id	sid	tid	token	lemma	pos
cana-4287	1	1	communications	communication	NOUN
cana-4287	1	2	on	on	ADP
cana-4287	1	3	applied	apply	VERB
cana-4287	1	4	nonlinear	nonlinear	ADJ
cana-4287	1	5	analysis	analysis	NOUN
cana-4287	1	6	issn	issn	NOUN
cana-4287	1	7	:	:	PUNCT
cana-4287	1	8	1074	1074	NUM
cana-4287	1	9	-	-	PUNCT
cana-4287	1	10	133x	133x	NUM
cana-4287	1	11	vol	vol	NOUN
cana-4287	1	12	32	32	NUM
cana-4287	1	13	no	no	NOUN
cana-4287	1	14	.	.	PUNCT
cana-4287	2	1	9s	9s	NUM
cana-4287	2	2	(	(	PUNCT
cana-4287	2	3	2025	2025	NUM
cana-4287	2	4	)	)	PUNCT
cana-4287	2	5	1728	1728	NUM
cana-4287	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	2	7	algebraic	algebraic	ADJ
cana-4287	2	8	topology	topology	NOUN
cana-4287	2	9	in	in	ADP
cana-4287	2	10	modern	modern	ADJ
cana-4287	2	11	cryptography	cryptography	NOUN
cana-4287	2	12	:	:	PUNCT
cana-4287	2	13	bridging	bridge	VERB
cana-4287	2	14	abstract	abstract	ADJ
cana-4287	2	15	structures	structure	NOUN
cana-4287	2	16	with	with	ADP
cana-4287	2	17	secure	secure	ADJ
cana-4287	2	18	computation	computation	NOUN
cana-4287	2	19	1dr	1dr	NOUN
cana-4287	2	20	.	.	PUNCT
cana-4287	3	1	radheshyam	radheshyam	NOUN
cana-4287	3	2	r	r	PROPN
cana-4287	3	3	sharma	sharma	PROPN
cana-4287	3	4	,	,	PUNCT
cana-4287	3	5	2dr	2dr	NOUN
cana-4287	3	6	.	.	PUNCT
cana-4287	4	1	ramesh	ramesh	PROPN
cana-4287	4	2	babu	babu	PROPN
cana-4287	4	3	amarapu	amarapu	PROPN
cana-4287	4	4	,	,	PUNCT
cana-4287	4	5	3dr	3dr	NOUN
cana-4287	4	6	.	.	PUNCT
cana-4287	5	1	g.	g.	PROPN
cana-4287	5	2	arul	arul	PROPN
cana-4287	5	3	freeda	freeda	PROPN
cana-4287	5	4	vinodhini	vinodhini	PROPN
cana-4287	5	5	,	,	PUNCT
cana-4287	5	6	4dr	4dr	NOUN
cana-4287	5	7	.	.	PUNCT
cana-4287	6	1	akshaya	akshaya	PROPN
cana-4287	6	2	kumar	kumar	PROPN
cana-4287	6	3	panda	panda	NOUN
cana-4287	6	4	,	,	PUNCT
cana-4287	6	5	5	5	NUM
cana-4287	6	6	dr	dr	PROPN
cana-4287	6	7	.	.	PROPN
cana-4287	6	8	m.	m.	PROPN
cana-4287	6	9	srinivasa	srinivasa	PROPN
cana-4287	6	10	narayana	narayana	PROPN
cana-4287	6	11	,	,	PUNCT
cana-4287	6	12	6dr	6dr	NOUN
cana-4287	6	13	.	.	PUNCT
cana-4287	7	1	maddikera	maddikera	PROPN
cana-4287	7	2	kalyan	kalyan	PROPN
cana-4287	7	3	chakravarthi,7	chakravarthi,7	PROPN
cana-4287	7	4	*	*	PROPN
cana-4287	7	5	dr	dr	PROPN
cana-4287	7	6	.	.	PROPN
cana-4287	7	7	r.	r.	PROPN
cana-4287	7	8	k.	k.	PROPN
cana-4287	7	9	davala	davala	PROPN
cana-4287	7	10	1	1	NUM
cana-4287	7	11	assistant	assistant	NOUN
cana-4287	7	12	professor	professor	NOUN
cana-4287	7	13	of	of	ADP
cana-4287	7	14	mathematics	mathematics	PROPN
cana-4287	7	15	,	,	PUNCT
cana-4287	7	16	podar	podar	NOUN
cana-4287	7	17	world	world	PROPN
cana-4287	7	18	college	college	PROPN
cana-4287	7	19	,	,	PUNCT
cana-4287	7	20	mumbai	mumbai	PROPN
cana-4287	7	21	,	,	PUNCT
cana-4287	7	22	india	india	PROPN
cana-4287	7	23	,	,	PUNCT
cana-4287	7	24	pincode	pincode	PROPN
cana-4287	7	25	:	:	PUNCT
cana-4287	7	26	400049	400049	NUM
cana-4287	7	27	,	,	PUNCT
cana-4287	7	28	email	email	NOUN
cana-4287	8	1	i	i	PROPN
cana-4287	8	2	d	d	PROPN
cana-4287	8	3	:	:	PUNCT
cana-4287	8	4	mathematics.29@gmail.com	mathematics.29@gmail.com	PROPN
cana-4287	8	5	2	2	NUM
cana-4287	8	6	assistant	assistant	NOUN
cana-4287	8	7	professor	professor	NOUN
cana-4287	8	8	,	,	PUNCT
cana-4287	8	9	department	department	NOUN
cana-4287	8	10	of	of	ADP
cana-4287	8	11	engineering	engineering	NOUN
cana-4287	8	12	mathematics	mathematic	NOUN
cana-4287	8	13	,	,	PUNCT
cana-4287	8	14	anil	anil	PROPN
cana-4287	8	15	neerukonda	neerukonda	PROPN
cana-4287	8	16	institute	institute	PROPN
cana-4287	8	17	of	of	ADP
cana-4287	8	18	technology	technology	PROPN
cana-4287	8	19	and	and	CCONJ
cana-4287	8	20	sciences	science	NOUN
cana-4287	8	21	(	(	PUNCT
cana-4287	8	22	a	a	NOUN
cana-4287	8	23	)	)	PUNCT
cana-4287	8	24	,	,	PUNCT
cana-4287	8	25	sangivalasa	sangivalasa	PROPN
cana-4287	8	26	,	,	PUNCT
cana-4287	8	27	visakhapatnam	visakhapatnam	PROPN
cana-4287	8	28	,	,	PUNCT
cana-4287	8	29	andhra	andhra	PROPN
cana-4287	8	30	pradesh	pradesh	PROPN
cana-4287	8	31	,	,	PUNCT
cana-4287	8	32	india	india	PROPN
cana-4287	8	33	,	,	PUNCT
cana-4287	8	34	pincode	pincode	ADJ
cana-4287	8	35	:	:	PUNCT
cana-4287	8	36	531162	531162	NUM
cana-4287	8	37	,	,	PUNCT
cana-4287	8	38	email	email	NOUN
cana-4287	9	1	i	i	PROPN
cana-4287	9	2	d	d	PROPN
cana-4287	9	3	:	:	PUNCT
cana-4287	9	4	rameshamarapu.maths@anits.edu.in	rameshamarapu.maths@anits.edu.in	VERB
cana-4287	9	5	3	3	NUM
cana-4287	9	6	professor	professor	NOUN
cana-4287	9	7	,	,	PUNCT
cana-4287	9	8	department	department	NOUN
cana-4287	9	9	of	of	ADP
cana-4287	9	10	pure	pure	ADJ
cana-4287	9	11	and	and	CCONJ
cana-4287	9	12	applied	applied	ADJ
cana-4287	9	13	mathematics	mathematic	NOUN
cana-4287	9	14	,	,	PUNCT
cana-4287	9	15	saveetha	saveetha	PROPN
cana-4287	9	16	school	school	PROPN
cana-4287	9	17	of	of	ADP
cana-4287	9	18	engineering	engineering	NOUN
cana-4287	9	19	,	,	PUNCT
cana-4287	9	20	simats	simat	NOUN
cana-4287	9	21	,	,	PUNCT
cana-4287	9	22	chennai	chennai	PROPN
cana-4287	9	23	,	,	PUNCT
cana-4287	9	24	tamilnadu	tamilnadu	NOUN
cana-4287	9	25	,	,	PUNCT
cana-4287	9	26	india	india	PROPN
cana-4287	9	27	,	,	PUNCT
cana-4287	9	28	pincode	pincode	ADJ
cana-4287	9	29	:	:	PUNCT
cana-4287	9	30	600032	600032	NUM
cana-4287	9	31	,	,	PUNCT
cana-4287	9	32	email	email	NOUN
cana-4287	10	1	i	i	PROPN
cana-4287	10	2	d	d	PROPN
cana-4287	10	3	:	:	PUNCT
cana-4287	10	4	arulfreedavinodhini@saveetha.com	arulfreedavinodhini@saveetha.com	PROPN
cana-4287	10	5	4	4	NUM
cana-4287	10	6	assistant	assistant	NOUN
cana-4287	10	7	professor	professor	NOUN
cana-4287	10	8	,	,	PUNCT
cana-4287	10	9	school	school	NOUN
cana-4287	10	10	of	of	ADP
cana-4287	10	11	applied	apply	VERB
cana-4287	10	12	sciences	science	NOUN
cana-4287	10	13	,	,	PUNCT
cana-4287	10	14	mathematics	mathematic	NOUN
cana-4287	10	15	,	,	PUNCT
cana-4287	10	16	kalinga	kalinga	PROPN
cana-4287	10	17	institute	institute	PROPN
cana-4287	10	18	of	of	ADP
cana-4287	10	19	industrial	industrial	ADJ
cana-4287	10	20	technology	technology	NOUN
cana-4287	10	21	(	(	PUNCT
cana-4287	10	22	kiit	kiit	PROPN
cana-4287	10	23	)	)	PUNCT
cana-4287	10	24	,	,	PUNCT
cana-4287	10	25	deemed	deem	VERB
cana-4287	10	26	to	to	PART
cana-4287	10	27	be	be	AUX
cana-4287	10	28	university	university	NOUN
cana-4287	10	29	,	,	PUNCT
cana-4287	10	30	bhubaneswar	bhubaneswar	NOUN
cana-4287	10	31	,	,	PUNCT
cana-4287	10	32	odisha	odisha	PROPN
cana-4287	10	33	,	,	PUNCT
cana-4287	10	34	india	india	PROPN
cana-4287	10	35	,	,	PUNCT
cana-4287	10	36	pincode	pincode	ADJ
cana-4287	10	37	:	:	PUNCT
cana-4287	10	38	751024	751024	NUM
cana-4287	10	39	,	,	PUNCT
cana-4287	10	40	email	email	NOUN
cana-4287	10	41	i	i	PROPN
cana-4287	10	42	d	d	PROPN
cana-4287	10	43	:	:	PUNCT
cana-4287	10	44	akshaya.pandafma@kiit.ac.in	akshaya.pandafma@kiit.ac.in	NUM
cana-4287	10	45	5	5	NUM
cana-4287	10	46	professor	professor	NOUN
cana-4287	10	47	,	,	PUNCT
cana-4287	10	48	department	department	NOUN
cana-4287	10	49	of	of	ADP
cana-4287	10	50	cdoe	cdoe	PROPN
cana-4287	10	51	,	,	PUNCT
cana-4287	10	52	klef	klef	NOUN
cana-4287	10	53	,	,	PUNCT
cana-4287	10	54	vaddeswaram	vaddeswaram	NOUN
cana-4287	10	55	,	,	PUNCT
cana-4287	10	56	guntur	guntur	PROPN
cana-4287	10	57	,	,	PUNCT
cana-4287	10	58	andhra	andhra	PROPN
cana-4287	10	59	pradesh	pradesh	PROPN
cana-4287	10	60	,	,	PUNCT
cana-4287	10	61	india	india	PROPN
cana-4287	10	62	,	,	PUNCT
cana-4287	10	63	pincode	pincode	PROPN
cana-4287	10	64	:	:	PUNCT
cana-4287	10	65	522502	522502	NUM
cana-4287	10	66	,	,	PUNCT
cana-4287	10	67	email	email	NOUN
cana-4287	10	68	i	i	PROPN
cana-4287	10	69	d	d	PROPN
cana-4287	10	70	:	:	PUNCT
cana-4287	10	71	msn@kluniversity.in	msn@kluniversity.in	ADJ
cana-4287	10	72	6	6	NUM
cana-4287	10	73	senior	senior	ADJ
cana-4287	10	74	lecturer	lecturer	NOUN
cana-4287	10	75	,	,	PUNCT
cana-4287	10	76	department	department	NOUN
cana-4287	10	77	of	of	ADP
cana-4287	10	78	electronics	electronic	NOUN
cana-4287	10	79	and	and	CCONJ
cana-4287	10	80	telecommunication	telecommunication	NOUN
cana-4287	10	81	engineering	engineering	NOUN
cana-4287	10	82	,	,	PUNCT
cana-4287	10	83	university	university	NOUN
cana-4287	10	84	of	of	ADP
cana-4287	10	85	technology	technology	NOUN
cana-4287	10	86	and	and	CCONJ
cana-4287	10	87	applied	apply	VERB
cana-4287	10	88	sciences	science	NOUN
cana-4287	10	89	,	,	PUNCT
cana-4287	10	90	po	po	PROPN
cana-4287	10	91	box	box	PROPN
cana-4287	10	92	74	74	NUM
cana-4287	10	93	,	,	PUNCT
cana-4287	10	94	al	al	PROPN
cana-4287	10	95	khuwair	khuwair	PROPN
cana-4287	10	96	,	,	PUNCT
cana-4287	10	97	muscat	muscat	PROPN
cana-4287	10	98	133	133	NUM
cana-4287	10	99	,	,	PUNCT
cana-4287	10	100	sultanate	sultanate	NOUN
cana-4287	10	101	of	of	ADP
cana-4287	10	102	oman	oman	NOUN
cana-4287	10	103	,	,	PUNCT
cana-4287	10	104	email	email	NOUN
cana-4287	11	1	i	i	PROPN
cana-4287	11	2	d	d	PROPN
cana-4287	11	3	:	:	PUNCT
cana-4287	12	1	kalyan.maddikera@utas.edu.om	kalyan.maddikera@utas.edu.om	PROPN
cana-4287	12	2	7	7	NUM
cana-4287	12	3	assistant	assistant	NOUN
cana-4287	12	4	professor	professor	NOUN
cana-4287	12	5	,	,	PUNCT
cana-4287	12	6	department	department	NOUN
cana-4287	12	7	of	of	ADP
cana-4287	12	8	mathematics	mathematic	NOUN
cana-4287	12	9	,	,	PUNCT
cana-4287	12	10	vit	vit	PROPN
cana-4287	12	11	-	-	PUNCT
cana-4287	12	12	ap	ap	PROPN
cana-4287	12	13	university	university	PROPN
cana-4287	12	14	,	,	PUNCT
cana-4287	12	15	amaravati	amaravati	PROPN
cana-4287	12	16	,	,	PUNCT
cana-4287	12	17	andhra	andhra	PROPN
cana-4287	12	18	pradesh	pradesh	PROPN
cana-4287	12	19	,	,	PUNCT
cana-4287	12	20	india	india	PROPN
cana-4287	12	21	,	,	PUNCT
cana-4287	12	22	pincode	pincode	PROPN
cana-4287	12	23	:	:	PUNCT
cana-4287	12	24	522237	522237	NUM
cana-4287	12	25	,	,	PUNCT
cana-4287	12	26	email	email	NOUN
cana-4287	12	27	i	i	PROPN
cana-4287	12	28	d	d	PROPN
cana-4287	12	29	:	:	PUNCT
cana-4287	12	30	davalaravikumar@gmail.com	davalaravikumar@gmail.com	X
cana-4287	12	31	article	article	NOUN
cana-4287	12	32	history	history	NOUN
cana-4287	12	33	:	:	PUNCT
cana-4287	12	34	received	receive	VERB
cana-4287	12	35	:	:	PUNCT
cana-4287	12	36	12	12	NUM
cana-4287	12	37	-	-	SYM
cana-4287	12	38	01	01	NUM
cana-4287	12	39	-	-	PUNCT
cana-4287	12	40	2025	2025	NUM
cana-4287	12	41	revised	revise	VERB
cana-4287	12	42	:	:	PUNCT
cana-4287	12	43	15	15	NUM
cana-4287	12	44	-	-	NUM
cana-4287	12	45	02	02	NUM
cana-4287	12	46	-	-	PUNCT
cana-4287	12	47	2025	2025	NUM
cana-4287	12	48	accepted	accept	VERB
cana-4287	12	49	:	:	PUNCT
cana-4287	12	50	01	01	NUM
cana-4287	12	51	-	-	SYM
cana-4287	12	52	03	03	NUM
cana-4287	12	53	-	-	PUNCT
cana-4287	12	54	2025	2025	NUM
cana-4287	12	55	abstract	abstract	NOUN
cana-4287	12	56	:	:	PUNCT
cana-4287	12	57	this	this	DET
cana-4287	12	58	study	study	NOUN
cana-4287	12	59	explores	explore	VERB
cana-4287	12	60	the	the	DET
cana-4287	12	61	intersection	intersection	NOUN
cana-4287	12	62	of	of	ADP
cana-4287	12	63	algebraic	algebraic	ADJ
cana-4287	12	64	topology	topology	NOUN
cana-4287	12	65	and	and	CCONJ
cana-4287	12	66	modern	modern	ADJ
cana-4287	12	67	cryptography	cryptography	NOUN
cana-4287	12	68	,	,	PUNCT
cana-4287	12	69	shedding	shed	VERB
cana-4287	12	70	light	light	NOUN
cana-4287	12	71	on	on	ADP
cana-4287	12	72	how	how	SCONJ
cana-4287	12	73	topological	topological	ADJ
cana-4287	12	74	concepts	concept	NOUN
cana-4287	12	75	can	can	AUX
cana-4287	12	76	enhance	enhance	VERB
cana-4287	12	77	cryptographic	cryptographic	ADJ
cana-4287	12	78	techniques	technique	NOUN
cana-4287	12	79	.	.	PUNCT
cana-4287	13	1	by	by	ADP
cana-4287	13	2	leveraging	leverage	VERB
cana-4287	13	3	algebraic	algebraic	ADJ
cana-4287	13	4	structures	structure	NOUN
cana-4287	13	5	and	and	CCONJ
cana-4287	13	6	their	their	PRON
cana-4287	13	7	applications	application	NOUN
cana-4287	13	8	,	,	PUNCT
cana-4287	13	9	it	it	PRON
cana-4287	13	10	introduces	introduce	VERB
cana-4287	13	11	novel	novel	ADJ
cana-4287	13	12	perspectives	perspective	NOUN
cana-4287	13	13	on	on	ADP
cana-4287	13	14	cryptographic	cryptographic	ADJ
cana-4287	13	15	frameworks	framework	NOUN
cana-4287	13	16	.	.	PUNCT
cana-4287	14	1	the	the	DET
cana-4287	14	2	research	research	NOUN
cana-4287	14	3	suggests	suggest	VERB
cana-4287	14	4	that	that	SCONJ
cana-4287	14	5	reorganizing	reorganize	VERB
cana-4287	14	6	cryptographic	cryptographic	ADJ
cana-4287	14	7	components	component	NOUN
cana-4287	14	8	through	through	ADP
cana-4287	14	9	algebraic	algebraic	PROPN
cana-4287	14	10	binary	binary	PROPN
cana-4287	14	11	relations	relation	NOUN
cana-4287	14	12	can	can	AUX
cana-4287	14	13	lead	lead	VERB
cana-4287	14	14	to	to	ADP
cana-4287	14	15	more	more	ADV
cana-4287	14	16	secure	secure	ADJ
cana-4287	14	17	and	and	CCONJ
cana-4287	14	18	efficient	efficient	ADJ
cana-4287	14	19	systems	system	NOUN
cana-4287	14	20	.	.	PUNCT
cana-4287	15	1	blending	blend	VERB
cana-4287	15	2	theoretical	theoretical	ADJ
cana-4287	15	3	insights	insight	NOUN
cana-4287	15	4	with	with	ADP
cana-4287	15	5	practical	practical	ADJ
cana-4287	15	6	implementations	implementation	NOUN
cana-4287	15	7	,	,	PUNCT
cana-4287	15	8	the	the	DET
cana-4287	15	9	study	study	NOUN
cana-4287	15	10	demonstrates	demonstrate	VERB
cana-4287	15	11	how	how	SCONJ
cana-4287	15	12	topological	topological	ADJ
cana-4287	15	13	principles	principle	NOUN
cana-4287	15	14	can	can	AUX
cana-4287	15	15	address	address	VERB
cana-4287	15	16	contemporary	contemporary	ADJ
cana-4287	15	17	cryptographic	cryptographic	ADJ
cana-4287	15	18	challenges	challenge	NOUN
cana-4287	15	19	.	.	PUNCT
cana-4287	16	1	furthermore	furthermore	ADV
cana-4287	16	2	,	,	PUNCT
cana-4287	16	3	it	it	PRON
cana-4287	16	4	underscores	underscore	VERB
cana-4287	16	5	the	the	DET
cana-4287	16	6	significance	significance	NOUN
cana-4287	16	7	of	of	ADP
cana-4287	16	8	interdisciplinary	interdisciplinary	ADJ
cana-4287	16	9	collaboration	collaboration	NOUN
cana-4287	16	10	by	by	ADP
cana-4287	16	11	highlighting	highlight	VERB
cana-4287	16	12	advancements	advancement	NOUN
cana-4287	16	13	in	in	ADP
cana-4287	16	14	secure	secure	ADJ
cana-4287	16	15	communication	communication	NOUN
cana-4287	16	16	and	and	CCONJ
cana-4287	16	17	data	datum	NOUN
cana-4287	16	18	integrity	integrity	NOUN
cana-4287	16	19	.	.	PUNCT
cana-4287	17	1	in	in	ADP
cana-4287	17	2	an	an	DET
cana-4287	17	3	increasingly	increasingly	ADV
cana-4287	17	4	digital	digital	ADJ
cana-4287	17	5	era	era	NOUN
cana-4287	17	6	,	,	PUNCT
cana-4287	17	7	the	the	DET
cana-4287	17	8	findings	finding	NOUN
cana-4287	17	9	advocate	advocate	VERB
cana-4287	17	10	for	for	ADP
cana-4287	17	11	the	the	DET
cana-4287	17	12	integration	integration	NOUN
cana-4287	17	13	of	of	ADP
cana-4287	17	14	mathematical	mathematical	ADJ
cana-4287	17	15	frameworks	framework	NOUN
cana-4287	17	16	into	into	ADP
cana-4287	17	17	cryptographic	cryptographic	ADJ
cana-4287	17	18	processes	process	NOUN
cana-4287	17	19	,	,	PUNCT
cana-4287	17	20	paving	pave	VERB
cana-4287	17	21	the	the	DET
cana-4287	17	22	way	way	NOUN
cana-4287	17	23	for	for	ADP
cana-4287	17	24	innovative	innovative	ADJ
cana-4287	17	25	security	security	NOUN
cana-4287	17	26	solutions	solution	NOUN
cana-4287	17	27	.	.	PUNCT
cana-4287	18	1	by	by	ADP
cana-4287	18	2	establishing	establish	VERB
cana-4287	18	3	algebraic	algebraic	ADJ
cana-4287	18	4	topology	topology	NOUN
cana-4287	18	5	as	as	ADP
cana-4287	18	6	a	a	DET
cana-4287	18	7	foundational	foundational	ADJ
cana-4287	18	8	element	element	NOUN
cana-4287	18	9	in	in	ADP
cana-4287	18	10	strengthening	strengthen	VERB
cana-4287	18	11	the	the	DET
cana-4287	18	12	resilience	resilience	NOUN
cana-4287	18	13	and	and	CCONJ
cana-4287	18	14	adaptability	adaptability	NOUN
cana-4287	18	15	of	of	ADP
cana-4287	18	16	cryptographic	cryptographic	ADJ
cana-4287	18	17	systems	system	NOUN
cana-4287	18	18	,	,	PUNCT
cana-4287	18	19	this	this	DET
cana-4287	18	20	work	work	NOUN
cana-4287	18	21	fosters	foster	VERB
cana-4287	18	22	interdisciplinary	interdisciplinary	ADJ
cana-4287	18	23	research	research	NOUN
cana-4287	18	24	and	and	CCONJ
cana-4287	18	25	the	the	DET
cana-4287	18	26	exploration	exploration	NOUN
cana-4287	18	27	of	of	ADP
cana-4287	18	28	new	new	ADJ
cana-4287	18	29	paradigms	paradigm	NOUN
cana-4287	18	30	in	in	ADP
cana-4287	18	31	secure	secure	ADJ
cana-4287	18	32	information	information	NOUN
cana-4287	18	33	processing	processing	NOUN
cana-4287	18	34	.	.	PUNCT
cana-4287	19	1	keywords	keyword	NOUN
cana-4287	19	2	:	:	PUNCT
cana-4287	19	3	algebraic	algebraic	ADJ
cana-4287	19	4	topology	topology	NOUN
cana-4287	19	5	,	,	PUNCT
cana-4287	19	6	betti	betti	NOUN
cana-4287	19	7	numbers	number	NOUN
cana-4287	19	8	,	,	PUNCT
cana-4287	19	9	cryptographic	cryptographic	ADJ
cana-4287	19	10	protocols	protocol	NOUN
cana-4287	19	11	,	,	PUNCT
cana-4287	19	12	elliptic	elliptic	ADJ
cana-4287	19	13	curve	curve	NOUN
cana-4287	19	14	cryptography	cryptography	NOUN
cana-4287	19	15	,	,	PUNCT
cana-4287	19	16	homology	homology	NOUN
cana-4287	19	17	theory	theory	NOUN
cana-4287	19	18	,	,	PUNCT
cana-4287	19	19	homomorphic	homomorphic	ADJ
cana-4287	19	20	encryption	encryption	NOUN
cana-4287	19	21	,	,	PUNCT
cana-4287	19	22	lattice	lattice	NOUN
cana-4287	19	23	-	-	PUNCT
cana-4287	19	24	based	base	VERB
cana-4287	19	25	cryptography	cryptography	NOUN
cana-4287	19	26	,	,	PUNCT
cana-4287	19	27	post	post	ADJ
cana-4287	19	28	-	-	ADJ
cana-4287	19	29	quantum	quantum	ADJ
cana-4287	19	30	cryptography	cryptography	NOUN
cana-4287	19	31	,	,	PUNCT
cana-4287	19	32	security	security	NOUN
cana-4287	19	33	vulnerabilities	vulnerability	NOUN
cana-4287	19	34	,	,	PUNCT
cana-4287	19	35	simplicial	simplicial	ADJ
cana-4287	19	36	complexes	complex	NOUN
cana-4287	19	37	,	,	PUNCT
cana-4287	19	38	topological	topological	ADJ
cana-4287	19	39	vector	vector	NOUN
cana-4287	19	40	spaces	space	NOUN
cana-4287	19	41	,	,	PUNCT
cana-4287	19	42	topology	topology	NOUN
cana-4287	19	43	-	-	PUNCT
cana-4287	19	44	based	base	VERB
cana-4287	19	45	cryptography	cryptography	NOUN
cana-4287	19	46	.	.	PUNCT
cana-4287	20	1	mailto:mathematics.29@gmail.com	mailto:mathematics.29@gmail.com	PROPN
cana-4287	21	1	mailto:rameshamarapu.maths@anits.edu.in	mailto:rameshamarapu.maths@anits.edu.in	PROPN
cana-4287	21	2	mailto:arulfreedavinodhini@saveetha.com	mailto:arulfreedavinodhini@saveetha.com	PROPN
cana-4287	21	3	mailto:akshaya.pandafma@kiit.ac.in	mailto:akshaya.pandafma@kiit.ac.in	PROPN
cana-4287	21	4	mailto:msn@kluniversity.in	mailto:msn@kluniversity.in	NOUN
cana-4287	21	5	mailto:kalyan.maddikera@utas.edu.om	mailto:kalyan.maddikera@utas.edu.om	PROPN
cana-4287	21	6	mailto:davalaravikumar@gmail.com	mailto:davalaravikumar@gmail.com	NOUN
cana-4287	21	7	communications	communication	NOUN
cana-4287	21	8	on	on	ADP
cana-4287	21	9	applied	apply	VERB
cana-4287	21	10	nonlinear	nonlinear	ADJ
cana-4287	21	11	analysis	analysis	NOUN
cana-4287	21	12	issn	issn	NOUN
cana-4287	21	13	:	:	PUNCT
cana-4287	21	14	1074	1074	NUM
cana-4287	21	15	-	-	PUNCT
cana-4287	21	16	133x	133x	NUM
cana-4287	21	17	vol	vol	NOUN
cana-4287	21	18	32	32	NUM
cana-4287	21	19	no	no	NOUN
cana-4287	21	20	.	.	PUNCT
cana-4287	22	1	9s	9s	NUM
cana-4287	22	2	(	(	PUNCT
cana-4287	22	3	2025	2025	NUM
cana-4287	22	4	)	)	PUNCT
cana-4287	22	5	1729	1729	NUM
cana-4287	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	22	7	i.	i.	NOUN
cana-4287	22	8	introduction	introduction	NOUN
cana-4287	22	9	in	in	ADP
cana-4287	22	10	a	a	DET
cana-4287	22	11	time	time	NOUN
cana-4287	22	12	when	when	SCONJ
cana-4287	22	13	digital	digital	ADJ
cana-4287	22	14	transformation	transformation	NOUN
cana-4287	22	15	is	be	AUX
cana-4287	22	16	the	the	DET
cana-4287	22	17	norm	norm	NOUN
cana-4287	22	18	,	,	PUNCT
cana-4287	22	19	cryptography	cryptography	NOUN
cana-4287	22	20	is	be	AUX
cana-4287	22	21	essential	essential	ADJ
cana-4287	22	22	for	for	ADP
cana-4287	22	23	protecting	protect	VERB
cana-4287	22	24	communications	communication	NOUN
cana-4287	22	25	,	,	PUNCT
cana-4287	22	26	guaranteeing	guarantee	VERB
cana-4287	22	27	data	datum	NOUN
cana-4287	22	28	integrity	integrity	NOUN
cana-4287	22	29	,	,	PUNCT
cana-4287	22	30	and	and	CCONJ
cana-4287	22	31	protecting	protect	VERB
cana-4287	22	32	sensitive	sensitive	ADJ
cana-4287	22	33	information	information	NOUN
cana-4287	22	34	.	.	PUNCT
cana-4287	23	1	the	the	DET
cana-4287	23	2	difficulties	difficulty	NOUN
cana-4287	23	3	that	that	PRON
cana-4287	23	4	cryptography	cryptography	NOUN
cana-4287	23	5	systems	system	NOUN
cana-4287	23	6	encounter	encounter	VERB
cana-4287	23	7	change	change	NOUN
cana-4287	23	8	along	along	ADP
cana-4287	23	9	with	with	ADP
cana-4287	23	10	the	the	DET
cana-4287	23	11	digital	digital	ADJ
cana-4287	23	12	environment	environment	NOUN
cana-4287	23	13	.	.	PUNCT
cana-4287	24	1	more	more	ADV
cana-4287	24	2	robust	robust	ADJ
cana-4287	24	3	,	,	PUNCT
cana-4287	24	4	effective	effective	ADJ
cana-4287	24	5	,	,	PUNCT
cana-4287	24	6	and	and	CCONJ
cana-4287	24	7	flexible	flexible	ADJ
cana-4287	24	8	cryptographic	cryptographic	ADJ
cana-4287	24	9	techniques	technique	NOUN
cana-4287	24	10	are	be	AUX
cana-4287	24	11	required	require	VERB
cana-4287	24	12	due	due	ADP
cana-4287	24	13	to	to	ADP
cana-4287	24	14	the	the	DET
cana-4287	24	15	increasing	increase	VERB
cana-4287	24	16	complexity	complexity	NOUN
cana-4287	24	17	of	of	ADP
cana-4287	24	18	cyberthreats	cyberthreat	NOUN
cana-4287	24	19	and	and	CCONJ
cana-4287	24	20	the	the	DET
cana-4287	24	21	introduction	introduction	NOUN
cana-4287	24	22	of	of	ADP
cana-4287	24	23	quantum	quantum	NOUN
cana-4287	24	24	computing	computing	NOUN
cana-4287	24	25	.	.	PUNCT
cana-4287	25	1	this	this	PRON
cana-4287	25	2	calls	call	VERB
cana-4287	25	3	for	for	ADP
cana-4287	25	4	a	a	DET
cana-4287	25	5	paradigm	paradigm	NOUN
cana-4287	25	6	change	change	NOUN
cana-4287	25	7	,	,	PUNCT
cana-4287	25	8	investigating	investigate	VERB
cana-4287	25	9	novel	novel	ADJ
cana-4287	25	10	mathematical	mathematical	ADJ
cana-4287	25	11	structures	structure	NOUN
cana-4287	25	12	—	—	PUNCT
cana-4287	25	13	like	like	ADP
cana-4287	25	14	algebraic	algebraic	ADJ
cana-4287	25	15	topology	topology	NOUN
cana-4287	25	16	—	—	PUNCT
cana-4287	25	17	to	to	PART
cana-4287	25	18	tackle	tackle	VERB
cana-4287	25	19	current	current	ADJ
cana-4287	25	20	cryptography	cryptography	NOUN
cana-4287	25	21	issues	issue	NOUN
cana-4287	25	22	.	.	PUNCT
cana-4287	26	1	in	in	ADP
cana-4287	26	2	a	a	DET
cana-4287	26	3	time	time	NOUN
cana-4287	26	4	when	when	SCONJ
cana-4287	26	5	digital	digital	ADJ
cana-4287	26	6	transformation	transformation	NOUN
cana-4287	26	7	is	be	AUX
cana-4287	26	8	the	the	DET
cana-4287	26	9	norm	norm	NOUN
cana-4287	26	10	,	,	PUNCT
cana-4287	26	11	cryptography	cryptography	NOUN
cana-4287	26	12	is	be	AUX
cana-4287	26	13	essential	essential	ADJ
cana-4287	26	14	for	for	ADP
cana-4287	26	15	protecting	protect	VERB
cana-4287	26	16	communications	communication	NOUN
cana-4287	26	17	,	,	PUNCT
cana-4287	26	18	guaranteeing	guarantee	VERB
cana-4287	26	19	data	datum	NOUN
cana-4287	26	20	integrity	integrity	NOUN
cana-4287	26	21	,	,	PUNCT
cana-4287	26	22	and	and	CCONJ
cana-4287	26	23	protecting	protect	VERB
cana-4287	26	24	sensitive	sensitive	ADJ
cana-4287	26	25	information	information	NOUN
cana-4287	26	26	.	.	PUNCT
cana-4287	27	1	the	the	DET
cana-4287	27	2	difficulties	difficulty	NOUN
cana-4287	27	3	that	that	PRON
cana-4287	27	4	cryptography	cryptography	NOUN
cana-4287	27	5	systems	system	NOUN
cana-4287	27	6	encounter	encounter	VERB
cana-4287	27	7	change	change	NOUN
cana-4287	27	8	along	along	ADP
cana-4287	27	9	with	with	ADP
cana-4287	27	10	the	the	DET
cana-4287	27	11	digital	digital	ADJ
cana-4287	27	12	environment	environment	NOUN
cana-4287	27	13	.	.	PUNCT
cana-4287	28	1	more	more	ADV
cana-4287	28	2	robust	robust	ADJ
cana-4287	28	3	,	,	PUNCT
cana-4287	28	4	effective	effective	ADJ
cana-4287	28	5	,	,	PUNCT
cana-4287	28	6	and	and	CCONJ
cana-4287	28	7	flexible	flexible	ADJ
cana-4287	28	8	cryptographic	cryptographic	ADJ
cana-4287	28	9	techniques	technique	NOUN
cana-4287	28	10	are	be	AUX
cana-4287	28	11	required	require	VERB
cana-4287	28	12	due	due	ADP
cana-4287	28	13	to	to	ADP
cana-4287	28	14	the	the	DET
cana-4287	28	15	increasing	increase	VERB
cana-4287	28	16	complexity	complexity	NOUN
cana-4287	28	17	of	of	ADP
cana-4287	28	18	cyberthreats	cyberthreat	NOUN
cana-4287	28	19	and	and	CCONJ
cana-4287	28	20	the	the	DET
cana-4287	28	21	introduction	introduction	NOUN
cana-4287	28	22	of	of	ADP
cana-4287	28	23	quantum	quantum	NOUN
cana-4287	28	24	computing	computing	NOUN
cana-4287	28	25	.	.	PUNCT
cana-4287	29	1	this	this	PRON
cana-4287	29	2	calls	call	VERB
cana-4287	29	3	for	for	ADP
cana-4287	29	4	a	a	DET
cana-4287	29	5	paradigm	paradigm	NOUN
cana-4287	29	6	change	change	NOUN
cana-4287	29	7	,	,	PUNCT
cana-4287	29	8	investigating	investigate	VERB
cana-4287	29	9	novel	novel	ADJ
cana-4287	29	10	mathematical	mathematical	ADJ
cana-4287	29	11	structures	structure	NOUN
cana-4287	29	12	—	—	PUNCT
cana-4287	29	13	like	like	ADP
cana-4287	29	14	algebraic	algebraic	ADJ
cana-4287	29	15	topology	topology	NOUN
cana-4287	29	16	—	—	PUNCT
cana-4287	29	17	to	to	PART
cana-4287	29	18	tackle	tackle	VERB
cana-4287	29	19	current	current	ADJ
cana-4287	29	20	cryptography	cryptography	NOUN
cana-4287	29	21	issues	issue	NOUN
cana-4287	29	22	.	.	PUNCT
cana-4287	30	1	as	as	SCONJ
cana-4287	30	2	digital	digital	ADJ
cana-4287	30	3	security	security	NOUN
cana-4287	30	4	threats	threat	NOUN
cana-4287	30	5	evolve	evolve	VERB
cana-4287	30	6	,	,	PUNCT
cana-4287	30	7	cryptographic	cryptographic	ADJ
cana-4287	30	8	techniques	technique	NOUN
cana-4287	30	9	must	must	AUX
cana-4287	30	10	advance	advance	VERB
cana-4287	30	11	to	to	PART
cana-4287	30	12	ensure	ensure	VERB
cana-4287	30	13	robust	robust	ADJ
cana-4287	30	14	data	datum	NOUN
cana-4287	30	15	protection	protection	NOUN
cana-4287	30	16	and	and	CCONJ
cana-4287	30	17	secure	secure	ADJ
cana-4287	30	18	communication	communication	NOUN
cana-4287	30	19	.	.	PUNCT
cana-4287	31	1	traditional	traditional	ADJ
cana-4287	31	2	cryptographic	cryptographic	ADJ
cana-4287	31	3	frameworks	framework	NOUN
cana-4287	31	4	,	,	PUNCT
cana-4287	31	5	including	include	VERB
cana-4287	31	6	rsa	rsa	NOUN
