id	sid	tid	token	lemma	pos
cana-6328	1	1	communications	communication	NOUN
cana-6328	1	2	on	on	ADP
cana-6328	1	3	applied	apply	VERB
cana-6328	1	4	nonlinear	nonlinear	ADJ
cana-6328	1	5	analysis	analysis	NOUN
cana-6328	1	6	issn	issn	NOUN
cana-6328	1	7	:	:	PUNCT
cana-6328	1	8	1074	1074	NUM
cana-6328	1	9	-	-	PUNCT
cana-6328	1	10	133x	133x	NUM
cana-6328	1	11	vol	vol	NOUN
cana-6328	1	12	32	32	NUM
cana-6328	1	13	no	no	NOUN
cana-6328	1	14	.	.	PUNCT
cana-6328	2	1	1s	1s	NUM
cana-6328	2	2	(	(	PUNCT
cana-6328	2	3	2025	2025	NUM
cana-6328	2	4	)	)	PUNCT
cana-6328	2	5	775	775	NUM
cana-6328	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	2	7	a	a	DET
cana-6328	2	8	novel	novel	ADJ
cana-6328	2	9	ntru	ntru	ADJ
cana-6328	2	10	cryptosystem	cryptosystem	NOUN
cana-6328	2	11	with	with	ADP
cana-6328	2	12	gell	gell	NOUN
cana-6328	2	13	maan	maan	PROPN
cana-6328	2	14	matrix	matrix	PROPN
cana-6328	2	15	swati	swati	PROPN
cana-6328	2	16	verma1	verma1	PROPN
cana-6328	2	17	,	,	PUNCT
cana-6328	2	18	debasmita	debasmita	PROPN
cana-6328	2	19	samal2	samal2	PROPN
cana-6328	2	20	,	,	PUNCT
cana-6328	2	21	khushboo	khushboo	ADP
cana-6328	2	22	thakur3	thakur3	PROPN
cana-6328	2	23	,	,	PUNCT
cana-6328	2	24	priya	priya	PROPN
cana-6328	2	25	verma4	verma4	PROPN
cana-6328	3	1	1	1	NUM
cana-6328	3	2	,	,	PUNCT
cana-6328	3	3	2	2	NUM
cana-6328	3	4	o.	o.	NOUN
cana-6328	3	5	p.	p.	PROPN
cana-6328	3	6	jindal	jindal	PROPN
cana-6328	3	7	university	university	PROPN
cana-6328	3	8	,	,	PUNCT
cana-6328	3	9	raigarh	raigarh	PROPN
cana-6328	3	10	(	(	PUNCT
cana-6328	3	11	c.g	c.g	PROPN
cana-6328	3	12	.	.	PROPN
cana-6328	3	13	)	)	PUNCT
cana-6328	3	14	,	,	PUNCT
cana-6328	3	15	india	india	PROPN
cana-6328	3	16	.	.	PUNCT
cana-6328	4	1	3govt	3govt	NUM
cana-6328	4	2	.	.	PUNCT
cana-6328	5	1	shahid	shahid	PROPN
cana-6328	5	2	koushal	koushal	PROPN
cana-6328	5	3	yadav	yadav	PROPN
cana-6328	5	4	college	college	PROPN
cana-6328	5	5	,	,	PUNCT
cana-6328	5	6	gundardehi	gundardehi	PROPN
cana-6328	5	7	,	,	PUNCT
cana-6328	5	8	dhamtari	dhamtari	NOUN
cana-6328	5	9	(	(	PUNCT
cana-6328	5	10	c.g	c.g	PROPN
cana-6328	5	11	)	)	PUNCT
cana-6328	5	12	.	.	PUNCT
cana-6328	6	1	4department	4department	NUM
cana-6328	6	2	of	of	ADP
cana-6328	6	3	mathematics	mathematic	NOUN
cana-6328	6	4	,	,	PUNCT
cana-6328	6	5	kalinga	kalinga	PROPN
cana-6328	6	6	university	university	PROPN
cana-6328	6	7	,	,	PUNCT
cana-6328	6	8	raipur	raipur	PROPN
