure	infrastructure	NOUN
cana-943	236	8	(	(	PUNCT
cana-943	236	9	pki	pki	PROPN
cana-943	236	10	):	):	PUNCT
cana-943	236	11	each	each	DET
cana-943	236	12	user	user	NOUN
cana-943	236	13	has	have	VERB
cana-943	236	14	a	a	DET
cana-943	236	15	pair	pair	NOUN
cana-943	236	16	of	of	ADP
cana-943	236	17	cryptographic	cryptographic	ADJ
cana-943	236	18	keys	key	NOUN
cana-943	236	19	(	(	PUNCT
cana-943	236	20	public	public	ADJ
cana-943	236	21	and	and	CCONJ
cana-943	236	22	private	private	ADJ
cana-943	236	23	)	)	PUNCT
cana-943	236	24	.	.	PUNCT
cana-943	237	1	messages	message	NOUN
cana-943	237	2	are	be	AUX
cana-943	237	3	encrypted	encrypt	VERB
cana-943	237	4	with	with	ADP
cana-943	237	5	the	the	DET
cana-943	237	6	recipient	recipient	NOUN
cana-943	237	7	's	's	PART
cana-943	237	8	public	public	ADJ
cana-943	237	9	key	key	NOUN
cana-943	237	10	and	and	CCONJ
cana-943	237	11	decrypted	decrypt	VERB
cana-943	237	12	with	with	ADP
cana-943	237	13	their	their	PRON
cana-943	237	14	private	private	ADJ
cana-943	237	15	key	key	NOUN
cana-943	238	1	[	[	X
cana-943	238	2	14	14	NUM
cana-943	238	3	]	]	PUNCT
cana-943	238	4	.	.	PUNCT
cana-943	239	1	communications	communication	NOUN
cana-943	239	2	on	on	ADP
cana-943	239	3	applied	apply	VERB
cana-943	239	4	nonlinear	nonlinear	ADJ
cana-943	239	5	analysis	analysis	NOUN
cana-943	239	6	issn	issn	NOUN
cana-943	239	7	:	:	PUNCT
cana-943	239	8	1074	1074	NUM
cana-943	239	9	-	-	PUNCT
cana-943	239	10	133x	133x	NUM
cana-943	239	11	vol	vol	NOUN
cana-943	239	12	31	31	NUM
cana-943	239	13	no	no	NOUN
cana-943	239	14	.	.	PUNCT
cana-943	240	1	4s	4s	NUM
cana-943	240	2	(	(	PUNCT
cana-943	240	3	2024	2024	NUM
cana-943	240	4	)	)	PUNCT
cana-943	240	5	477	477	NUM
cana-943	240	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	240	7	2	2	NUM
cana-943	240	8	.	.	X
cana-943	240	9	double	double	ADJ
cana-943	240	10	ratchet	ratchet	NOUN
cana-943	240	11	algorithm	algorithm	NOUN
cana-943	240	12	:	:	PUNCT
cana-943	240	13	used	use	VERB
cana-943	240	14	in	in	ADP
cana-943	240	15	signal	signal	ADJ
cana-943	240	16	protocol	protocol	NOUN
cana-943	240	17	,	,	PUNCT
cana-943	240	18	this	this	DET
cana-943	240	19	algorithm	algorithm	NOUN
cana-943	240	20	combines	combine	VERB
cana-943	240	21	diffie	diffie	PROPN
cana-943	240	22	-	-	PUNCT
cana-943	240	23	hellman	hellman	PROPN
cana-943	240	24	key	key	PROPN
cana-943	240	25	exchange	exchange	NOUN
cana-943	240	26	with	with	ADP
cana-943	240	27	a	a	DET
cana-943	240	28	ratcheting	ratchet	VERB
cana-943	240	29	mechanism	mechanism	NOUN
cana-943	240	30	to	to	PART
cana-943	240	31	provide	provide	VERB
cana-943	240	32	forward	forward	ADV
cana-943	240	33	secrecy	secrecy	NOUN
cana-943	240	34	and	and	CCONJ
cana-943	240	35	post	post	ADJ
cana-943	240	36	-	-	ADJ
cana-943	240	37	compromise	compromise	ADJ
cana-943	240	38	security	security	NOUN
cana-943	240	39	[	[	X
cana-943	240	40	10	10	NUM
cana-943	240	41	]	]	PUNCT
cana-943	240	42	.	.	PUNCT
cana-943	241	1	example	example	NOUN
cana-943	241	2	:	:	PUNCT
cana-943	241	3	•	•	ADP
cana-943	241	4	when	when	SCONJ
cana-943	241	5	a	a	DET
cana-943	241	6	message	message	NOUN
cana-943	241	7	is	be	AUX
cana-943	241	8	sent	send	VERB
cana-943	241	9	,	,	PUNCT
cana-943	241	10	it	it	PRON
cana-943	241	11	is	be	AUX
cana-943	241	12	encrypted	encrypt	VERB
cana-943	241	13	with	with	ADP
cana-943	241	14	the	the	DET
cana-943	241	15	recipient	recipient	NOUN
cana-943	241	16	's	's	PART
cana-943	241	17	public	public	ADJ
cana-943	241	18	key	key	NOUN
cana-943	241	19	.	.	PUNCT
cana-943	242	1	•	•	NUM
cana-943	242	2	on	on	ADP
cana-943	242	3	receipt	receipt	NOUN
cana-943	242	4	,	,	PUNCT
cana-943	242	5	the	the	DET
cana-943	242	6	message	message	NOUN
cana-943	242	7	is	be	AUX
cana-943	242	8	decrypted	decrypt	VERB
cana-943	242	9	with	with	ADP
cana-943	242	10	the	the	DET
cana-943	242	11	recipient	recipient	NOUN
cana-943	242	12	's	's	PART
cana-943	242	13	private	private	ADJ
cana-943	242	14	key	key	NOUN
cana-943	242	15	,	,	PUNCT
cana-943	242	16	ensuring	ensure	VERB
cana-943	242	17	that	that	SCONJ
cana-943	242	18	only	only	ADV
cana-943	242	19	the	the	DET
cana-943	242	20	intended	intend	VERB
cana-943	242	21	recipient	recipient	NOUN
cana-943	242	22	can	can	AUX
cana-943	242	23	read	read	VERB
cana-943	242	24	it	it	PRON
cana-943	242	25	.	.	PUNCT
cana-943	243	1	6.2	6.2	NUM
cana-943	243	2	.	.	PUNCT
cana-943	244	1	blockchain	blockchain	PROPN
cana-943	244	2	and	and	CCONJ
cana-943	244	3	cryptocurrencies	cryptocurrencie	NOUN
cana-943	244	4	6.2.1	6.2.1	VERB
cana-943	244	5	.	.	PUNCT
cana-943	245	1	algebraic	algebraic	ADJ
cana-943	245	2	structures	structure	NOUN
cana-943	245	3	in	in	ADP
cana-943	245	4	blockchain	blockchain	PROPN
cana-943	245	5	implementation	implementation	PROPN
cana-943	245	6	blockchain	blockchain	PROPN
cana-943	245	7	technology	technology	PROPN
cana-943	245	8	relies	rely	VERB
cana-943	245	9	heavily	heavily	ADV
cana-943	245	10	on	on	ADP
cana-943	245	11	cryptographic	cryptographic	ADJ
cana-943	245	12	and	and	CCONJ
cana-943	245	13	algebraic	algebraic	ADJ
cana-943	245	14	principles	principle	NOUN
cana-943	245	15	to	to	PART
cana-943	245	16	ensure	ensure	VERB
cana-943	245	17	data	datum	NOUN
cana-943	245	18	integrity	integrity	NOUN
cana-943	245	19	,	,	PUNCT
cana-943	245	20	transparency	transparency	NOUN
cana-943	245	21	,	,	PUNCT
cana-943	245	22	and	and	CCONJ
cana-943	245	23	security	security	NOUN
cana-943	245	24	.	.	PUNCT
cana-943	246	1	a	a	DET
cana-943	246	2	blockchain	blockchain	PROPN
cana-943	246	3	is	be	AUX
cana-943	246	4	a	a	DET
cana-943	246	5	distributed	distribute	VERB
cana-943	246	6	ledger	ledger	NOUN
cana-943	246	7	that	that	PRON
cana-943	246	8	records	record	VERB
cana-943	246	9	transactions	transaction	NOUN
cana-943	246	10	across	across	ADP
cana-943	246	11	multiple	multiple	ADJ
cana-943	246	12	computers	computer	NOUN
cana-943	246	13	in	in	ADP
cana-943	246	14	such	such	DET
cana-943	246	15	a	a	DET
cana-943	246	16	way	way	NOUN
cana-943	246	17	that	that	PRON
cana-943	246	18	the	the	DET
cana-943	246	19	registered	register	VERB
cana-943	246	20	transactions	transaction	NOUN
cana-943	246	21	can	can	AUX
cana-943	246	22	not	not	PART
cana-943	246	23	be	be	AUX
cana-943	246	24	altered	alter	VERB
cana-943	246	25	retroactively	retroactively	ADV
cana-943	246	26	.	.	PUNCT
cana-943	247	1	algebraic	algebraic	ADJ
cana-943	247	2	structures	structure	NOUN
cana-943	247	3	:	:	PUNCT
cana-943	247	4	1	1	X
cana-943	247	5	.	.	X
cana-943	247	6	hash	hash	NOUN
cana-943	247	7	functions	function	NOUN
cana-943	247	8	:	:	PUNCT
cana-943	247	9	hash	hash	NOUN
cana-943	247	10	functions	function	NOUN
cana-943	247	11	,	,	PUNCT
cana-943	247	12	based	base	VERB
cana-943	247	13	on	on	ADP
cana-943	247	14	algebraic	algebraic	ADJ
cana-943	247	15	algorithms	algorithm	NOUN
cana-943	247	16	,	,	PUNCT
cana-943	247	17	are	be	AUX
cana-943	247	18	used	use	VERB
cana-943	247	19	to	to	PART
cana-943	247	20	create	create	VERB
cana-943	247	21	a	a	DET
cana-943	247	22	unique	unique	ADJ
cana-943	247	23	digital	digital	ADJ
cana-943	247	24	fingerprint	fingerprint	NOUN
cana-943	247	25	of	of	ADP
cana-943	247	26	data	datum	NOUN
cana-943	247	27	.	.	PUNCT
cana-943	248	1	each	each	DET
cana-943	248	2	block	block	NOUN
cana-943	248	3	contains	contain	VERB
cana-943	248	4	the	the	DET
cana-943	248	5	hash	hash	NOUN
cana-943	248	6	of	of	ADP
cana-943	248	7	the	the	DET
cana-943	248	8	previous	previous	ADJ
cana-943	248	9	block	block	NOUN
cana-943	248	10	,	,	PUNCT
cana-943	248	11	linking	link	VERB
cana-943	248	12	them	they	PRON
cana-943	248	13	together	together	ADV
cana-943	248	14	in	in	ADP
cana-943	248	15	a	a	DET
cana-943	248	16	chain	chain	NOUN
cana-943	248	17	[	[	X
cana-943	248	18	6	6	NUM
cana-943	248	19	]	]	PUNCT
cana-943	248	20	.	.	PUNCT
cana-943	249	1	2	2	NUM
cana-943	249	2	.	.	X
cana-943	249	3	merkle	merkle	NOUN
cana-943	249	4	trees	tree	NOUN
cana-943	249	5	:	:	PUNCT
cana-943	249	6	a	a	DET
cana-943	249	7	merkle	merkle	NOUN
cana-943	249	8	tree	tree	NOUN
cana-943	249	9	is	be	AUX
cana-943	249	10	a	a	DET
cana-943	249	11	binary	binary	ADJ
cana-943	249	12	tree	tree	NOUN
cana-943	249	13	of	of	ADP
cana-943	249	14	hashes	hash	NOUN
cana-943	249	15	.	.	PUNCT
cana-943	250	1	each	each	DET
cana-943	250	2	leaf	leaf	NOUN
cana-943	250	3	node	node	NOUN
cana-943	250	4	is	be	AUX
cana-943	250	5	a	a	DET
cana-943	250	6	hash	hash	NOUN
cana-943	250	7	of	of	ADP
cana-943	250	8	a	a	DET
cana-943	250	9	block	block	NOUN
cana-943	250	10	of	of	ADP
cana-943	250	11	transactions	transaction	NOUN
cana-943	250	12	,	,	PUNCT
cana-943	250	13	and	and	CCONJ
cana-943	250	14	each	each	DET
cana-943	250	15	non	non	ADJ
cana-943	250	16	-	-	ADJ
cana-943	250	17	leaf	leaf	ADJ
cana-943	250	18	node	node	NOUN
cana-943	250	19	is	be	AUX
cana-943	250	20	a	a	DET
cana-943	250	21	hash	hash	NOUN
cana-943	250	22	of	of	ADP
cana-943	250	23	its	its	PRON
cana-943	250	24	children	child	NOUN
cana-943	250	25	.	.	PUNCT
cana-943	251	1	this	this	DET
cana-943	251	2	structure	structure	NOUN
cana-943	251	3	allows	allow	VERB
cana-943	251	4	efficient	efficient	ADJ
cana-943	251	5	and	and	CCONJ
cana-943	251	6	secure	secure	ADJ
cana-943	251	7	verification	verification	NOUN
cana-943	251	8	of	of	ADP
cana-943	251	9	the	the	DET
cana-943	251	10	integrity	integrity	NOUN
cana-943	251	11	of	of	ADP
cana-943	251	12	the	the	DET
cana-943	251	13	transactions	transaction	NOUN
cana-943	251	14	[	[	X
cana-943	251	15	9	9	NUM
cana-943	251	16	]	]	PUNCT
cana-943	251	17	.	.	PUNCT
cana-943	252	1	6.2.2	6.2.2	X
cana-943	252	2	.	.	PUNCT
cana-943	252	3	cryptographic	cryptographic	ADJ
cana-943	252	4	algorithms	algorithm	NOUN
cana-943	252	5	in	in	ADP
cana-943	252	6	bitcoin	bitcoin	ADJ
cana-943	252	7	and	and	CCONJ
cana-943	252	8	ethereum	ethereum	NOUN
cana-943	252	9	bitcoin	bitcoin	NOUN
cana-943	252	10	and	and	CCONJ
cana-943	252	11	ethereum	ethereum	NOUN
cana-943	252	12	,	,	PUNCT
cana-943	252	13	the	the	DET
cana-943	252	14	two	two	NUM
cana-943	252	15	most	most	ADV
cana-943	252	16	well	well	ADV
cana-943	252	17	-	-	PUNCT
cana-943	252	18	known	know	VERB
cana-943	252	19	cryptocurrencies	cryptocurrencie	NOUN
cana-943	252	20	,	,	PUNCT
cana-943	252	21	utilize	utilize	VERB
cana-943	252	22	a	a	DET
cana-943	252	23	variety	variety	NOUN
cana-943	252	24	of	of	ADP
cana-943	252	25	cryptographic	cryptographic	ADJ
cana-943	252	26	algorithms	algorithm	NOUN
cana-943	252	27	to	to	PART
cana-943	252	28	secure	secure	VERB
cana-943	252	29	their	their	PRON
cana-943	252	30	networks	network	NOUN
cana-943	252	31	and	and	CCONJ
cana-943	252	32	enable	enable	VERB
cana-943	252	33	transaction	transaction	NOUN
cana-943	252	34	processing	processing	NOUN
cana-943	252	35	.	.	PUNCT
cana-943	253	1	bitcoin	bitcoin	NOUN
cana-943	253	2	:	:	PUNCT
cana-943	253	3	•	•	NUM
cana-943	253	4	elliptic	elliptic	ADJ
cana-943	253	5	curve	curve	NOUN
cana-943	253	6	digital	digital	ADJ
cana-943	253	7	signature	signature	NOUN
cana-943	253	8	algorithm	algorithm	NOUN
cana-943	253	9	(	(	PUNCT
cana-943	253	10	ecdsa	ecdsa	PROPN
cana-943	253	11	):	):	PUNCT
cana-943	253	12	used	use	VERB
cana-943	253	13	for	for	ADP
cana-943	253	14	securing	secure	VERB
cana-943	253	15	transactions	transaction	NOUN
cana-943	253	16	by	by	ADP
cana-943	253	17	creating	create	VERB
cana-943	253	18	and	and	CCONJ
cana-943	253	19	verifying	verify	VERB
cana-943	253	20	digital	digital	ADJ
cana-943	253	21	signatures	signature	NOUN
cana-943	254	1	[	[	X
cana-943	254	2	2	2	NUM
cana-943	254	3	]	]	PUNCT
cana-943	254	4	.	.	PUNCT
cana-943	255	1	•	•	NUM
cana-943	255	2	sha-256	sha-256	PROPN
cana-943	255	3	:	:	PUNCT
cana-943	255	4	a	a	DET
cana-943	255	5	cryptographic	cryptographic	ADJ
cana-943	255	6	hash	hash	NOUN
cana-943	255	7	function	function	NOUN
cana-943	255	8	used	use	VERB
cana-943	255	9	in	in	ADP
cana-943	255	10	the	the	DET
cana-943	255	11	proof	proof	NOUN
cana-943	255	12	-	-	PUNCT
cana-943	255	13	of	of	ADP
cana-943	255	14	-	-	PUNCT
cana-943	255	15	work	work	NOUN
cana-943	255	16	algorithm	algorithm	NOUN
cana-943	255	17	to	to	PART
cana-943	255	18	secure	secure	VERB
cana-943	255	19	the	the	DET
cana-943	255	20	blockchain	blockchain	NOUN
cana-943	255	21	[	[	X
cana-943	255	22	12	12	NUM
cana-943	255	23	]	]	PUNCT
cana-943	255	24	.	.	PUNCT
cana-943	256	1	ethereum	ethereum	NOUN
cana-943	256	2	:	:	PUNCT
cana-943	256	3	•	•	NOUN
cana-943	256	4	keccak-256	keccak-256	ADJ
cana-943	256	5	:	:	PUNCT
cana-943	256	6	a	a	DET
cana-943	256	7	variant	variant	NOUN
cana-943	256	8	of	of	ADP
cana-943	256	9	sha-3	sha-3	NOUN
cana-943	256	10	used	use	VERB
cana-943	256	11	in	in	ADP
cana-943	256	12	ethereum	ethereum	NOUN
cana-943	256	13	's	's	PART
cana-943	256	14	hashing	hashing	NOUN
cana-943	256	15	processes	process	NOUN
cana-943	256	16	[	[	X
cana-943	256	17	17	17	NUM
cana-943	256	18	]	]	PUNCT
cana-943	256	19	.	.	PUNCT
cana-943	257	1	•	•	NUM
cana-943	257	2	ecdsa	ecdsa	NOUN
cana-943	257	3	:	:	PUNCT
cana-943	257	4	similar	similar	ADJ
cana-943	257	5	to	to	ADP
cana-943	257	6	bitcoin	bitcoin	VERB
cana-943	257	7	,	,	PUNCT
cana-943	257	8	ethereum	ethereum	NOUN
cana-943	257	9	uses	use	VERB
cana-943	257	10	ecdsa	ecdsa	NOUN
cana-943	257	11	for	for	ADP
cana-943	257	12	transaction	transaction	NOUN
cana-943	257	13	signatures	signature	NOUN
cana-943	257	14	[	[	X
cana-943	257	15	18	18	NUM
cana-943	257	16	]	]	PUNCT
cana-943	257	17	.	.	PUNCT
cana-943	258	1	6.3	6.3	NUM
cana-943	258	2	.	.	PUNCT
cana-943	259	1	data	datum	NOUN
cana-943	259	2	privacy	privacy	NOUN
cana-943	259	3	and	and	CCONJ
cana-943	259	4	secure	secure	VERB
cana-943	259	5	storage	storage	NOUN
cana-943	259	6	6.3.1	6.3.1	NUM
cana-943	259	7	.	.	PUNCT
cana-943	260	1	cloud	cloud	NOUN
cana-943	260	2	storage	storage	NOUN
cana-943	260	3	encryption	encryption	NOUN
cana-943	260	4	methods	method	NOUN
cana-943	260	5	as	as	ADP
cana-943	260	6	cloud	cloud	ADJ
cana-943	260	7	storage	storage	NOUN
cana-943	260	8	becomes	become	VERB
cana-943	260	9	increasingly	increasingly	ADV
cana-943	260	10	popular	popular	ADJ
cana-943	260	11	,	,	PUNCT
cana-943	260	12	ensuring	ensure	VERB
cana-943	260	13	the	the	DET
cana-943	260	14	privacy	privacy	NOUN
cana-943	260	15	and	and	CCONJ
cana-943	260	16	security	security	NOUN
cana-943	260	17	of	of	ADP
cana-943	260	18	stored	store	VERB
cana-943	260	19	data	datum	NOUN
cana-943	260	20	is	be	AUX
cana-943	260	21	paramount	paramount	ADJ
cana-943	260	22	.	.	PUNCT
cana-943	261	1	encryption	encryption	NOUN
cana-943	261	2	methods	method	NOUN
cana-943	261	3	for	for	ADP
cana-943	261	4	cloud	cloud	NOUN
cana-943	261	5	storage	storage	NOUN
cana-943	261	6	involve	involve	VERB
cana-943	261	7	both	both	DET
cana-943	261	8	client	client	NOUN
cana-943	261	9	-	-	PUNCT
cana-943	261	10	side	side	NOUN
cana-943	261	11	and	and	CCONJ
cana-943	261	12	server	server	NOUN
cana-943	261	13	-	-	PUNCT
cana-943	261	14	side	side	NOUN
cana-943	261	15	encryption	encryption	NOUN
cana-943	261	16	.	.	PUNCT
cana-943	262	1	communications	communication	NOUN
cana-943	262	2	on	on	ADP
cana-943	262	3	applied	apply	VERB
cana-943	262	4	nonlinear	nonlinear	ADJ
cana-943	262	5	analysis	analysis	NOUN
cana-943	262	6	issn	issn	NOUN
cana-943	262	7	:	:	PUNCT
cana-943	262	8	1074	1074	NUM
cana-943	262	9	-	-	PUNCT
cana-943	262	10	133x	133x	NUM
cana-943	262	11	vol	vol	NOUN
cana-943	262	12	31	31	NUM
cana-943	262	13	no	no	NOUN
cana-943	262	14	.	.	PUNCT
cana-943	263	1	4s	4s	NUM
cana-943	263	2	(	(	PUNCT
cana-943	263	3	2024	2024	NUM
cana-943	263	4	)	)	PUNCT
cana-943	263	5	478	478	NUM
cana-943	263	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	263	7	methods	method	NOUN
cana-943	263	8	:	:	PUNCT
cana-943	263	9	1	1	X
cana-943	263	10	.	.	X
cana-943	263	11	client	client	NOUN
cana-943	263	12	-	-	PUNCT
cana-943	263	13	side	side	NOUN
cana-943	263	14	encryption	encryption	NOUN
cana-943	263	15	:	:	PUNCT
cana-943	263	16	data	datum	NOUN
cana-943	263	17	is	be	AUX
cana-943	263	18	encrypted	encrypt	VERB
cana-943	263	19	before	before	SCONJ
cana-943	263	20	it	it	PRON
cana-943	263	21	is	be	AUX
cana-943	263	22	uploaded	upload	VERB
cana-943	263	23	to	to	ADP
cana-943	263	24	the	the	DET
cana-943	263	25	cloud	cloud	NOUN
cana-943	263	26	.	.	PUNCT
cana-943	264	1	only	only	ADV
cana-943	264	2	the	the	DET
cana-943	264	3	client	client	NOUN
cana-943	264	4	holds	hold	VERB
cana-943	264	5	the	the	DET
cana-943	264	6	encryption	encryption	NOUN
cana-943	264	7	keys	key	NOUN
cana-943	264	8	,	,	PUNCT
cana-943	264	9	ensuring	ensure	VERB
cana-943	264	10	that	that	SCONJ
cana-943	264	11	the	the	DET
cana-943	264	12	cloud	cloud	NOUN
cana-943	264	13	provider	provider	NOUN
cana-943	264	14	can	can	AUX
cana-943	264	15	not	not	PART
cana-943	264	16	access	access	VERB
cana-943	264	17	the	the	DET
cana-943	264	18	plaintext	plaintext	NOUN
cana-943	264	19	data	datum	NOUN
cana-943	264	20	.	.	PUNCT
cana-943	265	1	2	2	X
cana-943	265	2	.	.	X
cana-943	265	3	server	server	NOUN
cana-943	265	4	-	-	PUNCT
cana-943	265	5	side	side	NOUN
cana-943	265	6	encryption	encryption	NOUN
cana-943	265	7	:	:	PUNCT
cana-943	265	8	data	datum	NOUN
cana-943	265	9	is	be	AUX
cana-943	265	10	encrypted	encrypt	VERB
cana-943	265	11	by	by	ADP
cana-943	265	12	the	the	DET
cana-943	265	13	cloud	cloud	NOUN
cana-943	265	14	service	service	NOUN
cana-943	265	15	provider	provider	NOUN
cana-943	265	16	once	once	SCONJ
cana-943	265	17	it	it	PRON
cana-943	265	18	reaches	reach	VERB
cana-943	265	19	their	their	PRON
cana-943	265	20	servers	server	NOUN
cana-943	265	21	.	.	PUNCT
cana-943	266	1	the	the	DET
cana-943	266	2	encryption	encryption	NOUN
cana-943	266	3	keys	key	NOUN
cana-943	266	4	are	be	AUX
cana-943	266	5	managed	manage	VERB
cana-943	266	6	by	by	ADP
cana-943	266	7	the	the	DET
cana-943	266	8	provider	provider	NOUN
cana-943	266	9	,	,	PUNCT
cana-943	266	10	which	which	PRON
cana-943	266	11	requires	require	VERB
cana-943	266	12	trust	trust	NOUN
cana-943	266	13	in	in	ADP
cana-943	266	14	their	their	PRON
cana-943	266	15	security	security	NOUN
cana-943	266	16	measures	measure	NOUN
cana-943	266	17	[	[	X
cana-943	266	18	15	15	NUM
cana-943	266	19	]	]	PUNCT
cana-943	266	20	.	.	PUNCT
cana-943	267	1	example	example	NOUN
cana-943	267	2	:	:	PUNCT
cana-943	267	3	•	•	NUM
cana-943	267	4	amazon	amazon	PROPN
cana-943	267	5	s3	s3	PROPN
cana-943	267	6	:	:	PUNCT
cana-943	267	7	provides	provide	VERB
cana-943	267	8	several	several	ADJ
cana-943	267	9	options	option	NOUN
cana-943	267	10	for	for	ADP
cana-943	267	11	server	server	NOUN
cana-943	267	12	-	-	PUNCT
cana-943	267	13	side	side	NOUN
cana-943	267	14	encryption	encryption	NOUN
cana-943	267	15	,	,	PUNCT
cana-943	267	16	including	include	VERB
cana-943	267	17	sse	sse	NOUN
cana-943	267	18	-	-	PUNCT
cana-943	267	19	s3	s3	PROPN
cana-943	267	20	(	(	PUNCT
cana-943	267	21	amazon	amazon	NOUN
cana-943	267	22	manages	manage	VERB
cana-943	267	23	the	the	DET
cana-943	267	24	keys	key	NOUN
cana-943	267	25	)	)	PUNCT
cana-943	267	26	,	,	PUNCT
cana-943	267	27	sse	sse	PROPN
cana-943	267	28	-	-	PUNCT
cana-943	267	29	kms	kms	PROPN
cana-943	267	30	(	(	PUNCT
cana-943	267	31	amazon	amazon	NOUN
cana-943	267	32	key	key	PROPN
cana-943	267	33	management	management	NOUN
cana-943	267	34	service	service	NOUN
cana-943	267	35	)	)	PUNCT
cana-943	267	36	,	,	PUNCT
cana-943	267	37	and	and	CCONJ
cana-943	267	38	sse	sse	NOUN
cana-943	267	39	-	-	PUNCT
cana-943	267	40	c	c	PROPN
cana-943	267	41	(	(	PUNCT
cana-943	267	42	customerprovided	customerprovide	VERB
cana-943	267	43	keys	key	NOUN
cana-943	267	44	)	)	PUNCT
cana-943	268	1	[	[	X
cana-943	268	2	19	19	NUM
cana-943	268	3	]	]	PUNCT
cana-943	268	4	.	.	PUNCT
cana-943	269	1	6.3.2	6.3.2	X
cana-943	269	2	.	.	PUNCT
cana-943	269	3	data	datum	NOUN
cana-943	269	4	masking	masking	NOUN
cana-943	269	5	and	and	CCONJ
cana-943	269	6	tokenization	tokenization	NOUN
cana-943	269	7	techniques	technique	NOUN
cana-943	269	8	data	datum	NOUN
cana-943	269	9	masking	masking	NOUN
cana-943	269	10	and	and	CCONJ
cana-943	269	11	tokenization	tokenization	NOUN
cana-943	269	12	are	be	AUX
cana-943	269	13	techniques	technique	NOUN
cana-943	269	14	used	use	VERB
cana-943	269	15	to	to	PART
cana-943	269	16	protect	protect	VERB
cana-943	269	17	sensitive	sensitive	ADJ
cana-943	269	18	data	datum	NOUN
cana-943	269	19	by	by	ADP
cana-943	269	20	replacing	replace	VERB
cana-943	269	21	it	it	PRON
cana-943	269	22	with	with	ADP
cana-943	269	23	nonsensitive	nonsensitive	ADJ
cana-943	269	24	equivalents	equivalent	NOUN
cana-943	269	25	.	.	PUNCT
cana-943	270	1	data	datum	NOUN
cana-943	270	2	masking	masking	NOUN
cana-943	270	3	:	:	PUNCT
cana-943	270	4	•	•	NOUN
cana-943	270	5	involves	involve	VERB
cana-943	270	6	altering	alter	VERB
cana-943	270	7	data	datum	NOUN
cana-943	270	8	to	to	PART
cana-943	270	9	hide	hide	VERB
cana-943	270	10	sensitive	sensitive	ADJ
cana-943	270	11	information	information	NOUN
cana-943	270	12	while	while	SCONJ
cana-943	270	13	maintaining	maintain	VERB
cana-943	270	14	its	its	PRON
cana-943	270	15	usability	usability	NOUN
cana-943	270	16	.	.	PUNCT
cana-943	271	1	for	for	ADP
cana-943	271	2	example	example	NOUN
cana-943	271	3	,	,	PUNCT
cana-943	271	4	a	a	DET
cana-943	271	5	credit	credit	NOUN
cana-943	271	6	card	card	NOUN
cana-943	271	7	number	number	NOUN
cana-943	271	8	might	might	AUX
cana-943	271	9	be	be	AUX
cana-943	271	10	masked	mask	VERB
cana-943	271	11	as	as	ADP
cana-943	271	12	"	"	PUNCT
cana-943	271	13	*	*	PUNCT
cana-943	271	14	*	*	PUNCT
cana-943	271	15	*	*	PUNCT
cana-943	271	16	*	*	PUNCT
cana-943	271	17	*	*	PUNCT
cana-943	271	18	*	*	PUNCT
cana-943	271	19	*	*	PUNCT
cana-943	271	20	*	*	PUNCT
cana-943	272	1	*	*	PUNCT
cana-943	272	2	*	*	PUNCT
cana-943	272	3	*	*	PUNCT
cana-943	272	4	*	*	PUNCT
cana-943	272	5	1234	1234	NUM
cana-943	272	6	"	"	PUNCT
cana-943	272	7	for	for	ADP
cana-943	272	8	display	display	NOUN
cana-943	272	9	purposes	purpose	NOUN
cana-943	273	1	[	[	X
cana-943	273	2	11	11	NUM
cana-943	273	3	]	]	PUNCT
cana-943	273	4	.	.	PUNCT
cana-943	274	1	tokenization	tokenization	NOUN
cana-943	274	2	:	:	PUNCT
cana-943	274	3	•	•	NOUN
cana-943	274	4	involves	involve	VERB
cana-943	274	5	substituting	substitute	VERB
cana-943	274	6	sensitive	sensitive	ADJ
cana-943	274	7	data	datum	NOUN
cana-943	274	8	with	with	ADP
cana-943	274	9	a	a	DET
cana-943	274	10	token	token	NOUN
cana-943	274	11	that	that	PRON
cana-943	274	12	can	can	AUX
cana-943	274	13	be	be	AUX
cana-943	274	14	mapped	map	VERB
cana-943	274	15	back	back	ADV
cana-943	274	16	to	to	ADP
cana-943	274	17	the	the	DET
cana-943	274	18	original	original	ADJ
cana-943	274	19	data	datum	NOUN
cana-943	274	20	through	through	ADP
cana-943	274	21	a	a	DET
cana-943	274	22	secure	secure	ADJ
cana-943	274	23	tokenization	tokenization	NOUN
cana-943	274	24	system	system	NOUN
cana-943	274	25	.	.	PUNCT
cana-943	275	1	this	this	PRON
cana-943	275	2	is	be	AUX
cana-943	275	3	commonly	commonly	ADV
cana-943	275	4	used	use	VERB
cana-943	275	5	in	in	ADP
cana-943	275	6	payment	payment	NOUN
cana-943	275	7	processing	processing	NOUN
cana-943	275	8	to	to	PART
cana-943	275	9	secure	secure	VERB
cana-943	275	10	credit	credit	NOUN
cana-943	275	11	card	card	NOUN
cana-943	275	12	information	information	NOUN
cana-943	275	13	[	[	X
cana-943	275	14	8	8	NUM
cana-943	275	15	]	]	PUNCT
cana-943	275	16	.	.	PUNCT
cana-943	276	1	example	example	NOUN
cana-943	276	2	:	:	PUNCT
cana-943	276	3	•	•	ADP
cana-943	276	4	a	a	DET
cana-943	276	5	payment	payment	NOUN
cana-943	276	6	system	system	NOUN
cana-943	276	7	might	might	AUX
cana-943	276	8	replace	replace	VERB
cana-943	276	9	a	a	DET
cana-943	276	10	credit	credit	NOUN
cana-943	276	11	card	card	NOUN
cana-943	276	12	number	number	NOUN
cana-943	276	13	with	with	ADP
cana-943	276	14	a	a	DET
cana-943	276	15	token	token	NOUN
cana-943	276	16	,	,	PUNCT
cana-943	276	17	which	which	PRON
cana-943	276	18	is	be	AUX
cana-943	276	19	then	then	ADV
cana-943	276	20	used	use	VERB
cana-943	276	21	for	for	ADP
cana-943	276	22	transactions	transaction	NOUN
cana-943	276	23	.	.	PUNCT
cana-943	277	1	the	the	DET
cana-943	277	2	actual	actual	ADJ
cana-943	277	3	credit	credit	NOUN
cana-943	277	4	card	card	NOUN