cana-4287	31	7	,	,	PUNCT
cana-4287	31	8	elliptic	elliptic	ADJ
cana-4287	31	9	curve	curve	NOUN
cana-4287	31	10	cryptography	cryptography	NOUN
cana-4287	31	11	(	(	PUNCT
cana-4287	31	12	ecc	ecc	PROPN
cana-4287	31	13	)	)	PUNCT
cana-4287	31	14	,	,	PUNCT
cana-4287	31	15	and	and	CCONJ
cana-4287	31	16	lattice	lattice	NOUN
cana-4287	31	17	-	-	PUNCT
cana-4287	31	18	based	base	VERB
cana-4287	31	19	encryption	encryption	NOUN
cana-4287	31	20	,	,	PUNCT
cana-4287	31	21	have	have	AUX
cana-4287	31	22	been	be	AUX
cana-4287	31	23	widely	widely	ADV
cana-4287	31	24	employed	employ	VERB
cana-4287	31	25	to	to	PART
cana-4287	31	26	safeguard	safeguard	VERB
cana-4287	31	27	sensitive	sensitive	ADJ
cana-4287	31	28	information	information	NOUN
cana-4287	31	29	.	.	PUNCT
cana-4287	32	1	however	however	ADV
cana-4287	32	2	,	,	PUNCT
cana-4287	32	3	emerging	emerge	VERB
cana-4287	32	4	computational	computational	ADJ
cana-4287	32	5	challenges	challenge	NOUN
cana-4287	32	6	—	—	PUNCT
cana-4287	32	7	such	such	ADJ
cana-4287	32	8	as	as	ADP
cana-4287	32	9	quantum	quantum	NOUN
cana-4287	32	10	computing	computing	NOUN
cana-4287	32	11	threats	threat	NOUN
cana-4287	32	12	and	and	CCONJ
cana-4287	32	13	increasingly	increasingly	ADV
cana-4287	32	14	sophisticated	sophisticated	ADJ
cana-4287	32	15	attack	attack	NOUN
cana-4287	32	16	vectors	vector	NOUN
cana-4287	32	17	—	—	PUNCT
cana-4287	32	18	demand	demand	VERB
cana-4287	32	19	innovative	innovative	ADJ
cana-4287	32	20	security	security	NOUN
cana-4287	32	21	solutions	solution	NOUN
cana-4287	32	22	.	.	PUNCT
cana-4287	33	1	algebraic	algebraic	ADJ
cana-4287	33	2	topology	topology	NOUN
cana-4287	33	3	,	,	PUNCT
cana-4287	33	4	a	a	DET
cana-4287	33	5	branch	branch	NOUN
cana-4287	33	6	of	of	ADP
cana-4287	33	7	mathematics	mathematic	NOUN
cana-4287	33	8	that	that	PRON
cana-4287	33	9	studies	study	VERB
cana-4287	33	10	topological	topological	ADJ
cana-4287	33	11	spaces	space	NOUN
cana-4287	33	12	through	through	ADP
cana-4287	33	13	algebraic	algebraic	ADJ
cana-4287	33	14	structures	structure	NOUN
cana-4287	33	15	,	,	PUNCT
cana-4287	33	16	offers	offer	VERB
cana-4287	33	17	promising	promise	VERB
cana-4287	33	18	new	new	ADJ
cana-4287	33	19	approaches	approach	NOUN
cana-4287	33	20	to	to	ADP
cana-4287	33	21	cryptographic	cryptographic	ADJ
cana-4287	33	22	design	design	NOUN
cana-4287	33	23	.	.	PUNCT
cana-4287	34	1	by	by	ADP
cana-4287	34	2	leveraging	leverage	VERB
cana-4287	34	3	topological	topological	ADJ
cana-4287	34	4	invariants	invariant	NOUN
cana-4287	34	5	,	,	PUNCT
cana-4287	34	6	homotopy	homotopy	NOUN
cana-4287	34	7	theory	theory	NOUN
cana-4287	34	8	,	,	PUNCT
cana-4287	34	9	simplicial	simplicial	ADJ
cana-4287	34	10	complexes	complex	NOUN
cana-4287	34	11	,	,	PUNCT
cana-4287	34	12	and	and	CCONJ
cana-4287	34	13	vector	vector	NOUN
cana-4287	34	14	spaces	space	NOUN
cana-4287	34	15	,	,	PUNCT
cana-4287	34	16	cryptographic	cryptographic	ADJ
cana-4287	34	17	systems	system	NOUN
cana-4287	34	18	can	can	AUX
cana-4287	34	19	achieve	achieve	VERB
cana-4287	34	20	enhanced	enhanced	ADJ
cana-4287	34	21	resilience	resilience	NOUN
cana-4287	34	22	,	,	PUNCT
cana-4287	34	23	efficiency	efficiency	NOUN
cana-4287	34	24	,	,	PUNCT
cana-4287	34	25	and	and	CCONJ
cana-4287	34	26	adaptability	adaptability	NOUN
cana-4287	34	27	.	.	PUNCT
cana-4287	35	1	these	these	DET
cana-4287	35	2	mathematical	mathematical	ADJ
cana-4287	35	3	tools	tool	NOUN
cana-4287	35	4	help	help	AUX
cana-4287	35	5	redefine	redefine	VERB
cana-4287	35	6	cryptographic	cryptographic	ADJ
cana-4287	35	7	components	component	NOUN
cana-4287	35	8	,	,	PUNCT
cana-4287	35	9	optimizing	optimize	VERB
cana-4287	35	10	key	key	ADJ
cana-4287	35	11	generation	generation	NOUN
cana-4287	35	12	,	,	PUNCT
cana-4287	35	13	encryption	encryption	NOUN
cana-4287	35	14	-	-	PUNCT
cana-4287	35	15	decryption	decryption	NOUN
cana-4287	35	16	protocols	protocol	NOUN
cana-4287	35	17	,	,	PUNCT
cana-4287	35	18	and	and	CCONJ
cana-4287	35	19	error	error	NOUN
cana-4287	35	20	correction	correction	NOUN
cana-4287	35	21	mechanisms	mechanism	NOUN
cana-4287	35	22	.	.	PUNCT
cana-4287	36	1	this	this	DET
cana-4287	36	2	study	study	NOUN
cana-4287	36	3	explores	explore	VERB
cana-4287	36	4	how	how	SCONJ
cana-4287	36	5	algebraic	algebraic	ADJ
cana-4287	36	6	topology	topology	NOUN
cana-4287	36	7	can	can	AUX
cana-4287	36	8	reinforce	reinforce	VERB
cana-4287	36	9	modern	modern	ADJ
cana-4287	36	10	cryptographic	cryptographic	ADJ
cana-4287	36	11	frameworks	framework	NOUN
cana-4287	36	12	by	by	ADP
cana-4287	36	13	improving	improve	VERB
cana-4287	36	14	their	their	PRON
cana-4287	36	15	structural	structural	ADJ
cana-4287	36	16	robustness	robustness	NOUN
cana-4287	36	17	and	and	CCONJ
cana-4287	36	18	security	security	NOUN
cana-4287	36	19	guarantees	guarantee	NOUN
cana-4287	36	20	.	.	PUNCT
cana-4287	37	1	notably	notably	ADV
cana-4287	37	2	,	,	PUNCT
cana-4287	37	3	the	the	DET
cana-4287	37	4	application	application	NOUN
cana-4287	37	5	of	of	ADP
cana-4287	37	6	topological	topological	ADJ
cana-4287	37	7	methods	method	NOUN
cana-4287	37	8	has	have	AUX
cana-4287	37	9	demonstrated	demonstrate	VERB
cana-4287	37	10	measurable	measurable	ADJ
cana-4287	37	11	security	security	NOUN
cana-4287	37	12	enhancements	enhancement	NOUN
cana-4287	37	13	in	in	ADP
cana-4287	37	14	rsa	rsa	PROPN
cana-4287	37	15	,	,	PUNCT
cana-4287	37	16	ecc	ecc	PROPN
cana-4287	37	17	,	,	PUNCT
cana-4287	37	18	and	and	CCONJ
cana-4287	37	19	lattice	lattice	NOUN
cana-4287	37	20	-	-	PUNCT
cana-4287	37	21	based	base	VERB
cana-4287	37	22	cryptography	cryptography	NOUN
cana-4287	37	23	,	,	PUNCT
cana-4287	37	24	while	while	SCONJ
cana-4287	37	25	also	also	ADV
cana-4287	37	26	contributing	contribute	VERB
cana-4287	37	27	to	to	ADP
cana-4287	37	28	the	the	DET
cana-4287	37	29	efficiency	efficiency	NOUN
cana-4287	37	30	of	of	ADP
cana-4287	37	31	hash	hash	NOUN
cana-4287	37	32	functions	function	NOUN
cana-4287	37	33	and	and	CCONJ
cana-4287	37	34	post	post	ADJ
cana-4287	37	35	-	-	ADJ
cana-4287	37	36	quantum	quantum	ADJ
cana-4287	37	37	encryption	encryption	NOUN
cana-4287	37	38	techniques	technique	NOUN
cana-4287	37	39	.	.	PUNCT
cana-4287	38	1	by	by	ADP
cana-4287	38	2	integrating	integrate	VERB
cana-4287	38	3	topological	topological	ADJ
cana-4287	38	4	insights	insight	NOUN
cana-4287	38	5	with	with	ADP
cana-4287	38	6	cryptographic	cryptographic	ADJ
cana-4287	38	7	principles	principle	NOUN
cana-4287	38	8	,	,	PUNCT
cana-4287	38	9	this	this	DET
cana-4287	38	10	research	research	NOUN
cana-4287	38	11	highlights	highlight	VERB
cana-4287	38	12	a	a	DET
cana-4287	38	13	novel	novel	ADJ
cana-4287	38	14	interdisciplinary	interdisciplinary	ADJ
cana-4287	38	15	approach	approach	NOUN
cana-4287	38	16	to	to	ADP
cana-4287	38	17	strengthening	strengthen	VERB
cana-4287	38	18	cybersecurity	cybersecurity	NOUN
cana-4287	38	19	in	in	ADP
cana-4287	38	20	an	an	DET
cana-4287	38	21	era	era	NOUN
cana-4287	38	22	of	of	ADP
cana-4287	38	23	rapid	rapid	ADJ
cana-4287	38	24	technological	technological	ADJ
cana-4287	38	25	advancement	advancement	NOUN
cana-4287	38	26	.	.	PUNCT
cana-4287	39	1	the	the	DET
cana-4287	39	2	remainder	remainder	NOUN
cana-4287	39	3	of	of	ADP
cana-4287	39	4	this	this	DET
cana-4287	39	5	paper	paper	NOUN
cana-4287	39	6	delves	delf	NOUN
cana-4287	39	7	into	into	ADP
cana-4287	39	8	key	key	ADJ
cana-4287	39	9	topological	topological	ADJ
cana-4287	39	10	concepts	concept	NOUN
cana-4287	39	11	relevant	relevant	ADJ
cana-4287	39	12	to	to	ADP
cana-4287	39	13	cryptography	cryptography	NOUN
cana-4287	39	14	,	,	PUNCT
cana-4287	39	15	examines	examine	VERB
cana-4287	39	16	their	their	PRON
cana-4287	39	17	implementation	implementation	NOUN
cana-4287	39	18	across	across	ADP
cana-4287	39	19	different	different	ADJ
cana-4287	39	20	cryptographic	cryptographic	ADJ
cana-4287	39	21	protocols	protocol	NOUN
cana-4287	39	22	,	,	PUNCT
cana-4287	39	23	and	and	CCONJ
cana-4287	39	24	presents	present	VERB
cana-4287	39	25	empirical	empirical	ADJ
cana-4287	39	26	findings	finding	NOUN
cana-4287	39	27	that	that	PRON
cana-4287	39	28	demonstrate	demonstrate	VERB
cana-4287	39	29	their	their	PRON
cana-4287	39	30	impact	impact	NOUN
cana-4287	39	31	on	on	ADP
cana-4287	39	32	security	security	NOUN
cana-4287	39	33	and	and	CCONJ
cana-4287	39	34	computational	computational	ADJ
cana-4287	39	35	performance	performance	NOUN
cana-4287	39	36	.	.	PUNCT
cana-4287	40	1	ultimately	ultimately	ADV
cana-4287	40	2	,	,	PUNCT
cana-4287	40	3	this	this	DET
cana-4287	40	4	work	work	NOUN
cana-4287	40	5	advocates	advocate	VERB
cana-4287	40	6	for	for	ADP
cana-4287	40	7	the	the	DET
cana-4287	40	8	broader	broad	ADJ
cana-4287	40	9	adoption	adoption	NOUN
cana-4287	40	10	of	of	ADP
cana-4287	40	11	algebraic	algebraic	ADJ
cana-4287	40	12	topology	topology	NOUN
cana-4287	40	13	in	in	ADP
cana-4287	40	14	cryptographic	cryptographic	ADJ
cana-4287	40	15	research	research	NOUN
cana-4287	40	16	,	,	PUNCT
cana-4287	40	17	paving	pave	VERB
cana-4287	40	18	the	the	DET
cana-4287	40	19	way	way	NOUN
cana-4287	40	20	for	for	ADP
cana-4287	40	21	innovative	innovative	ADJ
cana-4287	40	22	security	security	NOUN
cana-4287	40	23	solutions	solution	NOUN
cana-4287	40	24	in	in	ADP
cana-4287	40	25	the	the	DET
cana-4287	40	26	digital	digital	ADJ
cana-4287	40	27	age	age	NOUN
cana-4287	40	28	.	.	PUNCT
cana-4287	41	1	in	in	ADP
cana-4287	41	2	the	the	DET
cana-4287	41	3	digital	digital	ADJ
cana-4287	41	4	era	era	NOUN
cana-4287	41	5	,	,	PUNCT
cana-4287	41	6	securing	secure	VERB
cana-4287	41	7	sensitive	sensitive	ADJ
cana-4287	41	8	data	datum	NOUN
cana-4287	41	9	and	and	CCONJ
cana-4287	41	10	communications	communication	NOUN
cana-4287	41	11	is	be	AUX
cana-4287	41	12	a	a	DET
cana-4287	41	13	growing	grow	VERB
cana-4287	41	14	challenge	challenge	NOUN
cana-4287	41	15	due	due	ADP
cana-4287	41	16	to	to	ADP
cana-4287	41	17	the	the	DET
cana-4287	41	18	increasing	increase	VERB
cana-4287	41	19	sophistication	sophistication	NOUN
cana-4287	41	20	of	of	ADP
cana-4287	41	21	cyber	cyber	ADJ
cana-4287	41	22	threats	threat	NOUN
cana-4287	41	23	.	.	PUNCT
cana-4287	42	1	while	while	SCONJ
cana-4287	42	2	traditional	traditional	ADJ
cana-4287	42	3	cryptographic	cryptographic	ADJ
cana-4287	42	4	methods	method	NOUN
cana-4287	42	5	such	such	ADJ
cana-4287	42	6	as	as	ADP
cana-4287	42	7	rsa	rsa	NOUN
cana-4287	42	8	,	,	PUNCT
cana-4287	42	9	elliptic	elliptic	ADJ
cana-4287	42	10	curve	curve	NOUN
cana-4287	42	11	cryptography	cryptography	NOUN
cana-4287	42	12	(	(	PUNCT
cana-4287	42	13	ecc	ecc	PROPN
cana-4287	42	14	)	)	PUNCT
cana-4287	42	15	,	,	PUNCT
cana-4287	42	16	and	and	CCONJ
cana-4287	42	17	lattice	lattice	NOUN
cana-4287	42	18	-	-	PUNCT
cana-4287	42	19	based	base	VERB
cana-4287	42	20	encryption	encryption	NOUN
cana-4287	42	21	have	have	AUX
cana-4287	42	22	provided	provide	VERB
cana-4287	42	23	robust	robust	ADJ
cana-4287	42	24	security	security	NOUN
cana-4287	42	25	,	,	PUNCT
cana-4287	42	26	emerging	emerge	VERB
cana-4287	42	27	attack	attack	NOUN
cana-4287	42	28	vectors	vector	NOUN
cana-4287	42	29	—	—	PUNCT
cana-4287	42	30	including	include	VERB
cana-4287	42	31	quantum	quantum	NOUN
cana-4287	42	32	computing	computing	NOUN
cana-4287	42	33	—	—	PUNCT
cana-4287	42	34	necessitate	necessitate	ADJ
cana-4287	42	35	more	more	ADV
cana-4287	42	36	advanced	advanced	ADJ
cana-4287	42	37	cryptographic	cryptographic	ADJ
cana-4287	42	38	solutions	solution	NOUN
cana-4287	42	39	.	.	PUNCT
cana-4287	43	1	this	this	PRON
cana-4287	43	2	has	have	AUX
cana-4287	43	3	led	lead	VERB
cana-4287	43	4	researchers	researcher	NOUN
cana-4287	43	5	to	to	PART
cana-4287	43	6	explore	explore	VERB
cana-4287	43	7	novel	novel	ADJ
cana-4287	43	8	mathematical	mathematical	ADJ
cana-4287	43	9	approaches	approach	NOUN
cana-4287	43	10	to	to	PART
cana-4287	43	11	enhance	enhance	VERB
cana-4287	43	12	the	the	DET
cana-4287	43	13	security	security	NOUN
cana-4287	43	14	and	and	CCONJ
cana-4287	43	15	efficiency	efficiency	NOUN
cana-4287	43	16	of	of	ADP
cana-4287	43	17	cryptographic	cryptographic	ADJ
cana-4287	43	18	protocols	protocol	NOUN
cana-4287	43	19	.	.	PUNCT
cana-4287	44	1	algebraic	algebraic	ADJ
cana-4287	44	2	topology	topology	NOUN
cana-4287	44	3	,	,	PUNCT
cana-4287	44	4	a	a	DET
cana-4287	44	5	branch	branch	NOUN
cana-4287	44	6	of	of	ADP
cana-4287	44	7	mathematics	mathematic	NOUN
cana-4287	44	8	that	that	PRON
cana-4287	44	9	studies	study	VERB
cana-4287	44	10	spatial	spatial	ADJ
cana-4287	44	11	properties	property	NOUN
cana-4287	44	12	through	through	ADP
cana-4287	44	13	algebraic	algebraic	ADJ
cana-4287	44	14	structures	structure	NOUN
cana-4287	44	15	,	,	PUNCT
cana-4287	44	16	presents	present	VERB
cana-4287	44	17	a	a	DET
cana-4287	44	18	promising	promising	ADJ
cana-4287	44	19	new	new	ADJ
cana-4287	44	20	direction	direction	NOUN
cana-4287	44	21	in	in	ADP
cana-4287	44	22	cryptographic	cryptographic	ADJ
cana-4287	44	23	research	research	NOUN
cana-4287	44	24	.	.	PUNCT
cana-4287	45	1	by	by	ADP
cana-4287	45	2	leveraging	leverage	VERB
cana-4287	45	3	concepts	concept	NOUN
cana-4287	45	4	such	such	ADJ
cana-4287	45	5	as	as	ADP
cana-4287	45	6	homology	homology	NOUN
cana-4287	45	7	theory	theory	NOUN
cana-4287	45	8	,	,	PUNCT
cana-4287	45	9	simplicial	simplicial	ADJ
cana-4287	45	10	complexes	complex	NOUN
cana-4287	45	11	,	,	PUNCT
cana-4287	45	12	and	and	CCONJ
cana-4287	45	13	topological	topological	ADJ
cana-4287	45	14	vector	vector	NOUN
cana-4287	45	15	spaces	space	NOUN
cana-4287	45	16	,	,	PUNCT
cana-4287	45	17	cryptographic	cryptographic	ADJ
cana-4287	45	18	systems	system	NOUN
cana-4287	45	19	can	can	AUX
cana-4287	45	20	be	be	AUX
cana-4287	45	21	structured	structure	VERB
cana-4287	45	22	to	to	PART
cana-4287	45	23	enhance	enhance	VERB
cana-4287	45	24	resilience	resilience	NOUN
cana-4287	45	25	,	,	PUNCT
cana-4287	45	26	optimize	optimize	VERB
cana-4287	45	27	key	key	ADJ
cana-4287	45	28	management	management	NOUN
cana-4287	45	29	,	,	PUNCT
cana-4287	45	30	and	and	CCONJ
cana-4287	45	31	improve	improve	VERB
cana-4287	45	32	data	datum	NOUN
cana-4287	45	33	integrity	integrity	NOUN
cana-4287	45	34	.	.	PUNCT
cana-4287	46	1	topological	topological	ADJ
cana-4287	46	2	invariants	invariant	NOUN
cana-4287	46	3	,	,	PUNCT
cana-4287	46	4	which	which	PRON
cana-4287	46	5	remain	remain	VERB
cana-4287	46	6	unchanged	unchanged	ADJ
cana-4287	46	7	under	under	ADP
cana-4287	46	8	continuous	continuous	ADJ
cana-4287	46	9	transformations	transformation	NOUN
cana-4287	46	10	,	,	PUNCT
cana-4287	46	11	provide	provide	VERB
cana-4287	46	12	additional	additional	ADJ
cana-4287	46	13	stability	stability	NOUN
cana-4287	46	14	to	to	ADP
cana-4287	46	15	cryptographic	cryptographic	ADJ
cana-4287	46	16	frameworks	framework	NOUN
cana-4287	46	17	,	,	PUNCT
cana-4287	46	18	making	make	VERB
cana-4287	46	19	them	they	PRON
cana-4287	46	20	more	more	ADV
cana-4287	46	21	resistant	resistant	ADJ
cana-4287	46	22	to	to	ADP
cana-4287	46	23	attacks	attack	NOUN
cana-4287	46	24	.	.	PUNCT
cana-4287	47	1	communications	communication	NOUN
cana-4287	47	2	on	on	ADP
cana-4287	47	3	applied	apply	VERB
cana-4287	47	4	nonlinear	nonlinear	ADJ
cana-4287	47	5	analysis	analysis	NOUN
cana-4287	47	6	issn	issn	NOUN
cana-4287	47	7	:	:	PUNCT
cana-4287	47	8	1074	1074	NUM
cana-4287	47	9	-	-	PUNCT
cana-4287	47	10	133x	133x	NUM
cana-4287	47	11	vol	vol	NOUN
cana-4287	47	12	32	32	NUM
cana-4287	47	13	no	no	NOUN
cana-4287	47	14	.	.	PUNCT
cana-4287	48	1	9s	9s	NUM
cana-4287	48	2	(	(	PUNCT
cana-4287	48	3	2025	2025	NUM
cana-4287	48	4	)	)	PUNCT
cana-4287	48	5	1730	1730	NUM
cana-4287	48	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	48	7	fig	fig	NOUN
cana-4287	48	8	.	.	PUNCT
cana-4287	49	1	1	1	NUM
cana-4287	49	2	:	:	PUNCT
cana-4287	49	3	topological	topological	ADJ
cana-4287	49	4	techniques	technique	NOUN
cana-4287	49	5	in	in	ADP
cana-4287	49	6	cryptography	cryptography	NOUN
cana-4287	49	7	the	the	DET
cana-4287	49	8	use	use	NOUN
cana-4287	49	9	of	of	ADP
cana-4287	49	10	algebraic	algebraic	ADJ
cana-4287	49	11	structures	structure	NOUN
cana-4287	49	12	like	like	ADP
cana-4287	49	13	groups	group	NOUN
cana-4287	49	14	,	,	PUNCT
cana-4287	49	15	rings	ring	NOUN
cana-4287	49	16	,	,	PUNCT
cana-4287	49	17	and	and	CCONJ
cana-4287	49	18	binary	binary	ADJ
cana-4287	49	19	relations	relation	NOUN
cana-4287	49	20	to	to	PART
cana-4287	49	21	optimize	optimize	VERB
cana-4287	49	22	and	and	CCONJ
cana-4287	49	23	restructure	restructure	VERB
cana-4287	49	24	cryptographic	cryptographic	ADJ
cana-4287	49	25	components	component	NOUN
cana-4287	49	26	is	be	AUX
cana-4287	49	27	at	at	ADP
cana-4287	49	28	the	the	DET
cana-4287	49	29	heart	heart	NOUN
cana-4287	49	30	of	of	ADP
cana-4287	49	31	this	this	DET
cana-4287	49	32	research	research	NOUN
cana-4287	49	33	.	.	PUNCT
cana-4287	50	1	these	these	DET
cana-4287	50	2	methods	method	NOUN
cana-4287	50	3	provide	provide	VERB
cana-4287	50	4	fresh	fresh	ADJ
cana-4287	50	5	viewpoints	viewpoint	NOUN
cana-4287	50	6	on	on	ADP
cana-4287	50	7	important	important	ADJ
cana-4287	50	8	procedures	procedure	NOUN
cana-4287	50	9	like	like	ADP
cana-4287	50	10	encryption	encryption	NOUN
cana-4287	50	11	-	-	PUNCT
cana-4287	50	12	decryption	decryption	NOUN
cana-4287	50	13	protocols	protocol	NOUN
cana-4287	50	14	,	,	PUNCT
cana-4287	50	15	key	key	ADJ
cana-4287	50	16	creation	creation	NOUN
cana-4287	50	17	,	,	PUNCT
cana-4287	50	18	and	and	CCONJ
cana-4287	50	19	error	error	NOUN
cana-4287	50	20	correction	correction	NOUN
cana-4287	50	21	.	.	PUNCT
cana-4287	51	1	even	even	ADV
cana-4287	51	2	in	in	ADP
cana-4287	51	3	the	the	DET
cana-4287	51	4	face	face	NOUN
cana-4287	51	5	of	of	ADP
cana-4287	51	6	hostile	hostile	ADJ
cana-4287	51	7	attacks	attack	NOUN
cana-4287	51	8	,	,	PUNCT
cana-4287	51	9	cryptographic	cryptographic	ADJ
cana-4287	51	10	algorithms	algorithm	NOUN
cana-4287	51	11	are	be	AUX
cana-4287	51	12	made	make	VERB
cana-4287	51	13	more	more	ADV
cana-4287	51	14	stable	stable	ADJ
cana-4287	51	15	by	by	ADP
cana-4287	51	16	the	the	DET
cana-4287	51	17	robustness	robustness	NOUN
cana-4287	51	18	of	of	ADP
cana-4287	51	19	topological	topological	ADJ
cana-4287	51	20	invariants	invariant	NOUN
cana-4287	51	21	,	,	PUNCT
cana-4287	51	22	which	which	PRON
cana-4287	51	23	remain	remain	VERB
cana-4287	51	24	intact	intact	ADJ
cana-4287	51	25	under	under	ADP
cana-4287	51	26	constant	constant	ADJ
cana-4287	51	27	transformations	transformation	NOUN
cana-4287	51	28	.	.	PUNCT
cana-4287	52	1	novel	novel	ADJ
cana-4287	52	2	techniques	technique	NOUN
cana-4287	52	3	to	to	ADP
cana-4287	52	4	data	data	NOUN
cana-4287	52	5	encoding	encoding	NOUN
cana-4287	52	6	and	and	CCONJ
cana-4287	52	7	safe	safe	ADJ
cana-4287	52	8	communication	communication	NOUN
cana-4287	52	9	protocols	protocol	NOUN
cana-4287	52	10	are	be	AUX
cana-4287	52	11	further	far	ADV
cana-4287	52	12	stimulated	stimulate	VERB
cana-4287	52	13	by	by	ADP
cana-4287	52	14	ideas	idea	NOUN
cana-4287	52	15	like	like	ADP
cana-4287	52	16	homotropy	homotropy	NOUN
cana-4287	52	17	and	and	CCONJ
cana-4287	52	18	simplicial	simplicial	ADJ
cana-4287	52	19	complexes	complex	NOUN
cana-4287	52	20	.	.	PUNCT
cana-4287	53	1	the	the	DET
cana-4287	53	2	significance	significance	NOUN
cana-4287	53	3	of	of	ADP
cana-4287	53	4	mathematical	mathematical	ADJ
cana-4287	53	5	abstraction	abstraction	NOUN
cana-4287	53	6	in	in	ADP
cana-4287	53	7	applied	apply	VERB
cana-4287	53	8	cryptography	cryptography	NOUN
cana-4287	53	9	is	be	AUX
cana-4287	53	10	highlighted	highlight	VERB
cana-4287	53	11	by	by	ADP
cana-4287	53	12	this	this	DET
cana-4287	53	13	multidisciplinary	multidisciplinary	ADJ
cana-4287	53	14	project	project	NOUN
cana-4287	53	15	.	.	PUNCT
cana-4287	54	1	the	the	DET
cana-4287	54	2	study	study	NOUN
cana-4287	54	3	illustrates	illustrate	VERB
cana-4287	54	4	how	how	SCONJ
cana-4287	54	5	algebraic	algebraic	ADJ
cana-4287	54	6	topology	topology	NOUN
cana-4287	54	7	can	can	AUX
cana-4287	54	8	result	result	VERB
cana-4287	54	9	in	in	ADP
cana-4287	54	10	quantifiable	quantifiable	ADJ
cana-4287	54	11	enhancements	enhancement	NOUN
cana-4287	54	12	to	to	PART
cana-4287	54	13	secure	secure	VERB
cana-4287	54	14	key	key	ADJ
cana-4287	54	15	distribution	distribution	NOUN
cana-4287	54	16	,	,	PUNCT
cana-4287	54	17	data	datum	NOUN
cana-4287	54	18	encryption	encryption	NOUN
cana-4287	54	19	,	,	PUNCT
cana-4287	54	20	and	and	CCONJ
cana-4287	54	21	authentication	authentication	NOUN
cana-4287	54	22	systems	system	NOUN
cana-4287	54	23	by	by	ADP
cana-4287	54	24	fusing	fuse	VERB
cana-4287	54	25	theoretical	theoretical	ADJ
cana-4287	54	26	understanding	understanding	NOUN
cana-4287	54	27	with	with	ADP
cana-4287	54	28	real	real	ADJ
cana-4287	54	29	-	-	PUNCT
cana-4287	54	30	world	world	NOUN
cana-4287	54	31	applications	application	NOUN
cana-4287	54	32	.	.	PUNCT
cana-4287	55	1	this	this	DET
cana-4287	55	2	study	study	NOUN
cana-4287	55	3	emphasizes	emphasize	VERB
cana-4287	55	4	the	the	DET
cana-4287	55	5	wider	wide	ADJ
cana-4287	55	6	ramifications	ramification	NOUN
cana-4287	55	7	of	of	ADP
cana-4287	55	8	interdisciplinary	interdisciplinary	ADJ
cana-4287	55	9	cooperation	cooperation	NOUN
cana-4287	55	10	in	in	ADP
cana-4287	55	11	addition	addition	NOUN
cana-4287	55	12	to	to	ADP
cana-4287	55	13	its	its	PRON
cana-4287	55	14	direct	direct	ADJ
cana-4287	55	15	applications	application	NOUN
cana-4287	55	16	.	.	PUNCT
cana-4287	56	1	in	in	ADP
cana-4287	56	2	addition	addition	NOUN
cana-4287	56	3	to	to	ADP
cana-4287	56	4	advancing	advance	VERB
cana-4287	56	5	cryptographic	cryptographic	ADJ
cana-4287	56	6	science	science	NOUN
cana-4287	56	7	,	,	PUNCT
cana-4287	56	8	algebraic	algebraic	ADJ
cana-4287	56	9	topology	topology	NOUN
cana-4287	56	10	's	's	PART
cana-4287	56	11	rigorous	rigorous	ADJ
cana-4287	56	12	mathematical	mathematical	ADJ
cana-4287	56	13	frameworks	framework	NOUN
cana-4287	56	14	enable	enable	VERB
cana-4287	56	15	deeper	deep	ADJ
cana-4287	56	16	understanding	understanding	NOUN
cana-4287	56	17	of	of	ADP
cana-4287	56	18	the	the	DET
cana-4287	56	19	structural	structural	ADJ
cana-4287	56	20	foundations	foundation	NOUN
cana-4287	56	21	of	of	ADP
cana-4287	56	22	cryptographic	cryptographic	ADJ
cana-4287	56	23	systems	system	NOUN
cana-4287	56	24	.	.	PUNCT
cana-4287	57	1	this	this	PRON
cana-4287	57	2	could	could	AUX
cana-4287	57	3	lead	lead	VERB
cana-4287	57	4	to	to	ADP
cana-4287	57	5	innovations	innovation	NOUN
cana-4287	57	6	in	in	ADP
cana-4287	57	7	cutting	cut	VERB
cana-4287	57	8	-	-	PUNCT
cana-4287	57	9	edge	edge	NOUN
cana-4287	57	10	domains	domain	NOUN
cana-4287	57	11	like	like	ADP
cana-4287	57	12	quantum	quantum	NOUN
cana-4287	57	13	-	-	PUNCT
cana-4287	57	14	resistant	resistant	ADJ
cana-4287	57	15	encryption	encryption	NOUN
cana-4287	57	16	and	and	CCONJ
cana-4287	57	17	blockchain	blockchain	PROPN
cana-4287	57	18	technology	technology	PROPN
cana-4287	57	19	.	.	PUNCT
cana-4287	58	1	beyond	beyond	ADP
cana-4287	58	2	its	its	PRON
cana-4287	58	3	direct	direct	ADJ
cana-4287	58	4	applications	application	NOUN
cana-4287	58	5	,	,	PUNCT
cana-4287	58	6	this	this	DET
cana-4287	58	7	study	study	NOUN
cana-4287	58	8	highlights	highlight	VERB
cana-4287	58	9	the	the	DET
cana-4287	58	10	broader	broad	ADJ
cana-4287	58	11	implications	implication	NOUN
cana-4287	58	12	of	of	ADP
cana-4287	58	13	interdisciplinary	interdisciplinary	ADJ
cana-4287	58	14	collaboration	collaboration	NOUN
cana-4287	58	15	.	.	PUNCT
cana-4287	59	1	the	the	DET
cana-4287	59	2	rigorous	rigorous	ADJ
cana-4287	59	3	mathematical	mathematical	ADJ
cana-4287	59	4	frameworks	framework	NOUN
cana-4287	59	5	of	of	ADP
cana-4287	59	6	algebraic	algebraic	ADJ
cana-4287	59	7	topology	topology	NOUN
cana-4287	59	8	not	not	PART
cana-4287	59	9	only	only	ADV
cana-4287	59	10	advance	advance	VERB
cana-4287	59	11	cryptographic	cryptographic	ADJ
cana-4287	59	12	science	science	NOUN
cana-4287	59	13	but	but	CCONJ
cana-4287	59	14	also	also	ADV
cana-4287	59	15	provide	provide	VERB
cana-4287	59	16	deeper	deep	ADJ
cana-4287	59	17	insights	insight	NOUN
cana-4287	59	18	into	into	ADP
cana-4287	59	19	the	the	DET
cana-4287	59	20	structural	structural	ADJ
cana-4287	59	21	foundations	foundation	NOUN
cana-4287	59	22	of	of	ADP
cana-4287	59	23	cryptographic	cryptographic	ADJ
cana-4287	59	24	systems	system	NOUN
cana-4287	59	25	.	.	PUNCT
cana-4287	60	1	this	this	DET
cana-4287	60	2	deeper	deep	ADJ
cana-4287	60	3	understanding	understanding	NOUN
cana-4287	60	4	has	have	VERB
cana-4287	60	5	the	the	DET
cana-4287	60	6	potential	potential	NOUN
cana-4287	60	7	to	to	PART
cana-4287	60	8	drive	drive	VERB
cana-4287	60	9	innovations	innovation	NOUN
cana-4287	60	10	in	in	ADP
cana-4287	60	11	emerging	emerge	VERB
cana-4287	60	12	fields	field	NOUN
cana-4287	60	13	such	such	ADJ
cana-4287	60	14	as	as	ADP
cana-4287	60	15	quantum	quantum	NOUN
cana-4287	60	16	-	-	PUNCT
cana-4287	60	17	resistant	resistant	ADJ
cana-4287	60	18	encryption	encryption	NOUN
cana-4287	60	19	and	and	CCONJ
cana-4287	60	20	blockchain	blockchain	PROPN
cana-4287	60	21	technology	technology	PROPN
cana-4287	60	22	,	,	PUNCT
cana-4287	60	23	paving	pave	VERB
cana-4287	60	24	the	the	DET
cana-4287	60	25	way	way	NOUN
cana-4287	60	26	for	for	ADP
cana-4287	60	27	more	more	ADV
cana-4287	60	28	secure	secure	ADJ
cana-4287	60	29	and	and	CCONJ
cana-4287	60	30	efficient	efficient	ADJ
cana-4287	60	31	digital	digital	ADJ
cana-4287	60	32	infrastructures	infrastructure	NOUN
cana-4287	60	33	.	.	PUNCT
cana-4287	61	1	communications	communication	NOUN
cana-4287	61	2	on	on	ADP
cana-4287	61	3	applied	apply	VERB
cana-4287	61	4	nonlinear	nonlinear	ADJ
cana-4287	61	5	analysis	analysis	NOUN
cana-4287	61	6	issn	issn	NOUN
cana-4287	61	7	:	:	PUNCT
cana-4287	61	8	1074	1074	NUM
cana-4287	61	9	-	-	PUNCT
cana-4287	61	10	133x	133x	NUM
cana-4287	61	11	vol	vol	NOUN
cana-4287	61	12	32	32	NUM
cana-4287	61	13	no	no	NOUN
cana-4287	61	14	.	.	PUNCT
cana-4287	62	1	9s	9s	NUM
cana-4287	62	2	(	(	PUNCT
cana-4287	62	3	2025	2025	NUM
cana-4287	62	4	)	)	PUNCT
cana-4287	62	5	1731	1731	NUM
cana-4287	62	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	62	7	fig	fig	NOUN
cana-4287	62	8	.	.	PUNCT