cana-6328	6	9	(	(	PUNCT
cana-6328	6	10	c.g	c.g	PROPN
cana-6328	6	11	.	.	PROPN
cana-6328	6	12	)	)	PUNCT
cana-6328	6	13	,	,	PUNCT
cana-6328	6	14	india	india	PROPN
cana-6328	6	15	.	.	PROPN
cana-6328	6	16	1	1	NUM
cana-6328	6	17	swati.verma@opju.ac.in	swati.verma@opju.ac.in	NUM
cana-6328	6	18	,	,	PUNCT
cana-6328	6	19	2debasmita.samal@opju.ac.in	2debasmita.samal@opju.ac.in	NUM
cana-6328	6	20	,	,	PUNCT
cana-6328	6	21	3khushboo.thakur784@gmail.com	3khushboo.thakur784@gmail.com	NUM
cana-6328	6	22	,	,	PUNCT
cana-6328	6	23	4priyavermatanu15@gmail.com	4priyavermatanu15@gmail.com	NOUN
cana-6328	6	24	article	article	NOUN
cana-6328	6	25	history	history	NOUN
cana-6328	6	26	:	:	PUNCT
cana-6328	6	27	received	receive	VERB
cana-6328	6	28	:	:	PUNCT
cana-6328	6	29	30	30	NUM
cana-6328	6	30	-	-	SYM
cana-6328	6	31	09	09	NUM
cana-6328	6	32	-	-	PUNCT
cana-6328	6	33	2024	2024	NUM
cana-6328	6	34	revised	revise	VERB
cana-6328	6	35	:	:	PUNCT
cana-6328	6	36	15	15	NUM
cana-6328	6	37	-	-	SYM
cana-6328	6	38	11	11	NUM
cana-6328	6	39	-	-	PUNCT
cana-6328	6	40	2024	2024	NUM
cana-6328	6	41	accepted	accept	VERB
cana-6328	6	42	:	:	PUNCT
cana-6328	6	43	20	20	NUM
cana-6328	6	44	-	-	SYM
cana-6328	6	45	01	01	NUM
cana-6328	6	46	-	-	PUNCT
cana-6328	6	47	2025	2025	NUM
cana-6328	6	48	abstract	abstract	NOUN
cana-6328	6	49	:	:	PUNCT
cana-6328	6	50	the	the	DET
cana-6328	6	51	ntru	ntru	ADJ
cana-6328	6	52	public	public	ADJ
cana-6328	6	53	key	key	ADJ
cana-6328	6	54	cryptosystem	cryptosystem	NOUN
cana-6328	6	55	was	be	AUX
cana-6328	6	56	first	first	ADV
cana-6328	6	57	presented	present	VERB
cana-6328	6	58	by	by	ADP
cana-6328	6	59	j.	j.	PROPN
cana-6328	6	60	hoffstein	hoffstein	PROPN
cana-6328	6	61	,	,	PUNCT
cana-6328	6	62	j.	j.	PROPN
cana-6328	6	63	h.	h.	PROPN
cana-6328	6	64	silverman	silverman	PROPN
cana-6328	6	65	and	and	CCONJ
cana-6328	6	66	j.	j.	PROPN
cana-6328	6	67	pipher	pipher	PROPN
cana-6328	6	68	in	in	ADP
cana-6328	6	69	1996	1996	NUM
cana-6328	6	70	.	.	PUNCT
cana-6328	7	1	this	this	DET
cana-6328	7	2	system	system	NOUN
cana-6328	7	3	is	be	AUX
cana-6328	7	4	based	base	VERB
cana-6328	7	5	on	on	ADP
cana-6328	7	6	shortest	short	ADJ
cana-6328	7	7	and	and	CCONJ
cana-6328	7	8	closest	close	ADJ
cana-6328	7	9	vector	vector	NOUN
cana-6328	7	10	problem	problem	NOUN
cana-6328	7	11	in	in	ADP
cana-6328	7	12	a	a	DET
cana-6328	7	13	lattice	lattice	NOUN
cana-6328	7	14	and	and	CCONJ
