id	sid	tid	token	lemma	pos
cana-1589	1	1	communications	communication	NOUN
cana-1589	1	2	on	on	ADP
cana-1589	1	3	applied	apply	VERB
cana-1589	1	4	nonlinear	nonlinear	ADJ
cana-1589	1	5	analysis	analysis	NOUN
cana-1589	1	6	issn	issn	NOUN
cana-1589	1	7	:	:	PUNCT
cana-1589	1	8	1074	1074	NUM
cana-1589	1	9	-	-	PUNCT
cana-1589	1	10	133x	133x	NUM
cana-1589	1	11	vol	vol	NOUN
cana-1589	1	12	31	31	NUM
cana-1589	1	13	no	no	NOUN
cana-1589	1	14	.	.	PUNCT
cana-1589	2	1	7s	7	NOUN
cana-1589	2	2	(	(	PUNCT
cana-1589	2	3	2024	2024	NUM
cana-1589	2	4	)	)	PUNCT
cana-1589	2	5	696	696	NUM
cana-1589	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	2	7	quantum	quantum	ADJ
cana-1589	2	8	resistant	resistant	ADJ
cana-1589	2	9	cryptosystem	cryptosystem	NOUN
cana-1589	2	10	-	-	PUNCT
cana-1589	2	11	based	base	VERB
cana-1589	2	12	security	security	NOUN
cana-1589	2	13	protocol	protocol	NOUN
cana-1589	2	14	for	for	ADP
cana-1589	2	15	5	5	NUM
cana-1589	2	16	g	g	PROPN
cana-1589	2	17	network	network	NOUN
cana-1589	2	18	hitesh	hitesh	PROPN
cana-1589	2	19	t	t	PROPN
cana-1589	2	20	loriya1	loriya1	PROPN
cana-1589	2	21	,	,	PUNCT
cana-1589	2	22	divyesh	divyesh	ADJ
cana-1589	2	23	r	r	NOUN
cana-1589	2	24	keraliya2	keraliya2	PROPN
cana-1589	2	25	,	,	PUNCT
cana-1589	2	26	rahul	rahul	PROPN
cana-1589	3	1	d	d	X
cana-1589	3	2	mehta3	mehta3	PROPN
cana-1589	3	3	1electronics	1electronics	PUNCT
cana-1589	3	4	and	and	CCONJ
cana-1589	3	5	communication	communication	NOUN
cana-1589	3	6	engineering	engineering	NOUN
cana-1589	3	7	department	department	NOUN
cana-1589	3	8	,	,	PUNCT
cana-1589	3	9	l	l	NOUN
cana-1589	3	10	e	e	PROPN
cana-1589	3	11	college	college	NOUN
cana-1589	3	12	morbi	morbi	NOUN
cana-1589	3	13	,	,	PUNCT
cana-1589	3	14	hitesh_loriya@yahoo.co.in	hitesh_loriya@yahoo.co.in	PROPN
cana-1589	3	15	2electronics	2electronics	NUM
cana-1589	3	16	and	and	CCONJ
cana-1589	3	17	communication	communication	NOUN
cana-1589	3	18	engineering	engineering	NOUN
cana-1589	3	19	department	department	PROPN
cana-1589	3	20	,	,	PUNCT
cana-1589	3	21	gec	gec	PROPN
cana-1589	3	22	rajkot	rajkot	NOUN
cana-1589	3	23	,	,	PUNCT
cana-1589	3	24	drkeraliya@gmail.com	drkeraliya@gmail.com	NOUN
cana-1589	3	25	3electronics	3electronics	PROPN
cana-1589	3	26	and	and	CCONJ
cana-1589	3	27	communication	communication	NOUN
cana-1589	3	28	engineering	engineering	NOUN
cana-1589	3	29	department	department	PROPN
cana-1589	3	30	,	,	PUNCT
cana-1589	3	31	gec	gec	PROPN
cana-1589	3	32	rajkot	rajkot	PROPN
cana-1589	3	33	,	,	PUNCT
cana-1589	3	34	rdmehta@hotmail.com	rdmehta@hotmail.com	X
cana-1589	4	1	article	article	NOUN
cana-1589	4	2	history	history	NOUN
cana-1589	4	3	:	:	PUNCT
cana-1589	4	4	received	receive	VERB
cana-1589	4	5	:	:	PUNCT
cana-1589	4	6	03	03	NUM
cana-1589	4	7	-	-	PUNCT
cana-1589	4	8	05	05	NUM
cana-1589	4	9	-	-	PUNCT
cana-1589	4	10	2024	2024	NUM
cana-1589	4	11	revised	revise	VERB
cana-1589	4	12	:	:	PUNCT
cana-1589	4	13	05	05	NUM
cana-1589	4	14	-	-	PUNCT
cana-1589	4	15	07	07	NUM
cana-1589	4	16	-	-	PUNCT
cana-1589	4	17	2024	2024	NUM
cana-1589	4	18	accepted	accept	VERB
cana-1589	4	19	:	:	PUNCT
cana-1589	4	20	25	25	NUM
cana-1589	4	21	-	-	PUNCT
cana-1589	4	22	07	07	NUM
cana-1589	4	23	-	-	PUNCT
cana-1589	4	24	2024	2024	NUM
cana-1589	4	25	abstract	abstract	ADJ
cana-1589	4	26	security	security	NOUN
cana-1589	4	27	is	be	AUX
cana-1589	4	28	crucial	crucial	ADJ
cana-1589	4	29	for	for	ADP
cana-1589	4	30	wireless	wireless	ADJ
cana-1589	4	31	communication	communication	NOUN
cana-1589	4	32	networks	network	NOUN
cana-1589	4	33	,	,	PUNCT
cana-1589	4	34	especially	especially	ADV
cana-1589	4	35	as	as	SCONJ
cana-1589	4	36	quantum	quantum	NOUN
cana-1589	4	37	computing	computing	NOUN
cana-1589	4	38	advances	advance	NOUN
cana-1589	4	39	rapidly	rapidly	ADV
cana-1589	4	40	.	.	PUNCT
cana-1589	5	1	it	it	PRON
cana-1589	5	2	wo	will	AUX
cana-1589	5	3	n’t	not	PART
cana-1589	5	4	be	be	AUX
cana-1589	5	5	long	long	ADJ
cana-1589	5	6	before	before	SCONJ
cana-1589	5	7	quantum	quantum	NOUN
cana-1589	5	8	attacks	attack	NOUN
cana-1589	5	9	become	become	VERB
cana-1589	5	10	feasible	feasible	ADJ
cana-1589	5	11	,	,	PUNCT
cana-1589	5	12	potentially	potentially	ADV
cana-1589	5	13	crippling	cripple	VERB
cana-1589	5	14	large	large	ADJ
cana-1589	5	15	wireless	wireless	ADJ
cana-1589	5	16	networks	network	NOUN
cana-1589	5	17	within	within	ADP
cana-1589	5	18	minutes	minute	NOUN
cana-1589	5	19	.	.	PUNCT
cana-1589	6	1	current	current	ADJ
cana-1589	6	2	methods	method	NOUN
cana-1589	6	3	for	for	ADP
cana-1589	6	4	securing	secure	VERB
cana-1589	6	5	connections	connection	NOUN
cana-1589	6	6	and	and	CCONJ
cana-1589	6	7	transactions	transaction	NOUN
cana-1589	6	8	—	—	PUNCT
cana-1589	6	9	such	such	ADJ
cana-1589	6	10	as	as	ADP
cana-1589	6	11	keys	key	NOUN
cana-1589	6	12	,	,	PUNCT
cana-1589	6	13	certificates	certificate	NOUN
cana-1589	6	14	,	,	PUNCT
cana-1589	6	15	and	and	CCONJ
cana-1589	6	16	data	datum	NOUN
cana-1589	6	17	—	—	PUNCT
cana-1589	6	18	could	could	AUX
cana-1589	6	19	be	be	AUX
cana-1589	6	20	compromised	compromise	VERB
cana-1589	6	21	by	by	ADP
cana-1589	6	22	quantum	quantum	ADJ
cana-1589	6	23	computers	computer	NOUN
cana-1589	6	24	.	.	PUNCT
cana-1589	7	1	one	one	NUM
cana-1589	7	2	concern	concern	NOUN
cana-1589	7	3	is	be	AUX
cana-1589	7	4	the	the	DET
cana-1589	7	5	use	use	NOUN
cana-1589	7	6	of	of	ADP
cana-1589	7	7	fake	fake	ADJ
cana-1589	7	8	base	base	NOUN
cana-1589	7	9	stations	station	NOUN
cana-1589	7	10	with	with	ADP
cana-1589	7	11	stronger	strong	ADJ
cana-1589	7	12	signal	signal	NOUN
cana-1589	7	13	strengths	strength	NOUN
cana-1589	7	14	to	to	PART
cana-1589	7	15	lure	lure	VERB
cana-1589	7	16	users	user	NOUN
cana-1589	7	17	into	into	ADP
cana-1589	7	18	connecting	connect	VERB
cana-1589	7	19	with	with	ADP
cana-1589	7	20	them	they	PRON
cana-1589	7	21	in	in	ADP
cana-1589	7	22	wireless	wireless	ADJ
cana-1589	7	23	communication	communication	NOUN
cana-1589	7	24	network	network	NOUN
cana-1589	7	25	.	.	PUNCT
cana-1589	8	1	a	a	DET
cana-1589	8	2	quantum	quantum	NOUN
cana-1589	8	3	-	-	PUNCT
cana-1589	8	4	powered	power	VERB
cana-1589	8	5	attacker	attacker	NOUN
cana-1589	8	6	could	could	AUX
cana-1589	8	7	easily	easily	ADV
cana-1589	8	8	break	break	VERB
cana-1589	8	9	traditional	traditional	ADJ
cana-1589	8	10	encryption	encryption	NOUN
cana-1589	8	11	algorithms	algorithm	NOUN
cana-1589	8	12	and	and	CCONJ
cana-1589	8	13	launch	launch	VERB
cana-1589	8	14	various	various	ADJ
cana-1589	8	15	attacks	attack	NOUN
cana-1589	8	16	almost	almost	ADV
cana-1589	8	17	instantly	instantly	ADV
cana-1589	8	18	.	.	PUNCT
cana-1589	9	1	an	an	DET
cana-1589	9	2	example	example	NOUN
cana-1589	9	3	of	of	ADP
cana-1589	9	4	this	this	PRON
cana-1589	9	5	is	be	AUX
cana-1589	9	6	the	the	DET
cana-1589	9	7	"	"	PUNCT
cana-1589	9	8	bidding	bid	VERB
cana-1589	9	9	down	down	ADP
cana-1589	9	10	"	"	PUNCT
cana-1589	9	11	attack	attack	NOUN
cana-1589	9	12	,	,	PUNCT
cana-1589	9	13	where	where	SCONJ
cana-1589	9	14	an	an	DET
cana-1589	9	15	attacker	attacker	NOUN
cana-1589	9	16	convinces	convince	VERB
cana-1589	9	17	both	both	CCONJ
cana-1589	9	18	the	the	DET
cana-1589	9	19	user	user	NOUN
cana-1589	9	20	and	and	CCONJ
cana-1589	9	21	network	network	NOUN
cana-1589	9	22	entities	entity	NOUN
cana-1589	9	23	that	that	SCONJ
cana-1589	9	24	security	security	NOUN
cana-1589	9	25	features	feature	NOUN
cana-1589	9	26	are	be	AUX
cana-1589	9	27	not	not	PART
cana-1589	9	28	upheld	uphold	VERB
cana-1589	9	29	,	,	PUNCT
cana-1589	9	30	despite	despite	SCONJ
cana-1589	9	31	their	their	PRON
cana-1589	9	32	actual	actual	ADJ
cana-1589	9	33	presence	presence	NOUN
cana-1589	9	34	.	.	PUNCT
cana-1589	10	1	this	this	DET
cana-1589	10	2	type	type	NOUN
cana-1589	10	3	of	of	ADP
cana-1589	10	4	attack	attack	NOUN
cana-1589	10	5	exploits	exploit	VERB
cana-1589	10	6	the	the	DET
cana-1589	10	7	security	security	NOUN
cana-1589	10	8	weaknesses	weakness	NOUN
cana-1589	10	9	of	of	ADP
cana-1589	10	10	older	old	ADJ
cana-1589	10	11	mobile	mobile	ADJ
cana-1589	10	12	networks	network	NOUN
cana-1589	10	13	.	.	PUNCT
cana-1589	11	1	this	this	DET
cana-1589	11	2	paper	paper	NOUN
cana-1589	11	3	explores	explore	VERB
cana-1589	11	4	security	security	NOUN
cana-1589	11	5	advancements	advancement	NOUN
cana-1589	11	6	and	and	CCONJ
cana-1589	11	7	challenges	challenge	NOUN
cana-1589	11	8	related	relate	VERB
cana-1589	11	9	to	to	ADP
cana-1589	11	10	contemporary	contemporary	ADJ
cana-1589	11	11	public	public	ADJ
cana-1589	11	12	key	key	ADJ
cana-1589	11	13	cryptography	cryptography	NOUN
cana-1589	11	14	,	,	PUNCT
cana-1589	11	15	including	include	VERB
cana-1589	11	16	rsa	rsa	PROPN
cana-1589	11	17	algorithms	algorithm	NOUN
cana-1589	11	18	based	base	VERB
cana-1589	11	19	on	on	ADP
cana-1589	11	20	factorization	factorization	NOUN
cana-1589	11	21	and	and	CCONJ
cana-1589	11	22	discrete	discrete	ADJ
cana-1589	11	23	logarithm	logarithm	NOUN
cana-1589	11	24	problems	problem	NOUN
cana-1589	11	25	with	with	ADP
cana-1589	11	26	diffiehellman	diffiehellman	ADJ
cana-1589	11	27	and	and	CCONJ
cana-1589	11	28	elliptic	elliptic	ADJ
cana-1589	11	29	-	-	PUNCT
cana-1589	11	30	curve	curve	NOUN
cana-1589	11	31	cryptography	cryptography	NOUN
cana-1589	11	32	(	(	PUNCT
cana-1589	11	33	ecc	ecc	PROPN
cana-1589	11	34	)	)	PUNCT
cana-1589	11	35	.	.	PUNCT
cana-1589	12	1	while	while	SCONJ
cana-1589	12	2	these	these	DET
cana-1589	12	3	methods	method	NOUN
cana-1589	12	4	provide	provide	VERB
cana-1589	12	5	adequate	adequate	ADJ
cana-1589	12	6	protection	protection	NOUN
cana-1589	12	7	today	today	NOUN
cana-1589	12	8	,	,	PUNCT
cana-1589	12	9	quantum	quantum	ADJ
cana-1589	12	10	computers	computer	NOUN
cana-1589	12	11	could	could	AUX
cana-1589	12	12	potentially	potentially	ADV
cana-1589	12	13	break	break	VERB
cana-1589	12	14	these	these	DET
cana-1589	12	15	algorithms	algorithm	NOUN
cana-1589	12	16	or	or	CCONJ
cana-1589	12	17	weaken	weaken	VERB
cana-1589	12	18	cryptographic	cryptographic	ADJ
cana-1589	12	19	keys	key	NOUN
cana-1589	12	20	and	and	CCONJ
cana-1589	12	21	hashes	hash	NOUN
cana-1589	12	22	within	within	ADP
cana-1589	12	23	minutes	minute	NOUN
cana-1589	12	24	.	.	PUNCT
cana-1589	13	1	quantum	quantum	ADJ
cana-1589	13	2	cryptography	cryptography	NOUN
cana-1589	13	3	,	,	PUNCT
cana-1589	13	4	or	or	CCONJ
cana-1589	13	5	quantumresistant	quantumresistant	ADJ
cana-1589	13	6	cryptography	cryptography	NOUN
cana-1589	13	7	,	,	PUNCT
cana-1589	13	8	objectives	objective	NOUN
cana-1589	13	9	to	to	PART
cana-1589	13	10	develop	develop	VERB
cana-1589	13	11	algorithms	algorithm	NOUN
cana-1589	13	12	and	and	CCONJ
cana-1589	13	13	protocols	protocol	NOUN
cana-1589	13	14	resilient	resilient	ADJ
cana-1589	13	15	to	to	ADP
cana-1589	13	16	quantum	quantum	ADJ
cana-1589	13	17	computing	computing	NOUN
cana-1589	13	18	threats	threat	NOUN
cana-1589	13	19	.	.	PUNCT
cana-1589	14	1	this	this	DET
cana-1589	14	2	paper	paper	NOUN
cana-1589	14	3	examines	examine	VERB
cana-1589	14	4	security	security	NOUN
cana-1589	14	5	vulnerabilities	vulnerability	NOUN
cana-1589	14	6	in	in	ADP
cana-1589	14	7	wireless	wireless	ADJ
cana-1589	14	8	communication	communication	NOUN
cana-1589	14	9	networks	network	NOUN
cana-1589	14	10	,	,	PUNCT
cana-1589	14	11	focusing	focus	VERB
cana-1589	14	12	on	on	ADP
cana-1589	14	13	key	key	ADJ
cana-1589	14	14	confirmation	confirmation	NOUN
cana-1589	14	15	and	and	CCONJ
cana-1589	14	16	authentication	authentication	NOUN
cana-1589	14	17	mechanisms	mechanism	NOUN
cana-1589	14	18	.	.	PUNCT
cana-1589	15	1	we	we	PRON
cana-1589	15	2	propose	propose	VERB
cana-1589	15	3	a	a	DET
cana-1589	15	4	robust	robust	ADJ
cana-1589	15	5	authentication	authentication	NOUN
cana-1589	15	6	and	and	CCONJ
cana-1589	15	7	key	key	ADJ
cana-1589	15	8	agreement	agreement	NOUN
cana-1589	15	9	protocol	protocol	NOUN
cana-1589	15	10	for	for	ADP
cana-1589	15	11	5	5	NUM
cana-1589	15	12	g	g	NOUN
cana-1589	15	13	networks	network	NOUN
cana-1589	15	14	using	use	VERB
cana-1589	15	15	quantum	quantum	NOUN
cana-1589	15	16	-	-	PUNCT
cana-1589	15	17	resistant	resistant	ADJ
cana-1589	15	18	cryptography	cryptography	NOUN
cana-1589	15	19	.	.	PUNCT
cana-1589	16	1	our	our	PRON
cana-1589	16	2	proposed	propose	VERB
cana-1589	16	3	protocol	protocol	NOUN
cana-1589	16	4	,	,	PUNCT
cana-1589	16	5	verified	verify	VERB
cana-1589	16	6	with	with	ADP
cana-1589	16	7	a	a	DET
cana-1589	16	8	verification	verification	NOUN
cana-1589	16	9	tool	tool	NOUN
cana-1589	16	10	,	,	PUNCT
cana-1589	16	11	enhances	enhance	VERB
cana-1589	16	12	the	the	DET
cana-1589	16	13	security	security	NOUN
cana-1589	16	14	of	of	ADP
cana-1589	16	15	the	the	DET
cana-1589	16	16	authentication	authentication	NOUN
cana-1589	16	17	and	and	CCONJ
cana-1589	16	18	key	key	ADJ
cana-1589	16	19	agreement	agreement	NOUN
cana-1589	16	20	procedures	procedure	NOUN
cana-1589	16	21	in	in	ADP
cana-1589	16	22	wireless	wireless	ADJ
cana-1589	16	23	communication	communication	NOUN
cana-1589	16	24	networks	network	NOUN
cana-1589	16	25	.	.	PUNCT
cana-1589	17	1	keywords	keyword	NOUN
cana-1589	17	2	:	:	PUNCT
cana-1589	17	3	security	security	NOUN
cana-1589	17	4	,	,	PUNCT
cana-1589	17	5	quantum	quantum	NOUN
cana-1589	17	6	attack	attack	NOUN
cana-1589	17	7	,	,	PUNCT
cana-1589	17	8	cryptosystem	cryptosystem	NOUN
cana-1589	17	9	,	,	PUNCT
cana-1589	17	10	ntru	ntru	ADJ
cana-1589	17	11	1	1	NUM
cana-1589	17	12	.	.	PUNCT
cana-1589	17	13	introduction	introduction	NOUN
cana-1589	17	14	cryptography	cryptography	NOUN
cana-1589	17	15	involves	involve	VERB
cana-1589	17	16	the	the	DET
cana-1589	17	17	study	study	NOUN
cana-1589	17	18	of	of	ADP
cana-1589	17	19	systems	system	NOUN
cana-1589	17	20	designed	design	VERB
cana-1589	17	21	to	to	PART
cana-1589	17	22	securely	securely	ADV
cana-1589	17	23	transfer	transfer	VERB
cana-1589	17	24	information	information	NOUN
cana-1589	17	25	among	among	ADP
cana-1589	17	26	users	user	NOUN
cana-1589	17	27	,	,	PUNCT
cana-1589	17	28	combining	combine	VERB
cana-1589	17	29	principles	principle	NOUN
cana-1589	17	30	from	from	ADP
cana-1589	17	31	engineering	engineering	NOUN
cana-1589	17	32	and	and	CCONJ
cana-1589	17	33	mathematics	mathematic	NOUN
cana-1589	17	34	.	.	PUNCT
cana-1589	18	1	its	its	PRON
cana-1589	18	2	primary	primary	ADJ
cana-1589	18	3	applications	application	NOUN
cana-1589	18	4	include	include	VERB
cana-1589	18	5	ensuring	ensure	VERB
cana-1589	18	6	authentication	authentication	NOUN
cana-1589	18	7	,	,	PUNCT
cana-1589	18	8	confidentiality	confidentiality	NOUN
cana-1589	18	9	,	,	PUNCT
cana-1589	18	10	key	key	ADJ
cana-1589	18	11	distribution	distribution	NOUN
cana-1589	18	12	and	and	CCONJ
cana-1589	18	13	integrity	integrity	NOUN
cana-1589	18	14	.	.	PUNCT
cana-1589	19	1	two	two	NUM
cana-1589	19	2	main	main	ADJ
cana-1589	19	3	types	type	NOUN
cana-1589	19	4	of	of	ADP
cana-1589	19	5	cryptosystems	cryptosystem	NOUN
cana-1589	19	6	used	use	VERB
cana-1589	19	7	for	for	ADP
cana-1589	19	8	secure	secure	ADJ
cana-1589	19	9	information	information	NOUN
cana-1589	19	10	transfer	transfer	NOUN
cana-1589	19	11	are	be	AUX
cana-1589	19	12	private	private	ADJ
cana-1589	19	13	key	key	ADJ
cana-1589	19	14	cryptosystems	cryptosystem	NOUN
cana-1589	19	15	and	and	CCONJ
cana-1589	19	16	public	public	ADJ
cana-1589	19	17	key	key	ADJ
cana-1589	19	18	cryptosystems	cryptosystem	NOUN
cana-1589	19	19	.	.	PUNCT
cana-1589	20	1	in	in	ADP
cana-1589	20	2	the	the	DET
cana-1589	20	3	context	context	NOUN
cana-1589	20	4	of	of	ADP
cana-1589	20	5	5	5	NUM
cana-1589	20	6	g	g	NOUN
cana-1589	20	7	networks	network	NOUN
cana-1589	20	8	,	,	PUNCT
cana-1589	20	9	the	the	DET
cana-1589	20	10	3gpp	3gpp	PROPN
cana-1589	20	11	defines	define	VERB
cana-1589	20	12	a	a	DET
cana-1589	20	13	security	security	NOUN
cana-1589	20	14	architecture	architecture	NOUN
cana-1589	20	15	[	[	X
cana-1589	20	16	1	1	X
cana-1589	20	17	]	]	PUNCT
cana-1589	20	18	that	that	PRON
cana-1589	20	19	employs	employ	VERB
cana-1589	20	20	cryptosystems	cryptosystem	NOUN
cana-1589	20	21	to	to	PART
cana-1589	20	22	protect	protect	VERB
cana-1589	20	23	subscriber	subscriber	NOUN
cana-1589	20	24	information	information	NOUN
cana-1589	20	25	exchanged	exchange	VERB
cana-1589	20	26	between	between	ADP
cana-1589	20	27	network	network	NOUN
cana-1589	20	28	entities	entity	NOUN
cana-1589	20	29	.	.	PUNCT
cana-1589	21	1	quantum	quantum	PROPN
cana-1589	21	2	computing	computing	NOUN
cana-1589	21	3	,	,	PUNCT
cana-1589	21	4	which	which	PRON
cana-1589	21	5	utilizes	utilize	VERB
cana-1589	21	6	quantum	quantum	ADJ
cana-1589	21	7	bits	bit	NOUN
cana-1589	21	8	or	or	CCONJ
cana-1589	21	9	qubits	qubit	NOUN
cana-1589	21	10	,	,	PUNCT
cana-1589	21	11	represents	represent	VERB
cana-1589	21	12	a	a	DET
cana-1589	21	13	significant	significant	ADJ
cana-1589	21	14	departure	departure	NOUN
cana-1589	21	15	from	from	ADP
cana-1589	21	16	traditional	traditional	ADJ
cana-1589	21	17	computing	computing	NOUN
cana-1589	21	18	.	.	PUNCT
cana-1589	22	1	unlike	unlike	ADP
cana-1589	22	2	classical	classical	ADJ
cana-1589	22	3	computers	computer	NOUN
cana-1589	22	4	,	,	PUNCT
cana-1589	22	5	which	which	PRON
cana-1589	22	6	process	process	VERB
cana-1589	22	7	information	information	NOUN
cana-1589	22	8	sequentially	sequentially	ADV
cana-1589	22	9	,	,	PUNCT
cana-1589	22	10	quantum	quantum	ADJ
cana-1589	22	11	computers	computer	NOUN
cana-1589	22	12	can	can	AUX
cana-1589	22	13	handle	handle	VERB
cana-1589	22	14	multiple	multiple	ADJ
cana-1589	22	15	communications	communication	NOUN
cana-1589	22	16	on	on	ADP
cana-1589	22	17	applied	apply	VERB
cana-1589	22	18	nonlinear	nonlinear	ADJ
cana-1589	22	19	analysis	analysis	NOUN
cana-1589	22	20	issn	issn	NOUN
cana-1589	22	21	:	:	PUNCT
cana-1589	22	22	1074	1074	NUM
cana-1589	22	23	-	-	PUNCT
cana-1589	22	24	133x	133x	NUM
cana-1589	22	25	vol	vol	NOUN
cana-1589	22	26	31	31	NUM
cana-1589	22	27	no	no	NOUN
cana-1589	22	28	.	.	PUNCT
cana-1589	23	1	7s	7	NOUN
cana-1589	23	2	(	(	PUNCT
cana-1589	23	3	2024	2024	NUM
cana-1589	23	4	)	)	PUNCT
cana-1589	23	5	697	697	NUM
cana-1589	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	23	7	pieces	piece	NOUN
cana-1589	23	8	of	of	ADP
cana-1589	23	9	information	information	NOUN
cana-1589	23	10	simultaneously	simultaneously	ADV
cana-1589	23	11	,	,	PUNCT
cana-1589	23	12	producing	produce	VERB
cana-1589	23	13	numerous	numerous	ADJ
cana-1589	23	14	possible	possible	ADJ
cana-1589	23	15	solutions	solution	NOUN
cana-1589	23	16	at	at	ADP
cana-1589	23	17	once	once	ADV
cana-1589	23	18	.	.	PUNCT
cana-1589	24	1	there	there	PRON
cana-1589	24	2	are	be	VERB
cana-1589	24	3	five	five	NUM
cana-1589	24	4	prominent	prominent	ADJ
cana-1589	24	5	public	public	ADJ
cana-1589	24	6	key	key	ADJ
cana-1589	24	7	cryptosystems	cryptosystem	NOUN
cana-1589	24	8	:	:	PUNCT
cana-1589	24	9	diffie	diffie	PROPN
cana-1589	24	10	-	-	PUNCT
cana-1589	24	11	hellman	hellman	PROPN
cana-1589	24	12	,	,	PUNCT
cana-1589	24	13	elliptic	elliptic	ADJ
cana-1589	24	14	curve	curve	NOUN
cana-1589	24	15	cryptography	cryptography	NOUN
cana-1589	24	16	(	(	PUNCT
cana-1589	24	17	ecc	ecc	PROPN
cana-1589	24	18	)	)	PUNCT
cana-1589	24	19	,	,	PUNCT
cana-1589	24	20	elgamal	elgamal	ADJ
cana-1589	24	21	cryptographic	cryptographic	ADJ
cana-1589	24	22	system	system	NOUN
cana-1589	24	23	(	(	PUNCT
cana-1589	24	24	ecs	ecs	PROPN
cana-1589	24	25	)	)	PUNCT
cana-1589	24	26	,	,	PUNCT
cana-1589	24	27	rsa	rsa	PROPN
cana-1589	24	28	,	,	PUNCT
cana-1589	24	29	and	and	CCONJ
cana-1589	24	30	ntru	ntru	PROPN
cana-1589	24	31	.	.	PUNCT
cana-1589	25	1	alese	alese	PROPN
cana-1589	25	2	et	et	PROPN
cana-1589	25	3	al	al	PROPN
cana-1589	25	4	.	.	PUNCT
cana-1589	26	1	[	[	X
cana-1589	26	2	2	2	X
cana-1589	26	3	]	]	PUNCT
cana-1589	26	4	conducted	conduct	VERB
cana-1589	26	5	a	a	DET
cana-1589	26	6	relative	relative	ADJ
cana-1589	26	7	analysis	analysis	NOUN
cana-1589	26	8	of	of	ADP
cana-1589	26	9	ecc	ecc	PROPN
cana-1589	26	10	,	,	PUNCT
cana-1589	26	11	rsa	rsa	PROPN
cana-1589	26	12	,	,	PUNCT
cana-1589	26	13	elgamal	elgamal	ADJ
cana-1589	26	14	,	,	PUNCT
cana-1589	26	15	and	and	CCONJ
cana-1589	26	16	menezes	menezes	PROPN
cana-1589	26	17	-	-	ADJ
cana-1589	26	18	vanstone	vanstone	NOUN
cana-1589	26	19	elliptic	elliptic	ADJ
cana-1589	26	20	curve	curve	NOUN
cana-1589	26	21	encryption	encryption	NOUN
cana-1589	26	22	algorithms	algorithm	NOUN