cana-4287	63	1	3	3	NUM
cana-4287	63	2	:	:	PUNCT
cana-4287	63	3	bridging	bridge	VERB
cana-4287	63	4	cryptography	cryptography	NOUN
cana-4287	63	5	and	and	CCONJ
cana-4287	63	6	algebraic	algebraic	ADJ
cana-4287	63	7	topology	topology	NOUN
cana-4287	63	8	in	in	ADP
cana-4287	63	9	the	the	DET
cana-4287	63	10	end	end	NOUN
cana-4287	63	11	,	,	PUNCT
cana-4287	63	12	our	our	PRON
cana-4287	63	13	work	work	NOUN
cana-4287	63	14	demonstrates	demonstrate	VERB
cana-4287	63	15	algebraic	algebraic	ADJ
cana-4287	63	16	topology	topology	NOUN
cana-4287	63	17	as	as	ADP
cana-4287	63	18	a	a	DET
cana-4287	63	19	crucial	crucial	ADJ
cana-4287	63	20	instrument	instrument	NOUN
cana-4287	63	21	in	in	ADP
cana-4287	63	22	contemporary	contemporary	ADJ
cana-4287	63	23	cryptography	cryptography	NOUN
cana-4287	63	24	,	,	PUNCT
cana-4287	63	25	opening	open	VERB
cana-4287	63	26	the	the	DET
cana-4287	63	27	door	door	NOUN
cana-4287	63	28	for	for	ADP
cana-4287	63	29	creative	creative	ADJ
cana-4287	63	30	approaches	approach	NOUN
cana-4287	63	31	and	and	CCONJ
cana-4287	63	32	cooperative	cooperative	ADJ
cana-4287	63	33	research	research	NOUN
cana-4287	63	34	.	.	PUNCT
cana-4287	64	1	it	it	PRON
cana-4287	64	2	establishes	establish	VERB
cana-4287	64	3	algebraic	algebraic	ADJ
cana-4287	64	4	topology	topology	NOUN
cana-4287	64	5	as	as	ADP
cana-4287	64	6	a	a	DET
cana-4287	64	7	revolutionary	revolutionary	ADJ
cana-4287	64	8	framework	framework	NOUN
cana-4287	64	9	in	in	ADP
cana-4287	64	10	the	the	DET
cana-4287	64	11	increasingly	increasingly	ADV
cana-4287	64	12	digital	digital	ADJ
cana-4287	64	13	and	and	CCONJ
cana-4287	64	14	security	security	NOUN
cana-4287	64	15	-	-	PUNCT
cana-4287	64	16	conscious	conscious	ADJ
cana-4287	64	17	society	society	NOUN
cana-4287	64	18	by	by	ADP
cana-4287	64	19	tackling	tackle	VERB
cana-4287	64	20	urgent	urgent	ADJ
cana-4287	64	21	issues	issue	NOUN
cana-4287	64	22	in	in	ADP
cana-4287	64	23	data	datum	NOUN
cana-4287	64	24	integrity	integrity	NOUN
cana-4287	64	25	and	and	CCONJ
cana-4287	64	26	safe	safe	ADJ
cana-4287	64	27	communication	communication	NOUN
cana-4287	64	28	.	.	PUNCT
cana-4287	65	1	literature	literature	NOUN
cana-4287	65	2	review	review	PROPN
cana-4287	65	3	[	[	X
cana-4287	65	4	1]this	1]this	NUM
cana-4287	65	5	study	study	NOUN
cana-4287	65	6	proposes	propose	VERB
cana-4287	65	7	the	the	DET
cana-4287	65	8	use	use	NOUN
cana-4287	65	9	of	of	ADP
cana-4287	65	10	algebraic	algebraic	ADJ
cana-4287	65	11	subsets	subset	NOUN
cana-4287	65	12	in	in	ADP
cana-4287	65	13	public	public	ADJ
cana-4287	65	14	-	-	PUNCT
cana-4287	65	15	key	key	NOUN
cana-4287	65	16	cryptography	cryptography	NOUN
cana-4287	65	17	protocols	protocol	NOUN
cana-4287	65	18	as	as	ADP
cana-4287	65	19	an	an	DET
cana-4287	65	20	alternative	alternative	NOUN
cana-4287	65	21	to	to	ADP
cana-4287	65	22	traditional	traditional	ADJ
cana-4287	65	23	subgroups	subgroup	NOUN
cana-4287	65	24	.	.	PUNCT
cana-4287	66	1	the	the	DET
cana-4287	66	2	authors	author	NOUN
cana-4287	66	3	use	use	VERB
cana-4287	66	4	subset	subset	NOUN
cana-4287	66	5	versions	version	NOUN
cana-4287	66	6	of	of	ADP
cana-4287	66	7	the	the	DET
cana-4287	66	8	protocols	protocol	NOUN
cana-4287	66	9	devised	devise	VERB
cana-4287	66	10	by	by	ADP
cana-4287	66	11	shpilrain	shpilrain	NOUN
cana-4287	66	12	and	and	CCONJ
cana-4287	66	13	ushakov	ushakov	NOUN
cana-4287	66	14	to	to	PART
cana-4287	66	15	demonstrate	demonstrate	VERB
cana-4287	66	16	ascending	ascend	VERB
cana-4287	66	17	hnn	hnn	PROPN
cana-4287	66	18	-	-	PUNCT
cana-4287	66	19	extensions	extension	NOUN
cana-4287	66	20	of	of	ADP
cana-4287	66	21	free	free	ADJ
cana-4287	66	22	-	-	PUNCT
cana-4287	66	23	abelian	abelian	ADJ
cana-4287	66	24	groups	group	NOUN
cana-4287	66	25	.	.	PUNCT
cana-4287	67	1	they	they	PRON
cana-4287	67	2	suggest	suggest	VERB
cana-4287	67	3	that	that	SCONJ
cana-4287	67	4	algebraic	algebraic	ADJ
cana-4287	67	5	subsets	subset	NOUN
cana-4287	67	6	can	can	AUX
cana-4287	67	7	offer	offer	VERB
cana-4287	67	8	additional	additional	ADJ
cana-4287	67	9	security	security	NOUN
cana-4287	67	10	features	feature	NOUN
cana-4287	67	11	and	and	CCONJ
cana-4287	67	12	discuss	discuss	VERB
cana-4287	67	13	how	how	SCONJ
cana-4287	67	14	these	these	DET
cana-4287	67	15	subset	subset	NOUN
cana-4287	67	16	-	-	PUNCT
cana-4287	67	17	based	base	VERB
cana-4287	67	18	protocols	protocol	NOUN
cana-4287	67	19	can	can	AUX
cana-4287	67	20	resist	resist	VERB
cana-4287	67	21	attacks	attack	NOUN
cana-4287	67	22	based	base	VERB
cana-4287	67	23	on	on	ADP
cana-4287	67	24	length	length	NOUN
cana-4287	67	25	and	and	CCONJ
cana-4287	67	26	distance	distance	NOUN
cana-4287	67	27	.	.	PUNCT
cana-4287	68	1	additionally	additionally	ADV
cana-4287	68	2	,	,	PUNCT
cana-4287	68	3	the	the	DET
cana-4287	68	4	work	work	NOUN
cana-4287	68	5	highlights	highlight	VERB
cana-4287	68	6	new	new	ADJ
cana-4287	68	7	group	group	NOUN
cana-4287	68	8	-	-	PUNCT
cana-4287	68	9	theoretic	theoretic	ADJ
cana-4287	68	10	problems	problem	NOUN
cana-4287	68	11	that	that	PRON
cana-4287	68	12	arise	arise	VERB
cana-4287	68	13	from	from	ADP
cana-4287	68	14	this	this	DET
cana-4287	68	15	approach	approach	NOUN
cana-4287	68	16	,	,	PUNCT
cana-4287	68	17	indicating	indicate	VERB
cana-4287	68	18	areas	area	NOUN
cana-4287	68	19	for	for	ADP
cana-4287	68	20	future	future	ADJ
cana-4287	68	21	research	research	NOUN
cana-4287	68	22	in	in	ADP
cana-4287	68	23	cryptography	cryptography	NOUN
cana-4287	68	24	based	base	VERB
cana-4287	68	25	on	on	ADP
cana-4287	68	26	algebraic	algebraic	ADJ
cana-4287	68	27	structures	structure	NOUN
cana-4287	68	28	.	.	PUNCT
cana-4287	69	1	[	[	X
cana-4287	69	2	2	2	X
cana-4287	69	3	]	]	PUNCT
cana-4287	69	4	gonzález	gonzález	PROPN
cana-4287	69	5	vasco	vasco	PROPN
cana-4287	69	6	et	et	PROPN
cana-4287	69	7	al	al	PROPN
cana-4287	69	8	.	.	PROPN
cana-4287	69	9	's	's	PART
cana-4287	69	10	paper	paper	NOUN
cana-4287	69	11	"	"	PUNCT
cana-4287	69	12	applications	application	NOUN
cana-4287	69	13	of	of	ADP
cana-4287	69	14	finite	finite	ADJ
cana-4287	69	15	non	non	ADJ
cana-4287	69	16	-	-	ADJ
cana-4287	69	17	abelian	abelian	ADJ
cana-4287	69	18	simple	simple	ADJ
cana-4287	69	19	groups	group	NOUN
cana-4287	69	20	to	to	ADP
cana-4287	69	21	cryptography	cryptography	NOUN
cana-4287	69	22	in	in	ADP
cana-4287	69	23	the	the	DET
cana-4287	69	24	quantum	quantum	ADJ
cana-4287	69	25	era	era	NOUN
cana-4287	69	26	"	"	PUNCT
cana-4287	69	27	(	(	PUNCT
cana-4287	69	28	2023	2023	NUM
cana-4287	69	29	):	):	PUNCT
cana-4287	69	30	this	this	DET
cana-4287	69	31	paper	paper	NOUN
cana-4287	69	32	explores	explore	VERB
cana-4287	69	33	the	the	DET
cana-4287	69	34	possibility	possibility	NOUN
cana-4287	69	35	of	of	ADP
cana-4287	69	36	using	use	VERB
cana-4287	69	37	finite	finite	PROPN
cana-4287	69	38	non	non	ADJ
cana-4287	69	39	-	-	ADJ
cana-4287	69	40	abelian	abelian	ADJ
cana-4287	69	41	simple	simple	ADJ
cana-4287	69	42	groups	group	NOUN
cana-4287	69	43	to	to	PART
cana-4287	69	44	develop	develop	VERB
cana-4287	69	45	cryptographic	cryptographic	ADJ
cana-4287	69	46	techniques	technique	NOUN
cana-4287	69	47	that	that	PRON
cana-4287	69	48	are	be	AUX
cana-4287	69	49	impervious	impervious	ADJ
cana-4287	69	50	to	to	ADP
cana-4287	69	51	quantum	quantum	ADJ
cana-4287	69	52	attacks	attack	NOUN
cana-4287	69	53	.	.	PUNCT
cana-4287	70	1	the	the	DET
cana-4287	70	2	authors	author	NOUN
cana-4287	70	3	look	look	VERB
cana-4287	70	4	at	at	ADP
cana-4287	70	5	several	several	ADJ
cana-4287	70	6	group	group	NOUN
cana-4287	70	7	-	-	PUNCT
cana-4287	70	8	theoretic	theoretic	ADJ
cana-4287	70	9	factorization	factorization	NOUN
cana-4287	70	10	problems	problem	NOUN
cana-4287	70	11	and	and	CCONJ
cana-4287	70	12	how	how	SCONJ
cana-4287	70	13	they	they	PRON
cana-4287	70	14	are	be	AUX
cana-4287	70	15	applied	apply	VERB
cana-4287	70	16	to	to	PART
cana-4287	70	17	construct	construct	VERB
cana-4287	70	18	cryptographic	cryptographic	ADJ
cana-4287	70	19	protocols	protocol	NOUN
cana-4287	70	20	,	,	PUNCT
cana-4287	70	21	including	include	VERB
cana-4287	70	22	group	group	NOUN
cana-4287	70	23	-	-	PUNCT
cana-4287	70	24	theoretic	theoretic	ADJ
cana-4287	70	25	hash	hash	NOUN
cana-4287	70	26	functions	function	NOUN
cana-4287	70	27	and	and	CCONJ
cana-4287	70	28	fully	fully	ADV
cana-4287	70	29	homomorphic	homomorphic	ADJ
cana-4287	70	30	encryption	encryption	NOUN
cana-4287	70	31	systems	system	NOUN
cana-4287	70	32	.	.	PUNCT
cana-4287	71	1	the	the	DET
cana-4287	71	2	study	study	NOUN
cana-4287	71	3	also	also	ADV
cana-4287	71	4	discusses	discuss	VERB
cana-4287	71	5	the	the	DET
cana-4287	71	6	relevance	relevance	NOUN
cana-4287	71	7	of	of	ADP
cana-4287	71	8	the	the	DET
cana-4287	71	9	hidden	hide	VERB
cana-4287	71	10	subgroup	subgroup	NOUN
cana-4287	71	11	problem	problem	NOUN
cana-4287	71	12	in	in	ADP
cana-4287	71	13	this	this	DET
cana-4287	71	14	context	context	NOUN
cana-4287	71	15	,	,	PUNCT
cana-4287	71	16	highlighting	highlight	VERB
cana-4287	71	17	the	the	DET
cana-4287	71	18	need	need	NOUN
cana-4287	71	19	for	for	ADP
cana-4287	71	20	increased	increased	ADJ
cana-4287	71	21	collaboration	collaboration	NOUN
cana-4287	71	22	between	between	ADP
cana-4287	71	23	group	group	NOUN
cana-4287	71	24	theorists	theorist	NOUN
cana-4287	71	25	and	and	CCONJ
cana-4287	71	26	cryptographers	cryptographer	NOUN
cana-4287	71	27	to	to	PART
cana-4287	71	28	develop	develop	VERB
cana-4287	71	29	quantum	quantum	NOUN
cana-4287	71	30	-	-	PUNCT
cana-4287	71	31	resistant	resistant	ADJ
cana-4287	71	32	cryptographic	cryptographic	ADJ
cana-4287	71	33	solutions	solution	NOUN
cana-4287	71	34	.	.	PUNCT
cana-4287	72	1	[	[	X
cana-4287	72	2	3	3	X
cana-4287	72	3	]	]	PUNCT
cana-4287	72	4	"	"	PUNCT
cana-4287	72	5	advancing	advance	VERB
cana-4287	72	6	scalability	scalability	NOUN
cana-4287	72	7	in	in	ADP
cana-4287	72	8	decentralised	decentralised	ADJ
cana-4287	72	9	storage	storage	NOUN
cana-4287	72	10	:	:	PUNCT
cana-4287	72	11	a	a	DET
cana-4287	72	12	novel	novel	ADJ
cana-4287	72	13	approach	approach	NOUN
cana-4287	72	14	to	to	ADP
cana-4287	72	15	proof	proof	NOUN
cana-4287	72	16	-	-	PUNCT
cana-4287	72	17	of	of	ADP
cana-4287	72	18	-	-	PUNCT
cana-4287	72	19	replication	replication	NOUN
cana-4287	72	20	via	via	ADP
cana-4287	72	21	polynomial	polynomial	ADJ
cana-4287	72	22	evaluation	evaluation	NOUN
cana-4287	72	23	"	"	PUNCT
cana-4287	72	24	(	(	PUNCT
cana-4287	72	25	2024	2024	NUM
cana-4287	72	26	):	):	PUNCT
cana-4287	72	27	in	in	ADP
cana-4287	72	28	order	order	NOUN
cana-4287	72	29	to	to	PART
cana-4287	72	30	solve	solve	VERB
cana-4287	72	31	scalability	scalability	NOUN
cana-4287	72	32	problems	problem	NOUN
cana-4287	72	33	in	in	ADP
cana-4287	72	34	decentralized	decentralize	VERB
cana-4287	72	35	storage	storage	NOUN
cana-4287	72	36	networks	network	NOUN
cana-4287	72	37	,	,	PUNCT
cana-4287	72	38	this	this	DET
cana-4287	72	39	study	study	NOUN
cana-4287	72	40	presents	present	VERB
cana-4287	72	41	a	a	DET
cana-4287	72	42	novel	novel	ADJ
cana-4287	72	43	proof	proof	NOUN
cana-4287	72	44	-	-	PUNCT
cana-4287	72	45	of	of	ADP
cana-4287	72	46	-	-	PUNCT
cana-4287	72	47	replication	replication	NOUN
cana-4287	72	48	(	(	PUNCT
cana-4287	72	49	porep	porep	NOUN
cana-4287	72	50	)	)	PUNCT
cana-4287	72	51	scheme	scheme	NOUN
cana-4287	72	52	based	base	VERB
cana-4287	72	53	on	on	ADP
cana-4287	72	54	polynomial	polynomial	ADJ
cana-4287	72	55	evaluation	evaluation	NOUN
cana-4287	72	56	.	.	PUNCT
cana-4287	73	1	this	this	DET
cana-4287	73	2	approach	approach	NOUN
cana-4287	73	3	improves	improve	VERB
cana-4287	73	4	security	security	NOUN
cana-4287	73	5	and	and	CCONJ
cana-4287	73	6	performance	performance	NOUN
cana-4287	73	7	while	while	SCONJ
cana-4287	73	8	verifying	verify	VERB
cana-4287	73	9	data	data	NOUN
cana-4287	73	10	replication	replication	NOUN
cana-4287	73	11	by	by	ADP
cana-4287	73	12	using	use	VERB
cana-4287	73	13	algebraic	algebraic	ADJ
cana-4287	73	14	techniques	technique	NOUN
cana-4287	73	15	,	,	PUNCT
cana-4287	73	16	as	as	SCONJ
cana-4287	73	17	opposed	oppose	VERB
cana-4287	73	18	to	to	ADP
cana-4287	73	19	traditional	traditional	ADJ
cana-4287	73	20	probabilistic	probabilistic	ADJ
cana-4287	73	21	checking	check	VERB
cana-4287	73	22	methods	method	NOUN
cana-4287	73	23	.	.	PUNCT
cana-4287	74	1	the	the	DET
cana-4287	74	2	authors	author	NOUN
cana-4287	74	3	demonstrate	demonstrate	VERB
cana-4287	74	4	how	how	SCONJ
cana-4287	74	5	their	their	PRON
cana-4287	74	6	method	method	NOUN
cana-4287	74	7	reduces	reduce	VERB
cana-4287	74	8	computing	compute	VERB
cana-4287	74	9	overhead	overhead	ADV
cana-4287	74	10	,	,	PUNCT
cana-4287	74	11	making	make	VERB
cana-4287	74	12	it	it	PRON
cana-4287	74	13	suitable	suitable	ADJ
cana-4287	74	14	for	for	ADP
cana-4287	74	15	usage	usage	NOUN
cana-4287	74	16	in	in	ADP
cana-4287	74	17	large	large	ADJ
cana-4287	74	18	-	-	PUNCT
cana-4287	74	19	scale	scale	NOUN
cana-4287	74	20	systems	system	NOUN
cana-4287	74	21	like	like	ADP
cana-4287	74	22	filecoin	filecoin	NOUN
cana-4287	74	23	.	.	PUNCT
cana-4287	75	1	this	this	DET
cana-4287	75	2	paper	paper	NOUN
cana-4287	75	3	shows	show	VERB
cana-4287	75	4	how	how	SCONJ
cana-4287	75	5	cryptographic	cryptographic	ADJ
cana-4287	75	6	protocols	protocol	NOUN
cana-4287	75	7	for	for	ADP
cana-4287	75	8	decentralized	decentralize	VERB
cana-4287	75	9	storage	storage	NOUN
cana-4287	75	10	systems	system	NOUN
cana-4287	75	11	can	can	AUX
cana-4287	75	12	be	be	AUX
cana-4287	75	13	improved	improve	VERB
cana-4287	75	14	through	through	ADP
cana-4287	75	15	the	the	DET
cana-4287	75	16	application	application	NOUN
cana-4287	75	17	of	of	ADP
cana-4287	75	18	algebraic	algebraic	ADJ
cana-4287	75	19	approaches	approach	NOUN
cana-4287	75	20	.	.	PUNCT
cana-4287	76	1	communications	communication	NOUN
cana-4287	76	2	on	on	ADP
cana-4287	76	3	applied	apply	VERB
cana-4287	76	4	nonlinear	nonlinear	ADJ
cana-4287	76	5	analysis	analysis	NOUN
cana-4287	76	6	issn	issn	NOUN
cana-4287	76	7	:	:	PUNCT
cana-4287	76	8	1074	1074	NUM
cana-4287	76	9	-	-	PUNCT
cana-4287	76	10	133x	133x	NUM
cana-4287	76	11	vol	vol	NOUN
cana-4287	76	12	32	32	NUM
cana-4287	76	13	no	no	NOUN
cana-4287	76	14	.	.	PUNCT
cana-4287	77	1	9s	9s	NUM
cana-4287	77	2	(	(	PUNCT
cana-4287	77	3	2025	2025	NUM
cana-4287	77	4	)	)	PUNCT
cana-4287	77	5	1732	1732	NUM
cana-4287	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	78	1	[	[	X
cana-4287	78	2	4	4	X
cana-4287	78	3	]	]	PUNCT
cana-4287	78	4	"	"	PUNCT
cana-4287	78	5	a	a	DET
cana-4287	78	6	new	new	ADJ
cana-4287	78	7	algebraic	algebraic	ADJ
cana-4287	78	8	approach	approach	NOUN
cana-4287	78	9	to	to	ADP
cana-4287	78	10	the	the	DET
cana-4287	78	11	regular	regular	ADJ
cana-4287	78	12	syndrome	syndrome	NOUN
cana-4287	78	13	decoding	decode	VERB
cana-4287	78	14	problem	problem	NOUN
cana-4287	78	15	and	and	CCONJ
cana-4287	78	16	implications	implication	NOUN
cana-4287	78	17	for	for	ADP
cana-4287	78	18	pcg	pcg	PROPN
cana-4287	78	19	constructions	construction	NOUN
cana-4287	78	20	"	"	PUNCT
cana-4287	78	21	(	(	PUNCT
cana-4287	78	22	2023	2023	NUM
cana-4287	78	23	):	):	PUNCT
cana-4287	78	24	in	in	ADP
cana-4287	78	25	order	order	NOUN
cana-4287	78	26	to	to	PART
cana-4287	78	27	solve	solve	VERB
cana-4287	78	28	scalability	scalability	NOUN
cana-4287	78	29	problems	problem	NOUN
cana-4287	78	30	in	in	ADP
cana-4287	78	31	decentralized	decentralize	VERB
cana-4287	78	32	storage	storage	NOUN
cana-4287	78	33	networks	network	NOUN
cana-4287	78	34	,	,	PUNCT
cana-4287	78	35	this	this	DET
cana-4287	78	36	study	study	NOUN
cana-4287	78	37	presents	present	VERB
cana-4287	78	38	a	a	DET
cana-4287	78	39	novel	novel	ADJ
cana-4287	78	40	proof	proof	NOUN
cana-4287	78	41	-	-	PUNCT
cana-4287	78	42	of	of	ADP
cana-4287	78	43	-	-	PUNCT
cana-4287	78	44	replication	replication	NOUN
cana-4287	78	45	(	(	PUNCT
cana-4287	78	46	porep	porep	NOUN
cana-4287	78	47	)	)	PUNCT
cana-4287	78	48	scheme	scheme	NOUN
cana-4287	78	49	based	base	VERB
cana-4287	78	50	on	on	ADP
cana-4287	78	51	polynomial	polynomial	ADJ
cana-4287	78	52	evaluation	evaluation	NOUN
cana-4287	78	53	.	.	PUNCT
cana-4287	79	1	this	this	DET
cana-4287	79	2	approach	approach	NOUN
cana-4287	79	3	improves	improve	VERB
cana-4287	79	4	security	security	NOUN
cana-4287	79	5	and	and	CCONJ
cana-4287	79	6	performance	performance	NOUN
cana-4287	79	7	while	while	SCONJ
cana-4287	79	8	verifying	verify	VERB
cana-4287	79	9	data	data	NOUN
cana-4287	79	10	replication	replication	NOUN
cana-4287	79	11	by	by	ADP
cana-4287	79	12	using	use	VERB
cana-4287	79	13	algebraic	algebraic	ADJ
cana-4287	79	14	techniques	technique	NOUN
cana-4287	79	15	,	,	PUNCT
cana-4287	79	16	as	as	SCONJ
cana-4287	79	17	opposed	oppose	VERB
cana-4287	79	18	to	to	ADP
cana-4287	79	19	traditional	traditional	ADJ
cana-4287	79	20	probabilistic	probabilistic	ADJ
cana-4287	79	21	checking	check	VERB
cana-4287	79	22	methods	method	NOUN
cana-4287	79	23	.	.	PUNCT
cana-4287	80	1	the	the	DET
cana-4287	80	2	authors	author	NOUN
cana-4287	80	3	demonstrate	demonstrate	VERB
cana-4287	80	4	how	how	SCONJ
cana-4287	80	5	their	their	PRON
cana-4287	80	6	method	method	NOUN
cana-4287	80	7	reduces	reduce	VERB
cana-4287	80	8	computing	compute	VERB
cana-4287	80	9	overhead	overhead	ADV
cana-4287	80	10	,	,	PUNCT
cana-4287	80	11	making	make	VERB
cana-4287	80	12	it	it	PRON
cana-4287	80	13	suitable	suitable	ADJ
cana-4287	80	14	for	for	ADP
cana-4287	80	15	usage	usage	NOUN
cana-4287	80	16	in	in	ADP
cana-4287	80	17	large	large	ADJ
cana-4287	80	18	-	-	PUNCT
cana-4287	80	19	scale	scale	NOUN
cana-4287	80	20	systems	system	NOUN
cana-4287	80	21	like	like	ADP
cana-4287	80	22	filecoin	filecoin	NOUN
cana-4287	80	23	.	.	PUNCT
cana-4287	81	1	this	this	DET
cana-4287	81	2	paper	paper	NOUN
cana-4287	81	3	shows	show	VERB
cana-4287	81	4	how	how	SCONJ
cana-4287	81	5	cryptographic	cryptographic	ADJ
cana-4287	81	6	protocols	protocol	NOUN
cana-4287	81	7	for	for	ADP
cana-4287	81	8	decentralized	decentralize	VERB
cana-4287	81	9	storage	storage	NOUN
cana-4287	81	10	systems	system	NOUN
cana-4287	81	11	can	can	AUX
cana-4287	81	12	be	be	AUX
cana-4287	81	13	improved	improve	VERB
cana-4287	81	14	through	through	ADP
cana-4287	81	15	the	the	DET
cana-4287	81	16	application	application	NOUN
cana-4287	81	17	of	of	ADP
cana-4287	81	18	algebraic	algebraic	ADJ
cana-4287	81	19	approaches	approach	NOUN
cana-4287	81	20	.	.	PUNCT
cana-4287	82	1	[	[	X
cana-4287	82	2	5	5	NUM
cana-4287	82	3	]	]	PUNCT
cana-4287	82	4	"	"	PUNCT
cana-4287	82	5	algebraic	algebraic	ADJ
cana-4287	82	6	topology	topology	NOUN
cana-4287	82	7	and	and	CCONJ
cana-4287	82	8	distributed	distributed	ADJ
cana-4287	82	9	computing	computing	NOUN
cana-4287	82	10	"	"	PUNCT
cana-4287	82	11	(	(	PUNCT
cana-4287	82	12	2024	2024	NUM
cana-4287	82	13	)	)	PUNCT
cana-4287	82	14	this	this	DET
cana-4287	82	15	work	work	NOUN
cana-4287	82	16	explores	explore	VERB
cana-4287	82	17	the	the	DET
cana-4287	82	18	application	application	NOUN
cana-4287	82	19	of	of	ADP
cana-4287	82	20	algebraic	algebraic	ADJ
cana-4287	82	21	topology	topology	NOUN
cana-4287	82	22	in	in	ADP
cana-4287	82	23	distributed	distribute	VERB
cana-4287	82	24	computing	computing	NOUN
cana-4287	82	25	systems	system	NOUN
cana-4287	82	26	with	with	ADP
cana-4287	82	27	implications	implication	NOUN
cana-4287	82	28	for	for	ADP
cana-4287	82	29	cryptographic	cryptographic	ADJ
cana-4287	82	30	protocols	protocol	NOUN
cana-4287	82	31	.	.	PUNCT
cana-4287	83	1	the	the	DET
cana-4287	83	2	authors	author	NOUN
cana-4287	83	3	investigate	investigate	VERB
cana-4287	83	4	how	how	SCONJ
cana-4287	83	5	topological	topological	ADJ
cana-4287	83	6	techniques	technique	NOUN
cana-4287	83	7	may	may	AUX
cana-4287	83	8	be	be	AUX
cana-4287	83	9	used	use	VERB
cana-4287	83	10	to	to	PART
cana-4287	83	11	represent	represent	VERB
cana-4287	83	12	and	and	CCONJ
cana-4287	83	13	analyze	analyze	VERB
cana-4287	83	14	the	the	DET
cana-4287	83	15	complexities	complexity	NOUN
cana-4287	83	16	of	of	ADP
cana-4287	83	17	distributed	distribute	VERB
cana-4287	83	18	networks	network	NOUN
cana-4287	83	19	in	in	ADP
cana-4287	83	20	order	order	NOUN
cana-4287	83	21	to	to	PART
cana-4287	83	22	gain	gain	VERB
cana-4287	83	23	a	a	DET
cana-4287	83	24	better	well	ADJ
cana-4287	83	25	understanding	understanding	NOUN
cana-4287	83	26	of	of	ADP
cana-4287	83	27	fault	fault	NOUN
cana-4287	83	28	tolerance	tolerance	NOUN
cana-4287	83	29	and	and	CCONJ
cana-4287	83	30	consensus	consensus	NOUN
cana-4287	83	31	procedures	procedure	NOUN
cana-4287	83	32	.	.	PUNCT
cana-4287	84	1	the	the	DET
cana-4287	84	2	paper	paper	NOUN
cana-4287	84	3	claims	claim	VERB
cana-4287	84	4	that	that	SCONJ
cana-4287	84	5	algebraic	algebraic	PROPN
cana-4287	84	6	topology	topology	NOUN
cana-4287	84	7	offers	offer	VERB
cana-4287	84	8	a	a	DET
cana-4287	84	9	disciplinary	disciplinary	ADJ
cana-4287	84	10	perspective	perspective	NOUN
cana-4287	84	11	that	that	PRON
cana-4287	84	12	bridges	bridge	VERB
cana-4287	84	13	the	the	DET
cana-4287	84	14	fields	field	NOUN
cana-4287	84	15	of	of	ADP
cana-4287	84	16	mathematics	mathematic	NOUN
cana-4287	84	17	and	and	CCONJ
cana-4287	84	18	computer	computer	NOUN
cana-4287	84	19	science	science	NOUN
cana-4287	84	20	and	and	CCONJ
cana-4287	84	21	can	can	AUX
cana-4287	84	22	enhance	enhance	VERB
cana-4287	84	23	the	the	DET
cana-4287	84	24	reliability	reliability	NOUN
cana-4287	84	25	and	and	CCONJ
cana-4287	84	26	security	security	NOUN
cana-4287	84	27	of	of	ADP
cana-4287	84	28	distributed	distribute	VERB
cana-4287	84	29	systems	system	NOUN
cana-4287	84	30	.	.	PUNCT
cana-4287	85	1	[	[	X
cana-4287	85	2	6	6	NUM
cana-4287	85	3	]	]	PUNCT
cana-4287	85	4	"	"	PUNCT
cana-4287	85	5	topology	topology	NOUN
cana-4287	85	6	-	-	PUNCT
cana-4287	85	7	based	base	VERB
cana-4287	85	8	key	key	ADJ
cana-4287	85	9	exchange	exchange	NOUN
cana-4287	85	10	mechanisms	mechanism	NOUN
cana-4287	85	11	in	in	ADP
cana-4287	85	12	quantum	quantum	ADJ
cana-4287	85	13	cryptography	cryptography	NOUN
cana-4287	85	14	"	"	PUNCT
cana-4287	85	15	(	(	PUNCT
cana-4287	85	16	2024	2024	NUM
cana-4287	85	17	)	)	PUNCT
cana-4287	85	18	:	:	PUNCT
cana-4287	85	19	this	this	DET
cana-4287	85	20	work	work	NOUN
cana-4287	85	21	investigates	investigate	VERB
cana-4287	85	22	how	how	SCONJ
cana-4287	85	23	algebraic	algebraic	ADJ
cana-4287	85	24	topology	topology	NOUN
cana-4287	85	25	can	can	AUX
cana-4287	85	26	improve	improve	VERB
cana-4287	85	27	key	key	ADJ
cana-4287	85	28	exchange	exchange	NOUN
cana-4287	85	29	techniques	technique	NOUN
cana-4287	85	30	in	in	ADP
cana-4287	85	31	quantum	quantum	ADJ
cana-4287	85	32	cryptography	cryptography	NOUN
cana-4287	85	33	.	.	PUNCT
cana-4287	86	1	the	the	DET
cana-4287	86	2	authors	author	NOUN
cana-4287	86	3	use	use	VERB
cana-4287	86	4	topological	topological	ADJ
cana-4287	86	5	invariants	invariant	NOUN
cana-4287	86	6	,	,	PUNCT
cana-4287	86	7	including	include	VERB
cana-4287	86	8	betti	betti	NOUN
cana-4287	86	9	numbers	number	NOUN
cana-4287	86	10	,	,	PUNCT
cana-4287	86	11	to	to	PART
cana-4287	86	12	establish	establish	VERB
cana-4287	86	13	secure	secure	ADJ
cana-4287	86	14	communication	communication	NOUN
cana-4287	86	15	channels	channel	NOUN
cana-4287	86	16	that	that	PRON
cana-4287	86	17	are	be	AUX
cana-4287	86	18	resistant	resistant	ADJ
cana-4287	86	19	to	to	ADP
cana-4287	86	20	quantum	quantum	NOUN
cana-4287	86	21	decryption	decryption	NOUN
cana-4287	86	22	techniques	technique	NOUN
cana-4287	86	23	.	.	PUNCT
cana-4287	87	1	the	the	DET
cana-4287	87	2	recommended	recommend	VERB
cana-4287	87	3	methods	method	NOUN
cana-4287	87	4	maintain	maintain	VERB
cana-4287	87	5	stringent	stringent	ADJ
cana-4287	87	6	security	security	NOUN
cana-4287	87	7	standards	standard	NOUN
cana-4287	87	8	while	while	SCONJ
cana-4287	87	9	demonstrating	demonstrate	VERB
cana-4287	87	10	increased	increase	VERB
cana-4287	87	11	computational	computational	ADJ
cana-4287	87	12	efficiency	efficiency	NOUN
cana-4287	87	13	.	.	PUNCT
cana-4287	88	1	the	the	DET
cana-4287	88	2	article	article	NOUN
cana-4287	88	3	shows	show	VERB
cana-4287	88	4	how	how	SCONJ
cana-4287	88	5	algebraic	algebraic	ADJ
cana-4287	88	6	topological	topological	ADJ
cana-4287	88	7	techniques	technique	NOUN
cana-4287	88	8	can	can	AUX
cana-4287	88	9	be	be	AUX
cana-4287	88	10	used	use	VERB
cana-4287	88	11	to	to	PART
cana-4287	88	12	close	close	VERB
cana-4287	88	13	gaps	gap	NOUN
cana-4287	88	14	in	in	ADP
cana-4287	88	15	both	both	CCONJ
cana-4287	88	16	classical	classical	ADJ
cana-4287	88	17	and	and	CCONJ
cana-4287	88	18	quantum	quantum	ADJ
cana-4287	88	19	cryptography	cryptography	NOUN
cana-4287	88	20	systems	system	NOUN
cana-4287	88	21	.	.	PUNCT
cana-4287	89	1	[	[	X
cana-4287	89	2	7	7	X
cana-4287	89	3	]	]	PUNCT
cana-4287	89	4	"	"	PUNCT
cana-4287	89	5	homotopy	homotopy	NOUN
cana-4287	89	6	-	-	PUNCT
cana-4287	89	7	theoretic	theoretic	NOUN
cana-4287	89	8	models	model	NOUN
cana-4287	89	9	for	for	ADP
cana-4287	89	10	cryptographic	cryptographic	ADJ
cana-4287	89	11	hash	hash	NOUN
cana-4287	89	12	functions	function	NOUN
cana-4287	89	13	"	"	PUNCT
cana-4287	89	14	(	(	PUNCT
cana-4287	89	15	2023	2023	NUM
cana-4287	89	16	):	):	PUNCT
cana-4287	89	17	this	this	DET
cana-4287	89	18	paper	paper	NOUN
cana-4287	89	19	presents	present	VERB
cana-4287	89	20	homotopytheoretic	homotopytheoretic	ADJ
cana-4287	89	21	frameworks	framework	NOUN
cana-4287	89	22	for	for	ADP
cana-4287	89	23	constructing	construct	VERB
cana-4287	89	24	cryptographic	cryptographic	ADJ
cana-4287	89	25	hash	hash	NOUN
cana-4287	89	26	functions	function	NOUN
cana-4287	89	27	.	.	PUNCT
cana-4287	90	1	the	the	DET
cana-4287	90	2	authors	author	NOUN
cana-4287	90	3	use	use	VERB
cana-4287	90	4	topological	topological	ADJ
cana-4287	90	5	invariants	invariant	NOUN
cana-4287	90	6	to	to	PART
cana-4287	90	7	ensure	ensure	VERB
cana-4287	90	8	collision	collision	NOUN
cana-4287	90	9	resistance	resistance	NOUN
cana-4287	90	10	and	and	CCONJ
cana-4287	90	11	pre	pre	ADJ
cana-4287	90	12	-	-	ADJ
cana-4287	90	13	image	image	ADJ
cana-4287	90	14	resistance	resistance	NOUN
cana-4287	90	15	in	in	ADP
cana-4287	90	16	hash	hash	NOUN
cana-4287	90	17	algorithms	algorithm	NOUN
cana-4287	90	18	.	.	PUNCT