cana-6328	7	15	its	its	PRON
cana-6328	7	16	operations	operation	NOUN
cana-6328	7	17	are	be	AUX
cana-6328	7	18	based	base	VERB
cana-6328	7	19	on	on	ADP
cana-6328	7	20	objects	object	NOUN
cana-6328	7	21	of	of	ADP
cana-6328	7	22	a	a	DET
cana-6328	7	23	truncated	truncate	VERB
cana-6328	7	24	polynomial	polynomial	ADJ
cana-6328	7	25	ring	ring	NOUN
cana-6328	7	26	.	.	PUNCT
cana-6328	8	1	in	in	ADP
cana-6328	8	2	this	this	DET
cana-6328	8	3	paper	paper	NOUN
cana-6328	8	4	,	,	PUNCT
cana-6328	8	5	we	we	PRON
cana-6328	8	6	have	have	AUX
cana-6328	8	7	show	show	VERB
cana-6328	8	8	that	that	SCONJ
cana-6328	8	9	applying	apply	VERB
cana-6328	8	10	gell	gell	NOUN
cana-6328	8	11	maan	maan	PROPN
cana-6328	8	12	matrix	matrix	NOUN
cana-6328	8	13	for	for	ADP
cana-6328	8	14	the	the	DET
cana-6328	8	15	matrix	matrix	NOUN
cana-6328	8	16	formulation	formulation	NOUN
cana-6328	8	17	algorithm	algorithm	NOUN
cana-6328	8	18	in	in	ADP
cana-6328	8	19	ntru	ntru	ADJ
cana-6328	8	20	public	public	ADJ
cana-6328	8	21	key	key	ADJ
cana-6328	8	22	cryptosystem	cryptosystem	NOUN
cana-6328	8	23	substantially	substantially	ADV
cana-6328	8	24	increases	increase	VERB
cana-6328	8	25	its	its	PRON
cana-6328	8	26	efficiency	efficiency	NOUN
cana-6328	8	27	as	as	SCONJ
cana-6328	8	28	compared	compare	VERB
cana-6328	8	29	to	to	ADP
cana-6328	8	30	other	other	ADJ
cana-6328	8	31	matrix	matrix	NOUN
cana-6328	8	32	formulation	formulation	NOUN
cana-6328	8	33	for	for	ADP
cana-6328	8	34	ntru	ntru	ADJ
cana-6328	8	35	cryptosystem	cryptosystem	NOUN
cana-6328	8	36	with	with	ADP
cana-6328	8	37	invertible	invertible	ADJ
cana-6328	8	38	matrix	matrix	NOUN
cana-6328	8	39	,	,	PUNCT
cana-6328	8	40	such	such	ADJ
cana-6328	8	41	as	as	ADP
cana-6328	8	42	nayak	nayak	PROPN
cana-6328	8	43	et	et	PROPN
cana-6328	8	44	al	al	PROPN
cana-6328	8	45	.	.	PUNCT
cana-6328	9	1	[	[	X
cana-6328	9	2	8	8	NUM
cana-6328	9	3	]	]	PUNCT
cana-6328	9	4	.	.	PUNCT
cana-6328	10	1	the	the	DET
cana-6328	10	2	gell	gell	PROPN
cana-6328	10	3	maan	maan	PROPN
cana-6328	10	4	matrix	matrix	NOUN
cana-6328	10	5	facilitates	facilitate	VERB
cana-6328	10	6	the	the	DET
cana-6328	10	7	development	development	NOUN
cana-6328	10	8	and	and	CCONJ
cana-6328	10	9	understanding	understanding	NOUN
cana-6328	10	10	of	of	ADP
cana-6328	10	11	numerical	numerical	ADJ
cana-6328	10	12	algorithms	algorithm	NOUN
cana-6328	10	13	.	.	PUNCT
cana-6328	11	1	keywords	keyword	NOUN