cana-1589	26	23	,	,	PUNCT
cana-1589	26	24	implemented	implement	VERB
cana-1589	26	25	in	in	ADP
cana-1589	26	26	java	java	PROPN
cana-1589	26	27	,	,	PUNCT
cana-1589	26	28	evaluating	evaluate	VERB
cana-1589	26	29	their	their	PRON
cana-1589	26	30	performance	performance	NOUN
cana-1589	26	31	based	base	VERB
cana-1589	26	32	on	on	ADP
cana-1589	26	33	key	key	ADJ
cana-1589	26	34	generation	generation	NOUN
cana-1589	26	35	,	,	PUNCT
cana-1589	26	36	encryption	encryption	NOUN
cana-1589	26	37	,	,	PUNCT
cana-1589	26	38	and	and	CCONJ
cana-1589	26	39	decryption	decryption	NOUN
cana-1589	26	40	times	time	NOUN
cana-1589	26	41	.	.	PUNCT
cana-1589	27	1	giripunje	giripunje	PROPN
cana-1589	27	2	et	et	PROPN
cana-1589	27	3	al	al	PROPN
cana-1589	27	4	.	.	PUNCT
cana-1589	28	1	[	[	X
cana-1589	28	2	3	3	NUM
cana-1589	28	3	]	]	PUNCT
cana-1589	28	4	discussed	discuss	VERB
cana-1589	28	5	asymmetric	asymmetric	ADJ
cana-1589	28	6	key	key	ADJ
cana-1589	28	7	cryptography	cryptography	NOUN
cana-1589	28	8	solutions	solution	NOUN
cana-1589	28	9	,	,	PUNCT
cana-1589	28	10	emphasizing	emphasize	VERB
cana-1589	28	11	the	the	DET
cana-1589	28	12	importance	importance	NOUN
cana-1589	28	13	of	of	ADP
cana-1589	28	14	secure	secure	ADJ
cana-1589	28	15	authentication	authentication	NOUN
cana-1589	28	16	in	in	ADP
cana-1589	28	17	mobile	mobile	ADJ
cana-1589	28	18	communications	communication	NOUN
cana-1589	28	19	.	.	PUNCT
cana-1589	29	1	this	this	DET
cana-1589	29	2	paper	paper	NOUN
cana-1589	29	3	highlighted	highlight	VERB
cana-1589	29	4	that	that	SCONJ
cana-1589	29	5	ecc	ecc	PROPN
cana-1589	29	6	,	,	PUNCT
cana-1589	29	7	requiring	require	VERB
cana-1589	29	8	smaller	small	ADJ
cana-1589	29	9	key	key	ADJ
cana-1589	29	10	sizes	size	NOUN
cana-1589	29	11	and	and	CCONJ
cana-1589	29	12	lower	low	ADJ
cana-1589	29	13	computational	computational	ADJ
cana-1589	29	14	power	power	NOUN
cana-1589	29	15	compared	compare	VERB
cana-1589	29	16	to	to	ADP
cana-1589	29	17	rsa	rsa	PROPN
cana-1589	29	18	,	,	PUNCT
cana-1589	29	19	is	be	AUX
cana-1589	29	20	more	more	ADV
cana-1589	29	21	suitable	suitable	ADJ
cana-1589	29	22	for	for	ADP
cana-1589	29	23	constrained	constrained	ADJ
cana-1589	29	24	devices	device	NOUN
cana-1589	29	25	such	such	ADJ
cana-1589	29	26	as	as	ADP
cana-1589	29	27	mobile	mobile	ADJ
cana-1589	29	28	phones	phone	NOUN
cana-1589	29	29	.	.	PUNCT
cana-1589	30	1	pallipamu	pallipamu	VERB
cana-1589	30	2	et	et	PROPN
cana-1589	30	3	al	al	PROPN
cana-1589	30	4	.	.	PUNCT
cana-1589	31	1	[	[	X
cana-1589	31	2	4	4	X
cana-1589	31	3	]	]	PUNCT
cana-1589	31	4	performed	perform	VERB
cana-1589	31	5	a	a	DET
cana-1589	31	6	security	security	NOUN
cana-1589	31	7	examination	examination	NOUN
cana-1589	31	8	of	of	ADP
cana-1589	31	9	digital	digital	ADJ
cana-1589	31	10	signature	signature	NOUN
cana-1589	31	11	schemes	scheme	NOUN
cana-1589	31	12	,	,	PUNCT
cana-1589	31	13	including	include	VERB
cana-1589	31	14	dsa	dsa	PROPN
cana-1589	31	15	,	,	PUNCT
cana-1589	31	16	and	and	CCONJ
cana-1589	31	17	elgamal	elgamal	ADJ
cana-1589	31	18	,	,	PUNCT
cana-1589	31	19	and	and	CCONJ
cana-1589	31	20	rsa	rsa	PROPN
cana-1589	31	21	,	,	PUNCT
cana-1589	31	22	assessing	assess	VERB
cana-1589	31	23	the	the	DET
cana-1589	31	24	mathematical	mathematical	ADJ
cana-1589	31	25	complexity	complexity	NOUN
cana-1589	31	26	of	of	ADP
cana-1589	31	27	key	key	ADJ
cana-1589	31	28	generation	generation	NOUN
cana-1589	31	29	,	,	PUNCT
cana-1589	31	30	signature	signature	NOUN
cana-1589	31	31	verification	verification	NOUN
cana-1589	31	32	,	,	PUNCT
cana-1589	31	33	and	and	CCONJ
cana-1589	31	34	overall	overall	ADJ
cana-1589	31	35	security	security	NOUN
cana-1589	31	36	strengths	strength	NOUN
cana-1589	31	37	of	of	ADP
cana-1589	31	38	these	these	DET
cana-1589	31	39	algorithms	algorithm	NOUN
cana-1589	31	40	.	.	PUNCT
cana-1589	32	1	2	2	X
cana-1589	32	2	.	.	X
cana-1589	32	3	objectives	objective	VERB
cana-1589	32	4	the	the	DET
cana-1589	32	5	security	security	NOUN
cana-1589	32	6	of	of	ADP
cana-1589	32	7	information	information	NOUN
cana-1589	32	8	is	be	AUX
cana-1589	32	9	a	a	DET
cana-1589	32	10	critical	critical	ADJ
cana-1589	32	11	concern	concern	NOUN
cana-1589	32	12	in	in	ADP
cana-1589	32	13	wireless	wireless	ADJ
cana-1589	32	14	communication	communication	NOUN
cana-1589	32	15	networks	network	NOUN
cana-1589	32	16	.	.	PUNCT
cana-1589	33	1	implementing	implement	VERB
cana-1589	33	2	public	public	ADJ
cana-1589	33	3	key	key	ADJ
cana-1589	33	4	algorithms	algorithm	NOUN
cana-1589	33	5	on	on	ADP
cana-1589	33	6	highly	highly	ADV
cana-1589	33	7	constrained	constrain	VERB
cana-1589	33	8	devices	device	NOUN
cana-1589	33	9	,	,	PUNCT
cana-1589	33	10	such	such	ADJ
cana-1589	33	11	as	as	ADP
cana-1589	33	12	mobile	mobile	ADJ
cana-1589	33	13	phones	phone	NOUN
cana-1589	33	14	and	and	CCONJ
cana-1589	33	15	pdas	pda	NOUN
cana-1589	33	16	,	,	PUNCT
cana-1589	33	17	necessitates	necessitate	VERB
cana-1589	33	18	the	the	DET
cana-1589	33	19	use	use	NOUN
cana-1589	33	20	of	of	ADP
cana-1589	33	21	fast	fast	ADJ
cana-1589	33	22	and	and	CCONJ
cana-1589	33	23	efficient	efficient	ADJ
cana-1589	33	24	cryptosystems	cryptosystem	NOUN
cana-1589	33	25	.	.	PUNCT
cana-1589	34	1	it	it	PRON
cana-1589	34	2	is	be	AUX
cana-1589	34	3	essential	essential	ADJ
cana-1589	34	4	to	to	PART
cana-1589	34	5	analyze	analyze	VERB
cana-1589	34	6	various	various	ADJ
cana-1589	34	7	public	public	ADJ
cana-1589	34	8	key	key	ADJ
cana-1589	34	9	cryptosystems	cryptosystem	NOUN
cana-1589	34	10	to	to	PART
cana-1589	34	11	identify	identify	VERB
cana-1589	34	12	the	the	DET
cana-1589	34	13	most	most	ADV
cana-1589	34	14	efficient	efficient	ADJ
cana-1589	34	15	option	option	NOUN
cana-1589	34	16	.	.	PUNCT
cana-1589	35	1	among	among	ADP
cana-1589	35	2	these	these	PRON
cana-1589	35	3	,	,	PUNCT
cana-1589	35	4	the	the	DET
cana-1589	35	5	ntru	ntru	ADJ
cana-1589	35	6	public	public	ADJ
cana-1589	35	7	key	key	ADJ
cana-1589	35	8	cryptosystem	cryptosystem	NOUN
cana-1589	35	9	stands	stand	VERB
cana-1589	35	10	out	out	ADP
cana-1589	35	11	as	as	ADP
cana-1589	35	12	the	the	DET
cana-1589	35	13	fastest	fast	ADJ
cana-1589	35	14	,	,	PUNCT
cana-1589	35	15	offering	offer	VERB
cana-1589	35	16	different	different	ADJ
cana-1589	35	17	levels	level	NOUN
cana-1589	35	18	of	of	ADP
cana-1589	35	19	security	security	NOUN
cana-1589	35	20	with	with	ADP
cana-1589	35	21	high	high	ADJ
cana-1589	35	22	performance	performance	NOUN
cana-1589	35	23	even	even	ADV
cana-1589	35	24	on	on	ADP
cana-1589	35	25	limited	limited	ADJ
cana-1589	35	26	resources	resource	NOUN
cana-1589	35	27	.	.	PUNCT
cana-1589	36	1	ntru	ntru	PROPN
cana-1589	36	2	employs	employ	VERB
cana-1589	36	3	lattice	lattice	NOUN
cana-1589	36	4	-	-	PUNCT
cana-1589	36	5	based	base	VERB
cana-1589	36	6	cryptography	cryptography	NOUN
cana-1589	36	7	for	for	ADP
cana-1589	36	8	data	data	NOUN
cana-1589	36	9	encryption	encryption	NOUN
cana-1589	36	10	and	and	CCONJ
cana-1589	36	11	decryption	decryption	NOUN
cana-1589	36	12	.	.	PUNCT
cana-1589	37	1	unlike	unlike	ADP
cana-1589	37	2	many	many	ADJ
cana-1589	37	3	other	other	ADJ
cana-1589	37	4	public	public	ADJ
cana-1589	37	5	key	key	ADJ
cana-1589	37	6	cryptosystems	cryptosystem	NOUN
cana-1589	37	7	,	,	PUNCT
cana-1589	37	8	ntru	ntru	PROPN
cana-1589	37	9	is	be	AUX
cana-1589	37	10	resistant	resistant	ADJ
cana-1589	37	11	to	to	ADP
cana-1589	37	12	quantum	quantum	ADJ
cana-1589	37	13	attacks	attack	NOUN
cana-1589	37	14	using	use	VERB
cana-1589	37	15	shor	shor	PROPN
cana-1589	37	16	's	's	PART
cana-1589	37	17	algorithm	algorithm	NOUN
cana-1589	37	18	.	.	PUNCT
cana-1589	38	1	3	3	X
cana-1589	38	2	.	.	X
cana-1589	38	3	ntru	ntru	ADJ
cana-1589	38	4	cryptosystem	cryptosystem	NOUN
cana-1589	38	5	here	here	ADV
cana-1589	38	6	is	be	AUX
cana-1589	38	7	a	a	DET
cana-1589	38	8	brief	brief	ADJ
cana-1589	38	9	overview	overview	NOUN
cana-1589	38	10	of	of	ADP
cana-1589	38	11	the	the	DET
cana-1589	38	12	well	well	ADV
cana-1589	38	13	-	-	PUNCT
cana-1589	38	14	known	know	VERB
cana-1589	38	15	rsa	rsa	NOUN
cana-1589	38	16	cryptosystem	cryptosystem	NOUN
cana-1589	38	17	.	.	PUNCT
cana-1589	39	1	the	the	DET
cana-1589	39	2	rsa	rsa	PROPN
cana-1589	39	3	cryptosystem	cryptosystem	NOUN
cana-1589	39	4	,	,	PUNCT
cana-1589	39	5	developed	develop	VERB
cana-1589	39	6	by	by	ADP
cana-1589	39	7	ron	ron	PROPN
cana-1589	39	8	rivest	rivest	PROPN
cana-1589	39	9	,	,	PUNCT
cana-1589	39	10	adi	adi	PROPN
cana-1589	39	11	shamir	shamir	PROPN
cana-1589	39	12	,	,	PUNCT
cana-1589	39	13	and	and	CCONJ
cana-1589	39	14	leonard	leonard	PROPN
cana-1589	39	15	adleman	adleman	PROPN
cana-1589	39	16	,	,	PUNCT
cana-1589	39	17	is	be	AUX
cana-1589	39	18	widely	widely	ADV
cana-1589	39	19	used	use	VERB
cana-1589	39	20	and	and	CCONJ
cana-1589	39	21	incorporated	incorporate	VERB
cana-1589	39	22	into	into	ADP
cana-1589	39	23	web	web	NOUN
cana-1589	39	24	browsers	browser	NOUN
cana-1589	39	25	from	from	ADP
cana-1589	39	26	microsoft	microsoft	PROPN
cana-1589	39	27	and	and	CCONJ
cana-1589	39	28	netscape	netscape	NOUN
cana-1589	39	29	.	.	PUNCT
cana-1589	40	1	the	the	DET
cana-1589	40	2	process	process	NOUN
cana-1589	40	3	for	for	ADP
cana-1589	40	4	generating	generate	VERB
cana-1589	40	5	rsa	rsa	PROPN
cana-1589	40	6	public	public	NOUN
cana-1589	40	7	and	and	CCONJ
cana-1589	40	8	private	private	ADJ
cana-1589	40	9	keys	key	NOUN
cana-1589	40	10	is	be	AUX
cana-1589	40	11	as	as	SCONJ
cana-1589	40	12	follows	follow	VERB
cana-1589	40	13	:	:	PUNCT
cana-1589	40	14	key	key	ADJ
cana-1589	40	15	generation	generation	NOUN
cana-1589	40	16	algorithm	algorithm	NOUN
cana-1589	40	17	:	:	PUNCT
cana-1589	40	18	1	1	X
cana-1589	40	19	.	.	X
cana-1589	40	20	select	select	VERB
cana-1589	40	21	two	two	NUM
cana-1589	40	22	large	large	ADJ
cana-1589	40	23	prime	prime	ADJ
cana-1589	40	24	numbers	number	NOUN
cana-1589	40	25	p	p	NOUN
cana-1589	40	26	and	and	CCONJ
cana-1589	40	27	q.	q.	PROPN
cana-1589	40	28	2	2	NUM
cana-1589	40	29	.	.	PUNCT
cana-1589	40	30	calculate	calculate	NOUN
cana-1589	40	31	n	n	CCONJ
cana-1589	40	32	=	=	NOUN
cana-1589	40	33	p×q	p×q	PROPN
cana-1589	40	34	.	.	PUNCT
cana-1589	41	1	3	3	X
cana-1589	41	2	.	.	X
cana-1589	41	3	compute	compute	PROPN
cana-1589	41	4	ϕ(n)=(p−1)×(q−1	ϕ(n)=(p−1)×(q−1	PROPN
cana-1589	41	5	)	)	PUNCT
cana-1589	41	6	.	.	PUNCT
cana-1589	42	1	4	4	X
cana-1589	42	2	.	.	X
cana-1589	42	3	select	select	VERB
cana-1589	42	4	a	a	DET
cana-1589	42	5	public	public	ADJ
cana-1589	42	6	key	key	ADJ
cana-1589	42	7	exponent	exponent	NOUN
cana-1589	42	8	e	e	PUNCT
cana-1589	42	9	such	such	ADJ
cana-1589	42	10	that	that	DET
cana-1589	42	11	gcd(ϕ(n),e)=1	gcd(ϕ(n),e)=1	NOUN
cana-1589	42	12	and	and	CCONJ
cana-1589	42	13	1	1	NUM
cana-1589	42	14	<	<	NOUN
cana-1589	42	15	e<ϕ(n	e<ϕ(n	X
cana-1589	42	16	)	)	PUNCT
cana-1589	42	17	.	.	PUNCT
cana-1589	43	1	5	5	X
cana-1589	43	2	.	.	X
cana-1589	43	3	determine	determine	VERB
cana-1589	43	4	the	the	DET
cana-1589	43	5	private	private	ADJ
cana-1589	43	6	key	key	NOUN
cana-1589	43	7	d	d	ADP
cana-1589	43	8	such	such	ADJ
cana-1589	43	9	that	that	SCONJ
cana-1589	43	10	d×e	d×e	PROPN
cana-1589	43	11	mod	mod	PROPN
cana-1589	43	12	  	  	SPACE
cana-1589	43	13	ϕ(n)=1	ϕ(n)=1	X
cana-1589	43	14	6	6	NUM
cana-1589	43	15	.	.	PUNCT
cana-1589	43	16	public	public	ADJ
cana-1589	43	17	key	key	NOUN
cana-1589	43	18	is	be	AUX
cana-1589	43	19	(	(	PUNCT
cana-1589	43	20	n	n	X
cana-1589	43	21	,	,	PUNCT
cana-1589	43	22	e	e	NOUN
cana-1589	43	23	)	)	PUNCT
cana-1589	43	24	and	and	CCONJ
cana-1589	43	25	private	private	ADJ
cana-1589	43	26	key	key	NOUN
cana-1589	43	27	is	be	AUX
cana-1589	43	28	(	(	PUNCT
cana-1589	43	29	n	n	X
cana-1589	43	30	,	,	PUNCT
cana-1589	43	31	d	d	NOUN
cana-1589	43	32	)	)	PUNCT
cana-1589	43	33	.	.	PUNCT
cana-1589	44	1	encryption	encryption	NOUN
cana-1589	44	2	and	and	CCONJ
cana-1589	44	3	decryption	decryption	NOUN
cana-1589	44	4	:	:	PUNCT
cana-1589	44	5	encryption	encryption	NOUN
cana-1589	44	6	:	:	PUNCT
cana-1589	44	7	to	to	PART
cana-1589	44	8	encrypt	encrypt	VERB
cana-1589	44	9	a	a	DET
cana-1589	44	10	message	message	NOUN
cana-1589	44	11	m	m	NOUN
cana-1589	44	12	,	,	PUNCT
cana-1589	44	13	compute	compute	NOUN
cana-1589	44	14	c	c	NOUN
cana-1589	44	15	=	=	PRON
cana-1589	44	16	me	i	PRON
cana-1589	44	17	mod	mod	NOUN
cana-1589	44	18	n	n	PRON
cana-1589	44	19	decryption	decryption	NOUN
cana-1589	44	20	:	:	PUNCT
cana-1589	44	21	to	to	PART
cana-1589	44	22	decrypt	decrypt	VERB
cana-1589	44	23	the	the	DET
cana-1589	44	24	ciphertext	ciphertext	NOUN
cana-1589	44	25	c	c	NOUN
cana-1589	44	26	,	,	PUNCT
cana-1589	44	27	compute	compute	NOUN
cana-1589	44	28	m	m	NOUN
cana-1589	44	29	=	=	ADJ
cana-1589	44	30	cd	cd	PROPN
cana-1589	44	31	mod	mod	PROPN
cana-1589	44	32	n	n	PROPN
cana-1589	44	33	=	=	SYM
cana-1589	44	34	(	(	PUNCT
cana-1589	44	35	me)d	me)d	X
cana-1589	44	36	mod	mod	NOUN
cana-1589	44	37	n	n	PROPN
cana-1589	44	38	=	=	PRON
cana-1589	44	39	(	(	PUNCT
cana-1589	44	40	m)ed	m)ed	PROPN
cana-1589	44	41	mod	mod	NOUN
cana-1589	44	42	n	n	CCONJ
cana-1589	44	43	which	which	PRON
cana-1589	44	44	retrieves	retrieve	VERB
cana-1589	44	45	the	the	DET
cana-1589	44	46	original	original	ADJ
cana-1589	44	47	message	message	NOUN
cana-1589	44	48	m.	m.	NOUN
cana-1589	44	49	this	this	DET
cana-1589	44	50	process	process	NOUN
cana-1589	44	51	ensures	ensure	VERB
cana-1589	44	52	secure	secure	ADJ
cana-1589	44	53	communication	communication	NOUN
cana-1589	44	54	by	by	ADP
cana-1589	44	55	using	use	VERB
cana-1589	44	56	the	the	DET
cana-1589	44	57	public	public	ADJ
cana-1589	44	58	key	key	NOUN
cana-1589	44	59	for	for	ADP
cana-1589	44	60	encryption	encryption	NOUN
cana-1589	44	61	and	and	CCONJ
cana-1589	44	62	the	the	DET
cana-1589	44	63	private	private	ADJ
cana-1589	44	64	key	key	NOUN
cana-1589	44	65	for	for	ADP
cana-1589	44	66	decryption	decryption	NOUN
cana-1589	44	67	.	.	PUNCT
cana-1589	45	1	communications	communication	NOUN
cana-1589	45	2	on	on	ADP
cana-1589	45	3	applied	apply	VERB
cana-1589	45	4	nonlinear	nonlinear	ADJ
cana-1589	45	5	analysis	analysis	NOUN
cana-1589	45	6	issn	issn	NOUN
cana-1589	45	7	:	:	PUNCT
cana-1589	45	8	1074	1074	NUM
cana-1589	45	9	-	-	PUNCT
cana-1589	45	10	133x	133x	NUM
cana-1589	45	11	vol	vol	NOUN
cana-1589	45	12	31	31	NUM
cana-1589	45	13	no	no	NOUN
cana-1589	45	14	.	.	PUNCT
cana-1589	46	1	7s	7	NOUN
cana-1589	46	2	(	(	PUNCT
cana-1589	46	3	2024	2024	NUM
cana-1589	46	4	)	)	PUNCT
cana-1589	46	5	698	698	NUM
cana-1589	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	47	1	the	the	DET
cana-1589	47	2	ntru	ntru	ADJ
cana-1589	47	3	cryptosystem	cryptosystem	NOUN
cana-1589	47	4	,	,	PUNCT
cana-1589	47	5	developed	develop	VERB
cana-1589	47	6	by	by	ADP
cana-1589	47	7	j	j	PROPN
cana-1589	47	8	h.	h.	PROPN
cana-1589	47	9	silverman	silverman	PROPN
cana-1589	47	10	,	,	PUNCT
cana-1589	47	11	j	j	PROPN
cana-1589	47	12	hoffstein	hoffstein	NOUN
cana-1589	47	13	,	,	PUNCT
cana-1589	47	14	and	and	CCONJ
cana-1589	47	15	j	j	PROPN
cana-1589	47	16	pipher	pipher	NOUN
cana-1589	47	17	,	,	PUNCT
cana-1589	47	18	is	be	AUX
cana-1589	47	19	named	name	VERB
cana-1589	47	20	after	after	ADP
cana-1589	47	21	the	the	DET
cana-1589	47	22	n	n	ADV
cana-1589	47	23	-	-	PUNCT
cana-1589	47	24	th	th	VERB
cana-1589	47	25	degree	degree	NOUN
cana-1589	47	26	truncated	truncate	VERB
cana-1589	47	27	polynomial	polynomial	ADJ
cana-1589	47	28	ring	ring	NOUN
cana-1589	47	29	[	[	X
cana-1589	47	30	5	5	NUM
cana-1589	47	31	]	]	PUNCT
cana-1589	47	32	.	.	PUNCT
cana-1589	48	1	ntru	ntru	PROPN
cana-1589	48	2	’s	’s	PART
cana-1589	48	3	operation	operation	NOUN
cana-1589	48	4	defines	define	NOUN
cana-1589	48	5	in	in	ADP
cana-1589	48	6	the	the	DET
cana-1589	48	7	ring	ring	NOUN
cana-1589	48	8	ℤ	ℤ	PROPN
cana-1589	49	1	[	[	X
cana-1589	49	2	𝑥	𝑥	X
cana-1589	49	3	]	]	X
cana-1589	49	4	(	(	PUNCT
cana-1589	49	5	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	49	6	−	−	PROPN
cana-1589	49	7	1)⁄	1)⁄	NUM
cana-1589	49	8	which	which	PRON
cana-1589	49	9	is	be	AUX
cana-1589	49	10	identified	identify	VERB
cana-1589	49	11	as	as	ADP
cana-1589	49	12	the	the	DET
cana-1589	49	13	ring	ring	NOUN
cana-1589	49	14	of	of	ADP
cana-1589	49	15	convolution	convolution	NOUN
cana-1589	49	16	polynomials	polynomial	NOUN
cana-1589	49	17	of	of	ADP
cana-1589	49	18	rank	rank	NOUN
cana-1589	49	19	“	"	PUNCT
cana-1589	49	20	n	n	CCONJ
cana-1589	49	21	”	"	PUNCT
cana-1589	49	22	,	,	PUNCT
cana-1589	49	23	where	where	SCONJ
cana-1589	49	24	“	"	PUNCT
cana-1589	49	25	n	n	CCONJ
cana-1589	49	26	"	"	PUNCT
cana-1589	49	27	is	be	AUX
cana-1589	49	28	a	a	DET
cana-1589	49	29	prime	prime	NOUN
cana-1589	49	30	.	.	PUNCT
cana-1589	50	1	addition	addition	NOUN
cana-1589	50	2	can	can	AUX
cana-1589	50	3	be	be	AUX
cana-1589	50	4	performed	perform	VERB
cana-1589	50	5	in	in	ADP
cana-1589	50	6	o(n	o(n	NUM
cana-1589	50	7	)	)	PUNCT
cana-1589	50	8	and	and	CCONJ
cana-1589	50	9	multiplication	multiplication	NOUN
cana-1589	50	10	requires	require	VERB
cana-1589	50	11	only	only	ADV
cana-1589	50	12	o(n2	o(n2	ADV
cana-1589	50	13	)	)	PUNCT
cana-1589	50	14	operations	operation	NOUN
cana-1589	50	15	in	in	ADP
cana-1589	50	16	the	the	DET
cana-1589	50	17	ring	ring	NOUN
cana-1589	50	18	of	of	ADP
cana-1589	50	19	convolution	convolution	NOUN
cana-1589	50	20	polynomials	polynomial	NOUN
cana-1589	50	21	.	.	PUNCT
cana-1589	51	1	ntru	ntru	PROPN
cana-1589	51	2	utilizes	utilize	VERB
cana-1589	51	3	three	three	NUM
cana-1589	51	4	primary	primary	ADJ
cana-1589	51	5	rings	ring	NOUN
cana-1589	51	6	:	:	PUNCT
cana-1589	52	1	1	1	X
cana-1589	52	2	.	.	X
cana-1589	52	3	r	r	NOUN
cana-1589	52	4	=	=	PUNCT
cana-1589	52	5	ℤ	ℤ	PROPN
cana-1589	53	1	[	[	X
cana-1589	53	2	𝑥	𝑥	X
cana-1589	53	3	]	]	X
cana-1589	53	4	(	(	PUNCT
cana-1589	53	5	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	53	6	−	−	PROPN
cana-1589	53	7	1)⁄	1)⁄	NUM
cana-1589	53	8	2	2	NUM
cana-1589	53	9	.	.	PUNCT
cana-1589	54	1	rp	rp	NOUN
cana-1589	54	2	=	=	SYM
cana-1589	54	3	ℤ/𝑝ℤ[𝑥	ℤ/𝑝ℤ[𝑥	X
cana-1589	54	4	]	]	PUNCT
cana-1589	54	5	(	(	PUNCT
cana-1589	54	6	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	54	7	−	−	PROPN
cana-1589	54	8	1)⁄	1)⁄	NUM
cana-1589	54	9	3	3	NUM
cana-1589	54	10	.	.	PUNCT
cana-1589	55	1	rq	rq	NOUN
cana-1589	55	2	=	=	PUNCT
cana-1589	55	3	ℤ/𝑞ℤ[𝑥	ℤ/𝑞ℤ[𝑥	NOUN
cana-1589	55	4	]	]	X
cana-1589	55	5	(	(	PUNCT
cana-1589	55	6	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	55	7	−	−	PROPN
cana-1589	55	8	1)⁄	1)⁄	NUM
cana-1589	55	9	here	here	ADV
cana-1589	55	10	,	,	PUNCT
cana-1589	55	11	p	p	X
cana-1589	55	12	(	(	PUNCT
cana-1589	55	13	specifying	specify	VERB
cana-1589	55	14	a	a	DET
cana-1589	55	15	ring	ring	NOUN
cana-1589	55	16	ℤ	ℤ	PROPN
cana-1589	55	17	𝑝ℤ⁄	𝑝ℤ⁄	PROPN
cana-1589	55	18	)	)	PUNCT
cana-1589	55	19	and	and	CCONJ
cana-1589	55	20	q	q	X
cana-1589	55	21	(	(	PUNCT
cana-1589	55	22	specifying	specify	VERB
cana-1589	55	23	a	a	DET
cana-1589	55	24	ring	ring	NOUN
cana-1589	55	25	ℤ	ℤ	PROPN
cana-1589	55	26	𝑞ℤ⁄	𝑞ℤ⁄	PROPN
cana-1589	55	27	)	)	PUNCT
cana-1589	55	28	are	be	AUX
cana-1589	55	29	positive	positive	ADJ
cana-1589	55	30	integers	integer	NOUN
cana-1589	55	31	used	use	VERB
cana-1589	55	32	to	to	PART
cana-1589	55	33	reduce	reduce	VERB
cana-1589	55	34	the	the	DET
cana-1589	55	35	coefficients	coefficient	NOUN
cana-1589	55	36	of	of	ADP
cana-1589	55	37	polynomials	polynomial	NOUN
cana-1589	55	38	during	during	ADP
cana-1589	55	39	encryption	encryption	NOUN
cana-1589	55	40	and	and	CCONJ
cana-1589	55	41	decryption	decryption	NOUN
cana-1589	55	42	.	.	PUNCT
cana-1589	56	1	polynomials	polynomial	NOUN
cana-1589	56	2	in	in	ADP
cana-1589	56	3	these	these	DET
cana-1589	56	4	rings	ring	NOUN
cana-1589	56	5	can	can	AUX
cana-1589	56	6	be	be	AUX
cana-1589	56	7	represented	represent	VERB
cana-1589	56	8	either	either	CCONJ
cana-1589	56	9	by	by	ADP
cana-1589	56	10	their	their	PRON
cana-1589	56	11	coefficients	coefficient	NOUN
cana-1589	56	12	or	or	CCONJ
cana-1589	56	13	directly	directly	ADV
cana-1589	56	14	in	in	ADP
cana-1589	56	15	polynomial	polynomial	ADJ
cana-1589	56	16	form	form	NOUN
cana-1589	56	17	.	.	PUNCT
cana-1589	57	1	operations	operation	NOUN
cana-1589	57	2	such	such	ADJ
cana-1589	57	3	as	as	ADP
cana-1589	57	4	addition	addition	NOUN
cana-1589	57	5	and	and	CCONJ
cana-1589	57	6	multiplication	multiplication	NOUN
cana-1589	57	7	in	in	ADP
cana-1589	57	8	rp	rp	NOUN
cana-1589	57	9	or	or	CCONJ