cana-4287	91	1	the	the	DET
cana-4287	91	2	experimental	experimental	ADJ
cana-4287	91	3	results	result	NOUN
cana-4287	91	4	demonstrate	demonstrate	VERB
cana-4287	91	5	improved	improved	ADJ
cana-4287	91	6	performance	performance	NOUN
cana-4287	91	7	and	and	CCONJ
cana-4287	91	8	resilience	resilience	NOUN
cana-4287	91	9	to	to	ADP
cana-4287	91	10	differential	differential	ADJ
cana-4287	91	11	attacks	attack	NOUN
cana-4287	91	12	.	.	PUNCT
cana-4287	92	1	the	the	DET
cana-4287	92	2	study	study	NOUN
cana-4287	92	3	claims	claim	VERB
cana-4287	92	4	that	that	SCONJ
cana-4287	92	5	algebraic	algebraic	ADJ
cana-4287	92	6	topology	topology	NOUN
cana-4287	92	7	can	can	AUX
cana-4287	92	8	offer	offer	VERB
cana-4287	92	9	novel	novel	ADJ
cana-4287	92	10	concepts	concept	NOUN
cana-4287	92	11	for	for	ADP
cana-4287	92	12	developing	develop	VERB
cana-4287	92	13	trustworthy	trustworthy	ADJ
cana-4287	92	14	hash	hash	NOUN
cana-4287	92	15	algorithms	algorithm	NOUN
cana-4287	92	16	,	,	PUNCT
cana-4287	92	17	which	which	PRON
cana-4287	92	18	are	be	AUX
cana-4287	92	19	crucial	crucial	ADJ
cana-4287	92	20	for	for	ADP
cana-4287	92	21	blockchain	blockchain	PROPN
cana-4287	92	22	security	security	NOUN
cana-4287	92	23	.	.	PUNCT
cana-4287	93	1	[	[	X
cana-4287	93	2	8	8	NUM
cana-4287	93	3	]	]	PUNCT
cana-4287	93	4	"	"	PUNCT
cana-4287	93	5	an	an	DET
cana-4287	93	6	exposition	exposition	NOUN
cana-4287	93	7	on	on	ADP
cana-4287	93	8	the	the	DET
cana-4287	93	9	algebra	algebra	NOUN
cana-4287	93	10	and	and	CCONJ
cana-4287	93	11	computation	computation	NOUN
cana-4287	93	12	of	of	ADP
cana-4287	93	13	persistent	persistent	ADJ
cana-4287	93	14	homology	homology	NOUN
cana-4287	93	15	"	"	PUNCT
cana-4287	93	16	(	(	PUNCT
cana-4287	93	17	2024	2024	NUM
cana-4287	93	18	):	):	PUNCT
cana-4287	93	19	the	the	DET
cana-4287	93	20	algebraic	algebraic	ADJ
cana-4287	93	21	foundations	foundation	NOUN
cana-4287	93	22	of	of	ADP
cana-4287	93	23	persistent	persistent	ADJ
cana-4287	93	24	homology	homology	NOUN
cana-4287	93	25	,	,	PUNCT
cana-4287	93	26	an	an	DET
cana-4287	93	27	essential	essential	ADJ
cana-4287	93	28	tool	tool	NOUN
cana-4287	93	29	for	for	ADP
cana-4287	93	30	studying	study	VERB
cana-4287	93	31	topological	topological	ADJ
cana-4287	93	32	data	datum	NOUN
cana-4287	93	33	,	,	PUNCT
cana-4287	93	34	and	and	CCONJ
cana-4287	93	35	its	its	PRON
cana-4287	93	36	computational	computational	ADJ
cana-4287	93	37	properties	property	NOUN
cana-4287	93	38	are	be	AUX
cana-4287	93	39	discussed	discuss	VERB
cana-4287	93	40	in	in	ADP
cana-4287	93	41	this	this	DET
cana-4287	93	42	presentation	presentation	NOUN
cana-4287	93	43	.	.	PUNCT
cana-4287	94	1	in	in	ADP
cana-4287	94	2	order	order	NOUN
cana-4287	94	3	to	to	PART
cana-4287	94	4	investigate	investigate	VERB
cana-4287	94	5	how	how	SCONJ
cana-4287	94	6	persistent	persistent	ADJ
cana-4287	94	7	homology	homology	NOUN
cana-4287	94	8	provides	provide	VERB
cana-4287	94	9	information	information	NOUN
cana-4287	94	10	on	on	ADP
cana-4287	94	11	the	the	DET
cana-4287	94	12	structure	structure	NOUN
cana-4287	94	13	of	of	ADP
cana-4287	94	14	data	datum	NOUN
cana-4287	94	15	,	,	PUNCT
cana-4287	94	16	the	the	DET
cana-4287	94	17	author	author	NOUN
cana-4287	94	18	looks	look	VERB
cana-4287	94	19	at	at	ADP
cana-4287	94	20	topological	topological	ADJ
cana-4287	94	21	elements	element	NOUN
cana-4287	94	22	such	such	ADJ
cana-4287	94	23	as	as	ADP
cana-4287	94	24	loops	loop	NOUN
cana-4287	94	25	,	,	PUNCT
cana-4287	94	26	voids	void	NOUN
cana-4287	94	27	,	,	PUNCT
cana-4287	94	28	and	and	CCONJ
cana-4287	94	29	related	related	ADJ
cana-4287	94	30	components	component	NOUN
cana-4287	94	31	on	on	ADP
cana-4287	94	32	a	a	DET
cana-4287	94	33	variety	variety	NOUN
cana-4287	94	34	of	of	ADP
cana-4287	94	35	scales	scale	NOUN
cana-4287	94	36	.	.	PUNCT
cana-4287	95	1	the	the	DET
cana-4287	95	2	work	work	NOUN
cana-4287	95	3	emphasizes	emphasize	VERB
cana-4287	95	4	the	the	DET
cana-4287	95	5	use	use	NOUN
cana-4287	95	6	of	of	ADP
cana-4287	95	7	algebraic	algebraic	ADJ
cana-4287	95	8	techniques	technique	NOUN
cana-4287	95	9	,	,	PUNCT
cana-4287	95	10	such	such	ADJ
cana-4287	95	11	as	as	ADP
cana-4287	95	12	chain	chain	NOUN
cana-4287	95	13	complexes	complex	NOUN
cana-4287	95	14	and	and	CCONJ
cana-4287	95	15	simplicial	simplicial	ADJ
cana-4287	95	16	complexes	complex	NOUN
cana-4287	95	17	,	,	PUNCT
cana-4287	95	18	to	to	PART
cana-4287	95	19	compute	compute	VERB
cana-4287	95	20	homology	homology	NOUN
cana-4287	95	21	groups	group	NOUN
cana-4287	95	22	and	and	CCONJ
cana-4287	95	23	their	their	PRON
cana-4287	95	24	resilience	resilience	NOUN
cana-4287	95	25	across	across	ADP
cana-4287	95	26	filtering	filtering	NOUN
cana-4287	95	27	processes	process	NOUN
cana-4287	95	28	.	.	PUNCT
cana-4287	96	1	ranoa	ranoa	PROPN
cana-4287	96	2	highlights	highlight	NOUN
cana-4287	96	3	the	the	DET
cana-4287	96	4	significance	significance	NOUN
cana-4287	96	5	of	of	ADP
cana-4287	96	6	persistent	persistent	ADJ
cana-4287	96	7	homology	homology	NOUN
cana-4287	96	8	in	in	ADP
cana-4287	96	9	cryptography	cryptography	NOUN
cana-4287	96	10	,	,	PUNCT
cana-4287	96	11	particularly	particularly	ADV
cana-4287	96	12	in	in	ADP
cana-4287	96	13	enhancing	enhance	VERB
cana-4287	96	14	the	the	DET
cana-4287	96	15	efficacy	efficacy	NOUN
cana-4287	96	16	and	and	CCONJ
cana-4287	96	17	security	security	NOUN
cana-4287	96	18	of	of	ADP
cana-4287	96	19	cryptographic	cryptographic	ADJ
cana-4287	96	20	techniques	technique	NOUN
cana-4287	96	21	.	.	PUNCT
cana-4287	97	1	the	the	DET
cana-4287	97	2	article	article	NOUN
cana-4287	97	3	discusses	discuss	VERB
cana-4287	97	4	useful	useful	ADJ
cana-4287	97	5	techniques	technique	NOUN
cana-4287	97	6	for	for	ADP
cana-4287	97	7	computing	compute	VERB
cana-4287	97	8	persistent	persistent	ADJ
cana-4287	97	9	homology	homology	NOUN
cana-4287	97	10	and	and	CCONJ
cana-4287	97	11	offers	offer	VERB
cana-4287	97	12	recommendations	recommendation	NOUN
cana-4287	97	13	for	for	ADP
cana-4287	97	14	how	how	SCONJ
cana-4287	97	15	to	to	PART
cana-4287	97	16	make	make	VERB
cana-4287	97	17	them	they	PRON
cana-4287	97	18	better	well	ADJ
cana-4287	97	19	for	for	ADP
cana-4287	97	20	integration	integration	NOUN
cana-4287	97	21	into	into	ADP
cana-4287	97	22	cryptographic	cryptographic	ADJ
cana-4287	97	23	systems	system	NOUN
cana-4287	97	24	.	.	PUNCT
cana-4287	98	1	the	the	DET
cana-4287	98	2	challenges	challenge	NOUN
cana-4287	98	3	of	of	ADP
cana-4287	98	4	applying	apply	VERB
cana-4287	98	5	these	these	DET
cana-4287	98	6	techniques	technique	NOUN
cana-4287	98	7	to	to	ADP
cana-4287	98	8	large	large	ADJ
cana-4287	98	9	data	datum	NOUN
cana-4287	98	10	sets	set	NOUN
cana-4287	98	11	are	be	AUX
cana-4287	98	12	also	also	ADV
cana-4287	98	13	covered	cover	VERB
cana-4287	98	14	,	,	PUNCT
cana-4287	98	15	and	and	CCONJ
cana-4287	98	16	future	future	ADJ
cana-4287	98	17	research	research	NOUN
cana-4287	98	18	objectives	objective	NOUN
cana-4287	98	19	are	be	AUX
cana-4287	98	20	suggested	suggest	VERB
cana-4287	98	21	,	,	PUNCT
cana-4287	98	22	particularly	particularly	ADV
cana-4287	98	23	with	with	ADP
cana-4287	98	24	regard	regard	NOUN
cana-4287	98	25	to	to	ADP
cana-4287	98	26	improving	improve	VERB
cana-4287	98	27	computational	computational	ADJ
cana-4287	98	28	efficiency	efficiency	NOUN
cana-4287	98	29	and	and	CCONJ
cana-4287	98	30	extending	extend	VERB
cana-4287	98	31	the	the	DET
cana-4287	98	32	applications	application	NOUN
cana-4287	98	33	of	of	ADP
cana-4287	98	34	persistent	persistent	ADJ
cana-4287	98	35	homology	homology	NOUN
cana-4287	98	36	in	in	ADP
cana-4287	98	37	cryptography	cryptography	NOUN
cana-4287	98	38	and	and	CCONJ
cana-4287	98	39	other	other	ADJ
cana-4287	98	40	domains	domain	NOUN
cana-4287	98	41	.	.	PUNCT
cana-4287	99	1	[	[	X
cana-4287	99	2	9	9	NUM
cana-4287	99	3	]	]	PUNCT
cana-4287	99	4	"	"	PUNCT
cana-4287	99	5	persistent	persistent	ADJ
cana-4287	99	6	homology	homology	NOUN
cana-4287	99	7	in	in	ADP
cana-4287	99	8	cryptographic	cryptographic	ADJ
cana-4287	99	9	protocol	protocol	NOUN
cana-4287	99	10	verification	verification	NOUN
cana-4287	99	11	"	"	PUNCT
cana-4287	99	12	(	(	PUNCT
cana-4287	99	13	2023	2023	NUM
cana-4287	99	14	)	)	PUNCT
cana-4287	99	15	this	this	DET
cana-4287	99	16	article	article	NOUN
cana-4287	99	17	investigates	investigate	VERB
cana-4287	99	18	the	the	DET
cana-4287	99	19	use	use	NOUN
cana-4287	99	20	of	of	ADP
cana-4287	99	21	persistent	persistent	ADJ
cana-4287	99	22	homology	homology	NOUN
cana-4287	99	23	to	to	PART
cana-4287	99	24	verify	verify	VERB
cana-4287	99	25	the	the	DET
cana-4287	99	26	security	security	NOUN
cana-4287	99	27	and	and	CCONJ
cana-4287	99	28	correctness	correctness	NOUN
cana-4287	99	29	of	of	ADP
cana-4287	99	30	cryptographic	cryptographic	ADJ
cana-4287	99	31	systems	system	NOUN
cana-4287	99	32	.	.	PUNCT
cana-4287	100	1	by	by	ADP
cana-4287	100	2	looking	look	VERB
cana-4287	100	3	at	at	ADP
cana-4287	100	4	topological	topological	ADJ
cana-4287	100	5	patterns	pattern	NOUN
cana-4287	100	6	that	that	PRON
cana-4287	100	7	persist	persist	VERB
cana-4287	100	8	across	across	ADP
cana-4287	100	9	a	a	DET
cana-4287	100	10	range	range	NOUN
cana-4287	100	11	of	of	ADP
cana-4287	100	12	sizes	size	NOUN
cana-4287	100	13	,	,	PUNCT
cana-4287	100	14	the	the	DET
cana-4287	100	15	authors	author	NOUN
cana-4287	100	16	find	find	VERB
cana-4287	100	17	flaws	flaw	NOUN
cana-4287	100	18	in	in	ADP
cana-4287	100	19	encryption	encryption	NOUN
cana-4287	100	20	and	and	CCONJ
cana-4287	100	21	authentication	authentication	NOUN
cana-4287	100	22	systems	system	NOUN
cana-4287	100	23	.	.	PUNCT
cana-4287	101	1	the	the	DET
cana-4287	101	2	results	result	NOUN
cana-4287	101	3	of	of	ADP
cana-4287	101	4	the	the	DET
cana-4287	101	5	study	study	NOUN
cana-4287	101	6	show	show	VERB
cana-4287	101	7	that	that	SCONJ
cana-4287	101	8	persistent	persistent	ADJ
cana-4287	101	9	homology	homology	NOUN
cana-4287	101	10	offers	offer	VERB
cana-4287	101	11	a	a	DET
cana-4287	101	12	unique	unique	ADJ
cana-4287	101	13	viewpoint	viewpoint	NOUN
cana-4287	101	14	for	for	ADP
cana-4287	101	15	spotting	spot	VERB
cana-4287	101	16	errors	error	NOUN
cana-4287	101	17	in	in	ADP
cana-4287	101	18	complex	complex	ADJ
cana-4287	101	19	cryptographic	cryptographic	ADJ
cana-4287	101	20	systems	system	NOUN
cana-4287	101	21	.	.	PUNCT
cana-4287	102	1	[	[	X
cana-4287	102	2	10	10	NUM
cana-4287	102	3	]	]	X
cana-4287	102	4	"	"	PUNCT
cana-4287	102	5	topological	topological	ADJ
cana-4287	102	6	spaces	space	NOUN
cana-4287	102	7	and	and	CCONJ
cana-4287	102	8	lattice	lattice	NOUN
cana-4287	102	9	-	-	PUNCT
cana-4287	102	10	based	base	VERB
cana-4287	102	11	cryptography	cryptography	NOUN
cana-4287	102	12	"	"	PUNCT
cana-4287	102	13	(	(	PUNCT
cana-4287	102	14	2024	2024	NUM
cana-4287	102	15	)	)	PUNCT
cana-4287	102	16	this	this	DET
cana-4287	102	17	research	research	NOUN
cana-4287	102	18	integrates	integrate	VERB
cana-4287	102	19	algebraic	algebraic	ADJ
cana-4287	102	20	topology	topology	NOUN
cana-4287	102	21	with	with	ADP
cana-4287	102	22	lattice	lattice	NOUN
cana-4287	102	23	-	-	PUNCT
cana-4287	102	24	based	base	VERB
cana-4287	102	25	cryptography	cryptography	NOUN
cana-4287	102	26	to	to	PART
cana-4287	102	27	provide	provide	VERB
cana-4287	102	28	novel	novel	ADJ
cana-4287	102	29	encryption	encryption	NOUN
cana-4287	102	30	algorithms	algorithms	NOUN
cana-4287	102	31	communications	communication	NOUN
cana-4287	102	32	on	on	ADP
cana-4287	102	33	applied	apply	VERB
cana-4287	102	34	nonlinear	nonlinear	ADJ
cana-4287	102	35	analysis	analysis	NOUN
cana-4287	102	36	issn	issn	NOUN
cana-4287	102	37	:	:	PUNCT
cana-4287	102	38	1074	1074	NUM
cana-4287	102	39	-	-	PUNCT
cana-4287	102	40	133x	133x	NUM
cana-4287	102	41	vol	vol	NOUN
cana-4287	102	42	32	32	NUM
cana-4287	102	43	no	no	NOUN
cana-4287	102	44	.	.	PUNCT
cana-4287	103	1	9s	9s	NUM
cana-4287	103	2	(	(	PUNCT
cana-4287	103	3	2025	2025	NUM
cana-4287	103	4	)	)	PUNCT
cana-4287	103	5	1733	1733	NUM
cana-4287	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	103	7	that	that	PRON
cana-4287	103	8	are	be	AUX
cana-4287	103	9	resistant	resistant	ADJ
cana-4287	103	10	to	to	ADP
cana-4287	103	11	quantum	quantum	ADJ
cana-4287	103	12	attacks	attack	NOUN
cana-4287	103	13	.	.	PUNCT
cana-4287	104	1	by	by	ADP
cana-4287	104	2	employing	employ	VERB
cana-4287	104	3	topological	topological	ADJ
cana-4287	104	4	spaces	space	NOUN
cana-4287	104	5	to	to	PART
cana-4287	104	6	express	express	VERB
cana-4287	104	7	cryptographic	cryptographic	ADJ
cana-4287	104	8	key	key	ADJ
cana-4287	104	9	structures	structure	NOUN
cana-4287	104	10	,	,	PUNCT
cana-4287	104	11	the	the	DET
cana-4287	104	12	authors	author	NOUN
cana-4287	104	13	propose	propose	VERB
cana-4287	104	14	a	a	DET
cana-4287	104	15	secure	secure	ADJ
cana-4287	104	16	lattice	lattice	NOUN
cana-4287	104	17	-	-	PUNCT
cana-4287	104	18	based	base	VERB
cana-4287	104	19	encryption	encryption	NOUN
cana-4287	104	20	framework	framework	NOUN
cana-4287	104	21	.	.	PUNCT
cana-4287	105	1	the	the	DET
cana-4287	105	2	study	study	NOUN
cana-4287	105	3	demonstrates	demonstrate	VERB
cana-4287	105	4	how	how	SCONJ
cana-4287	105	5	topological	topological	ADJ
cana-4287	105	6	insights	insight	NOUN
cana-4287	105	7	can	can	AUX
cana-4287	105	8	simplify	simplify	VERB
cana-4287	105	9	complex	complex	ADJ
cana-4287	105	10	mathematical	mathematical	ADJ
cana-4287	105	11	representations	representation	NOUN
cana-4287	105	12	while	while	SCONJ
cana-4287	105	13	ensuring	ensure	VERB
cana-4287	105	14	cryptographic	cryptographic	ADJ
cana-4287	105	15	strength	strength	NOUN
cana-4287	105	16	.	.	PUNCT
cana-4287	106	1	[	[	X
cana-4287	106	2	11	11	NUM
cana-4287	106	3	]	]	PUNCT
cana-4287	106	4	the	the	DET
cana-4287	106	5	study	study	NOUN
cana-4287	106	6	"	"	PUNCT
cana-4287	106	7	categorical	categorical	ADJ
cana-4287	106	8	topology	topology	NOUN
cana-4287	106	9	in	in	ADP
cana-4287	106	10	zero	zero	NUM
cana-4287	106	11	-	-	PUNCT
cana-4287	106	12	knowledge	knowledge	NOUN
cana-4287	106	13	proofs	proof	NOUN
cana-4287	106	14	"	"	PUNCT
cana-4287	106	15	(	(	PUNCT
cana-4287	106	16	2023	2023	NUM
cana-4287	106	17	)	)	PUNCT
cana-4287	106	18	enhances	enhance	VERB
cana-4287	106	19	the	the	DET
cana-4287	106	20	effectiveness	effectiveness	NOUN
cana-4287	106	21	of	of	ADP
cana-4287	106	22	zeroknowledge	zeroknowledge	NOUN
cana-4287	106	23	proofs	proof	NOUN
cana-4287	106	24	by	by	ADP
cana-4287	106	25	using	use	VERB
cana-4287	106	26	categorical	categorical	ADJ
cana-4287	106	27	topology	topology	NOUN
cana-4287	106	28	.	.	PUNCT
cana-4287	107	1	the	the	DET
cana-4287	107	2	authors	author	NOUN
cana-4287	107	3	create	create	VERB
cana-4287	107	4	topological	topological	ADJ
cana-4287	107	5	models	model	NOUN
cana-4287	107	6	to	to	PART
cana-4287	107	7	validate	validate	VERB
cana-4287	107	8	cryptographic	cryptographic	ADJ
cana-4287	107	9	claims	claim	NOUN
cana-4287	107	10	without	without	ADP
cana-4287	107	11	revealing	reveal	VERB
cana-4287	107	12	personal	personal	ADJ
cana-4287	107	13	data	datum	NOUN
cana-4287	107	14	.	.	PUNCT
cana-4287	108	1	they	they	PRON
cana-4287	108	2	found	find	VERB
cana-4287	108	3	that	that	SCONJ
cana-4287	108	4	by	by	ADP
cana-4287	108	5	reducing	reduce	VERB
cana-4287	108	6	the	the	DET
cana-4287	108	7	computational	computational	ADJ
cana-4287	108	8	overhead	overhead	NOUN
cana-4287	108	9	of	of	ADP
cana-4287	108	10	zero	zero	NUM
cana-4287	108	11	-	-	PUNCT
cana-4287	108	12	knowledge	knowledge	NOUN
cana-4287	108	13	systems	system	NOUN
cana-4287	108	14	,	,	PUNCT
cana-4287	108	15	category	category	NOUN
cana-4287	108	16	topology	topology	NOUN
cana-4287	108	17	can	can	AUX
cana-4287	108	18	make	make	VERB
cana-4287	108	19	them	they	PRON
cana-4287	108	20	more	more	ADV
cana-4287	108	21	viable	viable	ADJ
cana-4287	108	22	for	for	ADP
cana-4287	108	23	large	large	ADJ
cana-4287	108	24	-	-	PUNCT
cana-4287	108	25	scale	scale	NOUN
cana-4287	108	26	applications	application	NOUN
cana-4287	108	27	.	.	PUNCT
cana-4287	109	1	[	[	X
cana-4287	109	2	12	12	NUM
cana-4287	109	3	]	]	PUNCT
cana-4287	109	4	the	the	DET
cana-4287	109	5	paper	paper	NOUN
cana-4287	109	6	"	"	PUNCT
cana-4287	109	7	simplicial	simplicial	ADJ
cana-4287	109	8	complexes	complex	NOUN
cana-4287	109	9	in	in	ADP
cana-4287	109	10	cryptographic	cryptographic	ADJ
cana-4287	109	11	network	network	NOUN
cana-4287	109	12	design	design	NOUN
cana-4287	109	13	"	"	PUNCT
cana-4287	109	14	(	(	PUNCT
cana-4287	109	15	2024	2024	NUM
cana-4287	109	16	)	)	PUNCT
cana-4287	109	17	focuses	focus	VERB
cana-4287	109	18	on	on	ADP
cana-4287	109	19	using	use	VERB
cana-4287	109	20	simplicial	simplicial	ADJ
cana-4287	109	21	complexes	complex	NOUN
cana-4287	109	22	to	to	PART
cana-4287	109	23	develop	develop	VERB
cana-4287	109	24	and	and	CCONJ
cana-4287	109	25	optimize	optimize	VERB
cana-4287	109	26	cryptographic	cryptographic	ADJ
cana-4287	109	27	network	network	NOUN
cana-4287	109	28	architectures	architecture	NOUN
cana-4287	109	29	.	.	PUNCT
cana-4287	110	1	these	these	DET
cana-4287	110	2	mathematical	mathematical	ADJ
cana-4287	110	3	structures	structure	NOUN
cana-4287	110	4	are	be	AUX
cana-4287	110	5	used	use	VERB
cana-4287	110	6	to	to	PART
cana-4287	110	7	simulate	simulate	VERB
cana-4287	110	8	complex	complex	ADJ
cana-4287	110	9	network	network	NOUN
cana-4287	110	10	interactions	interaction	NOUN
cana-4287	110	11	and	and	CCONJ
cana-4287	110	12	identify	identify	VERB
cana-4287	110	13	faults	fault	NOUN
cana-4287	110	14	in	in	ADP
cana-4287	110	15	key	key	ADJ
cana-4287	110	16	exchange	exchange	NOUN
cana-4287	110	17	protocols	protocol	NOUN
cana-4287	110	18	.	.	PUNCT
cana-4287	111	1	the	the	DET
cana-4287	111	2	authors	author	NOUN
cana-4287	111	3	demonstrate	demonstrate	VERB
cana-4287	111	4	how	how	SCONJ
cana-4287	111	5	simplicial	simplicial	ADJ
cana-4287	111	6	complexes	complex	NOUN
cana-4287	111	7	improve	improve	VERB
cana-4287	111	8	cryptographic	cryptographic	ADJ
cana-4287	111	9	systems	system	NOUN
cana-4287	111	10	'	'	PART
cana-4287	111	11	fault	fault	NOUN
cana-4287	111	12	tolerance	tolerance	NOUN
cana-4287	111	13	and	and	CCONJ
cana-4287	111	14	network	network	NOUN
cana-4287	111	15	resilience	resilience	NOUN
cana-4287	111	16	.	.	PUNCT
cana-4287	112	1	[	[	X
cana-4287	112	2	13	13	NUM
cana-4287	112	3	]	]	PUNCT
cana-4287	112	4	"	"	PUNCT
cana-4287	112	5	topological	topological	ADJ
cana-4287	112	6	data	datum	NOUN
cana-4287	112	7	analysis	analysis	NOUN
cana-4287	112	8	in	in	ADP
cana-4287	112	9	side	side	ADJ
cana-4287	112	10	-	-	PUNCT
cana-4287	112	11	channel	channel	NOUN
cana-4287	112	12	attack	attack	NOUN
cana-4287	112	13	prevention	prevention	NOUN
cana-4287	112	14	"	"	PUNCT
cana-4287	112	15	(	(	PUNCT
cana-4287	112	16	2024	2024	NUM
cana-4287	112	17	):	):	PUNCT
cana-4287	112	18	the	the	DET
cana-4287	112	19	potential	potential	NOUN
cana-4287	112	20	of	of	ADP
cana-4287	112	21	topological	topological	ADJ
cana-4287	112	22	data	datum	NOUN
cana-4287	112	23	analysis	analysis	NOUN
cana-4287	112	24	(	(	PUNCT
cana-4287	112	25	tda	tda	NOUN
cana-4287	112	26	)	)	PUNCT
cana-4287	112	27	to	to	PART
cana-4287	112	28	prevent	prevent	VERB
cana-4287	112	29	side	side	ADJ
cana-4287	112	30	-	-	PUNCT
cana-4287	112	31	channel	channel	NOUN
cana-4287	112	32	attacks	attack	NOUN
cana-4287	112	33	in	in	ADP
cana-4287	112	34	hardware	hardware	NOUN
cana-4287	112	35	cryptography	cryptography	NOUN
cana-4287	112	36	implementations	implementation	NOUN
cana-4287	112	37	is	be	AUX
cana-4287	112	38	examined	examine	VERB
cana-4287	112	39	in	in	ADP
cana-4287	112	40	this	this	DET
cana-4287	112	41	work	work	NOUN
cana-4287	112	42	.	.	PUNCT
cana-4287	113	1	by	by	ADP
cana-4287	113	2	analyzing	analyze	VERB
cana-4287	113	3	data	datum	NOUN
cana-4287	113	4	flow	flow	NOUN
cana-4287	113	5	patterns	pattern	NOUN
cana-4287	113	6	and	and	CCONJ
cana-4287	113	7	identifying	identify	VERB
cana-4287	113	8	anomalies	anomaly	NOUN
cana-4287	113	9	using	use	VERB
cana-4287	113	10	topological	topological	ADJ
cana-4287	113	11	signatures	signature	NOUN
cana-4287	113	12	,	,	PUNCT
cana-4287	113	13	the	the	DET
cana-4287	113	14	article	article	NOUN
cana-4287	113	15	offers	offer	VERB
cana-4287	113	16	strategies	strategy	NOUN
cana-4287	113	17	for	for	ADP
cana-4287	113	18	identifying	identify	VERB
cana-4287	113	19	and	and	CCONJ
cana-4287	113	20	resolving	resolve	VERB
cana-4287	113	21	side	side	ADJ
cana-4287	113	22	-	-	PUNCT
cana-4287	113	23	channel	channel	NOUN
cana-4287	113	24	vulnerabilities	vulnerability	NOUN
cana-4287	113	25	in	in	ADP
cana-4287	113	26	realtime	realtime	NOUN
cana-4287	113	27	.	.	PUNCT
cana-4287	114	1	the	the	DET
cana-4287	114	2	results	result	NOUN
cana-4287	114	3	show	show	VERB
cana-4287	114	4	that	that	SCONJ
cana-4287	114	5	hardware	hardware	NOUN
cana-4287	114	6	systems	system	NOUN
cana-4287	114	7	for	for	ADP
cana-4287	114	8	cryptography	cryptography	NOUN
cana-4287	114	9	are	be	AUX
cana-4287	114	10	now	now	ADV
cana-4287	114	11	more	more	ADV
cana-4287	114	12	reliable	reliable	ADJ
cana-4287	114	13	.	.	PUNCT
cana-4287	115	1	[	[	X
cana-4287	115	2	14	14	NUM
cana-4287	115	3	]	]	X
cana-4287	115	4	"	"	PUNCT
cana-4287	115	5	cohomology	cohomology	NOUN
cana-4287	115	6	rings	ring	NOUN
cana-4287	115	7	in	in	ADP
cana-4287	115	8	symmetric	symmetric	ADJ
cana-4287	115	9	key	key	ADJ
cana-4287	115	10	cryptography	cryptography	NOUN
cana-4287	115	11	"	"	PUNCT
cana-4287	115	12	(	(	PUNCT
cana-4287	115	13	2023	2023	NUM
cana-4287	115	14	):	):	PUNCT
cana-4287	115	15	this	this	DET
cana-4287	115	16	paper	paper	NOUN
cana-4287	115	17	investigates	investigate	VERB
cana-4287	115	18	the	the	DET
cana-4287	115	19	use	use	NOUN
cana-4287	115	20	of	of	ADP
cana-4287	115	21	cohomology	cohomology	NOUN
cana-4287	115	22	rings	ring	NOUN
cana-4287	115	23	to	to	PART
cana-4287	115	24	optimize	optimize	VERB
cana-4287	115	25	symmetric	symmetric	ADJ
cana-4287	115	26	key	key	ADJ
cana-4287	115	27	cryptography	cryptography	NOUN
cana-4287	115	28	techniques	technique	NOUN
cana-4287	115	29	.	.	PUNCT
cana-4287	116	1	the	the	DET
cana-4287	116	2	authors	author	NOUN
cana-4287	116	3	demonstrate	demonstrate	VERB
cana-4287	116	4	how	how	SCONJ
cana-4287	116	5	algebraic	algebraic	ADJ
cana-4287	116	6	topology	topology	NOUN
cana-4287	116	7	can	can	AUX
cana-4287	116	8	be	be	AUX
cana-4287	116	9	used	use	VERB
cana-4287	116	10	to	to	PART
cana-4287	116	11	simplify	simplify	VERB
cana-4287	116	12	transformations	transformation	NOUN
cana-4287	116	13	within	within	ADP
cana-4287	116	14	cryptographic	cryptographic	ADJ
cana-4287	116	15	keys	key	NOUN
cana-4287	116	16	while	while	SCONJ
cana-4287	116	17	maintaining	maintain	VERB
cana-4287	116	18	their	their	PRON
cana-4287	116	19	structural	structural	ADJ
cana-4287	116	20	integrity	integrity	NOUN
cana-4287	116	21	.	.	PUNCT
cana-4287	117	1	experimental	experimental	ADJ
cana-4287	117	2	validation	validation	NOUN
cana-4287	117	3	shows	show	VERB
cana-4287	117	4	the	the	DET
cana-4287	117	5	advantages	advantage	NOUN
cana-4287	117	6	of	of	ADP
cana-4287	117	7	this	this	DET
cana-4287	117	8	approach	approach	NOUN
cana-4287	117	9	in	in	ADP
cana-4287	117	10	reducing	reduce	VERB
cana-4287	117	11	encryption	encryption	NOUN
cana-4287	117	12	and	and	CCONJ
cana-4287	117	13	decryption	decryption	NOUN
cana-4287	117	14	latency	latency	NOUN
cana-4287	117	15	.	.	PUNCT
cana-4287	118	1	[	[	X
cana-4287	118	2	15	15	NUM
cana-4287	118	3	]	]	X
cana-4287	118	4	"	"	PUNCT
cana-4287	118	5	geometric	geometric	ADJ
cana-4287	118	6	group	group	NOUN
cana-4287	118	7	theory	theory	NOUN
cana-4287	118	8	in	in	ADP
cana-4287	118	9	secure	secure	ADJ
cana-4287	118	10	multi	multi	ADJ
cana-4287	118	11	-	-	ADJ
cana-4287	118	12	party	party	ADJ
cana-4287	118	13	computation	computation	NOUN
cana-4287	118	14	"	"	PUNCT
cana-4287	118	15	(	(	PUNCT
cana-4287	118	16	2024	2024	NUM
cana-4287	118	17	):	):	PUNCT
cana-4287	118	18	this	this	DET
cana-4287	118	19	paper	paper	NOUN
cana-4287	118	20	explores	explore	VERB
cana-4287	118	21	the	the	DET
cana-4287	118	22	application	application	NOUN
cana-4287	118	23	of	of	ADP
cana-4287	118	24	geometric	geometric	ADJ
cana-4287	118	25	group	group	NOUN
cana-4287	118	26	theory	theory	NOUN
cana-4287	118	27	and	and	CCONJ
cana-4287	118	28	topological	topological	ADJ
cana-4287	118	29	structures	structure	NOUN
cana-4287	118	30	to	to	PART
cana-4287	118	31	secure	secure	VERB
cana-4287	118	32	multi	multi	ADJ
cana-4287	118	33	-	-	ADJ
cana-4287	118	34	party	party	ADJ
cana-4287	118	35	computation	computation	NOUN
cana-4287	118	36	(	(	PUNCT
cana-4287	118	37	smpc	smpc	NOUN
cana-4287	118	38	)	)	PUNCT
cana-4287	118	39	.	.	PUNCT
cana-4287	119	1	through	through	ADP
cana-4287	119	2	the	the	DET
cana-4287	119	3	representation	representation	NOUN
cana-4287	119	4	of	of	ADP
cana-4287	119	5	participant	participant	ADJ
cana-4287	119	6	interactions	interaction	NOUN
cana-4287	119	7	as	as	ADP
cana-4287	119	8	topological	topological	ADJ
cana-4287	119	9	graphs	graph	NOUN
cana-4287	119	10	,	,	PUNCT
cana-4287	119	11	the	the	DET
cana-4287	119	12	authors	author	NOUN
cana-4287	119	13	offer	offer	VERB
cana-4287	119	14	optimized	optimize	VERB
cana-4287	119	15	smpc	smpc	NOUN
cana-4287	119	16	protocols	protocol	NOUN
cana-4287	119	17	that	that	PRON
cana-4287	119	18	minimize	minimize	VERB
cana-4287	119	19	computing	compute	VERB
cana-4287	119	20	complexity	complexity	NOUN
cana-4287	119	21	while	while	SCONJ
cana-4287	119	22	preserving	preserve	VERB
cana-4287	119	23	data	datum	NOUN
cana-4287	119	24	privacy	privacy	NOUN
cana-4287	119	25	.	.	PUNCT
cana-4287	120	1	the	the	DET
cana-4287	120	2	study	study	NOUN
cana-4287	120	3	concludes	conclude	VERB
cana-4287	120	4	that	that	SCONJ
cana-4287	120	5	topological	topological	ADJ
cana-4287	120	6	approaches	approach	NOUN
cana-4287	120	7	significantly	significantly	ADV
cana-4287	120	8	increase	increase	VERB
cana-4287	120	9	the	the	DET
cana-4287	120	10	efficacy	efficacy	NOUN
cana-4287	120	11	and	and	CCONJ
cana-4287	120	12	scalability	scalability	NOUN
cana-4287	120	13	of	of	ADP
cana-4287	120	14	smpc	smpc	NOUN
cana-4287	120	15	systems	system	NOUN
cana-4287	120	16	.	.	PUNCT