cana-6328	11	2	:	:	PUNCT
cana-6328	11	3	gell	gell	NOUN
cana-6328	11	4	maan	maan	PROPN
cana-6328	11	5	matrix	matrix	NOUN
cana-6328	11	6	,	,	PUNCT
cana-6328	11	7	ntru	ntru	NOUN
cana-6328	11	8	,	,	PUNCT
cana-6328	11	9	encryption	encryption	NOUN
cana-6328	11	10	,	,	PUNCT
cana-6328	11	11	decryption	decryption	NOUN
cana-6328	11	12	,	,	PUNCT
cana-6328	11	13	security	security	NOUN
cana-6328	11	14	analysis	analysis	NOUN
cana-6328	11	15	.	.	PUNCT
cana-6328	11	16	.	.	PUNCT
cana-6328	12	1	(	(	PUNCT
cana-6328	12	2	ams	am	NOUN
cana-6328	12	3	)	)	PUNCT
cana-6328	12	4	mathematics	mathematic	NOUN
cana-6328	12	5	subject	subject	ADJ
cana-6328	12	6	classification	classification	NOUN
cana-6328	12	7	no	no	NOUN
cana-6328	12	8	:	:	PUNCT
cana-6328	12	9	94a60	94a60	NUM
cana-6328	12	10	,	,	PUNCT
cana-6328	12	11	15a23	15a23	NUM
cana-6328	12	12	,	,	PUNCT
cana-6328	12	13	15a57	15a57	NUM
cana-6328	12	14	.	.	PUNCT
cana-6328	13	1	1	1	X
cana-6328	13	2	.	.	X
cana-6328	13	3	introduction	introduction	NOUN
cana-6328	13	4	lattices	lattice	NOUN
cana-6328	13	5	were	be	AUX
cana-6328	13	6	first	first	ADV
cana-6328	13	7	studied	study	VERB
cana-6328	13	8	by	by	ADP
cana-6328	13	9	mathematician	mathematician	ADJ
cana-6328	13	10	joseph	joseph	PROPN
cana-6328	13	11	louis	louis	PROPN
cana-6328	13	12	lagrange	lagrange	PROPN
cana-6328	13	13	and	and	CCONJ
cana-6328	13	14	carl	carl	PROPN
cana-6328	13	15	friedrich	friedrich	PROPN
cana-6328	13	16	gauss	gauss	PROPN
cana-6328	13	17	.	.	PROPN
cana-6328	14	1	later	later	PROPN
cana-6328	14	2	lattices	lattice	NOUN
cana-6328	14	3	have	have	AUX
cana-6328	14	4	been	be	AUX
cana-6328	14	5	used	use	VERB
cana-6328	14	6	in	in	ADP
cana-6328	14	7	public	public	ADJ
cana-6328	14	8	key	key	ADJ
cana-6328	14	9	cryptosystems	cryptosystem	NOUN
cana-6328	14	10	by	by	ADP
cana-6328	14	11	ajtai	ajtai	ADJ
cana-6328	14	12	dwork	dwork	NOUN
cana-6328	14	13	(	(	PUNCT
cana-6328	14	14	ajtai	ajtai	ADJ
cana-6328	14	15	and	and	CCONJ
cana-6328	14	16	dwork	dwork	NOUN
cana-6328	14	17	1997	1997	NUM
cana-6328	14	18	)	)	PUNCT
cana-6328	14	19	,	,	PUNCT
cana-6328	14	20	goldreich	goldreich	PROPN
cana-6328	14	21	goldwasser	goldwasser	PROPN
cana-6328	14	22	halevi	halevi	PROPN
cana-6328	14	23	(	(	PUNCT
cana-6328	14	24	goldreich	goldreich	X
cana-6328	14	25	et	et	PROPN
cana-6328	14	26	al	al	PROPN
cana-6328	14	27	.	.	PROPN
cana-6328	14	28	1997	1997	NUM