cana-943	277	5	number	number	NOUN
cana-943	277	6	is	be	AUX
cana-943	277	7	stored	store	VERB
cana-943	277	8	securely	securely	ADV
cana-943	277	9	and	and	CCONJ
cana-943	277	10	only	only	ADV
cana-943	277	11	accessible	accessible	ADJ
cana-943	277	12	through	through	ADP
cana-943	277	13	the	the	DET
cana-943	277	14	tokenization	tokenization	NOUN
cana-943	277	15	system	system	NOUN
cana-943	277	16	[	[	X
cana-943	277	17	20	20	NUM
cana-943	277	18	]	]	PUNCT
cana-943	277	19	.	.	PUNCT
cana-943	278	1	7	7	X
cana-943	278	2	.	.	NOUN
cana-943	278	3	comparative	comparative	ADJ
cana-943	278	4	analysis	analysis	NOUN
cana-943	278	5	and	and	CCONJ
cana-943	278	6	evaluation	evaluation	NOUN
cana-943	278	7	7.1	7.1	NUM
cana-943	278	8	.	.	PUNCT
cana-943	279	1	performance	performance	NOUN
cana-943	279	2	metrics	metric	NOUN
cana-943	279	3	7.1.1	7.1.1	NUM
cana-943	279	4	.	.	PUNCT
cana-943	279	5	computational	computational	ADJ
cana-943	279	6	efficiency	efficiency	NOUN
cana-943	279	7	computational	computational	ADJ
cana-943	279	8	efficiency	efficiency	NOUN
cana-943	279	9	is	be	AUX
cana-943	279	10	a	a	DET
cana-943	279	11	critical	critical	ADJ
cana-943	279	12	performance	performance	NOUN
cana-943	279	13	metric	metric	ADJ
cana-943	279	14	in	in	ADP
cana-943	279	15	cryptographic	cryptographic	ADJ
cana-943	279	16	systems	system	NOUN
cana-943	279	17	,	,	PUNCT
cana-943	279	18	reflecting	reflect	VERB
cana-943	279	19	how	how	SCONJ
cana-943	279	20	quickly	quickly	ADV
cana-943	279	21	encryption	encryption	NOUN
cana-943	279	22	,	,	PUNCT
cana-943	279	23	decryption	decryption	NOUN
cana-943	279	24	,	,	PUNCT
cana-943	279	25	and	and	CCONJ
cana-943	279	26	key	key	ADJ
cana-943	279	27	generation	generation	NOUN
cana-943	279	28	processes	process	NOUN
cana-943	279	29	can	can	AUX
cana-943	279	30	be	be	AUX
cana-943	279	31	performed	perform	VERB
cana-943	279	32	.	.	PUNCT
cana-943	280	1	efficient	efficient	ADJ
cana-943	280	2	algorithms	algorithm	NOUN
cana-943	280	3	are	be	AUX
cana-943	280	4	crucial	crucial	ADJ
cana-943	280	5	for	for	ADP
cana-943	280	6	applications	application	NOUN
cana-943	280	7	requiring	require	VERB
cana-943	280	8	real	real	ADJ
cana-943	280	9	-	-	PUNCT
cana-943	280	10	time	time	NOUN
cana-943	280	11	data	datum	NOUN
cana-943	280	12	processing	processing	NOUN
cana-943	280	13	and	and	CCONJ
cana-943	280	14	low	low	ADJ
cana-943	280	15	-	-	PUNCT
cana-943	280	16	latency	latency	NOUN
cana-943	280	17	communications	communication	NOUN
cana-943	280	18	.	.	PUNCT
cana-943	281	1	factors	factor	NOUN
cana-943	281	2	influencing	influence	VERB
cana-943	281	3	computational	computational	ADJ
cana-943	281	4	efficiency	efficiency	NOUN
cana-943	281	5	:	:	PUNCT
cana-943	281	6	1	1	X
cana-943	281	7	.	.	PUNCT
cana-943	281	8	algorithm	algorithm	NOUN
cana-943	281	9	complexity	complexity	NOUN
cana-943	281	10	:	:	PUNCT
cana-943	281	11	the	the	DET
cana-943	281	12	computational	computational	ADJ
cana-943	281	13	complexity	complexity	NOUN
cana-943	281	14	of	of	ADP
cana-943	281	15	the	the	DET
cana-943	281	16	algorithm	algorithm	NOUN
cana-943	281	17	determines	determine	VERB
cana-943	281	18	how	how	SCONJ
cana-943	281	19	resources	resource	NOUN
cana-943	281	20	(	(	PUNCT
cana-943	281	21	cpu	cpu	NOUN
cana-943	281	22	,	,	PUNCT
cana-943	281	23	memory	memory	NOUN
cana-943	281	24	)	)	PUNCT
cana-943	281	25	are	be	AUX
cana-943	281	26	utilized	utilize	VERB
cana-943	281	27	.	.	PUNCT
cana-943	282	1	for	for	ADP
cana-943	282	2	example	example	NOUN
cana-943	282	3	,	,	PUNCT
cana-943	282	4	elliptic	elliptic	ADJ
cana-943	282	5	curve	curve	NOUN
cana-943	282	6	cryptography	cryptography	NOUN
cana-943	282	7	(	(	PUNCT
cana-943	282	8	ecc	ecc	PROPN
cana-943	282	9	)	)	PUNCT
cana-943	282	10	is	be	AUX
cana-943	282	11	generally	generally	ADV
cana-943	282	12	more	more	ADV
cana-943	282	13	efficient	efficient	ADJ
cana-943	282	14	than	than	ADP
cana-943	282	15	rsa	rsa	PROPN
cana-943	282	16	due	due	ADP
cana-943	282	17	to	to	ADP
cana-943	282	18	its	its	PRON
cana-943	282	19	lower	low	ADJ
cana-943	282	20	key	key	ADJ
cana-943	282	21	size	size	NOUN
cana-943	282	22	requirements	requirement	NOUN
cana-943	282	23	for	for	ADP
cana-943	282	24	equivalent	equivalent	ADJ
cana-943	282	25	security	security	NOUN
cana-943	282	26	levels	level	NOUN
cana-943	282	27	[	[	X
cana-943	282	28	2	2	NUM
cana-943	282	29	]	]	PUNCT
cana-943	282	30	.	.	PUNCT
cana-943	283	1	communications	communication	NOUN
cana-943	283	2	on	on	ADP
cana-943	283	3	applied	apply	VERB
cana-943	283	4	nonlinear	nonlinear	ADJ
cana-943	283	5	analysis	analysis	NOUN
cana-943	283	6	issn	issn	NOUN
cana-943	283	7	:	:	PUNCT
cana-943	283	8	1074	1074	NUM
cana-943	283	9	-	-	PUNCT
cana-943	283	10	133x	133x	NUM
cana-943	283	11	vol	vol	NOUN
cana-943	283	12	31	31	NUM
cana-943	283	13	no	no	NOUN
cana-943	283	14	.	.	PUNCT
cana-943	284	1	4s	4s	NUM
cana-943	284	2	(	(	PUNCT
cana-943	284	3	2024	2024	NUM
cana-943	284	4	)	)	PUNCT
cana-943	284	5	479	479	NUM
cana-943	284	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	284	7	2	2	NUM
cana-943	284	8	.	.	PUNCT
cana-943	284	9	implementation	implementation	NOUN
cana-943	284	10	techniques	technique	NOUN
cana-943	284	11	:	:	PUNCT
cana-943	284	12	optimizations	optimization	NOUN
cana-943	284	13	at	at	ADP
cana-943	284	14	the	the	DET
cana-943	284	15	software	software	NOUN
cana-943	284	16	and	and	CCONJ
cana-943	284	17	hardware	hardware	NOUN
cana-943	284	18	levels	level	NOUN
cana-943	284	19	can	can	AUX
cana-943	284	20	significantly	significantly	ADV
cana-943	284	21	enhance	enhance	VERB
cana-943	284	22	performance	performance	NOUN
cana-943	284	23	.	.	PUNCT
cana-943	285	1	libraries	library	NOUN
cana-943	285	2	such	such	ADJ
cana-943	285	3	as	as	ADP
cana-943	285	4	openssl	openssl	ADJ
cana-943	285	5	and	and	CCONJ
cana-943	285	6	hardware	hardware	NOUN
cana-943	285	7	accelerators	accelerator	NOUN
cana-943	285	8	like	like	ADP
cana-943	285	9	intel	intel	PROPN
cana-943	285	10	's	's	PART
cana-943	285	11	aes	aes	PROPN
cana-943	285	12	-	-	PROPN
cana-943	285	13	ni	ni	PROPN
cana-943	285	14	instructions	instruction	NOUN
cana-943	285	15	play	play	VERB
cana-943	285	16	a	a	DET
cana-943	285	17	vital	vital	ADJ
cana-943	285	18	role	role	NOUN
cana-943	285	19	in	in	ADP
cana-943	285	20	boosting	boost	VERB
cana-943	285	21	efficiency	efficiency	NOUN
cana-943	285	22	.	.	PUNCT
cana-943	286	1	comparison	comparison	NOUN
cana-943	286	2	of	of	ADP
cana-943	286	3	algorithms	algorithm	NOUN
cana-943	286	4	:	:	PUNCT
cana-943	286	5	table	table	NOUN
cana-943	286	6	1	1	NUM
cana-943	286	7	:	:	PUNCT
cana-943	286	8	comparison	comparison	NOUN
cana-943	286	9	of	of	ADP
cana-943	286	10	computational	computational	ADJ
cana-943	286	11	efficiency	efficiency	NOUN
cana-943	286	12	of	of	ADP
cana-943	286	13	various	various	ADJ
cana-943	286	14	cryptographic	cryptographic	ADJ
cana-943	286	15	algorithms	algorithm	NOUN
cana-943	286	16	algorithm	algorithm	NOUN
cana-943	286	17	key	key	ADJ
cana-943	286	18	size	size	NOUN
cana-943	286	19	(	(	PUNCT
cana-943	286	20	bits	bits	NOUN
cana-943	286	21	)	)	PUNCT
cana-943	286	22	encryption	encryption	NOUN
cana-943	286	23	time	time	NOUN
cana-943	286	24	(	(	PUNCT
cana-943	286	25	ms	ms	NOUN
cana-943	286	26	)	)	PUNCT
cana-943	286	27	decryption	decryption	NOUN
cana-943	286	28	time	time	NOUN
cana-943	286	29	(	(	PUNCT
cana-943	286	30	ms	ms	NOUN
cana-943	286	31	)	)	PUNCT
cana-943	286	32	notes	note	VERB
cana-943	286	33	rsa	rsa	PROPN
cana-943	286	34	2048	2048	NUM
cana-943	286	35	0.5	0.5	NUM
cana-943	286	36	30	30	NUM
cana-943	286	37	high	high	ADJ
cana-943	286	38	decryption	decryption	NOUN
cana-943	286	39	time	time	NOUN
cana-943	286	40	ecc	ecc	PROPN
cana-943	286	41	256	256	NUM
cana-943	286	42	0.3	0.3	NUM
cana-943	286	43	0.5	0.5	NUM
cana-943	286	44	lower	low	ADJ
cana-943	286	45	key	key	ADJ
cana-943	286	46	size	size	NOUN
cana-943	286	47	,	,	PUNCT
cana-943	286	48	faster	fast	ADJ
cana-943	286	49	operations	operation	NOUN
cana-943	286	50	aes	aes	VERB
cana-943	286	51	256	256	NUM
cana-943	286	52	0.2	0.2	NUM
cana-943	286	53	0.2	0.2	NUM
cana-943	286	54	symmetric	symmetric	ADJ
cana-943	286	55	encryption	encryption	NOUN
cana-943	286	56	7.1.2	7.1.2	NUM
cana-943	286	57	.	.	PUNCT
cana-943	286	58	security	security	NOUN
cana-943	286	59	strength	strength	NOUN
cana-943	286	60	security	security	NOUN
cana-943	286	61	strength	strength	NOUN
cana-943	286	62	measures	measure	VERB
cana-943	286	63	the	the	DET
cana-943	286	64	robustness	robustness	NOUN
cana-943	286	65	of	of	ADP
cana-943	286	66	cryptographic	cryptographic	ADJ
cana-943	286	67	algorithms	algorithm	NOUN
cana-943	286	68	against	against	ADP
cana-943	286	69	various	various	ADJ
cana-943	286	70	types	type	NOUN
cana-943	286	71	of	of	ADP
cana-943	286	72	attacks	attack	NOUN
cana-943	286	73	,	,	PUNCT
cana-943	286	74	including	include	VERB
cana-943	286	75	brute	brute	ADJ
cana-943	286	76	force	force	NOUN
cana-943	286	77	,	,	PUNCT
cana-943	286	78	mathematical	mathematical	ADJ
cana-943	286	79	,	,	PUNCT
cana-943	286	80	and	and	CCONJ
cana-943	286	81	quantum	quantum	ADJ
cana-943	286	82	attacks	attack	NOUN
cana-943	286	83	.	.	PUNCT
cana-943	287	1	factors	factor	NOUN
cana-943	287	2	influencing	influence	VERB
cana-943	287	3	security	security	NOUN
cana-943	287	4	strength	strength	NOUN
cana-943	287	5	:	:	PUNCT
cana-943	287	6	1	1	X
cana-943	287	7	.	.	PUNCT
cana-943	287	8	key	key	ADJ
cana-943	287	9	size	size	NOUN
cana-943	287	10	:	:	PUNCT
cana-943	287	11	larger	large	ADJ
cana-943	287	12	key	key	ADJ
cana-943	287	13	sizes	size	NOUN
cana-943	287	14	generally	generally	ADV
cana-943	287	15	offer	offer	VERB
cana-943	287	16	higher	high	ADJ
cana-943	287	17	security	security	NOUN
cana-943	287	18	but	but	CCONJ
cana-943	287	19	at	at	ADP
cana-943	287	20	the	the	DET
cana-943	287	21	cost	cost	NOUN
cana-943	287	22	of	of	ADP
cana-943	287	23	increased	increase	VERB
cana-943	287	24	computational	computational	ADJ
cana-943	287	25	requirements	requirement	NOUN
cana-943	287	26	.	.	PUNCT
cana-943	288	1	2	2	X
cana-943	288	2	.	.	X
cana-943	288	3	algorithm	algorithm	NOUN
cana-943	288	4	design	design	PROPN
cana-943	288	5	:	:	PUNCT
cana-943	288	6	the	the	DET
cana-943	288	7	inherent	inherent	ADJ
cana-943	288	8	security	security	NOUN
cana-943	288	9	features	feature	NOUN
cana-943	288	10	and	and	CCONJ
cana-943	288	11	resistance	resistance	NOUN
cana-943	288	12	to	to	ADP
cana-943	288	13	known	know	VERB
cana-943	288	14	attack	attack	NOUN
cana-943	288	15	vectors	vector	NOUN
cana-943	288	16	define	define	VERB
cana-943	288	17	the	the	DET
cana-943	288	18	strength	strength	NOUN
cana-943	288	19	of	of	ADP
cana-943	288	20	an	an	DET
cana-943	288	21	algorithm	algorithm	NOUN
cana-943	288	22	.	.	PUNCT
cana-943	289	1	comparison	comparison	NOUN
cana-943	289	2	of	of	ADP
cana-943	289	3	security	security	NOUN
cana-943	289	4	strength	strength	NOUN
cana-943	289	5	:	:	PUNCT
cana-943	289	6	table	table	NOUN
cana-943	289	7	2	2	NUM
cana-943	289	8	:	:	PUNCT
cana-943	289	9	comparison	comparison	NOUN
cana-943	289	10	of	of	ADP
cana-943	289	11	security	security	NOUN
cana-943	289	12	strength	strength	NOUN
cana-943	289	13	of	of	ADP
cana-943	289	14	various	various	ADJ
cana-943	289	15	cryptographic	cryptographic	ADJ
cana-943	289	16	algorithms	algorithm	NOUN
cana-943	289	17	algorithm	algorithm	NOUN
cana-943	289	18	key	key	ADJ
cana-943	289	19	size	size	NOUN
cana-943	289	20	(	(	PUNCT
cana-943	289	21	bits	bits	NOUN
cana-943	289	22	)	)	PUNCT
cana-943	289	23	security	security	NOUN
cana-943	289	24	level	level	NOUN
cana-943	289	25	quantum	quantum	NOUN
cana-943	289	26	resistance	resistance	NOUN
cana-943	289	27	rsa	rsa	PROPN
cana-943	289	28	2048	2048	NUM
cana-943	289	29	moderate	moderate	ADJ
cana-943	289	30	no	no	DET
cana-943	289	31	ecc	ecc	PROPN
cana-943	289	32	256	256	NUM
cana-943	289	33	high	high	ADJ
cana-943	289	34	no	no	DET
cana-943	289	35	aes	aes	NOUN
cana-943	289	36	256	256	NUM
cana-943	289	37	very	very	ADV
cana-943	289	38	high	high	ADJ
cana-943	289	39	yes	yes	INTJ
cana-943	289	40	(	(	PUNCT
cana-943	289	41	with	with	ADP
cana-943	289	42	larger	large	ADJ
cana-943	289	43	keys	key	NOUN
cana-943	289	44	)	)	PUNCT
cana-943	289	45	lattice	lattice	NOUN
cana-943	289	46	-	-	PUNCT
cana-943	289	47	based	base	VERB
cana-943	289	48	1024	1024	NUM
cana-943	289	49	(	(	PUNCT
cana-943	289	50	approx	approx	PROPN
cana-943	289	51	)	)	PUNCT
cana-943	289	52	very	very	ADV
cana-943	289	53	high	high	ADV
cana-943	290	1	yes	yes	INTJ
cana-943	290	2	7.2	7.2	NUM
cana-943	290	3	.	.	PUNCT
cana-943	291	1	comparative	comparative	ADJ
cana-943	291	2	study	study	NOUN
cana-943	291	3	of	of	ADP
cana-943	291	4	algebraic	algebraic	PROPN
cana-943	291	5	vs	vs	ADP
cana-943	291	6	non	non	ADJ
cana-943	291	7	-	-	ADJ
cana-943	291	8	algebraic	algebraic	ADJ
cana-943	291	9	techniques	technique	NOUN
cana-943	291	10	7.2.1	7.2.1	NUM
cana-943	291	11	.	.	PUNCT
cana-943	292	1	algebraic	algebraic	ADJ
cana-943	292	2	techniques	technique	NOUN
cana-943	292	3	algebraic	algebraic	ADJ
cana-943	292	4	techniques	technique	NOUN
cana-943	292	5	in	in	ADP
cana-943	292	6	cryptography	cryptography	NOUN
cana-943	292	7	leverage	leverage	NOUN
cana-943	292	8	mathematical	mathematical	ADJ
cana-943	292	9	structures	structure	NOUN
cana-943	292	10	such	such	ADJ
cana-943	292	11	as	as	ADP
cana-943	292	12	groups	group	NOUN
cana-943	292	13	,	,	PUNCT
cana-943	292	14	rings	ring	NOUN
cana-943	292	15	,	,	PUNCT
cana-943	292	16	and	and	CCONJ
cana-943	292	17	fields	field	NOUN
cana-943	292	18	to	to	PART
cana-943	292	19	design	design	VERB
cana-943	292	20	secure	secure	ADJ
cana-943	292	21	systems	system	NOUN
cana-943	292	22	.	.	PUNCT
cana-943	293	1	examples	example	NOUN
cana-943	293	2	include	include	VERB
cana-943	293	3	rsa	rsa	PROPN
cana-943	293	4	,	,	PUNCT
cana-943	293	5	ecc	ecc	PROPN
cana-943	293	6	,	,	PUNCT
cana-943	293	7	and	and	CCONJ
cana-943	293	8	lattice	lattice	NOUN
cana-943	293	9	-	-	PUNCT
cana-943	293	10	based	base	VERB
cana-943	293	11	cryptography	cryptography	NOUN
cana-943	293	12	.	.	PUNCT
cana-943	294	1	advantages	advantage	NOUN
cana-943	294	2	:	:	PUNCT
cana-943	294	3	1	1	X
cana-943	294	4	.	.	X
cana-943	294	5	mathematical	mathematical	ADJ
cana-943	294	6	rigor	rigor	NOUN
cana-943	294	7	:	:	PUNCT
cana-943	294	8	provides	provide	VERB
cana-943	294	9	strong	strong	ADJ
cana-943	294	10	theoretical	theoretical	ADJ
cana-943	294	11	foundations	foundation	NOUN
cana-943	294	12	and	and	CCONJ
cana-943	294	13	provable	provable	ADJ
cana-943	294	14	security	security	NOUN
cana-943	294	15	properties	property	NOUN
cana-943	294	16	[	[	X
cana-943	294	17	3	3	NUM
cana-943	294	18	]	]	PUNCT
cana-943	294	19	.	.	PUNCT
cana-943	295	1	2	2	X
cana-943	295	2	.	.	X
cana-943	295	3	efficiency	efficiency	NOUN
cana-943	295	4	:	:	PUNCT
cana-943	295	5	many	many	ADJ
cana-943	295	6	algebraic	algebraic	ADJ
cana-943	295	7	techniques	technique	NOUN
cana-943	295	8	offer	offer	VERB
cana-943	295	9	efficient	efficient	ADJ
cana-943	295	10	implementations	implementation	NOUN
cana-943	295	11	for	for	ADP
cana-943	295	12	both	both	DET
cana-943	295	13	software	software	NOUN
cana-943	295	14	and	and	CCONJ
cana-943	295	15	hardware	hardware	NOUN
cana-943	295	16	.	.	PUNCT
cana-943	296	1	communications	communication	NOUN
cana-943	296	2	on	on	ADP
cana-943	296	3	applied	apply	VERB
cana-943	296	4	nonlinear	nonlinear	ADJ
cana-943	296	5	analysis	analysis	NOUN
cana-943	296	6	issn	issn	NOUN
cana-943	296	7	:	:	PUNCT
cana-943	296	8	1074	1074	NUM
cana-943	296	9	-	-	PUNCT
cana-943	296	10	133x	133x	NUM
cana-943	296	11	vol	vol	NOUN
cana-943	296	12	31	31	NUM
cana-943	296	13	no	no	NOUN
cana-943	296	14	.	.	PUNCT
cana-943	297	1	4s	4s	NUM
cana-943	297	2	(	(	PUNCT
cana-943	297	3	2024	2024	NUM
cana-943	297	4	)	)	PUNCT
cana-943	297	5	480	480	NUM
cana-943	298	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	298	2	disadvantages	disadvantage	VERB
cana-943	298	3	:	:	PUNCT
cana-943	298	4	1	1	X
cana-943	298	5	.	.	X
cana-943	298	6	complexity	complexity	NOUN
cana-943	298	7	:	:	PUNCT
cana-943	298	8	requires	require	VERB
cana-943	298	9	a	a	DET
cana-943	298	10	deep	deep	ADJ
cana-943	298	11	understanding	understanding	NOUN
cana-943	298	12	of	of	ADP
cana-943	298	13	abstract	abstract	ADJ
cana-943	298	14	algebra	algebra	NOUN
cana-943	298	15	and	and	CCONJ
cana-943	298	16	number	number	NOUN
cana-943	298	17	theory	theory	NOUN
cana-943	298	18	.	.	PUNCT
cana-943	299	1	2	2	X
cana-943	299	2	.	.	PUNCT
cana-943	299	3	quantum	quantum	ADJ
cana-943	299	4	vulnerability	vulnerability	NOUN
cana-943	299	5	:	:	PUNCT
cana-943	299	6	some	some	DET
cana-943	299	7	algebraic	algebraic	ADJ
cana-943	299	8	techniques	technique	NOUN
cana-943	299	9	(	(	PUNCT
cana-943	299	10	e.g.	e.g.	ADV
cana-943	299	11	,	,	PUNCT
cana-943	299	12	rsa	rsa	PROPN
cana-943	299	13	,	,	PUNCT
cana-943	299	14	ecc	ecc	PROPN
cana-943	299	15	)	)	PUNCT
cana-943	299	16	are	be	AUX
cana-943	299	17	vulnerable	vulnerable	ADJ
cana-943	299	18	to	to	ADP
cana-943	299	19	quantum	quantum	ADJ
cana-943	299	20	attacks	attack	NOUN
cana-943	299	21	[	[	X
cana-943	299	22	18	18	NUM
cana-943	299	23	]	]	PUNCT
cana-943	299	24	.	.	PUNCT
cana-943	300	1	7.2.2	7.2.2	NUM
cana-943	300	2	.	.	PUNCT
cana-943	301	1	non	non	ADJ
cana-943	301	2	-	-	ADJ
cana-943	301	3	algebraic	algebraic	ADJ
cana-943	301	4	techniques	technique	NOUN
cana-943	301	5	non	non	ADJ
cana-943	301	6	-	-	ADJ
cana-943	301	7	algebraic	algebraic	ADJ
cana-943	301	8	techniques	technique	NOUN
cana-943	301	9	rely	rely	VERB
cana-943	301	10	on	on	ADP
cana-943	301	11	other	other	ADJ
cana-943	301	12	principles	principle	NOUN
cana-943	301	13	such	such	ADJ
cana-943	301	14	as	as	ADP
cana-943	301	15	heuristic	heuristic	ADJ
cana-943	301	16	or	or	CCONJ
cana-943	301	17	ad	ad	NOUN
cana-943	301	18	-	-	PUNCT
cana-943	301	19	hoc	hoc	ADJ
cana-943	301	20	methods	method	NOUN
cana-943	301	21	for	for	ADP
cana-943	301	22	securing	secure	VERB
cana-943	301	23	data	datum	NOUN
cana-943	301	24	.	.	PUNCT
cana-943	302	1	examples	example	NOUN
cana-943	302	2	include	include	VERB
cana-943	302	3	stream	stream	NOUN
cana-943	302	4	ciphers	cipher	NOUN
cana-943	302	5	and	and	CCONJ
cana-943	302	6	symmetric	symmetric	ADJ
cana-943	302	7	key	key	ADJ
cana-943	302	8	algorithms	algorithm	NOUN
cana-943	302	9	not	not	PART
cana-943	302	10	based	base	VERB
cana-943	302	11	on	on	ADP
cana-943	302	12	algebraic	algebraic	ADJ
cana-943	302	13	structures	structure	NOUN
cana-943	302	14	.	.	PUNCT
cana-943	303	1	advantages	advantage	NOUN
cana-943	303	2	:	:	PUNCT
cana-943	303	3	1	1	X
cana-943	303	4	.	.	X
cana-943	303	5	simplicity	simplicity	NOUN
cana-943	303	6	:	:	PUNCT
cana-943	303	7	often	often	ADV
cana-943	303	8	easier	easy	ADJ
cana-943	303	9	to	to	PART
cana-943	303	10	implement	implement	VERB
cana-943	303	11	and	and	CCONJ
cana-943	303	12	understand	understand	VERB
cana-943	303	13	.	.	PUNCT
cana-943	304	1	2	2	X
cana-943	304	2	.	.	X
cana-943	304	3	speed	speed	NOUN
cana-943	304	4	:	:	PUNCT
cana-943	304	5	generally	generally	ADV
cana-943	304	6	faster	fast	ADV
cana-943	304	7	due	due	ADJ
cana-943	304	8	to	to	ADP
cana-943	304	9	simpler	simple	ADJ
cana-943	304	10	mathematical	mathematical	ADJ
cana-943	304	11	operations	operation	NOUN
cana-943	304	12	.	.	PUNCT
cana-943	305	1	disadvantages	disadvantage	VERB
cana-943	305	2	:	:	PUNCT
cana-943	306	1	1	1	X
cana-943	306	2	.	.	X
cana-943	307	1	security	security	NOUN
cana-943	307	2	:	:	PUNCT
cana-943	307	3	may	may	AUX
cana-943	307	4	lack	lack	VERB
cana-943	307	5	the	the	DET
cana-943	307	6	theoretical	theoretical	ADJ
cana-943	307	7	guarantees	guarantee	NOUN
cana-943	307	8	provided	provide	VERB
cana-943	307	9	by	by	ADP
cana-943	307	10	algebraic	algebraic	ADJ
cana-943	307	11	methods	method	NOUN
cana-943	307	12	.	.	PUNCT
cana-943	308	1	2	2	X
cana-943	308	2	.	.	X
cana-943	308	3	scalability	scalability	NOUN
cana-943	308	4	:	:	PUNCT
cana-943	308	5	can	can	AUX
cana-943	308	6	be	be	AUX
cana-943	308	7	less	less	ADV
cana-943	308	8	adaptable	adaptable	ADJ
cana-943	308	9	to	to	ADP
cana-943	308	10	new	new	ADJ
cana-943	308	11	threats	threat	NOUN
cana-943	308	12	and	and	CCONJ
cana-943	308	13	larger	large	ADJ
cana-943	308	14	key	key	ADJ
cana-943	308	15	sizes	size	NOUN
cana-943	308	16	.	.	PUNCT
cana-943	309	1	performance	performance	NOUN
cana-943	309	2	comparison	comparison	NOUN
cana-943	309	3	:	:	PUNCT
cana-943	309	4	table	table	NOUN
cana-943	309	5	3	3	NUM
cana-943	309	6	:	:	PUNCT
cana-943	309	7	comparative	comparative	ADJ
cana-943	309	8	analysis	analysis	NOUN
cana-943	309	9	of	of	ADP
cana-943	309	10	algebraic	algebraic	PROPN
cana-943	309	11	vs	vs	ADP
cana-943	309	12	non	non	ADJ
cana-943	309	13	-	-	ADJ
cana-943	309	14	algebraic	algebraic	ADJ
cana-943	309	15	cryptographic	cryptographic	ADJ
cana-943	309	16	techniques	technique	NOUN
cana-943	309	17	metric	metric	ADJ
cana-943	309	18	algebraic	algebraic	PROPN
cana-943	309	19	techniques	technique	NOUN
cana-943	309	20	non	non	ADJ
cana-943	309	21	-	-	ADJ
cana-943	309	22	algebraic	algebraic	ADJ
cana-943	309	23	techniques	technique	NOUN
cana-943	309	24	computational	computational	ADJ
cana-943	309	25	efficiency	efficiency	NOUN
cana-943	309	26	high	high	ADJ
cana-943	309	27	(	(	PUNCT
cana-943	309	28	e.g.	e.g.	ADV
cana-943	309	29	,	,	PUNCT
cana-943	309	30	ecc	ecc	PROPN
cana-943	309	31	,	,	PUNCT
cana-943	309	32	lattice	lattice	NOUN
cana-943	309	33	)	)	PUNCT
cana-943	309	34	very	very	ADV
cana-943	309	35	high	high	ADJ
cana-943	309	36	(	(	PUNCT
cana-943	309	37	e.g.	e.g.	ADV
cana-943	309	38	,	,	PUNCT
cana-943	309	39	aes	aes	NOUN
cana-943	309	40	)	)	PUNCT
cana-943	309	41	security	security	NOUN
cana-943	309	42	strength	strength	NOUN
cana-943	309	43	high	high	ADJ
cana-943	309	44	(	(	PUNCT
cana-943	309	45	with	with	ADP
cana-943	309	46	provable	provable	ADJ
cana-943	309	47	security	security	NOUN
cana-943	309	48	)	)	PUNCT
cana-943	309	49	moderate	moderate	ADJ
cana-943	309	50	to	to	ADP
cana-943	309	51	high	high	ADJ
cana-943	309	52	quantum	quantum	NOUN
cana-943	309	53	resistance	resistance	NOUN
cana-943	309	54	limited	limit	VERB
cana-943	309	55	(	(	PUNCT
cana-943	309	56	except	except	SCONJ
cana-943	309	57	lattice	lattice	PROPN
cana-943	309	58	)	)	PUNCT
cana-943	309	59	varies	vary	VERB
cana-943	309	60	(	(	PUNCT
cana-943	309	61	dependent	dependent	ADJ
cana-943	309	62	on	on	ADP
cana-943	309	63	method	method	NOUN
cana-943	309	64	)	)	PUNCT
cana-943	309	65	7.3	7.3	NUM
cana-943	309	66	.	.	PUNCT
cana-943	310	1	real	real	ADJ
cana-943	310	2	-	-	PUNCT
cana-943	310	3	world	world	NOUN
cana-943	310	4	case	case	NOUN
cana-943	310	5	study	study	NOUN
cana-943	310	6	comparisons	comparison	NOUN
cana-943	310	7	7.3.1	7.3.1	NUM
cana-943	310	8	.	.	PUNCT
cana-943	311	1	case	case	NOUN
cana-943	311	2	study	study	NOUN
cana-943	311	3	1	1	NUM
cana-943	311	4	:	:	PUNCT
cana-943	311	5	secure	secure	VERB
cana-943	311	6	communications	communication	NOUN
cana-943	311	7	(	(	PUNCT
cana-943	311	8	tls	tls	PROPN
cana-943	311	9	/	/	SYM
cana-943	311	10	ssl	ssl	ADJ
cana-943	311	11	)	)	PUNCT
cana-943	311	12	ssl	ssl	PROPN
cana-943	311	13	/	/	SYM
cana-943	311	14	tls	tls	PROPN
cana-943	311	15	protocols	protocol	NOUN
cana-943	311	16	predominantly	predominantly	ADV
cana-943	311	17	use	use	VERB
cana-943	311	18	algebraic	algebraic	ADJ
cana-943	311	19	techniques	technique	NOUN
cana-943	311	20	such	such	ADJ
cana-943	311	21	as	as	ADP
cana-943	311	22	rsa	rsa	PROPN
cana-943	311	23	and	and	CCONJ
cana-943	311	24	ecc	ecc	PROPN
cana-943	311	25	for	for	ADP
cana-943	311	26	key	key	ADJ
cana-943	311	27	exchange	exchange	NOUN
cana-943	311	28	.	.	PUNCT
cana-943	312	1	the	the	DET
cana-943	312	2	shift	shift	NOUN
cana-943	312	3	from	from	ADP
cana-943	312	4	rsa	rsa	PROPN
cana-943	312	5	to	to	ADP
cana-943	312	6	ecc	ecc	PROPN
cana-943	312	7	in	in	ADP
cana-943	312	8	recent	recent	ADJ
cana-943	312	9	years	year	NOUN
cana-943	312	10	has	have	AUX
cana-943	312	11	enhanced	enhance	VERB
cana-943	312	12	both	both	DET
cana-943	312	13	security	security	NOUN
cana-943	312	14	and	and	CCONJ
cana-943	312	15	computational	computational	ADJ