cana-1589	57	10	rq	rq	NOUN
cana-1589	57	11	are	be	AUX
cana-1589	57	12	similar	similar	ADJ
cana-1589	57	13	to	to	ADP
cana-1589	57	14	those	those	PRON
cana-1589	57	15	in	in	ADP
cana-1589	57	16	r	r	NOUN
cana-1589	57	17	,	,	PUNCT
cana-1589	57	18	with	with	SCONJ
cana-1589	57	19	the	the	DET
cana-1589	57	20	result	result	NOUN
cana-1589	57	21	's	's	PART
cana-1589	57	22	coefficients	coefficient	NOUN
cana-1589	57	23	reduced	reduce	VERB
cana-1589	57	24	modulo	modulo	PROPN
cana-1589	57	25	p	p	NOUN
cana-1589	57	26	or	or	CCONJ
cana-1589	57	27	q.	q.	NOUN
cana-1589	57	28	an	an	DET
cana-1589	57	29	element	element	NOUN
cana-1589	57	30	f	f	X
cana-1589	57	31	(	(	PUNCT
cana-1589	57	32	a	a	DET
cana-1589	57	33	polynomial	polynomial	NOUN
cana-1589	57	34	in	in	ADP
cana-1589	57	35	ℤ	ℤ	PROPN
cana-1589	57	36	[	[	X
cana-1589	57	37	𝑥	𝑥	X
cana-1589	57	38	]	]	X
cana-1589	57	39	(	(	PUNCT
cana-1589	57	40	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	57	41	−	−	PROPN
cana-1589	57	42	1).⁄	1).⁄	NUM
cana-1589	57	43	)	)	PUNCT
cana-1589	57	44	of	of	ADP
cana-1589	57	45	the	the	DET
cana-1589	57	46	rings	ring	NOUN
cana-1589	57	47	r	r	NOUN
cana-1589	57	48	,	,	PUNCT
cana-1589	57	49	rp	rp	NOUN
cana-1589	57	50	and	and	CCONJ
cana-1589	57	51	rq	rq	NOUN
cana-1589	57	52	can	can	AUX
cana-1589	57	53	be	be	AUX
cana-1589	57	54	represented	represent	VERB
cana-1589	57	55	as	as	ADP
cana-1589	57	56	polynomial	polynomial	ADJ
cana-1589	57	57	or	or	CCONJ
cana-1589	57	58	vector	vector	NOUN
cana-1589	57	59	coefficients	coefficient	NOUN
cana-1589	57	60	.	.	PUNCT
cana-1589	58	1	ntru	ntru	PROPN
cana-1589	58	2	operate	operate	VERB
cana-1589	58	3	in	in	ADP
cana-1589	58	4	the	the	DET
cana-1589	58	5	ring	ring	NOUN
cana-1589	58	6	r	r	NOUN
cana-1589	58	7	=	=	PUNCT
cana-1589	58	8	ℤ	ℤ	PROPN
cana-1589	59	1	[	[	X
cana-1589	59	2	𝑥	𝑥	X
cana-1589	59	3	]	]	X
cana-1589	59	4	(	(	PUNCT
cana-1589	59	5	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	59	6	−	−	PROPN
cana-1589	59	7	1).⁄	1).⁄	PROPN
cana-1589	60	1	an	an	DET
cana-1589	60	2	element	element	NOUN
cana-1589	60	3	f	f	PROPN
cana-1589	60	4	∈	∈	PROPN
cana-1589	60	5	r	r	NOUN
cana-1589	60	6	represented	represent	VERB
cana-1589	60	7	as	as	ADP
cana-1589	60	8	a	a	DET
cana-1589	60	9	polynomial	polynomial	ADJ
cana-1589	60	10	,	,	PUNCT
cana-1589	60	11	𝑓	𝑓	PROPN
cana-1589	60	12	=	=	PUNCT
cana-1589	60	13	∑	∑	PART
cana-1589	60	14	𝑓𝑖𝑥𝑖	𝑓𝑖𝑥𝑖	NOUN
cana-1589	60	15	𝑛−1	𝑛−1	PROPN
cana-1589	60	16	𝑖=0	𝑖=0	PROPN
cana-1589	61	1	=	=	PUNCT
cana-1589	62	1	[	[	X
cana-1589	62	2	𝑓0	𝑓0	PROPN
cana-1589	62	3	,	,	PUNCT
cana-1589	62	4	𝑓1	𝑓1	PROPN
cana-1589	62	5	,	,	PUNCT
cana-1589	62	6	…	…	PUNCT
cana-1589	62	7	,	,	PUNCT
cana-1589	62	8	𝑓𝑛−1	𝑓𝑛−1	PROPN
cana-1589	62	9	]	]	X
cana-1589	62	10	f	f	PROPN
cana-1589	62	11	∗	∗	NOUN
cana-1589	62	12	𝑔	𝑔	PROPN
cana-1589	62	13	=	=	PUNCT
cana-1589	62	14	ℎ	ℎ	X
cana-1589	62	15	"	"	PUNCT
cana-1589	62	16	𝑔	𝑔	X
cana-1589	62	17	"	"	PUNCT
cana-1589	62	18	is	be	AUX
cana-1589	62	19	a	a	DET
cana-1589	62	20	polynomial	polynomial	NOUN
cana-1589	62	21	in	in	ADP
cana-1589	62	22	ℤ	ℤ	PROPN
cana-1589	62	23	[	[	X
cana-1589	62	24	𝑥	𝑥	X
cana-1589	62	25	]	]	X
cana-1589	62	26	(	(	PUNCT
cana-1589	62	27	𝑞	𝑞	PROPN
cana-1589	62	28	,	,	PUNCT
cana-1589	62	29	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	62	30	−	−	PROPN
cana-1589	62	31	1)⁄	1)⁄	NUM
cana-1589	62	32	used	use	VERB
cana-1589	62	33	with	with	ADP
cana-1589	62	34	𝑓𝑞	𝑓𝑞	DET
cana-1589	62	35	(	(	PUNCT
cana-1589	62	36	a	a	DET
cana-1589	62	37	polynomial	polynomial	NOUN
cana-1589	62	38	in	in	ADP
cana-1589	62	39	ℤ	ℤ	PROPN
cana-1589	62	40	[	[	X
cana-1589	62	41	𝑥	𝑥	X
cana-1589	62	42	]	]	X
cana-1589	62	43	(	(	PUNCT
cana-1589	62	44	𝑞	𝑞	PROPN
cana-1589	62	45	,	,	PUNCT
cana-1589	62	46	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	62	47	−	−	PROPN
cana-1589	62	48	1)⁄	1)⁄	NUM
cana-1589	62	49	)	)	PUNCT
cana-1589	62	50	.	.	PUNCT
cana-1589	63	1	this	this	DET
cana-1589	63	2	polynomial	polynomial	NOUN
cana-1589	63	3	is	be	AUX
cana-1589	63	4	obtained	obtain	VERB
cana-1589	63	5	by	by	ADP
cana-1589	63	6	reducing	reduce	VERB
cana-1589	63	7	the	the	DET
cana-1589	63	8	coefficients	coefficient	NOUN
cana-1589	63	9	of	of	ADP
cana-1589	63	10	f	f	PROPN
cana-1589	63	11	modulo	modulo	PROPN
cana-1589	63	12	q.	q.	PROPN
cana-1589	63	13	to	to	PART
cana-1589	63	14	construct	construct	VERB
cana-1589	63	15	the	the	DET
cana-1589	63	16	public	public	ADJ
cana-1589	63	17	key	key	ADJ
cana-1589	63	18	“	"	PUNCT
cana-1589	63	19	h	h	NOUN
cana-1589	63	20	”	"	PUNCT
cana-1589	63	21	is	be	AUX
cana-1589	63	22	the	the	DET
cana-1589	63	23	public	public	ADJ
cana-1589	63	24	key	key	NOUN
cana-1589	63	25	,	,	PUNCT
cana-1589	63	26	a	a	DET
cana-1589	63	27	polynomial	polynomial	NOUN
cana-1589	63	28	in	in	ADP
cana-1589	63	29	ℤ	ℤ	PROPN
cana-1589	64	1	[	[	X
cana-1589	64	2	𝑥	𝑥	X
cana-1589	64	3	]	]	X
cana-1589	64	4	(	(	PUNCT
cana-1589	64	5	𝑞	𝑞	PROPN
cana-1589	64	6	,	,	PUNCT
cana-1589	64	7	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	64	8	−	−	NUM
cana-1589	64	9	1).⁄	1).⁄	NUM
cana-1589	64	10	ℎ𝑘	ℎ𝑘	PROPN
cana-1589	64	11	=	=	SYM
cana-1589	64	12	∑	∑	PUNCT
cana-1589	64	13	𝑓𝑖𝑔𝑘−𝑖	𝑓𝑖𝑔𝑘−𝑖	PROPN
cana-1589	64	14	+	+	CCONJ
cana-1589	64	15	∑	∑	PROPN
cana-1589	64	16	𝑓𝑖𝑔𝑛+𝑘−𝑖	𝑓𝑖𝑔𝑛+𝑘−𝑖	NOUN
cana-1589	64	17	=	=	PUNCT
cana-1589	64	18	∑	∑	PUNCT
cana-1589	64	19	𝑓𝑖𝑔𝑖.	𝑓𝑖𝑔𝑖.	PROPN
cana-1589	64	20	𝑖+𝑗≡𝑘	𝑖+𝑗≡𝑘	NOUN
cana-1589	64	21	mod	mod	NOUN
cana-1589	64	22	𝑛	𝑛	DET
cana-1589	64	23	𝑛−1	𝑛−1	PROPN
cana-1589	64	24	𝑖=𝑘+1	𝑖=𝑘+1	NOUN
cana-1589	64	25	𝑘	𝑘	ADP
cana-1589	64	26	𝑖=0	𝑖=0	PUNCT
cana-1589	65	1	the	the	DET
cana-1589	65	2	variable	variable	ADJ
cana-1589	65	3	"	"	PUNCT
cana-1589	65	4	k	k	X
cana-1589	65	5	"	"	PUNCT
cana-1589	65	6	represents	represent	VERB
cana-1589	65	7	a	a	DET
cana-1589	65	8	security	security	NOUN
cana-1589	65	9	parameter	parameter	NOUN
cana-1589	65	10	that	that	PRON
cana-1589	65	11	determines	determine	VERB
cana-1589	65	12	the	the	DET
cana-1589	65	13	level	level	NOUN
cana-1589	65	14	of	of	ADP
cana-1589	65	15	protection	protection	NOUN
cana-1589	65	16	against	against	ADP
cana-1589	65	17	specific	specific	ADJ
cana-1589	65	18	types	type	NOUN
cana-1589	65	19	of	of	ADP
cana-1589	65	20	attacks	attack	NOUN
cana-1589	65	21	,	,	PUNCT
cana-1589	65	22	such	such	ADJ
cana-1589	65	23	as	as	ADP
cana-1589	65	24	plaintext	plaintext	NOUN
cana-1589	65	25	awareness	awareness	NOUN
cana-1589	65	26	.	.	PUNCT
cana-1589	66	1	the	the	DET
cana-1589	66	2	public	public	ADJ
cana-1589	66	3	key	key	NOUN
cana-1589	66	4	(	(	PUNCT
cana-1589	66	5	h	h	NOUN
cana-1589	66	6	)	)	PUNCT
cana-1589	66	7	is	be	AUX
cana-1589	66	8	computed	compute	VERB
cana-1589	66	9	by	by	ADP
cana-1589	66	10	performing	perform	VERB
cana-1589	66	11	a	a	DET
cana-1589	66	12	cyclic	cyclic	ADJ
cana-1589	66	13	convolution	convolution	NOUN
cana-1589	66	14	between	between	ADP
cana-1589	66	15	f	f	PROPN
cana-1589	66	16	and	and	CCONJ
cana-1589	66	17	g.	g.	PROPN
cana-1589	66	18	the	the	DET
cana-1589	66	19	output	output	NOUN
cana-1589	66	20	is	be	AUX
cana-1589	66	21	in	in	ADP
cana-1589	66	22	the	the	DET
cana-1589	66	23	r.	r.	NOUN
cana-1589	66	24	to	to	PART
cana-1589	66	25	minimize	minimize	VERB
cana-1589	66	26	the	the	DET
cana-1589	66	27	coefficient	coefficient	NOUN
cana-1589	66	28	,	,	PUNCT
cana-1589	66	29	it	it	PRON
cana-1589	66	30	is	be	AUX
cana-1589	66	31	necessary	necessary	ADJ
cana-1589	66	32	to	to	PART
cana-1589	66	33	calculate	calculate	VERB
cana-1589	66	34	the	the	DET
cana-1589	66	35	multiplication	multiplication	NOUN
cana-1589	66	36	modulo	modulo	NOUN
cana-1589	66	37	q.	q.	NOUN
cana-1589	66	38	this	this	PRON
cana-1589	66	39	will	will	AUX
cana-1589	66	40	ensure	ensure	VERB
cana-1589	66	41	that	that	SCONJ
cana-1589	66	42	the	the	DET
cana-1589	66	43	result	result	NOUN
cana-1589	66	44	is	be	AUX
cana-1589	66	45	of	of	ADP
cana-1589	66	46	the	the	DET
cana-1589	66	47	form	form	NOUN
cana-1589	66	48	ℤ	ℤ	PROPN
cana-1589	67	1	[	[	NOUN
cana-1589	67	2	x	x	X
cana-1589	67	3	]	]	X
cana-1589	67	4	(	(	PUNCT
cana-1589	67	5	𝑞	𝑞	PROPN
cana-1589	67	6	,	,	PUNCT
cana-1589	67	7	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	67	8	−	−	PROPN
cana-1589	67	9	1).⁄	1).⁄	PROPN
cana-1589	68	1	the	the	DET
cana-1589	68	2	computation	computation	NOUN
cana-1589	68	3	of	of	ADP
cana-1589	68	4	the	the	DET
cana-1589	68	5	product	product	NOUN
cana-1589	68	6	f	f	PROPN
cana-1589	68	7	*	*	PUNCT
cana-1589	68	8	g	g	PROPN
cana-1589	68	9	necessitates	necessitate	VERB
cana-1589	68	10	n^2	n^2	PROPN
cana-1589	68	11	multiplications	multiplications	PROPN
cana-1589	68	12	.	.	PUNCT
cana-1589	69	1	in	in	ADP
cana-1589	69	2	ntru	ntru	PROPN
cana-1589	69	3	,	,	PUNCT
cana-1589	69	4	either	either	CCONJ
cana-1589	69	5	f	f	PROPN
cana-1589	69	6	or	or	CCONJ
cana-1589	69	7	g	g	PROPN
cana-1589	69	8	has	have	VERB
cana-1589	69	9	coefficients	coefficient	NOUN
cana-1589	69	10	that	that	PRON
cana-1589	69	11	are	be	AUX
cana-1589	69	12	predominantly	predominantly	ADV
cana-1589	69	13	0	0	NUM
cana-1589	69	14	's	's	PART
cana-1589	69	15	and	and	CCONJ
cana-1589	69	16	±1	±1	NOUN
cana-1589	69	17	's	's	PART
cana-1589	69	18	,	,	PUNCT
cana-1589	69	19	allowing	allow	VERB
cana-1589	69	20	for	for	ADP
cana-1589	69	21	a	a	DET
cana-1589	69	22	very	very	ADV
cana-1589	69	23	efficient	efficient	ADJ
cana-1589	69	24	computation	computation	NOUN
cana-1589	69	25	of	of	ADP
cana-1589	69	26	f	f	PROPN
cana-1589	69	27	*	*	PUNCT
cana-1589	69	28	g.	g.	PROPN
cana-1589	69	29	in	in	ADP
cana-1589	69	30	addition	addition	NOUN
cana-1589	69	31	,	,	PUNCT
cana-1589	69	32	when	when	SCONJ
cana-1589	69	33	n	n	X
cana-1589	69	34	is	be	AUX
cana-1589	69	35	a	a	DET
cana-1589	69	36	large	large	ADJ
cana-1589	69	37	amount	amount	NOUN
cana-1589	69	38	,	,	PUNCT
cana-1589	69	39	one	one	PRON
cana-1589	69	40	can	can	AUX
cana-1589	69	41	select	select	VERB
cana-1589	69	42	n	n	PART
cana-1589	69	43	to	to	PART
cana-1589	69	44	have	have	VERB
cana-1589	69	45	a	a	DET
cana-1589	69	46	high	high	ADJ
cana-1589	69	47	degree	degree	NOUN
cana-1589	69	48	of	of	ADP
cana-1589	69	49	divisibility	divisibility	NOUN
cana-1589	69	50	by	by	ADP
cana-1589	69	51	2	2	NUM
cana-1589	69	52	.	.	PUNCT
cana-1589	70	1	in	in	ADP
cana-1589	70	2	this	this	DET
cana-1589	70	3	scenario	scenario	NOUN
cana-1589	70	4	,	,	PUNCT
cana-1589	70	5	the	the	DET
cana-1589	70	6	convolution	convolution	NOUN
cana-1589	70	7	product	product	NOUN
cana-1589	70	8	can	can	AUX
cana-1589	70	9	be	be	AUX
cana-1589	70	10	calculated	calculate	VERB
cana-1589	70	11	using	use	VERB
cana-1589	70	12	fast	fast	ADJ
cana-1589	70	13	fourier	fourier	NOUN
cana-1589	70	14	transforms	transform	NOUN
cana-1589	70	15	,	,	PUNCT
cana-1589	70	16	requiring	require	VERB
cana-1589	70	17	o	o	NOUN
cana-1589	70	18	(	(	PUNCT
cana-1589	70	19	n	n	CCONJ
cana-1589	70	20	log	log	NOUN
cana-1589	70	21	n	n	CCONJ
cana-1589	70	22	)	)	PUNCT
cana-1589	70	23	operations	operation	NOUN
cana-1589	70	24	.	.	PUNCT
cana-1589	71	1	operations	operation	NOUN
cana-1589	71	2	involving	involve	VERB
cana-1589	71	3	generating	generating	NOUN
cana-1589	71	4	functions	function	NOUN
cana-1589	71	5	(	(	PUNCT
cana-1589	71	6	g	g	NOUN
cana-1589	71	7	)	)	PUNCT
cana-1589	71	8	and	and	CCONJ
cana-1589	71	9	hashing	hashing	NOUN
cana-1589	71	10	functions	function	NOUN
cana-1589	71	11	(	(	PUNCT
cana-1589	71	12	h	h	NOUN
cana-1589	71	13	)	)	PUNCT
cana-1589	71	14	must	must	AUX
cana-1589	71	15	be	be	AUX
cana-1589	71	16	defined	define	VERB
cana-1589	71	17	on	on	ADP
cana-1589	71	18	rings	ring	NOUN
cana-1589	71	19	of	of	ADP
cana-1589	71	20	polynomials	polynomial	NOUN
cana-1589	71	21	.	.	PUNCT
cana-1589	72	1	the	the	DET
cana-1589	72	2	g	g	PROPN
cana-1589	72	3	and	and	CCONJ
cana-1589	72	4	h	h	NOUN
cana-1589	72	5	elements	element	NOUN
cana-1589	72	6	are	be	AUX
cana-1589	72	7	utilized	utilize	VERB
cana-1589	72	8	in	in	ADP
cana-1589	72	9	the	the	DET
cana-1589	72	10	construction	construction	NOUN
cana-1589	72	11	of	of	ADP
cana-1589	72	12	a	a	DET
cana-1589	72	13	digital	digital	ADJ
cana-1589	72	14	envelope	envelope	NOUN
cana-1589	72	15	within	within	ADP
cana-1589	72	16	the	the	DET
cana-1589	72	17	ntru	ntru	ADJ
cana-1589	72	18	protocol	protocol	NOUN
cana-1589	72	19	.	.	PUNCT
cana-1589	73	1	communications	communication	NOUN
cana-1589	73	2	on	on	ADP
cana-1589	73	3	applied	apply	VERB
cana-1589	73	4	nonlinear	nonlinear	ADJ
cana-1589	73	5	analysis	analysis	NOUN
cana-1589	73	6	issn	issn	NOUN
cana-1589	73	7	:	:	PUNCT
cana-1589	73	8	1074	1074	NUM
cana-1589	73	9	-	-	PUNCT
cana-1589	73	10	133x	133x	NUM
cana-1589	73	11	vol	vol	NOUN
cana-1589	73	12	31	31	NUM
cana-1589	73	13	no	no	NOUN
cana-1589	73	14	.	.	PUNCT
cana-1589	74	1	7s	7	NOUN
cana-1589	74	2	(	(	PUNCT
cana-1589	74	3	2024	2024	NUM
cana-1589	74	4	)	)	PUNCT
cana-1589	74	5	699	699	NUM
cana-1589	74	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	74	7	𝑝𝑝(n	𝑝𝑝(n	X
cana-1589	74	8	)	)	PUNCT
cana-1589	74	9	=	=	PRON
cana-1589	74	10	{	{	PUNCT
cana-1589	74	11	polynomials	polynomial	NOUN
cana-1589	74	12	with	with	ADP
cana-1589	74	13	coefficients	coefficient	NOUN
cana-1589	74	14	modulo	modulo	PROPN
cana-1589	74	15	p	p	NOUN
cana-1589	74	16	and	and	CCONJ
cana-1589	74	17	degree	degree	VERB
cana-1589	74	18	no	no	ADV
cana-1589	74	19	greater	great	ADJ
cana-1589	74	20	than	than	ADP
cana-1589	74	21	n−1	n−1	PROPN
cana-1589	74	22	}	}	PUNCT
cana-1589	74	23	,	,	PUNCT
cana-1589	74	24	and	and	CCONJ
cana-1589	74	25	[	[	X
cana-1589	74	26	𝑔]𝑝=	𝑔]𝑝=	NOUN
cana-1589	74	27	{	{	PUNCT
cana-1589	74	28	𝑔	𝑔	NOUN
cana-1589	74	29	with	with	ADP
cana-1589	74	30	its	its	PRON
cana-1589	74	31	cofficients	cofficient	NOUN
cana-1589	74	32	reduced	reduce	VERB
cana-1589	74	33	modulo	modulo	PROPN
cana-1589	74	34	𝑝	𝑝	NOUN
cana-1589	74	35	to	to	ADP
cana-1589	74	36	the	the	DET
cana-1589	74	37	range	range	NOUN
cana-1589	74	38	(	(	PUNCT
cana-1589	74	39	−	−	PROPN
cana-1589	74	40	𝑝	𝑝	PROPN
cana-1589	74	41	2	2	NUM
cana-1589	74	42	,	,	PUNCT
cana-1589	74	43	𝑝	𝑝	NOUN
cana-1589	74	44	2).⁄⁄	2).⁄⁄	NUM
cana-1589	74	45	g	g	NOUN
cana-1589	74	46	function	function	NOUN
cana-1589	74	47	and	and	CCONJ
cana-1589	74	48	a	a	DET
cana-1589	74	49	h	h	NOUN
cana-1589	74	50	function	function	NOUN
cana-1589	74	51	are	be	AUX
cana-1589	74	52	exactly	exactly	ADV
cana-1589	74	53	defining	define	VERB
cana-1589	74	54	as	as	ADP
cana-1589	74	55	𝐺	𝐺	PROPN
cana-1589	74	56	=	=	PROPN
cana-1589	74	57	𝑝𝑝	𝑝𝑝	NOUN
cana-1589	74	58	(	(	PUNCT
cana-1589	74	59	𝑁	𝑁	PROPN
cana-1589	74	60	)	)	PUNCT
cana-1589	74	61	→	→	SYM
cana-1589	74	62	𝑝𝑝	𝑝𝑝	PROPN
cana-1589	74	63	(	(	PUNCT
cana-1589	74	64	𝑁	𝑁	PROPN
cana-1589	74	65	)	)	PUNCT
cana-1589	74	66	and	and	CCONJ
cana-1589	74	67	𝐻	𝐻	PROPN
cana-1589	74	68	=	=	NOUN
cana-1589	74	69	𝑝𝑝	𝑝𝑝	NOUN
cana-1589	74	70	(	(	PUNCT
cana-1589	74	71	𝑁	𝑁	PROPN
cana-1589	74	72	)	)	PUNCT
cana-1589	74	73	×	×	NOUN
cana-1589	74	74	𝑝𝑝	𝑝𝑝	NOUN
cana-1589	74	75	(	(	PUNCT
cana-1589	74	76	𝑁	𝑁	PROPN
cana-1589	74	77	)	)	PUNCT
cana-1589	74	78	→	→	SYM
cana-1589	74	79	𝑝𝑝	𝑝𝑝	PROPN
cana-1589	74	80	(	(	PUNCT
cana-1589	74	81	𝐾	𝐾	NOUN
cana-1589	74	82	)	)	PUNCT
cana-1589	74	83	they	they	PRON
cana-1589	74	84	should	should	AUX
cana-1589	74	85	be	be	AUX
cana-1589	74	86	computationally	computationally	ADV
cana-1589	74	87	efficient	efficient	ADJ
cana-1589	74	88	,	,	PUNCT
cana-1589	74	89	highly	highly	ADV
cana-1589	74	90	non	non	ADJ
cana-1589	74	91	-	-	ADJ
cana-1589	74	92	linear	linear	ADJ
cana-1589	74	93	,	,	PUNCT
cana-1589	74	94	and	and	CCONJ
cana-1589	74	95	difficult	difficult	ADJ
cana-1589	74	96	to	to	PART
cana-1589	74	97	predict	predict	VERB
cana-1589	74	98	.	.	PUNCT
cana-1589	75	1	the	the	DET
cana-1589	75	2	digital	digital	ADJ
cana-1589	75	3	envelope	envelope	NOUN
cana-1589	75	4	in	in	ADP
cana-1589	75	5	the	the	DET
cana-1589	75	6	ntru	ntru	ADJ
cana-1589	75	7	public	public	ADJ
cana-1589	75	8	key	key	ADJ
cana-1589	75	9	cryptosystem	cryptosystem	NOUN
cana-1589	75	10	relies	rely	VERB
cana-1589	75	11	on	on	ADP
cana-1589	75	12	the	the	DET
cana-1589	75	13	selection	selection	NOUN
cana-1589	75	14	of	of	ADP
cana-1589	75	15	functions	function	NOUN
cana-1589	75	16	g	g	NOUN
cana-1589	75	17	and	and	CCONJ
cana-1589	75	18	h	h	NOUN
cana-1589	75	19	,	,	PUNCT
cana-1589	75	20	as	as	ADV
cana-1589	75	21	well	well	ADV
cana-1589	75	22	as	as	ADP
cana-1589	75	23	an	an	DET
cana-1589	75	24	integer	integer	NOUN
cana-1589	75	25	k.	k.	PROPN
cana-1589	76	1	the	the	DET
cana-1589	76	2	likelihood	likelihood	NOUN
cana-1589	76	3	of	of	ADP
cana-1589	76	4	successfully	successfully	ADV
cana-1589	76	5	forging	forge	VERB
cana-1589	76	6	a	a	DET
cana-1589	76	7	valid	valid	ADJ
cana-1589	76	8	ciphertext	ciphertext	NOUN
cana-1589	76	9	is	be	AUX
cana-1589	76	10	𝑝−𝑘.	𝑝−𝑘.	NOUN
cana-1589	76	11	key	key	ADJ
cana-1589	76	12	creation	creation	NOUN
cana-1589	76	13	:	:	PUNCT
cana-1589	76	14	two	two	NUM
cana-1589	76	15	small	small	ADJ
cana-1589	76	16	polynomials	polynomial	NOUN
cana-1589	76	17	f	f	X
cana-1589	76	18	∈	∈	NOUN
cana-1589	77	1	ℒ𝑓	ℒ𝑓	NOUN
cana-1589	77	2	(	(	PUNCT
cana-1589	77	3	polynomials	polynomial	NOUN
cana-1589	77	4	in	in	ADP
cana-1589	77	5	ℤ	ℤ	PROPN
cana-1589	78	1	[	[	X
cana-1589	78	2	𝑥	𝑥	X
cana-1589	78	3	]	]	X
cana-1589	78	4	(	(	PUNCT
cana-1589	78	5	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	78	6	−	−	PROPN
cana-1589	78	7	1)⁄	1)⁄	NUM
cana-1589	78	8	whose	whose	DET
cana-1589	78	9	coefficients	coefficient	NOUN
cana-1589	78	10	satisfy	satisfy	VERB
cana-1589	78	11	𝑑𝑓	𝑑𝑓	PROPN
cana-1589	78	12	(	(	PUNCT
cana-1589	78	13	distribution	distribution	NOUN
cana-1589	78	14	of	of	ADP
cana-1589	78	15	the	the	DET
cana-1589	78	16	coefficients	coefficient	NOUN
cana-1589	78	17	of	of	ADP
cana-1589	78	18	the	the	DET
cana-1589	78	19	polynomial	polynomial	ADJ
cana-1589	78	20	f	f	NOUN
cana-1589	78	21	(	(	PUNCT
cana-1589	78	22	part	part	NOUN
cana-1589	78	23	of	of	ADP
cana-1589	78	24	the	the	DET
cana-1589	78	25	private	private	ADJ
cana-1589	78	26	key	key	NOUN
cana-1589	78	27	)	)	PUNCT
cana-1589	78	28	)	)	PUNCT
cana-1589	78	29	and	and	CCONJ
cana-1589	78	30	𝑔	𝑔	PROPN
cana-1589	78	31	(	(	PUNCT
cana-1589	78	32	part	part	NOUN
cana-1589	78	33	of	of	ADP
cana-1589	78	34	public	public	ADJ
cana-1589	78	35	key	key	NOUN
cana-1589	78	36	)	)	PUNCT
cana-1589	78	37	∈	∈	PROPN
cana-1589	78	38	ℒ𝑔	ℒ𝑔	PROPN
cana-1589	78	39	(	(	PUNCT
cana-1589	78	40	the	the	DET
cana-1589	78	41	set	set	NOUN
cana-1589	78	42	of	of	ADP
cana-1589	78	43	polynomials	polynomial	NOUN
cana-1589	78	44	in	in	ADP
cana-1589	78	45	ℤ	ℤ	PROPN
cana-1589	79	1	[	[	X
cana-1589	79	2	𝑥	𝑥	X
cana-1589	79	3	]	]	X
cana-1589	79	4	(	(	PUNCT
cana-1589	79	5	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	79	6	−	−	PROPN
cana-1589	79	7	1)⁄	1)⁄	NUM
cana-1589	79	8	whose	whose	DET
cana-1589	79	9	coefficients	coefficient	NOUN
cana-1589	79	10	satisfy	satisfy	VERB
cana-1589	79	11	𝑑𝑔	𝑑𝑔	VERB
cana-1589	79	12	(	(	PUNCT
cana-1589	79	13	distribution	distribution	NOUN
cana-1589	79	14	of	of	ADP
cana-1589	79	15	the	the	DET
cana-1589	79	16	coefficients	coefficient	NOUN
cana-1589	79	17	of	of	ADP
cana-1589	79	18	the	the	DET
cana-1589	79	19	polynomial	polynomial	ADJ
cana-1589	79	20	g	g	NOUN
cana-1589	79	21	)	)	PUNCT
cana-1589	79	22	)	)	PUNCT
cana-1589	79	23	are	be	AUX
cana-1589	79	24	randomly	randomly	ADV
cana-1589	79	25	generated	generate	VERB
cana-1589	79	26	to	to	PART
cana-1589	79	27	produce	produce	VERB
cana-1589	79	28	a	a	DET
cana-1589	79	29	pair	pair	NOUN
cana-1589	79	30	of	of	ADP
cana-1589	79	31	public	public	ADJ
cana-1589	79	32	and	and	CCONJ
cana-1589	79	33	private	private	ADJ
cana-1589	79	34	keys	key	NOUN
cana-1589	79	35	.	.	PUNCT
cana-1589	80	1	the	the	DET
cana-1589	80	2	polynomial	polynomial	ADJ
cana-1589	80	3	f	f	PROPN
cana-1589	80	4	must	must	AUX
cana-1589	80	5	fulfil	fulfil	VERB
cana-1589	80	6	the	the	DET
cana-1589	80	7	extra	extra	ADJ
cana-1589	80	8	condition	condition	NOUN
cana-1589	80	9	of	of	ADP
cana-1589	80	10	having	have	VERB
cana-1589	80	11	modular	modular	ADJ
cana-1589	80	12	inverses	inverse	NOUN
cana-1589	80	13	both	both	PRON
cana-1589	80	14	modulo	modulo	VERB
cana-1589	80	15	q	q	NOUN
cana-1589	80	16	and	and	CCONJ
cana-1589	80	17	modulo	modulo	PROPN
cana-1589	80	18	p.	p.	PROPN
cana-1589	80	19	fp	fp	X
cana-1589	80	20	represents	represent	VERB
cana-1589	80	21	a	a	DET
cana-1589	80	22	polynomial	polynomial	NOUN
cana-1589	80	23	in	in	ADP
cana-1589	80	24	the	the	DET
cana-1589	80	25	quotient	quotient	NOUN