cana-6328	14	29	)	)	PUNCT
cana-6328	14	30	and	and	CCONJ
cana-6328	14	31	ntru	ntru	PROPN
cana-6328	14	32	(	(	PUNCT
cana-6328	14	33	hoffstein	hoffstein	ADV
cana-6328	14	34	et	et	NOUN
cana-6328	14	35	al.1998	al.1998	PROPN
cana-6328	14	36	)	)	PUNCT
cana-6328	14	37	cryptosystem	cryptosystem	NOUN
cana-6328	14	38	.	.	PUNCT
cana-6328	15	1	ntru	ntru	PROPN
cana-6328	15	2	the	the	DET
cana-6328	15	3	best	good	ADJ
cana-6328	15	4	among	among	ADP
cana-6328	15	5	the	the	DET
cana-6328	15	6	other	other	ADJ
cana-6328	15	7	lattice	lattice	NOUN
cana-6328	15	8	based	base	VERB
cana-6328	15	9	cryptosystems	cryptosystem	NOUN
cana-6328	15	10	.	.	PUNCT
cana-6328	16	1	the	the	DET
cana-6328	16	2	ntru	ntru	PROPN
cana-6328	16	3	pkc	pkc	PROPN
cana-6328	16	4	of	of	ADP
cana-6328	16	5	j.hoffstein	j.hoffstein	ADJ
cana-6328	16	6	,	,	PUNCT
cana-6328	16	7	silverman	silverman	NOUN
cana-6328	16	8	[	[	X
cana-6328	16	9	4	4	NUM
cana-6328	16	10	]	]	PUNCT
cana-6328	16	11	was	be	AUX
cana-6328	16	12	designed	design	VERB
cana-6328	16	13	with	with	ADP
cana-6328	16	14	lattice	lattice	NOUN
cana-6328	16	15	of	of	ADP
cana-6328	16	16	polynomial	polynomial	ADJ
cana-6328	16	17	.	.	PUNCT
cana-6328	17	1	next	next	ADJ
cana-6328	17	2	pkc	pkc	PROPN
cana-6328	17	3	of	of	ADP
cana-6328	17	4	j.	j.	PROPN
cana-6328	17	5	hoffstein	hoffstein	PROPN
cana-6328	18	1	[	[	X
cana-6328	18	2	10	10	NUM
cana-6328	18	3	]	]	PUNCT
cana-6328	18	4	was	be	AUX
cana-6328	18	5	designed	design	VERB
cana-6328	18	6	with	with	ADP
cana-6328	18	7	vector	vector	NOUN
cana-6328	18	8	space	space	NOUN
cana-6328	18	9	in	in	ADP
cana-6328	18	10	rn	rn	PROPN
cana-6328	18	11	dimension	dimension	PROPN
cana-6328	18	12	and	and	CCONJ
cana-6328	18	13	nayak	nayak	PROPN
cana-6328	18	14	et	et	PROPN
cana-6328	18	15	al	al	PROPN
cana-6328	18	16	.	.	PUNCT
cana-6328	19	1	[	[	X
cana-6328	19	2	8	8	NUM
cana-6328	19	3	]	]	PUNCT
cana-6328	19	4	was	be	AUX
cana-6328	19	5	designed	design	VERB
cana-6328	19	6	with	with	ADP
cana-6328	19	7	invertible	invertible	ADJ
cana-6328	19	8	matrix	matrix	NOUN
cana-6328	19	9	.	.	PUNCT
cana-6328	20	1	in	in	ADP
cana-6328	20	2	this	this	DET
cana-6328	20	3	paper	paper	NOUN
cana-6328	20	4	pkc	pkc	NOUN
cana-6328	20	5	were	be	AUX
cana-6328	20	6	found	find	VERB
cana-6328	20	7	use	use	NOUN
cana-6328	20	8	and	and	CCONJ
cana-6328	20	9	introduce	introduce	VERB
cana-6328	20	10	ntru	ntru	ADJ
cana-6328	20	11	cryptosystem	cryptosystem	NOUN