cana-943	312	16	efficiency	efficiency	NOUN
cana-943	312	17	.	.	PUNCT
cana-943	313	1	graph	graph	NOUN
cana-943	313	2	1	1	NUM
cana-943	313	3	:	:	PUNCT
cana-943	313	4	performance	performance	NOUN
cana-943	313	5	of	of	ADP
cana-943	313	6	rsa	rsa	PROPN
cana-943	313	7	vs	vs	ADP
cana-943	313	8	ecc	ecc	PROPN
cana-943	313	9	in	in	ADP
cana-943	313	10	tls	tls	PROPN
cana-943	313	11	handshakes.the	handshakes.the	DET
cana-943	313	12	graph	graph	NOUN
cana-943	313	13	compares	compare	VERB
cana-943	313	14	the	the	DET
cana-943	313	15	performance	performance	NOUN
cana-943	313	16	of	of	ADP
cana-943	313	17	rsa	rsa	PROPN
cana-943	313	18	and	and	CCONJ
cana-943	313	19	ecc	ecc	PROPN
cana-943	313	20	algorithms	algorithm	NOUN
cana-943	313	21	in	in	ADP
cana-943	313	22	terms	term	NOUN
cana-943	313	23	of	of	ADP
cana-943	313	24	handshake	handshake	ADJ
cana-943	313	25	time	time	NOUN
cana-943	313	26	and	and	CCONJ
cana-943	313	27	cpu	cpu	VERB
cana-943	313	28	usage	usage	NOUN
cana-943	313	29	during	during	ADP
cana-943	313	30	tls	tls	PROPN
cana-943	313	31	handshakes	handshake	NOUN
cana-943	313	32	.	.	PUNCT
cana-943	314	1	rsa	rsa	PROPN
cana-943	314	2	has	have	VERB
cana-943	314	3	a	a	DET
cana-943	314	4	higher	high	ADJ
cana-943	314	5	handshake	handshake	ADJ
cana-943	314	6	time	time	NOUN
cana-943	314	7	of	of	ADP
cana-943	314	8	0.5	0.5	NUM
cana-943	314	9	milliseconds	millisecond	NOUN
cana-943	314	10	and	and	CCONJ
cana-943	314	11	higher	high	ADJ
cana-943	314	12	cpu	cpu	NOUN
cana-943	314	13	usage	usage	NOUN
cana-943	314	14	at	at	ADP
cana-943	314	15	30	30	NUM
cana-943	314	16	%	%	NOUN
cana-943	314	17	,	,	PUNCT
cana-943	314	18	while	while	SCONJ
cana-943	314	19	ecc	ecc	PROPN
cana-943	314	20	shows	show	VERB
cana-943	314	21	improved	improved	ADJ
cana-943	314	22	performance	performance	NOUN
cana-943	314	23	with	with	ADP
cana-943	314	24	a	a	DET
cana-943	314	25	lower	low	ADJ
cana-943	314	26	handshake	handshake	ADJ
cana-943	314	27	time	time	NOUN
cana-943	314	28	of	of	ADP
cana-943	314	29	0.3	0.3	NUM
cana-943	314	30	milliseconds	millisecond	NOUN
cana-943	314	31	and	and	CCONJ
cana-943	314	32	reduced	reduce	VERB
cana-943	314	33	cpu	cpu	NOUN
cana-943	314	34	usage	usage	NOUN
cana-943	314	35	at	at	ADP
cana-943	314	36	15	15	NUM
cana-943	314	37	%	%	NOUN
cana-943	314	38	.	.	PUNCT
cana-943	315	1	this	this	DET
cana-943	315	2	visual	visual	ADJ
cana-943	315	3	representation	representation	NOUN
cana-943	315	4	highlights	highlight	VERB
cana-943	315	5	the	the	DET
cana-943	315	6	efficiency	efficiency	NOUN
cana-943	315	7	advantages	advantage	NOUN
cana-943	315	8	of	of	ADP
cana-943	315	9	ecc	ecc	PROPN
cana-943	315	10	over	over	ADP
cana-943	315	11	rsa	rsa	PROPN
cana-943	315	12	in	in	ADP
cana-943	315	13	tls	tls	PROPN
cana-943	315	14	handshakes	handshake	NOUN
cana-943	315	15	,	,	PUNCT
cana-943	315	16	supporting	support	VERB
cana-943	315	17	the	the	DET
cana-943	315	18	discussion	discussion	NOUN
cana-943	315	19	in	in	ADP
cana-943	315	20	the	the	DET
cana-943	315	21	"	"	PUNCT
cana-943	315	22	secure	secure	ADJ
cana-943	315	23	communications	communication	NOUN
cana-943	315	24	"	"	PUNCT
cana-943	315	25	section	section	NOUN
cana-943	315	26	.	.	PUNCT
cana-943	316	1	communications	communication	NOUN
cana-943	316	2	on	on	ADP
cana-943	316	3	applied	apply	VERB
cana-943	316	4	nonlinear	nonlinear	ADJ
cana-943	316	5	analysis	analysis	NOUN
cana-943	316	6	issn	issn	NOUN
cana-943	316	7	:	:	PUNCT
cana-943	316	8	1074	1074	NUM
cana-943	316	9	-	-	PUNCT
cana-943	316	10	133x	133x	NUM
cana-943	316	11	vol	vol	NOUN
cana-943	316	12	31	31	NUM
cana-943	316	13	no	no	NOUN
cana-943	316	14	.	.	PUNCT
cana-943	317	1	4s	4s	NUM
cana-943	317	2	(	(	PUNCT
cana-943	317	3	2024	2024	NUM
cana-943	317	4	)	)	PUNCT
cana-943	317	5	481	481	NUM
cana-943	317	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	317	7	graph	graph	NOUN
cana-943	317	8	1	1	NUM
cana-943	317	9	:	:	PUNCT
cana-943	317	10	performance	performance	NOUN
cana-943	317	11	of	of	ADP
cana-943	317	12	rsa	rsa	PROPN
cana-943	317	13	vs	vs	ADP
cana-943	317	14	ecc	ecc	PROPN
cana-943	317	15	in	in	ADP
cana-943	317	16	tls	tls	PROPN
cana-943	317	17	handshakes	handshake	VERB
cana-943	317	18	7.3.2	7.3.2	NUM
cana-943	317	19	.	.	PUNCT
cana-943	318	1	case	case	NOUN
cana-943	318	2	study	study	NOUN
cana-943	318	3	2	2	NUM
cana-943	318	4	:	:	PUNCT
cana-943	318	5	blockchain	blockchain	PROPN
cana-943	318	6	and	and	CCONJ
cana-943	318	7	cryptocurrencies	cryptocurrencie	NOUN
cana-943	318	8	bitcoin	bitcoin	PROPN
cana-943	318	9	and	and	CCONJ
cana-943	318	10	ethereum	ethereum	NOUN
cana-943	318	11	leverage	leverage	NOUN
cana-943	318	12	cryptographic	cryptographic	ADJ
cana-943	318	13	hash	hash	NOUN
cana-943	318	14	functions	function	NOUN
cana-943	318	15	and	and	CCONJ
cana-943	318	16	digital	digital	ADJ
cana-943	318	17	signatures	signature	NOUN
cana-943	318	18	.	.	PUNCT
cana-943	319	1	bitcoin	bitcoin	PROPN
cana-943	319	2	uses	use	VERB
cana-943	319	3	ecc	ecc	PROPN
cana-943	319	4	(	(	PUNCT
cana-943	319	5	specifically	specifically	ADV
cana-943	319	6	ecdsa	ecdsa	PROPN
cana-943	319	7	)	)	PUNCT
cana-943	319	8	for	for	ADP
cana-943	319	9	transaction	transaction	NOUN
cana-943	319	10	verification	verification	NOUN
cana-943	319	11	,	,	PUNCT
cana-943	319	12	while	while	SCONJ
cana-943	319	13	ethereum	ethereum	NOUN
cana-943	319	14	uses	use	VERB
cana-943	319	15	keccak-256	keccak-256	ADJ
cana-943	319	16	for	for	ADP
cana-943	319	17	hashing	hashing	NOUN
cana-943	319	18	and	and	CCONJ
cana-943	319	19	similar	similar	ADJ
cana-943	319	20	ecc	ecc	PROPN
cana-943	319	21	-	-	PUNCT
cana-943	319	22	based	base	VERB
cana-943	319	23	signatures	signature	NOUN
cana-943	319	24	.	.	PUNCT
cana-943	320	1	graph	graph	NOUN
cana-943	320	2	2	2	NUM
cana-943	320	3	:	:	PUNCT
cana-943	320	4	computational	computational	ADJ
cana-943	320	5	load	load	NOUN
cana-943	320	6	in	in	ADP
cana-943	320	7	bitcoin	bitcoin	NOUN
cana-943	320	8	vs	vs	ADP
cana-943	320	9	ethereum	ethereum	NOUN
cana-943	320	10	transactions	transaction	NOUN
cana-943	320	11	the	the	DET
cana-943	320	12	graph	graph	NOUN
cana-943	320	13	compares	compare	VERB
cana-943	320	14	the	the	DET
cana-943	320	15	computational	computational	ADJ
cana-943	320	16	load	load	NOUN
cana-943	320	17	of	of	ADP
cana-943	320	18	bitcoin	bitcoin	ADJ
cana-943	320	19	and	and	CCONJ
cana-943	320	20	ethereum	ethereum	NOUN
cana-943	320	21	transactions	transaction	NOUN
cana-943	320	22	in	in	ADP
cana-943	320	23	terms	term	NOUN
cana-943	320	24	of	of	ADP
cana-943	320	25	transaction	transaction	NOUN
cana-943	320	26	time	time	NOUN
cana-943	320	27	and	and	CCONJ
cana-943	320	28	energy	energy	NOUN
cana-943	320	29	usage	usage	NOUN
cana-943	320	30	.	.	PUNCT
cana-943	321	1	bitcoin	bitcoin	NOUN
cana-943	321	2	transactions	transaction	NOUN
cana-943	321	3	have	have	VERB
cana-943	321	4	a	a	DET
cana-943	321	5	higher	high	ADJ
cana-943	321	6	transaction	transaction	NOUN
cana-943	321	7	time	time	NOUN
cana-943	321	8	of	of	ADP
cana-943	321	9	10	10	NUM
cana-943	321	10	seconds	second	NOUN
cana-943	321	11	and	and	CCONJ
cana-943	321	12	energy	energy	NOUN
cana-943	321	13	usage	usage	NOUN
cana-943	321	14	of	of	ADP
cana-943	321	15	120	120	NUM
cana-943	321	16	watts	watt	NOUN
cana-943	321	17	,	,	PUNCT
cana-943	321	18	whereas	whereas	SCONJ
cana-943	321	19	ethereum	ethereum	NOUN
cana-943	321	20	transactions	transaction	NOUN
cana-943	321	21	show	show	VERB
cana-943	321	22	improved	improved	ADJ
cana-943	321	23	performance	performance	NOUN
cana-943	321	24	with	with	ADP
cana-943	321	25	a	a	DET
cana-943	321	26	lower	low	ADJ
cana-943	321	27	transaction	transaction	NOUN
cana-943	321	28	time	time	NOUN
cana-943	321	29	of	of	ADP
cana-943	321	30	5	5	NUM
cana-943	321	31	seconds	second	NOUN
cana-943	321	32	and	and	CCONJ
cana-943	321	33	reduced	reduce	VERB
cana-943	321	34	energy	energy	NOUN
cana-943	321	35	usage	usage	NOUN
cana-943	321	36	of	of	ADP
cana-943	321	37	80	80	NUM
cana-943	321	38	watts	watt	NOUN
cana-943	321	39	.	.	PUNCT
cana-943	322	1	this	this	DET
cana-943	322	2	visual	visual	ADJ
cana-943	322	3	representation	representation	NOUN
cana-943	322	4	highlights	highlight	VERB
cana-943	322	5	the	the	DET
cana-943	322	6	efficiency	efficiency	NOUN
cana-943	322	7	advantages	advantage	NOUN
cana-943	322	8	of	of	ADP
cana-943	322	9	ethereum	ethereum	NOUN
cana-943	322	10	over	over	ADP
cana-943	322	11	bitcoin	bitcoin	NOUN
cana-943	322	12	in	in	ADP
cana-943	322	13	transaction	transaction	NOUN
cana-943	322	14	processing	processing	NOUN
cana-943	322	15	,	,	PUNCT
cana-943	322	16	supporting	support	VERB
cana-943	322	17	the	the	DET
cana-943	322	18	discussion	discussion	NOUN
cana-943	322	19	in	in	ADP
cana-943	322	20	the	the	DET
cana-943	322	21	"	"	PUNCT
cana-943	322	22	blockchain	blockchain	NOUN
cana-943	322	23	and	and	CCONJ
cana-943	322	24	cryptocurrencies	cryptocurrencie	NOUN
cana-943	322	25	"	"	PUNCT
cana-943	322	26	section	section	NOUN
cana-943	322	27	.	.	PUNCT
cana-943	323	1	communications	communication	NOUN
cana-943	323	2	on	on	ADP
cana-943	323	3	applied	apply	VERB
cana-943	323	4	nonlinear	nonlinear	ADJ
cana-943	323	5	analysis	analysis	NOUN
cana-943	323	6	issn	issn	NOUN
cana-943	323	7	:	:	PUNCT
cana-943	323	8	1074	1074	NUM
cana-943	323	9	-	-	PUNCT
cana-943	323	10	133x	133x	NUM
cana-943	323	11	vol	vol	NOUN
cana-943	323	12	31	31	NUM
cana-943	323	13	no	no	NOUN
cana-943	323	14	.	.	PUNCT
cana-943	324	1	4s	4s	NUM
cana-943	324	2	(	(	PUNCT
cana-943	324	3	2024	2024	NUM
cana-943	324	4	)	)	PUNCT
cana-943	324	5	482	482	NUM
cana-943	324	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	324	7	7.3.3	7.3.3	NUM
cana-943	324	8	.	.	PUNCT
cana-943	325	1	case	case	NOUN
cana-943	325	2	study	study	NOUN
cana-943	325	3	3	3	NUM
cana-943	325	4	:	:	PUNCT
cana-943	325	5	data	datum	NOUN
cana-943	325	6	privacy	privacy	NOUN
cana-943	325	7	and	and	CCONJ
cana-943	325	8	secure	secure	VERB
cana-943	325	9	storage	storage	NOUN
cana-943	325	10	cloud	cloud	NOUN
cana-943	325	11	storage	storage	NOUN
cana-943	325	12	services	service	NOUN
cana-943	325	13	utilize	utilize	VERB
cana-943	325	14	a	a	DET
cana-943	325	15	combination	combination	NOUN
cana-943	325	16	of	of	ADP
cana-943	325	17	symmetric	symmetric	ADJ
cana-943	325	18	and	and	CCONJ
cana-943	325	19	asymmetric	asymmetric	ADJ
cana-943	325	20	encryption	encryption	NOUN
cana-943	325	21	.	.	PUNCT
cana-943	326	1	aes	aes	PROPN
cana-943	326	2	(	(	PUNCT
cana-943	326	3	a	a	DET
cana-943	326	4	nonalgebraic	nonalgebraic	ADJ
cana-943	326	5	technique	technique	NOUN
cana-943	326	6	)	)	PUNCT
cana-943	326	7	is	be	AUX
cana-943	326	8	widely	widely	ADV
cana-943	326	9	used	use	VERB
cana-943	326	10	for	for	ADP
cana-943	326	11	its	its	PRON
cana-943	326	12	speed	speed	NOUN
cana-943	326	13	and	and	CCONJ
cana-943	326	14	security	security	NOUN
cana-943	326	15	.	.	PUNCT
cana-943	327	1	however	however	ADV
cana-943	327	2	,	,	PUNCT
cana-943	327	3	public	public	ADJ
cana-943	327	4	key	key	ADJ
cana-943	327	5	encryption	encryption	NOUN
cana-943	327	6	(	(	PUNCT
cana-943	327	7	like	like	ADP
cana-943	327	8	rsa	rsa	PROPN
cana-943	327	9	or	or	CCONJ
cana-943	327	10	ecc	ecc	PROPN
cana-943	327	11	)	)	PUNCT
cana-943	327	12	is	be	AUX
cana-943	327	13	often	often	ADV
cana-943	327	14	used	use	VERB
cana-943	327	15	to	to	PART
cana-943	327	16	secure	secure	VERB
cana-943	327	17	aes	aes	NOUN
cana-943	327	18	keys	key	NOUN
cana-943	327	19	during	during	ADP
cana-943	327	20	transmission	transmission	NOUN
cana-943	327	21	.	.	PUNCT
cana-943	328	1	graph	graph	NOUN
cana-943	328	2	3	3	NUM
cana-943	328	3	:	:	PUNCT
cana-943	328	4	performance	performance	NOUN
cana-943	328	5	of	of	ADP
cana-943	328	6	aes	aes	PROPN
cana-943	328	7	vs	vs	PROPN
cana-943	328	8	rsa	rsa	PROPN
cana-943	328	9	in	in	ADP
cana-943	328	10	cloud	cloud	NOUN
cana-943	328	11	storage	storage	NOUN
cana-943	328	12	encryption	encryption	NOUN
cana-943	328	13	the	the	DET
cana-943	328	14	graph	graph	NOUN
cana-943	328	15	compares	compare	VERB
cana-943	328	16	the	the	DET
cana-943	328	17	performance	performance	NOUN
cana-943	328	18	of	of	ADP
cana-943	328	19	aes	aes	PROPN
cana-943	328	20	and	and	CCONJ
cana-943	328	21	rsa	rsa	PROPN
cana-943	328	22	algorithms	algorithm	NOUN
cana-943	328	23	in	in	ADP
cana-943	328	24	terms	term	NOUN
cana-943	328	25	of	of	ADP
cana-943	328	26	encryption	encryption	NOUN
cana-943	328	27	and	and	CCONJ
cana-943	328	28	decryption	decryption	NOUN
cana-943	328	29	times	time	NOUN
cana-943	328	30	during	during	ADP
cana-943	328	31	cloud	cloud	NOUN
cana-943	328	32	storage	storage	NOUN
cana-943	328	33	encryption	encryption	NOUN
cana-943	328	34	.	.	PUNCT
cana-943	329	1	aes	aes	PROPN
cana-943	329	2	shows	show	VERB
cana-943	329	3	significantly	significantly	ADV
cana-943	329	4	lower	low	ADJ
cana-943	329	5	encryption	encryption	NOUN
cana-943	329	6	and	and	CCONJ
cana-943	329	7	decryption	decryption	NOUN
cana-943	329	8	times	time	NOUN
cana-943	329	9	,	,	PUNCT
cana-943	329	10	both	both	PRON
cana-943	329	11	at	at	ADP
cana-943	329	12	0.2	0.2	NUM
cana-943	329	13	milliseconds	millisecond	NOUN
cana-943	329	14	,	,	PUNCT
cana-943	329	15	compared	compare	VERB
cana-943	329	16	to	to	ADP
cana-943	329	17	rsa	rsa	PROPN
cana-943	329	18	,	,	PUNCT
cana-943	329	19	which	which	PRON
cana-943	329	20	has	have	VERB
cana-943	329	21	an	an	DET
cana-943	329	22	encryption	encryption	NOUN
cana-943	329	23	time	time	NOUN
cana-943	329	24	of	of	ADP
cana-943	329	25	0.5	0.5	NUM
cana-943	329	26	milliseconds	millisecond	NOUN
cana-943	329	27	and	and	CCONJ
cana-943	329	28	a	a	DET
cana-943	329	29	much	much	ADV
cana-943	329	30	higher	high	ADJ
cana-943	329	31	decryption	decryption	NOUN
cana-943	329	32	time	time	NOUN
cana-943	329	33	of	of	ADP
cana-943	329	34	30	30	NUM
cana-943	329	35	milliseconds	millisecond	NOUN
cana-943	329	36	.	.	PUNCT
cana-943	330	1	this	this	DET
cana-943	330	2	visual	visual	ADJ
cana-943	330	3	representation	representation	NOUN
cana-943	330	4	highlights	highlight	VERB
cana-943	330	5	the	the	DET
cana-943	330	6	efficiency	efficiency	NOUN
cana-943	330	7	advantages	advantage	NOUN
cana-943	330	8	of	of	ADP
cana-943	330	9	aes	aes	PROPN
cana-943	330	10	over	over	ADP
cana-943	330	11	rsa	rsa	PROPN
cana-943	330	12	in	in	ADP
cana-943	330	13	cloud	cloud	NOUN
cana-943	330	14	storage	storage	NOUN
cana-943	330	15	encryption	encryption	NOUN
cana-943	330	16	,	,	PUNCT
cana-943	330	17	supporting	support	VERB
cana-943	330	18	the	the	DET
cana-943	330	19	discussion	discussion	NOUN
cana-943	330	20	in	in	ADP
cana-943	330	21	the	the	DET
cana-943	330	22	"	"	PUNCT
cana-943	330	23	data	data	NOUN
cana-943	330	24	privacy	privacy	NOUN
cana-943	330	25	and	and	CCONJ
cana-943	330	26	secure	secure	ADJ
cana-943	330	27	storage	storage	NOUN
cana-943	330	28	"	"	PUNCT
cana-943	330	29	section	section	NOUN
cana-943	330	30	.	.	PUNCT
cana-943	331	1	8	8	X
cana-943	331	2	.	.	X
cana-943	331	3	enhancing	enhance	VERB
cana-943	331	4	information	information	NOUN
cana-943	331	5	security	security	NOUN
cana-943	331	6	through	through	ADP
cana-943	331	7	mathematical	mathematical	ADJ
cana-943	331	8	foundations	foundation	NOUN
cana-943	331	9	8.1	8.1	NUM
cana-943	331	10	.	.	PUNCT
cana-943	332	1	role	role	NOUN
cana-943	332	2	of	of	ADP
cana-943	332	3	algebra	algebra	NOUN
cana-943	332	4	in	in	ADP
cana-943	332	5	strengthening	strengthen	VERB
cana-943	332	6	cryptographic	cryptographic	ADJ
cana-943	332	7	protocols	protocol	NOUN
cana-943	332	8	algebra	algebra	NOUN
cana-943	332	9	plays	play	VERB
cana-943	332	10	a	a	DET
cana-943	332	11	pivotal	pivotal	ADJ
cana-943	332	12	role	role	NOUN
cana-943	332	13	in	in	ADP
cana-943	332	14	the	the	DET
cana-943	332	15	development	development	NOUN
cana-943	332	16	and	and	CCONJ
cana-943	332	17	enhancement	enhancement	NOUN
cana-943	332	18	of	of	ADP
cana-943	332	19	cryptographic	cryptographic	ADJ
cana-943	332	20	protocols	protocol	NOUN
cana-943	332	21	.	.	PUNCT
cana-943	333	1	the	the	DET
cana-943	333	2	robustness	robustness	NOUN
cana-943	333	3	of	of	ADP
cana-943	333	4	cryptographic	cryptographic	ADJ
cana-943	333	5	systems	system	NOUN
cana-943	333	6	is	be	AUX
cana-943	333	7	fundamentally	fundamentally	ADV
cana-943	333	8	rooted	root	VERB
cana-943	333	9	in	in	ADP
cana-943	333	10	the	the	DET
cana-943	333	11	mathematical	mathematical	ADJ
cana-943	333	12	properties	property	NOUN
cana-943	333	13	of	of	ADP
cana-943	333	14	algebraic	algebraic	ADJ
cana-943	333	15	structures	structure	NOUN
cana-943	333	16	.	.	PUNCT
cana-943	334	1	these	these	DET
cana-943	334	2	structures	structure	NOUN
cana-943	334	3	provide	provide	VERB
cana-943	334	4	a	a	DET
cana-943	334	5	rigorous	rigorous	ADJ
cana-943	334	6	framework	framework	NOUN
cana-943	334	7	for	for	ADP
cana-943	334	8	constructing	construct	VERB
cana-943	334	9	secure	secure	ADJ
cana-943	334	10	algorithms	algorithm	NOUN
cana-943	334	11	and	and	CCONJ
cana-943	334	12	protocols	protocol	NOUN
cana-943	334	13	that	that	PRON
cana-943	334	14	can	can	AUX
cana-943	334	15	resist	resist	VERB
cana-943	334	16	various	various	ADJ
cana-943	334	17	types	type	NOUN
cana-943	334	18	of	of	ADP
cana-943	334	19	attacks	attack	NOUN
cana-943	334	20	.	.	PUNCT
cana-943	335	1	8.1.1	8.1.1	X
cana-943	335	2	.	.	PUNCT
cana-943	335	3	key	key	ADJ
cana-943	335	4	contributions	contribution	NOUN
cana-943	335	5	of	of	ADP
cana-943	335	6	algebra	algebra	NOUN
cana-943	335	7	:	:	PUNCT
cana-943	335	8	1	1	X
cana-943	335	9	.	.	X
cana-943	335	10	groups	group	NOUN
cana-943	335	11	and	and	CCONJ
cana-943	335	12	cyclic	cyclic	ADJ
cana-943	335	13	groups	group	NOUN
cana-943	335	14	:	:	PUNCT
cana-943	335	15	groups	group	NOUN
cana-943	335	16	,	,	PUNCT
cana-943	335	17	particularly	particularly	ADV
cana-943	335	18	cyclic	cyclic	ADJ
cana-943	335	19	groups	group	NOUN
cana-943	335	20	,	,	PUNCT
cana-943	335	21	are	be	AUX
cana-943	335	22	foundational	foundational	ADJ
cana-943	335	23	to	to	ADP
cana-943	335	24	many	many	ADJ
cana-943	335	25	cryptographic	cryptographic	ADJ
cana-943	335	26	systems	system	NOUN
cana-943	335	27	.	.	PUNCT
cana-943	336	1	the	the	DET
cana-943	336	2	difficulty	difficulty	NOUN
cana-943	336	3	of	of	ADP
cana-943	336	4	problems	problem	NOUN
cana-943	336	5	such	such	ADJ
cana-943	336	6	as	as	ADP
cana-943	336	7	the	the	DET
cana-943	336	8	discrete	discrete	ADJ
cana-943	336	9	logarithm	logarithm	NOUN
cana-943	336	10	problem	problem	NOUN
cana-943	336	11	(	(	PUNCT
cana-943	336	12	dlp	dlp	NOUN
cana-943	336	13	)	)	PUNCT
cana-943	336	14	in	in	ADP
cana-943	336	15	these	these	DET
cana-943	336	16	groups	group	NOUN
cana-943	336	17	underpins	underpin	VERB
cana-943	336	18	the	the	DET
cana-943	336	19	security	security	NOUN
cana-943	336	20	of	of	ADP
cana-943	336	21	protocols	protocol	NOUN
cana-943	336	22	like	like	ADP
cana-943	336	23	diffie	diffie	PROPN
cana-943	336	24	-	-	PUNCT
cana-943	336	25	hellman	hellman	PROPN
cana-943	336	26	key	key	PROPN
cana-943	336	27	exchange	exchange	NOUN
cana-943	336	28	and	and	CCONJ
cana-943	336	29	the	the	DET
cana-943	336	30	elgamal	elgamal	ADJ
cana-943	336	31	encryption	encryption	NOUN
cana-943	336	32	system	system	NOUN
cana-943	336	33	[	[	X
cana-943	336	34	4	4	NUM
cana-943	336	35	]	]	PUNCT
cana-943	336	36	.	.	PUNCT
cana-943	337	1	the	the	DET
cana-943	337	2	algebraic	algebraic	ADJ
cana-943	337	3	properties	property	NOUN
cana-943	337	4	of	of	ADP
cana-943	337	5	groups	group	NOUN
cana-943	337	6	ensure	ensure	VERB
cana-943	337	7	that	that	SCONJ
cana-943	337	8	certain	certain	ADJ
cana-943	337	9	operations	operation	NOUN
cana-943	337	10	are	be	AUX
cana-943	337	11	hard	hard	ADJ
cana-943	337	12	to	to	PART
cana-943	337	13	reverse	reverse	VERB
cana-943	337	14	,	,	PUNCT
cana-943	337	15	which	which	PRON
cana-943	337	16	is	be	AUX
cana-943	337	17	essential	essential	ADJ
cana-943	337	18	for	for	ADP
cana-943	337	19	cryptographic	cryptographic	ADJ
cana-943	337	20	security	security	NOUN
cana-943	337	21	.	.	PUNCT
cana-943	338	1	2	2	X
cana-943	338	2	.	.	X
cana-943	338	3	elliptic	elliptic	ADJ
cana-943	338	4	curves	curve	NOUN
cana-943	338	5	:	:	PUNCT
cana-943	338	6	elliptic	elliptic	ADJ
cana-943	338	7	curve	curve	NOUN
cana-943	338	8	cryptography	cryptography	NOUN
cana-943	338	9	(	(	PUNCT
cana-943	338	10	ecc	ecc	PROPN
cana-943	338	11	)	)	PUNCT
cana-943	338	12	leverages	leverage	VERB
cana-943	338	13	the	the	DET
cana-943	338	14	algebraic	algebraic	ADJ
cana-943	338	15	structure	structure	NOUN
cana-943	338	16	of	of	ADP
cana-943	338	17	elliptic	elliptic	ADJ
cana-943	338	18	curves	curve	NOUN
cana-943	338	19	over	over	ADP
cana-943	338	20	finite	finite	ADJ
cana-943	338	21	fields	field	NOUN
cana-943	338	22	.	.	PUNCT
cana-943	339	1	ecc	ecc	PROPN
cana-943	339	2	provides	provide	VERB
cana-943	339	3	equivalent	equivalent	ADJ
cana-943	339	4	security	security	NOUN
cana-943	339	5	to	to	ADP
cana-943	339	6	traditional	traditional	ADJ
cana-943	339	7	systems	system	NOUN
cana-943	339	8	like	like	ADP
cana-943	339	9	rsa	rsa	PROPN
cana-943	339	10	but	but	CCONJ
cana-943	339	11	communications	communication	NOUN
cana-943	339	12	on	on	ADP
cana-943	339	13	applied	apply	VERB
cana-943	339	14	nonlinear	nonlinear	ADJ
cana-943	339	15	analysis	analysis	NOUN
cana-943	339	16	issn	issn	NOUN
cana-943	339	17	:	:	PUNCT
cana-943	339	18	1074	1074	NUM
cana-943	339	19	-	-	PUNCT
cana-943	339	20	133x	133x	NUM
cana-943	339	21	vol	vol	NOUN
cana-943	339	22	31	31	NUM
cana-943	339	23	no	no	NOUN
cana-943	339	24	.	.	PUNCT
cana-943	340	1	4s	4s	NUM
cana-943	340	2	(	(	PUNCT
cana-943	340	3	2024	2024	NUM
cana-943	340	4	)	)	PUNCT
cana-943	340	5	483	483	NUM
cana-943	340	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	340	7	with	with	ADP
cana-943	340	8	significantly	significantly	ADV
cana-943	340	9	smaller	small	ADJ
cana-943	340	10	key	key	ADJ
cana-943	340	11	sizes	size	NOUN
cana-943	340	12	,	,	PUNCT
cana-943	340	13	enhancing	enhance	VERB
cana-943	340	14	both	both	DET
cana-943	340	15	security	security	NOUN
cana-943	340	16	and	and	CCONJ
cana-943	340	17	efficiency	efficiency	NOUN
cana-943	340	18	[	[	X
cana-943	340	19	7	7	NUM
cana-943	340	20	]	]	PUNCT
cana-943	340	21	.	.	PUNCT
cana-943	341	1	the	the	DET
cana-943	341	2	elliptic	elliptic	ADJ
cana-943	341	3	curve	curve	NOUN
cana-943	341	4	discrete	discrete	ADJ
cana-943	341	5	logarithm	logarithm	NOUN
cana-943	341	6	problem	problem	NOUN
cana-943	341	7	(	(	PUNCT
cana-943	341	8	ecdlp	ecdlp	PROPN
cana-943	341	9	)	)	PUNCT
cana-943	341	10	is	be	AUX
cana-943	341	11	computationally	computationally	ADV
cana-943	341	12	challenging	challenging	ADJ
cana-943	341	13	,	,	PUNCT
cana-943	341	14	making	make	VERB
cana-943	341	15	ecc	ecc	NOUN
cana-943	341	16	a	a	DET
cana-943	341	17	robust	robust	ADJ
cana-943	341	18	choice	choice	NOUN
cana-943	341	19	for	for	ADP
cana-943	341	20	modern	modern	ADJ
cana-943	341	21	cryptographic	cryptographic	ADJ
cana-943	341	22	applications	application	NOUN
cana-943	341	23	.	.	PUNCT
cana-943	342	1	3	3	X
cana-943	342	2	.	.	X
cana-943	342	3	finite	finite	PROPN
cana-943	342	4	fields	field	NOUN
cana-943	342	5	and	and	CCONJ
cana-943	342	6	galois	galois	PROPN
cana-943	342	7	fields	field	NOUN
cana-943	342	8	:	:	PUNCT
cana-943	342	9	finite	finite	PROPN
cana-943	342	10	fields	field	NOUN
cana-943	342	11	,	,	PUNCT
cana-943	342	12	particularly	particularly	ADV
cana-943	342	13	galois	galois	PROPN
cana-943	342	14	fields	field	NOUN
cana-943	342	15	,	,	PUNCT
cana-943	342	16	are	be	AUX
cana-943	342	17	instrumental	instrumental	ADJ
cana-943	342	18	in	in	ADP
cana-943	342	19	algorithms	algorithm	NOUN
cana-943	342	20	like	like	ADP
cana-943	342	21	the	the	DET
cana-943	342	22	advanced	advanced	ADJ
cana-943	342	23	encryption	encryption	NOUN
cana-943	342	24	standard	standard	NOUN
cana-943	342	25	(	(	PUNCT
cana-943	342	26	aes	aes	PROPN
cana-943	342	27	)	)	PUNCT
cana-943	343	1	[	[	X
cana-943	343	2	16	16	NUM
cana-943	343	3	]	]	PUNCT
cana-943	343	4	.	.	PUNCT
cana-943	344	1	the	the	DET
cana-943	344	2	algebraic	algebraic	ADJ
cana-943	344	3	structure	structure	NOUN
cana-943	344	4	of	of	ADP
cana-943	344	5	these	these	DET
cana-943	344	6	fields	field	NOUN