cana-1589	80	26	ring	re	VERB
cana-1589	80	27	ℤ	ℤ	PROPN
cana-1589	81	1	[	[	X
cana-1589	81	2	𝑥	𝑥	X
cana-1589	81	3	]	]	X
cana-1589	81	4	(	(	PUNCT
cana-1589	81	5	𝑝	𝑝	NOUN
cana-1589	81	6	,	,	PUNCT
cana-1589	81	7	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	81	8	−	−	PROPN
cana-1589	81	9	1)⁄	1)⁄	NUM
cana-1589	81	10	,	,	PUNCT
cana-1589	81	11	which	which	PRON
cana-1589	81	12	is	be	AUX
cana-1589	81	13	a	a	DET
cana-1589	81	14	crucial	crucial	ADJ
cana-1589	81	15	component	component	NOUN
cana-1589	81	16	of	of	ADP
cana-1589	81	17	the	the	DET
cana-1589	81	18	private	private	ADJ
cana-1589	81	19	key	key	NOUN
cana-1589	81	20	.	.	PUNCT
cana-1589	82	1	this	this	DET
cana-1589	82	2	polynomial	polynomial	NOUN
cana-1589	82	3	is	be	AUX
cana-1589	82	4	derived	derive	VERB
cana-1589	82	5	by	by	ADP
cana-1589	82	6	decreasing	decrease	VERB
cana-1589	82	7	the	the	DET
cana-1589	82	8	coefficients	coefficient	NOUN
cana-1589	82	9	of	of	ADP
cana-1589	82	10	f	f	PROPN
cana-1589	82	11	modulo	modulo	PROPN
cana-1589	82	12	p.	p.	NOUN
cana-1589	82	13	for	for	ADP
cana-1589	82	14	appropriate	appropriate	ADJ
cana-1589	82	15	parameter	parameter	NOUN
cana-1589	82	16	selections	selection	NOUN
cana-1589	82	17	,	,	PUNCT
cana-1589	82	18	this	this	DET
cana-1589	82	19	statement	statement	NOUN
cana-1589	82	20	holds	hold	VERB
cana-1589	82	21	true	true	ADJ
cana-1589	82	22	for	for	ADP
cana-1589	82	23	the	the	DET
cana-1589	82	24	majority	majority	NOUN
cana-1589	82	25	of	of	ADP
cana-1589	82	26	f	f	PROPN
cana-1589	82	27	choices	choice	NOUN
cana-1589	82	28	,	,	PUNCT
cana-1589	82	29	and	and	CCONJ
cana-1589	82	30	the	the	DET
cana-1589	82	31	computation	computation	NOUN
cana-1589	82	32	of	of	ADP
cana-1589	82	33	these	these	DET
cana-1589	82	34	inverses	inverse	NOUN
cana-1589	82	35	can	can	AUX
cana-1589	82	36	be	be	AUX
cana-1589	82	37	easily	easily	ADV
cana-1589	82	38	performed	perform	VERB
cana-1589	82	39	by	by	ADP
cana-1589	82	40	modifying	modify	VERB
cana-1589	82	41	the	the	DET
cana-1589	82	42	euclidean	euclidean	ADJ
cana-1589	82	43	method	method	NOUN
cana-1589	82	44	.	.	PUNCT
cana-1589	83	1	the	the	DET
cana-1589	83	2	inverses	inverse	NOUN
cana-1589	83	3	of	of	ADP
cana-1589	83	4	𝑓𝑞	𝑓𝑞	DET
cana-1589	83	5	−1	−1	NOUN
cana-1589	83	6	and	and	CCONJ
cana-1589	83	7	𝑓𝑝	𝑓𝑝	NOUN
cana-1589	83	8	−1	−1	NOUN
cana-1589	83	9	are	be	AUX
cana-1589	83	10	denoted	denote	VERB
cana-1589	83	11	as	as	ADP
cana-1589	83	12	mentioned	mention	VERB
cana-1589	83	13	above	above	ADP
cana-1589	83	14	𝑓𝑞	𝑓𝑞	ADP
cana-1589	83	15	−1	−1	NOUN
cana-1589	83	16	∗	∗	NOUN
cana-1589	83	17	𝑓	𝑓	PRON
cana-1589	83	18	≡	≡	PROPN
cana-1589	83	19	1	1	NUM
cana-1589	83	20	mod	mod	PROPN
cana-1589	83	21	q	q	NOUN
cana-1589	84	1	and	and	CCONJ
cana-1589	84	2	𝑓𝑝	𝑓𝑝	NOUN
cana-1589	84	3	−1	−1	NOUN
cana-1589	84	4	∗	∗	NOUN
cana-1589	85	1	𝑓	𝑓	PRON
cana-1589	85	2	≡	≡	PROPN
cana-1589	85	3	1	1	NUM
cana-1589	85	4	mod	mod	PROPN
cana-1589	86	1	p.	p.	PROPN
cana-1589	86	2	f	f	X
cana-1589	86	3	,	,	PUNCT
cana-1589	86	4	g	g	PROPN
cana-1589	86	5	,	,	PUNCT
cana-1589	86	6	𝑓𝑞	𝑓𝑞	PRON
cana-1589	86	7	−1	−1	NOUN
cana-1589	86	8	and	and	CCONJ
cana-1589	86	9	𝑓𝑝	𝑓𝑝	NOUN
cana-1589	86	10	−1are	−1are	ADV
cana-1589	86	11	kept	keep	VERB
cana-1589	86	12	secret	secret	ADJ
cana-1589	86	13	and	and	CCONJ
cana-1589	86	14	public	public	ADJ
cana-1589	86	15	key	key	NOUN
cana-1589	86	16	is	be	AUX
cana-1589	86	17	calculated	calculate	VERB
cana-1589	86	18	and	and	CCONJ
cana-1589	86	19	issued	issue	VERB
cana-1589	86	20	as	as	ADP
cana-1589	86	21	follow	follow	VERB
cana-1589	86	22	ℎ	ℎ	PRON
cana-1589	86	23	≡	≡	PROPN
cana-1589	86	24	𝑝𝑓𝑞	𝑝𝑓𝑞	VERB
cana-1589	86	25	−1	−1	NOUN
cana-1589	86	26	∗	∗	NOUN
cana-1589	86	27	𝑔	𝑔	PROPN
cana-1589	86	28	mod	mod	PROPN
cana-1589	86	29	𝑞.	𝑞.	PROPN
cana-1589	86	30	polynomial	polynomial	PROPN
cana-1589	86	31	of	of	ADP
cana-1589	86	32	f	f	PROPN
cana-1589	86	33	is	be	AUX
cana-1589	86	34	the	the	DET
cana-1589	86	35	private	private	ADJ
cana-1589	86	36	key	key	NOUN
cana-1589	86	37	and	and	CCONJ
cana-1589	86	38	polynomial	polynomial	ADJ
cana-1589	86	39	of	of	ADP
cana-1589	86	40	h	h	NOUN
cana-1589	86	41	is	be	AUX
cana-1589	86	42	the	the	DET
cana-1589	86	43	public	public	ADJ
cana-1589	86	44	key	key	ADJ
cana-1589	86	45	encryption	encryption	NOUN
cana-1589	86	46	:	:	PUNCT
cana-1589	86	47	ntru	ntru	PROPN
cana-1589	86	48	cryptosystem	cryptosystem	NOUN
cana-1589	86	49	chooses	choose	VERB
cana-1589	86	50	plaintext	plaintext	NOUN
cana-1589	86	51	m	m	PROPN
cana-1589	86	52	(	(	PUNCT
cana-1589	86	53	polynomial	polynomial	ADJ
cana-1589	86	54	in	in	ADP
cana-1589	86	55	ℤ	ℤ	PROPN
cana-1589	87	1	[	[	X
cana-1589	87	2	𝑥	𝑥	X
cana-1589	87	3	]	]	X
cana-1589	87	4	(	(	PUNCT
cana-1589	87	5	𝑝	𝑝	NOUN
cana-1589	87	6	,	,	PUNCT
cana-1589	87	7	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	87	8	−	−	PROPN
cana-1589	87	9	1))⁄	1))⁄	PROPN
cana-1589	87	10	.	.	PUNCT
cana-1589	88	1	from	from	ADP
cana-1589	88	2	the	the	DET
cana-1589	88	3	set	set	NOUN
cana-1589	88	4	𝑚	𝑚	X
cana-1589	88	5	∈	∈	PROPN
cana-1589	88	6	𝑝𝑝	𝑝𝑝	NOUN
cana-1589	88	7	(	(	PUNCT
cana-1589	88	8	𝑛	𝑛	PROPN
cana-1589	88	9	−	−	PROPN
cana-1589	88	10	𝑘	𝑘	NOUN
cana-1589	88	11	)	)	PUNCT
cana-1589	88	12	.	.	PUNCT
cana-1589	89	1	and	and	CCONJ
cana-1589	89	2	a	a	DET
cana-1589	89	3	polynomial	polynomial	NOUN
cana-1589	89	4	in	in	ADP
cana-1589	89	5	ℤ	ℤ	PROPN
cana-1589	89	6	[	[	X
cana-1589	89	7	𝑥	𝑥	X
cana-1589	89	8	]	]	X
cana-1589	89	9	(	(	PUNCT
cana-1589	89	10	𝑞	𝑞	PROPN
cana-1589	89	11	,	,	PUNCT
cana-1589	89	12	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	89	13	−	−	PROPN
cana-1589	89	14	1)⁄	1)⁄	NUM
cana-1589	89	15	(	(	PUNCT
cana-1589	89	16	used	use	VERB
cana-1589	89	17	with	with	ADP
cana-1589	89	18	h	h	NOUN
cana-1589	89	19	to	to	PART
cana-1589	89	20	encode	encode	VERB
cana-1589	89	21	a	a	DET
cana-1589	89	22	message	message	NOUN
cana-1589	89	23	)	)	PUNCT
cana-1589	89	24	which	which	PRON
cana-1589	89	25	is	be	AUX
cana-1589	89	26	random	random	ADJ
cana-1589	89	27	polynomial	polynomial	ADJ
cana-1589	89	28	𝑟	𝑟	NOUN
cana-1589	89	29	∈	∈	PROPN
cana-1589	89	30	ℒ𝑟	ℒ𝑟	PROPN
cana-1589	89	31	(	(	PUNCT
cana-1589	89	32	polynomials	polynomial	NOUN
cana-1589	89	33	in	in	ADP
cana-1589	89	34	ℤ	ℤ	PROPN
cana-1589	89	35	[	[	X
cana-1589	89	36	𝑥	𝑥	X
cana-1589	89	37	]	]	X
cana-1589	89	38	(	(	PUNCT
cana-1589	89	39	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	89	40	−	−	PROPN
cana-1589	89	41	1)⁄	1)⁄	NUM
cana-1589	89	42	whose	whose	DET
cana-1589	89	43	coefficients	coefficient	NOUN
cana-1589	89	44	satisfy	satisfy	VERB
cana-1589	89	45	𝑑𝑟	𝑑𝑟	ADP
cana-1589	89	46	(	(	PUNCT
cana-1589	89	47	number	number	NOUN
cana-1589	89	48	of	of	ADP
cana-1589	89	49	1s	1s	NUM
cana-1589	89	50	and	and	CCONJ
cana-1589	89	51	-1s	-1s	PROPN
cana-1589	89	52	used	use	VERB
cana-1589	89	53	in	in	ADP
cana-1589	89	54	a	a	DET
cana-1589	89	55	certain	certain	ADJ
cana-1589	89	56	random	random	ADJ
cana-1589	89	57	polynomial	polynomial	ADJ
cana-1589	89	58	r	r	NOUN
cana-1589	89	59	)	)	PUNCT
cana-1589	89	60	)	)	PUNCT
cana-1589	90	1	cipher	cipher	ADJ
cana-1589	90	2	text	text	NOUN
cana-1589	90	3	(	(	PUNCT
cana-1589	90	4	the	the	DET
cana-1589	90	5	encrypted	encrypt	VERB
cana-1589	90	6	message	message	NOUN
cana-1589	90	7	,	,	PUNCT
cana-1589	90	8	a	a	DET
cana-1589	90	9	polynomial	polynomial	NOUN
cana-1589	90	10	in	in	ADP
cana-1589	90	11	ℤ	ℤ	PROPN
cana-1589	90	12	[	[	X
cana-1589	90	13	𝑥	𝑥	X
cana-1589	90	14	]	]	X
cana-1589	90	15	(	(	PUNCT
cana-1589	90	16	𝑞	𝑞	PROPN
cana-1589	90	17	,	,	PUNCT
cana-1589	90	18	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	90	19	−	−	PROPN
cana-1589	90	20	1)⁄	1)⁄	NUM
cana-1589	90	21	)	)	PUNCT
cana-1589	90	22	is	be	AUX
cana-1589	90	23	computed	compute	VERB
cana-1589	90	24	as	as	ADP
cana-1589	90	25	follow	follow	VERB
cana-1589	90	26	𝑒	𝑒	PROPN
cana-1589	90	27	≡	≡	PROPN
cana-1589	90	28	𝑟	𝑟	NOUN
cana-1589	90	29	∗	∗	NOUN
cana-1589	90	30	ℎ	ℎ	PROPN
cana-1589	90	31	+	+	X
cana-1589	91	1	[	[	X
cana-1589	91	2	𝑚	𝑚	X
cana-1589	91	3	+	+	X
cana-1589	91	4	𝐻	𝐻	PROPN
cana-1589	91	5	(	(	PUNCT
cana-1589	91	6	𝑚	𝑚	PROPN
cana-1589	91	7	,	,	PUNCT
cana-1589	91	8	[	[	X
cana-1589	91	9	𝑟	𝑟	NOUN
cana-1589	91	10	∗	∗	NOUN
cana-1589	91	11	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	91	12	+	+	X
cana-1589	91	13	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	91	14	∗	∗	NOUN
cana-1589	91	15	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	91	16	)	)	PUNCT
cana-1589	91	17	]	]	PUNCT
cana-1589	91	18	𝑝	𝑝	X
cana-1589	91	19	(	(	PUNCT
cana-1589	91	20	mod	mod	PROPN
cana-1589	91	21	𝑞	𝑞	PROPN
cana-1589	91	22	)	)	PUNCT
cana-1589	91	23	.	.	PUNCT
cana-1589	92	1	decryption	decryption	NOUN
cana-1589	92	2	:	:	PUNCT
cana-1589	92	3	the	the	DET
cana-1589	92	4	decryption	decryption	NOUN
cana-1589	92	5	process	process	NOUN
cana-1589	92	6	begins	begin	VERB
cana-1589	92	7	with	with	ADP
cana-1589	92	8	multiplying	multiplying	NOUN
cana-1589	92	9	(	(	PUNCT
cana-1589	92	10	convolving	convolve	VERB
cana-1589	92	11	)	)	PUNCT
cana-1589	92	12	the	the	DET
cana-1589	92	13	received	receive	VERB
cana-1589	92	14	polynomial	polynomial	ADJ
cana-1589	92	15	e	e	NOUN
cana-1589	92	16	by	by	ADP
cana-1589	92	17	the	the	DET
cana-1589	92	18	private	private	ADJ
cana-1589	92	19	key	key	NOUN
cana-1589	92	20	f	f	PROPN
cana-1589	92	21	communications	communication	NOUN
cana-1589	92	22	on	on	ADP
cana-1589	92	23	applied	apply	VERB
cana-1589	92	24	nonlinear	nonlinear	ADJ
cana-1589	92	25	analysis	analysis	NOUN
cana-1589	92	26	issn	issn	NOUN
cana-1589	92	27	:	:	PUNCT
cana-1589	92	28	1074	1074	NUM
cana-1589	92	29	-	-	PUNCT
cana-1589	92	30	133x	133x	NUM
cana-1589	92	31	vol	vol	NOUN
cana-1589	92	32	31	31	NUM
cana-1589	92	33	no	no	NOUN
cana-1589	92	34	.	.	PUNCT
cana-1589	93	1	7s	7	NOUN
cana-1589	93	2	(	(	PUNCT
cana-1589	93	3	2024	2024	NUM
cana-1589	93	4	)	)	PUNCT
cana-1589	93	5	700	700	NUM
cana-1589	93	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	93	7	𝑎	𝑎	PRON
cana-1589	93	8	≡	≡	PROPN
cana-1589	93	9	𝑓	𝑓	DET
cana-1589	93	10	∗	∗	NOUN
cana-1589	93	11	𝑒	𝑒	PROPN
cana-1589	93	12	mod	mod	PROPN
cana-1589	93	13	𝑞	𝑞	PROPN
cana-1589	93	14	,	,	PUNCT
cana-1589	93	15	choose	choose	VERB
cana-1589	93	16	the	the	DET
cana-1589	93	17	coefficients	coefficient	NOUN
cana-1589	93	18	of	of	ADP
cana-1589	93	19	a	a	PRON
cana-1589	93	20	in	in	ADP
cana-1589	93	21	the	the	DET
cana-1589	93	22	interval	interval	NOUN
cana-1589	93	23	from	from	ADP
cana-1589	93	24	−𝑞	−𝑞	ADP
cana-1589	93	25	2⁄	2⁄	NUM
cana-1589	93	26	to	to	ADP
cana-1589	93	27	𝑞	𝑞	PROPN
cana-1589	93	28	2.⁄	2.⁄	NUM
cana-1589	93	29	now	now	ADV
cana-1589	93	30	treating	treat	VERB
cana-1589	93	31	a	a	PRON
cana-1589	93	32	as	as	ADP
cana-1589	93	33	a	a	DET
cana-1589	93	34	polynomial	polynomial	NOUN
cana-1589	93	35	with	with	ADP
cana-1589	93	36	integer	integer	NOUN
cana-1589	93	37	coefficients	coefficient	NOUN
cana-1589	93	38	,	,	PUNCT
cana-1589	93	39	computes	compute	VERB
cana-1589	93	40	the	the	DET
cana-1589	93	41	temporary	temporary	ADJ
cana-1589	93	42	polynomial	polynomial	ADJ
cana-1589	93	43	𝑡	𝑡	PROPN
cana-1589	93	44	∈	∈	PROPN
cana-1589	93	45	ℤ[𝑥]/(𝑝	ℤ[𝑥]/(𝑝	NOUN
cana-1589	93	46	,	,	PUNCT
cana-1589	93	47	𝑥𝑛	𝑥𝑛	PROPN
cana-1589	93	48	−	−	PROPN
cana-1589	93	49	1	1	NUM
cana-1589	93	50	)	)	PUNCT
cana-1589	93	51	by	by	ADP
cana-1589	93	52	𝑡	𝑡	X
cana-1589	93	53	=	=	VERB
cana-1589	93	54	𝑓𝑝	𝑓𝑝	NOUN
cana-1589	93	55	−1	−1	NOUN
cana-1589	93	56	∗	∗	NOUN
cana-1589	93	57	𝑎	𝑎	X
cana-1589	93	58	(	(	PUNCT
cana-1589	93	59	mod	mod	PROPN
cana-1589	93	60	𝑝	𝑝	PROPN
cana-1589	93	61	)	)	PUNCT
cana-1589	93	62	,	,	PUNCT
cana-1589	93	63	next	next	ADV
cana-1589	93	64	,	,	PUNCT
cana-1589	93	65	it	it	PRON
cana-1589	93	66	calculates	calculate	VERB
cana-1589	93	67	the	the	DET
cana-1589	93	68	two	two	NUM
cana-1589	93	69	intermediate	intermediate	ADJ
cana-1589	93	70	quantities	quantity	NOUN
cana-1589	93	71	𝑏	𝑏	PROPN
cana-1589	93	72	≡	≡	PROPN
cana-1589	93	73	𝑒	𝑒	ADP
cana-1589	93	74	−	−	PROPN
cana-1589	93	75	𝑡	𝑡	PROPN
cana-1589	93	76	(	(	PUNCT
cana-1589	93	77	mod	mod	PROPN
cana-1589	93	78	𝑝	𝑝	PROPN
cana-1589	93	79	)	)	PUNCT
cana-1589	93	80	and	and	CCONJ
cana-1589	93	81	≡	≡	PROPN
cana-1589	93	82	𝑡	𝑡	PROPN
cana-1589	93	83	−	−	NOUN
cana-1589	93	84	𝐺(𝑏	𝐺(𝑏	NUM
cana-1589	93	85	)	)	PUNCT
cana-1589	93	86	(	(	PUNCT
cana-1589	93	87	mod	mod	PROPN
cana-1589	93	88	𝑝	𝑝	PROPN
cana-1589	93	89	)	)	PUNCT
cana-1589	93	90	,	,	PUNCT
cana-1589	93	91	and	and	CCONJ
cana-1589	93	92	then	then	ADV
cana-1589	93	93	writes	write	VERB
cana-1589	93	94	c	c	PROPN
cana-1589	93	95	in	in	ADP
cana-1589	93	96	the	the	DET
cana-1589	93	97	form	form	NOUN
cana-1589	93	98	𝑐	𝑐	NOUN
cana-1589	93	99	=	=	SYM
cana-1589	93	100	𝑐′	𝑐′	X
cana-1589	94	1	+	+	CCONJ
cana-1589	94	2	𝑐"𝑥𝑛−𝑘	𝑐"𝑥𝑛−𝑘	NOUN
cana-1589	94	3	with	with	ADP
cana-1589	94	4	deg	deg	PROPN
cana-1589	94	5	(	(	PUNCT
cana-1589	94	6	𝑐′	𝑐′	NUM
cana-1589	94	7	)	)	PUNCT
cana-1589	94	8	<	<	X
cana-1589	94	9	𝑛	𝑛	DET
cana-1589	94	10	−	−	PROPN
cana-1589	94	11	𝑘	𝑘	PROPN
cana-1589	94	12	and	and	CCONJ
cana-1589	94	13	deg(c	deg(c	PROPN
cana-1589	94	14	"	"	PUNCT
cana-1589	94	15	)	)	PUNCT
cana-1589	94	16	<	<	X
cana-1589	94	17	𝑘.	𝑘.	PROPN
cana-1589	94	18	finally	finally	ADV
cana-1589	94	19	,	,	PUNCT
cana-1589	94	20	compares	compare	VERB
cana-1589	94	21	the	the	DET
cana-1589	94	22	quantities	quantity	NOUN
cana-1589	94	23	𝑐	𝑐	NOUN
cana-1589	94	24	"	"	PUNCT
cana-1589	94	25	and	and	CCONJ
cana-1589	94	26	𝐻(𝑐′	𝐻(𝑐′	PROPN
cana-1589	94	27	,	,	PUNCT
cana-1589	94	28	𝑏	𝑏	NOUN
cana-1589	94	29	)	)	PUNCT
cana-1589	94	30	.	.	PUNCT
cana-1589	95	1	if	if	SCONJ
cana-1589	95	2	the	the	DET
cana-1589	95	3	decrypted	decrypt	VERB
cana-1589	95	4	message	message	NOUN
cana-1589	95	5	matches	match	VERB
cana-1589	95	6	the	the	DET
cana-1589	95	7	original	original	NOUN
cana-1589	95	8	,	,	PUNCT
cana-1589	95	9	it	it	PRON
cana-1589	95	10	is	be	AUX
cana-1589	95	11	accepted	accept	VERB
cana-1589	95	12	𝑐′	𝑐′	ADV
cana-1589	95	13	as	as	ADP
cana-1589	95	14	valid	valid	ADJ
cana-1589	95	15	.	.	PUNCT
cana-1589	96	1	otherwise	otherwise	ADV
cana-1589	96	2	,	,	PUNCT
cana-1589	96	3	the	the	DET
cana-1589	96	4	message	message	NOUN
cana-1589	96	5	is	be	AUX
cana-1589	96	6	rejected	reject	VERB
cana-1589	96	7	as	as	ADP
cana-1589	96	8	invalid	invalid	ADJ
cana-1589	96	9	.	.	PUNCT
cana-1589	97	1	ntru	ntru	ADJ
cana-1589	97	2	decryption	decryption	NOUN
cana-1589	97	3	method	method	NOUN
cana-1589	97	4	is	be	AUX
cana-1589	97	5	given	give	VERB
cana-1589	97	6	below	below	ADV
cana-1589	97	7	.	.	PUNCT
cana-1589	98	1	𝑎	𝑎	PRON
cana-1589	98	2	≡	≡	PROPN
cana-1589	98	3	𝑓	𝑓	DET
cana-1589	98	4	∗	∗	NOUN
cana-1589	98	5	𝑒	𝑒	PROPN
cana-1589	98	6	≡	≡	PROPN
cana-1589	98	7	𝑓	𝑓	DET
cana-1589	98	8	∗	∗	NOUN
cana-1589	98	9	𝑟	𝑟	PRON
cana-1589	98	10	∗	∗	NOUN
cana-1589	98	11	ℎ	ℎ	PRON
cana-1589	98	12	+	+	CCONJ
cana-1589	98	13	𝑓	𝑓	DET
cana-1589	98	14	∗	∗	NOUN
cana-1589	98	15	[	[	X
cana-1589	98	16	𝑚	𝑚	X
cana-1589	98	17	+	+	NUM
cana-1589	98	18	𝐻(𝑚	𝐻(𝑚	NOUN
cana-1589	98	19	,	,	PUNCT
cana-1589	98	20	[	[	X
cana-1589	98	21	𝑟	𝑟	NOUN
cana-1589	98	22	∗	∗	NOUN
cana-1589	98	23	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	98	24	+	+	X
cana-1589	98	25	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	98	26	∗	∗	NOUN
cana-1589	98	27	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	98	28	)	)	PUNCT
cana-1589	98	29	]	]	PUNCT
cana-1589	99	1	𝑝	𝑝	X
cana-1589	99	2	(	(	PUNCT
cana-1589	99	3	mod	mod	PROPN
cana-1589	99	4	𝑞	𝑞	PROPN
cana-1589	99	5	)	)	PUNCT
cana-1589	99	6	≡	≡	PROPN
cana-1589	99	7	𝑓	𝑓	DET
cana-1589	99	8	∗	∗	X
cana-1589	99	9	𝑝𝑟	𝑝𝑟	PROPN
cana-1589	99	10	∗	∗	NOUN
cana-1589	99	11	𝑓𝑞	𝑓𝑞	ADP
cana-1589	99	12	−1	−1	NOUN
cana-1589	99	13	∗	∗	NOUN
cana-1589	99	14	𝑔	𝑔	PROPN
cana-1589	100	1	+	+	X
cana-1589	101	1	𝑓	𝑓	DET
cana-1589	101	2	∗	∗	NOUN
cana-1589	101	3	[	[	X
cana-1589	101	4	𝑚	𝑚	X
cana-1589	101	5	+	+	NUM
cana-1589	101	6	𝐻(𝑚	𝐻(𝑚	NOUN
cana-1589	101	7	,	,	PUNCT
cana-1589	101	8	[	[	X
cana-1589	101	9	𝑟	𝑟	NOUN
cana-1589	101	10	∗	∗	NOUN
cana-1589	101	11	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	101	12	+	+	X
cana-1589	101	13	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	101	14	∗	∗	NOUN
cana-1589	101	15	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	101	16	)	)	PUNCT
cana-1589	101	17	]	]	PUNCT
cana-1589	102	1	𝑝	𝑝	X
cana-1589	102	2	mod	mod	PROPN
cana-1589	102	3	𝑞	𝑞	PROPN
cana-1589	102	4	,	,	PUNCT
cana-1589	102	5	≡	≡	PROPN
cana-1589	102	6	𝑝𝑟	𝑝𝑟	PROPN
cana-1589	102	7	∗	∗	PROPN
cana-1589	102	8	𝑔	𝑔	PROPN
cana-1589	102	9	+	+	X
cana-1589	102	10	𝑓	𝑓	DET
cana-1589	102	11	∗	∗	NOUN
cana-1589	102	12	[	[	X
cana-1589	102	13	𝑚	𝑚	X
cana-1589	102	14	+	+	NUM
cana-1589	102	15	𝐻(𝑚	𝐻(𝑚	NOUN
cana-1589	102	16	,	,	PUNCT
cana-1589	102	17	[	[	X
cana-1589	102	18	𝑟	𝑟	NOUN
cana-1589	102	19	∗	∗	NOUN
cana-1589	102	20	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	102	21	+	+	X
cana-1589	102	22	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	102	23	∗	∗	NOUN
cana-1589	102	24	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	102	25	)	)	PUNCT
cana-1589	102	26	]	]	PUNCT
cana-1589	103	1	𝑝	𝑝	X
cana-1589	103	2	mod	mod	PROPN
cana-1589	103	3	𝑞	𝑞	PROPN
cana-1589	103	4	,	,	PUNCT
cana-1589	103	5	by	by	ADP
cana-1589	103	6	selecting	select	VERB
cana-1589	103	7	a	a	DET
cana-1589	103	8	suitable	suitable	ADJ
cana-1589	103	9	parameter	parameter	NOUN
cana-1589	103	10	,	,	PUNCT
cana-1589	103	11	it	it	PRON
cana-1589	103	12	is	be	AUX
cana-1589	103	13	ensured	ensure	VERB
cana-1589	103	14	that	that	SCONJ
cana-1589	103	15	all	all	DET
cana-1589	103	16	coefficients	coefficient	NOUN
cana-1589	103	17	of	of	ADP
cana-1589	103	18	the	the	DET
cana-1589	103	19	parameter	parameter	NOUN
cana-1589	103	20	lie	lie	NOUN
cana-1589	103	21	between	between	ADP
cana-1589	103	22	the	the	DET
cana-1589	103	23	range	range	NOUN
cana-1589	103	24	of	of	ADP
cana-1589	103	25	(	(	PUNCT
cana-1589	103	26	-q)⁄2	-q)⁄2	PROPN
cana-1589	103	27	and	and	CCONJ
cana-1589	103	28	(	(	PUNCT
cana-1589	103	29	q)⁄2	q)⁄2	PROPN
cana-1589	103	30	.	.	PUNCT
cana-1589	104	1	this	this	PRON
cana-1589	104	2	guarantees	guarantee	VERB
cana-1589	104	3	that	that	SCONJ
cana-1589	104	4	the	the	DET
cana-1589	104	5	parameter	parameter	NOUN
cana-1589	104	6	remains	remain	VERB
cana-1589	104	7	unchanged	unchanged	ADJ
cana-1589	104	8	even	even	ADV
cana-1589	104	9	if	if	SCONJ
cana-1589	104	10	its	its	PRON
cana-1589	104	11	coefficients	coefficient	NOUN
cana-1589	104	12	are	be	AUX
cana-1589	104	13	lowered	lower	VERB
cana-1589	104	14	modulo	modulo	ADJ
cana-1589	104	15	q.	q.	NOUN
cana-1589	104	16	this	this	PRON
cana-1589	104	17	implies	imply	VERB
cana-1589	104	18	that	that	SCONJ
cana-1589	104	19	by	by	ADP
cana-1589	104	20	reducing	reduce	VERB
cana-1589	104	21	the	the	DET
cana-1589	104	22	coefficients	coefficient	NOUN
cana-1589	104	23	of	of	ADP
cana-1589	104	24	the	the	DET
cana-1589	104	25	polynomial	polynomial	ADJ
cana-1589	104	26	f	f	NOUN
cana-1589	104	27	*	*	PUNCT
cana-1589	104	28	e	e	X
cana-1589	104	29	modulo	modulo	VERB
cana-1589	104	30	q	q	X
cana-1589	104	31	within	within	ADP
cana-1589	104	32	the	the	DET
cana-1589	104	33	range	range	NOUN
cana-1589	104	34	of	of	ADP
cana-1589	104	35	(	(	PUNCT
cana-1589	104	36	-q)/2	-q)/2	PROPN
cana-1589	104	37	to	to	ADP
cana-1589	104	38	q/2	q/2	NUM
cana-1589	104	39	,	,	PUNCT
cana-1589	104	40	it	it	PRON
cana-1589	104	41	becomes	become	VERB
cana-1589	104	42	feasible	feasible	ADJ
cana-1589	104	43	to	to	PART
cana-1589	104	44	precisely	precisely	ADV
cana-1589	104	45	recover	recover	VERB
cana-1589	104	46	the	the	DET
cana-1589	104	47	polynomial	polynomial	NOUN
cana-1589	104	48	.	.	PUNCT
cana-1589	105	1	a	a	DET
cana-1589	105	2	=	=	SYM
cana-1589	105	3	𝑝𝑟	𝑝𝑟	PROPN
cana-1589	105	4	∗	∗	NOUN
cana-1589	105	5	𝑔	𝑔	PROPN
cana-1589	105	6	+	+	X
cana-1589	105	7	𝑓	𝑓	DET
cana-1589	105	8	∗	∗	NOUN
cana-1589	105	9	[	[	X
cana-1589	105	10	𝑚	𝑚	X
cana-1589	105	11	+	+	NUM
cana-1589	105	12	𝐻(𝑚	𝐻(𝑚	NOUN
cana-1589	105	13	,	,	PUNCT
cana-1589	105	14	[	[	X
cana-1589	105	15	𝑟	𝑟	NOUN
cana-1589	105	16	∗	∗	NOUN
cana-1589	105	17	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	106	1	+	+	X
cana-1589	106	2	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	106	3	∗	∗	NOUN
cana-1589	106	4	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	106	5	)	)	PUNCT
cana-1589	106	6	]	]	PUNCT
cana-1589	106	7	𝑝	𝑝	NOUN
cana-1589	106	8	in	in	ADP