cana-4287	121	1	research	research	NOUN
cana-4287	121	2	gaps	gap	VERB
cana-4287	121	3	the	the	DET
cana-4287	121	4	following	follow	VERB
cana-4287	121	5	research	research	NOUN
cana-4287	121	6	gaps	gap	NOUN
cana-4287	121	7	have	have	AUX
cana-4287	121	8	been	be	AUX
cana-4287	121	9	found	find	VERB
cana-4287	121	10	:	:	PUNCT
cana-4287	121	11	•	•	ADP
cana-4287	121	12	the	the	DET
cana-4287	121	13	application	application	NOUN
cana-4287	121	14	of	of	ADP
cana-4287	121	15	algebraic	algebraic	ADJ
cana-4287	121	16	topology	topology	NOUN
cana-4287	121	17	in	in	ADP
cana-4287	121	18	developing	develop	VERB
cana-4287	121	19	safe	safe	ADJ
cana-4287	121	20	and	and	CCONJ
cana-4287	121	21	efficient	efficient	ADJ
cana-4287	121	22	cryptographic	cryptographic	ADJ
cana-4287	121	23	algorithms	algorithm	NOUN
cana-4287	121	24	is	be	AUX
cana-4287	121	25	still	still	ADV
cana-4287	121	26	little	little	ADJ
cana-4287	121	27	understood	understand	VERB
cana-4287	121	28	,	,	PUNCT
cana-4287	121	29	despite	despite	SCONJ
cana-4287	121	30	the	the	DET
cana-4287	121	31	fact	fact	NOUN
cana-4287	121	32	that	that	SCONJ
cana-4287	121	33	it	it	PRON
cana-4287	121	34	offers	offer	VERB
cana-4287	121	35	powerful	powerful	ADJ
cana-4287	121	36	mathematical	mathematical	ADJ
cana-4287	121	37	tools	tool	NOUN
cana-4287	121	38	.	.	PUNCT
cana-4287	122	1	while	while	SCONJ
cana-4287	122	2	most	most	ADJ
cana-4287	122	3	recent	recent	ADJ
cana-4287	122	4	work	work	NOUN
cana-4287	122	5	focuses	focus	VERB
cana-4287	122	6	on	on	ADP
cana-4287	122	7	discrete	discrete	ADJ
cana-4287	122	8	properties	property	NOUN
cana-4287	122	9	like	like	ADP
cana-4287	122	10	homology	homology	NOUN
cana-4287	122	11	or	or	CCONJ
cana-4287	122	12	topological	topological	ADJ
cana-4287	122	13	spaces	space	NOUN
cana-4287	122	14	,	,	PUNCT
cana-4287	122	15	there	there	PRON
cana-4287	122	16	is	be	VERB
cana-4287	122	17	a	a	DET
cana-4287	122	18	lack	lack	NOUN
cana-4287	122	19	of	of	ADP
cana-4287	122	20	comprehensive	comprehensive	ADJ
cana-4287	122	21	integration	integration	NOUN
cana-4287	122	22	of	of	ADP
cana-4287	122	23	these	these	DET
cana-4287	122	24	invariants	invariant	NOUN
cana-4287	122	25	into	into	ADP
cana-4287	122	26	cryptographic	cryptographic	ADJ
cana-4287	122	27	models	model	NOUN
cana-4287	122	28	.	.	PUNCT
cana-4287	123	1	•	•	NUM
cana-4287	123	2	topology	topology	NOUN
cana-4287	123	3	-	-	PUNCT
cana-4287	123	4	based	base	VERB
cana-4287	123	5	cryptographic	cryptographic	ADJ
cana-4287	123	6	solutions	solution	NOUN
cana-4287	123	7	'	'	PART
cana-4287	123	8	scalability	scalability	NOUN
cana-4287	123	9	:	:	PUNCT
cana-4287	123	10	while	while	SCONJ
cana-4287	123	11	prior	prior	ADJ
cana-4287	123	12	research	research	NOUN
cana-4287	123	13	has	have	AUX
cana-4287	123	14	demonstrated	demonstrate	VERB
cana-4287	123	15	the	the	DET
cana-4287	123	16	theoretical	theoretical	ADJ
cana-4287	123	17	potential	potential	NOUN
cana-4287	123	18	of	of	ADP
cana-4287	123	19	topological	topological	ADJ
cana-4287	123	20	techniques	technique	NOUN
cana-4287	123	21	in	in	ADP
cana-4287	123	22	cryptography	cryptography	NOUN
cana-4287	123	23	,	,	PUNCT
cana-4287	123	24	problems	problem	NOUN
cana-4287	123	25	with	with	ADP
cana-4287	123	26	scalability	scalability	NOUN
cana-4287	123	27	and	and	CCONJ
cana-4287	123	28	compute	compute	NOUN
cana-4287	123	29	viability	viability	NOUN
cana-4287	123	30	in	in	ADP
cana-4287	123	31	large	large	ADJ
cana-4287	123	32	-	-	PUNCT
cana-4287	123	33	scale	scale	NOUN
cana-4287	123	34	real	real	ADJ
cana-4287	123	35	-	-	PUNCT
cana-4287	123	36	world	world	NOUN
cana-4287	123	37	systems	system	NOUN
cana-4287	123	38	persist	persist	VERB
cana-4287	123	39	.	.	PUNCT
cana-4287	124	1	it	it	PRON
cana-4287	124	2	is	be	AUX
cana-4287	124	3	necessary	necessary	ADJ
cana-4287	124	4	to	to	PART
cana-4287	124	5	develop	develop	VERB
cana-4287	124	6	scalable	scalable	ADJ
cana-4287	124	7	models	model	NOUN
cana-4287	124	8	that	that	PRON
cana-4287	124	9	maintain	maintain	VERB
cana-4287	124	10	efficiency	efficiency	NOUN
cana-4287	124	11	and	and	CCONJ
cana-4287	124	12	security	security	NOUN
cana-4287	124	13	.	.	PUNCT
cana-4287	125	1	•	•	NUM
cana-4287	125	2	lack	lack	NOUN
cana-4287	125	3	of	of	ADP
cana-4287	125	4	standardized	standardized	ADJ
cana-4287	125	5	frameworks	framework	NOUN
cana-4287	125	6	for	for	ADP
cana-4287	125	7	topology	topology	NOUN
cana-4287	125	8	-	-	PUNCT
cana-4287	125	9	driven	drive	VERB
cana-4287	125	10	cryptographic	cryptographic	ADJ
cana-4287	125	11	protocols	protocol	NOUN
cana-4287	125	12	:	:	PUNCT
cana-4287	125	13	the	the	DET
cana-4287	125	14	absence	absence	NOUN
cana-4287	125	15	of	of	ADP
cana-4287	125	16	standardized	standardized	ADJ
cana-4287	125	17	frameworks	framework	NOUN
cana-4287	125	18	and	and	CCONJ
cana-4287	125	19	protocols	protocol	NOUN
cana-4287	125	20	that	that	PRON
cana-4287	125	21	take	take	VERB
cana-4287	125	22	algebraic	algebraic	ADJ
cana-4287	125	23	topology	topology	NOUN
cana-4287	125	24	into	into	ADP
cana-4287	125	25	account	account	NOUN
cana-4287	125	26	prevents	prevent	VERB
cana-4287	125	27	widespread	widespread	ADJ
cana-4287	125	28	use	use	NOUN
cana-4287	125	29	.	.	PUNCT
cana-4287	126	1	research	research	NOUN
cana-4287	126	2	must	must	AUX
cana-4287	126	3	focus	focus	VERB
cana-4287	126	4	on	on	ADP
cana-4287	126	5	developing	develop	VERB
cana-4287	126	6	widely	widely	ADV
cana-4287	126	7	-	-	PUNCT
cana-4287	126	8	accepted	accept	VERB
cana-4287	126	9	topological	topological	ADJ
cana-4287	126	10	structures	structure	NOUN
cana-4287	126	11	for	for	ADP
cana-4287	126	12	cryptographic	cryptographic	ADJ
cana-4287	126	13	processes	process	NOUN
cana-4287	126	14	to	to	PART
cana-4287	126	15	guarantee	guarantee	VERB
cana-4287	126	16	consistency	consistency	NOUN
cana-4287	126	17	and	and	CCONJ
cana-4287	126	18	interoperability	interoperability	NOUN
cana-4287	126	19	.	.	PUNCT
cana-4287	127	1	•	•	NUM
cana-4287	127	2	insufficient	insufficient	ADJ
cana-4287	127	3	persistent	persistent	ADJ
cana-4287	127	4	homology	homology	NOUN
cana-4287	127	5	research	research	NOUN
cana-4287	127	6	for	for	ADP
cana-4287	127	7	real	real	ADJ
cana-4287	127	8	-	-	PUNCT
cana-4287	127	9	time	time	NOUN
cana-4287	127	10	threat	threat	NOUN
cana-4287	127	11	identification	identification	NOUN
cana-4287	127	12	persistent	persistent	ADJ
cana-4287	127	13	homology	homology	NOUN
cana-4287	127	14	has	have	AUX
cana-4287	127	15	shown	show	VERB
cana-4287	127	16	promise	promise	NOUN
cana-4287	127	17	in	in	ADP
cana-4287	127	18	detecting	detect	VERB
cana-4287	127	19	anomalies	anomaly	NOUN
cana-4287	127	20	in	in	ADP
cana-4287	127	21	cryptographic	cryptographic	ADJ
cana-4287	127	22	systems	system	NOUN
cana-4287	127	23	,	,	PUNCT
cana-4287	127	24	but	but	CCONJ
cana-4287	127	25	its	its	PRON
cana-4287	127	26	real	real	ADJ
cana-4287	127	27	-	-	PUNCT
cana-4287	127	28	time	time	NOUN
cana-4287	127	29	application	application	NOUN
cana-4287	127	30	for	for	ADP
cana-4287	127	31	threat	threat	NOUN
cana-4287	127	32	communications	communication	NOUN
cana-4287	127	33	on	on	ADP
cana-4287	127	34	applied	apply	VERB
cana-4287	127	35	nonlinear	nonlinear	ADJ
cana-4287	127	36	analysis	analysis	NOUN
cana-4287	127	37	issn	issn	NOUN
cana-4287	127	38	:	:	PUNCT
cana-4287	127	39	1074	1074	NUM
cana-4287	127	40	-	-	PUNCT
cana-4287	127	41	133x	133x	NUM
cana-4287	127	42	vol	vol	NOUN
cana-4287	127	43	32	32	NUM
cana-4287	127	44	no	no	NOUN
cana-4287	127	45	.	.	PUNCT
cana-4287	128	1	9s	9s	NUM
cana-4287	128	2	(	(	PUNCT
cana-4287	128	3	2025	2025	NUM
cana-4287	128	4	)	)	PUNCT
cana-4287	128	5	1734	1734	NUM
cana-4287	128	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	128	7	detection	detection	NOUN
cana-4287	128	8	and	and	CCONJ
cana-4287	128	9	mitigation	mitigation	NOUN
cana-4287	128	10	is	be	AUX
cana-4287	128	11	still	still	ADV
cana-4287	128	12	in	in	ADP
cana-4287	128	13	its	its	PRON
cana-4287	128	14	infancy	infancy	NOUN
cana-4287	128	15	.	.	PUNCT
cana-4287	129	1	further	further	ADJ
cana-4287	129	2	study	study	NOUN
cana-4287	129	3	is	be	AUX
cana-4287	129	4	required	require	VERB
cana-4287	129	5	to	to	PART
cana-4287	129	6	bridge	bridge	VERB
cana-4287	129	7	this	this	DET
cana-4287	129	8	gap	gap	NOUN
cana-4287	129	9	and	and	CCONJ
cana-4287	129	10	enhance	enhance	VERB
cana-4287	129	11	realtime	realtime	NOUN
cana-4287	129	12	performance	performance	NOUN
cana-4287	129	13	.	.	PUNCT
cana-4287	130	1	•	•	NUM
cana-4287	130	2	multidisciplinary	multidisciplinary	ADJ
cana-4287	130	3	collaboration	collaboration	NOUN
cana-4287	130	4	between	between	ADP
cana-4287	130	5	cryptographers	cryptographer	NOUN
cana-4287	130	6	and	and	CCONJ
cana-4287	130	7	topology	topology	NOUN
cana-4287	130	8	experts	expert	NOUN
cana-4287	130	9	:	:	PUNCT
cana-4287	130	10	despite	despite	SCONJ
cana-4287	130	11	increased	increase	VERB
cana-4287	130	12	interest	interest	NOUN
cana-4287	130	13	,	,	PUNCT
cana-4287	130	14	there	there	PRON
cana-4287	130	15	is	be	VERB
cana-4287	130	16	still	still	ADV
cana-4287	130	17	a	a	DET
cana-4287	130	18	lack	lack	NOUN
cana-4287	130	19	of	of	ADP
cana-4287	130	20	collaboration	collaboration	NOUN
cana-4287	130	21	between	between	ADP
cana-4287	130	22	mathematicians	mathematician	NOUN
cana-4287	130	23	with	with	ADP
cana-4287	130	24	expertise	expertise	NOUN
cana-4287	130	25	in	in	ADP
cana-4287	130	26	algebraic	algebraic	ADJ
cana-4287	130	27	topology	topology	NOUN
cana-4287	130	28	and	and	CCONJ
cana-4287	130	29	cryptographers	cryptographer	NOUN
cana-4287	130	30	.	.	PUNCT
cana-4287	131	1	this	this	DET
cana-4287	131	2	disparity	disparity	NOUN
cana-4287	131	3	hinders	hinder	VERB
cana-4287	131	4	innovation	innovation	NOUN
cana-4287	131	5	and	and	CCONJ
cana-4287	131	6	postpones	postpone	VERB
cana-4287	131	7	the	the	DET
cana-4287	131	8	transformation	transformation	NOUN
cana-4287	131	9	of	of	ADP
cana-4287	131	10	theoretical	theoretical	ADJ
cana-4287	131	11	topological	topological	ADJ
cana-4287	131	12	concepts	concept	NOUN
cana-4287	131	13	into	into	ADP
cana-4287	131	14	practical	practical	ADJ
cana-4287	131	15	cryptography	cryptography	NOUN
cana-4287	131	16	solutions	solution	NOUN
cana-4287	131	17	.	.	PUNCT
cana-4287	132	1	methodology	methodology	NOUN
cana-4287	132	2	homomorphic	homomorphic	ADJ
cana-4287	132	3	encryption	encryption	NOUN
cana-4287	132	4	topological	topological	ADJ
cana-4287	132	5	equation	equation	NOUN
cana-4287	132	6	:	:	PUNCT
cana-4287	132	7	equation	equation	NOUN
cana-4287	132	8	(	(	PUNCT
cana-4287	132	9	1	1	X
cana-4287	132	10	)	)	PUNCT
cana-4287	132	11	ensures	ensure	VERB
cana-4287	132	12	the	the	DET
cana-4287	132	13	homomorphic	homomorphic	ADJ
cana-4287	132	14	property	property	NOUN
cana-4287	132	15	,	,	PUNCT
cana-4287	132	16	which	which	PRON
cana-4287	132	17	asserts	assert	VERB
cana-4287	132	18	that	that	SCONJ
cana-4287	132	19	operations	operation	NOUN
cana-4287	132	20	on	on	ADP
cana-4287	132	21	ciphertext	ciphertext	PROPN
cana-4287	132	22	correspond	correspond	ADV
cana-4287	132	23	to	to	ADP
cana-4287	132	24	those	those	PRON
cana-4287	132	25	on	on	ADP
cana-4287	132	26	plaintext	plaintext	NOUN
cana-4287	132	27	.	.	PUNCT
cana-4287	133	1	topological	topological	ADJ
cana-4287	133	2	algorithms	algorithm	NOUN
cana-4287	133	3	enhance	enhance	VERB
cana-4287	133	4	the	the	DET
cana-4287	133	5	security	security	NOUN
cana-4287	133	6	of	of	ADP
cana-4287	133	7	homomorphic	homomorphic	ADJ
cana-4287	133	8	encryption	encryption	NOUN
cana-4287	133	9	and	and	CCONJ
cana-4287	133	10	enable	enable	VERB
cana-4287	133	11	secure	secure	ADJ
cana-4287	133	12	processing	processing	NOUN
cana-4287	133	13	on	on	ADP
cana-4287	133	14	encrypted	encrypt	VERB
cana-4287	133	15	data	datum	NOUN
cana-4287	133	16	.	.	PUNCT
cana-4287	134	1	𝑐	𝑐	NOUN
cana-4287	134	2	=	=	SYM
cana-4287	134	3	𝑓(𝑛1	𝑓(𝑛1	PROPN
cana-4287	134	4	)	)	PUNCT
cana-4287	135	1	+	+	NUM
cana-4287	135	2	𝑓(𝑛2	𝑓(𝑛2	X
cana-4287	135	3	)	)	PUNCT
cana-4287	135	4	(	(	PUNCT
cana-4287	135	5	1	1	X
cana-4287	135	6	)	)	PUNCT
cana-4287	135	7	where	where	SCONJ
cana-4287	135	8	,	,	PUNCT
cana-4287	135	9	𝑓	𝑓	X
cana-4287	135	10	:	:	PUNCT
cana-4287	135	11	encryption	encryption	NOUN
cana-4287	135	12	function	function	NOUN
cana-4287	135	13	𝑛1	𝑛1	NOUN
cana-4287	135	14	,	,	PUNCT
cana-4287	135	15	𝑛2	𝑛2	NOUN
cana-4287	135	16	:	:	PUNCT
cana-4287	135	17	plaintext	plaintext	NOUN
cana-4287	135	18	messages	message	NOUN
cana-4287	135	19	serial	serial	ADJ
cana-4287	135	20	homology	homology	NOUN
cana-4287	135	21	equation	equation	NOUN
cana-4287	135	22	:	:	PUNCT
cana-4287	135	23	equation	equation	NOUN
cana-4287	135	24	(	(	PUNCT
cana-4287	135	25	2	2	X
cana-4287	135	26	)	)	PUNCT
cana-4287	135	27	calculates	calculate	VERB
cana-4287	135	28	betti	betti	ADJ
cana-4287	135	29	numbers	number	NOUN
cana-4287	135	30	,	,	PUNCT
cana-4287	135	31	a	a	DET
cana-4287	135	32	crucial	crucial	ADJ
cana-4287	135	33	statistic	statistic	NOUN
cana-4287	135	34	in	in	ADP
cana-4287	135	35	serial	serial	ADJ
cana-4287	135	36	homology	homology	NOUN
cana-4287	135	37	.	.	PUNCT
cana-4287	136	1	it	it	PRON
cana-4287	136	2	makes	make	VERB
cana-4287	136	3	it	it	PRON
cana-4287	136	4	easier	easy	ADJ
cana-4287	136	5	to	to	PART
cana-4287	136	6	analyze	analyze	VERB
cana-4287	136	7	the	the	DET
cana-4287	136	8	dimensions	dimension	NOUN
cana-4287	136	9	of	of	ADP
cana-4287	136	10	cryptographic	cryptographic	ADJ
cana-4287	136	11	structures	structure	NOUN
cana-4287	136	12	by	by	ADP
cana-4287	136	13	shedding	shed	VERB
cana-4287	136	14	light	light	NOUN
cana-4287	136	15	on	on	ADP
cana-4287	136	16	their	their	PRON
cana-4287	136	17	complexity	complexity	NOUN
cana-4287	136	18	and	and	CCONJ
cana-4287	136	19	helping	help	VERB
cana-4287	136	20	to	to	PART
cana-4287	136	21	build	build	VERB
cana-4287	136	22	topologically	topologically	ADV
cana-4287	136	23	robust	robust	ADJ
cana-4287	136	24	cryptosystems	cryptosystem	NOUN
cana-4287	136	25	.	.	PUNCT
cana-4287	137	1	𝑑𝑖𝑚(𝐴𝑘(𝑋	𝑑𝑖𝑚(𝐴𝑘(𝑋	NOUN
cana-4287	137	2	)	)	PUNCT
cana-4287	137	3	)	)	PUNCT
cana-4287	138	1	=	=	PUNCT
cana-4287	138	2	𝛼𝑘	𝛼𝑘	NOUN
cana-4287	138	3	(	(	PUNCT
cana-4287	138	4	2	2	NUM
cana-4287	138	5	)	)	PUNCT
cana-4287	138	6	where	where	SCONJ
cana-4287	138	7	,	,	PUNCT
cana-4287	138	8	𝐴𝑘(𝑋	𝐴𝑘(𝑋	PRON
cana-4287	138	9	):	):	PUNCT
cana-4287	138	10	k	k	X
cana-4287	138	11	-	-	PUNCT
cana-4287	138	12	th	th	VERB
cana-4287	138	13	homology	homology	NOUN
cana-4287	138	14	group	group	NOUN
cana-4287	138	15	of	of	ADP
cana-4287	138	16	𝑋	𝑋	PROPN
cana-4287	138	17	𝛼𝑘	𝛼𝑘	NOUN
cana-4287	138	18	:	:	PUNCT
cana-4287	138	19	betti	betti	ADJ
cana-4287	138	20	number	number	NOUN
cana-4287	138	21	indicating	indicate	VERB
cana-4287	138	22	the	the	DET
cana-4287	138	23	number	number	NOUN
cana-4287	138	24	of	of	ADP
cana-4287	138	25	k	k	ADJ
cana-4287	138	26	-	-	ADJ
cana-4287	138	27	dimensional	dimensional	ADJ
cana-4287	138	28	holes	hole	NOUN
cana-4287	138	29	topological	topological	ADJ
cana-4287	138	30	vector	vector	NOUN
cana-4287	138	31	space	space	NOUN
cana-4287	138	32	equation	equation	NOUN
cana-4287	138	33	:	:	PUNCT
cana-4287	138	34	cryptographic	cryptographic	ADJ
cana-4287	138	35	techniques	technique	NOUN
cana-4287	138	36	for	for	ADP
cana-4287	138	37	key	key	ADJ
cana-4287	138	38	distribution	distribution	NOUN
cana-4287	138	39	are	be	AUX
cana-4287	138	40	enhanced	enhance	VERB
cana-4287	138	41	by	by	ADP
cana-4287	138	42	the	the	DET
cana-4287	138	43	topological	topological	ADJ
cana-4287	138	44	vector	vector	NOUN
cana-4287	138	45	space	space	NOUN
cana-4287	138	46	provided	provide	VERB
cana-4287	138	47	by	by	ADP
cana-4287	138	48	equation	equation	NOUN
cana-4287	138	49	(	(	PUNCT
cana-4287	138	50	3	3	NUM
cana-4287	138	51	)	)	PUNCT
cana-4287	138	52	.	.	PUNCT
cana-4287	139	1	by	by	ADP
cana-4287	139	2	incorporating	incorporate	VERB
cana-4287	139	3	topological	topological	ADJ
cana-4287	139	4	approaches	approach	NOUN
cana-4287	139	5	,	,	PUNCT
cana-4287	139	6	it	it	PRON
cana-4287	139	7	ensures	ensure	VERB
cana-4287	139	8	the	the	DET
cana-4287	139	9	robustness	robustness	NOUN
cana-4287	139	10	and	and	CCONJ
cana-4287	139	11	efficiency	efficiency	NOUN
cana-4287	139	12	of	of	ADP
cana-4287	139	13	cryptographic	cryptographic	ADJ
cana-4287	139	14	communications	communication	NOUN
cana-4287	139	15	.	.	PUNCT
cana-4287	140	1	𝑇	𝑇	PROPN
cana-4287	140	2	=	=	PRON
cana-4287	140	3	{	{	PUNCT
cana-4287	140	4	𝑦	𝑦	NOUN
cana-4287	140	5	∈	∈	PROPN
cana-4287	140	6	𝑌	𝑌	PROPN
cana-4287	140	7	:	:	PUNCT
cana-4287	140	8	∥	∥	X
cana-4287	140	9	𝑦	𝑦	X
cana-4287	140	10	∥	∥	X
cana-4287	140	11	<	<	X
cana-4287	140	12	∞	∞	PROPN
cana-4287	140	13	}	}	PUNCT
cana-4287	140	14	(	(	PUNCT
cana-4287	140	15	3	3	NUM
cana-4287	140	16	)	)	PUNCT
cana-4287	140	17	where	where	SCONJ
cana-4287	140	18	,	,	PUNCT
cana-4287	140	19	𝑇	𝑇	PROPN
cana-4287	140	20	:	:	PUNCT
cana-4287	140	21	topological	topological	ADJ
cana-4287	140	22	vector	vector	NOUN
cana-4287	140	23	space	space	NOUN
cana-4287	140	24	𝑌	𝑌	PROPN
cana-4287	140	25	:	:	PUNCT
cana-4287	140	26	topological	topological	ADJ
cana-4287	140	27	space	space	NOUN
cana-4287	140	28	∥	∥	X
cana-4287	140	29	𝑦	𝑦	NOUN
cana-4287	140	30	∥	∥	PRON
cana-4287	140	31	:	:	PUNCT
cana-4287	140	32	norm	norm	NOUN
cana-4287	140	33	of	of	ADP
cana-4287	140	34	𝑦	𝑦	PROPN
cana-4287	140	35	elliptic	elliptic	ADJ
cana-4287	140	36	curve	curve	NOUN
cana-4287	140	37	equation	equation	NOUN
cana-4287	140	38	:	:	PUNCT
cana-4287	140	39	communications	communication	NOUN
cana-4287	140	40	on	on	ADP
cana-4287	140	41	applied	apply	VERB
cana-4287	140	42	nonlinear	nonlinear	ADJ
cana-4287	140	43	analysis	analysis	NOUN
cana-4287	140	44	issn	issn	NOUN
cana-4287	140	45	:	:	PUNCT
cana-4287	140	46	1074	1074	NUM
cana-4287	140	47	-	-	PUNCT
cana-4287	140	48	133x	133x	NUM
cana-4287	140	49	vol	vol	NOUN
cana-4287	140	50	32	32	NUM
cana-4287	140	51	no	no	NOUN
cana-4287	140	52	.	.	PUNCT
cana-4287	141	1	9s	9s	NUM
cana-4287	141	2	(	(	PUNCT
cana-4287	141	3	2025	2025	NUM
cana-4287	141	4	)	)	PUNCT
cana-4287	141	5	1735	1735	NUM
cana-4287	141	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	142	1	this	this	PRON
cana-4287	142	2	is	be	AUX
cana-4287	142	3	the	the	DET
cana-4287	142	4	typical	typical	ADJ
cana-4287	142	5	elliptic	elliptic	ADJ
cana-4287	142	6	curve	curve	NOUN
cana-4287	142	7	equation	equation	NOUN
cana-4287	142	8	(	(	PUNCT
cana-4287	142	9	4	4	NUM
cana-4287	142	10	)	)	PUNCT
cana-4287	142	11	in	in	ADP
cana-4287	142	12	modern	modern	ADJ
cana-4287	142	13	encryption	encryption	NOUN
cana-4287	142	14	.	.	PUNCT
cana-4287	143	1	by	by	ADP
cana-4287	143	2	using	use	VERB
cana-4287	143	3	algebraic	algebraic	ADJ
cana-4287	143	4	topology	topology	NOUN
cana-4287	143	5	approaches	approach	NOUN
cana-4287	143	6	,	,	PUNCT
cana-4287	143	7	researchers	researcher	NOUN
cana-4287	143	8	increase	increase	VERB
cana-4287	143	9	the	the	DET
cana-4287	143	10	computing	computing	NOUN
cana-4287	143	11	speed	speed	NOUN
cana-4287	143	12	and	and	CCONJ
cana-4287	143	13	security	security	NOUN
cana-4287	143	14	of	of	ADP
cana-4287	143	15	cryptographic	cryptographic	ADJ
cana-4287	143	16	systems	system	NOUN
cana-4287	143	17	,	,	PUNCT
cana-4287	143	18	two	two	NUM
cana-4287	143	19	essential	essential	ADJ
cana-4287	143	20	components	component	NOUN
cana-4287	143	21	for	for	ADP
cana-4287	143	22	secure	secure	ADJ
cana-4287	143	23	communications	communication	NOUN
cana-4287	143	24	.	.	PUNCT
cana-4287	144	1	𝑏2	𝑏2	NOUN
cana-4287	144	2	=	=	PROPN
cana-4287	144	3	𝑎3	𝑎3	PROPN
cana-4287	144	4	+	+	CCONJ
cana-4287	144	5	𝑥𝑎	𝑥𝑎	PROPN
cana-4287	145	1	+	+	NUM
cana-4287	145	2	𝑦	𝑦	SYM
cana-4287	145	3	(	(	PUNCT
cana-4287	145	4	4	4	NUM
cana-4287	145	5	)	)	PUNCT
cana-4287	145	6	where	where	SCONJ
cana-4287	145	7	,	,	PUNCT
cana-4287	145	8	𝑎	𝑎	X
cana-4287	145	9	,	,	PUNCT
cana-4287	145	10	𝑏	𝑏	NOUN
cana-4287	145	11	:	:	PUNCT
cana-4287	145	12	point	point	NOUN
cana-4287	145	13	coordinates	coordinate	NOUN
cana-4287	145	14	on	on	ADP
cana-4287	145	15	the	the	DET
cana-4287	145	16	elliptic	elliptic	ADJ
cana-4287	145	17	curve	curve	NOUN
cana-4287	145	18	𝑥	𝑥	PROPN
cana-4287	145	19	,	,	PUNCT
cana-4287	145	20	𝑦	𝑦	NOUN
cana-4287	145	21	:	:	PUNCT
cana-4287	145	22	curve	curve	NOUN
cana-4287	145	23	parameters	parameter	NOUN
cana-4287	145	24	the	the	DET
cana-4287	145	25	above	above	ADJ
cana-4287	145	26	equations	equation	NOUN
cana-4287	145	27	show	show	VERB
cana-4287	145	28	how	how	SCONJ
cana-4287	145	29	modern	modern	ADJ
cana-4287	145	30	encryption	encryption	NOUN
cana-4287	145	31	incorporates	incorporate	VERB
cana-4287	145	32	algebraic	algebraic	ADJ
cana-4287	145	33	topology	topology	NOUN
cana-4287	145	34	.	.	PUNCT
cana-4287	146	1	by	by	ADP
cana-4287	146	2	employing	employ	VERB
cana-4287	146	3	betti	betti	ADJ
cana-4287	146	4	numbers	number	NOUN
cana-4287	146	5	in	in	ADP
cana-4287	146	6	serial	serial	ADJ
cana-4287	146	7	homology	homology	NOUN
cana-4287	146	8	to	to	PART
cana-4287	146	9	analyze	analyze	VERB
cana-4287	146	10	the	the	DET
cana-4287	146	11	complexity	complexity	NOUN
cana-4287	146	12	of	of	ADP
cana-4287	146	13	cryptographic	cryptographic	ADJ
cana-4287	146	14	structures	structure	NOUN
cana-4287	146	15	,	,	PUNCT
cana-4287	146	16	equation	equation	NOUN
cana-4287	146	17	(	(	PUNCT
cana-4287	146	18	1	1	NUM
cana-4287	146	19	)	)	PUNCT
cana-4287	146	20	aids	aid	NOUN
cana-4287	146	21	in	in	ADP
cana-4287	146	22	the	the	DET
cana-4287	146	23	construction	construction	NOUN
cana-4287	146	24	of	of	ADP
cana-4287	146	25	robust	robust	ADJ
cana-4287	146	26	systems	system	NOUN
cana-4287	146	27	.	.	PUNCT
cana-4287	147	1	equation	equation	NOUN
cana-4287	147	2	(	(	PUNCT
cana-4287	147	3	2	2	X
cana-4287	147	4	)	)	PUNCT
cana-4287	147	5	increases	increase	VERB
cana-4287	147	6	the	the	DET
cana-4287	147	7	security	security	NOUN
cana-4287	147	8	of	of	ADP
cana-4287	147	9	homomorphic	homomorphic	ADJ
cana-4287	147	10	encryption	encryption	NOUN
cana-4287	147	11	by	by	ADP
cana-4287	147	12	ensuring	ensure	VERB
cana-4287	147	13	that	that	SCONJ
cana-4287	147	14	calculations	calculation	NOUN
cana-4287	147	15	on	on	ADP
cana-4287	147	16	encrypted	encrypt	VERB
cana-4287	147	17	data	datum	NOUN
cana-4287	147	18	are	be	AUX
cana-4287	147	19	secure	secure	ADJ
cana-4287	147	20	.	.	PUNCT
cana-4287	148	1	the	the	DET
cana-4287	148	2	speed	speed	NOUN
cana-4287	148	3	and	and	CCONJ
cana-4287	148	4	security	security	NOUN
cana-4287	148	5	of	of	ADP
cana-4287	148	6	cryptographic	cryptographic	ADJ
cana-4287	148	7	systems	system	NOUN
cana-4287	148	8	are	be	AUX
cana-4287	148	9	enhanced	enhance	VERB
cana-4287	148	10	by	by	ADP
cana-4287	148	11	the	the	DET
cana-4287	148	12	elliptic	elliptic	ADJ
cana-4287	148	13	curve	curve	NOUN
cana-4287	148	14	equation	equation	NOUN
cana-4287	148	15	(	(	PUNCT
cana-4287	148	16	3	3	NUM
cana-4287	148	17	)	)	PUNCT
cana-4287	148	18	,	,	PUNCT
cana-4287	148	19	which	which	PRON
cana-4287	148	20	is	be	AUX
cana-4287	148	21	crucial	crucial	ADJ
cana-4287	148	22	for	for	ADP
cana-4287	148	23	secure	secure	ADJ
cana-4287	148	24	communications	communication	NOUN
cana-4287	148	25	.	.	PUNCT
cana-4287	149	1	equation	equation	NOUN
cana-4287	149	2	(	(	PUNCT
cana-4287	149	3	4	4	NUM
cana-4287	149	4	)	)	PUNCT
cana-4287	149	5	,	,	PUNCT
cana-4287	149	6	defining	define	VERB
cana-4287	149	7	topological	topological	ADJ
cana-4287	149	8	vector	vector	NOUN
cana-4287	149	9	spaces	space	NOUN
cana-4287	149	10	,	,	PUNCT
cana-4287	149	11	strengthens	strengthen	VERB
cana-4287	149	12	key	key	ADJ
cana-4287	149	13	distribution	distribution	NOUN
cana-4287	149	14	methods	method	NOUN
cana-4287	149	15	by	by	ADP
cana-4287	149	16	ensuring	ensure	VERB
cana-4287	149	17	robustness	robustness	NOUN
cana-4287	149	18	and	and	CCONJ
cana-4287	149	19	effectiveness	effectiveness	NOUN
cana-4287	149	20	.	.	PUNCT
cana-4287	150	1	together	together	ADV
cana-4287	150	2	,	,	PUNCT
cana-4287	150	3	these	these	DET
cana-4287	150	4	formulas	formula	NOUN
cana-4287	150	5	demonstrate	demonstrate	VERB
cana-4287	150	6	how	how	SCONJ
cana-4287	150	7	topological	topological	ADJ
cana-4287	150	8	methods	method	NOUN
cana-4287	150	9	can	can	AUX
cana-4287	150	10	transform	transform	VERB
cana-4287	150	11	cryptography	cryptography	NOUN
cana-4287	150	12	's	's	PART
cana-4287	150	13	effectiveness	effectiveness	NOUN
cana-4287	150	14	and	and	CCONJ
cana-4287	150	15	security	security	NOUN
cana-4287	150	16	.	.	PUNCT
cana-4287	151	1	results	result	NOUN
cana-4287	151	2	and	and	CCONJ
cana-4287	151	3	discussions	discussion	NOUN
cana-4287	151	4	a.	a.	NOUN
cana-4287	151	5	cryptographic	cryptographic	ADJ
cana-4287	151	6	protocols	protocol	NOUN
cana-4287	151	7	'	'	PART
cana-4287	151	8	use	use	NOUN
cana-4287	151	9	of	of	ADP
cana-4287	151	10	algebraic	algebraic	ADJ
cana-4287	151	11	topology	topology	NOUN
cana-4287	151	12	techniques	technique	NOUN
cana-4287	151	13	(	(	PUNCT
cana-4287	151	14	2024	2024	NUM
cana-4287	151	15	)	)	PUNCT
cana-4287	151	16	figure	figure	NOUN
cana-4287	151	17	3	3	NUM
cana-4287	151	18	illustrates	illustrate	VERB
cana-4287	151	19	the	the	DET
cana-4287	151	20	distribution	distribution	NOUN
cana-4287	151	21	of	of	ADP
cana-4287	151	22	algebraic	algebraic	ADJ
cana-4287	151	23	topology	topology	NOUN
cana-4287	151	24	approaches	approach	NOUN
cana-4287	151	25	applied	apply	VERB
cana-4287	151	26	in	in	ADP
cana-4287	151	27	key	key	ADJ
cana-4287	151	28	cryptographic	cryptographic	ADJ
cana-4287	151	29	protocols	protocol	NOUN
cana-4287	151	30	.	.	PUNCT
cana-4287	152	1	the	the	DET
cana-4287	152	2	data	data	NOUN
cana-4287	152	3	highlights	highlight	VERB
cana-4287	152	4	the	the	DET
cana-4287	152	5	significance	significance	NOUN
cana-4287	152	6	of	of	ADP
cana-4287	152	7	various	various	ADJ
cana-4287	152	8	topological	topological	ADJ
cana-4287	152	9	techniques	technique	NOUN
cana-4287	152	10	in	in	ADP
cana-4287	152	11	modern	modern	ADJ
cana-4287	152	12	cryptography	cryptography	NOUN
cana-4287	152	13	,	,	PUNCT
cana-4287	152	14	offering	offer	VERB
cana-4287	152	15	valuable	valuable	ADJ
cana-4287	152	16	insights	insight	NOUN
cana-4287	152	17	into	into	ADP
cana-4287	152	18	their	their	PRON
cana-4287	152	19	applicability	applicability	NOUN
cana-4287	152	20	and	and	CCONJ