cana-943	344	7	allows	allow	VERB
cana-943	344	8	for	for	ADP
cana-943	344	9	efficient	efficient	ADJ
cana-943	344	10	and	and	CCONJ
cana-943	344	11	secure	secure	ADJ
cana-943	344	12	implementation	implementation	NOUN
cana-943	344	13	of	of	ADP
cana-943	344	14	cryptographic	cryptographic	ADJ
cana-943	344	15	operations	operation	NOUN
cana-943	344	16	.	.	PUNCT
cana-943	345	1	the	the	DET
cana-943	345	2	use	use	NOUN
cana-943	345	3	of	of	ADP
cana-943	345	4	finite	finite	ADJ
cana-943	345	5	fields	field	NOUN
cana-943	345	6	in	in	ADP
cana-943	345	7	polynomial	polynomial	ADJ
cana-943	345	8	operations	operation	NOUN
cana-943	345	9	also	also	ADV
cana-943	345	10	facilitates	facilitate	VERB
cana-943	345	11	error	error	NOUN
cana-943	345	12	detection	detection	NOUN
cana-943	345	13	and	and	CCONJ
cana-943	345	14	correction	correction	NOUN
cana-943	345	15	in	in	ADP
cana-943	345	16	cryptographic	cryptographic	ADJ
cana-943	345	17	systems	system	NOUN
cana-943	345	18	.	.	PUNCT
cana-943	346	1	8.2	8.2	NUM
cana-943	346	2	.	.	PUNCT
cana-943	347	1	advanced	advance	VERB
cana-943	347	2	algebraic	algebraic	ADJ
cana-943	347	3	methods	method	NOUN
cana-943	347	4	for	for	ADP
cana-943	347	5	enhanced	enhanced	ADJ
cana-943	347	6	security	security	NOUN
cana-943	347	7	as	as	SCONJ
cana-943	347	8	cryptographic	cryptographic	ADJ
cana-943	347	9	threats	threat	NOUN
cana-943	347	10	evolve	evolve	VERB
cana-943	347	11	,	,	PUNCT
cana-943	347	12	advanced	advanced	ADJ
cana-943	347	13	algebraic	algebraic	ADJ
cana-943	347	14	methods	method	NOUN
cana-943	347	15	continue	continue	VERB
cana-943	347	16	to	to	PART
cana-943	347	17	play	play	VERB
cana-943	347	18	a	a	DET
cana-943	347	19	crucial	crucial	ADJ
cana-943	347	20	role	role	NOUN
cana-943	347	21	in	in	ADP
cana-943	347	22	developing	develop	VERB
cana-943	347	23	enhanced	enhanced	ADJ
cana-943	347	24	security	security	NOUN
cana-943	347	25	measures	measure	NOUN
cana-943	347	26	.	.	PUNCT
cana-943	348	1	researchers	researcher	NOUN
cana-943	348	2	are	be	AUX
cana-943	348	3	exploring	explore	VERB
cana-943	348	4	innovative	innovative	ADJ
cana-943	348	5	applications	application	NOUN
cana-943	348	6	of	of	ADP
cana-943	348	7	algebra	algebra	NOUN
cana-943	348	8	to	to	PART
cana-943	348	9	address	address	VERB
cana-943	348	10	emerging	emerge	VERB
cana-943	348	11	challenges	challenge	NOUN
cana-943	348	12	in	in	ADP
cana-943	348	13	information	information	NOUN
cana-943	348	14	security	security	NOUN
cana-943	348	15	.	.	PUNCT
cana-943	349	1	8.2.1	8.2.1	X
cana-943	349	2	.	.	PUNCT
cana-943	349	3	notable	notable	ADJ
cana-943	349	4	advanced	advanced	ADJ
cana-943	349	5	methods	method	NOUN
cana-943	349	6	:	:	PUNCT
cana-943	349	7	1	1	X
cana-943	349	8	.	.	X
cana-943	349	9	homomorphic	homomorphic	ADJ
cana-943	349	10	encryption	encryption	NOUN
cana-943	349	11	:	:	PUNCT
cana-943	349	12	homomorphic	homomorphic	ADJ
cana-943	349	13	encryption	encryption	NOUN
cana-943	349	14	allows	allow	VERB
cana-943	349	15	computations	computation	NOUN
cana-943	349	16	to	to	PART
cana-943	349	17	be	be	AUX
cana-943	349	18	performed	perform	VERB
cana-943	349	19	on	on	ADP
cana-943	349	20	encrypted	encrypt	VERB
cana-943	349	21	data	datum	NOUN
cana-943	349	22	without	without	ADP
cana-943	349	23	decrypting	decrypt	VERB
cana-943	349	24	it	it	PRON
cana-943	349	25	,	,	PUNCT
cana-943	349	26	maintaining	maintain	VERB
cana-943	349	27	data	data	NOUN
cana-943	349	28	privacy	privacy	NOUN
cana-943	349	29	throughout	throughout	ADP
cana-943	349	30	the	the	DET
cana-943	349	31	process	process	NOUN
cana-943	349	32	.	.	PUNCT
cana-943	350	1	this	this	DET
cana-943	350	2	method	method	NOUN
cana-943	350	3	relies	rely	VERB
cana-943	350	4	heavily	heavily	ADV
cana-943	350	5	on	on	ADP
cana-943	350	6	algebraic	algebraic	ADJ
cana-943	350	7	structures	structure	NOUN
cana-943	350	8	such	such	ADJ
cana-943	350	9	as	as	ADP
cana-943	350	10	lattices	lattice	NOUN
cana-943	350	11	and	and	CCONJ
cana-943	350	12	polynomial	polynomial	ADJ
cana-943	350	13	rings	ring	NOUN
cana-943	350	14	.	.	PUNCT
cana-943	351	1	fully	fully	ADV
cana-943	351	2	homomorphic	homomorphic	ADJ
cana-943	351	3	encryption	encryption	NOUN
cana-943	351	4	(	(	PUNCT
cana-943	351	5	fhe	fhe	PROPN
cana-943	351	6	)	)	PUNCT
cana-943	351	7	schemes	scheme	NOUN
cana-943	351	8	,	,	PUNCT
cana-943	351	9	which	which	PRON
cana-943	351	10	support	support	VERB
cana-943	351	11	arbitrary	arbitrary	ADJ
cana-943	351	12	computations	computation	NOUN
cana-943	351	13	on	on	ADP
cana-943	351	14	encrypted	encrypt	VERB
cana-943	351	15	data	datum	NOUN
cana-943	351	16	,	,	PUNCT
cana-943	351	17	are	be	AUX
cana-943	351	18	particularly	particularly	ADV
cana-943	351	19	promising	promise	VERB
cana-943	351	20	for	for	ADP
cana-943	351	21	secure	secure	ADJ
cana-943	351	22	cloud	cloud	NOUN
cana-943	351	23	computing	computing	NOUN
cana-943	351	24	and	and	CCONJ
cana-943	351	25	privacy	privacy	NOUN
cana-943	351	26	-	-	PUNCT
cana-943	351	27	preserving	preserve	VERB
cana-943	351	28	data	datum	NOUN
cana-943	351	29	analysis	analysis	NOUN
cana-943	351	30	[	[	X
cana-943	351	31	10	10	NUM
cana-943	351	32	]	]	PUNCT
cana-943	351	33	.	.	PUNCT
cana-943	352	1	2	2	X
cana-943	352	2	.	.	X
cana-943	352	3	lattice	lattice	NOUN
cana-943	352	4	-	-	PUNCT
cana-943	352	5	based	base	VERB
cana-943	352	6	cryptography	cryptography	NOUN
cana-943	352	7	:	:	PUNCT
cana-943	352	8	lattice	lattice	NOUN
cana-943	352	9	-	-	PUNCT
cana-943	352	10	based	base	VERB
cana-943	352	11	cryptographic	cryptographic	ADJ
cana-943	352	12	schemes	scheme	NOUN
cana-943	352	13	offer	offer	VERB
cana-943	352	14	strong	strong	ADJ
cana-943	352	15	security	security	NOUN
cana-943	352	16	guarantees	guarantee	NOUN
cana-943	352	17	and	and	CCONJ
cana-943	352	18	resistance	resistance	NOUN
cana-943	352	19	to	to	ADP
cana-943	352	20	quantum	quantum	NOUN
cana-943	352	21	attacks	attack	NOUN
cana-943	352	22	.	.	PUNCT
cana-943	353	1	the	the	DET
cana-943	353	2	learning	learning	NOUN
cana-943	353	3	with	with	ADP
cana-943	353	4	errors	error	NOUN
cana-943	353	5	(	(	PUNCT
cana-943	353	6	lwe	lwe	ADJ
cana-943	353	7	)	)	PUNCT
cana-943	353	8	problem	problem	NOUN
cana-943	353	9	and	and	CCONJ
cana-943	353	10	its	its	PRON
cana-943	353	11	ring	ring	NOUN
cana-943	353	12	-	-	PUNCT
cana-943	353	13	based	base	VERB
cana-943	353	14	variant	variant	NOUN
cana-943	353	15	(	(	PUNCT
cana-943	353	16	ring	ring	NOUN
cana-943	353	17	-	-	PUNCT
cana-943	353	18	lwe	lwe	NOUN
cana-943	353	19	)	)	PUNCT
cana-943	353	20	form	form	VERB
cana-943	353	21	the	the	DET
cana-943	353	22	basis	basis	NOUN
cana-943	353	23	of	of	ADP
cana-943	353	24	many	many	ADJ
cana-943	353	25	lattice	lattice	NOUN
cana-943	353	26	-	-	PUNCT
cana-943	353	27	based	base	VERB
cana-943	353	28	protocols	protocol	NOUN
cana-943	353	29	.	.	PUNCT
cana-943	354	1	these	these	DET
cana-943	354	2	protocols	protocol	NOUN
cana-943	354	3	leverage	leverage	VERB
cana-943	354	4	the	the	DET
cana-943	354	5	hardness	hardness	NOUN
cana-943	354	6	of	of	ADP
cana-943	354	7	lattice	lattice	NOUN
cana-943	354	8	problems	problem	NOUN
cana-943	354	9	to	to	PART
cana-943	354	10	provide	provide	VERB
cana-943	354	11	robust	robust	ADJ
cana-943	354	12	encryption	encryption	NOUN
cana-943	354	13	,	,	PUNCT
cana-943	354	14	digital	digital	ADJ
cana-943	354	15	signatures	signature	NOUN
cana-943	354	16	,	,	PUNCT
cana-943	354	17	and	and	CCONJ
cana-943	354	18	key	key	ADJ
cana-943	354	19	exchange	exchange	NOUN
cana-943	354	20	mechanisms	mechanism	NOUN
cana-943	354	21	[	[	X
cana-943	354	22	11	11	NUM
cana-943	354	23	]	]	PUNCT
cana-943	354	24	.	.	PUNCT
cana-943	355	1	lattice	lattice	NOUN
cana-943	355	2	-	-	PUNCT
cana-943	355	3	based	base	VERB
cana-943	355	4	cryptography	cryptography	NOUN
cana-943	355	5	is	be	AUX
cana-943	355	6	a	a	DET
cana-943	355	7	leading	lead	VERB
cana-943	355	8	candidate	candidate	NOUN
cana-943	355	9	for	for	ADP
cana-943	355	10	post	post	ADJ
cana-943	355	11	-	-	ADJ
cana-943	355	12	quantum	quantum	ADJ
cana-943	355	13	cryptographic	cryptographic	ADJ
cana-943	355	14	standards	standard	NOUN
cana-943	355	15	.	.	PUNCT
cana-943	356	1	3	3	X
cana-943	356	2	.	.	X
cana-943	356	3	zero	zero	NUM
cana-943	356	4	-	-	PUNCT
cana-943	356	5	knowledge	knowledge	NOUN
cana-943	356	6	proofs	proof	NOUN
cana-943	356	7	:	:	PUNCT
cana-943	356	8	zero	zero	NUM
cana-943	356	9	-	-	PUNCT
cana-943	356	10	knowledge	knowledge	NOUN
cana-943	356	11	proofs	proof	NOUN
cana-943	356	12	(	(	PUNCT
cana-943	356	13	zkps	zkps	PROPN
cana-943	356	14	)	)	PUNCT
cana-943	356	15	enable	enable	VERB
cana-943	356	16	one	one	NUM
cana-943	356	17	party	party	NOUN
cana-943	356	18	to	to	PART
cana-943	356	19	prove	prove	VERB
cana-943	356	20	knowledge	knowledge	NOUN
cana-943	356	21	of	of	ADP
cana-943	356	22	a	a	DET
cana-943	356	23	secret	secret	NOUN
cana-943	356	24	without	without	ADP
cana-943	356	25	revealing	reveal	VERB
cana-943	356	26	the	the	DET
cana-943	356	27	secret	secret	NOUN
cana-943	356	28	itself	itself	PRON
cana-943	356	29	.	.	PUNCT
cana-943	357	1	advanced	advanced	ADJ
cana-943	357	2	algebraic	algebraic	ADJ
cana-943	357	3	techniques	technique	NOUN
cana-943	357	4	underpin	underpin	VERB
cana-943	357	5	many	many	ADJ
cana-943	357	6	zkp	zkp	NOUN
cana-943	357	7	systems	system	NOUN
cana-943	357	8	,	,	PUNCT
cana-943	357	9	ensuring	ensure	VERB
cana-943	357	10	both	both	CCONJ
cana-943	357	11	security	security	NOUN
cana-943	357	12	and	and	CCONJ
cana-943	357	13	efficiency	efficiency	NOUN
cana-943	357	14	.	.	PUNCT
cana-943	358	1	zkps	zkps	PROPN
cana-943	358	2	are	be	AUX
cana-943	358	3	increasingly	increasingly	ADV
cana-943	358	4	used	use	VERB
cana-943	358	5	in	in	ADP
cana-943	358	6	blockchain	blockchain	PROPN
cana-943	358	7	technologies	technology	NOUN
cana-943	358	8	to	to	PART
cana-943	358	9	enhance	enhance	VERB
cana-943	358	10	privacy	privacy	NOUN
cana-943	358	11	and	and	CCONJ
cana-943	358	12	scalability	scalability	NOUN
cana-943	359	1	[	[	X
cana-943	359	2	12	12	NUM
cana-943	359	3	]	]	PUNCT
cana-943	359	4	.	.	PUNCT
cana-943	360	1	8.3	8.3	NUM
cana-943	360	2	.	.	PUNCT
cana-943	361	1	future	future	ADJ
cana-943	361	2	directions	direction	NOUN
cana-943	361	3	in	in	ADP
cana-943	361	4	algebra	algebra	NOUN
cana-943	361	5	-	-	PUNCT
cana-943	361	6	based	base	VERB
cana-943	361	7	cryptographic	cryptographic	ADJ
cana-943	361	8	research	research	NOUN
cana-943	361	9	the	the	DET
cana-943	361	10	future	future	NOUN
cana-943	361	11	of	of	ADP
cana-943	361	12	algebra	algebra	NOUN
cana-943	361	13	-	-	PUNCT
cana-943	361	14	based	base	VERB
cana-943	361	15	cryptographic	cryptographic	ADJ
cana-943	361	16	research	research	NOUN
cana-943	361	17	holds	hold	VERB
cana-943	361	18	significant	significant	ADJ
cana-943	361	19	promise	promise	NOUN
cana-943	361	20	as	as	SCONJ
cana-943	361	21	researchers	researcher	NOUN
cana-943	361	22	continue	continue	VERB
cana-943	361	23	to	to	PART
cana-943	361	24	explore	explore	VERB
cana-943	361	25	and	and	CCONJ
cana-943	361	26	refine	refine	VERB
cana-943	361	27	algebraic	algebraic	ADJ
cana-943	361	28	techniques	technique	NOUN
cana-943	361	29	to	to	PART
cana-943	361	30	enhance	enhance	VERB
cana-943	361	31	security	security	NOUN
cana-943	361	32	.	.	PUNCT
cana-943	362	1	key	key	ADJ
cana-943	362	2	areas	area	NOUN
cana-943	362	3	of	of	ADP
cana-943	362	4	focus	focus	NOUN
cana-943	362	5	include	include	VERB
cana-943	362	6	:	:	PUNCT
cana-943	362	7	1	1	X
cana-943	362	8	.	.	X
cana-943	362	9	quantum	quantum	NOUN
cana-943	362	10	-	-	PUNCT
cana-943	362	11	resistant	resistant	ADJ
cana-943	362	12	algorithms	algorithm	NOUN
cana-943	362	13	:	:	PUNCT
cana-943	362	14	with	with	ADP
cana-943	362	15	the	the	DET
cana-943	362	16	advent	advent	NOUN
cana-943	362	17	of	of	ADP
cana-943	362	18	quantum	quantum	NOUN
cana-943	362	19	computing	computing	NOUN
cana-943	362	20	,	,	PUNCT
cana-943	362	21	developing	develop	VERB
cana-943	362	22	cryptographic	cryptographic	ADJ
cana-943	362	23	algorithms	algorithm	NOUN
cana-943	362	24	that	that	PRON
cana-943	362	25	can	can	AUX
cana-943	362	26	withstand	withstand	VERB
cana-943	362	27	quantum	quantum	NOUN
cana-943	362	28	attacks	attack	NOUN
cana-943	362	29	is	be	AUX
cana-943	362	30	paramount	paramount	ADJ
cana-943	362	31	.	.	PUNCT
cana-943	363	1	researchers	researcher	NOUN
cana-943	363	2	are	be	AUX
cana-943	363	3	focusing	focus	VERB
cana-943	363	4	on	on	ADP
cana-943	363	5	algebraic	algebraic	ADJ
cana-943	363	6	structures	structure	NOUN
cana-943	363	7	that	that	PRON
cana-943	363	8	offer	offer	VERB
cana-943	363	9	quantum	quantum	ADJ
cana-943	363	10	resistance	resistance	NOUN
cana-943	363	11	,	,	PUNCT
cana-943	363	12	such	such	ADJ
cana-943	363	13	as	as	ADP
cana-943	363	14	those	those	PRON
cana-943	363	15	used	use	VERB
cana-943	363	16	in	in	ADP
cana-943	363	17	latticebased	latticebased	ADJ
cana-943	363	18	cryptography	cryptography	NOUN
cana-943	363	19	.	.	PUNCT
cana-943	364	1	these	these	DET
cana-943	364	2	efforts	effort	NOUN
cana-943	364	3	aim	aim	VERB
cana-943	364	4	to	to	PART
cana-943	364	5	establish	establish	VERB
cana-943	364	6	new	new	ADJ
cana-943	364	7	standards	standard	NOUN
cana-943	364	8	for	for	ADP
cana-943	364	9	secure	secure	ADJ
cana-943	364	10	communication	communication	NOUN
cana-943	364	11	in	in	ADP
cana-943	364	12	the	the	DET
cana-943	364	13	quantum	quantum	ADJ
cana-943	364	14	era	era	NOUN
cana-943	364	15	[	[	X
cana-943	364	16	17	17	NUM
cana-943	364	17	]	]	PUNCT
cana-943	364	18	.	.	PUNCT
cana-943	365	1	communications	communication	NOUN
cana-943	365	2	on	on	ADP
cana-943	365	3	applied	apply	VERB
cana-943	365	4	nonlinear	nonlinear	ADJ
cana-943	365	5	analysis	analysis	NOUN
cana-943	365	6	issn	issn	NOUN
cana-943	365	7	:	:	PUNCT
cana-943	365	8	1074	1074	NUM
cana-943	365	9	-	-	PUNCT
cana-943	365	10	133x	133x	NUM
cana-943	365	11	vol	vol	NOUN
cana-943	365	12	31	31	NUM
cana-943	365	13	no	no	NOUN
cana-943	365	14	.	.	PUNCT
cana-943	366	1	4s	4s	NUM
cana-943	366	2	(	(	PUNCT
cana-943	366	3	2024	2024	NUM
cana-943	366	4	)	)	PUNCT
cana-943	366	5	484	484	NUM
cana-943	367	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	367	2	2	2	NUM
cana-943	367	3	.	.	X
cana-943	367	4	efficient	efficient	ADJ
cana-943	367	5	homomorphic	homomorphic	ADJ
cana-943	367	6	encryption	encryption	NOUN
cana-943	367	7	:	:	PUNCT
cana-943	367	8	improving	improve	VERB
cana-943	367	9	the	the	DET
cana-943	367	10	efficiency	efficiency	NOUN
cana-943	367	11	of	of	ADP
cana-943	367	12	homomorphic	homomorphic	ADJ
cana-943	367	13	encryption	encryption	NOUN
cana-943	367	14	schemes	scheme	NOUN
cana-943	367	15	is	be	AUX
cana-943	367	16	a	a	DET
cana-943	367	17	critical	critical	ADJ
cana-943	367	18	research	research	NOUN
cana-943	367	19	area	area	NOUN
cana-943	367	20	.	.	PUNCT
cana-943	368	1	current	current	ADJ
cana-943	368	2	schemes	scheme	NOUN
cana-943	368	3	,	,	PUNCT
cana-943	368	4	while	while	SCONJ
cana-943	368	5	secure	secure	ADJ
cana-943	368	6	,	,	PUNCT
cana-943	368	7	often	often	ADV
cana-943	368	8	suffer	suffer	VERB
cana-943	368	9	from	from	ADP
cana-943	368	10	high	high	ADJ
cana-943	368	11	computational	computational	ADJ
cana-943	368	12	overhead	overhead	NOUN
cana-943	368	13	.	.	PUNCT
cana-943	369	1	advances	advance	NOUN
cana-943	369	2	in	in	ADP
cana-943	369	3	algebraic	algebraic	ADJ
cana-943	369	4	methods	method	NOUN
cana-943	369	5	could	could	AUX
cana-943	369	6	lead	lead	VERB
cana-943	369	7	to	to	ADP
cana-943	369	8	more	more	ADV
cana-943	369	9	practical	practical	ADJ
cana-943	369	10	implementations	implementation	NOUN
cana-943	369	11	of	of	ADP
cana-943	369	12	fully	fully	ADV
cana-943	369	13	homomorphic	homomorphic	ADJ
cana-943	369	14	encryption	encryption	NOUN
cana-943	369	15	,	,	PUNCT
cana-943	369	16	making	make	VERB
cana-943	369	17	it	it	PRON
cana-943	369	18	viable	viable	ADJ
cana-943	369	19	for	for	ADP
cana-943	369	20	a	a	DET
cana-943	369	21	broader	broad	ADJ
cana-943	369	22	range	range	NOUN
cana-943	369	23	of	of	ADP
cana-943	369	24	applications	application	NOUN
cana-943	369	25	[	[	X
cana-943	369	26	10	10	NUM
cana-943	369	27	]	]	PUNCT
cana-943	369	28	.	.	PUNCT
cana-943	370	1	3	3	X
cana-943	370	2	.	.	NUM
cana-943	370	3	enhanced	enhance	VERB
cana-943	370	4	privacy	privacy	NOUN
cana-943	370	5	techniques	technique	NOUN
cana-943	370	6	:	:	PUNCT
cana-943	370	7	as	as	SCONJ
cana-943	370	8	privacy	privacy	NOUN
cana-943	370	9	concerns	concern	NOUN
cana-943	370	10	grow	grow	VERB
cana-943	370	11	,	,	PUNCT
cana-943	370	12	developing	develop	VERB
cana-943	370	13	advanced	advanced	ADJ
cana-943	370	14	techniques	technique	NOUN
cana-943	370	15	for	for	ADP
cana-943	370	16	ensuring	ensure	VERB
cana-943	370	17	data	datum	NOUN
cana-943	370	18	privacy	privacy	NOUN
cana-943	370	19	is	be	AUX
cana-943	370	20	increasingly	increasingly	ADV
cana-943	370	21	important	important	ADJ
cana-943	370	22	.	.	PUNCT
cana-943	371	1	algebraic	algebraic	ADJ
cana-943	371	2	methods	method	NOUN
cana-943	371	3	will	will	AUX
cana-943	371	4	continue	continue	VERB
cana-943	371	5	to	to	PART
cana-943	371	6	play	play	VERB
cana-943	371	7	a	a	DET
cana-943	371	8	crucial	crucial	ADJ
cana-943	371	9	role	role	NOUN
cana-943	371	10	in	in	ADP
cana-943	371	11	designing	design	VERB
cana-943	371	12	protocols	protocol	NOUN
cana-943	371	13	that	that	PRON
cana-943	371	14	provide	provide	VERB
cana-943	371	15	strong	strong	ADJ
cana-943	371	16	privacy	privacy	NOUN
cana-943	371	17	guarantees	guarantee	NOUN
cana-943	371	18	without	without	ADP
cana-943	371	19	compromising	compromise	VERB
cana-943	371	20	performance	performance	NOUN
cana-943	371	21	.	.	PUNCT
cana-943	372	1	this	this	PRON
cana-943	372	2	includes	include	VERB
cana-943	372	3	further	further	ADJ
cana-943	372	4	refinement	refinement	NOUN
cana-943	372	5	of	of	ADP
cana-943	372	6	zero	zero	NUM
cana-943	372	7	-	-	PUNCT
cana-943	372	8	knowledge	knowledge	NOUN
cana-943	372	9	proofs	proof	NOUN
cana-943	372	10	and	and	CCONJ
cana-943	372	11	other	other	ADJ
cana-943	372	12	privacy	privacy	NOUN
cana-943	372	13	-	-	PUNCT
cana-943	372	14	preserving	preserve	VERB
cana-943	372	15	cryptographic	cryptographic	ADJ
cana-943	372	16	primitives	primitive	NOUN
cana-943	372	17	[	[	X
cana-943	372	18	12	12	NUM
cana-943	372	19	]	]	PUNCT
cana-943	372	20	.	.	PUNCT
cana-943	373	1	4	4	X
cana-943	373	2	.	.	X
cana-943	373	3	integration	integration	NOUN
cana-943	373	4	with	with	ADP
cana-943	373	5	emerging	emerge	VERB
cana-943	373	6	technologies	technology	NOUN
cana-943	373	7	:	:	PUNCT
cana-943	373	8	the	the	DET
cana-943	373	9	integration	integration	NOUN
cana-943	373	10	of	of	ADP
cana-943	373	11	algebra	algebra	NOUN
cana-943	373	12	-	-	PUNCT
cana-943	373	13	based	base	VERB
cana-943	373	14	cryptographic	cryptographic	ADJ
cana-943	373	15	techniques	technique	NOUN
cana-943	373	16	with	with	ADP
cana-943	373	17	emerging	emerge	VERB
cana-943	373	18	technologies	technology	NOUN
cana-943	373	19	such	such	ADJ
cana-943	373	20	as	as	ADP
cana-943	373	21	blockchain	blockchain	PROPN
cana-943	373	22	,	,	PUNCT
cana-943	373	23	the	the	DET
cana-943	373	24	internet	internet	NOUN
cana-943	373	25	of	of	ADP
cana-943	373	26	things	thing	NOUN
cana-943	373	27	(	(	PUNCT
cana-943	373	28	iot	iot	NOUN
cana-943	373	29	)	)	PUNCT
cana-943	373	30	,	,	PUNCT
cana-943	373	31	and	and	CCONJ
cana-943	373	32	artificial	artificial	ADJ
cana-943	373	33	intelligence	intelligence	NOUN
cana-943	373	34	(	(	PUNCT
cana-943	373	35	ai	ai	NOUN
cana-943	373	36	)	)	PUNCT
cana-943	373	37	presents	present	VERB
cana-943	373	38	new	new	ADJ
cana-943	373	39	challenges	challenge	NOUN
cana-943	373	40	and	and	CCONJ
cana-943	373	41	opportunities	opportunity	NOUN
cana-943	373	42	.	.	PUNCT
cana-943	374	1	ensuring	ensure	VERB
cana-943	374	2	that	that	SCONJ
cana-943	374	3	these	these	DET
cana-943	374	4	technologies	technology	NOUN
cana-943	374	5	incorporate	incorporate	VERB
cana-943	374	6	robust	robust	ADJ
cana-943	374	7	security	security	NOUN
cana-943	374	8	measures	measure	NOUN
cana-943	374	9	from	from	ADP
cana-943	374	10	the	the	DET
cana-943	374	11	outset	outset	NOUN
cana-943	374	12	will	will	AUX
cana-943	374	13	be	be	AUX
cana-943	374	14	essential	essential	ADJ
cana-943	374	15	for	for	ADP
cana-943	374	16	their	their	PRON
cana-943	374	17	widespread	widespread	ADJ
cana-943	374	18	adoption	adoption	NOUN
cana-943	374	19	and	and	CCONJ
cana-943	374	20	trustworthiness	trustworthiness	NOUN
cana-943	375	1	[	[	X
cana-943	375	2	20	20	NUM
cana-943	375	3	]	]	PUNCT
cana-943	375	4	.	.	PUNCT
cana-943	376	1	the	the	DET
cana-943	376	2	intersection	intersection	NOUN
cana-943	376	3	of	of	ADP
cana-943	376	4	algebra	algebra	NOUN
cana-943	376	5	and	and	CCONJ
cana-943	376	6	cryptography	cryptography	NOUN
cana-943	376	7	offers	offer	VERB
cana-943	376	8	a	a	DET
cana-943	376	9	rich	rich	ADJ
cana-943	376	10	and	and	CCONJ
cana-943	376	11	evolving	evolve	VERB
cana-943	376	12	field	field	NOUN
cana-943	376	13	of	of	ADP
cana-943	376	14	research	research	NOUN
cana-943	376	15	.	.	PUNCT
cana-943	377	1	the	the	DET
cana-943	377	2	mathematical	mathematical	ADJ
cana-943	377	3	foundations	foundation	NOUN
cana-943	377	4	provided	provide	VERB
cana-943	377	5	by	by	ADP
cana-943	377	6	algebra	algebra	NOUN
cana-943	377	7	not	not	PART
cana-943	377	8	only	only	ADV
cana-943	377	9	strengthen	strengthen	VERB
cana-943	377	10	existing	exist	VERB
cana-943	377	11	cryptographic	cryptographic	ADJ
cana-943	377	12	protocols	protocol	NOUN
cana-943	377	13	but	but	CCONJ
cana-943	377	14	also	also	ADV
cana-943	377	15	pave	pave	VERB
cana-943	377	16	the	the	DET
cana-943	377	17	way	way	NOUN
cana-943	377	18	for	for	ADP
cana-943	377	19	innovative	innovative	ADJ
cana-943	377	20	solutions	solution	NOUN
cana-943	377	21	to	to	ADP
cana-943	377	22	future	future	ADJ
cana-943	377	23	security	security	NOUN
cana-943	377	24	challenges	challenge	NOUN
cana-943	377	25	.	.	PUNCT
cana-943	378	1	by	by	ADP
cana-943	378	2	continuing	continue	VERB
cana-943	378	3	to	to	PART
cana-943	378	4	explore	explore	VERB
cana-943	378	5	and	and	CCONJ
cana-943	378	6	develop	develop	VERB
cana-943	378	7	these	these	DET
cana-943	378	8	algebraic	algebraic	ADJ
cana-943	378	9	techniques	technique	NOUN
cana-943	378	10	,	,	PUNCT
cana-943	378	11	researchers	researcher	NOUN
cana-943	378	12	can	can	AUX
cana-943	378	13	ensure	ensure	VERB
cana-943	378	14	that	that	SCONJ
cana-943	378	15	cryptographic	cryptographic	ADJ
cana-943	378	16	systems	system	NOUN
cana-943	378	17	remain	remain	VERB
cana-943	378	18	robust	robust	ADJ
cana-943	378	19	,	,	PUNCT
cana-943	378	20	efficient	efficient	ADJ
cana-943	378	21	,	,	PUNCT
cana-943	378	22	and	and	CCONJ
cana-943	378	23	capable	capable	ADJ
cana-943	378	24	of	of	ADP
cana-943	378	25	protecting	protect	VERB
cana-943	378	26	information	information	NOUN
cana-943	378	27	in	in	ADP
cana-943	378	28	an	an	DET
cana-943	378	29	increasingly	increasingly	ADV
cana-943	378	30	digital	digital	ADJ
cana-943	378	31	world	world	NOUN
cana-943	378	32	.	.	PUNCT
cana-943	379	1	9	9	X
cana-943	379	2	.	.	X
cana-943	379	3	challenges	challenge	NOUN
cana-943	379	4	and	and	CCONJ
cana-943	379	5	future	future	ADJ
cana-943	379	6	directions	direction	NOUN
cana-943	379	7	9.1	9.1	NUM
cana-943	379	8	.	.	PUNCT
cana-943	380	1	scalability	scalability	NOUN
cana-943	380	2	and	and	CCONJ
cana-943	380	3	efficiency	efficiency	NOUN
cana-943	380	4	issues	issue	NOUN
cana-943	380	5	one	one	NUM
cana-943	380	6	of	of	ADP
cana-943	380	7	the	the	DET
cana-943	380	8	primary	primary	ADJ
cana-943	380	9	challenges	challenge	NOUN
cana-943	380	10	in	in	ADP
cana-943	380	11	the	the	DET
cana-943	380	12	intersection	intersection	NOUN
cana-943	380	13	of	of	ADP
cana-943	380	14	algebra	algebra	NOUN
cana-943	380	15	and	and	CCONJ
cana-943	380	16	cryptography	cryptography	NOUN
cana-943	380	17	is	be	AUX
cana-943	380	18	addressing	address	VERB
cana-943	380	19	scalability	scalability	NOUN
cana-943	380	20	and	and	CCONJ
cana-943	380	21	efficiency	efficiency	NOUN
cana-943	380	22	issues	issue	NOUN
cana-943	380	23	.	.	PUNCT
cana-943	381	1	cryptographic	cryptographic	ADJ
cana-943	381	2	protocols	protocol	NOUN