cana-1589	106	9	r	r	NOUN
cana-1589	106	10	reducing	reduce	VERB
cana-1589	106	11	a	a	DET
cana-1589	106	12	modulo	modulo	NOUN
cana-1589	106	13	p	p	NOUN
cana-1589	106	14	then	then	ADV
cana-1589	106	15	gives	give	VERB
cana-1589	106	16	the	the	DET
cana-1589	106	17	polynomial	polynomial	NOUN
cana-1589	106	18	𝑓	𝑓	DET
cana-1589	106	19	∗	∗	NOUN
cana-1589	106	20	[	[	X
cana-1589	106	21	𝑚	𝑚	X
cana-1589	106	22	+	+	NUM
cana-1589	106	23	𝐻(𝑚	𝐻(𝑚	NOUN
cana-1589	106	24	,	,	PUNCT
cana-1589	106	25	[	[	X
cana-1589	106	26	𝑟	𝑟	NOUN
cana-1589	106	27	∗	∗	NOUN
cana-1589	106	28	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	107	1	+	+	X
cana-1589	107	2	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	107	3	∗	∗	NOUN
cana-1589	107	4	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	107	5	)	)	PUNCT
cana-1589	107	6	]	]	PUNCT
cana-1589	108	1	𝑝	𝑝	NOUN
cana-1589	108	2	in	in	ADP
cana-1589	108	3	r	r	NOUN
cana-1589	108	4	and	and	CCONJ
cana-1589	108	5	then	then	ADV
cana-1589	108	6	multiplying	multiply	VERB
cana-1589	108	7	by	by	ADP
cana-1589	108	8	𝑓𝑝	𝑓𝑝	NOUN
cana-1589	108	9	−1	−1	NOUN
cana-1589	108	10	produces	produce	VERB
cana-1589	108	11	t	t	NOUN
cana-1589	108	12	=	=	SYM
cana-1589	108	13	𝑚	𝑚	PROPN
cana-1589	108	14	+	+	SYM
cana-1589	108	15	𝐻(𝑚	𝐻(𝑚	X
cana-1589	108	16	,	,	PUNCT
cana-1589	108	17	[	[	X
cana-1589	108	18	𝑟	𝑟	NOUN
cana-1589	108	19	∗	∗	NOUN
cana-1589	108	20	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	108	21	+	+	X
cana-1589	108	22	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	108	23	∗	∗	NOUN
cana-1589	108	24	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	108	25	)	)	PUNCT
cana-1589	108	26	in	in	ADP
cana-1589	108	27	ℤ[𝑋]/(𝑝	ℤ[𝑋]/(𝑝	PROPN
cana-1589	108	28	,	,	PUNCT
cana-1589	108	29	𝑋𝑛	𝑋𝑛	NOUN
cana-1589	108	30	−	−	PROPN
cana-1589	108	31	1	1	X
cana-1589	108	32	)	)	PUNCT
cana-1589	108	33	compute	compute	NOUN
cana-1589	108	34	𝑏	𝑏	NOUN
cana-1589	108	35	=	=	PUNCT
cana-1589	108	36	𝑒	𝑒	PROPN
cana-1589	108	37	−	−	PROPN
cana-1589	108	38	𝑡	𝑡	NOUN
cana-1589	108	39	and	and	CCONJ
cana-1589	108	40	recover	recover	VERB
cana-1589	108	41	𝑏	𝑏	NOUN
cana-1589	108	42	=	=	NOUN
cana-1589	108	43	𝑟	𝑟	NOUN
cana-1589	108	44	∗	∗	NOUN
cana-1589	108	45	ℎ.	ℎ.	NOUN
cana-1589	108	46	therefore	therefore	ADV
cana-1589	108	47	computation	computation	NOUN
cana-1589	108	48	of	of	ADP
cana-1589	108	49	c	c	PROPN
cana-1589	108	50	yields	yield	NOUN
cana-1589	108	51	𝑐	𝑐	NOUN
cana-1589	108	52	=	=	SYM
cana-1589	108	53	𝑚	𝑚	PROPN
cana-1589	108	54	+	+	SYM
cana-1589	108	55	𝐻(𝑚	𝐻(𝑚	X
cana-1589	108	56	,	,	PUNCT
cana-1589	108	57	[	[	X
cana-1589	108	58	𝑟	𝑟	NOUN
cana-1589	108	59	∗	∗	NOUN
cana-1589	108	60	ℎ]𝑝)𝑋𝑛−𝑘.	ℎ]𝑝)𝑋𝑛−𝑘.	NUM
cana-1589	108	61	accordingly	accordingly	ADV
cana-1589	108	62	,	,	PUNCT
cana-1589	108	63	𝑐′	𝑐′	PROPN
cana-1589	108	64	is	be	AUX
cana-1589	108	65	the	the	DET
cana-1589	108	66	original	original	ADJ
cana-1589	108	67	message	message	NOUN
cana-1589	108	68	m	m	NOUN
cana-1589	108	69	,	,	PUNCT
cana-1589	108	70	and	and	CCONJ
cana-1589	108	71	𝑐	𝑐	X
cana-1589	108	72	"	"	PUNCT
cana-1589	108	73	should	should	AUX
cana-1589	108	74	match	match	VERB
cana-1589	108	75	up	up	ADP
cana-1589	108	76	with	with	ADP
cana-1589	108	77	the	the	DET
cana-1589	108	78	hash	hash	NOUN
cana-1589	108	79	communications	communication	NOUN
cana-1589	108	80	on	on	ADP
cana-1589	108	81	applied	apply	VERB
cana-1589	108	82	nonlinear	nonlinear	ADJ
cana-1589	108	83	analysis	analysis	NOUN
cana-1589	108	84	issn	issn	NOUN
cana-1589	108	85	:	:	PUNCT
cana-1589	108	86	1074	1074	NUM
cana-1589	108	87	-	-	PUNCT
cana-1589	108	88	133x	133x	NUM
cana-1589	108	89	vol	vol	NOUN
cana-1589	108	90	31	31	NUM
cana-1589	108	91	no	no	NOUN
cana-1589	108	92	.	.	PUNCT
cana-1589	109	1	7s	7	NOUN
cana-1589	109	2	(	(	PUNCT
cana-1589	109	3	2024	2024	NUM
cana-1589	109	4	)	)	PUNCT
cana-1589	109	5	701	701	NUM
cana-1589	109	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	109	7	𝐻(𝑚	𝐻(𝑚	X
cana-1589	109	8	,	,	PUNCT
cana-1589	109	9	[	[	X
cana-1589	109	10	𝑟	𝑟	NOUN
cana-1589	109	11	∗	∗	X
cana-1589	109	12	ℎ]𝑝	ℎ]𝑝	PART
cana-1589	109	13	)	)	PUNCT
cana-1589	110	1	=	=	SYM
cana-1589	110	2	𝐻(𝑚	𝐻(𝑚	X
cana-1589	110	3	,	,	PUNCT
cana-1589	110	4	𝑏	𝑏	NOUN
cana-1589	110	5	)	)	PUNCT
cana-1589	110	6	,	,	PUNCT
cana-1589	110	7	as	as	SCONJ
cana-1589	110	8	noted	note	VERB
cana-1589	110	9	above	above	ADV
cana-1589	110	10	.	.	PUNCT
cana-1589	111	1	parameter	parameter	PROPN
cana-1589	111	2	selection	selection	PROPN
cana-1589	111	3	:	:	PUNCT
cana-1589	111	4	with	with	ADP
cana-1589	111	5	appropriately	appropriately	ADV
cana-1589	111	6	chosen	choose	VERB
cana-1589	111	7	parameters	parameter	NOUN
cana-1589	111	8	,	,	PUNCT
cana-1589	111	9	the	the	DET
cana-1589	111	10	decryption	decryption	NOUN
cana-1589	111	11	process	process	NOUN
cana-1589	111	12	has	have	VERB
cana-1589	111	13	a	a	DET
cana-1589	111	14	very	very	ADV
cana-1589	111	15	high	high	ADJ
cana-1589	111	16	probability	probability	NOUN
cana-1589	111	17	of	of	ADP
cana-1589	111	18	successfully	successfully	ADV
cana-1589	111	19	recovering	recover	VERB
cana-1589	111	20	the	the	DET
cana-1589	111	21	original	original	ADJ
cana-1589	111	22	message	message	NOUN
cana-1589	111	23	.	.	PUNCT
cana-1589	112	1	however	however	ADV
cana-1589	112	2	,	,	PUNCT
cana-1589	112	3	occasional	occasional	ADJ
cana-1589	112	4	decryption	decryption	NOUN
cana-1589	112	5	failures	failure	NOUN
cana-1589	112	6	can	can	AUX
cana-1589	112	7	occur	occur	VERB
cana-1589	112	8	,	,	PUNCT
cana-1589	112	9	often	often	ADV
cana-1589	112	10	due	due	ADP
cana-1589	112	11	to	to	ADP
cana-1589	112	12	improper	improper	ADJ
cana-1589	112	13	centering	centering	NOUN
cana-1589	112	14	of	of	ADP
cana-1589	112	15	the	the	DET
cana-1589	112	16	message	message	NOUN
cana-1589	112	17	.	.	PUNCT
cana-1589	113	1	to	to	PART
cana-1589	113	2	address	address	VERB
cana-1589	113	3	this	this	PRON
cana-1589	113	4	,	,	PUNCT
cana-1589	113	5	it	it	PRON
cana-1589	113	6	is	be	AUX
cana-1589	113	7	advisable	advisable	ADJ
cana-1589	113	8	to	to	PART
cana-1589	113	9	include	include	VERB
cana-1589	113	10	a	a	DET
cana-1589	113	11	few	few	ADJ
cana-1589	113	12	check	check	NOUN
cana-1589	113	13	bits	bit	NOUN
cana-1589	113	14	in	in	ADP
cana-1589	113	15	each	each	DET
cana-1589	113	16	message	message	NOUN
cana-1589	113	17	block	block	NOUN
cana-1589	113	18	.	.	PUNCT
cana-1589	114	1	if	if	SCONJ
cana-1589	114	2	decryption	decryption	NOUN
cana-1589	114	3	fails	fail	VERB
cana-1589	114	4	due	due	ADJ
cana-1589	114	5	to	to	ADP
cana-1589	114	6	improper	improper	ADJ
cana-1589	114	7	centering	centering	NOUN
cana-1589	114	8	,	,	PUNCT
cana-1589	114	9	you	you	PRON
cana-1589	114	10	can	can	AUX
cana-1589	114	11	attempt	attempt	VERB
cana-1589	114	12	to	to	PART
cana-1589	114	13	recover	recover	VERB
cana-1589	114	14	the	the	DET
cana-1589	114	15	message	message	NOUN
cana-1589	114	16	by	by	ADP
cana-1589	114	17	adjusting	adjust	VERB
cana-1589	114	18	the	the	DET
cana-1589	114	19	coefficients	coefficient	NOUN
cana-1589	114	20	of	of	ADP
cana-1589	114	21	𝑎	𝑎	PRON
cana-1589	114	22	≡	≡	PROPN
cana-1589	114	23	𝑓	𝑓	DET
cana-1589	114	24	∗	∗	NOUN
cana-1589	114	25	𝑒	𝑒	PROPN
cana-1589	114	26	mod	mod	PROPN
cana-1589	114	27	𝑞	𝑞	PROPN
cana-1589	114	28	within	within	ADP
cana-1589	114	29	a	a	DET
cana-1589	114	30	slightly	slightly	ADV
cana-1589	114	31	different	different	ADJ
cana-1589	114	32	range	range	NOUN
cana-1589	114	33	,	,	PUNCT
cana-1589	114	34	for	for	ADP
cana-1589	114	35	example	example	NOUN
cana-1589	114	36	,	,	PUNCT
cana-1589	114	37	from	from	ADP
cana-1589	114	38	−𝑞	−𝑞	ADP
cana-1589	114	39	2	2	NUM
cana-1589	114	40	+	+	CCONJ
cana-1589	114	41	𝑥⁄	𝑥⁄	PROPN
cana-1589	114	42	to	to	ADP
cana-1589	114	43	𝑞	𝑞	PROPN
cana-1589	114	44	2	2	NUM
cana-1589	115	1	+	+	CCONJ
cana-1589	115	2	𝑥.⁄	𝑥.⁄	NOUN
cana-1589	115	3	where	where	SCONJ
cana-1589	115	4	x	x	PRON
cana-1589	115	5	is	be	AUX
cana-1589	115	6	a	a	DET
cana-1589	115	7	small	small	ADJ
cana-1589	115	8	positive	positive	ADJ
cana-1589	115	9	or	or	CCONJ
cana-1589	115	10	negative	negative	ADJ
cana-1589	115	11	value	value	NOUN
cana-1589	115	12	.	.	PUNCT
cana-1589	116	1	if	if	SCONJ
cana-1589	116	2	no	no	DET
cana-1589	116	3	such	such	ADJ
cana-1589	116	4	adjustment	adjustment	NOUN
cana-1589	116	5	yields	yield	VERB
cana-1589	116	6	a	a	DET
cana-1589	116	7	valid	valid	ADJ
cana-1589	116	8	decryption	decryption	NOUN
cana-1589	116	9	,	,	PUNCT
cana-1589	116	10	a	a	DET
cana-1589	116	11	gap	gap	NOUN
cana-1589	116	12	failure	failure	NOUN
cana-1589	116	13	occurs	occur	VERB
cana-1589	116	14	,	,	PUNCT
cana-1589	116	15	making	make	VERB
cana-1589	116	16	the	the	DET
cana-1589	116	17	message	message	NOUN
cana-1589	116	18	difficult	difficult	ADJ
cana-1589	116	19	to	to	PART
cana-1589	116	20	decrypt	decrypt	VERB
cana-1589	116	21	.	.	PUNCT
cana-1589	117	1	for	for	ADP
cana-1589	117	2	well	well	ADV
cana-1589	117	3	-	-	PUNCT
cana-1589	117	4	chosen	choose	VERB
cana-1589	117	5	parameters	parameter	NOUN
cana-1589	117	6	,	,	PUNCT
cana-1589	117	7	such	such	ADJ
cana-1589	117	8	failures	failure	NOUN
cana-1589	117	9	are	be	AUX
cana-1589	117	10	infrequent	infrequent	ADJ
cana-1589	117	11	and	and	CCONJ
cana-1589	117	12	can	can	AUX
cana-1589	117	13	generally	generally	ADV
cana-1589	117	14	be	be	AUX
cana-1589	117	15	considered	consider	VERB
cana-1589	117	16	negligible	negligible	ADJ
cana-1589	117	17	in	in	ADP
cana-1589	117	18	practice	practice	NOUN
cana-1589	117	19	.	.	PUNCT
cana-1589	118	1	(	(	PUNCT
cana-1589	118	2	a	a	X
cana-1589	118	3	)	)	PUNCT
cana-1589	118	4	sample	sample	NOUN
cana-1589	118	5	spaces	space	NOUN
cana-1589	118	6	.	.	PUNCT
cana-1589	119	1	the	the	DET
cana-1589	119	2	space	space	NOUN
cana-1589	119	3	of	of	ADP
cana-1589	119	4	messages	message	NOUN
cana-1589	119	5	ℒ𝑚	ℒ𝑚	PROPN
cana-1589	119	6	consists	consist	VERB
cana-1589	119	7	of	of	ADP
cana-1589	119	8	all	all	DET
cana-1589	119	9	polynomials	polynomial	NOUN
cana-1589	119	10	modulo	modulo	VERB
cana-1589	119	11	p.	p.	NOUN
cana-1589	119	12	ℒ𝑚	ℒ𝑚	PROPN
cana-1589	120	1	=	=	PUNCT
cana-1589	120	2	{	{	PUNCT
cana-1589	120	3	𝑚	𝑚	PROPN
cana-1589	120	4	∈	∈	PROPN
cana-1589	120	5	𝑅	𝑅	PROPN
cana-1589	120	6	:	:	PUNCT
cana-1589	120	7	𝑚	𝑚	PROPN
cana-1589	120	8	has	have	VERB
cana-1589	120	9	coefficients	coefficient	NOUN
cana-1589	120	10	lying	lie	VERB
cana-1589	120	11	between	between	ADP
cana-1589	120	12	−	−	PROPN
cana-1589	120	13	1	1	NUM
cana-1589	120	14	2	2	NUM
cana-1589	120	15	(	(	PUNCT
cana-1589	120	16	p	p	NOUN
cana-1589	120	17	−	−	PROPN
cana-1589	120	18	1	1	NUM
cana-1589	120	19	)	)	PUNCT
cana-1589	120	20	and	and	CCONJ
cana-1589	120	21	1	1	NUM
cana-1589	120	22	2	2	NUM
cana-1589	120	23	(	(	PUNCT
cana-1589	120	24	p	p	NOUN
cana-1589	120	25	−	−	PROPN
cana-1589	120	26	1	1	NUM
cana-1589	120	27	)	)	PUNCT
cana-1589	120	28	and	and	CCONJ
cana-1589	120	29	has	have	VERB
cana-1589	120	30	degree	degree	NOUN
cana-1589	120	31	at	at	ADP
cana-1589	120	32	most	most	ADJ
cana-1589	120	33	𝑁	𝑁	ADJ
cana-1589	120	34	−	−	NOUN
cana-1589	120	35	𝑘	𝑘	PRON
cana-1589	120	36	−	−	PROPN
cana-1589	120	37	1	1	NUM
cana-1589	120	38	}	}	PUNCT
cana-1589	120	39	.	.	PUNCT
cana-1589	121	1	it	it	PRON
cana-1589	121	2	is	be	AUX
cana-1589	121	3	most	most	ADV
cana-1589	121	4	suitable	suitable	ADJ
cana-1589	121	5	to	to	PART
cana-1589	121	6	take	take	VERB
cana-1589	121	7	assume	assume	VERB
cana-1589	121	8	p	p	PROPN
cana-1589	121	9	is	be	AUX
cana-1589	121	10	odd	odd	ADJ
cana-1589	121	11	.	.	PUNCT
cana-1589	122	1	sets	set	NOUN
cana-1589	122	2	of	of	ADP
cana-1589	122	3	the	the	DET
cana-1589	122	4	form	form	NOUN
cana-1589	122	5	are	be	AUX
cana-1589	122	6	used	use	VERB
cana-1589	122	7	to	to	PART
cana-1589	122	8	describe	describe	VERB
cana-1589	122	9	the	the	DET
cana-1589	122	10	other	other	ADJ
cana-1589	122	11	sample	sample	NOUN
cana-1589	122	12	spaces	space	NOUN
cana-1589	122	13	.	.	PUNCT
cana-1589	123	1	ℒ(𝑑1	ℒ(𝑑1	ADJ
cana-1589	123	2	,	,	PUNCT
cana-1589	123	3	𝑑2	𝑑2	NOUN
cana-1589	123	4	)	)	PUNCT
cana-1589	123	5	=	=	SYM
cana-1589	123	6	{	{	PUNCT
cana-1589	123	7	𝑓	𝑓	PROPN
cana-1589	123	8	∈	∈	PROPN
cana-1589	123	9	𝑅	𝑅	PROPN
cana-1589	123	10	:	:	PUNCT
cana-1589	123	11	𝑓	𝑓	PROPN
cana-1589	123	12	has	have	VERB
cana-1589	123	13	𝑑1cofficients	𝑑1cofficient	NOUN
cana-1589	123	14	equal	equal	ADJ
cana-1589	123	15	1	1	NUM
cana-1589	123	16	,	,	PUNCT
cana-1589	123	17	𝑑2	𝑑2	NOUN
cana-1589	123	18	cofficients	cofficient	NOUN
cana-1589	123	19	equal	equal	ADJ
cana-1589	123	20	−	−	PROPN
cana-1589	123	21	1	1	NUM
cana-1589	123	22	,	,	PUNCT
cana-1589	123	23	the	the	DET
cana-1589	123	24	rest	rest	NOUN
cana-1589	123	25	0	0	NUM
cana-1589	123	26	}	}	PUNCT
cana-1589	123	27	.	.	PUNCT
cana-1589	124	1	with	with	ADP
cana-1589	124	2	this	this	DET
cana-1589	124	3	notation	notation	NOUN
cana-1589	124	4	,	,	PUNCT
cana-1589	124	5	choose	choose	VERB
cana-1589	124	6	three	three	NUM
cana-1589	124	7	positive	positive	ADJ
cana-1589	124	8	integers	integer	NOUN
cana-1589	124	9	𝑑𝑓	𝑑𝑓	PROPN
cana-1589	124	10	,	,	PUNCT
cana-1589	124	11	𝑑𝑔	𝑑𝑔	ADJ
cana-1589	124	12	,	,	PUNCT
cana-1589	124	13	𝑑𝑟and	𝑑𝑟and	NOUN
cana-1589	124	14	set	set	VERB
cana-1589	124	15	ℒ𝑓	ℒ𝑓	NOUN
cana-1589	124	16	=	=	PUNCT
cana-1589	124	17	ℒ(𝑑𝑓	ℒ(𝑑𝑓	INTJ
cana-1589	124	18	,	,	PUNCT
cana-1589	124	19	𝑑𝑓	𝑑𝑓	PROPN
cana-1589	124	20	−	−	PROPN
cana-1589	124	21	1	1	NUM
cana-1589	124	22	)	)	PUNCT
cana-1589	124	23	,	,	PUNCT
cana-1589	125	1	ℒ𝑔	ℒ𝑔	PROPN
cana-1589	125	2	=	=	SYM
cana-1589	125	3	ℒ(𝑑𝑔	ℒ(𝑑𝑔	PROPN
cana-1589	125	4	,	,	PUNCT
cana-1589	125	5	𝑑𝑔	𝑑𝑔	NOUN
cana-1589	125	6	)	)	PUNCT
cana-1589	125	7	,	,	PUNCT
cana-1589	125	8	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1589	125	9	ℒ𝑟	ℒ𝑟	PROPN
cana-1589	125	10	=	=	PUNCT
cana-1589	125	11	ℒ(𝑑𝑟	ℒ(𝑑𝑟	PROPN
cana-1589	125	12	,	,	PUNCT
cana-1589	125	13	𝑑𝑟	𝑑𝑟	PROPN
cana-1589	125	14	)	)	PUNCT
cana-1589	125	15	.	.	PUNCT
cana-1589	126	1	(	(	PUNCT
cana-1589	126	2	do	do	AUX
cana-1589	126	3	n't	not	PART
cana-1589	126	4	set	set	VERB
cana-1589	126	5	ℒ𝑓	ℒ𝑓	NOUN
cana-1589	126	6	=	=	PUNCT
cana-1589	126	7	ℒ(𝑑𝑓	ℒ(𝑑𝑓	INTJ
cana-1589	126	8	,	,	PUNCT
cana-1589	126	9	𝑑𝑓	𝑑𝑓	PROPN
cana-1589	126	10	)	)	PUNCT
cana-1589	126	11	and	and	CCONJ
cana-1589	126	12	a	a	DET
cana-1589	126	13	polynomial	polynomial	ADJ
cana-1589	126	14	satisfying	satisfying	ADJ
cana-1589	126	15	𝑓(1	𝑓(1	NOUN
cana-1589	126	16	)	)	PUNCT
cana-1589	127	1	=	=	SYM
cana-1589	127	2	0	0	PUNCT
cana-1589	127	3	can	can	AUX
cana-1589	127	4	never	never	ADV
cana-1589	127	5	be	be	AUX
cana-1589	127	6	invertible	invertible	ADJ
cana-1589	127	7	.	.	PUNCT
cana-1589	127	8	)	)	PUNCT
cana-1589	128	1	notice	notice	VERB
cana-1589	128	2	that	that	SCONJ
cana-1589	128	3	𝑓	𝑓	DET
cana-1589	128	4	∈	∈	ADJ
cana-1589	128	5	ℒ𝑓	ℒ𝑓	VERB
cana-1589	128	6	,	,	PUNCT
cana-1589	128	7	𝑔	𝑔	PROPN
cana-1589	128	8	∈	∈	PROPN
cana-1589	128	9	ℒ𝑔and	ℒ𝑔and	PROPN
cana-1589	128	10	r	r	NOUN
cana-1589	128	11	∈	∈	PROPN
cana-1589	128	12	ℒ𝑟	ℒ𝑟	PROPN
cana-1589	128	13	have	have	VERB
cana-1589	128	14	𝐿2norms	𝐿2norm	NOUN
cana-1589	128	15	|𝑓|2	|𝑓|2	PROPN
cana-1589	128	16	=	=	PUNCT
cana-1589	129	1	√2𝑑𝑓	√2𝑑𝑓	ADJ
cana-1589	129	2	−	−	NUM
cana-1589	129	3	1	1	NUM
cana-1589	129	4	−	−	PROPN
cana-1589	129	5	𝑛−1	𝑛−1	PROPN
cana-1589	129	6	,	,	PUNCT
cana-1589	129	7	|𝑔|2	|𝑔|2	PROPN
cana-1589	129	8	=	=	SYM
cana-1589	129	9	√2𝑑𝑔	√2𝑑𝑔	PROPN
cana-1589	129	10	,	,	PUNCT
cana-1589	129	11	|𝑟|2	|𝑟|2	PROPN
cana-1589	129	12	=	=	SYM
cana-1589	129	13	√2𝑑𝑟	√2𝑑𝑟	PROPN
cana-1589	129	14	.	.	PUNCT
cana-1589	130	1	give	give	VERB
cana-1589	130	2	values	value	NOUN
cana-1589	130	3	for	for	ADP
cana-1589	130	4	𝑑𝑓	𝑑𝑓	PROPN
cana-1589	130	5	,	,	PUNCT
cana-1589	130	6	𝑑𝑔	𝑑𝑔	PROPN
cana-1589	130	7	,	,	PUNCT
cana-1589	130	8	𝑑𝑟	𝑑𝑟	NOUN
cana-1589	130	9	that	that	PRON
cana-1589	130	10	allow	allow	VERB
cana-1589	130	11	decryption	decryption	NOUN
cana-1589	130	12	while	while	SCONJ
cana-1589	130	13	maintaining	maintain	VERB
cana-1589	130	14	various	various	ADJ
cana-1589	130	15	security	security	NOUN
cana-1589	130	16	levels	level	NOUN
cana-1589	130	17	.	.	PUNCT
cana-1589	131	1	(	(	PUNCT
cana-1589	131	2	b	b	X
cana-1589	131	3	)	)	PUNCT
cana-1589	131	4	define	define	VERB
cana-1589	131	5	the	the	DET
cana-1589	131	6	width	width	NOUN
cana-1589	131	7	of	of	ADP
cana-1589	131	8	an	an	DET
cana-1589	131	9	element	element	NOUN
cana-1589	131	10	𝑓	𝑓	PRON
cana-1589	131	11	∈	∈	PROPN
cana-1589	131	12	𝑅	𝑅	PROPN
cana-1589	131	13	|𝑓|∞	|𝑓|∞	NOUN
cana-1589	131	14	=	=	SYM
cana-1589	131	15	max	max	NOUN
cana-1589	131	16	0	0	X
cana-1589	131	17	≤	≤	PROPN
cana-1589	131	18	𝑖	𝑖	PUNCT
cana-1589	131	19	≤	≤	NOUN
cana-1589	132	1	𝑁	𝑁	ADP
cana-1589	132	2	−	−	PROPN
cana-1589	132	3	1	1	NUM
cana-1589	132	4	{	{	PUNCT
cana-1589	132	5	𝑓𝑖	𝑓𝑖	NOUN
cana-1589	132	6	}	}	PUNCT
cana-1589	132	7	−	−	PROPN
cana-1589	132	8	min	min	NOUN
cana-1589	132	9	0	0	NUM
cana-1589	132	10	≤	≤	NUM
cana-1589	132	11	𝑖	𝑖	PUNCT
cana-1589	132	12	≤	≤	NOUN
cana-1589	133	1	𝑁	𝑁	ADP
cana-1589	133	2	−	−	PROPN
cana-1589	133	3	1	1	NUM
cana-1589	133	4	{	{	PUNCT
cana-1589	133	5	𝑓𝑖	𝑓𝑖	NOUN
cana-1589	133	6	}	}	PUNCT
cana-1589	133	7	.	.	PUNCT
cana-1589	134	1	this	this	PRON
cana-1589	134	2	is	be	AUX
cana-1589	134	3	a	a	DET
cana-1589	134	4	sort	sort	NOUN
cana-1589	134	5	of	of	ADP
cana-1589	134	6	𝐿∞	𝐿∞	NOUN
cana-1589	134	7	norm	norm	NOUN
cana-1589	134	8	on	on	ADP
cana-1589	134	9	r.	r.	PROPN
cana-1589	134	10	similarly	similarly	ADV
cana-1589	134	11	,	,	PUNCT
cana-1589	134	12	describe	describe	VERB
cana-1589	134	13	a	a	DET
cana-1589	134	14	cantered	canter	VERB
cana-1589	134	15	𝐿2norm	𝐿2norm	NOUN
cana-1589	134	16	on	on	ADP
cana-1589	134	17	r	r	NOUN
cana-1589	134	18	by	by	ADP
cana-1589	134	19	|𝑓|2	|𝑓|2	PROPN
cana-1589	134	20	=	=	SYM
cana-1589	134	21	(	(	PUNCT
cana-1589	134	22	∑(𝑓𝑖	∑(𝑓𝑖	PROPN
cana-1589	134	23	−	−	NOUN
cana-1589	134	24	𝑓)̅	𝑓)̅	NOUN
cana-1589	134	25	2	2	NUM
cana-1589	134	26	𝑛−1	𝑛−1	PROPN
cana-1589	134	27	𝑖=0	𝑖=0	PROPN
cana-1589	134	28	)	)	PUNCT
cana-1589	134	29	1	1	NUM
cana-1589	134	30	2⁄	2⁄	NUM
cana-1589	134	31	,	,	PUNCT
cana-1589	134	32	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
cana-1589	134	33	𝑓̅	𝑓̅	ADP
cana-1589	134	34	=	=	SYM
cana-1589	135	1	1	1	NUM
cana-1589	135	2	𝑛	𝑛	PRON
cana-1589	135	3	∑	∑	PUNCT
cana-1589	135	4	𝑓𝑖.	𝑓𝑖.	NOUN
cana-1589	135	5	𝑛−1	𝑛−1	PROPN
cana-1589	135	6	𝑖=0	𝑖=0	PROPN
cana-1589	135	7	(	(	PUNCT
cana-1589	135	8	equivalently	equivalently	ADV
cana-1589	135	9	,	,	PUNCT
cana-1589	135	10	|f|2	|f|2	NOUN
cana-1589	135	11	√n⁄	√n⁄	VERB
cana-1589	135	12	is	be	AUX
cana-1589	135	13	the	the	DET
cana-1589	135	14	standard	standard	ADJ
cana-1589	135	15	deviation	deviation	NOUN
cana-1589	135	16	of	of	ADP
cana-1589	135	17	the	the	DET
cana-1589	135	18	coefficients	coefficient	NOUN
cana-1589	135	19	of	of	ADP
cana-1589	135	20	f.	f.	PROPN
cana-1589	135	21	)	)	PUNCT
cana-1589	136	1	the	the	DET
cana-1589	136	2	following	follow	VERB
cana-1589	136	3	proposition	proposition	NOUN
cana-1589	136	4	was	be	AUX
cana-1589	136	5	suggested	suggest	VERB
cana-1589	136	6	by	by	ADP
cana-1589	136	7	don	don	PROPN
cana-1589	136	8	coppersmith	coppersmith	PROPN
cana-1589	136	9	.	.	PUNCT
cana-1589	137	1	communications	communication	NOUN
cana-1589	137	2	on	on	ADP
cana-1589	137	3	applied	apply	VERB
cana-1589	137	4	nonlinear	nonlinear	ADJ
cana-1589	137	5	analysis	analysis	NOUN
cana-1589	137	6	issn	issn	NOUN
cana-1589	137	7	:	:	PUNCT
cana-1589	137	8	1074	1074	NUM
cana-1589	137	9	-	-	PUNCT
cana-1589	137	10	133x	133x	NUM
cana-1589	137	11	vol	vol	NOUN
cana-1589	137	12	31	31	NUM
cana-1589	137	13	no	no	NOUN
cana-1589	137	14	.	.	PUNCT
cana-1589	138	1	7s	7	NOUN
cana-1589	138	2	(	(	PUNCT
cana-1589	138	3	2024	2024	NUM
cana-1589	138	4	)	)	PUNCT
cana-1589	138	5	702	702	NUM
cana-1589	138	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	138	7	proposition	proposition	NOUN
cana-1589	138	8	:	:	PUNCT
cana-1589	138	9	for	for	ADP
cana-1589	138	10	any	any	PRON
cana-1589	138	11	ϵ	ϵ	X
cana-1589	138	12	>	>	X
cana-1589	138	13	0	0	PUNCT
cana-1589	139	1	there	there	PRON
cana-1589	139	2	are	be	VERB
cana-1589	139	3	constants	constant	NOUN
cana-1589	139	4	γ1	γ1	NOUN
cana-1589	139	5	,	,	PUNCT
cana-1589	139	6	γ2	γ2	PROPN
cana-1589	139	7	>	>	X
cana-1589	139	8	0	0	NUM
cana-1589	139	9	,	,	PUNCT
cana-1589	139	10	depending	depend	VERB
cana-1589	139	11	on	on	ADP
cana-1589	139	12	ϵ	ϵ	PROPN
cana-1589	139	13	and	and	CCONJ
cana-1589	139	14	n	n	CCONJ
cana-1589	139	15	,	,	PUNCT