cana-4287	152	21	practical	practical	ADJ
cana-4287	152	22	implementation	implementation	NOUN
cana-4287	152	23	.	.	PUNCT
cana-4287	153	1	according	accord	VERB
cana-4287	153	2	to	to	ADP
cana-4287	153	3	the	the	DET
cana-4287	153	4	figure	figure	NOUN
cana-4287	153	5	,	,	PUNCT
cana-4287	153	6	homology	homology	NOUN
cana-4287	153	7	theory	theory	NOUN
cana-4287	153	8	is	be	AUX
cana-4287	153	9	the	the	DET
cana-4287	153	10	method	method	NOUN
cana-4287	153	11	that	that	PRON
cana-4287	153	12	is	be	AUX
cana-4287	153	13	used	use	VERB
cana-4287	153	14	the	the	DET
cana-4287	153	15	most	most	ADV
cana-4287	153	16	frequently	frequently	ADV
cana-4287	153	17	,	,	PUNCT
cana-4287	153	18	showing	show	VERB
cana-4287	153	19	up	up	ADP
cana-4287	153	20	in	in	ADP
cana-4287	153	21	35	35	NUM
cana-4287	153	22	%	%	NOUN
cana-4287	153	23	of	of	ADP
cana-4287	153	24	cryptographic	cryptographic	ADJ
cana-4287	153	25	protocols	protocol	NOUN
cana-4287	153	26	.	.	PUNCT
cana-4287	154	1	this	this	PRON
cana-4287	154	2	implies	imply	VERB
cana-4287	154	3	that	that	SCONJ
cana-4287	154	4	durable	durable	ADJ
cana-4287	154	5	encryption	encryption	NOUN
cana-4287	154	6	and	and	CCONJ
cana-4287	154	7	secure	secure	ADJ
cana-4287	154	8	data	datum	NOUN
cana-4287	154	9	transfer	transfer	NOUN
cana-4287	154	10	depend	depend	VERB
cana-4287	154	11	heavily	heavily	ADV
cana-4287	154	12	on	on	ADP
cana-4287	154	13	homology	homology	NOUN
cana-4287	154	14	,	,	PUNCT
cana-4287	154	15	which	which	PRON
cana-4287	154	16	studies	study	VERB
cana-4287	154	17	the	the	DET
cana-4287	154	18	topological	topological	ADJ
cana-4287	154	19	properties	property	NOUN
cana-4287	154	20	that	that	PRON
cana-4287	154	21	remain	remain	VERB
cana-4287	154	22	constant	constant	ADJ
cana-4287	154	23	under	under	ADP
cana-4287	154	24	continuous	continuous	ADJ
cana-4287	154	25	deformations	deformation	NOUN
cana-4287	154	26	.	.	PUNCT
cana-4287	155	1	simpliccial	simpliccial	ADJ
cana-4287	155	2	complexes	complex	NOUN
cana-4287	155	3	are	be	AUX
cana-4287	155	4	the	the	DET
cana-4287	155	5	second	second	ADJ
cana-4287	155	6	most	most	ADV
cana-4287	155	7	common	common	ADJ
cana-4287	155	8	approach	approach	NOUN
cana-4287	155	9	,	,	PUNCT
cana-4287	155	10	with	with	ADP
cana-4287	155	11	a	a	DET
cana-4287	155	12	percentage	percentage	NOUN
cana-4287	155	13	of	of	ADP
cana-4287	155	14	25	25	NUM
cana-4287	155	15	%	%	NOUN
cana-4287	155	16	.	.	PUNCT
cana-4287	156	1	in	in	ADP
cana-4287	156	2	order	order	NOUN
cana-4287	156	3	to	to	PART
cana-4287	156	4	facilitate	facilitate	VERB
cana-4287	156	5	the	the	DET
cana-4287	156	6	creation	creation	NOUN
cana-4287	156	7	of	of	ADP
cana-4287	156	8	secure	secure	ADJ
cana-4287	156	9	networks	network	NOUN
cana-4287	156	10	,	,	PUNCT
cana-4287	156	11	these	these	DET
cana-4287	156	12	structures	structure	NOUN
cana-4287	156	13	are	be	AUX
cana-4287	156	14	frequently	frequently	ADV
cana-4287	156	15	used	use	VERB
cana-4287	156	16	to	to	PART
cana-4287	156	17	represent	represent	VERB
cana-4287	156	18	the	the	DET
cana-4287	156	19	interactions	interaction	NOUN
cana-4287	156	20	between	between	ADP
cana-4287	156	21	various	various	ADJ
cana-4287	156	22	components	component	NOUN
cana-4287	156	23	in	in	ADP
cana-4287	156	24	cryptographic	cryptographic	ADJ
cana-4287	156	25	protocols	protocol	NOUN
cana-4287	156	26	.	.	PUNCT
cana-4287	157	1	fig	fig	NOUN
cana-4287	157	2	.	.	PUNCT
cana-4287	158	1	5	5	NUM
cana-4287	158	2	:	:	PUNCT
cana-4287	158	3	cryptographic	cryptographic	ADJ
cana-4287	158	4	protocols	protocol	NOUN
cana-4287	158	5	'	'	PART
cana-4287	158	6	use	use	NOUN
cana-4287	158	7	of	of	ADP
cana-4287	158	8	algebraic	algebraic	ADJ
cana-4287	158	9	topology	topology	NOUN
cana-4287	158	10	techniques	technique	NOUN
cana-4287	158	11	(	(	PUNCT
cana-4287	158	12	2024	2024	NUM
cana-4287	158	13	)	)	PUNCT
cana-4287	158	14	communications	communication	NOUN
cana-4287	158	15	on	on	ADP
cana-4287	158	16	applied	apply	VERB
cana-4287	158	17	nonlinear	nonlinear	ADJ
cana-4287	158	18	analysis	analysis	NOUN
cana-4287	158	19	issn	issn	NOUN
cana-4287	158	20	:	:	PUNCT
cana-4287	158	21	1074	1074	NUM
cana-4287	158	22	-	-	PUNCT
cana-4287	158	23	133x	133x	NUM
cana-4287	158	24	vol	vol	NOUN
cana-4287	158	25	32	32	NUM
cana-4287	158	26	no	no	NOUN
cana-4287	158	27	.	.	PUNCT
cana-4287	159	1	9s	9s	NUM
cana-4287	159	2	(	(	PUNCT
cana-4287	159	3	2025	2025	NUM
cana-4287	159	4	)	)	PUNCT
cana-4287	159	5	1736	1736	NUM
cana-4287	159	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	159	7	persistent	persistent	ADJ
cana-4287	159	8	homology	homology	NOUN
cana-4287	159	9	,	,	PUNCT
cana-4287	159	10	which	which	PRON
cana-4287	159	11	contributes	contribute	VERB
cana-4287	159	12	15	15	NUM
cana-4287	159	13	%	%	NOUN
cana-4287	159	14	,	,	PUNCT
cana-4287	159	15	is	be	AUX
cana-4287	159	16	becoming	become	VERB
cana-4287	159	17	increasingly	increasingly	ADV
cana-4287	159	18	popular	popular	ADJ
cana-4287	159	19	due	due	ADP
cana-4287	159	20	to	to	ADP
cana-4287	159	21	its	its	PRON
cana-4287	159	22	capacity	capacity	NOUN
cana-4287	159	23	to	to	PART
cana-4287	159	24	spot	spot	VERB
cana-4287	159	25	data	datum	NOUN
cana-4287	159	26	patterns	pattern	NOUN
cana-4287	159	27	and	and	CCONJ
cana-4287	159	28	structures	structure	NOUN
cana-4287	159	29	,	,	PUNCT
cana-4287	159	30	which	which	PRON
cana-4287	159	31	aids	aid	VERB
cana-4287	159	32	in	in	ADP
cana-4287	159	33	the	the	DET
cana-4287	159	34	detection	detection	NOUN
cana-4287	159	35	of	of	ADP
cana-4287	159	36	anomalies	anomaly	NOUN
cana-4287	159	37	and	and	CCONJ
cana-4287	159	38	threats	threat	NOUN
cana-4287	159	39	in	in	ADP
cana-4287	159	40	cryptographic	cryptographic	ADJ
cana-4287	159	41	systems	system	NOUN
cana-4287	159	42	.	.	PUNCT
cana-4287	160	1	the	the	DET
cana-4287	160	2	other	other	ADJ
cana-4287	160	3	techniques	technique	NOUN
cana-4287	160	4	—	—	PUNCT
cana-4287	160	5	topological	topological	ADJ
cana-4287	160	6	spaces	space	NOUN
cana-4287	160	7	and	and	CCONJ
cana-4287	160	8	fundamental	fundamental	ADJ
cana-4287	160	9	groups	group	NOUN
cana-4287	160	10	—	—	PUNCT
cana-4287	160	11	contribute	contribute	VERB
cana-4287	160	12	10	10	NUM
cana-4287	160	13	%	%	NOUN
cana-4287	160	14	and	and	CCONJ
cana-4287	160	15	15	15	NUM
cana-4287	160	16	%	%	NOUN
cana-4287	160	17	,	,	PUNCT
cana-4287	160	18	respectively	respectively	ADV
cana-4287	160	19	,	,	PUNCT
cana-4287	160	20	suggesting	suggest	VERB
cana-4287	160	21	that	that	SCONJ
cana-4287	160	22	they	they	PRON
cana-4287	160	23	are	be	AUX
cana-4287	160	24	specifically	specifically	ADV
cana-4287	160	25	used	use	VERB
cana-4287	160	26	in	in	ADP
cana-4287	160	27	particular	particular	ADJ
cana-4287	160	28	cryptographic	cryptographic	ADJ
cana-4287	160	29	scenarios	scenario	NOUN
cana-4287	160	30	,	,	PUNCT
cana-4287	160	31	such	such	ADJ
cana-4287	160	32	as	as	ADP
cana-4287	160	33	the	the	DET
cana-4287	160	34	development	development	NOUN
cana-4287	160	35	of	of	ADP
cana-4287	160	36	secure	secure	ADJ
cana-4287	160	37	key	key	ADJ
cana-4287	160	38	exchange	exchange	NOUN
cana-4287	160	39	protocols	protocol	NOUN
cana-4287	160	40	and	and	CCONJ
cana-4287	160	41	cryptographic	cryptographic	ADJ
cana-4287	160	42	hash	hash	NOUN
cana-4287	160	43	functions	function	NOUN
cana-4287	160	44	.	.	PUNCT
cana-4287	161	1	this	this	DET
cana-4287	161	2	publication	publication	NOUN
cana-4287	161	3	demonstrates	demonstrate	VERB
cana-4287	161	4	the	the	DET
cana-4287	161	5	growing	grow	VERB
cana-4287	161	6	application	application	NOUN
cana-4287	161	7	of	of	ADP
cana-4287	161	8	algebraic	algebraic	ADJ
cana-4287	161	9	topology	topology	NOUN
cana-4287	161	10	in	in	ADP
cana-4287	161	11	cryptographic	cryptographic	ADJ
cana-4287	161	12	research	research	NOUN
cana-4287	161	13	and	and	CCONJ
cana-4287	161	14	its	its	PRON
cana-4287	161	15	potential	potential	NOUN
cana-4287	161	16	to	to	PART
cana-4287	161	17	increase	increase	VERB
cana-4287	161	18	system	system	NOUN
cana-4287	161	19	security	security	NOUN
cana-4287	161	20	and	and	CCONJ
cana-4287	161	21	resilience	resilience	NOUN
cana-4287	161	22	.	.	PUNCT
cana-4287	162	1	b.	b.	PROPN
cana-4287	162	2	topology	topology	NOUN
cana-4287	162	3	-	-	PUNCT
cana-4287	162	4	based	base	VERB
cana-4287	162	5	cryptographic	cryptographic	ADJ
cana-4287	162	6	algorithms	algorithm	NOUN
cana-4287	162	7	’	'	PUNCT
cana-4287	162	8	performance	performance	NOUN
cana-4287	162	9	analysis	analysis	NOUN
cana-4287	162	10	figure	figure	NOUN
cana-4287	162	11	4	4	NUM
cana-4287	162	12	presents	present	VERB
cana-4287	162	13	a	a	DET
cana-4287	162	14	comparison	comparison	NOUN
cana-4287	162	15	of	of	ADP
cana-4287	162	16	the	the	DET
cana-4287	162	17	performance	performance	NOUN
cana-4287	162	18	characteristics	characteristic	NOUN
cana-4287	162	19	of	of	ADP
cana-4287	162	20	four	four	NUM
cana-4287	162	21	different	different	ADJ
cana-4287	162	22	topology	topology	NOUN
cana-4287	162	23	-	-	PUNCT
cana-4287	162	24	based	base	VERB
cana-4287	162	25	encryption	encryption	NOUN
cana-4287	162	26	algorithms	algorithm	NOUN
cana-4287	162	27	:	:	PUNCT
cana-4287	162	28	topocrypt-1	topocrypt-1	NUM
cana-4287	162	29	,	,	PUNCT
cana-4287	162	30	topocrypt-2	topocrypt-2	NUM
cana-4287	162	31	,	,	PUNCT
cana-4287	162	32	topocrypt-3	topocrypt-3	NUM
cana-4287	162	33	,	,	PUNCT
cana-4287	162	34	and	and	CCONJ
cana-4287	162	35	topocrypt-4	topocrypt-4	NUM
cana-4287	162	36	.	.	PUNCT
cana-4287	163	1	the	the	DET
cana-4287	163	2	investigation	investigation	NOUN
cana-4287	163	3	focuses	focus	VERB
cana-4287	163	4	on	on	ADP
cana-4287	163	5	three	three	NUM
cana-4287	163	6	key	key	ADJ
cana-4287	163	7	performance	performance	NOUN
cana-4287	163	8	metrics	metric	NOUN
cana-4287	163	9	:	:	PUNCT
cana-4287	163	10	encryption	encryption	NOUN
cana-4287	163	11	speed	speed	NOUN
cana-4287	163	12	,	,	PUNCT
cana-4287	163	13	decryption	decryption	NOUN
cana-4287	163	14	speed	speed	NOUN
cana-4287	163	15	,	,	PUNCT
cana-4287	163	16	and	and	CCONJ
cana-4287	163	17	computing	compute	VERB
cana-4287	163	18	overhead	overhead	NOUN
cana-4287	163	19	.	.	PUNCT
cana-4287	164	1	the	the	DET
cana-4287	164	2	fastest	fast	ADJ
cana-4287	164	3	encryption	encryption	NOUN
cana-4287	164	4	speed	speed	NOUN
cana-4287	164	5	(	(	PUNCT
cana-4287	164	6	50	50	NUM
cana-4287	164	7	ms	ms	NOUN
cana-4287	164	8	)	)	PUNCT
cana-4287	164	9	,	,	PUNCT
cana-4287	164	10	the	the	DET
cana-4287	164	11	fastest	fast	ADJ
cana-4287	164	12	decryption	decryption	NOUN
cana-4287	164	13	speed	speed	NOUN
cana-4287	164	14	(	(	PUNCT
cana-4287	164	15	60	60	NUM
cana-4287	164	16	ms	ms	NOUN
cana-4287	164	17	)	)	PUNCT
cana-4287	164	18	,	,	PUNCT
cana-4287	164	19	and	and	CCONJ
cana-4287	164	20	a	a	DET
cana-4287	164	21	relatively	relatively	ADV
cana-4287	164	22	low	low	ADJ
cana-4287	164	23	computational	computational	ADJ
cana-4287	164	24	overhead	overhead	NOUN
cana-4287	164	25	(	(	PUNCT
cana-4287	164	26	10	10	NUM
cana-4287	164	27	%	%	NOUN
cana-4287	164	28	)	)	PUNCT
cana-4287	164	29	are	be	AUX
cana-4287	164	30	all	all	PRON
cana-4287	164	31	displayed	display	VERB
cana-4287	164	32	in	in	ADP
cana-4287	164	33	the	the	DET
cana-4287	164	34	figure	figure	NOUN
cana-4287	164	35	for	for	ADP
cana-4287	164	36	topocrypt-1	topocrypt-1	PROPN
cana-4287	164	37	.	.	PUNCT
cana-4287	165	1	this	this	PRON
cana-4287	165	2	demonstrates	demonstrate	VERB
cana-4287	165	3	that	that	SCONJ
cana-4287	165	4	topocrypt-1	topocrypt-1	NUM
cana-4287	165	5	is	be	AUX
cana-4287	165	6	suitable	suitable	ADJ
cana-4287	165	7	for	for	ADP
cana-4287	165	8	scenarios	scenario	NOUN
cana-4287	165	9	requiring	require	VERB
cana-4287	165	10	fast	fast	ADJ
cana-4287	165	11	encryption	encryption	NOUN
cana-4287	165	12	and	and	CCONJ
cana-4287	165	13	decryption	decryption	NOUN
cana-4287	165	14	since	since	SCONJ
cana-4287	165	15	it	it	PRON
cana-4287	165	16	balances	balance	VERB
cana-4287	165	17	effectiveness	effectiveness	NOUN
cana-4287	165	18	with	with	ADP
cana-4287	165	19	minimal	minimal	ADJ
cana-4287	165	20	extra	extra	ADJ
cana-4287	165	21	computational	computational	ADJ
cana-4287	165	22	expense	expense	NOUN
cana-4287	165	23	.	.	PUNCT
cana-4287	166	1	topocrypt-2	topocrypt-2	PROPN
cana-4287	166	2	also	also	ADV
cana-4287	166	3	exhibits	exhibit	VERB
cana-4287	166	4	outstanding	outstanding	ADJ
cana-4287	166	5	speed	speed	NOUN
cana-4287	166	6	,	,	PUNCT
cana-4287	166	7	with	with	ADP
cana-4287	166	8	encryption	encryption	NOUN
cana-4287	166	9	and	and	CCONJ
cana-4287	166	10	decryption	decryption	NOUN
cana-4287	166	11	timings	timing	NOUN
cana-4287	166	12	of	of	ADP
cana-4287	166	13	45	45	NUM
cana-4287	166	14	ms	ms	NOUN
cana-4287	166	15	and	and	CCONJ
cana-4287	166	16	55	55	NUM
cana-4287	166	17	ms	ms	NOUN
cana-4287	166	18	,	,	PUNCT
cana-4287	166	19	respectively	respectively	ADV
cana-4287	166	20	.	.	PUNCT
cana-4287	167	1	however	however	ADV
cana-4287	167	2	,	,	PUNCT
cana-4287	167	3	it	it	PRON
cana-4287	167	4	has	have	VERB
cana-4287	167	5	a	a	DET
cana-4287	167	6	somewhat	somewhat	ADV
cana-4287	167	7	higher	high	ADJ
cana-4287	167	8	processing	processing	NOUN
cana-4287	167	9	overhead	overhead	NOUN
cana-4287	167	10	of	of	ADP
cana-4287	167	11	12	12	NUM
cana-4287	167	12	%	%	NOUN
cana-4287	167	13	.	.	PUNCT
cana-4287	168	1	fig	fig	NOUN
cana-4287	168	2	.	.	PUNCT
cana-4287	169	1	6	6	NUM
cana-4287	169	2	:	:	PUNCT
cana-4287	169	3	topology	topology	NOUN
cana-4287	169	4	-	-	PUNCT
cana-4287	169	5	based	base	VERB
cana-4287	169	6	cryptographic	cryptographic	ADJ
cana-4287	169	7	algorithms	algorithm	NOUN
cana-4287	169	8	’	'	PUNCT
cana-4287	169	9	performance	performance	NOUN
cana-4287	169	10	analysis	analysis	NOUN
cana-4287	169	11	this	this	DET
cana-4287	169	12	cost	cost	NOUN
cana-4287	169	13	increase	increase	NOUN
cana-4287	169	14	may	may	AUX
cana-4287	169	15	be	be	AUX
cana-4287	169	16	due	due	ADJ
cana-4287	169	17	to	to	ADP
cana-4287	169	18	the	the	DET
cana-4287	169	19	additional	additional	ADJ
cana-4287	169	20	cryptographic	cryptographic	ADJ
cana-4287	169	21	capabilities	capability	NOUN
cana-4287	169	22	provided	provide	VERB
cana-4287	169	23	by	by	ADP
cana-4287	169	24	the	the	DET
cana-4287	169	25	topology	topology	NOUN
cana-4287	169	26	-	-	PUNCT
cana-4287	169	27	based	base	VERB
cana-4287	169	28	enhancements	enhancement	NOUN
cana-4287	169	29	.	.	PUNCT
cana-4287	170	1	because	because	SCONJ
cana-4287	170	2	topocrypt-3	topocrypt-3	NUM
cana-4287	170	3	has	have	VERB
cana-4287	170	4	the	the	DET
cana-4287	170	5	slowest	slow	ADJ
cana-4287	170	6	encryption	encryption	NOUN
cana-4287	170	7	and	and	CCONJ
cana-4287	170	8	decryption	decryption	NOUN
cana-4287	170	9	speeds	speed	NOUN
cana-4287	170	10	(	(	PUNCT
cana-4287	170	11	70	70	NUM
cana-4287	170	12	ms	ms	NOUN
cana-4287	170	13	and	and	CCONJ
cana-4287	170	14	75	75	NUM
cana-4287	170	15	ms	ms	NOUN
cana-4287	170	16	,	,	PUNCT
cana-4287	170	17	respectively	respectively	ADV
cana-4287	170	18	)	)	PUNCT
cana-4287	170	19	,	,	PUNCT
cana-4287	170	20	it	it	PRON
cana-4287	170	21	may	may	AUX
cana-4287	170	22	be	be	AUX
cana-4287	170	23	optimized	optimize	VERB
cana-4287	170	24	for	for	ADP
cana-4287	170	25	security	security	NOUN
cana-4287	170	26	at	at	ADP
cana-4287	170	27	the	the	DET
cana-4287	170	28	price	price	NOUN
cana-4287	170	29	of	of	ADP
cana-4287	170	30	efficiency	efficiency	NOUN
cana-4287	170	31	;	;	PUNCT
cana-4287	170	32	however	however	ADV
cana-4287	170	33	,	,	PUNCT
cana-4287	170	34	it	it	PRON
cana-4287	170	35	compensates	compensate	VERB
cana-4287	170	36	for	for	ADP
cana-4287	170	37	this	this	PRON
cana-4287	170	38	with	with	ADP
cana-4287	170	39	a	a	DET
cana-4287	170	40	lower	low	ADJ
cana-4287	170	41	computational	computational	ADJ
cana-4287	170	42	overhead	overhead	NOUN
cana-4287	170	43	of	of	ADP
cana-4287	170	44	8	8	NUM
cana-4287	170	45	%	%	NOUN
cana-4287	170	46	.	.	PUNCT
cana-4287	171	1	topocrypt-4	topocrypt-4	PRON
cana-4287	171	2	has	have	VERB
cana-4287	171	3	a	a	DET
cana-4287	171	4	modest	modest	ADJ
cana-4287	171	5	performance	performance	NOUN
cana-4287	171	6	profile	profile	NOUN
cana-4287	171	7	with	with	ADP
cana-4287	171	8	encryption	encryption	NOUN
cana-4287	171	9	and	and	CCONJ
cana-4287	171	10	decryption	decryption	NOUN
cana-4287	171	11	timings	timing	NOUN
cana-4287	171	12	of	of	ADP
cana-4287	171	13	55	55	NUM
cana-4287	171	14	ms	ms	NOUN
cana-4287	171	15	and	and	CCONJ
cana-4287	171	16	65	65	NUM
cana-4287	171	17	ms	ms	PROPN
cana-4287	171	18	,	,	PUNCT
cana-4287	171	19	respectively	respectively	ADV
cana-4287	171	20	,	,	PUNCT
cana-4287	171	21	with	with	ADP
cana-4287	171	22	the	the	DET
cana-4287	171	23	maximum	maximum	ADJ
cana-4287	171	24	computational	computational	ADJ
cana-4287	171	25	overhead	overhead	NOUN
cana-4287	171	26	of	of	ADP
cana-4287	171	27	15	15	NUM
cana-4287	171	28	%	%	NOUN
cana-4287	171	29	.	.	PUNCT
cana-4287	172	1	this	this	PRON
cana-4287	172	2	suggests	suggest	VERB
cana-4287	172	3	that	that	SCONJ
cana-4287	172	4	the	the	DET
cana-4287	172	5	increased	increase	VERB
cana-4287	172	6	security	security	NOUN
cana-4287	172	7	features	feature	NOUN
cana-4287	172	8	of	of	ADP
cana-4287	172	9	topocrypt-4	topocrypt-4	NUM
cana-4287	172	10	come	come	VERB
cana-4287	172	11	with	with	ADP
cana-4287	172	12	a	a	DET
cana-4287	172	13	trade	trade	NOUN
cana-4287	172	14	-	-	PUNCT
cana-4287	172	15	off	off	NOUN
cana-4287	172	16	in	in	ADP
cana-4287	172	17	terms	term	NOUN
cana-4287	172	18	of	of	ADP
cana-4287	172	19	processing	processing	NOUN
cana-4287	172	20	resources	resource	NOUN
cana-4287	172	21	.	.	PUNCT
cana-4287	173	1	communications	communication	NOUN
cana-4287	173	2	on	on	ADP
cana-4287	173	3	applied	apply	VERB
cana-4287	173	4	nonlinear	nonlinear	ADJ
cana-4287	173	5	analysis	analysis	NOUN
cana-4287	173	6	issn	issn	NOUN
cana-4287	173	7	:	:	PUNCT
cana-4287	173	8	1074	1074	NUM
cana-4287	173	9	-	-	PUNCT
cana-4287	173	10	133x	133x	NUM
cana-4287	173	11	vol	vol	NOUN
cana-4287	173	12	32	32	NUM
cana-4287	173	13	no	no	NOUN
cana-4287	173	14	.	.	PUNCT
cana-4287	174	1	9s	9s	NUM
cana-4287	174	2	(	(	PUNCT
cana-4287	174	3	2025	2025	NUM
cana-4287	174	4	)	)	PUNCT
cana-4287	174	5	1737	1737	NUM
cana-4287	174	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	174	7	c.	c.	PROPN
cana-4287	174	8	topology	topology	NOUN
cana-4287	174	9	-	-	PUNCT
cana-4287	174	10	based	base	VERB
cana-4287	174	11	cryptographic	cryptographic	ADJ
cana-4287	174	12	models	model	NOUN
cana-4287	174	13	solve	solve	VERB
cana-4287	174	14	security	security	NOUN
cana-4287	174	15	vulnerabilities	vulnerability	NOUN
cana-4287	174	16	(	(	PUNCT
cana-4287	174	17	2024	2024	NUM
cana-4287	174	18	)	)	PUNCT
cana-4287	174	19	fig	fig	NOUN
cana-4287	174	20	.	.	PUNCT
cana-4287	175	1	5	5	NUM
cana-4287	175	2	shows	show	VERB
cana-4287	175	3	how	how	SCONJ
cana-4287	175	4	frequently	frequently	ADV
cana-4287	175	5	topology	topology	NOUN
cana-4287	175	6	-	-	PUNCT
cana-4287	175	7	based	base	VERB
cana-4287	175	8	cryptography	cryptography	NOUN
cana-4287	175	9	models	model	NOUN
cana-4287	175	10	resolve	resolve	VERB
cana-4287	175	11	various	various	ADJ
cana-4287	175	12	security	security	NOUN
cana-4287	175	13	flaws	flaw	NOUN
cana-4287	175	14	.	.	PUNCT
cana-4287	176	1	the	the	DET
cana-4287	176	2	data	datum	NOUN
cana-4287	176	3	demonstrates	demonstrate	VERB
cana-4287	176	4	the	the	DET
cana-4287	176	5	areas	area	NOUN
cana-4287	176	6	of	of	ADP
cana-4287	176	7	current	current	ADJ
cana-4287	176	8	research	research	NOUN
cana-4287	176	9	focused	focus	VERB
cana-4287	176	10	on	on	ADP
cana-4287	176	11	defending	defend	VERB
cana-4287	176	12	cryptographic	cryptographic	ADJ
cana-4287	176	13	systems	system	NOUN
cana-4287	176	14	against	against	ADP
cana-4287	176	15	different	different	ADJ
cana-4287	176	16	types	type	NOUN
cana-4287	176	17	of	of	ADP
cana-4287	176	18	attacks	attack	NOUN
cana-4287	176	19	.	.	PUNCT
cana-4287	177	1	the	the	DET
cana-4287	177	2	most	most	ADV
cana-4287	177	3	commonly	commonly	ADV
cana-4287	177	4	addressed	address	VERB
cana-4287	177	5	vulnerability	vulnerability	NOUN
cana-4287	177	6	is	be	AUX
cana-4287	177	7	the	the	DET
cana-4287	177	8	man	man	NOUN
cana-4287	177	9	-	-	PUNCT
cana-4287	177	10	in	in	ADP
cana-4287	177	11	-	-	PUNCT
cana-4287	177	12	the	the	DET
cana-4287	177	13	-	-	PUNCT
cana-4287	177	14	middle	middle	ADJ
cana-4287	177	15	attack	attack	NOUN
cana-4287	177	16	,	,	PUNCT
cana-4287	177	17	with	with	ADP
cana-4287	177	18	25	25	NUM
cana-4287	177	19	cryptographic	cryptographic	ADJ
cana-4287	177	20	models	model	NOUN
cana-4287	177	21	developed	develop	VERB
cana-4287	177	22	to	to	PART
cana-4287	177	23	mitigate	mitigate	VERB
cana-4287	177	24	the	the	DET
cana-4287	177	25	threat	threat	NOUN
cana-4287	177	26	.	.	PUNCT
cana-4287	178	1	this	this	DET
cana-4287	178	2	high	high	ADJ
cana-4287	178	3	number	number	NOUN
cana-4287	178	4	suggests	suggest	VERB
cana-4287	178	5	that	that	SCONJ
cana-4287	178	6	researchers	researcher	NOUN
cana-4287	178	7	are	be	AUX
cana-4287	178	8	working	work	VERB
cana-4287	178	9	hard	hard	ADV
cana-4287	178	10	to	to	PART
cana-4287	178	11	ensure	ensure	VERB
cana-4287	178	12	that	that	SCONJ
cana-4287	178	13	communication	communication	NOUN
cana-4287	178	14	channels	channel	NOUN
cana-4287	178	15	are	be	AUX
cana-4287	178	16	secure	secure	ADJ
cana-4287	178	17	,	,	PUNCT
cana-4287	178	18	given	give	VERB
cana-4287	178	19	the	the	DET
cana-4287	178	20	possibility	possibility	NOUN
cana-4287	178	21	that	that	SCONJ
cana-4287	178	22	attackers	attacker	NOUN
cana-4287	178	23	could	could	AUX
cana-4287	178	24	intercept	intercept	VERB
cana-4287	178	25	or	or	CCONJ
cana-4287	178	26	alter	alter	VERB
cana-4287	178	27	messages	message	NOUN
cana-4287	178	28	between	between	ADP
cana-4287	178	29	two	two	NUM
cana-4287	178	30	parties	party	NOUN
cana-4287	178	31	.	.	PUNCT
cana-4287	179	1	while	while	SCONJ
cana-4287	179	2	preserving	preserve	VERB
cana-4287	179	3	communication	communication	NOUN
cana-4287	179	4	integrity	integrity	NOUN
cana-4287	179	5	,	,	PUNCT
cana-4287	179	6	topological	topological	ADJ
cana-4287	179	7	techniques	technique	NOUN
cana-4287	179	8	offer	offer	VERB
cana-4287	179	9	unique	unique	ADJ
cana-4287	179	10	opportunities	opportunity	NOUN
cana-4287	179	11	to	to	PART
cana-4287	179	12	enhance	enhance	VERB
cana-4287	179	13	encryption	encryption	NOUN
cana-4287	179	14	keys	key	NOUN
cana-4287	179	15	and	and	CCONJ
cana-4287	179	16	data	datum	NOUN
cana-4287	179	17	structures	structure	NOUN
cana-4287	179	18	.	.	PUNCT
cana-4287	180	1	quantum	quantum	NOUN
cana-4287	180	2	dangers	danger	NOUN
cana-4287	180	3	rank	rank	VERB
cana-4287	180	4	second	second	ADV
cana-4287	180	5	with	with	ADP
cana-4287	180	6	30	30	NUM
cana-4287	180	7	models	model	NOUN
cana-4287	180	8	that	that	PRON
cana-4287	180	9	address	address	VERB
cana-4287	180	10	them	they	PRON
cana-4287	180	11	.	.	PUNCT
cana-4287	181	1	as	as	ADP
cana-4287	181	2	quantum	quantum	NOUN
cana-4287	181	3	computing	computing	NOUN
cana-4287	181	4	advances	advance	NOUN
cana-4287	181	5	,	,	PUNCT
cana-4287	181	6	traditional	traditional	ADJ
cana-4287	181	7	cryptography	cryptography	NOUN
cana-4287	181	8	systems	system	NOUN
cana-4287	181	9	are	be	AUX
cana-4287	181	10	become	become	VERB
cana-4287	181	11	increasingly	increasingly	ADV
cana-4287	181	12	susceptible	susceptible	ADJ
cana-4287	181	13	,	,	PUNCT
cana-4287	181	14	and	and	CCONJ
cana-4287	181	15	topology	topology	NOUN
cana-4287	181	16	-	-	PUNCT
cana-4287	181	17	based	base	VERB
cana-4287	181	18	approaches	approach	NOUN
cana-4287	181	19	are	be	AUX
cana-4287	181	20	gaining	gain	VERB
cana-4287	181	21	attention	attention	NOUN
cana-4287	181	22	as	as	ADP
cana-4287	181	23	a	a	DET
cana-4287	181	24	potential	potential	ADJ
cana-4287	181	25	means	mean	NOUN
cana-4287	181	26	of	of	ADP
cana-4287	181	27	developing	develop	VERB
cana-4287	181	28	encryption	encryption	NOUN
cana-4287	181	29	protocols	protocol	NOUN
cana-4287	181	30	that	that	PRON
cana-4287	181	31	are	be	AUX
cana-4287	181	32	impervious	impervious	ADJ
cana-4287	181	33	to	to	ADP
cana-4287	181	34	quantum	quantum	ADJ
cana-4287	181	35	mistakes	mistake	NOUN
cana-4287	181	36	.	.	PUNCT
cana-4287	182	1	the	the	DET
cana-4287	182	2	importance	importance	NOUN
cana-4287	182	3	of	of	ADP
cana-4287	182	4	creating	create	VERB
cana-4287	182	5	algorithms	algorithm	NOUN
cana-4287	182	6	that	that	PRON
cana-4287	182	7	can	can	AUX
cana-4287	182	8	resist	resist	VERB
cana-4287	182	9	exhaustive	exhaustive	ADJ
cana-4287	182	10	search	search	NOUN
cana-4287	182	11	attempts	attempt	NOUN
cana-4287	182	12	to	to	PART
cana-4287	182	13	decode	decode	VERB
cana-4287	182	14	data	datum	NOUN
cana-4287	182	15	is	be	AUX
cana-4287	182	16	highlighted	highlight	VERB
cana-4287	182	17	by	by	ADP
cana-4287	182	18	the	the	DET
cana-4287	182	19	twenty	twenty	NUM
cana-4287	182	20	models	model	NOUN
cana-4287	182	21	that	that	PRON
cana-4287	182	22	combat	combat	VERB
cana-4287	182	23	brute	brute	ADJ
cana-4287	182	24	force	force	NOUN
cana-4287	182	25	attacks	attack	NOUN
cana-4287	182	26	.	.	PUNCT
cana-4287	183	1	fig	fig	NOUN
cana-4287	183	2	.	.	PUNCT
cana-4287	184	1	7	7	NUM
cana-4287	184	2	:	:	PUNCT
cana-4287	184	3	topology	topology	NOUN
cana-4287	184	4	-	-	PUNCT
cana-4287	184	5	based	base	VERB
cana-4287	184	6	cryptographic	cryptographic	ADJ
cana-4287	184	7	models	model	NOUN
cana-4287	184	8	solve	solve	VERB
cana-4287	184	9	security	security	NOUN
cana-4287	184	10	vulnerabilities	vulnerability	NOUN
cana-4287	184	11	(	(	PUNCT
cana-4287	184	12	2024	2024	NUM
cana-4287	184	13	)	)	PUNCT
cana-4287	184	14	replay	replay	NOUN
cana-4287	184	15	attacks	attack	NOUN
cana-4287	184	16	and	and	CCONJ
cana-4287	184	17	side	side	ADJ
cana-4287	184	18	-	-	PUNCT
cana-4287	184	19	channel	channel	NOUN
cana-4287	184	20	attacks	attack	NOUN
cana-4287	184	21	are	be	AUX
cana-4287	184	22	addressed	address	VERB
cana-4287	184	23	in	in	ADP
cana-4287	184	24	models	model	NOUN
cana-4287	184	25	10	10	NUM
cana-4287	184	26	and	and	CCONJ
cana-4287	184	27	15	15	NUM
cana-4287	184	28	,	,	PUNCT
cana-4287	184	29	respectively	respectively	ADV
cana-4287	184	30	.	.	PUNCT
cana-4287	185	1	these	these	DET
cana-4287	185	2	attacks	attack	NOUN
cana-4287	185	3	exploit	exploit	VERB
cana-4287	185	4	weaknesses	weakness	NOUN
cana-4287	185	5	in	in	ADP