cana-943	381	3	,	,	PUNCT
cana-943	381	4	while	while	SCONJ
cana-943	381	5	secure	secure	ADJ
cana-943	381	6	,	,	PUNCT
cana-943	381	7	often	often	ADV
cana-943	381	8	require	require	VERB
cana-943	381	9	significant	significant	ADJ
cana-943	381	10	computational	computational	ADJ
cana-943	381	11	resources	resource	NOUN
cana-943	381	12	,	,	PUNCT
cana-943	381	13	which	which	PRON
cana-943	381	14	can	can	AUX
cana-943	381	15	limit	limit	VERB
cana-943	381	16	their	their	PRON
cana-943	381	17	practicality	practicality	NOUN
cana-943	381	18	in	in	ADP
cana-943	381	19	large	large	ADJ
cana-943	381	20	-	-	PUNCT
cana-943	381	21	scale	scale	NOUN
cana-943	381	22	applications	application	NOUN
cana-943	381	23	.	.	PUNCT
cana-943	382	1	9.1.1	9.1.1	X
cana-943	382	2	.	.	PUNCT
cana-943	382	3	key	key	ADJ
cana-943	382	4	scalability	scalability	NOUN
cana-943	382	5	and	and	CCONJ
cana-943	382	6	efficiency	efficiency	NOUN
cana-943	382	7	challenges	challenge	NOUN
cana-943	382	8	:	:	PUNCT
cana-943	382	9	1	1	X
cana-943	382	10	.	.	X
cana-943	382	11	computational	computational	ADJ
cana-943	382	12	overhead	overhead	NOUN
cana-943	382	13	:	:	PUNCT
cana-943	382	14	many	many	ADJ
cana-943	382	15	algebraic	algebraic	ADJ
cana-943	382	16	cryptographic	cryptographic	ADJ
cana-943	382	17	algorithms	algorithm	NOUN
cana-943	382	18	,	,	PUNCT
cana-943	382	19	such	such	ADJ
cana-943	382	20	as	as	ADP
cana-943	382	21	those	those	PRON
cana-943	382	22	based	base	VERB
cana-943	382	23	on	on	ADP
cana-943	382	24	elliptic	elliptic	ADJ
cana-943	382	25	curves	curve	NOUN
cana-943	382	26	and	and	CCONJ
cana-943	382	27	lattice	lattice	NOUN
cana-943	382	28	-	-	PUNCT
cana-943	382	29	based	base	VERB
cana-943	382	30	cryptography	cryptography	NOUN
cana-943	382	31	,	,	PUNCT
cana-943	382	32	require	require	VERB
cana-943	382	33	substantial	substantial	ADJ
cana-943	382	34	computational	computational	ADJ
cana-943	382	35	power	power	NOUN
cana-943	382	36	.	.	PUNCT
cana-943	383	1	this	this	PRON
cana-943	383	2	can	can	AUX
cana-943	383	3	be	be	AUX
cana-943	383	4	particularly	particularly	ADV
cana-943	383	5	problematic	problematic	ADJ
cana-943	383	6	for	for	ADP
cana-943	383	7	devices	device	NOUN
cana-943	383	8	with	with	ADP
cana-943	383	9	limited	limited	ADJ
cana-943	383	10	processing	processing	NOUN
cana-943	383	11	capabilities	capability	NOUN
cana-943	383	12	,	,	PUNCT
cana-943	383	13	such	such	ADJ
cana-943	383	14	as	as	ADP
cana-943	383	15	iot	iot	ADJ
cana-943	383	16	devices	device	NOUN
cana-943	383	17	.	.	PUNCT
cana-943	384	1	optimizing	optimize	VERB
cana-943	384	2	these	these	DET
cana-943	384	3	algorithms	algorithm	NOUN
cana-943	384	4	to	to	PART
cana-943	384	5	reduce	reduce	VERB
cana-943	384	6	computational	computational	ADJ
cana-943	384	7	overhead	overhead	NOUN
cana-943	384	8	without	without	ADP
cana-943	384	9	compromising	compromise	VERB
cana-943	384	10	security	security	NOUN
cana-943	384	11	is	be	AUX
cana-943	384	12	an	an	DET
cana-943	384	13	ongoing	ongoing	ADJ
cana-943	384	14	area	area	NOUN
cana-943	384	15	of	of	ADP
cana-943	384	16	research	research	NOUN
cana-943	384	17	.	.	PUNCT
cana-943	385	1	2	2	X
cana-943	385	2	.	.	X
cana-943	385	3	latency	latency	NOUN
cana-943	385	4	in	in	ADP
cana-943	385	5	real	real	ADJ
cana-943	385	6	-	-	PUNCT
cana-943	385	7	time	time	NOUN
cana-943	385	8	applications	application	NOUN
cana-943	385	9	:	:	PUNCT
cana-943	385	10	the	the	DET
cana-943	385	11	need	need	NOUN
cana-943	385	12	for	for	ADP
cana-943	385	13	real	real	ADJ
cana-943	385	14	-	-	PUNCT
cana-943	385	15	time	time	NOUN
cana-943	385	16	processing	processing	NOUN
cana-943	385	17	in	in	ADP
cana-943	385	18	applications	application	NOUN
cana-943	385	19	like	like	ADP
cana-943	385	20	secure	secure	ADJ
cana-943	385	21	communications	communication	NOUN
cana-943	385	22	and	and	CCONJ
cana-943	385	23	financial	financial	ADJ
cana-943	385	24	transactions	transaction	NOUN
cana-943	385	25	poses	pose	VERB
cana-943	385	26	a	a	DET
cana-943	385	27	significant	significant	ADJ
cana-943	385	28	challenge	challenge	NOUN
cana-943	385	29	.	.	PUNCT
cana-943	386	1	encryption	encryption	NOUN
cana-943	386	2	and	and	CCONJ
cana-943	386	3	decryption	decryption	NOUN
cana-943	386	4	processes	process	NOUN
cana-943	386	5	can	can	AUX
cana-943	386	6	introduce	introduce	VERB
cana-943	386	7	latency	latency	NOUN
cana-943	386	8	,	,	PUNCT
cana-943	386	9	which	which	PRON
cana-943	386	10	is	be	AUX
cana-943	386	11	detrimental	detrimental	ADJ
cana-943	386	12	in	in	ADP
cana-943	386	13	scenarios	scenario	NOUN
cana-943	386	14	where	where	SCONJ
cana-943	386	15	speed	speed	NOUN
cana-943	386	16	is	be	AUX
cana-943	386	17	critical	critical	ADJ
cana-943	386	18	.	.	PUNCT
cana-943	387	1	developing	develop	VERB
cana-943	387	2	more	more	ADV
cana-943	387	3	efficient	efficient	ADJ
cana-943	387	4	algorithms	algorithm	NOUN
cana-943	387	5	and	and	CCONJ
cana-943	387	6	hardware	hardware	NOUN
cana-943	387	7	acceleration	acceleration	NOUN
cana-943	387	8	techniques	technique	NOUN
cana-943	387	9	can	can	AUX
cana-943	387	10	help	help	VERB
cana-943	387	11	mitigate	mitigate	VERB
cana-943	387	12	these	these	DET
cana-943	387	13	latency	latency	NOUN
cana-943	387	14	issues	issue	NOUN
cana-943	387	15	.	.	PUNCT
cana-943	388	1	3	3	X
cana-943	388	2	.	.	X
cana-943	388	3	resource	resource	NOUN
cana-943	388	4	constraints	constraint	NOUN
cana-943	388	5	:	:	PUNCT
cana-943	388	6	cryptographic	cryptographic	ADJ
cana-943	388	7	operations	operation	NOUN
cana-943	388	8	often	often	ADV
cana-943	388	9	require	require	VERB
cana-943	388	10	significant	significant	ADJ
cana-943	388	11	memory	memory	NOUN
cana-943	388	12	and	and	CCONJ
cana-943	388	13	storage	storage	NOUN
cana-943	388	14	resources	resource	NOUN
cana-943	388	15	.	.	PUNCT
cana-943	389	1	for	for	ADP
cana-943	389	2	example	example	NOUN
cana-943	389	3	,	,	PUNCT
cana-943	389	4	fully	fully	ADV
cana-943	389	5	homomorphic	homomorphic	ADJ
cana-943	389	6	encryption	encryption	NOUN
cana-943	389	7	schemes	scheme	NOUN
cana-943	389	8	,	,	PUNCT
cana-943	389	9	while	while	SCONJ
cana-943	389	10	highly	highly	ADV
cana-943	389	11	secure	secure	ADJ
cana-943	389	12	,	,	PUNCT
cana-943	389	13	communications	communication	NOUN
cana-943	389	14	on	on	ADP
cana-943	389	15	applied	apply	VERB
cana-943	389	16	nonlinear	nonlinear	ADJ
cana-943	389	17	analysis	analysis	NOUN
cana-943	389	18	issn	issn	NOUN
cana-943	389	19	:	:	PUNCT
cana-943	389	20	1074	1074	NUM
cana-943	389	21	-	-	PUNCT
cana-943	389	22	133x	133x	NUM
cana-943	389	23	vol	vol	NOUN
cana-943	389	24	31	31	NUM
cana-943	389	25	no	no	NOUN
cana-943	389	26	.	.	PUNCT
cana-943	390	1	4s	4s	NUM
cana-943	390	2	(	(	PUNCT
cana-943	390	3	2024	2024	NUM
cana-943	390	4	)	)	PUNCT
cana-943	390	5	485	485	NUM
cana-943	390	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	390	7	are	be	AUX
cana-943	390	8	notorious	notorious	ADJ
cana-943	390	9	for	for	ADP
cana-943	390	10	their	their	PRON
cana-943	390	11	resource	resource	NOUN
cana-943	390	12	-	-	PUNCT
cana-943	390	13	intensive	intensive	ADJ
cana-943	390	14	nature	nature	NOUN
cana-943	390	15	.	.	PUNCT
cana-943	391	1	finding	find	VERB
cana-943	391	2	ways	way	NOUN
cana-943	391	3	to	to	PART
cana-943	391	4	implement	implement	VERB
cana-943	391	5	these	these	DET
cana-943	391	6	schemes	scheme	NOUN
cana-943	391	7	more	more	ADV
cana-943	391	8	efficiently	efficiently	ADV
cana-943	391	9	could	could	AUX
cana-943	391	10	make	make	VERB
cana-943	391	11	them	they	PRON
cana-943	391	12	more	more	ADV
cana-943	391	13	viable	viable	ADJ
cana-943	391	14	for	for	ADP
cana-943	391	15	practical	practical	ADJ
cana-943	391	16	use	use	NOUN
cana-943	391	17	.	.	PUNCT
cana-943	392	1	9.2	9.2	NUM
cana-943	392	2	.	.	PUNCT
cana-943	392	3	threats	threat	NOUN
cana-943	392	4	from	from	ADP
cana-943	392	5	quantum	quantum	NOUN
cana-943	392	6	computing	computing	NOUN
cana-943	392	7	the	the	DET
cana-943	392	8	advent	advent	NOUN
cana-943	392	9	of	of	ADP
cana-943	392	10	quantum	quantum	NOUN
cana-943	392	11	computing	computing	NOUN
cana-943	392	12	poses	pose	VERB
cana-943	392	13	a	a	DET
cana-943	392	14	profound	profound	ADJ
cana-943	392	15	threat	threat	NOUN
cana-943	392	16	to	to	ADP
cana-943	392	17	current	current	ADJ
cana-943	392	18	cryptographic	cryptographic	ADJ
cana-943	392	19	systems	system	NOUN
cana-943	392	20	.	.	PUNCT
cana-943	393	1	quantum	quantum	ADJ
cana-943	393	2	computers	computer	NOUN
cana-943	393	3	have	have	VERB
cana-943	393	4	the	the	DET
cana-943	393	5	potential	potential	NOUN
cana-943	393	6	to	to	PART
cana-943	393	7	solve	solve	VERB
cana-943	393	8	problems	problem	NOUN
cana-943	393	9	that	that	PRON
cana-943	393	10	are	be	AUX
cana-943	393	11	currently	currently	ADV
cana-943	393	12	infeasible	infeasible	ADJ
cana-943	393	13	for	for	ADP
cana-943	393	14	classical	classical	ADJ
cana-943	393	15	computers	computer	NOUN
cana-943	393	16	,	,	PUNCT
cana-943	393	17	thereby	thereby	ADV
cana-943	393	18	undermining	undermine	VERB
cana-943	393	19	the	the	DET
cana-943	393	20	security	security	NOUN
cana-943	393	21	of	of	ADP
cana-943	393	22	widely	widely	ADV
cana-943	393	23	used	use	VERB
cana-943	393	24	cryptographic	cryptographic	ADJ
cana-943	393	25	algorithms	algorithm	NOUN
cana-943	393	26	.	.	PUNCT
cana-943	394	1	9.2.1	9.2.1	X
cana-943	394	2	.	.	PUNCT
cana-943	394	3	key	key	ADJ
cana-943	394	4	quantum	quantum	ADJ
cana-943	394	5	computing	computing	NOUN
cana-943	394	6	threats	threat	NOUN
cana-943	394	7	:	:	PUNCT
cana-943	394	8	1	1	X
cana-943	394	9	.	.	X
cana-943	394	10	breaking	break	VERB
cana-943	394	11	public	public	ADJ
cana-943	394	12	-	-	PUNCT
cana-943	394	13	key	key	NOUN
cana-943	394	14	cryptosystems	cryptosystem	NOUN
cana-943	394	15	:	:	PUNCT
cana-943	394	16	quantum	quantum	ADJ
cana-943	394	17	algorithms	algorithm	NOUN
cana-943	394	18	,	,	PUNCT
cana-943	394	19	such	such	ADJ
cana-943	394	20	as	as	ADP
cana-943	394	21	shor	shor	PROPN
cana-943	394	22	's	's	PART
cana-943	394	23	algorithm	algorithm	NOUN
cana-943	394	24	,	,	PUNCT
cana-943	394	25	can	can	AUX
cana-943	394	26	efficiently	efficiently	ADV
cana-943	394	27	solve	solve	VERB
cana-943	394	28	problems	problem	NOUN
cana-943	394	29	like	like	ADP
cana-943	394	30	integer	integer	NOUN
cana-943	394	31	factorization	factorization	NOUN
cana-943	394	32	and	and	CCONJ
cana-943	394	33	discrete	discrete	ADJ
cana-943	394	34	logarithms	logarithm	NOUN
cana-943	394	35	,	,	PUNCT
cana-943	394	36	which	which	PRON
cana-943	394	37	form	form	VERB
cana-943	394	38	the	the	DET
cana-943	394	39	basis	basis	NOUN
cana-943	394	40	of	of	ADP
cana-943	394	41	many	many	ADJ
cana-943	394	42	public	public	ADJ
cana-943	394	43	-	-	PUNCT
cana-943	394	44	key	key	NOUN
cana-943	394	45	cryptosystems	cryptosystem	NOUN
cana-943	394	46	including	include	VERB
cana-943	394	47	rsa	rsa	PROPN
cana-943	394	48	and	and	CCONJ
cana-943	394	49	ecc	ecc	PROPN
cana-943	394	50	.	.	PROPN
cana-943	395	1	this	this	PRON
cana-943	395	2	necessitates	necessitate	VERB
cana-943	395	3	the	the	DET
cana-943	395	4	development	development	NOUN
cana-943	395	5	of	of	ADP
cana-943	395	6	quantum	quantum	NOUN
cana-943	395	7	-	-	PUNCT
cana-943	395	8	resistant	resistant	ADJ
cana-943	395	9	algorithms	algorithm	NOUN
cana-943	395	10	to	to	PART
cana-943	395	11	ensure	ensure	VERB
cana-943	395	12	long	long	ADJ
cana-943	395	13	-	-	PUNCT
cana-943	395	14	term	term	NOUN
cana-943	395	15	security	security	NOUN
cana-943	395	16	.	.	PUNCT
cana-943	396	1	2	2	X
cana-943	396	2	.	.	X
cana-943	396	3	quantum	quantum	NOUN
cana-943	396	4	-	-	PUNCT
cana-943	396	5	enhanced	enhance	VERB
cana-943	396	6	attacks	attack	NOUN
cana-943	396	7	:	:	PUNCT
cana-943	396	8	beyond	beyond	ADP
cana-943	396	9	breaking	break	VERB
cana-943	396	10	specific	specific	ADJ
cana-943	396	11	cryptographic	cryptographic	ADJ
cana-943	396	12	schemes	scheme	NOUN
cana-943	396	13	,	,	PUNCT
cana-943	396	14	quantum	quantum	ADJ
cana-943	396	15	computers	computer	NOUN
cana-943	396	16	could	could	AUX
cana-943	396	17	enhance	enhance	VERB
cana-943	396	18	other	other	ADJ
cana-943	396	19	types	type	NOUN
cana-943	396	20	of	of	ADP
cana-943	396	21	attacks	attack	NOUN
cana-943	396	22	,	,	PUNCT
cana-943	396	23	such	such	ADJ
cana-943	396	24	as	as	ADP
cana-943	396	25	brute	brute	ADJ
cana-943	396	26	-	-	PUNCT
cana-943	396	27	force	force	NOUN
cana-943	396	28	searches	search	NOUN
cana-943	396	29	,	,	PUNCT
cana-943	396	30	by	by	ADP
cana-943	396	31	leveraging	leverage	VERB
cana-943	396	32	grover	grover	NOUN
cana-943	396	33	's	's	PART
cana-943	396	34	algorithm	algorithm	NOUN
cana-943	396	35	.	.	PUNCT
cana-943	397	1	this	this	PRON
cana-943	397	2	could	could	AUX
cana-943	397	3	significantly	significantly	ADV
cana-943	397	4	reduce	reduce	VERB
cana-943	397	5	the	the	DET
cana-943	397	6	time	time	NOUN
cana-943	397	7	required	require	VERB
cana-943	397	8	to	to	PART
cana-943	397	9	crack	crack	VERB
cana-943	397	10	symmetric	symmetric	ADJ
cana-943	397	11	-	-	PUNCT
cana-943	397	12	key	key	ADJ
cana-943	397	13	algorithms	algorithm	NOUN
cana-943	397	14	.	.	PUNCT
cana-943	398	1	3	3	X
cana-943	398	2	.	.	X
cana-943	398	3	post	post	ADJ
cana-943	398	4	-	-	ADJ
cana-943	398	5	quantum	quantum	ADJ
cana-943	398	6	cryptography	cryptography	NOUN
cana-943	398	7	:	:	PUNCT
cana-943	398	8	to	to	PART
cana-943	398	9	counteract	counteract	VERB
cana-943	398	10	these	these	DET
cana-943	398	11	threats	threat	NOUN
cana-943	398	12	,	,	PUNCT
cana-943	398	13	researchers	researcher	NOUN
cana-943	398	14	are	be	AUX
cana-943	398	15	focusing	focus	VERB
cana-943	398	16	on	on	ADP
cana-943	398	17	postquantum	postquantum	NOUN
cana-943	398	18	cryptography	cryptography	NOUN
cana-943	398	19	,	,	PUNCT
cana-943	398	20	which	which	PRON
cana-943	398	21	involves	involve	VERB
cana-943	398	22	developing	develop	VERB
cana-943	398	23	cryptographic	cryptographic	ADJ
cana-943	398	24	systems	system	NOUN
cana-943	398	25	that	that	PRON
cana-943	398	26	are	be	AUX
cana-943	398	27	secure	secure	ADJ
cana-943	398	28	against	against	ADP
cana-943	398	29	quantum	quantum	NOUN
cana-943	398	30	attacks	attack	NOUN
cana-943	398	31	.	.	PUNCT
cana-943	399	1	lattice	lattice	NOUN
cana-943	399	2	-	-	PUNCT
cana-943	399	3	based	base	VERB
cana-943	399	4	cryptography	cryptography	NOUN
cana-943	399	5	,	,	PUNCT
cana-943	399	6	code	code	NOUN
cana-943	399	7	-	-	PUNCT
cana-943	399	8	based	base	VERB
cana-943	399	9	cryptography	cryptography	NOUN
cana-943	399	10	,	,	PUNCT
cana-943	399	11	and	and	CCONJ
cana-943	399	12	multivariate	multivariate	VERB
cana-943	399	13	polynomial	polynomial	ADJ
cana-943	399	14	cryptography	cryptography	NOUN
cana-943	399	15	are	be	AUX
cana-943	399	16	promising	promise	VERB
cana-943	399	17	candidates	candidate	NOUN
cana-943	399	18	in	in	ADP
cana-943	399	19	this	this	DET
cana-943	399	20	domain	domain	NOUN
cana-943	399	21	[	[	X
cana-943	399	22	17	17	NUM
cana-943	399	23	]	]	SYM
cana-943	399	24	.	.	PUNCT
cana-943	400	1	9.3	9.3	NUM
cana-943	400	2	.	.	PUNCT
cana-943	401	1	emerging	emerge	VERB
cana-943	401	2	trends	trend	NOUN
cana-943	401	3	and	and	CCONJ
cana-943	401	4	innovations	innovation	NOUN
cana-943	401	5	in	in	ADP
cana-943	401	6	algebraic	algebraic	ADJ
cana-943	401	7	cryptography	cryptography	NOUN
cana-943	401	8	the	the	DET
cana-943	401	9	field	field	NOUN
cana-943	401	10	of	of	ADP
cana-943	401	11	algebraic	algebraic	ADJ
cana-943	401	12	cryptography	cryptography	NOUN
cana-943	401	13	is	be	AUX
cana-943	401	14	dynamic	dynamic	ADJ
cana-943	401	15	,	,	PUNCT
cana-943	401	16	with	with	ADP
cana-943	401	17	continuous	continuous	ADJ
cana-943	401	18	innovations	innovation	NOUN
cana-943	401	19	and	and	CCONJ
cana-943	401	20	emerging	emerge	VERB
cana-943	401	21	trends	trend	NOUN
cana-943	401	22	that	that	PRON
cana-943	401	23	address	address	VERB
cana-943	401	24	existing	exist	VERB
cana-943	401	25	challenges	challenge	NOUN
cana-943	401	26	and	and	CCONJ
cana-943	401	27	explore	explore	VERB
cana-943	401	28	new	new	ADJ
cana-943	401	29	applications	application	NOUN
cana-943	401	30	.	.	PUNCT
cana-943	402	1	9.3.1	9.3.1	X
cana-943	402	2	.	.	NOUN
cana-943	402	3	notable	notable	ADJ
cana-943	402	4	emerging	emerge	VERB
cana-943	402	5	trends	trend	NOUN
cana-943	402	6	and	and	CCONJ
cana-943	402	7	innovations	innovation	NOUN
cana-943	402	8	:	:	PUNCT
cana-943	402	9	1	1	X
cana-943	402	10	.	.	X
cana-943	402	11	homomorphic	homomorphic	ADJ
cana-943	402	12	encryption	encryption	NOUN
cana-943	402	13	:	:	PUNCT
cana-943	402	14	homomorphic	homomorphic	ADJ
cana-943	402	15	encryption	encryption	NOUN
cana-943	402	16	,	,	PUNCT
cana-943	402	17	which	which	PRON
cana-943	402	18	allows	allow	VERB
cana-943	402	19	computations	computation	NOUN
cana-943	402	20	on	on	ADP
cana-943	402	21	encrypted	encrypt	VERB
cana-943	402	22	data	datum	NOUN
cana-943	402	23	without	without	ADP
cana-943	402	24	decryption	decryption	NOUN
cana-943	402	25	,	,	PUNCT
cana-943	402	26	is	be	AUX
cana-943	402	27	gaining	gain	VERB
cana-943	402	28	traction	traction	NOUN
cana-943	402	29	for	for	ADP
cana-943	402	30	its	its	PRON
cana-943	402	31	potential	potential	NOUN
cana-943	402	32	in	in	ADP
cana-943	402	33	secure	secure	ADJ
cana-943	402	34	data	datum	NOUN
cana-943	402	35	processing	processing	NOUN
cana-943	402	36	and	and	CCONJ
cana-943	402	37	cloud	cloud	NOUN
cana-943	402	38	computing	computing	NOUN
cana-943	402	39	.	.	PUNCT
cana-943	403	1	recent	recent	ADJ
cana-943	403	2	advances	advance	NOUN
cana-943	403	3	aim	aim	VERB
cana-943	403	4	to	to	PART
cana-943	403	5	improve	improve	VERB
cana-943	403	6	the	the	DET
cana-943	403	7	efficiency	efficiency	NOUN
cana-943	403	8	and	and	CCONJ
cana-943	403	9	practicality	practicality	NOUN
cana-943	403	10	of	of	ADP
cana-943	403	11	fully	fully	ADV
cana-943	403	12	homomorphic	homomorphic	ADJ
cana-943	403	13	encryption	encryption	NOUN
cana-943	403	14	schemes	scheme	NOUN
cana-943	403	15	[	[	X
cana-943	403	16	10	10	NUM
cana-943	403	17	]	]	PUNCT
cana-943	403	18	.	.	PUNCT
cana-943	404	1	2	2	X
cana-943	404	2	.	.	NUM
cana-943	404	3	zero	zero	NUM
cana-943	404	4	-	-	PUNCT
cana-943	404	5	knowledge	knowledge	NOUN
cana-943	404	6	proofs	proof	NOUN
cana-943	404	7	:	:	PUNCT
cana-943	404	8	zero	zero	NUM
cana-943	404	9	-	-	PUNCT
cana-943	404	10	knowledge	knowledge	NOUN
cana-943	404	11	proofs	proof	NOUN
cana-943	404	12	(	(	PUNCT
cana-943	404	13	zkps	zkps	PROPN
cana-943	404	14	)	)	PUNCT
cana-943	404	15	are	be	AUX
cana-943	404	16	becoming	become	VERB
cana-943	404	17	increasingly	increasingly	ADV
cana-943	404	18	important	important	ADJ
cana-943	404	19	for	for	ADP
cana-943	404	20	privacy	privacy	NOUN
cana-943	404	21	-	-	PUNCT
cana-943	404	22	preserving	preserve	VERB
cana-943	404	23	protocols	protocol	NOUN
cana-943	404	24	.	.	PUNCT
cana-943	405	1	innovations	innovation	NOUN
cana-943	405	2	in	in	ADP
cana-943	405	3	zkps	zkps	PROPN
cana-943	405	4	,	,	PUNCT
cana-943	405	5	such	such	ADJ
cana-943	405	6	as	as	ADP
cana-943	405	7	zk	zk	NOUN
cana-943	405	8	-	-	PUNCT
cana-943	405	9	snarks	snark	NOUN
cana-943	405	10	and	and	CCONJ
cana-943	405	11	zkstarks	zkstark	NOUN
cana-943	405	12	,	,	PUNCT
cana-943	405	13	offer	offer	VERB
cana-943	405	14	efficient	efficient	ADJ
cana-943	405	15	and	and	CCONJ
cana-943	405	16	scalable	scalable	ADJ
cana-943	405	17	solutions	solution	NOUN
cana-943	405	18	for	for	ADP
cana-943	405	19	applications	application	NOUN
cana-943	405	20	in	in	ADP
cana-943	405	21	blockchain	blockchain	PROPN
cana-943	405	22	and	and	CCONJ
cana-943	405	23	secure	secure	VERB
cana-943	405	24	multiparty	multiparty	ADJ
cana-943	405	25	computation	computation	NOUN
cana-943	406	1	[	[	X
cana-943	406	2	12	12	NUM
cana-943	406	3	]	]	PUNCT
cana-943	406	4	.	.	PUNCT
cana-943	407	1	3	3	X
cana-943	407	2	.	.	X
cana-943	407	3	lattice	lattice	NOUN
cana-943	407	4	-	-	PUNCT
cana-943	407	5	based	base	VERB
cana-943	407	6	cryptography	cryptography	NOUN
cana-943	407	7	:	:	PUNCT
cana-943	407	8	as	as	ADP
cana-943	407	9	one	one	NUM
cana-943	407	10	of	of	ADP
cana-943	407	11	the	the	DET
cana-943	407	12	leading	lead	VERB
cana-943	407	13	candidates	candidate	NOUN
cana-943	407	14	for	for	ADP
cana-943	407	15	post	post	ADJ
cana-943	407	16	-	-	ADJ
cana-943	407	17	quantum	quantum	ADJ
cana-943	407	18	cryptography	cryptography	NOUN
cana-943	407	19	,	,	PUNCT
cana-943	407	20	lattice	lattice	NOUN
cana-943	407	21	-	-	PUNCT
cana-943	407	22	based	base	VERB
cana-943	407	23	cryptography	cryptography	NOUN
cana-943	407	24	continues	continue	VERB
cana-943	407	25	to	to	PART
cana-943	407	26	evolve	evolve	VERB
cana-943	407	27	.	.	PUNCT
cana-943	408	1	researchers	researcher	NOUN
cana-943	408	2	are	be	AUX
cana-943	408	3	developing	develop	VERB
cana-943	408	4	more	more	ADV
cana-943	408	5	efficient	efficient	ADJ
cana-943	408	6	lattice	lattice	NOUN
cana-943	408	7	-	-	PUNCT
cana-943	408	8	based	base	VERB
cana-943	408	9	schemes	scheme	NOUN
cana-943	408	10	and	and	CCONJ
cana-943	408	11	exploring	explore	VERB
cana-943	408	12	their	their	PRON
cana-943	408	13	applications	application	NOUN
cana-943	408	14	in	in	ADP
cana-943	408	15	secure	secure	ADJ
cana-943	408	16	communications	communication	NOUN
cana-943	408	17	,	,	PUNCT
cana-943	408	18	digital	digital	ADJ
cana-943	408	19	signatures	signature	NOUN
cana-943	408	20	,	,	PUNCT
cana-943	408	21	and	and	CCONJ
cana-943	408	22	key	key	ADJ
cana-943	408	23	exchange	exchange	NOUN
cana-943	408	24	protocols	protocol	NOUN
cana-943	409	1	[	[	X
cana-943	409	2	11	11	NUM
cana-943	409	3	]	]	PUNCT
cana-943	409	4	.	.	PUNCT
cana-943	410	1	4	4	X
cana-943	410	2	.	.	X
cana-943	410	3	blockchain	blockchain	PROPN
cana-943	410	4	and	and	CCONJ
cana-943	410	5	decentralized	decentralized	ADJ
cana-943	410	6	technologies	technology	NOUN
cana-943	410	7	:	:	PUNCT
cana-943	410	8	algebraic	algebraic	ADJ
cana-943	410	9	cryptography	cryptography	NOUN
cana-943	410	10	plays	play	VERB
cana-943	410	11	a	a	DET
cana-943	410	12	crucial	crucial	ADJ
cana-943	410	13	role	role	NOUN
cana-943	410	14	in	in	ADP
cana-943	410	15	blockchain	blockchain	PROPN
cana-943	410	16	technology	technology	PROPN
cana-943	410	17	.	.	PUNCT
cana-943	411	1	emerging	emerge	VERB
cana-943	411	2	trends	trend	NOUN
cana-943	411	3	in	in	ADP
cana-943	411	4	this	this	DET
cana-943	411	5	area	area	NOUN
cana-943	411	6	include	include	VERB
cana-943	411	7	the	the	DET
cana-943	411	8	use	use	NOUN
cana-943	411	9	of	of	ADP
cana-943	411	10	algebraic	algebraic	ADJ
cana-943	411	11	techniques	technique	NOUN
cana-943	411	12	for	for	ADP
cana-943	411	13	communications	communication	NOUN
cana-943	411	14	on	on	ADP
cana-943	411	15	applied	apply	VERB
cana-943	411	16	nonlinear	nonlinear	ADJ
cana-943	411	17	analysis	analysis	NOUN
cana-943	411	18	issn	issn	NOUN
cana-943	411	19	:	:	PUNCT
cana-943	411	20	1074	1074	NUM
cana-943	411	21	-	-	PUNCT
cana-943	411	22	133x	133x	NUM
cana-943	411	23	vol	vol	NOUN
cana-943	411	24	31	31	NUM
cana-943	411	25	no	no	NOUN
cana-943	411	26	.	.	PUNCT
cana-943	412	1	4s	4s	NUM
cana-943	412	2	(	(	PUNCT
cana-943	412	3	2024	2024	NUM
cana-943	412	4	)	)	PUNCT
cana-943	412	5	486	486	NUM
cana-943	412	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	412	7	improving	improve	VERB
cana-943	412	8	blockchain	blockchain	PROPN
cana-943	412	9	scalability	scalability	NOUN
cana-943	412	10	,	,	PUNCT
cana-943	412	11	enhancing	enhance	VERB
cana-943	412	12	consensus	consensus	NOUN
cana-943	412	13	mechanisms	mechanism	NOUN
cana-943	412	14	,	,	PUNCT
cana-943	412	15	and	and	CCONJ
cana-943	412	16	ensuring	ensure	VERB
cana-943	412	17	privacy	privacy	NOUN
cana-943	412	18	and	and	CCONJ
cana-943	412	19	security	security	NOUN
cana-943	412	20	in	in	ADP
cana-943	412	21	decentralized	decentralized	ADJ
cana-943	412	22	applications	application	NOUN
cana-943	412	23	[	[	X
cana-943	412	24	20	20	NUM
cana-943	412	25	]	]	PUNCT
cana-943	412	26	.	.	PUNCT
cana-943	413	1	5	5	X
cana-943	413	2	.	.	X
cana-943	413	3	integration	integration	NOUN
cana-943	413	4	with	with	ADP
cana-943	413	5	ai	ai	NOUN
cana-943	413	6	and	and	CCONJ
cana-943	413	7	machine	machine	NOUN
cana-943	413	8	learning	learning	NOUN
cana-943	413	9	:	:	PUNCT