cana-1589	139	16	such	such	ADJ
cana-1589	139	17	that	that	SCONJ
cana-1589	139	18	for	for	ADP
cana-1589	139	19	randomly	randomly	ADV
cana-1589	139	20	chosen	choose	VERB
cana-1589	139	21	polynomials	polynomial	NOUN
cana-1589	139	22	f	f	NOUN
cana-1589	139	23	,	,	PUNCT
cana-1589	139	24	g	g	PROPN
cana-1589	139	25	∈	∈	PROPN
cana-1589	139	26	r	r	NOUN
cana-1589	139	27	,	,	PUNCT
cana-1589	139	28	the	the	DET
cana-1589	139	29	probability	probability	NOUN
cana-1589	139	30	is	be	AUX
cana-1589	139	31	greater	great	ADJ
cana-1589	139	32	than	than	ADP
cana-1589	139	33	1	1	NUM
cana-1589	139	34	−	−	NOUN
cana-1589	139	35	ε	ε	PROPN
cana-1589	139	36	that	that	SCONJ
cana-1589	139	37	they	they	PRON
cana-1589	139	38	satisfy	satisfy	VERB
cana-1589	139	39	𝛾1|𝑓|2|𝑔|2	𝛾1|𝑓|2|𝑔|2	PROPN
cana-1589	139	40	≤	≤	PROPN
cana-1589	139	41	|𝑓	|𝑓	NOUN
cana-1589	139	42	∗	∗	NOUN
cana-1589	139	43	𝑔|∞	𝑔|∞	PROPN
cana-1589	139	44	≤	≤	NOUN
cana-1589	139	45	𝛾2|𝑓|2|𝑔|2	𝛾2|𝑓|2|𝑔|2	NOUN
cana-1589	139	46	.	.	PUNCT
cana-1589	140	1	of	of	ADP
cana-1589	140	2	course	course	NOUN
cana-1589	140	3	,	,	PUNCT
cana-1589	140	4	this	this	DET
cana-1589	140	5	proposition	proposition	NOUN
cana-1589	140	6	would	would	AUX
cana-1589	140	7	be	be	AUX
cana-1589	140	8	useless	useless	ADJ
cana-1589	140	9	from	from	ADP
cana-1589	140	10	a	a	DET
cana-1589	140	11	practical	practical	ADJ
cana-1589	140	12	viewpoint	viewpoint	NOUN
cana-1589	140	13	if	if	SCONJ
cana-1589	140	14	the	the	DET
cana-1589	140	15	ratio	ratio	NOUN
cana-1589	140	16	𝛾2	𝛾2	VERB
cana-1589	140	17	𝛾1⁄	𝛾1⁄	PROPN
cana-1589	140	18	were	be	AUX
cana-1589	140	19	very	very	ADV
cana-1589	140	20	large	large	ADJ
cana-1589	140	21	for	for	ADP
cana-1589	140	22	small	small	ADJ
cana-1589	140	23	𝜀′s	𝜀′	NOUN
cana-1589	140	24	.	.	PUNCT
cana-1589	141	1	however	however	ADV
cana-1589	141	2	;	;	PUNCT
cana-1589	141	3	it	it	PRON
cana-1589	141	4	turns	turn	VERB
cana-1589	141	5	out	out	ADP
cana-1589	141	6	that	that	SCONJ
cana-1589	141	7	even	even	ADV
cana-1589	141	8	for	for	ADP
cana-1589	141	9	moderately	moderately	ADV
cana-1589	141	10	large	large	ADJ
cana-1589	141	11	values	value	NOUN
cana-1589	141	12	of	of	ADP
cana-1589	141	13	n	n	PRON
cana-1589	141	14	and	and	CCONJ
cana-1589	141	15	very	very	ADV
cana-1589	141	16	small	small	ADJ
cana-1589	141	17	values	value	NOUN
cana-1589	141	18	of	of	ADP
cana-1589	141	19	𝜖	𝜖	PROPN
cana-1589	141	20	,	,	PUNCT
cana-1589	141	21	the	the	DET
cana-1589	141	22	constants	constant	NOUN
cana-1589	141	23	𝛾1	𝛾1	PROPN
cana-1589	141	24	,	,	PUNCT
cana-1589	141	25	𝛾2	𝛾2	NOUN
cana-1589	141	26	are	be	AUX
cana-1589	141	27	not	not	PART
cana-1589	141	28	at	at	ADV
cana-1589	141	29	all	all	ADV
cana-1589	141	30	extreme	extreme	ADJ
cana-1589	141	31	.	.	PUNCT
cana-1589	142	1	(	(	PUNCT
cana-1589	142	2	c	c	X
cana-1589	142	3	)	)	PUNCT
cana-1589	142	4	a	a	DET
cana-1589	142	5	decryption	decryption	NOUN
cana-1589	142	6	criterion	criterion	NOUN
cana-1589	142	7	.	.	PUNCT
cana-1589	143	1	let	let	VERB
cana-1589	143	2	𝑚′	𝑚′	NOUN
cana-1589	144	1	=	=	PUNCT
cana-1589	145	1	[	[	X
cana-1589	145	2	𝑚	𝑚	X
cana-1589	145	3	+	+	SYM
cana-1589	145	4	𝐻(𝑚	𝐻(𝑚	X
cana-1589	145	5	,	,	PUNCT
cana-1589	145	6	[	[	X
cana-1589	145	7	𝑟	𝑟	NOUN
cana-1589	145	8	∗	∗	NOUN
cana-1589	145	9	ℎ]𝑝)𝑋𝑛−𝑘	ℎ]𝑝)𝑋𝑛−𝑘	NOUN
cana-1589	145	10	+	+	X
cana-1589	145	11	𝐺([𝑟	𝐺([𝑟	PROPN
cana-1589	145	12	∗	∗	NOUN
cana-1589	145	13	ℎ]𝑝	ℎ]𝑝	NOUN
cana-1589	145	14	)	)	PUNCT
cana-1589	145	15	]	]	PUNCT
cana-1589	146	1	𝑝	𝑝	X
cana-1589	146	2	polynomial	polynomial	ADJ
cana-1589	146	3	used	use	VERB
cana-1589	146	4	(	(	PUNCT
cana-1589	146	5	𝑒	𝑒	PROPN
cana-1589	146	6	≡	≡	PROPN
cana-1589	146	7	𝑟	𝑟	NOUN
cana-1589	146	8	∗	∗	NOUN
cana-1589	146	9	ℎ	ℎ	ADP
cana-1589	146	10	+	+	CCONJ
cana-1589	146	11	𝑚′	𝑚′	NUM
cana-1589	146	12	mod	mod	PROPN
cana-1589	146	13	𝑞.	𝑞.	NOUN
cana-1589	146	14	)	)	PUNCT
cana-1589	146	15	for	for	ADP
cana-1589	146	16	encryption	encryption	NOUN
cana-1589	146	17	.	.	PUNCT
cana-1589	147	1	in	in	ADP
cana-1589	147	2	order	order	NOUN
cana-1589	147	3	for	for	SCONJ
cana-1589	147	4	the	the	DET
cana-1589	147	5	decryption	decryption	NOUN
cana-1589	147	6	process	process	NOUN
cana-1589	147	7	to	to	PART
cana-1589	147	8	operate	operate	VERB
cana-1589	147	9	,	,	PUNCT
cana-1589	147	10	it	it	PRON
cana-1589	147	11	is	be	AUX
cana-1589	147	12	necessary	necessary	ADJ
cana-1589	147	13	that	that	SCONJ
cana-1589	147	14	|𝑓	|𝑓	PROPN
cana-1589	147	15	∗	∗	VERB
cana-1589	147	16	𝑚′	𝑚′	PUNCT
cana-1589	148	1	+	+	CCONJ
cana-1589	148	2	𝑝𝑟	𝑝𝑟	PROPN
cana-1589	148	3	∗	∗	X
cana-1589	148	4	𝑔|∞	𝑔|∞	PROPN
cana-1589	148	5	<	<	X
cana-1589	148	6	𝑞.	𝑞.	NOUN
cana-1589	148	7	this	this	PRON
cana-1589	148	8	will	will	AUX
cana-1589	148	9	almost	almost	ADV
cana-1589	148	10	always	always	ADV
cana-1589	148	11	be	be	AUX
cana-1589	148	12	true	true	ADJ
cana-1589	148	13	if	if	SCONJ
cana-1589	148	14	parameters	parameter	NOUN
cana-1589	148	15	are	be	AUX
cana-1589	148	16	selected	select	VERB
cana-1589	148	17	so	so	SCONJ
cana-1589	148	18	that	that	SCONJ
cana-1589	148	19	|𝑓	|𝑓	PROPN
cana-1589	148	20	∗	∗	VERB
cana-1589	148	21	𝑚′|∞	𝑚′|∞	NOUN
cana-1589	148	22	≤	≤	NOUN
cana-1589	148	23	𝑞	𝑞	SYM
cana-1589	148	24	4⁄	4⁄	NUM
cana-1589	148	25	and	and	CCONJ
cana-1589	148	26	|𝑝𝑟	|𝑝𝑟	SYM
cana-1589	148	27	∗	∗	NOUN
cana-1589	148	28	𝑔|∞	𝑔|∞	PROPN
cana-1589	148	29	≤	≤	NOUN
cana-1589	148	30	𝑞	𝑞	X
cana-1589	148	31	4⁄	4⁄	NUM
cana-1589	148	32	;	;	PUNCT
cana-1589	148	33	this	this	PRON
cana-1589	148	34	proposes	propose	VERB
cana-1589	148	35	that	that	PRON
cana-1589	148	36	take	take	VERB
cana-1589	148	37	|𝑓|2|𝑚|2	|𝑓|2|𝑚|2	PROPN
cana-1589	149	1	≈	≈	PROPN
cana-1589	149	2	𝑞	𝑞	X
cana-1589	149	3	4𝛾2	4𝛾2	NUM
cana-1589	149	4	and	and	CCONJ
cana-1589	149	5	|𝑟|2|𝑔|2	|𝑟|2|𝑔|2	PROPN
cana-1589	150	1	≈	≈	PROPN
cana-1589	150	2	𝑞	𝑞	SYM
cana-1589	150	3	4𝑝𝛾2⁄⁄	4𝑝𝛾2⁄⁄	NOUN
cana-1589	150	4	for	for	ADP
cana-1589	150	5	a	a	DET
cana-1589	150	6	𝛾2	𝛾2	NOUN
cana-1589	150	7	matching	match	VERB
cana-1589	150	8	to	to	ADP
cana-1589	150	9	a	a	DET
cana-1589	150	10	small	small	ADJ
cana-1589	150	11	value	value	NOUN
cana-1589	150	12	for	for	ADP
cana-1589	150	13	𝜖.	𝜖.	NOUN
cana-1589	150	14	for	for	ADP
cana-1589	150	15	example	example	NOUN
cana-1589	151	1	,	,	PUNCT
cana-1589	151	2	experimental	experimental	ADJ
cana-1589	151	3	evidence	evidence	NOUN
cana-1589	151	4	recommends	recommend	VERB
cana-1589	151	5	that	that	SCONJ
cana-1589	151	6	for	for	ADP
cana-1589	151	7	n	n	NOUN
cana-1589	151	8	=	=	SYM
cana-1589	151	9	167	167	NUM
cana-1589	151	10	and	and	CCONJ
cana-1589	151	11	n	n	CCONJ
cana-1589	151	12	=	=	SYM
cana-1589	151	13	503	503	NUM
cana-1589	151	14	,	,	PUNCT
cana-1589	151	15	suitable	suitable	ADJ
cana-1589	151	16	values	value	NOUN
cana-1589	151	17	for	for	ADP
cana-1589	151	18	𝛾2	𝛾2	NOUN
cana-1589	151	19	are	be	AUX
cana-1589	151	20	0.27	0.27	NUM
cana-1589	151	21	and	and	CCONJ
cana-1589	151	22	0.17	0.17	NUM
cana-1589	151	23	respectively	respectively	ADV
cana-1589	151	24	.	.	PUNCT
cana-1589	152	1	ntru	ntru	PROPN
cana-1589	152	2	is	be	AUX
cana-1589	152	3	a	a	DET
cana-1589	152	4	lattice	lattice	NOUN
cana-1589	152	5	-	-	PUNCT
cana-1589	152	6	based	base	VERB
cana-1589	152	7	public	public	ADJ
cana-1589	152	8	-	-	PUNCT
cana-1589	152	9	key	key	NOUN
cana-1589	152	10	cryptosystem	cryptosystem	NOUN
cana-1589	152	11	recognized	recognize	VERB
cana-1589	152	12	for	for	ADP
cana-1589	152	13	its	its	PRON
cana-1589	152	14	high	high	ADJ
cana-1589	152	15	performance	performance	NOUN
cana-1589	152	16	and	and	CCONJ
cana-1589	152	17	strong	strong	ADJ
cana-1589	152	18	resistance	resistance	NOUN
cana-1589	152	19	to	to	ADP
cana-1589	152	20	quantum	quantum	ADJ
cana-1589	152	21	computing	computing	NOUN
cana-1589	152	22	attacks	attack	NOUN
cana-1589	152	23	,	,	PUNCT
cana-1589	152	24	making	make	VERB
cana-1589	152	25	it	it	PRON
cana-1589	152	26	a	a	DET
cana-1589	152	27	leading	lead	VERB
cana-1589	152	28	alternative	alternative	NOUN
cana-1589	152	29	to	to	ADP
cana-1589	152	30	rsa	rsa	NOUN
cana-1589	152	31	and	and	CCONJ
cana-1589	152	32	elliptic	elliptic	ADJ
cana-1589	152	33	curve	curve	NOUN
cana-1589	152	34	cryptography	cryptography	NOUN
cana-1589	152	35	(	(	PUNCT
cana-1589	152	36	ecc	ecc	PROPN
cana-1589	152	37	)	)	PUNCT
cana-1589	152	38	.	.	PUNCT
cana-1589	153	1	it	it	PRON
cana-1589	153	2	is	be	AUX
cana-1589	153	3	built	build	VERB
cana-1589	153	4	on	on	ADP
cana-1589	153	5	the	the	DET
cana-1589	153	6	“	"	PUNCT
cana-1589	153	7	approximate	approximate	ADJ
cana-1589	153	8	close	close	ADJ
cana-1589	153	9	lattice	lattice	NOUN
cana-1589	153	10	vector	vector	NOUN
cana-1589	153	11	problem	problem	NOUN
cana-1589	153	12	,	,	PUNCT
cana-1589	153	13	”	"	PUNCT
cana-1589	153	14	a	a	DET
cana-1589	153	15	mathematical	mathematical	ADJ
cana-1589	153	16	challenge	challenge	NOUN
cana-1589	153	17	that	that	PRON
cana-1589	153	18	underpins	underpin	VERB
cana-1589	153	19	its	its	PRON
cana-1589	153	20	security	security	NOUN
cana-1589	153	21	.	.	PUNCT
cana-1589	154	1	one	one	NUM
cana-1589	154	2	of	of	ADP
cana-1589	154	3	ntru	ntru	PROPN
cana-1589	154	4	’s	’s	PART
cana-1589	154	5	defining	define	VERB
cana-1589	154	6	features	feature	NOUN
cana-1589	154	7	is	be	AUX
cana-1589	154	8	its	its	PRON
cana-1589	154	9	efficient	efficient	ADJ
cana-1589	154	10	polynomial	polynomial	ADJ
cana-1589	154	11	multiplication	multiplication	NOUN
cana-1589	154	12	,	,	PUNCT
cana-1589	154	13	which	which	PRON
cana-1589	154	14	is	be	AUX
cana-1589	154	15	the	the	DET
cana-1589	154	16	most	most	ADV
cana-1589	154	17	complex	complex	ADJ
cana-1589	154	18	operation	operation	NOUN
cana-1589	154	19	during	during	ADP
cana-1589	154	20	encryption	encryption	NOUN
cana-1589	154	21	and	and	CCONJ
cana-1589	154	22	decryption	decryption	NOUN
cana-1589	154	23	.	.	PUNCT
cana-1589	155	1	this	this	DET
cana-1589	155	2	operation	operation	NOUN
cana-1589	155	3	is	be	AUX
cana-1589	155	4	notably	notably	ADV
cana-1589	155	5	faster	fast	ADV
cana-1589	155	6	compared	compare	VERB
cana-1589	155	7	to	to	ADP
cana-1589	155	8	the	the	DET
cana-1589	155	9	corresponding	correspond	VERB
cana-1589	155	10	processes	process	NOUN
cana-1589	155	11	in	in	ADP
cana-1589	155	12	other	other	ADJ
cana-1589	155	13	asymmetric	asymmetric	ADJ
cana-1589	155	14	cryptosystems	cryptosystem	NOUN
cana-1589	155	15	such	such	ADJ
cana-1589	155	16	as	as	ADP
cana-1589	155	17	rsa	rsa	NOUN
cana-1589	155	18	,	,	PUNCT
cana-1589	155	19	elgamal	elgamal	ADJ
cana-1589	155	20	,	,	PUNCT
cana-1589	155	21	and	and	CCONJ
cana-1589	155	22	ecc	ecc	PROPN
cana-1589	155	23	.	.	PROPN
cana-1589	155	24	performance	performance	NOUN
cana-1589	155	25	comparisons	comparison	NOUN
cana-1589	155	26	between	between	ADP
cana-1589	155	27	the	the	DET
cana-1589	155	28	ntru	ntru	ADJ
cana-1589	155	29	cryptosystem	cryptosystem	NOUN
cana-1589	155	30	and	and	CCONJ
cana-1589	155	31	rsa	rsa	PROPN
cana-1589	155	32	focusing	focus	VERB
cana-1589	155	33	on	on	ADP
cana-1589	155	34	key	key	ADJ
cana-1589	155	35	-	-	PUNCT
cana-1589	155	36	size	size	NOUN
cana-1589	155	37	,	,	PUNCT
cana-1589	155	38	key	key	ADJ
cana-1589	155	39	-	-	PUNCT
cana-1589	155	40	generation	generation	NOUN
cana-1589	155	41	,	,	PUNCT
cana-1589	155	42	encryption	encryption	NOUN
cana-1589	155	43	,	,	PUNCT
cana-1589	155	44	and	and	CCONJ
cana-1589	155	45	decryption	decryption	NOUN
cana-1589	155	46	—	—	PUNCT
cana-1589	155	47	are	be	AUX
cana-1589	155	48	illustrated	illustrate	VERB
cana-1589	155	49	in	in	ADP
cana-1589	155	50	figures	figure	NOUN
cana-1589	155	51	1	1	NUM
cana-1589	155	52	,	,	PUNCT
cana-1589	155	53	2	2	NUM
cana-1589	155	54	,	,	PUNCT
cana-1589	155	55	and	and	CCONJ
cana-1589	155	56	3	3	NUM
cana-1589	155	57	,	,	PUNCT
cana-1589	155	58	respectively	respectively	ADV
cana-1589	155	59	[	[	X
cana-1589	155	60	6	6	NUM
cana-1589	155	61	]	]	PUNCT
cana-1589	155	62	.	.	PUNCT
cana-1589	156	1	communications	communication	NOUN
cana-1589	156	2	on	on	ADP
cana-1589	156	3	applied	apply	VERB
cana-1589	156	4	nonlinear	nonlinear	ADJ
cana-1589	156	5	analysis	analysis	NOUN
cana-1589	156	6	issn	issn	NOUN
cana-1589	156	7	:	:	PUNCT
cana-1589	156	8	1074	1074	NUM
cana-1589	156	9	-	-	PUNCT
cana-1589	156	10	133x	133x	NUM
cana-1589	156	11	vol	vol	NOUN
cana-1589	156	12	31	31	NUM
cana-1589	156	13	no	no	NOUN
cana-1589	156	14	.	.	PUNCT
cana-1589	157	1	7s	7	NOUN
cana-1589	157	2	(	(	PUNCT
cana-1589	157	3	2024	2024	NUM
cana-1589	157	4	)	)	PUNCT
cana-1589	157	5	703	703	NUM
cana-1589	157	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	157	7	figure-1	figure-1	PROPN
cana-1589	157	8	key	key	ADJ
cana-1589	157	9	-	-	PUNCT
cana-1589	157	10	size	size	NOUN
cana-1589	157	11	v	v	ADP
cana-1589	157	12	/	/	SYM
cana-1589	157	13	s	s	PART
cana-1589	157	14	key	key	ADJ
cana-1589	157	15	-	-	PUNCT
cana-1589	157	16	generation	generation	NOUN
cana-1589	157	17	figure-2	figure-2	NUM
cana-1589	157	18	key	key	ADJ
cana-1589	157	19	-	-	PUNCT
cana-1589	157	20	size	size	NOUN
cana-1589	157	21	v	v	ADP
cana-1589	157	22	/	/	SYM
cana-1589	157	23	s	s	PART
cana-1589	157	24	encryption	encryption	NOUN
cana-1589	157	25	(	(	PUNCT
cana-1589	157	26	blocks	blocks	PROPN
cana-1589	157	27	/	/	SYM
cana-1589	157	28	sec	sec	PROPN
cana-1589	157	29	)	)	PUNCT
cana-1589	157	30	figure-3	figure-3	NUM
cana-1589	157	31	key	key	ADJ
cana-1589	157	32	-	-	PUNCT
cana-1589	157	33	size	size	NOUN
cana-1589	157	34	v	v	ADP
cana-1589	157	35	/	/	SYM
cana-1589	157	36	s	s	PART
cana-1589	157	37	decryption	decryption	NOUN
cana-1589	157	38	(	(	PUNCT
cana-1589	157	39	blocks	block	NOUN
cana-1589	157	40	/	/	SYM
cana-1589	157	41	sec	sec	PROPN
cana-1589	157	42	)	)	PUNCT
cana-1589	157	43	the	the	DET
cana-1589	157	44	performance	performance	NOUN
cana-1589	157	45	analysis	analysis	NOUN
cana-1589	157	46	from	from	ADP
cana-1589	157	47	the	the	DET
cana-1589	157	48	figures	figure	NOUN
cana-1589	157	49	clearly	clearly	ADV
cana-1589	157	50	indicates	indicate	VERB
cana-1589	157	51	that	that	SCONJ
cana-1589	157	52	ntru	ntru	PROPN
cana-1589	157	53	outperforms	outperform	NOUN
cana-1589	157	54	rsa	rsa	PROPN
cana-1589	157	55	in	in	ADP
cana-1589	157	56	key	key	ADJ
cana-1589	157	57	generation	generation	NOUN
cana-1589	157	58	,	,	PUNCT
cana-1589	157	59	encryption	encryption	NOUN
cana-1589	157	60	,	,	PUNCT
cana-1589	157	61	and	and	CCONJ
cana-1589	157	62	decryption	decryption	NOUN
cana-1589	157	63	.	.	PUNCT
cana-1589	158	1	ntru	ntru	PROPN
cana-1589	158	2	has	have	AUX
cana-1589	158	3	been	be	AUX
cana-1589	158	4	endorsed	endorse	VERB
cana-1589	158	5	by	by	ADP
cana-1589	158	6	two	two	NUM
cana-1589	158	7	prominent	prominent	ADJ
cana-1589	158	8	standards	standard	NOUN
cana-1589	158	9	organizations	organization	NOUN
cana-1589	158	10	:	:	PUNCT
cana-1589	158	11	the	the	DET
cana-1589	158	12	ieee	ieee	NOUN
cana-1589	158	13	and	and	CCONJ
cana-1589	158	14	the	the	DET
cana-1589	158	15	financial	financial	ADJ
cana-1589	158	16	-	-	PUNCT
cana-1589	158	17	services	service	NOUN
cana-1589	158	18	industry	industry	NOUN
cana-1589	158	19	standards	standard	NOUN
cana-1589	158	20	committee	committee	NOUN
cana-1589	158	21	-	-	PUNCT
cana-1589	158	22	x9	x9	NOUN
cana-1589	158	23	,	,	PUNCT
cana-1589	158	24	specifically	specifically	ADV
cana-1589	158	25	through	through	ADP
cana-1589	158	26	the	the	DET
cana-1589	158	27	x9.98	x9.98	PROPN
cana-1589	158	28	lattice	lattice	NOUN
cana-1589	158	29	-	-	PUNCT
cana-1589	158	30	based	base	VERB
cana-1589	158	31	polynomial	polynomial	ADJ
cana-1589	158	32	public	public	ADJ
cana-1589	158	33	-	-	PUNCT
cana-1589	158	34	key	key	NOUN
cana-1589	158	35	establishment	establishment	NOUN
cana-1589	158	36	algorithm	algorithm	NOUN
cana-1589	158	37	.	.	PUNCT
cana-1589	159	1	this	this	DET
cana-1589	159	2	endorsement	endorsement	NOUN
cana-1589	159	3	highlights	highlight	VERB
cana-1589	159	4	ntru	ntru	PROPN
cana-1589	159	5	's	's	PART
cana-1589	159	6	role	role	NOUN
cana-1589	159	7	in	in	ADP
cana-1589	159	8	securing	secure	VERB
cana-1589	159	9	communications	communication	NOUN
cana-1589	159	10	within	within	ADP
cana-1589	159	11	the	the	DET
cana-1589	159	12	financial	financial	ADJ
cana-1589	159	13	sector	sector	NOUN
cana-1589	159	14	.	.	PUNCT
cana-1589	160	1	the	the	DET
cana-1589	160	2	x9.98	x9.98	PROPN
cana-1589	160	3	standard	standard	NOUN
cana-1589	160	4	represents	represent	VERB
cana-1589	160	5	a	a	DET
cana-1589	160	6	significant	significant	ADJ
cana-1589	160	7	advancement	advancement	NOUN
cana-1589	160	8	by	by	ADP
cana-1589	160	9	enhancing	enhance	VERB
cana-1589	160	10	the	the	DET
cana-1589	160	11	resilience	resilience	NOUN
cana-1589	160	12	of	of	ADP
cana-1589	160	13	systems	system	NOUN
cana-1589	160	14	against	against	ADP
cana-1589	160	15	both	both	CCONJ
cana-1589	160	16	quantum	quantum	ADJ
cana-1589	160	17	and	and	CCONJ
cana-1589	160	18	classical	classical	ADJ
cana-1589	160	19	attacks	attack	NOUN
cana-1589	160	20	,	,	PUNCT
cana-1589	160	21	thereby	thereby	ADV
cana-1589	160	22	strengthening	strengthen	VERB
cana-1589	160	23	the	the	DET
cana-1589	160	24	overall	overall	ADJ
cana-1589	160	25	security	security	NOUN
cana-1589	160	26	of	of	ADP
cana-1589	160	27	financial	financial	ADJ
cana-1589	160	28	services	service	NOUN
cana-1589	160	29	systems	system	NOUN
cana-1589	160	30	.	.	PUNCT
cana-1589	161	1	4	4	X
cana-1589	161	2	.	.	NUM
cana-1589	161	3	proposed	propose	VERB
cana-1589	161	4	aka	aka	ADV
cana-1589	161	5	security	security	NOUN
cana-1589	161	6	protocol	protocol	NOUN
cana-1589	161	7	the	the	DET
cana-1589	161	8	3gpp	3gpp	PROPN
cana-1589	161	9	committee	committee	NOUN
cana-1589	161	10	has	have	AUX
cana-1589	161	11	established	establish	VERB
cana-1589	161	12	the	the	DET
cana-1589	161	13	security	security	NOUN
cana-1589	161	14	architecture	architecture	NOUN
cana-1589	161	15	for	for	ADP
cana-1589	161	16	the	the	DET
cana-1589	161	17	5	5	NUM
cana-1589	161	18	g	g	NOUN
cana-1589	161	19	network	network	NOUN
cana-1589	161	20	[	[	X
cana-1589	161	21	2	2	NUM
cana-1589	161	22	]	]	PUNCT
cana-1589	161	23	.	.	PUNCT
cana-1589	162	1	the	the	DET
cana-1589	162	2	proposed	propose	VERB
cana-1589	162	3	aka	aka	ADV
cana-1589	162	4	protocol	protocol	NOUN
cana-1589	162	5	involves	involve	VERB
cana-1589	162	6	four	four	NUM
cana-1589	162	7	main	main	ADJ
cana-1589	162	8	entities	entity	NOUN
cana-1589	162	9	:	:	PUNCT
cana-1589	162	10	ue	ue	INTJ
cana-1589	162	11	(	(	PUNCT
cana-1589	162	12	user	user	NOUN
cana-1589	162	13	-	-	PUNCT
cana-1589	162	14	equipment	equipment	NOUN
cana-1589	162	15	)	)	PUNCT
cana-1589	162	16	,	,	PUNCT
cana-1589	162	17	seaf	seaf	NOUN
cana-1589	162	18	(	(	PUNCT
cana-1589	162	19	subscription	subscription	NOUN
cana-1589	162	20	-	-	PUNCT
cana-1589	162	21	encryption	encryption	NOUN
cana-1589	162	22	and	and	CCONJ
cana-1589	162	23	authentication	authentication	NOUN
cana-1589	162	24	function	function	NOUN
cana-1589	162	25	)	)	PUNCT
cana-1589	162	26	,	,	PUNCT
cana-1589	162	27	ausf	ausf	NOUN
cana-1589	162	28	(	(	PUNCT
cana-1589	162	29	authentication	authentication	NOUN
cana-1589	162	30	-	-	PUNCT
cana-1589	162	31	server	server	NOUN
cana-1589	162	32	function	function	NOUN
cana-1589	162	33	)	)	PUNCT
cana-1589	162	34	,	,	PUNCT
cana-1589	162	35	and	and	CCONJ
cana-1589	162	36	udm	udm	PROPN
cana-1589	162	37	/	/	SYM
cana-1589	162	38	arpf	arpf	NOUN
cana-1589	162	39	(	(	PUNCT
cana-1589	162	40	unified	unified	ADJ
cana-1589	162	41	data	data	NOUN
cana-1589	162	42	management	management	NOUN
cana-1589	162	43	/	/	SYM
cana-1589	162	44	authentication	authentication	NOUN
cana-1589	162	45	-	-	PUNCT
cana-1589	162	46	repository	repository	NOUN
cana-1589	162	47	and	and	CCONJ
cana-1589	162	48	processing	processing	NOUN
cana-1589	162	49	function	function	NOUN
cana-1589	162	50	)	)	PUNCT
cana-1589	162	51	,	,	PUNCT
cana-1589	162	52	as	as	SCONJ
cana-1589	162	53	illustrated	illustrate	VERB
cana-1589	162	54	in	in	ADP
cana-1589	162	55	figure	figure	NOUN
cana-1589	162	56	4	4	NUM
cana-1589	162	57	.	.	PUNCT
cana-1589	163	1	the	the	DET
cana-1589	163	2	ntru	ntru	ADJ
cana-1589	163	3	cryptosystem	cryptosystem	NOUN
cana-1589	163	4	is	be	AUX
cana-1589	163	5	employed	employ	VERB
cana-1589	163	6	to	to	PART
cana-1589	163	7	secure	secure	VERB
cana-1589	163	8	message	message	NOUN
cana-1589	163	9	exchanges	exchange	NOUN
cana-1589	163	10	between	between	ADP
cana-1589	163	11	these	these	DET
cana-1589	163	12	entities	entity	NOUN
cana-1589	163	13	.	.	PUNCT
cana-1589	164	1	communications	communication	NOUN