cana-4287	185	6	the	the	DET
cana-4287	185	7	physical	physical	ADJ
cana-4287	185	8	implementation	implementation	NOUN
cana-4287	185	9	of	of	ADP
cana-4287	185	10	cryptographic	cryptographic	ADJ
cana-4287	185	11	systems	system	NOUN
cana-4287	185	12	,	,	PUNCT
cana-4287	185	13	such	such	ADJ
cana-4287	185	14	as	as	ADP
cana-4287	185	15	timing	timing	NOUN
cana-4287	185	16	or	or	CCONJ
cana-4287	185	17	power	power	NOUN
cana-4287	185	18	consumption	consumption	NOUN
cana-4287	185	19	issues	issue	NOUN
cana-4287	185	20	that	that	PRON
cana-4287	185	21	let	let	VERB
cana-4287	185	22	data	datum	NOUN
cana-4287	185	23	leak	leak	VERB
cana-4287	185	24	.	.	PUNCT
cana-4287	186	1	topological	topological	ADJ
cana-4287	186	2	approaches	approach	NOUN
cana-4287	186	3	are	be	AUX
cana-4287	186	4	being	be	AUX
cana-4287	186	5	researched	research	VERB
cana-4287	186	6	to	to	PART
cana-4287	186	7	apply	apply	VERB
cana-4287	186	8	more	more	ADV
cana-4287	186	9	complex	complex	ADJ
cana-4287	186	10	,	,	PUNCT
cana-4287	186	11	multidimensional	multidimensional	ADJ
cana-4287	186	12	encryption	encryption	NOUN
cana-4287	186	13	systems	system	NOUN
cana-4287	186	14	in	in	ADP
cana-4287	186	15	order	order	NOUN
cana-4287	186	16	to	to	PART
cana-4287	186	17	get	get	VERB
cana-4287	186	18	around	around	ADP
cana-4287	186	19	these	these	DET
cana-4287	186	20	drawbacks	drawback	NOUN
cana-4287	186	21	.	.	PUNCT
cana-4287	187	1	d.	d.	PROPN
cana-4287	187	2	cryptographic	cryptographic	ADJ
cana-4287	187	3	security	security	NOUN
cana-4287	187	4	and	and	CCONJ
cana-4287	187	5	algebraic	algebraic	ADJ
cana-4287	187	6	topology	topology	NOUN
cana-4287	187	7	(	(	PUNCT
cana-4287	187	8	2024	2024	NUM
cana-4287	187	9	)	)	PUNCT
cana-4287	187	10	fig	fig	NOUN
cana-4287	187	11	.	.	PUNCT
cana-4287	188	1	6	6	NUM
cana-4287	188	2	compares	compare	VERB
cana-4287	188	3	the	the	DET
cana-4287	188	4	security	security	NOUN
cana-4287	188	5	improvements	improvement	NOUN
cana-4287	188	6	achieved	achieve	VERB
cana-4287	188	7	by	by	ADP
cana-4287	188	8	incorporating	incorporate	VERB
cana-4287	188	9	algebraic	algebraic	ADJ
cana-4287	188	10	topology	topology	NOUN
cana-4287	188	11	approaches	approach	NOUN
cana-4287	188	12	into	into	ADP
cana-4287	188	13	various	various	ADJ
cana-4287	188	14	cryptographic	cryptographic	ADJ
cana-4287	188	15	systems	system	NOUN
cana-4287	188	16	.	.	PUNCT
cana-4287	189	1	the	the	DET
cana-4287	189	2	information	information	NOUN
cana-4287	189	3	shows	show	VERB
cana-4287	189	4	the	the	DET
cana-4287	189	5	percentage	percentage	NOUN
cana-4287	189	6	gain	gain	NOUN
cana-4287	189	7	in	in	ADP
cana-4287	189	8	security	security	NOUN
cana-4287	189	9	for	for	ADP
cana-4287	189	10	each	each	DET
cana-4287	189	11	protocol	protocol	NOUN
cana-4287	189	12	when	when	SCONJ
cana-4287	189	13	topological	topological	ADJ
cana-4287	189	14	enhancements	enhancement	NOUN
cana-4287	189	15	are	be	AUX
cana-4287	189	16	applied	apply	VERB
cana-4287	189	17	.	.	PUNCT
cana-4287	190	1	among	among	ADP
cana-4287	190	2	the	the	DET
cana-4287	190	3	protocols	protocol	NOUN
cana-4287	190	4	,	,	PUNCT
cana-4287	190	5	post	post	ADJ
cana-4287	190	6	-	-	ADJ
cana-4287	190	7	quantum	quantum	ADJ
cana-4287	190	8	cryptography	cryptography	NOUN
cana-4287	190	9	stands	stand	VERB
cana-4287	190	10	out	out	ADP
cana-4287	190	11	with	with	ADP
cana-4287	190	12	a	a	DET
cana-4287	190	13	security	security	NOUN
cana-4287	190	14	improvement	improvement	NOUN
cana-4287	190	15	of	of	ADP
cana-4287	190	16	30	30	NUM
cana-4287	190	17	%	%	NOUN
cana-4287	190	18	,	,	PUNCT
cana-4287	190	19	demonstrating	demonstrate	VERB
cana-4287	190	20	the	the	DET
cana-4287	190	21	growing	grow	VERB
cana-4287	190	22	need	need	NOUN
cana-4287	190	23	for	for	ADP
cana-4287	190	24	encryption	encryption	NOUN
cana-4287	190	25	methods	method	NOUN
cana-4287	190	26	that	that	PRON
cana-4287	190	27	are	be	AUX
cana-4287	190	28	impervious	impervious	ADJ
cana-4287	190	29	to	to	ADP
cana-4287	190	30	quantum	quantum	ADJ
cana-4287	190	31	defects	defect	NOUN
cana-4287	190	32	.	.	PUNCT
cana-4287	191	1	since	since	SCONJ
cana-4287	191	2	it	it	PRON
cana-4287	191	3	is	be	AUX
cana-4287	191	4	predicted	predict	VERB
cana-4287	191	5	that	that	SCONJ
cana-4287	191	6	quantum	quantum	NOUN
cana-4287	191	7	computers	computer	NOUN
cana-4287	191	8	will	will	AUX
cana-4287	191	9	violate	violate	VERB
cana-4287	191	10	current	current	ADJ
cana-4287	191	11	encryption	encryption	NOUN
cana-4287	191	12	standards	standard	NOUN
cana-4287	191	13	,	,	PUNCT
cana-4287	191	14	the	the	DET
cana-4287	191	15	use	use	NOUN
cana-4287	191	16	of	of	ADP
cana-4287	191	17	topological	topological	ADJ
cana-4287	191	18	approaches	approach	NOUN
cana-4287	191	19	in	in	ADP
cana-4287	191	20	post	post	ADJ
cana-4287	191	21	-	-	ADJ
cana-4287	191	22	quantum	quantum	ADJ
cana-4287	191	23	protocols	protocol	NOUN
cana-4287	191	24	presents	present	VERB
cana-4287	191	25	a	a	DET
cana-4287	191	26	potential	potential	ADJ
cana-4287	191	27	means	mean	NOUN
cana-4287	191	28	of	of	ADP
cana-4287	191	29	fortifying	fortify	VERB
cana-4287	191	30	these	these	DET
cana-4287	191	31	systems	system	NOUN
cana-4287	191	32	against	against	ADP
cana-4287	191	33	quantum	quantum	NOUN
cana-4287	191	34	threats	threat	NOUN
cana-4287	191	35	.	.	PUNCT
cana-4287	192	1	communications	communication	NOUN
cana-4287	192	2	on	on	ADP
cana-4287	192	3	applied	apply	VERB
cana-4287	192	4	nonlinear	nonlinear	ADJ
cana-4287	192	5	analysis	analysis	NOUN
cana-4287	192	6	issn	issn	NOUN
cana-4287	192	7	:	:	PUNCT
cana-4287	192	8	1074	1074	NUM
cana-4287	192	9	-	-	PUNCT
cana-4287	192	10	133x	133x	NUM
cana-4287	192	11	vol	vol	NOUN
cana-4287	192	12	32	32	NUM
cana-4287	192	13	no	no	NOUN
cana-4287	192	14	.	.	PUNCT
cana-4287	193	1	9s	9s	NUM
cana-4287	193	2	(	(	PUNCT
cana-4287	193	3	2025	2025	NUM
cana-4287	193	4	)	)	PUNCT
cana-4287	193	5	1738	1738	NUM
cana-4287	193	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	193	7	lattice	lattice	NOUN
cana-4287	193	8	-	-	PUNCT
cana-4287	193	9	based	base	VERB
cana-4287	193	10	cryptography	cryptography	NOUN
cana-4287	193	11	,	,	PUNCT
cana-4287	193	12	already	already	ADV
cana-4287	193	13	considered	consider	VERB
cana-4287	193	14	resistant	resistant	ADJ
cana-4287	193	15	to	to	ADP
cana-4287	193	16	quantum	quantum	ADJ
cana-4287	193	17	attacks	attack	NOUN
cana-4287	193	18	,	,	PUNCT
cana-4287	193	19	shows	show	VERB
cana-4287	193	20	further	further	ADJ
cana-4287	193	21	promise	promise	NOUN
cana-4287	193	22	with	with	ADP
cana-4287	193	23	a	a	DET
cana-4287	193	24	25	25	NUM
cana-4287	193	25	%	%	NOUN
cana-4287	193	26	security	security	NOUN
cana-4287	193	27	improvement	improvement	NOUN
cana-4287	193	28	through	through	ADP
cana-4287	193	29	topological	topological	ADJ
cana-4287	193	30	enhancements	enhancement	NOUN
cana-4287	193	31	.	.	PUNCT
cana-4287	194	1	algebraic	algebraic	ADJ
cana-4287	194	2	topology	topology	NOUN
cana-4287	194	3	strengthens	strengthen	VERB
cana-4287	194	4	these	these	DET
cana-4287	194	5	structures	structure	NOUN
cana-4287	194	6	by	by	ADP
cana-4287	194	7	providing	provide	VERB
cana-4287	194	8	more	more	ADV
cana-4287	194	9	effective	effective	ADJ
cana-4287	194	10	ways	way	NOUN
cana-4287	194	11	to	to	PART
cana-4287	194	12	represent	represent	VERB
cana-4287	194	13	and	and	CCONJ
cana-4287	194	14	manipulate	manipulate	VERB
cana-4287	194	15	complex	complex	ADJ
cana-4287	194	16	data	datum	NOUN
cana-4287	194	17	relationships	relationship	NOUN
cana-4287	194	18	within	within	ADP
cana-4287	194	19	the	the	DET
cana-4287	194	20	lattice	lattice	NOUN
cana-4287	194	21	,	,	PUNCT
cana-4287	194	22	increasing	increase	VERB
cana-4287	194	23	their	their	PRON
cana-4287	194	24	resilience	resilience	NOUN
cana-4287	194	25	.	.	PUNCT
cana-4287	195	1	additionally	additionally	ADV
cana-4287	195	2	,	,	PUNCT
cana-4287	195	3	hash	hash	NOUN
cana-4287	195	4	algorithms	algorithm	NOUN
cana-4287	195	5	incorporating	incorporate	VERB
cana-4287	195	6	topological	topological	ADJ
cana-4287	195	7	features	feature	NOUN
cana-4287	195	8	exhibit	exhibit	VERB
cana-4287	195	9	a	a	DET
cana-4287	195	10	22	22	NUM
cana-4287	195	11	%	%	NOUN
cana-4287	195	12	improvement	improvement	NOUN
cana-4287	195	13	,	,	PUNCT
cana-4287	195	14	demonstrating	demonstrate	VERB
cana-4287	195	15	how	how	SCONJ
cana-4287	195	16	topology	topology	NOUN
cana-4287	195	17	can	can	AUX
cana-4287	195	18	enhance	enhance	VERB
cana-4287	195	19	data	data	NOUN
cana-4287	195	20	integrity	integrity	NOUN
cana-4287	195	21	and	and	CCONJ
cana-4287	195	22	mitigate	mitigate	VERB
cana-4287	195	23	vulnerabilities	vulnerability	NOUN
cana-4287	195	24	such	such	ADJ
cana-4287	195	25	as	as	ADP
cana-4287	195	26	collisions	collision	NOUN
cana-4287	195	27	.	.	PUNCT
cana-4287	196	1	fig	fig	NOUN
cana-4287	196	2	.	.	PUNCT
cana-4287	197	1	8	8	NUM
cana-4287	197	2	:	:	PUNCT
cana-4287	197	3	cryptographic	cryptographic	ADJ
cana-4287	197	4	security	security	NOUN
cana-4287	197	5	and	and	CCONJ
cana-4287	197	6	algebraic	algebraic	ADJ
cana-4287	197	7	topology	topology	NOUN
cana-4287	197	8	(	(	PUNCT
cana-4287	197	9	2024	2024	NUM
cana-4287	197	10	)	)	PUNCT
cana-4287	197	11	both	both	DET
cana-4287	197	12	rsa	rsa	PROPN
cana-4287	197	13	with	with	ADP
cana-4287	197	14	topological	topological	ADJ
cana-4287	197	15	enhancements	enhancement	NOUN
cana-4287	197	16	and	and	CCONJ
cana-4287	197	17	elliptic	elliptic	ADJ
cana-4287	197	18	curve	curve	NOUN
cana-4287	197	19	cryptography	cryptography	NOUN
cana-4287	197	20	(	(	PUNCT
cana-4287	197	21	ecc	ecc	NOUN
cana-4287	197	22	)	)	PUNCT
cana-4287	197	23	benefit	benefit	NOUN
cana-4287	197	24	from	from	ADP
cana-4287	197	25	topological	topological	ADJ
cana-4287	197	26	techniques	technique	NOUN
cana-4287	197	27	,	,	PUNCT
cana-4287	197	28	which	which	PRON
cana-4287	197	29	raise	raise	VERB
cana-4287	197	30	security	security	NOUN
cana-4287	197	31	by	by	ADP
cana-4287	197	32	18	18	NUM
cana-4287	197	33	%	%	NOUN
cana-4287	197	34	and	and	CCONJ
cana-4287	197	35	20	20	NUM
cana-4287	197	36	%	%	NOUN
cana-4287	197	37	,	,	PUNCT
cana-4287	197	38	respectively	respectively	ADV
cana-4287	197	39	.	.	PUNCT
cana-4287	198	1	even	even	ADV
cana-4287	198	2	though	though	SCONJ
cana-4287	198	3	these	these	DET
cana-4287	198	4	traditional	traditional	ADJ
cana-4287	198	5	protocols	protocol	NOUN
cana-4287	198	6	are	be	AUX
cana-4287	198	7	extensively	extensively	ADV
cana-4287	198	8	used	use	VERB
cana-4287	198	9	,	,	PUNCT
cana-4287	198	10	they	they	PRON
cana-4287	198	11	are	be	AUX
cana-4287	198	12	becoming	become	VERB
cana-4287	198	13	more	more	ADV
cana-4287	198	14	secure	secure	ADJ
cana-4287	198	15	through	through	ADP
cana-4287	198	16	the	the	DET
cana-4287	198	17	application	application	NOUN
cana-4287	198	18	of	of	ADP
cana-4287	198	19	topological	topological	ADJ
cana-4287	198	20	approaches	approach	NOUN
cana-4287	198	21	,	,	PUNCT
cana-4287	198	22	which	which	PRON
cana-4287	198	23	increases	increase	VERB
cana-4287	198	24	their	their	PRON
cana-4287	198	25	resilience	resilience	NOUN
cana-4287	198	26	to	to	ADP
cana-4287	198	27	modern	modern	ADJ
cana-4287	198	28	threats	threat	NOUN
cana-4287	198	29	.	.	PUNCT
cana-4287	199	1	conclusion	conclusion	NOUN
cana-4287	199	2	this	this	DET
cana-4287	199	3	essay	essay	NOUN
cana-4287	199	4	focuses	focus	VERB
cana-4287	199	5	on	on	ADP
cana-4287	199	6	how	how	SCONJ
cana-4287	199	7	algebraic	algebraic	ADJ
cana-4287	199	8	topology	topology	NOUN
cana-4287	199	9	might	might	AUX
cana-4287	199	10	transform	transform	VERB
cana-4287	199	11	modern	modern	ADJ
cana-4287	199	12	cryptography	cryptography	NOUN
cana-4287	199	13	by	by	ADP
cana-4287	199	14	enhancing	enhance	VERB
cana-4287	199	15	resilience	resilience	NOUN
cana-4287	199	16	,	,	PUNCT
cana-4287	199	17	efficacy	efficacy	NOUN
cana-4287	199	18	,	,	PUNCT
cana-4287	199	19	and	and	CCONJ
cana-4287	199	20	security	security	NOUN
cana-4287	199	21	.	.	PUNCT
cana-4287	200	1	topological	topological	ADJ
cana-4287	200	2	concepts	concept	NOUN
cana-4287	200	3	like	like	ADP
cana-4287	200	4	homology	homology	NOUN
cana-4287	200	5	theory	theory	NOUN
cana-4287	200	6	,	,	PUNCT
cana-4287	200	7	simplicial	simplicial	ADJ
cana-4287	200	8	complexes	complex	NOUN
cana-4287	200	9	,	,	PUNCT
cana-4287	200	10	and	and	CCONJ
cana-4287	200	11	topological	topological	ADJ
cana-4287	200	12	vector	vector	NOUN
cana-4287	200	13	spaces	space	NOUN
cana-4287	200	14	are	be	AUX
cana-4287	200	15	used	use	VERB
cana-4287	200	16	to	to	PART
cana-4287	200	17	strengthen	strengthen	VERB
cana-4287	200	18	cryptographic	cryptographic	ADJ
cana-4287	200	19	protocols	protocol	NOUN
cana-4287	200	20	against	against	ADP
cana-4287	200	21	a	a	DET
cana-4287	200	22	range	range	NOUN
cana-4287	200	23	of	of	ADP
cana-4287	200	24	attack	attack	NOUN
cana-4287	200	25	vectors	vector	NOUN
cana-4287	200	26	,	,	PUNCT
cana-4287	200	27	including	include	VERB
cana-4287	200	28	brute	brute	ADJ
cana-4287	200	29	-	-	PUNCT
cana-4287	200	30	force	force	NOUN
cana-4287	200	31	attempts	attempt	NOUN
cana-4287	200	32	and	and	CCONJ
cana-4287	200	33	quantum	quantum	NOUN
cana-4287	200	34	threats	threat	NOUN
cana-4287	200	35	.	.	PUNCT
cana-4287	201	1	performance	performance	NOUN
cana-4287	201	2	measurements	measurement	NOUN
cana-4287	201	3	show	show	VERB
cana-4287	201	4	that	that	SCONJ
cana-4287	201	5	topology	topology	NOUN
cana-4287	201	6	-	-	PUNCT
cana-4287	201	7	based	base	VERB
cana-4287	201	8	techniques	technique	NOUN
cana-4287	201	9	,	,	PUNCT
cana-4287	201	10	such	such	ADJ
cana-4287	201	11	versions	version	NOUN
cana-4287	201	12	of	of	ADP
cana-4287	201	13	topocrypt	topocrypt	NOUN
cana-4287	201	14	,	,	PUNCT
cana-4287	201	15	effectively	effectively	ADV
cana-4287	201	16	balance	balance	VERB
cana-4287	201	17	computational	computational	ADJ
cana-4287	201	18	overhead	overhead	NOUN
cana-4287	201	19	with	with	ADP
cana-4287	201	20	encryption	encryption	NOUN
cana-4287	201	21	and	and	CCONJ
cana-4287	201	22	decryption	decryption	NOUN
cana-4287	201	23	speed	speed	NOUN
cana-4287	201	24	.	.	PUNCT
cana-4287	202	1	furthermore	furthermore	ADV
cana-4287	202	2	,	,	PUNCT
cana-4287	202	3	the	the	DET
cana-4287	202	4	reduction	reduction	NOUN
cana-4287	202	5	in	in	ADP
cana-4287	202	6	time	time	NOUN
cana-4287	202	7	complexity	complexity	NOUN
cana-4287	202	8	for	for	ADP
cana-4287	202	9	advanced	advanced	ADJ
cana-4287	202	10	techniques	technique	NOUN
cana-4287	202	11	like	like	ADP
cana-4287	202	12	lattice	lattice	NOUN
cana-4287	202	13	-	-	PUNCT
cana-4287	202	14	based	base	VERB
cana-4287	202	15	and	and	CCONJ
cana-4287	202	16	homomorphic	homomorphic	ADJ
cana-4287	202	17	encryption	encryption	NOUN
cana-4287	202	18	shows	show	VERB
cana-4287	202	19	the	the	DET
cana-4287	202	20	practical	practical	ADJ
cana-4287	202	21	feasibility	feasibility	NOUN
cana-4287	202	22	of	of	ADP
cana-4287	202	23	topological	topological	ADJ
cana-4287	202	24	enhancements	enhancement	NOUN
cana-4287	202	25	.	.	PUNCT
cana-4287	203	1	security	security	NOUN
cana-4287	203	2	improvements	improvement	NOUN
cana-4287	203	3	across	across	ADP
cana-4287	203	4	protocols	protocol	NOUN
cana-4287	203	5	,	,	PUNCT
cana-4287	203	6	particularly	particularly	ADV
cana-4287	203	7	in	in	ADP
cana-4287	203	8	postquantum	postquantum	PROPN
cana-4287	203	9	cryptography	cryptography	NOUN
cana-4287	203	10	,	,	PUNCT
cana-4287	203	11	demonstrate	demonstrate	VERB
cana-4287	203	12	algebraic	algebraic	ADJ
cana-4287	203	13	topology	topology	NOUN
cana-4287	203	14	's	's	PART
cana-4287	203	15	transdisciplinary	transdisciplinary	ADJ
cana-4287	203	16	potential	potential	NOUN
cana-4287	203	17	to	to	PART
cana-4287	203	18	address	address	VERB
cana-4287	203	19	contemporary	contemporary	ADJ
cana-4287	203	20	cryptographic	cryptographic	NOUN
cana-4287	203	21	.	.	PUNCT
cana-4287	204	1	in	in	ADP
cana-4287	204	2	an	an	DET
cana-4287	204	3	increasingly	increasingly	ADV
cana-4287	204	4	digital	digital	ADJ
cana-4287	204	5	world	world	NOUN
cana-4287	204	6	,	,	PUNCT
cana-4287	204	7	this	this	DET
cana-4287	204	8	approach	approach	NOUN
cana-4287	204	9	creates	create	VERB
cana-4287	204	10	a	a	DET
cana-4287	204	11	more	more	ADV
cana-4287	204	12	secure	secure	ADJ
cana-4287	204	13	and	and	CCONJ
cana-4287	204	14	adaptable	adaptable	ADJ
cana-4287	204	15	cryptographic	cryptographic	ADJ
cana-4287	204	16	environment	environment	NOUN
cana-4287	204	17	by	by	ADP
cana-4287	204	18	combining	combine	VERB
cana-4287	204	19	encryption	encryption	NOUN
cana-4287	204	20	techniques	technique	NOUN
cana-4287	204	21	with	with	ADP
cana-4287	204	22	mathematical	mathematical	ADJ
cana-4287	204	23	frameworks	framework	NOUN
cana-4287	204	24	,	,	PUNCT
cana-4287	204	25	opening	open	VERB
cana-4287	204	26	the	the	DET
cana-4287	204	27	possibility	possibility	NOUN
cana-4287	204	28	for	for	ADP
cana-4287	204	29	innovative	innovative	ADJ
cana-4287	204	30	solutions	solution	NOUN
cana-4287	204	31	.	.	PUNCT
cana-4287	205	1	further	further	ADJ
cana-4287	205	2	research	research	NOUN
cana-4287	205	3	in	in	ADP
cana-4287	205	4	this	this	DET
cana-4287	205	5	area	area	NOUN
cana-4287	205	6	is	be	AUX
cana-4287	205	7	expected	expect	VERB
cana-4287	205	8	to	to	PART
cana-4287	205	9	yield	yield	VERB
cana-4287	205	10	significant	significant	ADJ
cana-4287	205	11	improvements	improvement	NOUN
cana-4287	205	12	in	in	ADP
cana-4287	205	13	secure	secure	ADJ
cana-4287	205	14	communications	communication	NOUN
cana-4287	205	15	and	and	CCONJ
cana-4287	205	16	data	datum	NOUN
cana-4287	205	17	integrity	integrity	NOUN
cana-4287	205	18	.	.	PUNCT
cana-4287	206	1	this	this	DET
cana-4287	206	2	study	study	NOUN
cana-4287	206	3	explores	explore	VERB
cana-4287	206	4	how	how	SCONJ
cana-4287	206	5	algebraic	algebraic	ADJ
cana-4287	206	6	topology	topology	NOUN
cana-4287	206	7	can	can	AUX
cana-4287	206	8	revolutionize	revolutionize	VERB
cana-4287	206	9	modern	modern	ADJ
cana-4287	206	10	cryptography	cryptography	NOUN
cana-4287	206	11	by	by	ADP
cana-4287	206	12	enhancing	enhance	VERB
cana-4287	206	13	resilience	resilience	NOUN
cana-4287	206	14	,	,	PUNCT
cana-4287	206	15	efficiency	efficiency	NOUN
cana-4287	206	16	,	,	PUNCT
cana-4287	206	17	and	and	CCONJ
cana-4287	206	18	security	security	NOUN
cana-4287	206	19	.	.	PUNCT
cana-4287	207	1	topological	topological	ADJ
cana-4287	207	2	concepts	concept	NOUN
cana-4287	207	3	such	such	ADJ
cana-4287	207	4	as	as	ADP
cana-4287	207	5	homology	homology	NOUN
cana-4287	207	6	theory	theory	NOUN
cana-4287	207	7	,	,	PUNCT
cana-4287	207	8	simplicial	simplicial	ADJ
cana-4287	207	9	complexes	complex	NOUN
cana-4287	207	10	,	,	PUNCT
cana-4287	207	11	and	and	CCONJ
cana-4287	207	12	topological	topological	ADJ
cana-4287	207	13	vector	vector	NOUN
cana-4287	207	14	spaces	space	NOUN
cana-4287	207	15	are	be	AUX
cana-4287	207	16	employed	employ	VERB
cana-4287	207	17	to	to	PART
cana-4287	207	18	fortify	fortify	VERB
cana-4287	207	19	cryptographic	cryptographic	ADJ
cana-4287	207	20	protocols	protocol	NOUN
cana-4287	207	21	against	against	ADP
cana-4287	207	22	diverse	diverse	ADJ
cana-4287	207	23	attack	attack	NOUN
cana-4287	207	24	vectors	vector	NOUN
cana-4287	207	25	,	,	PUNCT
cana-4287	207	26	including	include	VERB
cana-4287	207	27	brute	brute	ADJ
cana-4287	207	28	-	-	PUNCT
cana-4287	207	29	force	force	NOUN
cana-4287	207	30	methods	method	NOUN
cana-4287	207	31	and	and	CCONJ
cana-4287	207	32	emerging	emerge	VERB
cana-4287	207	33	quantum	quantum	NOUN
cana-4287	207	34	threats	threat	NOUN
cana-4287	207	35	.	.	PUNCT
cana-4287	208	1	performance	performance	NOUN
cana-4287	208	2	evaluations	evaluation	NOUN
cana-4287	208	3	indicate	indicate	VERB
cana-4287	208	4	that	that	SCONJ
cana-4287	208	5	topology	topology	NOUN
cana-4287	208	6	-	-	PUNCT
cana-4287	208	7	based	base	VERB
cana-4287	208	8	approaches	approach	NOUN
cana-4287	208	9	,	,	PUNCT
cana-4287	208	10	such	such	ADJ
cana-4287	208	11	as	as	ADP
cana-4287	208	12	variations	variation	NOUN
cana-4287	208	13	of	of	ADP
cana-4287	208	14	topocrypt	topocrypt	NOUN
cana-4287	208	15	,	,	PUNCT
cana-4287	208	16	effectively	effectively	ADV
cana-4287	208	17	balance	balance	VERB
cana-4287	208	18	computational	computational	ADJ
cana-4287	208	19	overhead	overhead	NOUN
cana-4287	208	20	with	with	ADP
cana-4287	208	21	encryption	encryption	NOUN
cana-4287	208	22	and	and	CCONJ
cana-4287	208	23	decryption	decryption	NOUN
cana-4287	208	24	speed	speed	NOUN
cana-4287	208	25	.	.	PUNCT
cana-4287	209	1	additionally	additionally	ADV
cana-4287	209	2	,	,	PUNCT
cana-4287	209	3	reductions	reduction	NOUN
cana-4287	209	4	in	in	ADP
cana-4287	209	5	time	time	NOUN
cana-4287	209	6	complexity	complexity	NOUN
cana-4287	209	7	for	for	ADP
cana-4287	209	8	advanced	advanced	ADJ
cana-4287	209	9	cryptographic	cryptographic	ADJ
cana-4287	209	10	techniques	technique	NOUN
cana-4287	209	11	—	—	PUNCT
cana-4287	209	12	such	such	ADJ
cana-4287	209	13	as	as	ADP
cana-4287	209	14	lattice	lattice	NOUN
cana-4287	209	15	-	-	PUNCT
cana-4287	209	16	based	base	VERB
cana-4287	209	17	and	and	CCONJ
cana-4287	209	18	homomorphic	homomorphic	ADJ
cana-4287	209	19	encryption	encryption	NOUN
cana-4287	209	20	—	—	PUNCT
cana-4287	209	21	highlight	highlight	VERB
cana-4287	209	22	the	the	DET
cana-4287	209	23	practical	practical	ADJ
cana-4287	209	24	feasibility	feasibility	NOUN
cana-4287	209	25	of	of	ADP
cana-4287	209	26	topological	topological	ADJ
cana-4287	209	27	enhancements	enhancement	NOUN
cana-4287	209	28	.	.	PUNCT
cana-4287	210	1	notably	notably	ADV
cana-4287	210	2	,	,	PUNCT
cana-4287	210	3	security	security	NOUN
cana-4287	210	4	improvements	improvement	NOUN
cana-4287	210	5	across	across	ADP
cana-4287	210	6	cryptographic	cryptographic	ADJ
cana-4287	210	7	protocols	protocol	NOUN
cana-4287	210	8	,	,	PUNCT
cana-4287	210	9	particularly	particularly	ADV
cana-4287	210	10	in	in	ADP
cana-4287	210	11	post	post	ADJ
cana-4287	210	12	-	-	ADJ
cana-4287	210	13	quantum	quantum	ADJ
cana-4287	210	14	cryptography	cryptography	NOUN
cana-4287	210	15	,	,	PUNCT
cana-4287	210	16	communications	communication	NOUN
cana-4287	210	17	on	on	ADP
cana-4287	210	18	applied	apply	VERB
cana-4287	210	19	nonlinear	nonlinear	ADJ
cana-4287	210	20	analysis	analysis	NOUN
cana-4287	210	21	issn	issn	NOUN
cana-4287	210	22	:	:	PUNCT
cana-4287	210	23	1074	1074	NUM
cana-4287	210	24	-	-	PUNCT
cana-4287	210	25	133x	133x	NUM
cana-4287	210	26	vol	vol	NOUN
cana-4287	210	27	32	32	NUM
cana-4287	210	28	no	no	NOUN
cana-4287	210	29	.	.	PUNCT
cana-4287	211	1	9s	9s	NUM
cana-4287	211	2	(	(	PUNCT
cana-4287	211	3	2025	2025	NUM
cana-4287	211	4	)	)	PUNCT
cana-4287	211	5	1739	1739	NUM
cana-4287	212	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4287	212	2	underscore	underscore	VERB
cana-4287	212	3	the	the	DET
cana-4287	212	4	transdisciplinary	transdisciplinary	ADJ
cana-4287	212	5	potential	potential	NOUN
cana-4287	212	6	of	of	ADP
cana-4287	212	7	algebraic	algebraic	ADJ
cana-4287	212	8	topology	topology	NOUN
cana-4287	212	9	in	in	ADP
cana-4287	212	10	addressing	address	VERB
cana-4287	212	11	contemporary	contemporary	ADJ
cana-4287	212	12	cryptographic	cryptographic	ADJ
cana-4287	212	13	challenges	challenge	NOUN
cana-4287	212	14	.	.	PUNCT
cana-4287	213	1	in	in	ADP
cana-4287	213	2	an	an	DET
cana-4287	213	3	increasingly	increasingly	ADV
cana-4287	213	4	digital	digital	ADJ
cana-4287	213	5	landscape	landscape	NOUN
cana-4287	213	6	,	,	PUNCT
cana-4287	213	7	integrating	integrate	VERB
cana-4287	213	8	encryption	encryption	NOUN
cana-4287	213	9	techniques	technique	NOUN
cana-4287	213	10	with	with	ADP
cana-4287	213	11	mathematical	mathematical	ADJ
cana-4287	213	12	frameworks	framework	NOUN
cana-4287	213	13	fosters	foster	VERB
cana-4287	213	14	a	a	DET
cana-4287	213	15	more	more	ADV
cana-4287	213	16	secure	secure	ADJ
cana-4287	213	17	and	and	CCONJ
cana-4287	213	18	adaptable	adaptable	ADJ
cana-4287	213	19	cryptographic	cryptographic	ADJ
cana-4287	213	20	environment	environment	NOUN
cana-4287	213	21	,	,	PUNCT
cana-4287	213	22	paving	pave	VERB
cana-4287	213	23	the	the	DET
cana-4287	213	24	way	way	NOUN
cana-4287	213	25	for	for	ADP
cana-4287	213	26	innovative	innovative	ADJ
cana-4287	213	27	security	security	NOUN
cana-4287	213	28	solutions	solution	NOUN
cana-4287	213	29	.	.	PUNCT
cana-4287	214	1	continued	continue	VERB
cana-4287	214	2	research	research	NOUN
cana-4287	214	3	in	in	ADP
cana-4287	214	4	this	this	DET
cana-4287	214	5	area	area	NOUN
cana-4287	214	6	is	be	AUX
cana-4287	214	7	expected	expect	VERB
cana-4287	214	8	to	to	PART
cana-4287	214	9	drive	drive	VERB
cana-4287	214	10	significant	significant	ADJ
cana-4287	214	11	advancements	advancement	NOUN
cana-4287	214	12	in	in	ADP
cana-4287	214	13	secure	secure	ADJ
cana-4287	214	14	communication	communication	NOUN
cana-4287	214	15	and	and	CCONJ
cana-4287	214	16	data	datum	NOUN
cana-4287	214	17	integrity	integrity	NOUN
cana-4287	214	18	.	.	PUNCT
cana-4287	215	1	his	his	PRON
cana-4287	215	2	study	study	NOUN
cana-4287	215	3	demonstrates	demonstrate	VERB
cana-4287	215	4	the	the	DET
cana-4287	215	5	transformative	transformative	ADJ
cana-4287	215	6	potential	potential	NOUN
cana-4287	215	7	of	of	ADP
cana-4287	215	8	algebraic	algebraic	ADJ
cana-4287	215	9	topology	topology	NOUN
cana-4287	215	10	in	in	ADP
cana-4287	215	11	modern	modern	ADJ
cana-4287	215	12	cryptography	cryptography	NOUN
cana-4287	215	13	,	,	PUNCT
cana-4287	215	14	offering	offer	VERB
cana-4287	215	15	a	a	DET
cana-4287	215	16	novel	novel	ADJ
cana-4287	215	17	approach	approach	NOUN
cana-4287	215	18	to	to	ADP
cana-4287	215	19	strengthening	strengthen	VERB
cana-4287	215	20	security	security	NOUN
cana-4287	215	21	,	,	PUNCT
cana-4287	215	22	efficiency	efficiency	NOUN
cana-4287	215	23	,	,	PUNCT
cana-4287	215	24	and	and	CCONJ
cana-4287	215	25	resilience	resilience	NOUN
cana-4287	215	26	against	against	ADP
cana-4287	215	27	emerging	emerge	VERB
cana-4287	215	28	threats	threat	NOUN
cana-4287	215	29	.	.	PUNCT
cana-4287	216	1	by	by	ADP
cana-4287	216	2	leveraging	leverage	VERB
cana-4287	216	3	topological	topological	ADJ
cana-4287	216	4	invariants	invariant	NOUN
cana-4287	216	5	,	,	PUNCT
cana-4287	216	6	homology	homology	NOUN
cana-4287	216	7	theory	theory	NOUN