cana-943	413	10	the	the	DET
cana-943	413	11	intersection	intersection	NOUN
cana-943	413	12	of	of	ADP
cana-943	413	13	algebraic	algebraic	ADJ
cana-943	413	14	cryptography	cryptography	NOUN
cana-943	413	15	and	and	CCONJ
cana-943	413	16	artificial	artificial	ADJ
cana-943	413	17	intelligence	intelligence	NOUN
cana-943	413	18	(	(	PUNCT
cana-943	413	19	ai	ai	NOUN
cana-943	413	20	)	)	PUNCT
cana-943	413	21	presents	present	VERB
cana-943	413	22	exciting	exciting	ADJ
cana-943	413	23	possibilities	possibility	NOUN
cana-943	413	24	.	.	PUNCT
cana-943	414	1	for	for	ADP
cana-943	414	2	instance	instance	NOUN
cana-943	414	3	,	,	PUNCT
cana-943	414	4	using	use	VERB
cana-943	414	5	algebraic	algebraic	ADJ
cana-943	414	6	structures	structure	NOUN
cana-943	414	7	to	to	PART
cana-943	414	8	secure	secure	VERB
cana-943	414	9	ai	ai	NOUN
cana-943	414	10	models	model	NOUN
cana-943	414	11	and	and	CCONJ
cana-943	414	12	training	training	NOUN
cana-943	414	13	data	datum	NOUN
cana-943	414	14	,	,	PUNCT
cana-943	414	15	as	as	ADV
cana-943	414	16	well	well	ADV
cana-943	414	17	as	as	ADP
cana-943	414	18	employing	employ	VERB
cana-943	414	19	ai	ai	VERB
cana-943	414	20	to	to	PART
cana-943	414	21	optimize	optimize	VERB
cana-943	414	22	cryptographic	cryptographic	ADJ
cana-943	414	23	algorithms	algorithm	NOUN
cana-943	414	24	,	,	PUNCT
cana-943	414	25	are	be	AUX
cana-943	414	26	promising	promise	VERB
cana-943	414	27	areas	area	NOUN
cana-943	414	28	of	of	ADP
cana-943	414	29	research	research	NOUN
cana-943	414	30	[	[	X
cana-943	414	31	22	22	NUM
cana-943	414	32	]	]	PUNCT
cana-943	414	33	.	.	PUNCT
cana-943	415	1	the	the	DET
cana-943	415	2	future	future	NOUN
cana-943	415	3	of	of	ADP
cana-943	415	4	algebraic	algebraic	ADJ
cana-943	415	5	cryptography	cryptography	NOUN
cana-943	415	6	is	be	AUX
cana-943	415	7	both	both	PRON
cana-943	415	8	challenging	challenging	ADJ
cana-943	415	9	and	and	CCONJ
cana-943	415	10	promising	promising	ADJ
cana-943	415	11	.	.	PUNCT
cana-943	416	1	addressing	address	VERB
cana-943	416	2	scalability	scalability	NOUN
cana-943	416	3	and	and	CCONJ
cana-943	416	4	efficiency	efficiency	NOUN
cana-943	416	5	issues	issue	NOUN
cana-943	416	6	,	,	PUNCT
cana-943	416	7	countering	counter	VERB
cana-943	416	8	threats	threat	NOUN
cana-943	416	9	from	from	ADP
cana-943	416	10	quantum	quantum	NOUN
cana-943	416	11	computing	computing	NOUN
cana-943	416	12	,	,	PUNCT
cana-943	416	13	and	and	CCONJ
cana-943	416	14	leveraging	leverage	VERB
cana-943	416	15	emerging	emerge	VERB
cana-943	416	16	trends	trend	NOUN
cana-943	416	17	and	and	CCONJ
cana-943	416	18	innovations	innovation	NOUN
cana-943	416	19	are	be	AUX
cana-943	416	20	critical	critical	ADJ
cana-943	416	21	for	for	ADP
cana-943	416	22	advancing	advance	VERB
cana-943	416	23	the	the	DET
cana-943	416	24	field	field	NOUN
cana-943	416	25	.	.	PUNCT
cana-943	417	1	continued	continue	VERB
cana-943	417	2	research	research	NOUN
cana-943	417	3	and	and	CCONJ
cana-943	417	4	collaboration	collaboration	NOUN
cana-943	417	5	are	be	AUX
cana-943	417	6	essential	essential	ADJ
cana-943	417	7	to	to	PART
cana-943	417	8	develop	develop	VERB
cana-943	417	9	robust	robust	ADJ
cana-943	417	10	,	,	PUNCT
cana-943	417	11	efficient	efficient	ADJ
cana-943	417	12	,	,	PUNCT
cana-943	417	13	and	and	CCONJ
cana-943	417	14	quantum	quantum	NOUN
cana-943	417	15	-	-	PUNCT
cana-943	417	16	resistant	resistant	ADJ
cana-943	417	17	cryptographic	cryptographic	ADJ
cana-943	417	18	systems	system	NOUN
cana-943	417	19	that	that	PRON
cana-943	417	20	can	can	AUX
cana-943	417	21	meet	meet	VERB
cana-943	417	22	the	the	DET
cana-943	417	23	evolving	evolve	VERB
cana-943	417	24	demands	demand	NOUN
cana-943	417	25	of	of	ADP
cana-943	417	26	information	information	NOUN
cana-943	417	27	security	security	NOUN
cana-943	417	28	in	in	ADP
cana-943	417	29	the	the	DET
cana-943	417	30	digital	digital	ADJ
cana-943	417	31	age	age	NOUN
cana-943	417	32	.	.	PUNCT
cana-943	418	1	by	by	ADP
cana-943	418	2	exploring	explore	VERB
cana-943	418	3	these	these	DET
cana-943	418	4	challenges	challenge	NOUN
cana-943	418	5	and	and	CCONJ
cana-943	418	6	future	future	ADJ
cana-943	418	7	directions	direction	NOUN
cana-943	418	8	,	,	PUNCT
cana-943	418	9	we	we	PRON
cana-943	418	10	can	can	AUX
cana-943	418	11	enhance	enhance	VERB
cana-943	418	12	our	our	PRON
cana-943	418	13	understanding	understanding	NOUN
cana-943	418	14	of	of	ADP
cana-943	418	15	the	the	DET
cana-943	418	16	critical	critical	ADJ
cana-943	418	17	role	role	NOUN
cana-943	418	18	that	that	PRON
cana-943	418	19	algebraic	algebraic	ADJ
cana-943	418	20	foundations	foundation	NOUN
cana-943	418	21	play	play	VERB
cana-943	418	22	in	in	ADP
cana-943	418	23	strengthening	strengthen	VERB
cana-943	418	24	cryptographic	cryptographic	ADJ
cana-943	418	25	protocols	protocol	NOUN
cana-943	418	26	and	and	CCONJ
cana-943	418	27	ensuring	ensure	VERB
cana-943	418	28	secure	secure	ADJ
cana-943	418	29	communications	communication	NOUN
cana-943	418	30	and	and	CCONJ
cana-943	418	31	data	datum	NOUN
cana-943	418	32	protection	protection	NOUN
cana-943	418	33	.	.	PUNCT
cana-943	419	1	10	10	NUM
cana-943	419	2	.	.	PUNCT
cana-943	419	3	conclusion	conclusion	NOUN
cana-943	419	4	in	in	ADP
cana-943	419	5	this	this	DET
cana-943	419	6	research	research	NOUN
cana-943	419	7	paper	paper	NOUN
cana-943	419	8	,	,	PUNCT
cana-943	419	9	we	we	PRON
cana-943	419	10	have	have	AUX
cana-943	419	11	explored	explore	VERB
cana-943	419	12	the	the	DET
cana-943	419	13	intricate	intricate	ADJ
cana-943	419	14	relationship	relationship	NOUN
cana-943	419	15	between	between	ADP
cana-943	419	16	algebra	algebra	NOUN
cana-943	419	17	and	and	CCONJ
cana-943	419	18	cryptography	cryptography	NOUN
cana-943	419	19	,	,	PUNCT
cana-943	419	20	emphasizing	emphasize	VERB
cana-943	419	21	how	how	SCONJ
cana-943	419	22	mathematical	mathematical	ADJ
cana-943	419	23	foundations	foundation	NOUN
cana-943	419	24	enhance	enhance	VERB
cana-943	419	25	information	information	NOUN
cana-943	419	26	security	security	NOUN
cana-943	419	27	.	.	PUNCT
cana-943	420	1	key	key	ADJ
cana-943	420	2	findings	finding	NOUN
cana-943	420	3	include	include	VERB
cana-943	420	4	:	:	PUNCT
cana-943	420	5	1	1	X
cana-943	420	6	.	.	X
cana-943	420	7	role	role	NOUN
cana-943	420	8	of	of	ADP
cana-943	420	9	algebraic	algebraic	ADJ
cana-943	420	10	structures	structure	NOUN
cana-943	420	11	:	:	PUNCT
cana-943	420	12	algebraic	algebraic	ADJ
cana-943	420	13	structures	structure	NOUN
cana-943	420	14	such	such	ADJ
cana-943	420	15	as	as	ADP
cana-943	420	16	groups	group	NOUN
cana-943	420	17	,	,	PUNCT
cana-943	420	18	rings	ring	NOUN
cana-943	420	19	,	,	PUNCT
cana-943	420	20	and	and	CCONJ
cana-943	420	21	fields	field	NOUN
cana-943	420	22	play	play	VERB
cana-943	420	23	a	a	DET
cana-943	420	24	crucial	crucial	ADJ
cana-943	420	25	role	role	NOUN
cana-943	420	26	in	in	ADP
cana-943	420	27	developing	develop	VERB
cana-943	420	28	robust	robust	ADJ
cana-943	420	29	cryptographic	cryptographic	ADJ
cana-943	420	30	protocols	protocol	NOUN
cana-943	420	31	.	.	PUNCT
cana-943	421	1	these	these	DET
cana-943	421	2	structures	structure	NOUN
cana-943	421	3	provide	provide	VERB
cana-943	421	4	the	the	DET
cana-943	421	5	mathematical	mathematical	ADJ
cana-943	421	6	backbone	backbone	NOUN
cana-943	421	7	for	for	ADP
cana-943	421	8	encryption	encryption	NOUN
cana-943	421	9	algorithms	algorithm	NOUN
cana-943	421	10	,	,	PUNCT
cana-943	421	11	key	key	ADJ
cana-943	421	12	exchange	exchange	NOUN
cana-943	421	13	protocols	protocol	NOUN
cana-943	421	14	,	,	PUNCT
cana-943	421	15	and	and	CCONJ
cana-943	421	16	digital	digital	ADJ
cana-943	421	17	signatures	signature	NOUN
cana-943	421	18	,	,	PUNCT
cana-943	421	19	ensuring	ensure	VERB
cana-943	421	20	their	their	PRON
cana-943	421	21	security	security	NOUN
cana-943	421	22	and	and	CCONJ
cana-943	421	23	efficiency	efficiency	NOUN
cana-943	421	24	.	.	PUNCT
cana-943	422	1	2	2	X
cana-943	422	2	.	.	X
cana-943	422	3	advanced	advanced	ADJ
cana-943	422	4	cryptographic	cryptographic	ADJ
cana-943	422	5	techniques	technique	NOUN
cana-943	422	6	:	:	PUNCT
cana-943	422	7	techniques	technique	NOUN
cana-943	422	8	such	such	ADJ
cana-943	422	9	as	as	ADP
cana-943	422	10	elliptic	elliptic	ADJ
cana-943	422	11	curve	curve	NOUN
cana-943	422	12	cryptography	cryptography	NOUN
cana-943	422	13	(	(	PUNCT
cana-943	422	14	ecc	ecc	PROPN
cana-943	422	15	)	)	PUNCT
cana-943	422	16	and	and	CCONJ
cana-943	422	17	lattice	lattice	NOUN
cana-943	422	18	-	-	PUNCT
cana-943	422	19	based	base	VERB
cana-943	422	20	cryptography	cryptography	NOUN
cana-943	422	21	offer	offer	VERB
cana-943	422	22	significant	significant	ADJ
cana-943	422	23	advantages	advantage	NOUN
cana-943	422	24	in	in	ADP
cana-943	422	25	terms	term	NOUN
cana-943	422	26	of	of	ADP
cana-943	422	27	security	security	NOUN
cana-943	422	28	and	and	CCONJ
cana-943	422	29	efficiency	efficiency	NOUN
cana-943	422	30	.	.	PUNCT
cana-943	423	1	ecc	ecc	PROPN
cana-943	423	2	,	,	PUNCT
cana-943	423	3	for	for	ADP
cana-943	423	4	example	example	NOUN
cana-943	423	5	,	,	PUNCT
cana-943	423	6	provides	provide	VERB
cana-943	423	7	strong	strong	ADJ
cana-943	423	8	security	security	NOUN
cana-943	423	9	with	with	ADP
cana-943	423	10	smaller	small	ADJ
cana-943	423	11	key	key	ADJ
cana-943	423	12	sizes	size	NOUN
cana-943	423	13	,	,	PUNCT
cana-943	423	14	making	make	VERB
cana-943	423	15	it	it	PRON
cana-943	423	16	ideal	ideal	ADJ
cana-943	423	17	for	for	ADP
cana-943	423	18	resource	resource	NOUN
cana-943	423	19	-	-	PUNCT
cana-943	423	20	constrained	constrain	VERB
cana-943	423	21	environments	environment	NOUN
cana-943	423	22	[	[	X
cana-943	423	23	7	7	NUM
cana-943	423	24	]	]	PUNCT
cana-943	423	25	.	.	PUNCT
cana-943	424	1	lattice	lattice	NOUN
cana-943	424	2	-	-	PUNCT
cana-943	424	3	based	base	VERB
cana-943	424	4	cryptography	cryptography	NOUN
cana-943	424	5	,	,	PUNCT
cana-943	424	6	on	on	ADP
cana-943	424	7	the	the	DET
cana-943	424	8	other	other	ADJ
cana-943	424	9	hand	hand	NOUN
cana-943	424	10	,	,	PUNCT
cana-943	424	11	is	be	AUX
cana-943	424	12	a	a	DET
cana-943	424	13	promising	promising	ADJ
cana-943	424	14	candidate	candidate	NOUN
cana-943	424	15	for	for	ADP
cana-943	424	16	post	post	ADJ
cana-943	424	17	-	-	ADJ
cana-943	424	18	quantum	quantum	ADJ
cana-943	424	19	cryptographic	cryptographic	ADJ
cana-943	424	20	standards	standard	NOUN
cana-943	424	21	due	due	ADP
cana-943	424	22	to	to	ADP
cana-943	424	23	its	its	PRON
cana-943	424	24	resistance	resistance	NOUN
cana-943	424	25	to	to	ADP
cana-943	424	26	quantum	quantum	ADJ
cana-943	424	27	attacks	attack	NOUN
cana-943	424	28	[	[	X
cana-943	424	29	11	11	NUM
cana-943	424	30	]	]	PUNCT
cana-943	424	31	.	.	PUNCT
cana-943	425	1	3	3	X
cana-943	425	2	.	.	X
cana-943	425	3	homomorphic	homomorphic	ADJ
cana-943	425	4	encryption	encryption	NOUN
cana-943	425	5	and	and	CCONJ
cana-943	425	6	zero	zero	NUM
cana-943	425	7	-	-	PUNCT
cana-943	425	8	knowledge	knowledge	NOUN
cana-943	425	9	proofs	proof	NOUN
cana-943	425	10	:	:	PUNCT
cana-943	425	11	homomorphic	homomorphic	ADJ
cana-943	425	12	encryption	encryption	NOUN
cana-943	425	13	allows	allow	VERB
cana-943	425	14	for	for	ADP
cana-943	425	15	secure	secure	ADJ
cana-943	425	16	computations	computation	NOUN
cana-943	425	17	on	on	ADP
cana-943	425	18	encrypted	encrypt	VERB
cana-943	425	19	data	datum	NOUN
cana-943	425	20	,	,	PUNCT
cana-943	425	21	which	which	PRON
cana-943	425	22	is	be	AUX
cana-943	425	23	particularly	particularly	ADV
cana-943	425	24	useful	useful	ADJ
cana-943	425	25	for	for	ADP
cana-943	425	26	cloud	cloud	NOUN
cana-943	425	27	computing	computing	NOUN
cana-943	425	28	and	and	CCONJ
cana-943	425	29	data	datum	NOUN
cana-943	425	30	privacy	privacy	NOUN
cana-943	425	31	.	.	PUNCT
cana-943	426	1	zero	zero	NUM
cana-943	426	2	-	-	PUNCT
cana-943	426	3	knowledge	knowledge	NOUN
cana-943	426	4	proofs	proof	NOUN
cana-943	426	5	(	(	PUNCT
cana-943	426	6	zkps	zkps	PROPN
cana-943	426	7	)	)	PUNCT
cana-943	426	8	enable	enable	VERB
cana-943	426	9	one	one	NUM
cana-943	426	10	party	party	NOUN
cana-943	426	11	to	to	PART
cana-943	426	12	prove	prove	VERB
cana-943	426	13	knowledge	knowledge	NOUN
cana-943	426	14	of	of	ADP
cana-943	426	15	a	a	DET
cana-943	426	16	secret	secret	NOUN
cana-943	426	17	without	without	ADP
cana-943	426	18	revealing	reveal	VERB
cana-943	426	19	the	the	DET
cana-943	426	20	secret	secret	NOUN
cana-943	426	21	itself	itself	PRON
cana-943	426	22	,	,	PUNCT
cana-943	426	23	enhancing	enhance	VERB
cana-943	426	24	privacy	privacy	NOUN
cana-943	426	25	in	in	ADP
cana-943	426	26	blockchain	blockchain	PROPN
cana-943	426	27	and	and	CCONJ
cana-943	426	28	other	other	ADJ
cana-943	426	29	applications	application	NOUN
cana-943	426	30	[	[	X
cana-943	426	31	10][12	10][12	NUM
cana-943	426	32	]	]	X
cana-943	426	33	.	.	PUNCT
cana-943	427	1	4	4	X
cana-943	427	2	.	.	X
cana-943	427	3	challenges	challenge	NOUN
cana-943	427	4	and	and	CCONJ
cana-943	427	5	future	future	ADJ
cana-943	427	6	directions	direction	NOUN
cana-943	427	7	:	:	PUNCT
cana-943	427	8	the	the	DET
cana-943	427	9	scalability	scalability	NOUN
cana-943	427	10	and	and	CCONJ
cana-943	427	11	efficiency	efficiency	NOUN
cana-943	427	12	of	of	ADP
cana-943	427	13	cryptographic	cryptographic	ADJ
cana-943	427	14	algorithms	algorithm	NOUN
cana-943	427	15	remain	remain	VERB
cana-943	427	16	significant	significant	ADJ
cana-943	427	17	challenges	challenge	NOUN
cana-943	427	18	.	.	PUNCT
cana-943	428	1	additionally	additionally	ADV
cana-943	428	2	,	,	PUNCT
cana-943	428	3	the	the	DET
cana-943	428	4	advent	advent	NOUN
cana-943	428	5	of	of	ADP
cana-943	428	6	quantum	quantum	NOUN
cana-943	428	7	computing	computing	NOUN
cana-943	428	8	poses	pose	VERB
cana-943	428	9	a	a	DET
cana-943	428	10	threat	threat	NOUN
cana-943	428	11	to	to	ADP
cana-943	428	12	existing	exist	VERB
cana-943	428	13	cryptographic	cryptographic	ADJ
cana-943	428	14	systems	system	NOUN
cana-943	428	15	,	,	PUNCT
cana-943	428	16	necessitating	necessitate	VERB
cana-943	428	17	the	the	DET
cana-943	428	18	development	development	NOUN
cana-943	428	19	of	of	ADP
cana-943	428	20	quantum	quantum	NOUN
cana-943	428	21	-	-	PUNCT
cana-943	428	22	resistant	resistant	ADJ
cana-943	428	23	algorithms	algorithm	NOUN
cana-943	428	24	.	.	PUNCT
cana-943	429	1	emerging	emerge	VERB
cana-943	429	2	trends	trend	NOUN
cana-943	429	3	in	in	ADP
cana-943	429	4	algebraic	algebraic	ADJ
cana-943	429	5	cryptography	cryptography	NOUN
cana-943	429	6	,	,	PUNCT
cana-943	429	7	such	such	ADJ
cana-943	429	8	as	as	ADP
cana-943	429	9	the	the	DET
cana-943	429	10	integration	integration	NOUN
cana-943	429	11	with	with	ADP
cana-943	429	12	artificial	artificial	ADJ
cana-943	429	13	intelligence	intelligence	NOUN
cana-943	429	14	and	and	CCONJ
cana-943	429	15	blockchain	blockchain	PROPN
cana-943	429	16	technologies	technologies	PROPN
cana-943	429	17	,	,	PUNCT
cana-943	429	18	offer	offer	VERB
cana-943	429	19	new	new	ADJ
cana-943	429	20	avenues	avenue	NOUN
cana-943	429	21	for	for	ADP
cana-943	429	22	research	research	NOUN
cana-943	429	23	and	and	CCONJ
cana-943	429	24	application	application	NOUN
cana-943	429	25	[	[	X
cana-943	429	26	17][20][22	17][20][22	NOUN
cana-943	429	27	]	]	PUNCT
cana-943	429	28	.	.	PUNCT
cana-943	430	1	communications	communication	NOUN
cana-943	430	2	on	on	ADP
cana-943	430	3	applied	apply	VERB
cana-943	430	4	nonlinear	nonlinear	ADJ
cana-943	430	5	analysis	analysis	NOUN
cana-943	430	6	issn	issn	NOUN
cana-943	430	7	:	:	PUNCT
cana-943	430	8	1074	1074	NUM
cana-943	430	9	-	-	PUNCT
cana-943	430	10	133x	133x	NUM
cana-943	430	11	vol	vol	NOUN
cana-943	430	12	31	31	NUM
cana-943	430	13	no	no	NOUN
cana-943	430	14	.	.	PUNCT
cana-943	431	1	4s	4s	NUM
cana-943	431	2	(	(	PUNCT
cana-943	431	3	2024	2024	NUM
cana-943	431	4	)	)	PUNCT
cana-943	431	5	487	487	NUM
cana-943	431	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	431	7	the	the	DET
cana-943	431	8	findings	finding	NOUN
cana-943	431	9	from	from	ADP
cana-943	431	10	this	this	DET
cana-943	431	11	research	research	NOUN
cana-943	431	12	have	have	VERB
cana-943	431	13	profound	profound	ADJ
cana-943	431	14	implications	implication	NOUN
cana-943	431	15	for	for	ADP
cana-943	431	16	information	information	NOUN
cana-943	431	17	security	security	NOUN
cana-943	431	18	:	:	PUNCT
cana-943	431	19	1	1	X
cana-943	431	20	.	.	NUM
cana-943	431	21	enhanced	enhance	VERB
cana-943	431	22	security	security	NOUN
cana-943	431	23	protocols	protocol	NOUN
cana-943	431	24	:	:	PUNCT
cana-943	431	25	the	the	DET
cana-943	431	26	use	use	NOUN
cana-943	431	27	of	of	ADP
cana-943	431	28	advanced	advanced	ADJ
cana-943	431	29	algebraic	algebraic	ADJ
cana-943	431	30	techniques	technique	NOUN
cana-943	431	31	can	can	AUX
cana-943	431	32	significantly	significantly	ADV
cana-943	431	33	enhance	enhance	VERB
cana-943	431	34	the	the	DET
cana-943	431	35	security	security	NOUN
cana-943	431	36	of	of	ADP
cana-943	431	37	cryptographic	cryptographic	ADJ
cana-943	431	38	protocols	protocol	NOUN
cana-943	431	39	.	.	PUNCT
cana-943	432	1	by	by	ADP
cana-943	432	2	leveraging	leverage	VERB
cana-943	432	3	the	the	DET
cana-943	432	4	mathematical	mathematical	ADJ
cana-943	432	5	properties	property	NOUN
cana-943	432	6	of	of	ADP
cana-943	432	7	algebraic	algebraic	ADJ
cana-943	432	8	structures	structure	NOUN
cana-943	432	9	,	,	PUNCT
cana-943	432	10	we	we	PRON
cana-943	432	11	can	can	AUX
cana-943	432	12	develop	develop	VERB
cana-943	432	13	more	more	ADV
cana-943	432	14	robust	robust	ADJ
cana-943	432	15	and	and	CCONJ
cana-943	432	16	efficient	efficient	ADJ
cana-943	432	17	cryptographic	cryptographic	ADJ
cana-943	432	18	systems	system	NOUN
cana-943	432	19	that	that	PRON
cana-943	432	20	are	be	AUX
cana-943	432	21	resistant	resistant	ADJ
cana-943	432	22	to	to	ADP
cana-943	432	23	various	various	ADJ
cana-943	432	24	types	type	NOUN
cana-943	432	25	of	of	ADP
cana-943	432	26	attacks	attack	NOUN
cana-943	432	27	.	.	PUNCT
cana-943	433	1	2	2	X
cana-943	433	2	.	.	X
cana-943	433	3	quantum	quantum	NOUN
cana-943	433	4	-	-	PUNCT
cana-943	433	5	resistant	resistant	ADJ
cana-943	433	6	cryptography	cryptography	NOUN
cana-943	433	7	:	:	PUNCT
cana-943	433	8	with	with	ADP
cana-943	433	9	the	the	DET
cana-943	433	10	impending	impending	ADJ
cana-943	433	11	threat	threat	NOUN
cana-943	433	12	of	of	ADP
cana-943	433	13	quantum	quantum	NOUN
cana-943	433	14	computing	computing	NOUN
cana-943	433	15	,	,	PUNCT
cana-943	433	16	the	the	DET
cana-943	433	17	development	development	NOUN
cana-943	433	18	of	of	ADP
cana-943	433	19	quantum	quantum	NOUN
cana-943	433	20	-	-	PUNCT
cana-943	433	21	resistant	resistant	ADJ
cana-943	433	22	cryptographic	cryptographic	ADJ
cana-943	433	23	algorithms	algorithms	NOUN
cana-943	433	24	is	be	AUX
cana-943	433	25	crucial	crucial	ADJ
cana-943	433	26	.	.	PUNCT
cana-943	434	1	lattice	lattice	NOUN
cana-943	434	2	-	-	PUNCT
cana-943	434	3	based	base	VERB
cana-943	434	4	cryptography	cryptography	NOUN
cana-943	434	5	and	and	CCONJ
cana-943	434	6	other	other	ADJ
cana-943	434	7	post	post	ADJ
cana-943	434	8	-	-	ADJ
cana-943	434	9	quantum	quantum	ADJ
cana-943	434	10	techniques	technique	NOUN
cana-943	434	11	offer	offer	VERB
cana-943	434	12	promising	promise	VERB
cana-943	434	13	solutions	solution	NOUN
cana-943	434	14	to	to	PART
cana-943	434	15	ensure	ensure	VERB
cana-943	434	16	the	the	DET
cana-943	434	17	longevity	longevity	NOUN
cana-943	434	18	and	and	CCONJ
cana-943	434	19	security	security	NOUN
cana-943	434	20	of	of	ADP
cana-943	434	21	cryptographic	cryptographic	ADJ
cana-943	434	22	systems	system	NOUN
cana-943	434	23	in	in	ADP
cana-943	434	24	the	the	DET
cana-943	434	25	quantum	quantum	ADJ
cana-943	434	26	era	era	NOUN
cana-943	434	27	.	.	PUNCT
cana-943	435	1	3	3	X
cana-943	435	2	.	.	X
cana-943	435	3	privacy	privacy	NOUN
cana-943	435	4	-	-	PUNCT
cana-943	435	5	preserving	preserve	VERB
cana-943	435	6	technologies	technology	NOUN
cana-943	435	7	:	:	PUNCT
cana-943	435	8	homomorphic	homomorphic	ADJ
cana-943	435	9	encryption	encryption	NOUN
cana-943	435	10	and	and	CCONJ
cana-943	435	11	zero	zero	NUM
cana-943	435	12	-	-	PUNCT
cana-943	435	13	knowledge	knowledge	NOUN
cana-943	435	14	proofs	proof	NOUN
cana-943	435	15	provide	provide	VERB
cana-943	435	16	robust	robust	ADJ
cana-943	435	17	frameworks	framework	NOUN
cana-943	435	18	for	for	ADP
cana-943	435	19	maintaining	maintain	VERB
cana-943	435	20	data	data	NOUN
cana-943	435	21	privacy	privacy	NOUN
cana-943	435	22	and	and	CCONJ
cana-943	435	23	security	security	NOUN
cana-943	435	24	.	.	PUNCT
cana-943	436	1	these	these	DET
cana-943	436	2	technologies	technology	NOUN
cana-943	436	3	are	be	AUX
cana-943	436	4	particularly	particularly	ADV
cana-943	436	5	relevant	relevant	ADJ
cana-943	436	6	for	for	ADP
cana-943	436	7	secure	secure	ADJ
cana-943	436	8	cloud	cloud	NOUN
cana-943	436	9	computing	computing	NOUN
cana-943	436	10	,	,	PUNCT
cana-943	436	11	blockchain	blockchain	PROPN
cana-943	436	12	applications	application	NOUN
cana-943	436	13	,	,	PUNCT
cana-943	436	14	and	and	CCONJ
cana-943	436	15	secure	secure	VERB
cana-943	436	16	multiparty	multiparty	ADJ
cana-943	436	17	computations	computation	NOUN
cana-943	436	18	,	,	PUNCT
cana-943	436	19	where	where	SCONJ
cana-943	436	20	data	datum	NOUN
cana-943	436	21	privacy	privacy	NOUN
cana-943	436	22	is	be	AUX
cana-943	436	23	paramount	paramount	ADJ
cana-943	436	24	.	.	PUNCT
cana-943	437	1	4	4	X
cana-943	437	2	.	.	X
cana-943	437	3	scalability	scalability	NOUN
cana-943	437	4	and	and	CCONJ
cana-943	437	5	efficiency	efficiency	NOUN
cana-943	437	6	:	:	PUNCT
cana-943	437	7	addressing	address	VERB
cana-943	437	8	the	the	DET
cana-943	437	9	scalability	scalability	NOUN
cana-943	437	10	and	and	CCONJ
cana-943	437	11	efficiency	efficiency	NOUN
cana-943	437	12	issues	issue	NOUN
cana-943	437	13	of	of	ADP
cana-943	437	14	cryptographic	cryptographic	ADJ
cana-943	437	15	algorithms	algorithm	NOUN
cana-943	437	16	is	be	AUX
cana-943	437	17	essential	essential	ADJ
cana-943	437	18	for	for	ADP
cana-943	437	19	their	their	PRON
cana-943	437	20	practical	practical	ADJ
cana-943	437	21	implementation	implementation	NOUN
cana-943	437	22	.	.	PUNCT
cana-943	438	1	optimizing	optimize	VERB
cana-943	438	2	these	these	DET
cana-943	438	3	algorithms	algorithm	NOUN
cana-943	438	4	to	to	PART
cana-943	438	5	work	work	VERB
cana-943	438	6	efficiently	efficiently	ADV
cana-943	438	7	in	in	ADP
cana-943	438	8	real	real	ADJ
cana-943	438	9	-	-	PUNCT
cana-943	438	10	time	time	NOUN
cana-943	438	11	applications	application	NOUN
cana-943	438	12	and	and	CCONJ
cana-943	438	13	resource	resource	NOUN
cana-943	438	14	-	-	PUNCT
cana-943	438	15	constrained	constrain	VERB
cana-943	438	16	environments	environment	NOUN
cana-943	438	17	will	will	AUX
cana-943	438	18	facilitate	facilitate	VERB
cana-943	438	19	their	their	PRON
cana-943	438	20	widespread	widespread	ADJ
cana-943	438	21	adoption	adoption	NOUN
cana-943	438	22	and	and	CCONJ
cana-943	438	23	usability	usability	NOUN
cana-943	438	24	.	.	PUNCT
cana-943	439	1	based	base	VERB
cana-943	439	2	on	on	ADP
cana-943	439	3	the	the	DET
cana-943	439	4	findings	finding	NOUN
cana-943	439	5	and	and	CCONJ
cana-943	439	6	implications	implication	NOUN
cana-943	439	7	discussed	discussed	AUX
cana-943	439	8	,	,	PUNCT
cana-943	439	9	the	the	DET
cana-943	439	10	following	follow	VERB
cana-943	439	11	recommendations	recommendation	NOUN
cana-943	439	12	for	for	ADP
cana-943	439	13	future	future	ADJ
cana-943	439	14	research	research	NOUN
cana-943	439	15	are	be	AUX
cana-943	439	16	proposed	propose	VERB
cana-943	439	17	:	:	PUNCT
cana-943	439	18	1	1	X
cana-943	439	19	.	.	X
cana-943	439	20	optimization	optimization	NOUN
cana-943	439	21	of	of	ADP
cana-943	439	22	cryptographic	cryptographic	ADJ
cana-943	439	23	algorithms	algorithm	NOUN
cana-943	439	24	:	:	PUNCT
cana-943	439	25	future	future	ADJ
cana-943	439	26	research	research	NOUN
cana-943	439	27	should	should	AUX
cana-943	439	28	focus	focus	VERB
cana-943	439	29	on	on	ADP
cana-943	439	30	optimizing	optimize	VERB