cana-1589	164	2	on	on	ADP
cana-1589	164	3	applied	apply	VERB
cana-1589	164	4	nonlinear	nonlinear	ADJ
cana-1589	164	5	analysis	analysis	NOUN
cana-1589	164	6	issn	issn	NOUN
cana-1589	164	7	:	:	PUNCT
cana-1589	164	8	1074	1074	NUM
cana-1589	164	9	-	-	PUNCT
cana-1589	164	10	133x	133x	NUM
cana-1589	164	11	vol	vol	NOUN
cana-1589	164	12	31	31	NUM
cana-1589	164	13	no	no	NOUN
cana-1589	164	14	.	.	PUNCT
cana-1589	165	1	7s	7	NOUN
cana-1589	165	2	(	(	PUNCT
cana-1589	165	3	2024	2024	NUM
cana-1589	165	4	)	)	PUNCT
cana-1589	165	5	704	704	NUM
cana-1589	165	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	165	7	figure	figure	NOUN
cana-1589	165	8	4	4	NUM
cana-1589	165	9	proposed	propose	VERB
cana-1589	165	10	aka	aka	ADV
cana-1589	165	11	security	security	NOUN
cana-1589	165	12	protocol	protocol	NOUN
cana-1589	165	13	.	.	PUNCT
cana-1589	166	1	in	in	ADP
cana-1589	166	2	the	the	DET
cana-1589	166	3	protocol	protocol	NOUN
cana-1589	166	4	,	,	PUNCT
cana-1589	166	5	the	the	DET
cana-1589	166	6	ue	ue	PROPN
cana-1589	166	7	sends	send	VERB
cana-1589	166	8	its	its	PRON
cana-1589	166	9	subscriber	subscriber	NOUN
cana-1589	166	10	identity	identity	NOUN
cana-1589	166	11	in	in	ADP
cana-1589	166	12	message	message	NOUN
cana-1589	166	13	-	-	PUNCT
cana-1589	166	14	m1	m1	NOUN
cana-1589	166	15	to	to	PART
cana-1589	166	16	seaf	seaf	VERB
cana-1589	166	17	,	,	PUNCT
cana-1589	166	18	encrypted	encrypt	VERB
cana-1589	166	19	with	with	ADP
cana-1589	166	20	the	the	DET
cana-1589	166	21	ntru	ntru	ADJ
cana-1589	166	22	public	public	ADJ
cana-1589	166	23	key	key	NOUN
cana-1589	166	24	of	of	ADP
cana-1589	166	25	udm	udm	PROPN
cana-1589	166	26	/	/	SYM
cana-1589	166	27	arpf	arpf	NOUN
cana-1589	166	28	.	.	PUNCT
cana-1589	167	1	seaf	seaf	NOUN
cana-1589	167	2	then	then	ADV
cana-1589	167	3	forwards	forward	VERB
cana-1589	167	4	a	a	DET
cana-1589	167	5	request	request	NOUN
cana-1589	167	6	containing	contain	VERB
cana-1589	167	7	the	the	DET
cana-1589	167	8	subscriber	subscriber	NOUN
cana-1589	167	9	identity	identity	NOUN
cana-1589	167	10	to	to	AUX
cana-1589	167	11	ausf	ausf	NOUN
cana-1589	167	12	and	and	CCONJ
cana-1589	167	13	sends	send	VERB
cana-1589	167	14	snn	snn	PROPN
cana-1589	167	15	in	in	ADP
cana-1589	167	16	message	message	NOUN
cana-1589	167	17	-	-	PUNCT
cana-1589	167	18	m2	m2	PROPN
cana-1589	167	19	,	,	PUNCT
cana-1589	167	20	also	also	ADV
cana-1589	167	21	encrypted	encrypt	VERB
cana-1589	167	22	with	with	ADP
cana-1589	167	23	udm	udm	PROPN
cana-1589	167	24	/	/	SYM
cana-1589	167	25	arpf	arpf	NOUN
cana-1589	167	26	's	's	PART
cana-1589	167	27	ntru	ntru	ADJ
cana-1589	167	28	public	public	ADJ
cana-1589	167	29	key	key	NOUN
cana-1589	167	30	.	.	PUNCT
cana-1589	168	1	ausf	ausf	NOUN
cana-1589	168	2	passes	pass	VERB
cana-1589	168	3	the	the	DET
cana-1589	168	4	received	received	ADJ
cana-1589	168	5	message	message	NOUN
cana-1589	168	6	to	to	ADP
cana-1589	168	7	udm	udm	PROPN
cana-1589	168	8	/	/	SYM
cana-1589	168	9	arpf	arpf	NOUN
cana-1589	168	10	as	as	ADP
cana-1589	168	11	av_req	av_req	PROPN
cana-1589	168	12	message	message	NOUN
cana-1589	168	13	-	-	PUNCT
cana-1589	168	14	m3	m3	PROPN
cana-1589	168	15	.	.	PUNCT
cana-1589	169	1	udm	udm	PROPN
cana-1589	169	2	/	/	SYM
cana-1589	169	3	arpf	arpf	NOUN
cana-1589	169	4	decrypts	decrypt	NOUN
cana-1589	169	5	the	the	DET
cana-1589	169	6	authentication	authentication	NOUN
cana-1589	169	7	request	request	NOUN
cana-1589	169	8	using	use	VERB
cana-1589	169	9	its	its	PRON
cana-1589	169	10	ntru	ntru	ADJ
cana-1589	169	11	private	private	ADJ
cana-1589	169	12	key	key	NOUN
cana-1589	169	13	and	and	CCONJ
cana-1589	169	14	generates	generate	VERB
cana-1589	169	15	an	an	DET
cana-1589	169	16	authentication	authentication	NOUN
cana-1589	169	17	response	response	NOUN
cana-1589	169	18	,	,	PUNCT
cana-1589	169	19	udm_av_res	udm_av_res	PROPN
cana-1589	169	20	.	.	PUNCT
cana-1589	170	1	this	this	DET
cana-1589	170	2	response	response	NOUN
cana-1589	170	3	,	,	PUNCT
cana-1589	170	4	which	which	PRON
cana-1589	170	5	contains	contain	VERB
cana-1589	170	6	validation	validation	NOUN
cana-1589	170	7	information	information	NOUN
cana-1589	170	8	,	,	PUNCT
cana-1589	170	9	is	be	AUX
cana-1589	170	10	sent	send	VERB
cana-1589	170	11	to	to	AUX
cana-1589	170	12	ausf	ausf	VERB
cana-1589	170	13	in	in	ADP
cana-1589	170	14	messagem4	messagem4	PROPN
cana-1589	170	15	(	(	PUNCT
cana-1589	170	16	avs	avs	PROPN
cana-1589	170	17	)	)	PUNCT
cana-1589	170	18	,	,	PUNCT
cana-1589	170	19	encoded	encode	VERB
cana-1589	170	20	with	with	ADP
cana-1589	170	21	ausf	ausf	NOUN
cana-1589	170	22	's	's	PART
cana-1589	170	23	ntru	ntru	ADJ
cana-1589	170	24	public	public	ADJ
cana-1589	170	25	key	key	NOUN
cana-1589	170	26	.	.	PUNCT
cana-1589	171	1	this	this	PRON
cana-1589	171	2	allows	allow	VERB
cana-1589	171	3	ausf	ausf	NOUN
cana-1589	171	4	to	to	PART
cana-1589	171	5	confirm	confirm	VERB
cana-1589	171	6	the	the	DET
cana-1589	171	7	ue	ue	PROPN
cana-1589	171	8	's	's	PART
cana-1589	171	9	identity	identity	NOUN
cana-1589	171	10	.	.	PUNCT
cana-1589	172	1	ausf	ausf	VERB
cana-1589	172	2	stores	store	NOUN
cana-1589	172	3	the	the	DET
cana-1589	172	4	validation	validation	NOUN
cana-1589	172	5	vectors	vector	NOUN
cana-1589	172	6	(	(	PUNCT
cana-1589	172	7	avs	avs	PROPN
cana-1589	172	8	)	)	PUNCT
cana-1589	172	9	and	and	CCONJ
cana-1589	172	10	uses	use	VERB
cana-1589	172	11	the	the	DET
cana-1589	172	12	ntru	ntru	ADJ
cana-1589	172	13	public	public	ADJ
cana-1589	172	14	key	key	NOUN
cana-1589	172	15	of	of	ADP
cana-1589	172	16	seaf	seaf	NOUN
cana-1589	172	17	to	to	PART
cana-1589	172	18	send	send	VERB
cana-1589	172	19	rand	rand	NOUN
cana-1589	172	20	and	and	CCONJ
cana-1589	172	21	autn	autn	VERB
cana-1589	172	22	from	from	ADP
cana-1589	172	23	the	the	DET
cana-1589	172	24	selected	select	VERB
cana-1589	172	25	av	av	PRON
cana-1589	172	26	to	to	PART
cana-1589	172	27	seaf	seaf	VERB
cana-1589	172	28	in	in	ADP
cana-1589	172	29	message	message	NOUN
cana-1589	172	30	-	-	PUNCT
cana-1589	172	31	m5	m5	NOUN
cana-1589	172	32	.	.	PUNCT
cana-1589	173	1	seaf	seaf	NOUN
cana-1589	173	2	then	then	ADV
cana-1589	173	3	decrypts	decrypt	VERB
cana-1589	173	4	these	these	DET
cana-1589	173	5	messages	message	NOUN
cana-1589	173	6	using	use	VERB
cana-1589	173	7	its	its	PRON
cana-1589	173	8	ntru	ntru	ADJ
cana-1589	173	9	private	private	ADJ
cana-1589	173	10	key	key	NOUN
cana-1589	173	11	and	and	CCONJ
cana-1589	173	12	forwards	forwards	ADJ
cana-1589	173	13	rand	rand	NOUN
cana-1589	173	14	and	and	CCONJ
cana-1589	173	15	autn	autn	VERB
cana-1589	173	16	to	to	ADP
cana-1589	173	17	ue	ue	PROPN
cana-1589	173	18	in	in	ADP
cana-1589	173	19	message	message	NOUN
cana-1589	173	20	-	-	PUNCT
cana-1589	173	21	m6	m6	VERB
cana-1589	173	22	,	,	PUNCT
cana-1589	173	23	encrypted	encrypt	VERB
cana-1589	173	24	with	with	ADP
cana-1589	173	25	ue	ue	PROPN
cana-1589	173	26	's	's	PART
cana-1589	173	27	ntru	ntru	ADJ
cana-1589	173	28	public	public	ADJ
cana-1589	173	29	key	key	NOUN
cana-1589	173	30	.	.	PUNCT
cana-1589	174	1	ue	ue	ADJ
cana-1589	174	2	verifies	verifie	NOUN
cana-1589	174	3	the	the	DET
cana-1589	174	4	mac	mac	PROPN
cana-1589	174	5	in	in	SCONJ
cana-1589	174	6	autn	autn	VERB
cana-1589	174	7	by	by	ADP
cana-1589	174	8	decoding	decode	VERB
cana-1589	174	9	it	it	PRON
cana-1589	174	10	with	with	ADP
cana-1589	174	11	its	its	PRON
cana-1589	174	12	ntru	ntru	ADJ
cana-1589	174	13	private	private	ADJ
cana-1589	174	14	key	key	NOUN
cana-1589	174	15	,	,	PUNCT
cana-1589	174	16	xmac	xmac	PROPN
cana-1589	174	17	.	.	PUNCT
cana-1589	175	1	if	if	SCONJ
cana-1589	175	2	the	the	DET
cana-1589	175	3	macs	macs	PROPN
cana-1589	175	4	match	match	NOUN
cana-1589	175	5	,	,	PUNCT
cana-1589	175	6	ue	ue	ADJ
cana-1589	175	7	calculates	calculate	NOUN
cana-1589	175	8	and	and	CCONJ
cana-1589	175	9	returns	return	VERB
cana-1589	175	10	the	the	DET
cana-1589	175	11	response	response	NOUN
cana-1589	175	12	res	re	NOUN
cana-1589	175	13	to	to	ADP
cana-1589	175	14	seaf	seaf	NOUN
cana-1589	175	15	in	in	ADP
cana-1589	175	16	message	message	NOUN
cana-1589	175	17	-	-	PUNCT
cana-1589	175	18	m7	m7	PROPN
cana-1589	175	19	.	.	PUNCT
cana-1589	176	1	ue	ue	PROPN
cana-1589	176	2	also	also	ADV
cana-1589	176	3	computes	compute	VERB
cana-1589	176	4	ck	ck	PROPN
cana-1589	176	5	and	and	CCONJ
cana-1589	176	6	ik	ik	NOUN
cana-1589	176	7	,	,	PUNCT
cana-1589	176	8	similar	similar	ADJ
cana-1589	176	9	to	to	ADP
cana-1589	176	10	the	the	DET
cana-1589	176	11	calculations	calculation	NOUN
cana-1589	176	12	in	in	ADP
cana-1589	176	13	udm	udm	PROPN
cana-1589	176	14	/	/	SYM
cana-1589	176	15	arpf	arpf	NOUN
cana-1589	176	16	.	.	PUNCT
cana-1589	177	1	seaf	seaf	NOUN
cana-1589	177	2	then	then	ADV
cana-1589	177	3	sends	send	VERB
cana-1589	177	4	the	the	DET
cana-1589	177	5	received	receive	VERB
cana-1589	177	6	message	message	NOUN
cana-1589	177	7	to	to	AUX
cana-1589	177	8	ausf	ausf	VERB
cana-1589	177	9	as	as	ADP
cana-1589	177	10	auth_ue_auth_req	auth_ue_auth_req	NUM
cana-1589	177	11	in	in	ADP
cana-1589	177	12	message	message	NOUN
cana-1589	177	13	-	-	PUNCT
cana-1589	177	14	m8	m8	NOUN
cana-1589	177	15	.	.	PUNCT
cana-1589	178	1	upon	upon	SCONJ
cana-1589	178	2	receiving	receive	VERB
cana-1589	178	3	res	re	NOUN
cana-1589	178	4	from	from	ADP
cana-1589	178	5	ue	ue	ADJ
cana-1589	178	6	,	,	PUNCT
cana-1589	178	7	ausf	ausf	NOUN
cana-1589	178	8	compares	compare	VERB
cana-1589	178	9	it	it	PRON
cana-1589	178	10	with	with	ADP
cana-1589	178	11	xres	xre	NOUN
cana-1589	178	12	from	from	ADP
cana-1589	178	13	the	the	DET
cana-1589	178	14	av	av	PROPN
cana-1589	178	15	.	.	PUNCT
cana-1589	179	1	if	if	SCONJ
cana-1589	179	2	they	they	PRON
cana-1589	179	3	match	match	VERB
cana-1589	179	4	,	,	PUNCT
cana-1589	179	5	the	the	DET
cana-1589	179	6	authentication	authentication	NOUN
cana-1589	179	7	is	be	AUX
cana-1589	179	8	deemed	deem	VERB
cana-1589	179	9	successful	successful	ADJ
cana-1589	179	10	,	,	PUNCT
cana-1589	179	11	and	and	CCONJ
cana-1589	179	12	ausf	ausf	VERB
cana-1589	179	13	computes	compute	VERB
cana-1589	179	14	the	the	DET
cana-1589	179	15	session	session	NOUN
cana-1589	179	16	key	key	ADJ
cana-1589	179	17	kausf	kausf	NOUN
cana-1589	179	18	from	from	ADP
cana-1589	179	19	ck	ck	PROPN
cana-1589	179	20	and	and	CCONJ
cana-1589	179	21	ik	ik	PROPN
cana-1589	179	22	to	to	PART
cana-1589	179	23	secure	secure	VERB
cana-1589	179	24	the	the	DET
cana-1589	179	25	wireless	wireless	ADJ
cana-1589	179	26	communication	communication	NOUN
cana-1589	179	27	with	with	ADP
cana-1589	179	28	ue	ue	PROPN
cana-1589	179	29	.	.	PROPN
cana-1589	179	30	ausf	ausf	NOUN
cana-1589	179	31	also	also	ADV
cana-1589	179	32	derives	derive	VERB
cana-1589	179	33	kseaf	kseaf	NOUN
cana-1589	179	34	from	from	ADP
cana-1589	179	35	kausf	kausf	NOUN
cana-1589	179	36	and	and	CCONJ
cana-1589	179	37	sends	send	VERB
cana-1589	179	38	it	it	PRON
cana-1589	179	39	to	to	PART
cana-1589	179	40	seaf	seaf	VERB
cana-1589	179	41	in	in	ADP
cana-1589	179	42	message	message	NOUN
cana-1589	179	43	-	-	PUNCT
cana-1589	179	44	m9	m9	NOUN
cana-1589	179	45	.	.	PUNCT
cana-1589	180	1	ue	ue	PROPN
cana-1589	180	2	independently	independently	ADV
cana-1589	180	3	calculates	calculate	VERB
cana-1589	180	4	kausf	kausf	NOUN
cana-1589	180	5	and	and	CCONJ
cana-1589	180	6	kseaf	kseaf	NOUN
cana-1589	180	7	.	.	PUNCT
cana-1589	181	1	this	this	DET
cana-1589	181	2	process	process	NOUN
cana-1589	181	3	ensures	ensure	VERB
cana-1589	181	4	that	that	SCONJ
cana-1589	181	5	(	(	PUNCT
cana-1589	181	6	i	i	NOUN
cana-1589	181	7	)	)	PUNCT
cana-1589	181	8	ue	ue	PROPN
cana-1589	181	9	and	and	CCONJ
cana-1589	181	10	ausf	ausf	VERB
cana-1589	181	11	share	share	VERB
cana-1589	181	12	the	the	DET
cana-1589	181	13	same	same	ADJ
cana-1589	181	14	session	session	NOUN
cana-1589	181	15	key	key	ADJ
cana-1589	181	16	kausf	kausf	NOUN
cana-1589	181	17	,	,	PUNCT
cana-1589	181	18	and	and	CCONJ
cana-1589	181	19	(	(	PUNCT
cana-1589	181	20	ii	ii	NOUN
cana-1589	181	21	)	)	PUNCT
cana-1589	181	22	ue	ue	PROPN
cana-1589	181	23	and	and	CCONJ
cana-1589	181	24	seaf	seaf	ADJ
cana-1589	181	25	share	share	NOUN
cana-1589	181	26	the	the	DET
cana-1589	181	27	same	same	ADJ
cana-1589	181	28	session	session	NOUN
cana-1589	181	29	key	key	ADJ
cana-1589	181	30	kseaf	kseaf	NOUN
cana-1589	181	31	.	.	PUNCT
cana-1589	182	1	an	an	DET
cana-1589	182	2	optional	optional	ADJ
cana-1589	182	3	eap	eap	NOUN
cana-1589	182	4	(	(	PUNCT
cana-1589	182	5	extensible	extensible	ADJ
cana-1589	182	6	authentication	authentication	NOUN
cana-1589	182	7	protocol	protocol	NOUN
cana-1589	182	8	)	)	PUNCT
cana-1589	182	9	procedure	procedure	NOUN
cana-1589	182	10	follows	follow	VERB
cana-1589	182	11	message	message	NOUN
cana-1589	182	12	-	-	PUNCT
cana-1589	182	13	m8	m8	NOUN
cana-1589	182	14	,	,	PUNCT
cana-1589	182	15	where	where	SCONJ
cana-1589	182	16	seaf	seaf	NOUN
cana-1589	182	17	sends	send	VERB
cana-1589	182	18	an	an	DET
cana-1589	182	19	n1	n1	ADJ
cana-1589	182	20	message	message	NOUN
cana-1589	182	21	(	(	PUNCT
cana-1589	182	22	eap	eap	NOUN
cana-1589	182	23	success	success	NOUN
cana-1589	182	24	)	)	PUNCT
cana-1589	182	25	to	to	PART
cana-1589	182	26	ue	ue	PROPN
cana-1589	182	27	with	with	ADP
cana-1589	182	28	kgnb	kgnb	NOUN
cana-1589	182	29	in	in	ADP
cana-1589	182	30	messagem10	messagem10	NOUN
cana-1589	182	31	.	.	PUNCT
cana-1589	183	1	the	the	DET
cana-1589	183	2	security	security	NOUN
cana-1589	183	3	of	of	ADP
cana-1589	183	4	the	the	DET
cana-1589	183	5	protocol	protocol	NOUN
cana-1589	183	6	has	have	AUX
cana-1589	183	7	been	be	AUX
cana-1589	183	8	verified	verify	VERB
cana-1589	183	9	using	use	VERB
cana-1589	183	10	proverif	proverif	NOUN
cana-1589	183	11	,	,	PUNCT
cana-1589	183	12	a	a	DET
cana-1589	183	13	cryptographic	cryptographic	ADJ
cana-1589	183	14	verifier	verifier	NOUN
cana-1589	183	15	based	base	VERB
cana-1589	183	16	on	on	ADP
cana-1589	183	17	the	the	DET
cana-1589	183	18	dolev	dolev	ADJ
cana-1589	183	19	-	-	PUNCT
cana-1589	183	20	yao	yao	NOUN
cana-1589	183	21	model	model	NOUN
cana-1589	183	22	.	.	PUNCT
cana-1589	184	1	proverif	proverif	PROPN
cana-1589	184	2	,	,	PUNCT
cana-1589	184	3	which	which	PRON
cana-1589	184	4	uses	use	VERB
cana-1589	184	5	a	a	DET
cana-1589	184	6	modified	modify	VERB
cana-1589	184	7	form	form	NOUN
cana-1589	184	8	of	of	ADP
cana-1589	184	9	pi	pi	NOUN
cana-1589	184	10	-	-	PUNCT
cana-1589	184	11	calculus	calculus	NOUN
cana-1589	184	12	,	,	PUNCT
cana-1589	184	13	assesses	assess	VERB
cana-1589	184	14	secrecy	secrecy	NOUN
cana-1589	184	15	and	and	CCONJ
cana-1589	184	16	authentication	authentication	NOUN
cana-1589	184	17	properties	property	NOUN
cana-1589	184	18	.	.	PUNCT
cana-1589	185	1	the	the	DET
cana-1589	185	2	absence	absence	NOUN
cana-1589	185	3	of	of	ADP
cana-1589	185	4	detected	detect	VERB
cana-1589	185	5	attacks	attack	NOUN
cana-1589	185	6	indicates	indicate	VERB
cana-1589	185	7	that	that	SCONJ
cana-1589	185	8	the	the	DET
cana-1589	185	9	subscriber	subscriber	NOUN
cana-1589	185	10	identity	identity	NOUN
cana-1589	185	11	can	can	AUX
cana-1589	185	12	be	be	AUX
cana-1589	185	13	securely	securely	ADV
cana-1589	185	14	transferred	transfer	VERB
cana-1589	185	15	across	across	ADP
cana-1589	185	16	insecure	insecure	ADJ
cana-1589	185	17	channels	channel	NOUN
cana-1589	185	18	between	between	ADP
cana-1589	185	19	network	network	NOUN
cana-1589	185	20	entities	entity	NOUN
cana-1589	185	21	.	.	PUNCT
cana-1589	186	1	even	even	ADV
cana-1589	186	2	if	if	SCONJ
cana-1589	186	3	an	an	DET
cana-1589	186	4	attacker	attacker	NOUN
cana-1589	186	5	controls	control	VERB
cana-1589	186	6	the	the	DET
cana-1589	186	7	channel	channel	NOUN
cana-1589	186	8	,	,	PUNCT
cana-1589	186	9	the	the	DET
cana-1589	186	10	subscriber	subscriber	NOUN
cana-1589	186	11	identity	identity	NOUN
cana-1589	186	12	and	and	CCONJ
cana-1589	186	13	other	other	ADJ
cana-1589	186	14	messages	message	NOUN
cana-1589	186	15	remain	remain	VERB
cana-1589	186	16	secure	secure	ADJ
cana-1589	186	17	.	.	PUNCT
cana-1589	187	1	communications	communication	NOUN
cana-1589	187	2	on	on	ADP
cana-1589	187	3	applied	apply	VERB
cana-1589	187	4	nonlinear	nonlinear	ADJ
cana-1589	187	5	analysis	analysis	NOUN
cana-1589	187	6	issn	issn	NOUN
cana-1589	187	7	:	:	PUNCT
cana-1589	187	8	1074	1074	NUM
cana-1589	187	9	-	-	PUNCT
cana-1589	187	10	133x	133x	NUM
cana-1589	187	11	vol	vol	NOUN
cana-1589	187	12	31	31	NUM
cana-1589	187	13	no	no	NOUN
cana-1589	187	14	.	.	PUNCT
cana-1589	188	1	7s	7	NOUN
cana-1589	188	2	(	(	PUNCT
cana-1589	188	3	2024	2024	NUM
cana-1589	188	4	)	)	PUNCT
cana-1589	188	5	705	705	NUM
cana-1589	189	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1589	189	2	5	5	NUM
cana-1589	189	3	.	.	PUNCT
cana-1589	189	4	discussion	discussion	NOUN
cana-1589	189	5	this	this	DET
cana-1589	189	6	paper	paper	NOUN
cana-1589	189	7	demonstrates	demonstrate	VERB
cana-1589	189	8	that	that	SCONJ
cana-1589	189	9	the	the	DET
cana-1589	189	10	ntru	ntru	ADJ
cana-1589	189	11	cryptosystem	cryptosystem	NOUN
cana-1589	189	12	is	be	AUX
cana-1589	189	13	one	one	NUM
cana-1589	189	14	of	of	ADP
cana-1589	189	15	the	the	DET
cana-1589	189	16	fastest	fast	ADJ
cana-1589	189	17	public	public	ADJ
cana-1589	189	18	key	key	ADJ
cana-1589	189	19	cryptosystems	cryptosystem	NOUN
cana-1589	189	20	,	,	PUNCT
cana-1589	189	21	offering	offer	VERB
cana-1589	189	22	various	various	ADJ
cana-1589	189	23	levels	level	NOUN
cana-1589	189	24	of	of	ADP
cana-1589	189	25	security	security	NOUN
cana-1589	189	26	at	at	ADP
cana-1589	189	27	high	high	ADJ
cana-1589	189	28	speeds	speed	NOUN
cana-1589	189	29	.	.	PUNCT
cana-1589	190	1	unlike	unlike	ADP
cana-1589	190	2	rsa	rsa	NOUN
cana-1589	190	3	and	and	CCONJ
cana-1589	190	4	similar	similar	ADJ
cana-1589	190	5	algorithms	algorithm	NOUN
cana-1589	190	6	,	,	PUNCT
cana-1589	190	7	which	which	PRON
cana-1589	190	8	are	be	AUX
cana-1589	190	9	vulnerable	vulnerable	ADJ
cana-1589	190	10	to	to	ADP
cana-1589	190	11	quantum	quantum	NOUN
cana-1589	190	12	computing	computing	NOUN
cana-1589	190	13	techniques	technique	NOUN
cana-1589	190	14	capable	capable	ADJ
cana-1589	190	15	of	of	ADP
cana-1589	190	16	factoring	factor	VERB
cana-1589	190	17	integers	integer	NOUN
cana-1589	190	18	and	and	CCONJ
cana-1589	190	19	computing	compute	VERB
cana-1589	190	20	discrete	discrete	ADJ
cana-1589	190	21	logarithms	logarithm	NOUN
cana-1589	190	22	in	in	ADP
cana-1589	190	23	polynomial	polynomial	ADJ
cana-1589	190	24	time	time	NOUN
cana-1589	190	25	,	,	PUNCT
cana-1589	190	26	ntru	ntru	PROPN
cana-1589	190	27	remains	remain	VERB
cana-1589	190	28	robust	robust	ADJ
cana-1589	190	29	.	.	PUNCT
cana-1589	191	1	the	the	DET
cana-1589	191	2	security	security	NOUN
cana-1589	191	3	of	of	ADP
cana-1589	191	4	ntru	ntru	PROPN
cana-1589	191	5	is	be	AUX
cana-1589	191	6	based	base	VERB
cana-1589	191	7	on	on	ADP
cana-1589	191	8	the	the	DET
cana-1589	191	9	challenging	challenging	ADJ
cana-1589	191	10	problem	problem	NOUN
cana-1589	191	11	of	of	ADP
cana-1589	191	12	lattice	lattice	NOUN
cana-1589	191	13	reduction	reduction	NOUN
cana-1589	191	14	,	,	PUNCT
cana-1589	191	15	making	make	VERB
cana-1589	191	16	it	it	PRON
cana-1589	191	17	resistant	resistant	ADJ
cana-1589	191	18	to	to	ADP
cana-1589	191	19	quantum	quantum	ADJ
cana-1589	191	20	computing	computing	NOUN
cana-1589	191	21	attacks	attack	NOUN
cana-1589	191	22	.	.	PUNCT
cana-1589	192	1	approved	approve	VERB
cana-1589	192	2	for	for	ADP
cana-1589	192	3	standardization	standardization	NOUN
cana-1589	192	4	by	by	ADP
cana-1589	192	5	ieee	ieee	NOUN
cana-1589	192	6	in	in	ADP
cana-1589	192	7	2009	2009	NUM
cana-1589	192	8	,	,	PUNCT
cana-1589	192	9	ntru	ntru	PROPN
cana-1589	192	10	offers	offer	VERB
cana-1589	192	11	strong	strong	ADJ
cana-1589	192	12	security	security	NOUN
cana-1589	192	13	even	even	ADV
cana-1589	192	14	on	on	ADP
cana-1589	192	15	devices	device	NOUN
cana-1589	192	16	with	with	ADP
cana-1589	192	17	constrained	constrained	ADJ
cana-1589	192	18	resources	resource	NOUN
cana-1589	192	19	,	,	PUNCT
cana-1589	192	20	where	where	SCONJ
cana-1589	192	21	computing	computing	NOUN
cana-1589	192	22	power	power	NOUN
cana-1589	192	23	bandwidth	bandwidth	NOUN
cana-1589	192	24	and	and	CCONJ
cana-1589	192	25	storage	storage	NOUN
cana-1589	192	26	are	be	AUX
cana-1589	192	27	limited	limited	ADJ
cana-1589	192	28	.	.	PUNCT
cana-1589	193	1	it	it	PRON