cana-6328	20	12	for	for	ADP
cana-6328	20	13	companion	companion	NOUN
cana-6328	20	14	matrix	matrix	NOUN
cana-6328	20	15	.	.	PUNCT
cana-6328	21	1	we	we	PRON
cana-6328	21	2	also	also	ADV
cana-6328	21	3	find	find	VERB
cana-6328	21	4	key	key	ADJ
cana-6328	21	5	generation	generation	NOUN
cana-6328	21	6	,	,	PUNCT
cana-6328	21	7	encryption	encryption	NOUN
cana-6328	21	8	and	and	CCONJ
cana-6328	21	9	decryption	decryption	NOUN
cana-6328	21	10	by	by	ADP
cana-6328	21	11	companion	companion	NOUN
cana-6328	21	12	matrix	matrix	NOUN
cana-6328	21	13	.	.	PUNCT
cana-6328	22	1	this	this	DET
cana-6328	22	2	cryptosystem	cryptosystem	NOUN
cana-6328	22	3	is	be	AUX
cana-6328	22	4	new	new	ADJ
cana-6328	22	5	design	design	NOUN
cana-6328	22	6	of	of	ADP
cana-6328	22	7	matrix	matrix	NOUN
cana-6328	22	8	formulation	formulation	NOUN
cana-6328	22	9	algorithm	algorithm	NOUN
cana-6328	22	10	.	.	PUNCT
cana-6328	23	1	ntru	ntru	PROPN
cana-6328	23	2	allegedly	allegedly	ADV
cana-6328	23	3	stands	stand	VERB
cana-6328	23	4	for	for	ADP
cana-6328	23	5	“	"	PUNCT
cana-6328	23	6	nth	nth	NOUN
cana-6328	23	7	degree	degree	NOUN
cana-6328	23	8	truncated	truncate	VERB
cana-6328	23	9	polynomial	polynomial	ADJ
cana-6328	23	10	ring	ring	NOUN
cana-6328	23	11	units	unit	NOUN
cana-6328	23	12	"	"	PUNCT
cana-6328	23	13	.	.	PUNCT
cana-6328	24	1	ntru	ntru	PROPN
cana-6328	24	2	is	be	AUX
cana-6328	24	3	a	a	DET
cana-6328	24	4	public	public	ADJ
cana-6328	24	5	key	key	ADJ
cana-6328	24	6	cryptosystem	cryptosystem	NOUN
cana-6328	24	7	presented	present	VERB
cana-6328	24	8	by	by	ADP
cana-6328	24	9	j.	j.	PROPN
cana-6328	24	10	hoffstein	hoffstein	PROPN
cana-6328	24	11	,	,	PUNCT
cana-6328	24	12	j.	j.	PROPN
cana-6328	24	13	pipher	pipher	PROPN
cana-6328	24	14	and	and	CCONJ
cana-6328	24	15	j.	j.	PROPN
cana-6328	24	16	silverman	silverman	PROPN
cana-6328	25	1	[	[	X
cana-6328	25	2	4	4	NUM
cana-6328	25	3	]	]	PUNCT
cana-6328	25	4	.	.	PUNCT
cana-6328	26	1	the	the	DET
cana-6328	26	2	first	first	ADJ
cana-6328	26	3	version	version	NOUN
cana-6328	26	4	of	of	ADP
cana-6328	26	5	the	the	DET
cana-6328	26	6	ntru	ntru	ADJ
cana-6328	26	7	encryption	encryption	NOUN
cana-6328	26	8	system	system	NOUN
cana-6328	26	9	was	be	AUX
cana-6328	26	10	presented	present	VERB
cana-6328	26	11	at	at	ADP
cana-6328	26	12	the	the	DET
cana-6328	26	13	crypto	crypto	NOUN
cana-6328	26	14	96	96	NUM
cana-6328	26	15	conference	conference	NOUN