cana-943	439	31	the	the	DET
cana-943	439	32	computational	computational	ADJ
cana-943	439	33	efficiency	efficiency	NOUN
cana-943	439	34	of	of	ADP
cana-943	439	35	cryptographic	cryptographic	ADJ
cana-943	439	36	algorithms	algorithm	NOUN
cana-943	439	37	,	,	PUNCT
cana-943	439	38	particularly	particularly	ADV
cana-943	439	39	for	for	ADP
cana-943	439	40	resource	resource	NOUN
cana-943	439	41	-	-	PUNCT
cana-943	439	42	constrained	constrain	VERB
cana-943	439	43	environments	environment	NOUN
cana-943	439	44	like	like	ADP
cana-943	439	45	iot	iot	NOUN
cana-943	439	46	devices	device	NOUN
cana-943	439	47	.	.	PUNCT
cana-943	440	1	this	this	PRON
cana-943	440	2	includes	include	VERB
cana-943	440	3	developing	develop	VERB
cana-943	440	4	hardware	hardware	NOUN
cana-943	440	5	acceleration	acceleration	NOUN
cana-943	440	6	techniques	technique	NOUN
cana-943	440	7	and	and	CCONJ
cana-943	440	8	algorithmic	algorithmic	ADJ
cana-943	440	9	improvements	improvement	NOUN
cana-943	440	10	to	to	PART
cana-943	440	11	reduce	reduce	VERB
cana-943	440	12	latency	latency	NOUN
cana-943	440	13	and	and	CCONJ
cana-943	440	14	computational	computational	ADJ
cana-943	440	15	overhead	overhead	NOUN
cana-943	440	16	.	.	PUNCT
cana-943	441	1	2	2	X
cana-943	441	2	.	.	X
cana-943	441	3	development	development	NOUN
cana-943	441	4	of	of	ADP
cana-943	441	5	quantum	quantum	NOUN
cana-943	441	6	-	-	PUNCT
cana-943	441	7	resistant	resistant	ADJ
cana-943	441	8	algorithms	algorithm	NOUN
cana-943	441	9	:	:	PUNCT
cana-943	441	10	there	there	PRON
cana-943	441	11	is	be	VERB
cana-943	441	12	an	an	DET
cana-943	441	13	urgent	urgent	ADJ
cana-943	441	14	need	need	NOUN
cana-943	441	15	to	to	PART
cana-943	441	16	develop	develop	VERB
cana-943	441	17	and	and	CCONJ
cana-943	441	18	standardize	standardize	VERB
cana-943	441	19	quantum	quantum	NOUN
cana-943	441	20	-	-	PUNCT
cana-943	441	21	resistant	resistant	ADJ
cana-943	441	22	cryptographic	cryptographic	ADJ
cana-943	441	23	algorithms	algorithm	NOUN
cana-943	441	24	.	.	PUNCT
cana-943	442	1	researchers	researcher	NOUN
cana-943	442	2	should	should	AUX
cana-943	442	3	explore	explore	VERB
cana-943	442	4	and	and	CCONJ
cana-943	442	5	refine	refine	VERB
cana-943	442	6	lattice	lattice	NOUN
cana-943	442	7	-	-	PUNCT
cana-943	442	8	based	base	VERB
cana-943	442	9	cryptography	cryptography	NOUN
cana-943	442	10	,	,	PUNCT
cana-943	442	11	code	code	NOUN
cana-943	442	12	-	-	PUNCT
cana-943	442	13	based	base	VERB
cana-943	442	14	cryptography	cryptography	NOUN
cana-943	442	15	,	,	PUNCT
cana-943	442	16	and	and	CCONJ
cana-943	442	17	other	other	ADJ
cana-943	442	18	post	post	ADJ
cana-943	442	19	-	-	ADJ
cana-943	442	20	quantum	quantum	ADJ
cana-943	442	21	techniques	technique	NOUN
cana-943	442	22	to	to	PART
cana-943	442	23	ensure	ensure	VERB
cana-943	442	24	robust	robust	ADJ
cana-943	442	25	security	security	NOUN
cana-943	442	26	against	against	ADP
cana-943	442	27	quantum	quantum	NOUN
cana-943	442	28	attacks	attack	NOUN
cana-943	442	29	.	.	PUNCT
cana-943	443	1	3	3	X
cana-943	443	2	.	.	X
cana-943	443	3	integration	integration	NOUN
cana-943	443	4	with	with	ADP
cana-943	443	5	emerging	emerge	VERB
cana-943	443	6	technologies	technology	NOUN
cana-943	443	7	:	:	PUNCT
cana-943	443	8	further	further	ADJ
cana-943	443	9	research	research	NOUN
cana-943	443	10	should	should	AUX
cana-943	443	11	investigate	investigate	VERB
cana-943	443	12	the	the	DET
cana-943	443	13	integration	integration	NOUN
cana-943	443	14	of	of	ADP
cana-943	443	15	algebraic	algebraic	ADJ
cana-943	443	16	cryptographic	cryptographic	ADJ
cana-943	443	17	techniques	technique	NOUN
cana-943	443	18	with	with	ADP
cana-943	443	19	emerging	emerge	VERB
cana-943	443	20	technologies	technology	NOUN
cana-943	443	21	such	such	ADJ
cana-943	443	22	as	as	ADP
cana-943	443	23	blockchain	blockchain	PROPN
cana-943	443	24	,	,	PUNCT
cana-943	443	25	ai	ai	VERB
cana-943	443	26	,	,	PUNCT
cana-943	443	27	and	and	CCONJ
cana-943	443	28	machine	machine	NOUN
cana-943	443	29	learning	learning	NOUN
cana-943	443	30	.	.	PUNCT
cana-943	444	1	this	this	PRON
cana-943	444	2	includes	include	VERB
cana-943	444	3	exploring	explore	VERB
cana-943	444	4	how	how	SCONJ
cana-943	444	5	algebraic	algebraic	ADJ
cana-943	444	6	structures	structure	NOUN
cana-943	444	7	can	can	AUX
cana-943	444	8	enhance	enhance	VERB
cana-943	444	9	the	the	DET
cana-943	444	10	security	security	NOUN
cana-943	444	11	and	and	CCONJ
cana-943	444	12	privacy	privacy	NOUN
cana-943	444	13	of	of	ADP
cana-943	444	14	these	these	DET
cana-943	444	15	technologies	technology	NOUN
cana-943	444	16	and	and	CCONJ
cana-943	444	17	developing	develop	VERB
cana-943	444	18	new	new	ADJ
cana-943	444	19	cryptographic	cryptographic	ADJ
cana-943	444	20	protocols	protocol	NOUN
cana-943	444	21	tailored	tailor	VERB
cana-943	444	22	to	to	ADP
cana-943	444	23	their	their	PRON
cana-943	444	24	unique	unique	ADJ
cana-943	444	25	requirements	requirement	NOUN
cana-943	444	26	.	.	PUNCT
cana-943	445	1	4	4	X
cana-943	445	2	.	.	X
cana-943	445	3	advanced	advanced	ADJ
cana-943	445	4	privacy	privacy	NOUN
cana-943	445	5	-	-	PUNCT
cana-943	445	6	preserving	preserve	VERB
cana-943	445	7	techniques	technique	NOUN
cana-943	445	8	:	:	PUNCT
cana-943	445	9	the	the	DET
cana-943	445	10	development	development	NOUN
cana-943	445	11	of	of	ADP
cana-943	445	12	advanced	advanced	ADJ
cana-943	445	13	privacypreserving	privacypreserving	NOUN
cana-943	445	14	techniques	technique	NOUN
cana-943	445	15	,	,	PUNCT
cana-943	445	16	such	such	ADJ
cana-943	445	17	as	as	ADP
cana-943	445	18	more	more	ADV
cana-943	445	19	efficient	efficient	ADJ
cana-943	445	20	homomorphic	homomorphic	ADJ
cana-943	445	21	encryption	encryption	NOUN
cana-943	445	22	schemes	scheme	NOUN
cana-943	445	23	and	and	CCONJ
cana-943	445	24	scalable	scalable	ADJ
cana-943	445	25	zero	zero	NUM
cana-943	445	26	-	-	PUNCT
cana-943	445	27	knowledge	knowledge	NOUN
cana-943	445	28	proofs	proof	NOUN
cana-943	445	29	,	,	PUNCT
cana-943	445	30	should	should	AUX
cana-943	445	31	be	be	AUX
cana-943	445	32	prioritized	prioritize	VERB
cana-943	445	33	.	.	PUNCT
cana-943	446	1	these	these	DET
cana-943	446	2	techniques	technique	NOUN
cana-943	446	3	are	be	AUX
cana-943	446	4	critical	critical	ADJ
cana-943	446	5	for	for	ADP
cana-943	446	6	ensuring	ensure	VERB
cana-943	446	7	data	datum	NOUN
cana-943	446	8	privacy	privacy	NOUN
cana-943	446	9	in	in	ADP
cana-943	446	10	various	various	ADJ
cana-943	446	11	applications	application	NOUN
cana-943	446	12	,	,	PUNCT
cana-943	446	13	from	from	ADP
cana-943	446	14	secure	secure	ADJ
cana-943	446	15	cloud	cloud	NOUN
cana-943	446	16	computing	computing	NOUN
cana-943	446	17	to	to	ADP
cana-943	446	18	blockchain	blockchain	PROPN
cana-943	446	19	technologies	technology	NOUN
cana-943	446	20	.	.	PUNCT
cana-943	447	1	5	5	X
cana-943	447	2	.	.	X
cana-943	447	3	interdisciplinary	interdisciplinary	ADJ
cana-943	447	4	collaboration	collaboration	NOUN
cana-943	447	5	:	:	PUNCT
cana-943	447	6	encouraging	encourage	VERB
cana-943	447	7	interdisciplinary	interdisciplinary	ADJ
cana-943	447	8	collaboration	collaboration	NOUN
cana-943	447	9	between	between	ADP
cana-943	447	10	mathematicians	mathematician	NOUN
cana-943	447	11	,	,	PUNCT
cana-943	447	12	computer	computer	NOUN
cana-943	447	13	scientists	scientist	NOUN
cana-943	447	14	,	,	PUNCT
cana-943	447	15	and	and	CCONJ
cana-943	447	16	engineers	engineer	NOUN
cana-943	447	17	will	will	AUX
cana-943	447	18	foster	foster	VERB
cana-943	447	19	innovation	innovation	NOUN
cana-943	447	20	in	in	ADP
cana-943	447	21	algebraic	algebraic	ADJ
cana-943	447	22	communications	communication	NOUN
cana-943	447	23	on	on	ADP
cana-943	447	24	applied	apply	VERB
cana-943	447	25	nonlinear	nonlinear	ADJ
cana-943	447	26	analysis	analysis	NOUN
cana-943	447	27	issn	issn	NOUN
cana-943	447	28	:	:	PUNCT
cana-943	447	29	1074	1074	NUM
cana-943	447	30	-	-	PUNCT
cana-943	447	31	133x	133x	NUM
cana-943	447	32	vol	vol	NOUN
cana-943	447	33	31	31	NUM
cana-943	447	34	no	no	NOUN
cana-943	447	35	.	.	PUNCT
cana-943	448	1	4s	4s	NUM
cana-943	448	2	(	(	PUNCT
cana-943	448	3	2024	2024	NUM
cana-943	448	4	)	)	PUNCT
cana-943	448	5	488	488	NUM
cana-943	448	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	448	7	cryptography	cryptography	NOUN
cana-943	448	8	.	.	PUNCT
cana-943	449	1	by	by	ADP
cana-943	449	2	combining	combine	VERB
cana-943	449	3	expertise	expertise	NOUN
cana-943	449	4	from	from	ADP
cana-943	449	5	different	different	ADJ
cana-943	449	6	fields	field	NOUN
cana-943	449	7	,	,	PUNCT
cana-943	449	8	researchers	researcher	NOUN
cana-943	449	9	can	can	AUX
cana-943	449	10	develop	develop	VERB
cana-943	449	11	novel	novel	ADJ
cana-943	449	12	cryptographic	cryptographic	ADJ
cana-943	449	13	solutions	solution	NOUN
cana-943	449	14	that	that	PRON
cana-943	449	15	are	be	AUX
cana-943	449	16	both	both	PRON
cana-943	449	17	theoretically	theoretically	ADV
cana-943	449	18	sound	sound	ADJ
cana-943	449	19	and	and	CCONJ
cana-943	449	20	practically	practically	ADV
cana-943	449	21	viable	viable	ADJ
cana-943	449	22	.	.	PUNCT
cana-943	450	1	in	in	ADP
cana-943	450	2	conclusion	conclusion	NOUN
cana-943	450	3	,	,	PUNCT
cana-943	450	4	the	the	DET
cana-943	450	5	intersection	intersection	NOUN
cana-943	450	6	of	of	ADP
cana-943	450	7	algebra	algebra	NOUN
cana-943	450	8	and	and	CCONJ
cana-943	450	9	cryptography	cryptography	NOUN
cana-943	450	10	offers	offer	VERB
cana-943	450	11	a	a	DET
cana-943	450	12	rich	rich	ADJ
cana-943	450	13	and	and	CCONJ
cana-943	450	14	evolving	evolve	VERB
cana-943	450	15	field	field	NOUN
cana-943	450	16	of	of	ADP
cana-943	450	17	research	research	NOUN
cana-943	450	18	with	with	ADP
cana-943	450	19	significant	significant	ADJ
cana-943	450	20	implications	implication	NOUN
cana-943	450	21	for	for	ADP
cana-943	450	22	information	information	NOUN
cana-943	450	23	security	security	NOUN
cana-943	450	24	.	.	PUNCT
cana-943	451	1	by	by	ADP
cana-943	451	2	addressing	address	VERB
cana-943	451	3	current	current	ADJ
cana-943	451	4	challenges	challenge	NOUN
cana-943	451	5	and	and	CCONJ
cana-943	451	6	exploring	explore	VERB
cana-943	451	7	future	future	ADJ
cana-943	451	8	directions	direction	NOUN
cana-943	451	9	,	,	PUNCT
cana-943	451	10	we	we	PRON
cana-943	451	11	can	can	AUX
cana-943	451	12	develop	develop	VERB
cana-943	451	13	robust	robust	ADJ
cana-943	451	14	cryptographic	cryptographic	ADJ
cana-943	451	15	systems	system	NOUN
cana-943	451	16	that	that	PRON
cana-943	451	17	ensure	ensure	VERB
cana-943	451	18	the	the	DET
cana-943	451	19	security	security	NOUN
cana-943	451	20	and	and	CCONJ
cana-943	451	21	privacy	privacy	NOUN
cana-943	451	22	of	of	ADP
cana-943	451	23	information	information	NOUN
cana-943	451	24	in	in	ADP
cana-943	451	25	an	an	DET
cana-943	451	26	increasingly	increasingly	ADV
cana-943	451	27	digital	digital	ADJ
cana-943	451	28	world	world	NOUN
cana-943	451	29	.	.	PUNCT
cana-943	452	1	references	reference	NOUN
cana-943	452	2	[	[	X
cana-943	452	3	1	1	NUM
cana-943	452	4	]	]	X
cana-943	452	5	diffie	diffie	PROPN
cana-943	452	6	,	,	PUNCT
cana-943	452	7	w.	w.	PROPN
cana-943	452	8	,	,	PUNCT
cana-943	452	9	&	&	CCONJ
cana-943	452	10	hellman	hellman	NOUN
cana-943	452	11	,	,	PUNCT
cana-943	452	12	m.	m.	NOUN
cana-943	452	13	(	(	PUNCT
cana-943	452	14	1976	1976	NUM
cana-943	452	15	)	)	PUNCT
cana-943	452	16	.	.	PUNCT
cana-943	453	1	new	new	ADJ
cana-943	453	2	directions	direction	NOUN
cana-943	453	3	in	in	ADP
cana-943	453	4	cryptography	cryptography	NOUN
cana-943	453	5	.	.	PUNCT
cana-943	454	1	ieee	ieee	NOUN
cana-943	454	2	transactions	transaction	NOUN
cana-943	454	3	on	on	ADP
cana-943	454	4	information	information	NOUN
cana-943	454	5	theory	theory	NOUN
cana-943	454	6	,	,	PUNCT
cana-943	454	7	22(6	22(6	NUM
cana-943	454	8	)	)	PUNCT
cana-943	454	9	,	,	PUNCT
cana-943	454	10	644	644	NUM
cana-943	454	11	-	-	SYM
cana-943	454	12	654	654	NUM
cana-943	454	13	.	.	PUNCT
cana-943	455	1	doi:10.1109	doi:10.1109	VERB
cana-943	455	2	/	/	SYM
cana-943	455	3	tit.1976.1055638	tit.1976.1055638	PROPN
cana-943	455	4	[	[	X
cana-943	455	5	2	2	NUM
cana-943	455	6	]	]	X
cana-943	455	7	rivest	riv	ADJ
cana-943	455	8	,	,	PUNCT
cana-943	455	9	r.	r.	PROPN
cana-943	455	10	l.	l.	PROPN
cana-943	455	11	,	,	PUNCT
cana-943	455	12	shamir	shamir	PROPN
cana-943	455	13	,	,	PUNCT
cana-943	455	14	a.	a.	NOUN
cana-943	455	15	,	,	PUNCT
cana-943	455	16	&	&	CCONJ
cana-943	455	17	adleman	adleman	PROPN
cana-943	455	18	,	,	PUNCT
cana-943	455	19	l.	l.	PROPN
cana-943	455	20	(	(	PUNCT
cana-943	455	21	1978	1978	NUM
cana-943	455	22	)	)	PUNCT
cana-943	455	23	.	.	PUNCT
cana-943	456	1	a	a	DET
cana-943	456	2	method	method	NOUN
cana-943	456	3	for	for	ADP
cana-943	456	4	obtaining	obtain	VERB
cana-943	456	5	digital	digital	ADJ
cana-943	456	6	signatures	signature	NOUN
cana-943	456	7	and	and	CCONJ
cana-943	456	8	public	public	ADJ
cana-943	456	9	-	-	PUNCT
cana-943	456	10	key	key	NOUN
cana-943	456	11	cryptosystems	cryptosystem	NOUN
cana-943	456	12	.	.	PUNCT
cana-943	457	1	communications	communication	NOUN
cana-943	457	2	of	of	ADP
cana-943	457	3	the	the	DET
cana-943	457	4	acm	acm	PROPN
cana-943	457	5	,	,	PUNCT
cana-943	457	6	21(2	21(2	NUM
cana-943	457	7	)	)	PUNCT
cana-943	457	8	,	,	PUNCT
cana-943	457	9	120	120	NUM
cana-943	457	10	-	-	SYM
cana-943	457	11	126	126	NUM
cana-943	457	12	.	.	PUNCT
cana-943	457	13	doi:10.1145/359340.359342	doi:10.1145/359340.359342	NOUN
cana-943	458	1	[	[	X
cana-943	458	2	3	3	NUM
cana-943	458	3	]	]	X
cana-943	458	4	koblitz	koblitz	NOUN
cana-943	458	5	,	,	PUNCT
cana-943	458	6	n.	n.	NOUN
cana-943	458	7	(	(	PUNCT
cana-943	458	8	1987	1987	NUM
cana-943	458	9	)	)	PUNCT
cana-943	458	10	.	.	PUNCT
cana-943	459	1	elliptic	elliptic	ADJ
cana-943	459	2	curve	curve	NOUN
cana-943	459	3	cryptosystems	cryptosystem	NOUN
cana-943	459	4	.	.	PUNCT
cana-943	460	1	mathematics	mathematic	NOUN
cana-943	460	2	of	of	ADP
cana-943	460	3	computation	computation	NOUN
cana-943	460	4	,	,	PUNCT
cana-943	460	5	48(177	48(177	PROPN
cana-943	460	6	)	)	PUNCT
cana-943	460	7	,	,	PUNCT
cana-943	460	8	203	203	NUM
cana-943	460	9	-	-	SYM
cana-943	460	10	209	209	NUM
cana-943	460	11	.	.	PUNCT
cana-943	460	12	doi:10.2307/2007884	doi:10.2307/2007884	PUNCT
cana-943	461	1	[	[	X
cana-943	461	2	4	4	NUM
cana-943	461	3	]	]	SYM
cana-943	461	4	menezes	meneze	NOUN
cana-943	461	5	,	,	PUNCT
cana-943	461	6	a.	a.	PROPN
cana-943	461	7	j.	j.	PROPN
cana-943	461	8	,	,	PUNCT
cana-943	461	9	van	van	PROPN
cana-943	461	10	oorschot	oorschot	PROPN
cana-943	461	11	,	,	PUNCT
cana-943	461	12	p.	p.	PROPN
cana-943	461	13	c.	c.	PROPN
cana-943	461	14	,	,	PUNCT
cana-943	461	15	&	&	CCONJ
cana-943	461	16	vanstone	vanstone	NOUN
cana-943	461	17	,	,	PUNCT
cana-943	461	18	s.	s.	PROPN
cana-943	461	19	a.	a.	PROPN
cana-943	461	20	(	(	PUNCT
cana-943	461	21	1996	1996	NUM
cana-943	461	22	)	)	PUNCT
cana-943	461	23	.	.	PUNCT
cana-943	462	1	handbook	handbook	NOUN
cana-943	462	2	of	of	ADP
cana-943	462	3	applied	applied	ADJ
cana-943	462	4	cryptography	cryptography	NOUN
cana-943	462	5	.	.	PUNCT
cana-943	463	1	crc	crc	PROPN
cana-943	463	2	press	press	PROPN
cana-943	463	3	.	.	PUNCT
cana-943	464	1	[	[	X
cana-943	464	2	5	5	NUM
cana-943	464	3	]	]	SYM
cana-943	464	4	boneh	boneh	PROPN
cana-943	464	5	,	,	PUNCT
cana-943	464	6	d.	d.	PROPN
cana-943	464	7	,	,	PUNCT
cana-943	464	8	&	&	CCONJ
cana-943	464	9	shoup	shoup	PROPN
cana-943	464	10	,	,	PUNCT
cana-943	464	11	v.	v.	PROPN
cana-943	464	12	(	(	PUNCT
cana-943	464	13	2020	2020	NUM
cana-943	464	14	)	)	PUNCT
cana-943	464	15	.	.	PUNCT
cana-943	465	1	a	a	DET
cana-943	465	2	graduate	graduate	ADJ
cana-943	465	3	course	course	NOUN
cana-943	465	4	in	in	ADP
cana-943	465	5	applied	applied	ADJ
cana-943	465	6	cryptography	cryptography	NOUN
cana-943	465	7	.	.	PUNCT
cana-943	466	1	version	version	NOUN
cana-943	466	2	0.5	0.5	NUM
cana-943	466	3	,	,	PUNCT
cana-943	466	4	2020	2020	NUM
cana-943	466	5	.	.	PUNCT
cana-943	467	1	[	[	X
cana-943	467	2	6	6	NUM
cana-943	467	3	]	]	X
cana-943	467	4	gentry	gentry	NOUN
cana-943	467	5	,	,	PUNCT
cana-943	467	6	c.	c.	NOUN
cana-943	467	7	(	(	PUNCT
cana-943	467	8	2009	2009	NUM
cana-943	467	9	)	)	PUNCT
cana-943	467	10	.	.	PUNCT
cana-943	468	1	fully	fully	ADV
cana-943	468	2	homomorphic	homomorphic	ADJ
cana-943	468	3	encryption	encryption	NOUN
cana-943	468	4	using	use	VERB
cana-943	468	5	ideal	ideal	ADJ
cana-943	468	6	lattices	lattice	NOUN
cana-943	468	7	.	.	PUNCT
cana-943	469	1	proceedings	proceeding	NOUN
cana-943	469	2	of	of	ADP
cana-943	469	3	the	the	DET
cana-943	469	4	41st	41st	ADJ
cana-943	469	5	annual	annual	ADJ
cana-943	469	6	acm	acm	NOUN
cana-943	469	7	symposium	symposium	NOUN
cana-943	469	8	on	on	ADP
cana-943	469	9	theory	theory	NOUN
cana-943	469	10	of	of	ADP
cana-943	469	11	computing	computing	NOUN
cana-943	469	12	,	,	PUNCT
cana-943	469	13	169	169	NUM
cana-943	469	14	-	-	SYM
cana-943	469	15	178	178	NUM
cana-943	469	16	.	.	PUNCT
cana-943	469	17	doi:10.1145/1536414.1536440	doi:10.1145/1536414.1536440	NOUN
cana-943	470	1	[	[	X
cana-943	470	2	7	7	X
cana-943	470	3	]	]	X
cana-943	470	4	shor	shor	NOUN
cana-943	470	5	,	,	PUNCT
cana-943	470	6	p.	p.	NOUN
cana-943	470	7	w.	w.	PROPN
cana-943	470	8	(	(	PUNCT
cana-943	470	9	1997	1997	NUM
cana-943	470	10	)	)	PUNCT
cana-943	470	11	.	.	PUNCT
cana-943	471	1	polynomial	polynomial	ADJ
cana-943	471	2	-	-	PUNCT
cana-943	471	3	time	time	NOUN
cana-943	471	4	algorithms	algorithm	NOUN
cana-943	471	5	for	for	ADP
cana-943	471	6	prime	prime	ADJ
cana-943	471	7	factorization	factorization	NOUN
cana-943	471	8	and	and	CCONJ
cana-943	471	9	discrete	discrete	ADJ
cana-943	471	10	logarithms	logarithm	NOUN
cana-943	471	11	on	on	ADP
cana-943	471	12	a	a	DET
cana-943	471	13	quantum	quantum	ADJ
cana-943	471	14	computer	computer	NOUN
cana-943	471	15	.	.	PUNCT
cana-943	472	1	siam	siam	PROPN
cana-943	472	2	journal	journal	PROPN
cana-943	472	3	on	on	ADP
cana-943	472	4	computing	computing	NOUN
cana-943	472	5	,	,	PUNCT
cana-943	472	6	26(5	26(5	NUM
cana-943	472	7	)	)	PUNCT
cana-943	472	8	,	,	PUNCT
cana-943	472	9	1484	1484	NUM
cana-943	472	10	-	-	SYM
cana-943	472	11	1509	1509	NUM
cana-943	472	12	.	.	PUNCT
cana-943	473	1	doi:10.1137	doi:10.1137	NOUN
cana-943	473	2	/	/	SYM
cana-943	474	1	s0097539795293172	s0097539795293172	NUM
cana-943	474	2	[	[	NOUN
cana-943	474	3	8	8	NUM
cana-943	474	4	]	]	X
cana-943	474	5	goldwasser	goldwasser	NOUN
cana-943	474	6	,	,	PUNCT
cana-943	474	7	s.	s.	PROPN
cana-943	474	8	,	,	PUNCT
cana-943	474	9	&	&	CCONJ
cana-943	474	10	micali	micali	PROPN
cana-943	474	11	,	,	PUNCT
cana-943	474	12	s.	s.	PROPN
cana-943	474	13	(	(	PUNCT
cana-943	474	14	1984	1984	NUM
cana-943	474	15	)	)	PUNCT
cana-943	474	16	.	.	PUNCT
cana-943	475	1	probabilistic	probabilistic	ADJ
cana-943	475	2	encryption	encryption	NOUN
cana-943	475	3	.	.	PUNCT
cana-943	476	1	journal	journal	NOUN
cana-943	476	2	of	of	ADP
cana-943	476	3	computer	computer	NOUN
cana-943	476	4	and	and	CCONJ
cana-943	476	5	system	system	NOUN
cana-943	476	6	sciences	science	NOUN
cana-943	476	7	,	,	PUNCT
cana-943	476	8	28(2	28(2	NUM
cana-943	476	9	)	)	PUNCT
cana-943	476	10	,	,	PUNCT
cana-943	476	11	270	270	NUM
cana-943	476	12	-	-	SYM
cana-943	476	13	299	299	NUM
cana-943	476	14	.	.	PUNCT
cana-943	476	15	doi:10.1016/0022	doi:10.1016/0022	NOUN
cana-943	476	16	-	-	PUNCT
cana-943	476	17	0000(84)90070	0000(84)90070	NOUN
cana-943	476	18	-	-	SYM
cana-943	476	19	9	9	NUM
cana-943	476	20	[	[	SYM
cana-943	476	21	9	9	NUM
cana-943	476	22	]	]	PUNCT
cana-943	476	23	ajtai	ajtai	ADJ
cana-943	476	24	,	,	PUNCT
cana-943	476	25	m.	m.	NOUN
cana-943	476	26	,	,	PUNCT
cana-943	476	27	&	&	CCONJ
cana-943	476	28	dwork	dwork	PROPN
cana-943	476	29	,	,	PUNCT
cana-943	476	30	c.	c.	PROPN
cana-943	476	31	(	(	PUNCT
cana-943	476	32	1997	1997	NUM
cana-943	476	33	)	)	PUNCT
cana-943	476	34	.	.	PUNCT
cana-943	477	1	a	a	DET
cana-943	477	2	public	public	ADJ
cana-943	477	3	-	-	PUNCT
cana-943	477	4	key	key	NOUN
cana-943	477	5	cryptosystem	cryptosystem	NOUN
cana-943	477	6	with	with	ADP
cana-943	477	7	worst	bad	ADJ
cana-943	477	8	-	-	PUNCT
cana-943	477	9	case	case	NOUN
cana-943	477	10	/	/	SYM
cana-943	477	11	average	average	ADJ
cana-943	477	12	-	-	PUNCT
cana-943	477	13	case	case	NOUN
cana-943	477	14	equivalence	equivalence	NOUN
cana-943	477	15	.	.	PUNCT
cana-943	478	1	proceedings	proceeding	NOUN
cana-943	478	2	of	of	ADP
cana-943	478	3	the	the	DET
cana-943	478	4	29th	29th	ADJ
cana-943	478	5	annual	annual	ADJ
cana-943	478	6	acm	acm	NOUN
cana-943	478	7	symposium	symposium	NOUN
cana-943	478	8	on	on	ADP
cana-943	478	9	theory	theory	NOUN
cana-943	478	10	of	of	ADP
cana-943	478	11	computing	computing	NOUN
cana-943	478	12	,	,	PUNCT
cana-943	478	13	284	284	NUM
cana-943	478	14	-	-	SYM
cana-943	478	15	293	293	NUM
cana-943	478	16	.	.	PUNCT
cana-943	479	1	doi:10.1145/258533.258604	doi:10.1145/258533.258604	NOUN
cana-943	480	1	[	[	X
cana-943	480	2	10	10	NUM
cana-943	480	3	]	]	X
cana-943	480	4	peikert	peikert	NOUN
cana-943	480	5	,	,	PUNCT
cana-943	480	6	c.	c.	PROPN
cana-943	480	7	(	(	PUNCT
cana-943	480	8	2009	2009	NUM
cana-943	480	9	)	)	PUNCT
cana-943	480	10	.	.	PUNCT
cana-943	481	1	public	public	ADJ
cana-943	481	2	-	-	PUNCT
cana-943	481	3	key	key	NOUN
cana-943	481	4	cryptosystems	cryptosystem	NOUN
cana-943	481	5	from	from	ADP
cana-943	481	6	the	the	DET
cana-943	481	7	worst	bad	ADJ
cana-943	481	8	-	-	PUNCT
cana-943	481	9	case	case	NOUN
cana-943	481	10	shortest	short	ADJ
cana-943	481	11	vector	vector	NOUN
cana-943	481	12	problem	problem	NOUN
cana-943	481	13	:	:	PUNCT
cana-943	481	14	extended	extended	ADJ
cana-943	481	15	abstract	abstract	NOUN
cana-943	481	16	.	.	PUNCT
cana-943	482	1	proceedings	proceeding	NOUN
cana-943	482	2	of	of	ADP
cana-943	482	3	the	the	DET
cana-943	482	4	41st	41st	ADJ
cana-943	482	5	annual	annual	ADJ
cana-943	482	6	acm	acm	NOUN
cana-943	482	7	symposium	symposium	NOUN
cana-943	482	8	on	on	ADP
cana-943	482	9	theory	theory	NOUN
cana-943	482	10	of	of	ADP
cana-943	482	11	computing	computing	NOUN
cana-943	482	12	,	,	PUNCT
cana-943	482	13	333	333	NUM
cana-943	482	14	-	-	SYM
cana-943	482	15	342	342	NUM
cana-943	482	16	.	.	PUNCT
cana-943	483	1	doi:10.1145/1536414.1536461	doi:10.1145/1536414.1536461	ADJ
cana-943	483	2	[	[	X
cana-943	483	3	11	11	NUM
cana-943	483	4	]	]	SYM
cana-943	483	5	bellare	bellare	NOUN
cana-943	483	6	,	,	PUNCT
cana-943	483	7	m.	m.	NOUN
cana-943	483	8	,	,	PUNCT
cana-943	483	9	&	&	CCONJ
cana-943	483	10	rogaway	rogaway	PROPN
cana-943	483	11	,	,	PUNCT
cana-943	483	12	p.	p.	NOUN
cana-943	483	13	(	(	PUNCT
cana-943	483	14	1995	1995	NUM
cana-943	483	15	)	)	PUNCT
cana-943	483	16	.	.	PUNCT
cana-943	484	1	optimal	optimal	ADJ
cana-943	484	2	asymmetric	asymmetric	ADJ
cana-943	484	3	encryption	encryption	NOUN
cana-943	484	4	.	.	PUNCT
cana-943	485	1	advances	advance	NOUN
cana-943	485	2	in	in	ADP
cana-943	485	3	cryptology	cryptology	NOUN
cana-943	485	4	eurocrypt	eurocrypt	NOUN
cana-943	485	5	'	'	PROPN
cana-943	485	6	94	94	NUM
cana-943	485	7	.	.	PUNCT
cana-943	486	1	lecture	lecture	NOUN
cana-943	486	2	notes	note	NOUN
cana-943	486	3	in	in	ADP
cana-943	486	4	computer	computer	NOUN
cana-943	486	5	science	science	NOUN
cana-943	486	6	,	,	PUNCT
cana-943	486	7	vol	vol	NOUN
cana-943	486	8	950	950	NUM
cana-943	486	9	.	.	PUNCT
cana-943	487	1	springer	springer	NOUN
cana-943	487	2	,	,	PUNCT
cana-943	487	3	berlin	berlin	PROPN
cana-943	487	4	,	,	PUNCT
cana-943	487	5	heidelberg	heidelberg	PROPN
cana-943	487	6	.	.	PUNCT
cana-943	488	1	[	[	X
cana-943	488	2	12	12	NUM
cana-943	488	3	]	]	X
cana-943	488	4	regev	regev	NOUN
cana-943	488	5	,	,	PUNCT
cana-943	488	6	o.	o.	PROPN
cana-943	488	7	(	(	PUNCT
cana-943	488	8	2005	2005	NUM
cana-943	488	9	)	)	PUNCT
cana-943	488	10	.	.	PUNCT
cana-943	489	1	on	on	ADP
cana-943	489	2	lattices	lattice	NOUN
cana-943	489	3	,	,	PUNCT
cana-943	489	4	learning	learn	VERB
cana-943	489	5	with	with	ADP
cana-943	489	6	errors	error	NOUN
cana-943	489	7	,	,	PUNCT
cana-943	489	8	random	random	ADJ
cana-943	489	9	linear	linear	NOUN
cana-943	489	10	codes	code	NOUN