cana-4287	216	8	,	,	PUNCT
cana-4287	216	9	and	and	CCONJ
cana-4287	216	10	simplicial	simplicial	ADJ
cana-4287	216	11	complexes	complex	NOUN
cana-4287	216	12	,	,	PUNCT
cana-4287	216	13	cryptographic	cryptographic	ADJ
cana-4287	216	14	protocols	protocol	NOUN
cana-4287	216	15	can	can	AUX
cana-4287	216	16	be	be	AUX
cana-4287	216	17	restructured	restructure	VERB
cana-4287	216	18	to	to	PART
cana-4287	216	19	enhance	enhance	VERB
cana-4287	216	20	encryption	encryption	NOUN
cana-4287	216	21	,	,	PUNCT
cana-4287	216	22	key	key	ADJ
cana-4287	216	23	management	management	NOUN
cana-4287	216	24	,	,	PUNCT
cana-4287	216	25	and	and	CCONJ
cana-4287	216	26	error	error	NOUN
cana-4287	216	27	correction	correction	NOUN
cana-4287	216	28	.	.	PUNCT
cana-4287	217	1	the	the	DET
cana-4287	217	2	integration	integration	NOUN
cana-4287	217	3	of	of	ADP
cana-4287	217	4	algebraic	algebraic	ADJ
cana-4287	217	5	topology	topology	NOUN
cana-4287	217	6	not	not	PART
cana-4287	217	7	only	only	ADV
cana-4287	217	8	reinforces	reinforce	VERB
cana-4287	217	9	traditional	traditional	ADJ
cana-4287	217	10	cryptographic	cryptographic	ADJ
cana-4287	217	11	systems	system	NOUN
cana-4287	217	12	like	like	ADP
cana-4287	217	13	rsa	rsa	PROPN
cana-4287	217	14	and	and	CCONJ
cana-4287	217	15	ecc	ecc	PROPN
cana-4287	217	16	but	but	CCONJ
cana-4287	217	17	also	also	ADV
cana-4287	217	18	contributes	contribute	VERB
cana-4287	217	19	to	to	ADP
cana-4287	217	20	the	the	DET
cana-4287	217	21	advancement	advancement	NOUN
cana-4287	217	22	of	of	ADP
cana-4287	217	23	post	post	ADJ
cana-4287	217	24	-	-	ADJ
cana-4287	217	25	quantum	quantum	ADJ
cana-4287	217	26	encryption	encryption	NOUN
cana-4287	217	27	and	and	CCONJ
cana-4287	217	28	blockchain	blockchain	PROPN
cana-4287	217	29	security	security	PROPN
cana-4287	217	30	.	.	PUNCT
cana-4287	218	1	beyond	beyond	ADP
cana-4287	218	2	its	its	PRON
cana-4287	218	3	direct	direct	ADJ
cana-4287	218	4	applications	application	NOUN
cana-4287	218	5	,	,	PUNCT
cana-4287	218	6	this	this	DET
cana-4287	218	7	interdisciplinary	interdisciplinary	ADJ
cana-4287	218	8	approach	approach	NOUN
cana-4287	218	9	highlights	highlight	VERB
cana-4287	218	10	the	the	DET
cana-4287	218	11	broader	broad	ADJ
cana-4287	218	12	impact	impact	NOUN
cana-4287	218	13	of	of	ADP
cana-4287	218	14	mathematical	mathematical	ADJ
cana-4287	218	15	frameworks	framework	NOUN
cana-4287	218	16	in	in	ADP
cana-4287	218	17	cybersecurity	cybersecurity	NOUN
cana-4287	218	18	.	.	PUNCT
cana-4287	219	1	the	the	DET
cana-4287	219	2	structural	structural	ADJ
cana-4287	219	3	insights	insight	NOUN
cana-4287	219	4	provided	provide	VERB
cana-4287	219	5	by	by	ADP
cana-4287	219	6	algebraic	algebraic	ADJ
cana-4287	219	7	topology	topology	NOUN
cana-4287	219	8	enable	enable	VERB
cana-4287	219	9	a	a	DET
cana-4287	219	10	deeper	deep	ADJ
cana-4287	219	11	understanding	understanding	NOUN
cana-4287	219	12	of	of	ADP
cana-4287	219	13	cryptographic	cryptographic	ADJ
cana-4287	219	14	foundations	foundation	NOUN
cana-4287	219	15	,	,	PUNCT
cana-4287	219	16	opening	open	VERB
cana-4287	219	17	new	new	ADJ
cana-4287	219	18	avenues	avenue	NOUN
cana-4287	219	19	for	for	ADP
cana-4287	219	20	innovation	innovation	NOUN
cana-4287	219	21	.	.	PUNCT
cana-4287	220	1	as	as	SCONJ
cana-4287	220	2	digital	digital	ADJ
cana-4287	220	3	security	security	NOUN
cana-4287	220	4	challenges	challenge	NOUN
cana-4287	220	5	continue	continue	VERB
cana-4287	220	6	to	to	PART
cana-4287	220	7	evolve	evolve	VERB
cana-4287	220	8	,	,	PUNCT
cana-4287	220	9	further	further	ADJ
cana-4287	220	10	exploration	exploration	NOUN
cana-4287	220	11	of	of	ADP
cana-4287	220	12	topology	topology	NOUN
cana-4287	220	13	-	-	PUNCT
cana-4287	220	14	based	base	VERB
cana-4287	220	15	techniques	technique	NOUN
cana-4287	220	16	is	be	AUX
cana-4287	220	17	expected	expect	VERB
cana-4287	220	18	to	to	PART
cana-4287	220	19	drive	drive	VERB
cana-4287	220	20	significant	significant	ADJ
cana-4287	220	21	advancements	advancement	NOUN
cana-4287	220	22	in	in	ADP
cana-4287	220	23	secure	secure	ADJ
cana-4287	220	24	communication	communication	NOUN
cana-4287	220	25	and	and	CCONJ
cana-4287	220	26	data	datum	NOUN
cana-4287	220	27	integrity	integrity	NOUN
cana-4287	220	28	.	.	PUNCT
cana-4287	221	1	by	by	ADP
cana-4287	221	2	bridging	bridge	VERB
cana-4287	221	3	abstract	abstract	ADJ
cana-4287	221	4	mathematical	mathematical	ADJ
cana-4287	221	5	structures	structure	NOUN
cana-4287	221	6	with	with	ADP
cana-4287	221	7	practical	practical	ADJ
cana-4287	221	8	cryptographic	cryptographic	ADJ
cana-4287	221	9	solutions	solution	NOUN
cana-4287	221	10	,	,	PUNCT
cana-4287	221	11	this	this	DET
cana-4287	221	12	research	research	NOUN
cana-4287	221	13	underscores	underscore	VERB
cana-4287	221	14	the	the	DET
cana-4287	221	15	importance	importance	NOUN
cana-4287	221	16	of	of	ADP
cana-4287	221	17	interdisciplinary	interdisciplinary	ADJ
cana-4287	221	18	collaboration	collaboration	NOUN
cana-4287	221	19	in	in	ADP
cana-4287	221	20	addressing	address	VERB
cana-4287	221	21	modern	modern	ADJ
cana-4287	221	22	security	security	NOUN
cana-4287	221	23	concerns	concern	NOUN
cana-4287	221	24	.	.	PUNCT
cana-4287	222	1	the	the	DET
cana-4287	222	2	findings	finding	NOUN
cana-4287	222	3	presented	present	VERB
cana-4287	222	4	here	here	ADV
cana-4287	222	5	pave	pave	VERB
cana-4287	222	6	the	the	DET
cana-4287	222	7	way	way	NOUN
cana-4287	222	8	for	for	ADP
cana-4287	222	9	the	the	DET
cana-4287	222	10	continued	continue	VERB
cana-4287	222	11	integration	integration	NOUN
cana-4287	222	12	of	of	ADP
cana-4287	222	13	algebraic	algebraic	ADJ
cana-4287	222	14	topology	topology	NOUN
cana-4287	222	15	into	into	ADP
cana-4287	222	16	cryptographic	cryptographic	ADJ
cana-4287	222	17	research	research	NOUN
cana-4287	222	18	,	,	PUNCT
cana-4287	222	19	fostering	foster	VERB
cana-4287	222	20	the	the	DET
cana-4287	222	21	development	development	NOUN
cana-4287	222	22	of	of	ADP
cana-4287	222	23	next	next	ADJ
cana-4287	222	24	-	-	PUNCT
cana-4287	222	25	generation	generation	NOUN
cana-4287	222	26	security	security	NOUN
cana-4287	222	27	systems	system	NOUN
cana-4287	222	28	in	in	ADP
cana-4287	222	29	an	an	DET
cana-4287	222	30	increasingly	increasingly	ADV
cana-4287	222	31	complex	complex	ADJ
cana-4287	222	32	digital	digital	ADJ
cana-4287	222	33	landscape	landscape	NOUN
cana-4287	222	34	.	.	PUNCT
cana-4287	223	1	references	reference	NOUN
cana-4287	223	2	[	[	X
cana-4287	223	3	1	1	NUM
cana-4287	223	4	]	]	PUNCT
cana-4287	223	5	.	.	PUNCT
cana-4287	224	1	carvalho	carvalho	PROPN
cana-4287	224	2	,	,	PUNCT
cana-4287	224	3	c.	c.	PROPN
cana-4287	224	4	,	,	PUNCT
cana-4287	224	5	and	and	CCONJ
cana-4287	224	6	malheiro	malheiro	NOUN
cana-4287	224	7	,	,	PUNCT
cana-4287	224	8	a.	a.	NOUN
cana-4287	224	9	,	,	PUNCT
cana-4287	224	10	“	"	PUNCT
cana-4287	224	11	subsets	subset	NOUN
cana-4287	224	12	of	of	ADP
cana-4287	224	13	groups	group	NOUN
cana-4287	224	14	in	in	ADP
cana-4287	224	15	public	public	ADJ
cana-4287	224	16	-	-	PUNCT
cana-4287	224	17	key	key	NOUN
cana-4287	224	18	cryptography	cryptography	NOUN
cana-4287	224	19	,	,	PUNCT
cana-4287	224	20	”	"	PUNCT
cana-4287	224	21	journal	journal	NOUN
cana-4287	224	22	of	of	ADP
cana-4287	224	23	algebra	algebra	NOUN
cana-4287	224	24	and	and	CCONJ
cana-4287	224	25	cryptography	cryptography	NOUN
cana-4287	224	26	,	,	PUNCT
cana-4287	224	27	vol	vol	NOUN
cana-4287	224	28	.	.	PROPN
cana-4287	224	29	35	35	NUM
cana-4287	224	30	,	,	PUNCT
cana-4287	224	31	no	no	INTJ
cana-4287	224	32	.	.	NOUN
cana-4287	224	33	2	2	NUM
cana-4287	224	34	,	,	PUNCT
cana-4287	224	35	pp	pp	ADJ
cana-4287	224	36	.	.	PUNCT
cana-4287	225	1	112–128	112–128	NUM
cana-4287	225	2	,	,	PUNCT
cana-4287	225	3	2023	2023	NUM
cana-4287	225	4	.	.	PUNCT
cana-4287	226	1	[	[	X
cana-4287	226	2	2	2	NUM
cana-4287	226	3	]	]	PUNCT
cana-4287	226	4	.	.	PUNCT
cana-4287	227	1	gonzález	gonzález	PROPN
cana-4287	227	2	vasco	vasco	PROPN
cana-4287	227	3	,	,	PUNCT
cana-4287	227	4	m.	m.	NOUN
cana-4287	227	5	,	,	PUNCT
cana-4287	227	6	et	et	PROPN
cana-4287	227	7	al	al	PROPN
cana-4287	227	8	.	.	PROPN
cana-4287	227	9	,	,	PUNCT
cana-4287	227	10	“	"	PUNCT
cana-4287	227	11	applications	application	NOUN
cana-4287	227	12	of	of	ADP
cana-4287	227	13	finite	finite	ADJ
cana-4287	227	14	non	non	ADJ
cana-4287	227	15	-	-	ADJ
cana-4287	227	16	abelian	abelian	ADJ
cana-4287	227	17	simple	simple	ADJ
cana-4287	227	18	groups	group	NOUN
cana-4287	227	19	to	to	ADP
cana-4287	227	20	cryptography	cryptography	NOUN
cana-4287	227	21	in	in	ADP
cana-4287	227	22	the	the	DET
cana-4287	227	23	quantum	quantum	ADJ
cana-4287	227	24	era	era	NOUN
cana-4287	227	25	,	,	PUNCT
cana-4287	227	26	”	"	PUNCT
cana-4287	227	27	advances	advance	NOUN
cana-4287	227	28	in	in	ADP
cana-4287	227	29	cryptology	cryptology	NOUN
cana-4287	227	30	–	–	PUNCT
cana-4287	227	31	proceedings	proceeding	NOUN
cana-4287	227	32	of	of	ADP
cana-4287	227	33	crypto	crypto	NOUN
cana-4287	227	34	2023	2023	NUM
cana-4287	227	35	,	,	PUNCT
cana-4287	227	36	pp	pp	ADJ
cana-4287	227	37	.	.	PUNCT
cana-4287	228	1	215–230	215–230	NUM
cana-4287	228	2	,	,	PUNCT
cana-4287	228	3	2023	2023	NUM
cana-4287	228	4	.	.	PUNCT
cana-4287	229	1	[	[	X
cana-4287	229	2	3	3	NUM
cana-4287	229	3	]	]	PUNCT
cana-4287	229	4	.	.	PUNCT
cana-4287	230	1	ateniese	ateniese	PROPN
cana-4287	230	2	,	,	PUNCT
cana-4287	230	3	g.	g.	PROPN
cana-4287	230	4	,	,	PUNCT
cana-4287	230	5	et	et	PROPN
cana-4287	230	6	al	al	PROPN
cana-4287	230	7	.	.	PROPN
cana-4287	230	8	,	,	PUNCT
cana-4287	230	9	“	"	PUNCT
cana-4287	230	10	advancing	advance	VERB
cana-4287	230	11	scalability	scalability	NOUN
cana-4287	230	12	in	in	ADP
cana-4287	230	13	decentralized	decentralized	ADJ
cana-4287	230	14	storage	storage	NOUN
cana-4287	230	15	:	:	PUNCT
cana-4287	230	16	a	a	DET
cana-4287	230	17	novel	novel	ADJ
cana-4287	230	18	approach	approach	NOUN
cana-4287	230	19	to	to	ADP
cana-4287	230	20	proof	proof	NOUN
cana-4287	230	21	-	-	PUNCT
cana-4287	230	22	ofreplication	ofreplication	NOUN
cana-4287	230	23	via	via	ADP
cana-4287	230	24	polynomial	polynomial	ADJ
cana-4287	230	25	evaluation	evaluation	NOUN
cana-4287	230	26	,	,	PUNCT
cana-4287	230	27	”	"	PUNCT
cana-4287	230	28	decentralized	decentralize	VERB
cana-4287	230	29	systems	system	NOUN
cana-4287	230	30	journal	journal	NOUN
cana-4287	230	31	,	,	PUNCT
cana-4287	230	32	vol	vol	NOUN
cana-4287	230	33	.	.	PROPN
cana-4287	230	34	12	12	NUM
cana-4287	230	35	,	,	PUNCT
cana-4287	230	36	no	no	INTJ
cana-4287	230	37	.	.	NOUN
cana-4287	230	38	4	4	NUM
cana-4287	230	39	,	,	PUNCT
cana-4287	230	40	pp	pp	ADJ
cana-4287	230	41	.	.	PUNCT
cana-4287	231	1	53–68	53–68	NUM
cana-4287	231	2	,	,	PUNCT
cana-4287	231	3	2024	2024	NUM
cana-4287	231	4	.	.	PUNCT
cana-4287	232	1	[	[	X
cana-4287	232	2	4	4	NUM
cana-4287	232	3	]	]	PUNCT
cana-4287	232	4	.	.	PUNCT
cana-4287	233	1	briaud	briaud	PROPN
cana-4287	233	2	,	,	PUNCT
cana-4287	233	3	p.	p.	NOUN
cana-4287	233	4	,	,	PUNCT
cana-4287	233	5	and	and	CCONJ
cana-4287	233	6	øygarden	øygarden	ADJ
cana-4287	233	7	,	,	PUNCT
cana-4287	233	8	h.	h.	PROPN
cana-4287	233	9	,	,	PUNCT
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cana-4287	233	11	a	a	DET
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cana-4287	233	13	algebraic	algebraic	ADJ
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cana-4287	233	15	to	to	ADP
cana-4287	233	16	the	the	DET
cana-4287	233	17	regular	regular	ADJ
cana-4287	233	18	syndrome	syndrome	NOUN
cana-4287	233	19	decoding	decode	VERB
cana-4287	233	20	problem	problem	NOUN
cana-4287	233	21	and	and	CCONJ
cana-4287	233	22	implications	implication	NOUN
cana-4287	233	23	for	for	ADP
cana-4287	233	24	pcg	pcg	PROPN
cana-4287	233	25	constructions	construction	NOUN
cana-4287	233	26	,	,	PUNCT
cana-4287	233	27	”	"	PUNCT
cana-4287	233	28	ieee	ieee	NOUN
cana-4287	233	29	transactions	transaction	NOUN
cana-4287	233	30	on	on	ADP
cana-4287	233	31	information	information	NOUN
cana-4287	233	32	theory	theory	NOUN
cana-4287	233	33	,	,	PUNCT
cana-4287	233	34	vol	vol	NOUN
cana-4287	233	35	.	.	PROPN
cana-4287	233	36	70	70	NUM
cana-4287	233	37	,	,	PUNCT
cana-4287	233	38	no	no	INTJ
cana-4287	233	39	.	.	NOUN
cana-4287	233	40	1	1	NUM
cana-4287	233	41	,	,	PUNCT
cana-4287	233	42	pp	pp	ADJ
cana-4287	233	43	.	.	PUNCT
cana-4287	234	1	45–58	45–58	NUM
cana-4287	234	2	,	,	PUNCT
cana-4287	234	3	2023	2023	NUM
cana-4287	234	4	.	.	PUNCT
cana-4287	235	1	[	[	X
cana-4287	235	2	5	5	NUM
cana-4287	235	3	]	]	PUNCT
cana-4287	235	4	.	.	PUNCT
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cana-4287	236	2	,	,	PUNCT
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cana-4287	236	4	,	,	PUNCT
cana-4287	236	5	et	et	PROPN
cana-4287	236	6	al	al	PROPN
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cana-4287	236	8	,	,	PUNCT
cana-4287	236	9	“	"	PUNCT
cana-4287	236	10	algebraic	algebraic	ADJ
cana-4287	236	11	topology	topology	NOUN
cana-4287	236	12	and	and	CCONJ
cana-4287	236	13	distributed	distributed	ADJ
cana-4287	236	14	computing	computing	NOUN
cana-4287	236	15	,	,	PUNCT
cana-4287	236	16	”	"	PUNCT
cana-4287	236	17	ieee	ieee	NOUN
cana-4287	236	18	transactions	transaction	NOUN
cana-4287	236	19	on	on	ADP
cana-4287	236	20	secure	secure	ADJ
cana-4287	236	21	systems	system	NOUN
cana-4287	236	22	,	,	PUNCT
cana-4287	236	23	vol	vol	NOUN
cana-4287	236	24	.	.	PROPN
cana-4287	236	25	15	15	NUM
cana-4287	236	26	,	,	PUNCT
cana-4287	236	27	no	no	INTJ
cana-4287	236	28	.	.	NOUN
cana-4287	236	29	3	3	NUM
cana-4287	236	30	,	,	PUNCT
cana-4287	236	31	pp	pp	ADJ
cana-4287	236	32	.	.	PUNCT
cana-4287	237	1	150–164	150–164	NUM
cana-4287	237	2	,	,	PUNCT
cana-4287	237	3	2024	2024	NUM
cana-4287	237	4	.	.	PUNCT
cana-4287	238	1	[	[	X
cana-4287	238	2	6	6	NUM
cana-4287	238	3	]	]	PUNCT
cana-4287	238	4	.	.	PUNCT
cana-4287	239	1	yamamoto	yamamoto	PROPN
cana-4287	239	2	,	,	PUNCT
cana-4287	239	3	s.	s.	PROPN
cana-4287	239	4	,	,	PUNCT
cana-4287	239	5	et	et	PROPN
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cana-4287	239	9	“	"	PUNCT
cana-4287	239	10	topology	topology	NOUN
cana-4287	239	11	-	-	PUNCT
cana-4287	239	12	based	base	VERB
cana-4287	239	13	key	key	ADJ
cana-4287	239	14	exchange	exchange	NOUN
cana-4287	239	15	mechanisms	mechanism	NOUN
cana-4287	239	16	in	in	ADP
cana-4287	239	17	quantum	quantum	ADJ
cana-4287	239	18	cryptography	cryptography	NOUN
cana-4287	239	19	,	,	PUNCT
cana-4287	239	20	”	"	PUNCT
cana-4287	239	21	quantum	quantum	ADJ
cana-4287	239	22	information	information	NOUN
cana-4287	239	23	and	and	CCONJ
cana-4287	239	24	cryptographic	cryptographic	ADJ
cana-4287	239	25	systems	system	NOUN
cana-4287	239	26	,	,	PUNCT
cana-4287	239	27	vol	vol	NOUN
cana-4287	239	28	.	.	PROPN
cana-4287	239	29	8	8	NUM
cana-4287	239	30	,	,	PUNCT
cana-4287	239	31	no	no	INTJ
cana-4287	239	32	.	.	NOUN
cana-4287	239	33	2	2	NUM
cana-4287	239	34	,	,	PUNCT
cana-4287	239	35	pp	pp	ADJ
cana-4287	239	36	.	.	PUNCT
cana-4287	240	1	92–105	92–105	NUM
cana-4287	240	2	,	,	PUNCT
cana-4287	240	3	2024	2024	NUM
cana-4287	240	4	.	.	PUNCT
cana-4287	241	1	[	[	X
cana-4287	241	2	7	7	NUM
cana-4287	241	3	]	]	PUNCT
cana-4287	241	4	.	.	PUNCT
cana-4287	242	1	müller	müller	PROPN
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cana-4287	242	8	,	,	PUNCT
cana-4287	242	9	“	"	PUNCT
cana-4287	242	10	homotopy	homotopy	NOUN
cana-4287	242	11	-	-	PUNCT
cana-4287	242	12	theoretic	theoretic	NOUN
cana-4287	242	13	models	model	NOUN
cana-4287	242	14	for	for	ADP
cana-4287	242	15	cryptographic	cryptographic	ADJ
cana-4287	242	16	hash	hash	NOUN
cana-4287	242	17	functions	function	NOUN
cana-4287	242	18	,	,	PUNCT
cana-4287	242	19	”	"	PUNCT
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cana-4287	242	23	,	,	PUNCT
cana-4287	242	24	vol	vol	NOUN
cana-4287	242	25	.	.	PROPN
cana-4287	242	26	29	29	NUM
cana-4287	242	27	,	,	PUNCT
cana-4287	242	28	no	no	INTJ
cana-4287	242	29	.	.	NOUN
cana-4287	242	30	1	1	NUM
cana-4287	242	31	,	,	PUNCT
cana-4287	242	32	pp	pp	ADJ
cana-4287	242	33	.	.	PUNCT
cana-4287	243	1	77–89	77–89	NUM
cana-4287	243	2	,	,	PUNCT
cana-4287	243	3	2023	2023	NUM
cana-4287	243	4	.	.	PUNCT
cana-4287	244	1	[	[	X
cana-4287	244	2	8	8	NUM
cana-4287	244	3	]	]	PUNCT
cana-4287	244	4	.	.	PUNCT
cana-4287	244	5	ranoa	ranoa	NOUN
cana-4287	244	6	,	,	PUNCT
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cana-4287	244	8	(	(	PUNCT
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cana-4287	244	10	)	)	PUNCT
cana-4287	244	11	.	.	PUNCT
cana-4287	245	1	an	an	DET
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cana-4287	245	3	on	on	ADP
cana-4287	245	4	the	the	DET
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cana-4287	245	6	and	and	CCONJ
cana-4287	245	7	computation	computation	NOUN
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cana-4287	246	5	,	,	PUNCT
cana-4287	246	6	18(2	18(2	NUM
cana-4287	246	7	)	)	PUNCT
cana-4287	246	8	,	,	PUNCT
cana-4287	246	9	234	234	NUM
cana-4287	246	10	-	-	SYM
cana-4287	246	11	250	250	NUM
cana-4287	246	12	.	.	PUNCT
cana-4287	247	1	communications	communication	NOUN
cana-4287	247	2	on	on	ADP
cana-4287	247	3	applied	apply	VERB
cana-4287	247	4	nonlinear	nonlinear	ADJ
cana-4287	247	5	analysis	analysis	NOUN
cana-4287	247	6	issn	issn	NOUN
cana-4287	247	7	:	:	PUNCT
cana-4287	247	8	1074	1074	NUM
cana-4287	247	9	-	-	PUNCT
cana-4287	247	10	133x	133x	NUM
cana-4287	247	11	vol	vol	NOUN
cana-4287	247	12	32	32	NUM
cana-4287	247	13	no	no	NOUN
cana-4287	247	14	.	.	PUNCT
cana-4287	248	1	9s	9s	NUM
cana-4287	248	2	(	(	PUNCT
cana-4287	248	3	2025	2025	NUM
cana-4287	248	4	)	)	PUNCT
cana-4287	248	5	1740	1740	NUM
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cana-4287	249	2	9	9	NUM
cana-4287	249	3	]	]	PUNCT
cana-4287	249	4	.	.	PUNCT
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cana-4287	250	8	,	,	PUNCT
cana-4287	250	9	“	"	PUNCT
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cana-4287	250	11	homology	homology	NOUN
cana-4287	250	12	in	in	ADP
cana-4287	250	13	cryptographic	cryptographic	ADJ
cana-4287	250	14	protocol	protocol	NOUN
cana-4287	250	15	verification	verification	NOUN
cana-4287	250	16	,	,	PUNCT
cana-4287	250	17	”	"	PUNCT
cana-4287	250	18	acm	acm	NOUN
cana-4287	250	19	transactions	transaction	NOUN
cana-4287	250	20	on	on	ADP
cana-4287	250	21	cryptography	cryptography	NOUN
cana-4287	250	22	and	and	CCONJ
cana-4287	250	23	security	security	NOUN
cana-4287	250	24	,	,	PUNCT
cana-4287	250	25	vol	vol	NOUN
cana-4287	250	26	.	.	PROPN
cana-4287	250	27	15	15	NUM
cana-4287	250	28	,	,	PUNCT
cana-4287	250	29	no	no	INTJ
cana-4287	250	30	.	.	NOUN
cana-4287	250	31	3	3	NUM
cana-4287	250	32	,	,	PUNCT
cana-4287	250	33	pp	pp	ADJ
cana-4287	250	34	.	.	PUNCT
cana-4287	251	1	130–144	130–144	NUM
cana-4287	251	2	,	,	PUNCT
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cana-4287	251	4	.	.	PUNCT
cana-4287	252	1	[	[	X
cana-4287	252	2	10	10	NUM
cana-4287	252	3	]	]	PUNCT
cana-4287	252	4	.	.	PUNCT
cana-4287	253	1	zhang	zhang	PROPN
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cana-4287	253	3	y.	y.	PROPN
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cana-4287	253	13	lattice	lattice	NOUN
cana-4287	253	14	-	-	PUNCT
cana-4287	253	15	based	base	VERB
cana-4287	253	16	cryptography	cryptography	NOUN
cana-4287	253	17	,	,	PUNCT
cana-4287	253	18	”	"	PUNCT
cana-4287	253	19	journal	journal	NOUN
cana-4287	253	20	of	of	ADP
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cana-4287	253	23	,	,	PUNCT
cana-4287	253	24	vol	vol	NOUN
cana-4287	253	25	.	.	PROPN
cana-4287	253	26	10	10	NUM
cana-4287	253	27	,	,	PUNCT
cana-4287	253	28	no	no	INTJ
cana-4287	253	29	.	.	NOUN
cana-4287	253	30	4	4	NUM
cana-4287	253	31	,	,	PUNCT
cana-4287	253	32	pp	pp	ADV
cana-4287	253	33	.	.	PUNCT
cana-4287	254	1	45–61	45–61	NUM
cana-4287	254	2	,	,	PUNCT
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cana-4287	254	4	.	.	PUNCT
cana-4287	255	1	[	[	X
cana-4287	255	2	11	11	NUM
cana-4287	255	3	]	]	PUNCT
cana-4287	255	4	.	.	PUNCT
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cana-4287	256	12	in	in	ADP
cana-4287	256	13	zero	zero	NUM
cana-4287	256	14	-	-	PUNCT
cana-4287	256	15	knowledge	knowledge	NOUN
cana-4287	256	16	proofs	proof	NOUN
cana-4287	256	17	,	,	PUNCT
cana-4287	256	18	”	"	PUNCT
cana-4287	256	19	ieee	ieee	NOUN
cana-4287	256	20	journal	journal	NOUN
cana-4287	256	21	on	on	ADP
cana-4287	256	22	secure	secure	ADJ
cana-4287	256	23	protocols	protocol	NOUN
cana-4287	256	24	,	,	PUNCT
cana-4287	256	25	vol	vol	NOUN
cana-4287	256	26	.	.	PROPN
cana-4287	256	27	22	22	NUM
cana-4287	256	28	,	,	PUNCT
cana-4287	256	29	no	no	INTJ
cana-4287	256	30	.	.	NOUN
cana-4287	256	31	5	5	NUM
cana-4287	256	32	,	,	PUNCT
cana-4287	256	33	pp	pp	ADJ
cana-4287	256	34	.	.	PUNCT
cana-4287	256	35	68–82	68–82	NUM
cana-4287	256	36	,	,	PUNCT
cana-4287	256	37	2023	2023	NUM
cana-4287	256	38	.	.	PUNCT
cana-4287	257	1	[	[	X
cana-4287	257	2	12	12	NUM
cana-4287	257	3	]	]	PUNCT
cana-4287	257	4	.	.	PUNCT
cana-4287	258	1	chen	chen	PROPN
cana-4287	258	2	,	,	PUNCT
cana-4287	258	3	l.	l.	PROPN
cana-4287	258	4	,	,	PUNCT
cana-4287	258	5	et	et	PROPN
cana-4287	258	6	al	al	PROPN
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cana-4287	258	8	,	,	PUNCT
cana-4287	258	9	“	"	PUNCT
cana-4287	258	10	simplicial	simplicial	ADJ
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cana-4287	258	12	in	in	ADP
cana-4287	258	13	cryptographic	cryptographic	ADJ
cana-4287	258	14	network	network	NOUN
cana-4287	258	15	design	design	NOUN
cana-4287	258	16	,	,	PUNCT
cana-4287	258	17	”	"	PUNCT
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cana-4287	258	19	in	in	ADP
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cana-4287	258	21	systems	system	NOUN
cana-4287	258	22	,	,	PUNCT
cana-4287	258	23	vol	vol	NOUN
cana-4287	258	24	.	.	PROPN
cana-4287	258	25	18	18	NUM
cana-4287	258	26	,	,	PUNCT
cana-4287	258	27	no	no	INTJ
cana-4287	258	28	.	.	NOUN
cana-4287	258	29	2	2	NUM
cana-4287	258	30	,	,	PUNCT
cana-4287	258	31	pp	pp	ADJ
cana-4287	258	32	.	.	PUNCT
cana-4287	259	1	39–54	39–54	NUM
cana-4287	259	2	,	,	PUNCT
cana-4287	259	3	2024	2024	NUM
cana-4287	259	4	.	.	PUNCT
cana-4287	260	1	[	[	X
cana-4287	260	2	13	13	NUM
cana-4287	260	3	]	]	PUNCT
cana-4287	260	4	.	.	PUNCT
cana-4287	261	1	patel	patel	PROPN
cana-4287	261	2	,	,	PUNCT
cana-4287	261	3	r.	r.	PROPN
cana-4287	261	4	,	,	PUNCT
cana-4287	261	5	et	et	PROPN
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cana-4287	261	8	,	,	PUNCT
cana-4287	261	9	“	"	PUNCT
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cana-4287	261	12	analysis	analysis	NOUN
cana-4287	261	13	in	in	ADP
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cana-4287	261	15	-	-	PUNCT
cana-4287	261	16	channel	channel	NOUN
cana-4287	261	17	attack	attack	NOUN
cana-4287	261	18	prevention	prevention	NOUN
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cana-4287	261	20	”	"	PUNCT
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cana-4287	261	23	on	on	ADP
cana-4287	261	24	cryptographic	cryptographic	ADJ
cana-4287	261	25	hardware	hardware	NOUN
cana-4287	261	26	and	and	CCONJ
cana-4287	261	27	embedded	embed	VERB
cana-4287	261	28	systems	system	NOUN
cana-4287	261	29	,	,	PUNCT
cana-4287	261	30	vol	vol	NOUN
cana-4287	261	31	.	.	PROPN
cana-4287	261	32	11	11	NUM
cana-4287	261	33	,	,	PUNCT
cana-4287	261	34	no	no	INTJ
cana-4287	261	35	.	.	NOUN
cana-4287	261	36	1	1	NUM
cana-4287	261	37	,	,	PUNCT
cana-4287	261	38	pp	pp	ADJ
cana-4287	261	39	.	.	PUNCT
cana-4287	262	1	25–40	25–40	NUM
cana-4287	262	2	,	,	PUNCT
cana-4287	262	3	2024	2024	NUM
cana-4287	262	4	.	.	PUNCT
cana-4287	263	1	[	[	X
cana-4287	263	2	14	14	NUM
cana-4287	263	3	]	]	PUNCT
cana-4287	263	4	.	.	PUNCT
cana-4287	264	1	ivanov	ivanov	PROPN
cana-4287	264	2	,	,	PUNCT
cana-4287	264	3	d.	d.	PROPN
cana-4287	264	4	,	,	PUNCT
cana-4287	264	5	et	et	PROPN
cana-4287	264	6	al	al	PROPN
cana-4287	264	7	.	.	PROPN
cana-4287	264	8	,	,	PUNCT
cana-4287	264	9	“	"	PUNCT
cana-4287	264	10	cohomology	cohomology	NOUN
cana-4287	264	11	rings	ring	NOUN
cana-4287	264	12	in	in	ADP
cana-4287	264	13	symmetric	symmetric	ADJ
cana-4287	264	14	key	key	ADJ
cana-4287	264	15	cryptography	cryptography	NOUN
cana-4287	264	16	,	,	PUNCT
cana-4287	264	17	”	"	PUNCT
cana-4287	264	18	mathematical	mathematical	ADJ
cana-4287	264	19	structures	structure	NOUN
cana-4287	264	20	in	in	ADP
cana-4287	264	21	cryptography	cryptography	NOUN
cana-4287	264	22	,	,	PUNCT
cana-4287	264	23	vol	vol	NOUN
cana-4287	264	24	.	.	PROPN
cana-4287	264	25	19	19	NUM
cana-4287	264	26	,	,	PUNCT
cana-4287	264	27	no	no	INTJ
cana-4287	264	28	.	.	NOUN
cana-4287	264	29	3	3	NUM
cana-4287	264	30	,	,	PUNCT
cana-4287	264	31	pp	pp	ADJ
cana-4287	264	32	.	.	PUNCT
cana-4287	265	1	110–125	110–125	NUM
cana-4287	265	2	,	,	PUNCT
cana-4287	265	3	2023	2023	NUM
cana-4287	265	4	.	.	PUNCT
cana-4287	266	1	[	[	X
cana-4287	266	2	15	15	NUM
cana-4287	266	3	]	]	PUNCT
cana-4287	266	4	.	.	PUNCT
cana-4287	267	1	kim	kim	PROPN
cana-4287	267	2	,	,	PUNCT
cana-4287	267	3	h.	h.	PROPN
cana-4287	267	4	,	,	PUNCT
cana-4287	267	5	et	et	PROPN
cana-4287	267	6	al	al	PROPN
cana-4287	267	7	.	.	PROPN
cana-4287	267	8	,	,	PUNCT
cana-4287	267	9	“	"	PUNCT
cana-4287	267	10	geometric	geometric	ADJ
cana-4287	267	11	group	group	NOUN
cana-4287	267	12	theory	theory	NOUN
cana-4287	267	13	in	in	ADP
cana-4287	267	14	secure	secure	ADJ
cana-4287	267	15	multi	multi	ADJ
cana-4287	267	16	-	-	ADJ
cana-4287	267	17	party	party	ADJ
cana-4287	267	18	computation	computation	NOUN
cana-4287	267	19	,	,	PUNCT
cana-4287	267	20	”	"	PUNCT
cana-4287	267	21	ieee	ieee	NOUN
cana-4287	267	22	transactions	transaction	NOUN
cana-4287	267	23	on	on	ADP
cana-4287	267	24	secure	secure	ADJ
cana-4287	267	25	distributed	distribute	VERB
cana-4287	267	26	systems	system	NOUN
cana-4287	267	27	,	,	PUNCT
cana-4287	267	28	vol	vol	NOUN
cana-4287	267	29	.	.	PROPN
cana-4287	267	30	14	14	NUM
cana-4287	267	31	,	,	PUNCT
cana-4287	267	32	no	no	INTJ
cana-4287	267	33	.	.	NOUN
cana-4287	267	34	2	2	NUM
cana-4287	267	35	,	,	PUNCT
cana-4287	267	36	pp	pp	ADJ
cana-4287	267	37	.	.	PUNCT
cana-4287	268	1	87–101	87–101	NUM
cana-4287	268	2	,	,	PUNCT
cana-4287	268	3	2024	2024	NUM
cana-4287	268	4	.	.	PUNCT