cana-1589	193	2	is	be	AUX
cana-1589	193	3	known	know	VERB
cana-1589	193	4	for	for	ADP
cana-1589	193	5	its	its	PRON
cana-1589	193	6	low	low	ADJ
cana-1589	193	7	cpu	cpu	NOUN
cana-1589	193	8	and	and	CCONJ
cana-1589	193	9	battery	battery	NOUN
cana-1589	193	10	consumption	consumption	NOUN
cana-1589	193	11	,	,	PUNCT
cana-1589	193	12	reducing	reduce	VERB
cana-1589	193	13	server	server	NOUN
cana-1589	193	14	utilization	utilization	NOUN
cana-1589	193	15	significantly	significantly	ADV
cana-1589	193	16	.	.	PUNCT
cana-1589	194	1	ntru	ntru	PROPN
cana-1589	194	2	's	's	PART
cana-1589	194	3	efficiency	efficiency	NOUN
cana-1589	194	4	surpasses	surpass	VERB
cana-1589	194	5	that	that	PRON
cana-1589	194	6	of	of	ADP
cana-1589	194	7	other	other	ADJ
cana-1589	194	8	public	public	ADJ
cana-1589	194	9	key	key	ADJ
cana-1589	194	10	cryptosystems	cryptosystem	NOUN
cana-1589	194	11	in	in	ADP
cana-1589	194	12	both	both	DET
cana-1589	194	13	hardware	hardware	NOUN
cana-1589	194	14	and	and	CCONJ
cana-1589	194	15	software	software	NOUN
cana-1589	194	16	implementations	implementation	NOUN
cana-1589	194	17	.	.	PUNCT
cana-1589	195	1	the	the	DET
cana-1589	195	2	proposed	propose	VERB
cana-1589	195	3	aka	aka	ADV
cana-1589	195	4	protocol	protocol	NOUN
cana-1589	195	5	,	,	PUNCT
cana-1589	195	6	which	which	PRON
cana-1589	195	7	leverages	leverage	VERB
cana-1589	195	8	the	the	DET
cana-1589	195	9	ntru	ntru	ADJ
cana-1589	195	10	cryptosystem	cryptosystem	NOUN
cana-1589	195	11	,	,	PUNCT
cana-1589	195	12	ensures	ensure	VERB
cana-1589	195	13	the	the	DET
cana-1589	195	14	confidentiality	confidentiality	NOUN
cana-1589	195	15	of	of	ADP
cana-1589	195	16	subscriber	subscriber	NOUN
cana-1589	195	17	identities	identity	NOUN
cana-1589	195	18	and	and	CCONJ
cana-1589	195	19	other	other	ADJ
cana-1589	195	20	messages	message	NOUN
cana-1589	195	21	within	within	ADP
cana-1589	195	22	wireless	wireless	ADJ
cana-1589	195	23	communication	communication	NOUN
cana-1589	195	24	networks	network	NOUN
cana-1589	195	25	.	.	PUNCT
cana-1589	196	1	we	we	PRON
cana-1589	196	2	used	use	VERB
cana-1589	196	3	the	the	DET
cana-1589	196	4	proverif	proverif	ADJ
cana-1589	196	5	tool	tool	NOUN
cana-1589	196	6	to	to	PART
cana-1589	196	7	validate	validate	VERB
cana-1589	196	8	this	this	DET
cana-1589	196	9	approach	approach	NOUN
cana-1589	196	10	.	.	PUNCT
cana-1589	197	1	while	while	SCONJ
cana-1589	197	2	the	the	DET
cana-1589	197	3	ntru	ntru	PROPN
cana-1589	197	4	-	-	PUNCT
cana-1589	197	5	based	base	VERB
cana-1589	197	6	solution	solution	NOUN
cana-1589	197	7	may	may	AUX
cana-1589	197	8	introduce	introduce	VERB
cana-1589	197	9	more	more	ADJ
cana-1589	197	10	delay	delay	NOUN
cana-1589	197	11	compared	compare	VERB
cana-1589	197	12	to	to	ADP
cana-1589	197	13	existing	exist	VERB
cana-1589	197	14	methods	method	NOUN
cana-1589	197	15	,	,	PUNCT
cana-1589	197	16	it	it	PRON
cana-1589	197	17	provides	provide	VERB
cana-1589	197	18	enhanced	enhanced	ADJ
cana-1589	197	19	security	security	NOUN
cana-1589	197	20	.	.	PUNCT
cana-1589	198	1	this	this	PRON
cana-1589	198	2	highlights	highlight	VERB
cana-1589	198	3	a	a	DET
cana-1589	198	4	trade	trade	NOUN
cana-1589	198	5	-	-	PUNCT
cana-1589	198	6	off	off	NOUN
cana-1589	198	7	between	between	ADP
cana-1589	198	8	security	security	NOUN
cana-1589	198	9	and	and	CCONJ
cana-1589	198	10	computational	computational	ADJ
cana-1589	198	11	overhead	overhead	NOUN
cana-1589	198	12	,	,	PUNCT
cana-1589	198	13	but	but	CCONJ
cana-1589	198	14	ultimately	ultimately	ADV
cana-1589	198	15	,	,	PUNCT
cana-1589	198	16	the	the	DET
cana-1589	198	17	improved	improved	ADJ
cana-1589	198	18	security	security	NOUN
cana-1589	198	19	justifies	justify	VERB
cana-1589	198	20	the	the	DET
cana-1589	198	21	added	add	VERB
cana-1589	198	22	computational	computational	ADJ
cana-1589	198	23	cost	cost	NOUN
cana-1589	198	24	.	.	PUNCT
cana-1589	199	1	acknowledgement	acknowledgement	NOUN
cana-1589	199	2	we	we	PRON
cana-1589	199	3	would	would	AUX
cana-1589	199	4	like	like	VERB
cana-1589	199	5	to	to	PART
cana-1589	199	6	convey	convey	VERB
cana-1589	199	7	our	our	PRON
cana-1589	199	8	sincere	sincere	ADJ
cana-1589	199	9	thanks	thank	NOUN
cana-1589	199	10	to	to	ADP
cana-1589	199	11	dr	dr	PROPN
cana-1589	199	12	.	.	PROPN
cana-1589	200	1	k	k	PROPN
cana-1589	200	2	r	r	PROPN
cana-1589	200	3	parmar	parmar	PROPN
cana-1589	200	4	and	and	CCONJ
cana-1589	200	5	dr	dr	PROPN
cana-1589	200	6	.	.	PROPN
cana-1589	200	7	a.	a.	PROPN
cana-1589	200	8	kulshreshta	kulshreshta	PROPN
cana-1589	200	9	for	for	ADP
cana-1589	200	10	their	their	PRON
cana-1589	200	11	guidance	guidance	NOUN
cana-1589	200	12	and	and	CCONJ
cana-1589	200	13	support	support	NOUN
cana-1589	200	14	.	.	PUNCT
cana-1589	201	1	conflicts	conflict	NOUN
cana-1589	201	2	of	of	ADP
cana-1589	201	3	interest	interest	NOUN
cana-1589	201	4	“	"	PUNCT
cana-1589	201	5	the	the	DET
cana-1589	201	6	authors	author	NOUN
cana-1589	201	7	declare	declare	VERB
cana-1589	201	8	that	that	SCONJ
cana-1589	201	9	there	there	PRON
cana-1589	201	10	is	be	VERB
cana-1589	201	11	no	no	DET
cana-1589	201	12	conflict	conflict	NOUN
cana-1589	201	13	of	of	ADP
cana-1589	201	14	interest	interest	NOUN
cana-1589	201	15	regarding	regard	VERB
cana-1589	201	16	the	the	DET
cana-1589	201	17	publication	publication	NOUN
cana-1589	201	18	of	of	ADP
cana-1589	201	19	this	this	DET
cana-1589	201	20	paper	paper	NOUN
cana-1589	201	21	.	.	PUNCT
cana-1589	201	22	”	"	PUNCT
cana-1589	202	1	references	reference	NOUN
cana-1589	202	2	[	[	X
cana-1589	202	3	1	1	NUM
cana-1589	202	4	]	]	X
cana-1589	202	5	3gpp	3gpp	NUM
cana-1589	202	6	,	,	PUNCT
cana-1589	202	7	“	"	PUNCT
cana-1589	202	8	security	security	NOUN
cana-1589	202	9	architecture	architecture	NOUN
cana-1589	202	10	and	and	CCONJ
cana-1589	202	11	procedures	procedure	NOUN
cana-1589	202	12	for	for	ADP
cana-1589	202	13	the	the	DET
cana-1589	202	14	5	5	NUM
cana-1589	202	15	g	g	NOUN
cana-1589	202	16	system	system	NOUN
cana-1589	202	17	”	"	PUNCT
cana-1589	202	18	,	,	PUNCT
cana-1589	202	19	3gpp	3gpp	PROPN
cana-1589	202	20	ts	ts	ADP
cana-1589	202	21	33.501	33.501	NUM
cana-1589	202	22	version	version	NOUN
cana-1589	202	23	15.2.0	15.2.0	NUM
cana-1589	202	24	.	.	PUNCT
cana-1589	203	1	technical	technical	ADJ
cana-1589	203	2	report	report	PROPN
cana-1589	203	3	,	,	PUNCT
cana-1589	203	4	the	the	DET
cana-1589	203	5	3rd	3rd	ADJ
cana-1589	203	6	generation	generation	NOUN
cana-1589	203	7	partnership	partnership	NOUN
cana-1589	203	8	project	project	NOUN
cana-1589	203	9	.	.	PUNCT
cana-1589	204	1	[	[	X
cana-1589	204	2	2	2	NUM
cana-1589	204	3	]	]	PUNCT
cana-1589	204	4	alese	alese	PROPN
cana-1589	204	5	,	,	PUNCT
cana-1589	204	6	b.	b.	PROPN
cana-1589	204	7	k.	k.	PROPN
cana-1589	204	8	,	,	PUNCT
cana-1589	204	9	philemon	philemon	PROPN
cana-1589	204	10	e.	e.	PROPN
cana-1589	204	11	d.	d.	PROPN
cana-1589	204	12	,	,	PUNCT
cana-1589	204	13	falaki	falaki	PROPN
cana-1589	204	14	,	,	PUNCT
cana-1589	204	15	s.	s.	PROPN
cana-1589	204	16	o.	o.	PROPN
cana-1589	204	17	,	,	PUNCT
cana-1589	204	18	“	"	PUNCT
cana-1589	204	19	comparative	comparative	ADJ
cana-1589	204	20	analysis	analysis	NOUN
cana-1589	204	21	of	of	ADP
cana-1589	204	22	public	public	ADJ
cana-1589	204	23	-	-	PUNCT
cana-1589	204	24	key	key	NOUN
cana-1589	204	25	encryption	encryption	NOUN
cana-1589	204	26	schemes	scheme	NOUN
cana-1589	204	27	”	"	PUNCT
cana-1589	204	28	,	,	PUNCT
cana-1589	204	29	international	international	ADJ
cana-1589	204	30	journal	journal	NOUN
cana-1589	204	31	of	of	ADP
cana-1589	204	32	engineering	engineering	NOUN
cana-1589	204	33	and	and	CCONJ
cana-1589	204	34	technology	technology	NOUN
cana-1589	204	35	,	,	PUNCT
cana-1589	204	36	volume	volume	NOUN
cana-1589	204	37	2	2	NUM
cana-1589	204	38	,	,	PUNCT
cana-1589	204	39	no	no	INTJ
cana-1589	204	40	.	.	NOUN
cana-1589	204	41	9	9	NUM
cana-1589	204	42	,	,	PUNCT
cana-1589	204	43	september	september	PROPN
cana-1589	204	44	2012	2012	NUM
cana-1589	204	45	.	.	PUNCT
cana-1589	205	1	[	[	X
cana-1589	205	2	3	3	NUM
cana-1589	205	3	]	]	X
cana-1589	205	4	giripunje	giripunje	PROPN
cana-1589	205	5	lokesh	lokesh	PROPN
cana-1589	205	6	,	,	PUNCT
cana-1589	205	7	nimbhorkar	nimbhorkar	PROPN
cana-1589	205	8	sonali	sonali	PROPN
cana-1589	205	9	,	,	PUNCT
cana-1589	205	10	“	"	PUNCT
cana-1589	205	11	comprehensive	comprehensive	ADJ
cana-1589	205	12	security	security	NOUN
cana-1589	205	13	system	system	NOUN
cana-1589	205	14	for	for	ADP
cana-1589	205	15	mobile	mobile	ADJ
cana-1589	205	16	network	network	NOUN
cana-1589	205	17	using	use	VERB
cana-1589	205	18	elliptic	elliptic	ADJ
cana-1589	205	19	curve	curve	NOUN
cana-1589	205	20	cryptography	cryptography	NOUN
cana-1589	205	21	over	over	ADP
cana-1589	205	22	gf	gf	PROPN
cana-1589	205	23	(	(	PUNCT
cana-1589	205	24	p	p	NOUN
cana-1589	205	25	)	)	PUNCT
cana-1589	205	26	”	"	PUNCT
cana-1589	205	27	,	,	PUNCT
cana-1589	205	28	international	international	ADJ
cana-1589	205	29	journal	journal	NOUN
cana-1589	205	30	of	of	ADP
cana-1589	205	31	advanced	advanced	ADJ
cana-1589	205	32	research	research	NOUN
cana-1589	205	33	in	in	ADP
cana-1589	205	34	computer	computer	NOUN
cana-1589	205	35	science	science	NOUN
cana-1589	205	36	and	and	CCONJ
cana-1589	205	37	software	software	NOUN
cana-1589	205	38	engineering	engineering	NOUN
cana-1589	205	39	,	,	PUNCT
cana-1589	205	40	volume	volume	NOUN
cana-1589	205	41	3	3	NUM
cana-1589	205	42	,	,	PUNCT
cana-1589	205	43	issue	issue	NOUN
cana-1589	205	44	5	5	NUM
cana-1589	205	45	,	,	PUNCT
cana-1589	205	46	may	may	AUX
cana-1589	205	47	2013	2013	NUM
cana-1589	205	48	.	.	PUNCT
cana-1589	206	1	[	[	X
cana-1589	206	2	4	4	NUM
cana-1589	206	3	]	]	PUNCT
cana-1589	206	4	pallipamu	pallipamu	ADJ
cana-1589	206	5	venkateswara	venkateswara	PROPN
cana-1589	206	6	rao	rao	PROPN
cana-1589	206	7	,	,	PUNCT
cana-1589	206	8	k	k	PROPN
cana-1589	206	9	thammi	thammi	PROPN
cana-1589	206	10	reddy	reddy	PROPN
cana-1589	206	11	,	,	PUNCT
cana-1589	206	12	p	p	PROPN
cana-1589	206	13	suresh	suresh	PROPN
cana-1589	206	14	varma	varma	PROPN
cana-1589	206	15	“	"	PUNCT
cana-1589	206	16	a	a	DET
cana-1589	206	17	survey	survey	NOUN
cana-1589	206	18	on	on	ADP
cana-1589	206	19	digital	digital	ADJ
cana-1589	206	20	signatures	signature	NOUN
cana-1589	206	21	”	"	PUNCT
cana-1589	206	22	,	,	PUNCT
cana-1589	206	23	international	international	ADJ
cana-1589	206	24	journal	journal	NOUN
cana-1589	206	25	of	of	ADP
cana-1589	206	26	advanced	advanced	ADJ
cana-1589	206	27	research	research	NOUN
cana-1589	206	28	in	in	ADP
cana-1589	206	29	computer	computer	NOUN
cana-1589	206	30	and	and	CCONJ
cana-1589	206	31	communication	communication	NOUN
cana-1589	206	32	engineering	engineering	NOUN
cana-1589	206	33	,	,	PUNCT
cana-1589	206	34	volume	volume	NOUN
cana-1589	206	35	3	3	NUM
cana-1589	206	36	,	,	PUNCT
cana-1589	206	37	issue	issue	NOUN
cana-1589	206	38	6	6	NUM
cana-1589	206	39	,	,	PUNCT
cana-1589	206	40	june	june	PROPN
cana-1589	206	41	2014	2014	NUM
cana-1589	207	1	[	[	X
cana-1589	207	2	5	5	NUM
cana-1589	207	3	]	]	SYM
cana-1589	207	4	hoffstein	hoffstein	NOUN
cana-1589	207	5	,	,	PUNCT
cana-1589	207	6	j.	j.	PROPN
cana-1589	207	7	,	,	PUNCT
cana-1589	207	8	lieman	lieman	PROPN
cana-1589	207	9	,	,	PUNCT
cana-1589	207	10	d.	d.	PROPN
cana-1589	207	11	,	,	PUNCT
cana-1589	207	12	pipher	pipher	PROPN
cana-1589	207	13	,	,	PUNCT
cana-1589	207	14	j.	j.	PROPN
cana-1589	207	15	and	and	CCONJ
cana-1589	207	16	silverman	silverman	PROPN
cana-1589	207	17	,	,	PUNCT
cana-1589	207	18	j.h	j.h	PROPN
cana-1589	207	19	.	.	PROPN
cana-1589	207	20	,	,	PUNCT
cana-1589	207	21	“	"	PUNCT
cana-1589	207	22	ntru	ntru	PROPN
cana-1589	207	23	:	:	PUNCT
cana-1589	207	24	a	a	DET
cana-1589	207	25	ring	ring	NOUN
cana-1589	207	26	-	-	PUNCT
cana-1589	207	27	based	base	VERB
cana-1589	207	28	public	public	ADJ
cana-1589	207	29	key	key	ADJ
cana-1589	207	30	cryptosystem	cryptosystem	NOUN
cana-1589	207	31	”	"	PUNCT
cana-1589	207	32	available	available	ADJ
cana-1589	207	33	online	online	ADV
cana-1589	207	34	on	on	ADP
cana-1589	207	35	www.ntru.org	www.ntru.org	NOUN
cana-1589	207	36	.	.	PUNCT
cana-1589	208	1	[	[	X
cana-1589	208	2	6	6	NUM
cana-1589	208	3	]	]	SYM
cana-1589	208	4	hoffstein	hoffstein	NOUN
cana-1589	208	5	,	,	PUNCT
cana-1589	208	6	j.	j.	PROPN
cana-1589	208	7	,	,	PUNCT
cana-1589	208	8	lieman	lieman	PROPN
cana-1589	208	9	,	,	PUNCT
cana-1589	208	10	d.	d.	PROPN
cana-1589	208	11	,	,	PUNCT
cana-1589	208	12	pipher	pipher	PROPN
cana-1589	208	13	,	,	PUNCT
cana-1589	208	14	j.	j.	PROPN
cana-1589	208	15	and	and	CCONJ
cana-1589	208	16	silverman	silverman	PROPN
cana-1589	208	17	,	,	PUNCT
cana-1589	208	18	j.h	j.h	PROPN
cana-1589	208	19	.	.	PROPN
cana-1589	208	20	,	,	PUNCT
cana-1589	208	21	“	"	PUNCT
cana-1589	208	22	ntru	ntru	PROPN
cana-1589	208	23	:	:	PUNCT
cana-1589	208	24	a	a	DET
cana-1589	208	25	public	public	ADJ
cana-1589	208	26	key	key	ADJ
cana-1589	208	27	cryptosystem	cryptosystem	NOUN
cana-1589	208	28	”	"	PUNCT
cana-1589	208	29	.	.	PUNCT
cana-1589	209	1	http://grouper.ieee.org/	http://grouper.ieee.org/	PROPN
cana-1589	209	2	groups/1363	groups/1363	PROPN
cana-1589	209	3	/	/	SYM
cana-1589	209	4	lattpk	lattpk	PROPN
cana-1589	209	5	/	/	SYM
cana-1589	209	6	submissions.html#ntru1	submissions.html#ntru1	VERB
cana-1589	210	1	[	[	X
cana-1589	210	2	7	7	X
cana-1589	210	3	]	]	PUNCT
cana-1589	210	4	hien	hien	PROPN
cana-1589	210	5	ba	ba	PROPN
cana-1589	210	6	nguyen	nguyen	PROPN
cana-1589	210	7	,	,	PUNCT
cana-1589	210	8	thesis	thesis	NOUN
cana-1589	210	9	on	on	ADP
cana-1589	210	10	“	"	PUNCT
cana-1589	210	11	an	an	DET
cana-1589	210	12	overview	overview	NOUN
cana-1589	210	13	of	of	ADP
cana-1589	210	14	the	the	DET
cana-1589	210	15	ntru	ntru	ADJ
cana-1589	210	16	cryptographic	cryptographic	ADJ
cana-1589	210	17	system	system	NOUN
cana-1589	210	18	”	"	PUNCT
cana-1589	210	19	,	,	PUNCT
cana-1589	210	20	san	san	PROPN
cana-1589	210	21	diego	diego	PROPN
cana-1589	210	22	state	state	PROPN
cana-1589	210	23	university	university	PROPN
cana-1589	210	24	,	,	PUNCT
cana-1589	210	25	2014	2014	NUM
cana-1589	210	26	.	.	PUNCT
cana-1589	211	1	[	[	X
cana-1589	211	2	8	8	NUM
cana-1589	211	3	]	]	X
cana-1589	211	4	jover	jover	NOUN
cana-1589	211	5	r	r	PROPN
cana-1589	211	6	p	p	PROPN
cana-1589	211	7	,	,	PUNCT
cana-1589	211	8	marojevic	marojevic	ADJ
cana-1589	211	9	v	v	NOUN
cana-1589	211	10	,	,	PUNCT
cana-1589	211	11	“	"	PUNCT
cana-1589	211	12	security	security	NOUN
cana-1589	211	13	and	and	CCONJ
cana-1589	211	14	protocol	protocol	NOUN
cana-1589	211	15	exploit	exploit	VERB
cana-1589	211	16	analysis	analysis	NOUN
cana-1589	211	17	of	of	ADP
cana-1589	211	18	the	the	DET
cana-1589	211	19	5	5	NUM
cana-1589	211	20	g	g	NOUN
cana-1589	211	21	specifications	specification	NOUN
cana-1589	211	22	”	"	PUNCT
cana-1589	211	23	,	,	PUNCT
cana-1589	211	24	ieee	ieee	NOUN
cana-1589	211	25	access	access	NOUN
cana-1589	211	26	2019	2019	NUM
cana-1589	211	27	,	,	PUNCT
cana-1589	211	28	7	7	NUM
cana-1589	211	29	,	,	PUNCT
cana-1589	211	30	24956–24963	24956–24963	NUM
cana-1589	211	31	.	.	PUNCT
cana-1589	212	1	[	[	X
cana-1589	212	2	9	9	NUM
cana-1589	212	3	]	]	X
cana-1589	212	4	ahmad	ahmad	PROPN
cana-1589	212	5	i	i	PRON
cana-1589	212	6	,	,	PUNCT
cana-1589	212	7	shahabuddin	shahabuddin	VERB
cana-1589	212	8	s	s	PRON
cana-1589	212	9	,	,	PUNCT
cana-1589	212	10	kumar	kumar	PROPN
cana-1589	212	11	t	t	PROPN
cana-1589	212	12	,	,	PUNCT
cana-1589	212	13	okwuibe	okwuibe	PROPN
cana-1589	212	14	,	,	PUNCT
cana-1589	212	15	j	j	PROPN
cana-1589	212	16	,	,	PUNCT
cana-1589	212	17	ylianttila	ylianttila	NOUN
cana-1589	212	18	m	m	PROPN
cana-1589	212	19	,	,	PUNCT
cana-1589	212	20	“	"	PUNCT
cana-1589	212	21	security	security	NOUN
cana-1589	212	22	for	for	ADP
cana-1589	212	23	5	5	NUM
cana-1589	212	24	g	g	NOUN
cana-1589	212	25	and	and	CCONJ
cana-1589	212	26	beyond	beyond	ADP
cana-1589	212	27	”	"	PUNCT
cana-1589	212	28	,	,	PUNCT
cana-1589	212	29	ieee	ieee	PROPN
cana-1589	212	30	commun	commun	PROPN
cana-1589	212	31	.	.	PUNCT
cana-1589	213	1	surv	surv	PROPN
cana-1589	213	2	.	.	PUNCT
cana-1589	214	1	tutor	tutor	NOUN
cana-1589	214	2	.	.	PUNCT
cana-1589	215	1	2019	2019	NUM
cana-1589	215	2	,	,	PUNCT
cana-1589	215	3	21	21	NUM
cana-1589	215	4	,	,	PUNCT
cana-1589	215	5	3682–3722	3682–3722	NUM
cana-1589	215	6	.	.	PUNCT
cana-1589	216	1	[	[	X
cana-1589	216	2	10	10	NUM
cana-1589	216	3	]	]	X
cana-1589	216	4	hu	hu	PROPN
cana-1589	216	5	x.	x.	PROPN
cana-1589	216	6	,	,	PUNCT
cana-1589	216	7	liu	liu	PROPN
cana-1589	216	8	c.	c.	PROPN
cana-1589	216	9	,	,	PUNCT
cana-1589	216	10	liu	liu	PROPN
cana-1589	216	11	s.	s.	PROPN
cana-1589	216	12	,	,	PUNCT
cana-1589	216	13	li	li	PROPN
cana-1589	216	14	j.	j.	PROPN
cana-1589	216	15	,	,	PUNCT
cana-1589	216	16	cheng	cheng	PROPN
cana-1589	216	17	x.	x.	PROPN
cana-1589	216	18	,	,	PUNCT
cana-1589	216	19	“	"	PUNCT
cana-1589	216	20	a	a	DET
cana-1589	216	21	vulnerability	vulnerability	NOUN
cana-1589	216	22	in	in	ADP
cana-1589	216	23	5	5	NUM
cana-1589	216	24	g	g	NOUN
cana-1589	216	25	authentication	authentication	NOUN
cana-1589	216	26	protocols	protocol	NOUN
cana-1589	216	27	and	and	CCONJ
cana-1589	216	28	its	its	PRON
cana-1589	216	29	countermeasure	countermeasure	NOUN
cana-1589	216	30	”	"	PUNCT
cana-1589	216	31	,	,	PUNCT
cana-1589	216	32	ieice	ieice	PROPN
cana-1589	216	33	trans	trans	PROPN
cana-1589	216	34	.	.	PROPN
cana-1589	216	35	inf	inf	PROPN
cana-1589	216	36	.	.	PUNCT
cana-1589	216	37	syst	syst	PROPN
cana-1589	216	38	.	.	PUNCT
cana-1589	216	39	2020	2020	NUM
cana-1589	216	40	,	,	PUNCT
cana-1589	216	41	103	103	NUM
cana-1589	216	42	,	,	PUNCT
cana-1589	216	43	1806–1809	1806–1809	NUM
cana-1589	216	44	.	.	PUNCT
cana-1589	217	1	[	[	X
cana-1589	217	2	11	11	NUM
cana-1589	217	3	]	]	X
cana-1589	217	4	khan	khan	PROPN
cana-1589	217	5	h.	h.	PROPN
cana-1589	217	6	,	,	PUNCT
cana-1589	217	7	martin	martin	PROPN
cana-1589	217	8	k.m	k.m	PROPN
cana-1589	217	9	.	.	PROPN
cana-1589	217	10	,	,	PUNCT
cana-1589	217	11	“	"	PUNCT
cana-1589	217	12	a	a	DET
cana-1589	217	13	survey	survey	NOUN
cana-1589	217	14	of	of	ADP
cana-1589	217	15	subscription	subscription	NOUN
cana-1589	217	16	privacy	privacy	NOUN
cana-1589	217	17	on	on	ADP
cana-1589	217	18	the	the	DET
cana-1589	217	19	5	5	NUM
cana-1589	217	20	g	g	NOUN
cana-1589	217	21	radio	radio	NOUN
cana-1589	217	22	interface	interface	NOUN
cana-1589	217	23	-	-	PUNCT
cana-1589	217	24	the	the	DET
cana-1589	217	25	past	past	NOUN
cana-1589	217	26	,	,	PUNCT
cana-1589	217	27	present	present	ADJ
cana-1589	217	28	and	and	CCONJ
cana-1589	217	29	future	future	ADJ
cana-1589	217	30	”	"	PUNCT
cana-1589	217	31	,	,	PUNCT
cana-1589	217	32	j.	j.	PROPN
cana-1589	217	33	inf	inf	PROPN
cana-1589	217	34	.	.	PUNCT
cana-1589	217	35	secure	secure	PROPN
cana-1589	217	36	.	.	PUNCT
cana-1589	218	1	appl	appl	PROPN
cana-1589	218	2	.	.	PUNCT
cana-1589	219	1	2020	2020	NUM
cana-1589	219	2	,	,	PUNCT
cana-1589	219	3	53	53	NUM
cana-1589	219	4	,	,	PUNCT
cana-1589	219	5	102537	102537	NUM
cana-1589	219	6	.	.	PUNCT
cana-1589	220	1	[	[	X
cana-1589	220	2	12	12	NUM
cana-1589	220	3	]	]	PUNCT
cana-1589	220	4	blanchet	blanchet	PROPN
cana-1589	220	5	,	,	PUNCT
cana-1589	220	6	b.	b.	PROPN
cana-1589	220	7	;	;	PUNCT
cana-1589	220	8	smyth	smyth	PROPN
cana-1589	220	9	,	,	PUNCT
cana-1589	220	10	b.	b.	PROPN
cana-1589	220	11	;	;	PUNCT
cana-1589	220	12	cheval	cheval	NOUN
cana-1589	220	13	,	,	PUNCT
cana-1589	220	14	v.	v.	PROPN
cana-1589	220	15	;	;	PUNCT
cana-1589	220	16	sylvestre	sylvestre	NOUN
cana-1589	220	17	,	,	PUNCT
cana-1589	220	18	m.	m.	NOUN
cana-1589	220	19	“	"	PUNCT
cana-1589	220	20	proverif	proverif	VERB
cana-1589	220	21	2.05	2.05	NUM
cana-1589	220	22	:	:	PUNCT
cana-1589	220	23	automatic	automatic	ADJ
cana-1589	220	24	cryptographic	cryptographic	ADJ
cana-1589	220	25	protocol	protocol	NOUN
cana-1589	220	26	verifier	verifier	NOUN
cana-1589	220	27	,	,	PUNCT
cana-1589	220	28	user	user	NOUN
cana-1589	220	29	manual	manual	NOUN
cana-1589	220	30	and	and	CCONJ
cana-1589	220	31	tutorial	tutorial	NOUN
cana-1589	220	32	”	"	PUNCT
cana-1589	220	33	.	.	PUNCT
cana-1589	221	1	proverif	proverif	PROPN
cana-1589	221	2	user	user	PROPN
cana-1589	221	3	manual	manual	NOUN
cana-1589	221	4	,	,	PUNCT
cana-1589	221	5	2023	2023	NUM
cana-1589	221	6	.	.	PUNCT
cana-1589	222	1	https://bblanche.gitlabpages.inria.fr/proverif/	https://bblanche.gitlabpages.inria.fr/proverif/	PROPN