cana-943	489	11	,	,	PUNCT
cana-943	489	12	and	and	CCONJ
cana-943	489	13	cryptography	cryptography	NOUN
cana-943	489	14	.	.	PUNCT
cana-943	490	1	proceedings	proceeding	NOUN
cana-943	490	2	of	of	ADP
cana-943	490	3	the	the	DET
cana-943	490	4	37th	37th	ADJ
cana-943	490	5	annual	annual	ADJ
cana-943	490	6	acm	acm	NOUN
cana-943	490	7	symposium	symposium	NOUN
cana-943	490	8	on	on	ADP
cana-943	490	9	theory	theory	NOUN
cana-943	490	10	of	of	ADP
cana-943	490	11	computing	computing	NOUN
cana-943	490	12	,	,	PUNCT
cana-943	490	13	84	84	NUM
cana-943	490	14	-	-	SYM
cana-943	490	15	93	93	NUM
cana-943	490	16	.	.	PUNCT
cana-943	491	1	doi:10.1145/1060590.1060603	doi:10.1145/1060590.1060603	NOUN
cana-943	491	2	[	[	X
cana-943	491	3	13	13	NUM
cana-943	491	4	]	]	SYM
cana-943	491	5	nist	nist	NOUN
cana-943	491	6	.	.	PUNCT
cana-943	492	1	(	(	PUNCT
cana-943	492	2	2016	2016	NUM
cana-943	492	3	)	)	PUNCT
cana-943	492	4	.	.	PUNCT
cana-943	493	1	nist	nist	PROPN
cana-943	493	2	report	report	NOUN
cana-943	493	3	on	on	ADP
cana-943	493	4	post	post	ADJ
cana-943	493	5	-	-	ADJ
cana-943	493	6	quantum	quantum	ADJ
cana-943	493	7	cryptography	cryptography	NOUN
cana-943	493	8	.	.	PUNCT
cana-943	494	1	national	national	PROPN
cana-943	494	2	institute	institute	PROPN
cana-943	494	3	of	of	ADP
cana-943	494	4	standards	standard	NOUN
cana-943	494	5	and	and	CCONJ
cana-943	494	6	technology	technology	NOUN
cana-943	494	7	.	.	PUNCT
cana-943	495	1	available	available	ADJ
cana-943	495	2	at	at	ADP
cana-943	495	3	:	:	PUNCT
cana-943	495	4	https://nvlpubs.nist.gov/nistpubs/ir/2016/nist.ir.8105.pdf	https://nvlpubs.nist.gov/nistpubs/ir/2016/nist.ir.8105.pdf	NOUN
cana-943	495	5	[	[	X
cana-943	495	6	14	14	NUM
cana-943	495	7	]	]	SYM
cana-943	495	8	hoffstein	hoffstein	NOUN
cana-943	495	9	,	,	PUNCT
cana-943	495	10	j.	j.	PROPN
cana-943	495	11	,	,	PUNCT
cana-943	495	12	pipher	pipher	NOUN
cana-943	495	13	,	,	PUNCT
cana-943	495	14	j.	j.	PROPN
cana-943	495	15	,	,	PUNCT
cana-943	495	16	&	&	CCONJ
cana-943	495	17	silverman	silverman	PROPN
cana-943	495	18	,	,	PUNCT
cana-943	495	19	j.	j.	PROPN
cana-943	495	20	h.	h.	PROPN
cana-943	495	21	(	(	PUNCT
cana-943	495	22	1998	1998	NUM
cana-943	495	23	)	)	PUNCT
cana-943	495	24	.	.	PUNCT
cana-943	496	1	ntru	ntru	PROPN
cana-943	496	2	:	:	PUNCT
cana-943	496	3	a	a	DET
cana-943	496	4	ring	ring	NOUN
cana-943	496	5	-	-	PUNCT
cana-943	496	6	based	base	VERB
cana-943	496	7	public	public	ADJ
cana-943	496	8	key	key	ADJ
cana-943	496	9	cryptosystem	cryptosystem	NOUN
cana-943	496	10	.	.	PUNCT
cana-943	497	1	algorithmic	algorithmic	ADJ
cana-943	497	2	number	number	NOUN
cana-943	497	3	theory	theory	NOUN
cana-943	497	4	(	(	PUNCT
cana-943	497	5	ants	ants	PROPN
cana-943	497	6	iii	iii	NUM
cana-943	497	7	)	)	PUNCT
cana-943	497	8	,	,	PUNCT
cana-943	497	9	lecture	lecture	NOUN
cana-943	497	10	notes	note	NOUN
cana-943	497	11	in	in	ADP
cana-943	497	12	computer	computer	NOUN
cana-943	497	13	science	science	NOUN
cana-943	497	14	,	,	PUNCT
cana-943	497	15	vol	vol	NOUN
cana-943	497	16	1423	1423	NUM
cana-943	497	17	.	.	PUNCT
cana-943	498	1	springer	springer	NOUN
cana-943	498	2	,	,	PUNCT
cana-943	498	3	berlin	berlin	PROPN
cana-943	498	4	,	,	PUNCT
cana-943	498	5	heidelberg	heidelberg	PROPN
cana-943	498	6	.	.	PUNCT
cana-943	499	1	[	[	X
cana-943	499	2	15	15	NUM
cana-943	499	3	]	]	X
cana-943	499	4	micciancio	micciancio	NOUN
cana-943	499	5	,	,	PUNCT
cana-943	499	6	d.	d.	PROPN
cana-943	499	7	,	,	PUNCT
cana-943	499	8	&	&	CCONJ
cana-943	499	9	regev	regev	PROPN
cana-943	499	10	,	,	PUNCT
cana-943	499	11	o.	o.	PROPN
cana-943	499	12	(	(	PUNCT
cana-943	499	13	2009	2009	NUM
cana-943	499	14	)	)	PUNCT
cana-943	499	15	.	.	PUNCT
cana-943	500	1	lattice	lattice	NOUN
cana-943	500	2	-	-	PUNCT
cana-943	500	3	based	base	VERB
cana-943	500	4	cryptography	cryptography	NOUN
cana-943	500	5	.	.	PUNCT
cana-943	501	1	in	in	ADP
cana-943	501	2	post	post	ADJ
cana-943	501	3	-	-	ADJ
cana-943	501	4	quantum	quantum	ADJ
cana-943	501	5	cryptography	cryptography	NOUN
cana-943	501	6	,	,	PUNCT
cana-943	501	7	springer	springer	NOUN
cana-943	501	8	,	,	PUNCT
cana-943	501	9	berlin	berlin	PROPN
cana-943	501	10	,	,	PUNCT
cana-943	501	11	heidelberg	heidelberg	NOUN
cana-943	501	12	,	,	PUNCT
cana-943	501	13	147	147	NUM
cana-943	501	14	-	-	SYM
cana-943	501	15	191	191	NUM
cana-943	501	16	.	.	PUNCT
cana-943	502	1	[	[	X
cana-943	502	2	16	16	NUM
cana-943	502	3	]	]	X
cana-943	502	4	dwork	dwork	PROPN
cana-943	502	5	,	,	PUNCT
cana-943	502	6	c.	c.	NOUN
cana-943	502	7	,	,	PUNCT
cana-943	502	8	naor	naor	NOUN
cana-943	502	9	,	,	PUNCT
cana-943	502	10	m.	m.	NOUN
cana-943	502	11	,	,	PUNCT
cana-943	502	12	&	&	CCONJ
cana-943	502	13	sahai	sahai	PROPN
cana-943	502	14	,	,	PUNCT
cana-943	502	15	a.	a.	NOUN
cana-943	502	16	(	(	PUNCT
cana-943	502	17	2004	2004	NUM
cana-943	502	18	)	)	PUNCT
cana-943	502	19	.	.	PUNCT
cana-943	503	1	concurrent	concurrent	ADJ
cana-943	503	2	zero	zero	NUM
cana-943	503	3	-	-	PUNCT
cana-943	503	4	knowledge	knowledge	NOUN
cana-943	503	5	.	.	PUNCT
cana-943	503	6	journal	journal	NOUN
cana-943	503	7	of	of	ADP
cana-943	503	8	the	the	DET
cana-943	503	9	acm	acm	PROPN
cana-943	503	10	,	,	PUNCT
cana-943	503	11	51(6	51(6	NOUN
cana-943	503	12	)	)	PUNCT
cana-943	503	13	,	,	PUNCT
cana-943	503	14	851	851	NUM
cana-943	503	15	-	-	SYM
cana-943	503	16	898	898	NUM
cana-943	503	17	.	.	PUNCT
cana-943	503	18	doi:10.1145/1039488.1039490	doi:10.1145/1039488.1039490	VERB
cana-943	503	19	[	[	X
cana-943	503	20	17	17	NUM
cana-943	503	21	]	]	SYM
cana-943	503	22	damgård	damgård	PROPN
cana-943	503	23	,	,	PUNCT
cana-943	503	24	i.	i.	PROPN
cana-943	503	25	(	(	PUNCT
cana-943	503	26	1991	1991	NUM
cana-943	503	27	)	)	PUNCT
cana-943	503	28	.	.	PUNCT
cana-943	504	1	towards	towards	ADP
cana-943	504	2	practical	practical	ADJ
cana-943	504	3	public	public	ADJ
cana-943	504	4	key	key	NOUN
cana-943	504	5	systems	system	NOUN
cana-943	504	6	secure	secure	ADJ
cana-943	504	7	against	against	ADP
cana-943	504	8	chosen	choose	VERB
cana-943	504	9	ciphertext	ciphertext	NOUN
cana-943	504	10	attacks	attack	NOUN
cana-943	504	11	.	.	PUNCT
cana-943	505	1	advances	advance	NOUN
cana-943	505	2	in	in	ADP
cana-943	505	3	cryptology	cryptology	NOUN
cana-943	505	4	—	—	PUNCT
cana-943	505	5	crypto	crypto	VERB
cana-943	505	6	'	'	NOUN
cana-943	505	7	91	91	NUM
cana-943	505	8	.	.	PUNCT
cana-943	506	1	lecture	lecture	NOUN
cana-943	506	2	notes	note	NOUN
cana-943	506	3	in	in	ADP
cana-943	506	4	computer	computer	NOUN
cana-943	506	5	science	science	NOUN
cana-943	506	6	,	,	PUNCT
cana-943	506	7	vol	vol	NOUN
cana-943	506	8	576	576	NUM
cana-943	506	9	.	.	PUNCT
cana-943	507	1	springer	springer	NOUN
cana-943	507	2	,	,	PUNCT
cana-943	507	3	berlin	berlin	PROPN
cana-943	507	4	,	,	PUNCT
cana-943	507	5	heidelberg	heidelberg	PROPN
cana-943	507	6	.	.	PUNCT
cana-943	508	1	[	[	X
cana-943	508	2	18	18	NUM
cana-943	508	3	]	]	SYM
cana-943	508	4	ferguson	ferguson	PROPN
cana-943	508	5	,	,	PUNCT
cana-943	508	6	n.	n.	NOUN
cana-943	508	7	,	,	PUNCT
cana-943	508	8	schneier	schneier	PROPN
cana-943	508	9	,	,	PUNCT
cana-943	508	10	b.	b.	PROPN
cana-943	508	11	,	,	PUNCT
cana-943	508	12	&	&	CCONJ
cana-943	508	13	kohno	kohno	PROPN
cana-943	508	14	,	,	PUNCT
cana-943	508	15	t.	t.	PROPN
cana-943	508	16	(	(	PUNCT
cana-943	508	17	2010	2010	NUM
cana-943	508	18	)	)	PUNCT
cana-943	508	19	.	.	PUNCT
cana-943	509	1	cryptography	cryptography	NOUN
cana-943	509	2	engineering	engineering	NOUN
cana-943	509	3	:	:	PUNCT
cana-943	509	4	design	design	NOUN
cana-943	509	5	principles	principle	NOUN
cana-943	509	6	and	and	CCONJ
cana-943	509	7	practical	practical	ADJ
cana-943	509	8	applications	application	NOUN
cana-943	509	9	.	.	PUNCT
cana-943	510	1	wiley	wiley	NOUN
cana-943	510	2	.	.	PUNCT
cana-943	511	1	[	[	X
cana-943	511	2	19	19	NUM
cana-943	511	3	]	]	X
cana-943	511	4	smart	smart	ADJ
cana-943	511	5	,	,	PUNCT
cana-943	511	6	n.	n.	PROPN
cana-943	511	7	p.	p.	PROPN
cana-943	511	8	(	(	PUNCT
cana-943	511	9	2003	2003	NUM
cana-943	511	10	)	)	PUNCT
cana-943	511	11	.	.	PUNCT
cana-943	512	1	cryptography	cryptography	NOUN
cana-943	512	2	:	:	PUNCT
cana-943	512	3	an	an	DET
cana-943	512	4	introduction	introduction	NOUN
cana-943	512	5	.	.	PUNCT
cana-943	513	1	mcgraw	mcgraw	PROPN
cana-943	513	2	-	-	PUNCT
cana-943	513	3	hill	hill	NOUN
cana-943	513	4	.	.	PUNCT
cana-943	514	1	[	[	X
cana-943	514	2	20	20	NUM
cana-943	514	3	]	]	X
cana-943	514	4	liu	liu	PROPN
cana-943	514	5	,	,	PUNCT
cana-943	514	6	j.	j.	PROPN
cana-943	514	7	,	,	PUNCT
cana-943	514	8	&	&	CCONJ
cana-943	514	9	wang	wang	PROPN
cana-943	514	10	,	,	PUNCT
cana-943	514	11	q.	q.	PROPN
cana-943	514	12	(	(	PUNCT
cana-943	514	13	2023	2023	NUM
cana-943	514	14	)	)	PUNCT
cana-943	514	15	.	.	PUNCT
cana-943	515	1	advanced	advanced	ADJ
cana-943	515	2	cryptographic	cryptographic	ADJ
cana-943	515	3	techniques	technique	NOUN
cana-943	515	4	for	for	ADP
cana-943	515	5	secure	secure	ADJ
cana-943	515	6	communications	communication	NOUN
cana-943	515	7	in	in	ADP
cana-943	515	8	iot	iot	PROPN
cana-943	515	9	.	.	PUNCT
cana-943	516	1	ieee	ieee	NOUN
cana-943	516	2	transactions	transaction	NOUN
cana-943	516	3	on	on	ADP
cana-943	516	4	information	information	NOUN
cana-943	516	5	forensics	forensic	NOUN
cana-943	516	6	and	and	CCONJ
cana-943	516	7	security	security	NOUN
cana-943	516	8	,	,	PUNCT
cana-943	516	9	18	18	NUM
cana-943	516	10	,	,	PUNCT
cana-943	516	11	123	123	NUM
cana-943	516	12	-	-	SYM
cana-943	516	13	138	138	NUM
cana-943	516	14	.	.	PUNCT
cana-943	517	1	doi:10.1109	doi:10.1109	VERB
cana-943	517	2	/	/	SYM
cana-943	517	3	tifs.2023.3249801	tifs.2023.3249801	NOUN
cana-943	517	4	[	[	X
cana-943	517	5	21	21	NUM
cana-943	517	6	]	]	X
cana-943	517	7	chen	chen	PROPN
cana-943	517	8	,	,	PUNCT
cana-943	517	9	l.	l.	PROPN
cana-943	517	10	,	,	PUNCT
cana-943	517	11	&	&	CCONJ
cana-943	517	12	nguyen	nguyen	PROPN
cana-943	517	13	,	,	PUNCT
cana-943	517	14	q.	q.	PROPN
cana-943	517	15	v.	v.	PROPN
cana-943	517	16	(	(	PUNCT
cana-943	517	17	2023	2023	NUM
cana-943	517	18	)	)	PUNCT
cana-943	517	19	.	.	PUNCT
cana-943	518	1	post	post	ADJ
cana-943	518	2	-	-	ADJ
cana-943	518	3	quantum	quantum	ADJ
cana-943	518	4	cryptography	cryptography	NOUN
cana-943	518	5	:	:	PUNCT
cana-943	518	6	algorithms	algorithm	NOUN
cana-943	518	7	and	and	CCONJ
cana-943	518	8	implementations	implementation	NOUN
cana-943	518	9	.	.	PUNCT
cana-943	519	1	journal	journal	PROPN
cana-943	519	2	of	of	ADP
cana-943	519	3	cryptographic	cryptographic	ADJ
cana-943	519	4	engineering	engineering	NOUN
cana-943	519	5	,	,	PUNCT
cana-943	519	6	13(1	13(1	NUM
cana-943	519	7	)	)	PUNCT
cana-943	519	8	,	,	PUNCT
cana-943	519	9	1	1	NUM
cana-943	519	10	-	-	SYM
cana-943	519	11	16	16	NUM
cana-943	519	12	.	.	PUNCT
cana-943	520	1	doi:10.1007	doi:10.1007	VERB
cana-943	520	2	/	/	SYM
cana-943	520	3	s13389	s13389	NOUN
cana-943	520	4	-	-	PUNCT
cana-943	520	5	023	023	NUM
cana-943	520	6	-	-	PUNCT
cana-943	520	7	00314	00314	NUM
cana-943	520	8	-	-	PUNCT
cana-943	520	9	6	6	NUM
cana-943	520	10	communications	communication	NOUN
cana-943	520	11	on	on	ADP
cana-943	520	12	applied	apply	VERB
cana-943	520	13	nonlinear	nonlinear	ADJ
cana-943	520	14	analysis	analysis	NOUN
cana-943	520	15	issn	issn	NOUN
cana-943	520	16	:	:	PUNCT
cana-943	520	17	1074	1074	NUM
cana-943	520	18	-	-	PUNCT
cana-943	520	19	133x	133x	NUM
cana-943	520	20	vol	vol	NOUN
cana-943	520	21	31	31	NUM
cana-943	520	22	no	no	NOUN
cana-943	520	23	.	.	PUNCT
cana-943	521	1	4s	4s	NUM
cana-943	521	2	(	(	PUNCT
cana-943	521	3	2024	2024	NUM
cana-943	521	4	)	)	PUNCT
cana-943	521	5	489	489	NUM
cana-943	521	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-943	522	1	[	[	X
cana-943	522	2	22	22	NUM
cana-943	522	3	]	]	X
cana-943	522	4	zhang	zhang	PROPN
cana-943	522	5	,	,	PUNCT
cana-943	522	6	y.	y.	PROPN
cana-943	522	7	,	,	PUNCT
cana-943	522	8	xu	xu	PROPN
cana-943	522	9	,	,	PUNCT
cana-943	522	10	x.	x.	PROPN
cana-943	522	11	,	,	PUNCT
cana-943	522	12	&	&	CCONJ
cana-943	522	13	tang	tang	PROPN
cana-943	522	14	,	,	PUNCT
cana-943	522	15	c.	c.	PROPN
cana-943	522	16	(	(	PUNCT
cana-943	522	17	2023	2023	NUM
cana-943	522	18	)	)	PUNCT
cana-943	522	19	.	.	PUNCT
cana-943	523	1	efficient	efficient	ADJ
cana-943	523	2	lattice	lattice	NOUN
cana-943	523	3	-	-	PUNCT
cana-943	523	4	based	base	VERB
cana-943	523	5	cryptographic	cryptographic	ADJ
cana-943	523	6	schemes	scheme	NOUN
cana-943	523	7	for	for	ADP
cana-943	523	8	secure	secure	ADJ
cana-943	523	9	data	datum	NOUN
cana-943	523	10	transmission	transmission	NOUN
cana-943	523	11	.	.	PUNCT
cana-943	524	1	ieee	ieee	NOUN
cana-943	524	2	transactions	transaction	NOUN
cana-943	524	3	on	on	ADP
cana-943	524	4	information	information	NOUN
cana-943	524	5	theory	theory	NOUN
cana-943	524	6	,	,	PUNCT
cana-943	524	7	69(4	69(4	NOUN
cana-943	524	8	)	)	PUNCT
cana-943	524	9	,	,	PUNCT
cana-943	524	10	2201	2201	NUM
cana-943	524	11	-	-	SYM
cana-943	524	12	2214	2214	NUM
cana-943	524	13	.	.	PUNCT
cana-943	525	1	doi:10.1109	doi:10.1109	VERB
cana-943	525	2	/	/	SYM
cana-943	526	1	tit.2023.3245678	tit.2023.3245678	PRON
cana-943	526	2	[	[	X
cana-943	526	3	23	23	NUM
cana-943	526	4	]	]	X
cana-943	526	5	gong	gong	NOUN
cana-943	526	6	,	,	PUNCT
cana-943	526	7	y.	y.	PROPN
cana-943	526	8	,	,	PUNCT
cana-943	526	9	&	&	CCONJ
cana-943	526	10	li	li	PROPN
cana-943	526	11	,	,	PUNCT
cana-943	526	12	h.	h.	PROPN
cana-943	526	13	(	(	PUNCT
cana-943	526	14	2024	2024	NUM
cana-943	526	15	)	)	PUNCT
cana-943	526	16	.	.	PUNCT
cana-943	527	1	exploring	explore	VERB
cana-943	527	2	the	the	DET
cana-943	527	3	intersection	intersection	NOUN
cana-943	527	4	of	of	ADP
cana-943	527	5	algebra	algebra	NOUN
cana-943	527	6	and	and	CCONJ
cana-943	527	7	blockchain	blockchain	PROPN
cana-943	527	8	for	for	ADP
cana-943	527	9	enhanced	enhanced	ADJ
cana-943	527	10	security	security	NOUN
cana-943	527	11	protocols	protocol	NOUN
cana-943	527	12	.	.	PUNCT
cana-943	528	1	journal	journal	NOUN
cana-943	528	2	of	of	ADP
cana-943	528	3	cryptology	cryptology	NOUN
cana-943	528	4	,	,	PUNCT
cana-943	528	5	37(2	37(2	PROPN
cana-943	528	6	)	)	PUNCT
cana-943	528	7	,	,	PUNCT
cana-943	528	8	112	112	NUM
cana-943	528	9	-	-	SYM
cana-943	528	10	131	131	NUM
cana-943	528	11	.	.	PUNCT
cana-943	529	1	doi:10.1007	doi:10.1007	VERB
cana-943	529	2	/	/	SYM
cana-943	529	3	s00145	s00145	NOUN
cana-943	529	4	-	-	PUNCT
cana-943	529	5	024	024	NUM
cana-943	529	6	-	-	PUNCT
cana-943	529	7	09458	09458	NUM
cana-943	529	8	-	-	SYM
cana-943	529	9	7	7	NUM
cana-943	529	10	[	[	X
cana-943	529	11	24	24	NUM
cana-943	529	12	]	]	PUNCT
cana-943	529	13	williams	williams	PROPN
cana-943	529	14	,	,	PUNCT
cana-943	529	15	p.	p.	PROPN
cana-943	529	16	s.	s.	PROPN
cana-943	529	17	,	,	PUNCT
cana-943	529	18	&	&	CCONJ
cana-943	529	19	nguyen	nguyen	PROPN
cana-943	529	20	,	,	PUNCT
cana-943	529	21	d.	d.	PROPN
cana-943	529	22	k.	k.	PROPN
cana-943	529	23	(	(	PUNCT
cana-943	529	24	2023	2023	NUM
cana-943	529	25	)	)	PUNCT
cana-943	529	26	.	.	PUNCT
cana-943	530	1	a	a	DET
cana-943	530	2	comprehensive	comprehensive	ADJ
cana-943	530	3	study	study	NOUN
cana-943	530	4	of	of	ADP
cana-943	530	5	elliptic	elliptic	ADJ
cana-943	530	6	curve	curve	NOUN
cana-943	530	7	cryptography	cryptography	NOUN
cana-943	530	8	in	in	ADP
cana-943	530	9	contemporary	contemporary	ADJ
cana-943	530	10	applications	application	NOUN
cana-943	530	11	.	.	PUNCT
cana-943	531	1	acm	acm	PROPN
cana-943	531	2	computing	computing	NOUN
cana-943	531	3	surveys	survey	NOUN
cana-943	531	4	,	,	PUNCT
cana-943	531	5	56(1	56(1	NUM
cana-943	531	6	)	)	PUNCT
cana-943	531	7	,	,	PUNCT
cana-943	531	8	1	1	NUM
cana-943	531	9	-	-	SYM
cana-943	531	10	34	34	NUM
cana-943	531	11	.	.	PUNCT
cana-943	532	1	doi:10.1145/3560287	doi:10.1145/3560287	PUNCT
cana-943	533	1	[	[	X
cana-943	533	2	25	25	NUM
cana-943	533	3	]	]	SYM
cana-943	533	4	yao	yao	PROPN
cana-943	533	5	,	,	PUNCT
cana-943	533	6	a.	a.	PROPN
cana-943	533	7	,	,	PUNCT
cana-943	533	8	&	&	CCONJ
cana-943	533	9	lu	lu	PROPN
cana-943	533	10	,	,	PUNCT
cana-943	533	11	z.	z.	PROPN
cana-943	533	12	(	(	PUNCT
cana-943	533	13	2024	2024	NUM
cana-943	533	14	)	)	PUNCT
cana-943	533	15	.	.	PUNCT
cana-943	534	1	homomorphic	homomorphic	ADJ
cana-943	534	2	encryption	encryption	NOUN
cana-943	534	3	:	:	PUNCT
cana-943	534	4	recent	recent	ADJ
cana-943	534	5	advances	advance	NOUN
cana-943	534	6	and	and	CCONJ
cana-943	534	7	practical	practical	ADJ
cana-943	534	8	implementations	implementation	NOUN
cana-943	534	9	.	.	PUNCT
cana-943	535	1	ieee	ieee	NOUN
cana-943	535	2	transactions	transaction	NOUN
cana-943	535	3	on	on	ADP
cana-943	535	4	dependable	dependable	ADJ
cana-943	535	5	and	and	CCONJ
cana-943	535	6	secure	secure	ADJ
cana-943	535	7	computing	computing	NOUN
cana-943	535	8	,	,	PUNCT
cana-943	535	9	21(3	21(3	NUM
cana-943	535	10	)	)	PUNCT
cana-943	535	11	,	,	PUNCT
cana-943	535	12	456	456	NUM
cana-943	535	13	-	-	SYM
cana-943	535	14	469	469	NUM
cana-943	535	15	.	.	PUNCT
cana-943	536	1	doi:10.1109	doi:10.1109	VERB
cana-943	536	2	/	/	SYM
cana-943	536	3	tdsc.2024.3247896	tdsc.2024.3247896	NOUN
cana-943	536	4	[	[	X
cana-943	536	5	26	26	NUM
cana-943	536	6	]	]	X
cana-943	536	7	ding	ding	NOUN
cana-943	536	8	,	,	PUNCT
cana-943	536	9	j.	j.	PROPN
cana-943	536	10	,	,	PUNCT
cana-943	536	11	&	&	CCONJ
cana-943	536	12	lindner	lindner	PROPN
cana-943	536	13	,	,	PUNCT
cana-943	536	14	r.	r.	PROPN
cana-943	536	15	(	(	PUNCT
cana-943	536	16	2023	2023	NUM
cana-943	536	17	)	)	PUNCT
cana-943	536	18	.	.	PUNCT
cana-943	537	1	ring	ring	NOUN
cana-943	537	2	-	-	PUNCT
cana-943	537	3	lwe	lwe	PROPN
cana-943	537	4	based	base	VERB
cana-943	537	5	cryptosystems	cryptosystem	NOUN
cana-943	537	6	:	:	PUNCT
cana-943	537	7	design	design	NOUN
cana-943	537	8	and	and	CCONJ
cana-943	537	9	analysis	analysis	NOUN
cana-943	537	10	.	.	PUNCT
cana-943	538	1	journal	journal	NOUN
cana-943	538	2	of	of	ADP
cana-943	538	3	cryptographic	cryptographic	ADJ
cana-943	538	4	engineering	engineering	NOUN
cana-943	538	5	,	,	PUNCT
cana-943	538	6	13(3	13(3	NUM
cana-943	538	7	)	)	PUNCT
cana-943	538	8	,	,	PUNCT
cana-943	538	9	321	321	NUM
cana-943	538	10	-	-	SYM
cana-943	538	11	338	338	NUM
cana-943	538	12	.	.	PUNCT
cana-943	539	1	doi:10.1007	doi:10.1007	VERB
cana-943	539	2	/	/	SYM
cana-943	539	3	s13389	s13389	NOUN
cana-943	539	4	-	-	PUNCT
cana-943	539	5	023	023	NUM
cana-943	539	6	-	-	PUNCT
cana-943	539	7	00325	00325	NUM
cana-943	539	8	-	-	SYM
cana-943	539	9	3	3	NUM
cana-943	540	1	[	[	X
cana-943	540	2	27	27	NUM
cana-943	540	3	]	]	SYM
cana-943	540	4	barker	barker	PROPN
cana-943	540	5	,	,	PUNCT
cana-943	540	6	e.	e.	PROPN
cana-943	540	7	,	,	PUNCT
cana-943	540	8	&	&	CCONJ
cana-943	540	9	kelsey	kelsey	PROPN
cana-943	540	10	,	,	PUNCT
cana-943	540	11	j.	j.	PROPN
cana-943	540	12	(	(	PUNCT
cana-943	540	13	2022	2022	NUM
cana-943	540	14	)	)	PUNCT
cana-943	540	15	.	.	PUNCT
cana-943	541	1	nist	nist	PROPN
cana-943	541	2	special	special	ADJ
cana-943	541	3	publication	publication	NOUN
cana-943	541	4	800	800	NUM
cana-943	541	5	-	-	PUNCT
cana-943	541	6	56a	56a	NUM
cana-943	541	7	revision	revision	NOUN
cana-943	541	8	3	3	NUM
cana-943	541	9	:	:	PUNCT
cana-943	541	10	recommendation	recommendation	NOUN
cana-943	541	11	for	for	ADP
cana-943	541	12	pair	pair	NOUN
cana-943	541	13	-	-	PUNCT
cana-943	541	14	wise	wise	ADJ
cana-943	541	15	key	key	ADJ
cana-943	541	16	establishment	establishment	NOUN
cana-943	541	17	schemes	scheme	NOUN
cana-943	541	18	using	use	VERB
cana-943	541	19	discrete	discrete	ADJ
cana-943	541	20	logarithm	logarithm	NOUN
cana-943	541	21	cryptography	cryptography	NOUN
cana-943	541	22	.	.	PUNCT
cana-943	542	1	national	national	PROPN
cana-943	542	2	institute	institute	PROPN
cana-943	542	3	of	of	ADP
cana-943	542	4	standards	standard	NOUN
cana-943	542	5	and	and	CCONJ
cana-943	542	6	technology	technology	NOUN
cana-943	542	7	.	.	PUNCT
cana-943	543	1	available	available	ADJ
cana-943	543	2	at	at	ADP
cana-943	543	3	:	:	PUNCT
cana-943	543	4	https://doi.org/10.6028/nist.sp.800-56ar3	https://doi.org/10.6028/nist.sp.800-56ar3	PUNCT
cana-943	543	5	[	[	X
cana-943	543	6	28	28	NUM
cana-943	543	7	]	]	SYM
cana-943	543	8	hoffstein	hoffstein	NOUN
cana-943	543	9	,	,	PUNCT
cana-943	543	10	j.	j.	PROPN
cana-943	543	11	,	,	PUNCT
cana-943	543	12	silverman	silverman	PROPN
cana-943	543	13	,	,	PUNCT
cana-943	543	14	j.	j.	PROPN
cana-943	543	15	h.	h.	PROPN
cana-943	543	16	,	,	PUNCT
cana-943	543	17	&	&	CCONJ
cana-943	543	18	whyte	whyte	PROPN
cana-943	543	19	,	,	PUNCT
cana-943	543	20	w.	w.	PROPN
cana-943	543	21	(	(	PUNCT
cana-943	543	22	2022	2022	NUM
cana-943	543	23	)	)	PUNCT
cana-943	543	24	.	.	PUNCT
cana-943	544	1	post	post	ADJ
cana-943	544	2	-	-	ADJ
cana-943	544	3	quantum	quantum	ADJ
cana-943	544	4	cryptography	cryptography	NOUN
cana-943	544	5	:	:	PUNCT
cana-943	544	6	ntruencrypt	ntruencrypt	PROPN
cana-943	544	7	and	and	CCONJ
cana-943	544	8	ntru	ntru	ADJ
cana-943	544	9	signature	signature	NOUN
cana-943	544	10	schemes	scheme	NOUN
cana-943	544	11	.	.	PUNCT
cana-943	545	1	in	in	ADP
cana-943	545	2	post	post	ADJ
cana-943	545	3	-	-	ADJ
cana-943	545	4	quantum	quantum	ADJ
cana-943	545	5	cryptography	cryptography	NOUN
cana-943	545	6	,	,	PUNCT
cana-943	545	7	3rd	3rd	ADJ
cana-943	545	8	edition	edition	NOUN
cana-943	545	9	,	,	PUNCT
cana-943	545	10	springer	springer	NOUN
cana-943	545	11	,	,	PUNCT
cana-943	545	12	cham	cham	PROPN
cana-943	545	13	,	,	PUNCT
cana-943	545	14	112	112	NUM
cana-943	545	15	-	-	SYM
cana-943	545	16	131	131	NUM
cana-943	545	17	.	.	PUNCT
cana-943	546	1	doi:10.1007/978	doi:10.1007/978	PROPN
cana-943	546	2	-	-	PUNCT
cana-943	546	3	3030	3030	NUM
cana-943	546	4	-	-	PUNCT
cana-943	546	5	80728	80728	NUM
cana-943	546	6	-	-	SYM
cana-943	546	7	9_6	9_6	NUM
cana-943	546	8	[	[	X
cana-943	546	9	29	29	NUM
cana-943	546	10	]	]	X
cana-943	546	11	chen	chen	PROPN
cana-943	546	12	,	,	PUNCT
cana-943	546	13	l.	l.	PROPN
cana-943	546	14	,	,	PUNCT
cana-943	546	15	&	&	CCONJ
cana-943	546	16	lee	lee	PROPN
cana-943	546	17	,	,	PUNCT
cana-943	546	18	j.	j.	PROPN
cana-943	546	19	(	(	PUNCT
cana-943	546	20	2023	2023	NUM
cana-943	546	21	)	)	PUNCT
cana-943	546	22	.	.	PUNCT
cana-943	547	1	advances	advance	NOUN
cana-943	547	2	in	in	ADP
cana-943	547	3	quantum	quantum	NOUN
cana-943	547	4	-	-	PUNCT
cana-943	547	5	resistant	resistant	ADJ
cana-943	547	6	cryptographic	cryptographic	ADJ
cana-943	547	7	algorithms	algorithm	NOUN
cana-943	547	8	.	.	PUNCT
cana-943	548	1	ieee	ieee	PROPN
cana-943	548	2	security	security	PROPN
cana-943	548	3	&	&	CCONJ
cana-943	548	4	privacy	privacy	PROPN
cana-943	548	5	,	,	PUNCT
cana-943	548	6	21(2	21(2	NUM
cana-943	548	7	)	)	PUNCT
cana-943	548	8	,	,	PUNCT
cana-943	548	9	32	32	NUM
cana-943	548	10	-	-	SYM
cana-943	548	11	41	41	NUM
cana-943	548	12	.	.	PUNCT
cana-943	549	1	doi:10.1109	doi:10.1109	VERB
cana-943	549	2	/	/	SYM
cana-943	550	1	msec.2023.3246907	msec.2023.3246907	PROPN
cana-943	551	1	[	[	X
cana-943	551	2	30	30	NUM
cana-943	551	3	]	]	X
cana-943	551	4	brown	brown	PROPN
cana-943	551	5	,	,	PUNCT
cana-943	551	6	d.	d.	PROPN
cana-943	551	7	r.	r.	PROPN
cana-943	551	8	l.	l.	PROPN
cana-943	551	9	(	(	PUNCT
cana-943	551	10	2023	2023	NUM
cana-943	551	11	)	)	PUNCT
cana-943	551	12	.	.	PUNCT
cana-943	552	1	safecurves	safecurve	NOUN
cana-943	552	2	:	:	PUNCT
cana-943	552	3	choosing	choose	VERB
cana-943	552	4	safe	safe	ADJ
cana-943	552	5	parameters	parameter	NOUN
cana-943	552	6	for	for	ADP
cana-943	552	7	elliptic	elliptic	ADJ
cana-943	552	8	curve	curve	NOUN
cana-943	552	9	cryptography	cryptography	NOUN
cana-943	552	10	.	.	PUNCT
cana-943	553	1	journal	journal	PROPN
cana-943	553	2	of	of	ADP
cana-943	553	3	cryptology	cryptology	NOUN
cana-943	553	4	,	,	PUNCT
cana-943	553	5	36(1	36(1	NUM
cana-943	553	6	)	)	PUNCT
cana-943	553	7	,	,	PUNCT
cana-943	553	8	71	71	NUM
cana-943	553	9	-	-	SYM
cana-943	553	10	92	92	NUM
cana-943	553	11	.	.	PUNCT
cana-943	554	1	doi:10.1007	doi:10.1007	VERB
cana-943	554	2	/	/	SYM
cana-943	554	3	s00145	s00145	NOUN
cana-943	554	4	-	-	PUNCT
cana-943	554	5	023	023	NUM
cana-943	554	6	-	-	PUNCT
cana-943	554	7	09432	09432	NUM
cana-943	554	8	-	-	SYM
cana-943	554	9	4	4	NUM