cana-6328	26	16	[	[	X
cana-6328	26	17	4	4	NUM
cana-6328	26	18	]	]	PUNCT
cana-6328	26	19	.	.	PUNCT
cana-6328	27	1	the	the	DET
cana-6328	27	2	computational	computational	ADJ
cana-6328	27	3	basis	basis	NOUN
cana-6328	27	4	of	of	ADP
cana-6328	27	5	the	the	DET
cana-6328	27	6	ntru	ntru	PROPN
cana-6328	27	7	lies	lie	VERB
cana-6328	27	8	in	in	ADP
cana-6328	27	9	polynomial	polynomial	ADJ
cana-6328	27	10	algebra	algebra	NOUN
cana-6328	27	11	and	and	CCONJ
cana-6328	27	12	it	it	PRON
cana-6328	27	13	is	be	AUX
cana-6328	27	14	a	a	DET
cana-6328	27	15	relatively	relatively	ADV
cana-6328	27	16	new	new	ADJ
cana-6328	27	17	cryptosystem	cryptosystem	NOUN
cana-6328	27	18	.	.	PUNCT
cana-6328	28	1	ntru	ntru	PROPN
cana-6328	28	2	is	be	AUX
cana-6328	28	3	based	base	VERB
cana-6328	28	4	on	on	ADP
cana-6328	28	5	lattice	lattice	NOUN
cana-6328	28	6	-	-	PUNCT
cana-6328	28	7	based	base	VERB
cana-6328	28	8	cryptography	cryptography	NOUN
cana-6328	28	9	it	it	PRON
cana-6328	28	10	has	have	VERB
cana-6328	28	11	different	different	ADJ
cana-6328	28	12	cryptographic	cryptographic	ADJ
cana-6328	28	13	properties	property	NOUN
cana-6328	28	14	from	from	ADP
cana-6328	28	15	rsa	rsa	PROPN
cana-6328	28	16	and	and	CCONJ
cana-6328	28	17	ecc	ecc	PROPN
cana-6328	29	1	[	[	X
cana-6328	29	2	3	3	NUM
cana-6328	29	3	]	]	PUNCT
cana-6328	29	4	.	.	PUNCT
cana-6328	30	1	the	the	DET
cana-6328	30	2	strength	strength	NOUN
cana-6328	30	3	of	of	ADP
cana-6328	30	4	cryptographic	cryptographic	ADJ
cana-6328	30	5	ntru	ntru	NOUN
cana-6328	30	6	performs	perform	VERB
cana-6328	30	7	valuable	valuable	ADJ
cana-6328	30	8	private	private	ADJ
cana-6328	30	9	key	key	ADJ
cana-6328	30	10	operations	operation	NOUN
cana-6328	30	11	much	much	ADV
cana-6328	30	12	faster	fast	ADV
cana-6328	30	13	in	in	ADP
cana-6328	30	14	comparison	comparison	NOUN
cana-6328	30	15	to	to	ADP
cana-6328	30	16	rsa	rsa	PROPN
cana-6328	30	17	.	.	PUNCT
cana-6328	31	1	polynomial	polynomial	ADJ
cana-6328	31	2	algebra	algebra	PROPN
cana-6328	31	3	is	be	AUX
cana-6328	31	4	the	the	DET
cana-6328	31	5	basic	basic	ADJ
cana-6328	31	6	building	building	NOUN
cana-6328	31	7	block	block	NOUN
cana-6328	31	8	of	of	ADP
cana-6328	31	9	the	the	DET
cana-6328	31	10	ntru	ntru	ADJ
cana-6328	31	11	encryption	encryption	NOUN
cana-6328	31	12	system	system	NOUN
cana-6328	31	13	.	.	PUNCT
cana-6328	32	1	the	the	DET
cana-6328	32	2	truncated	truncated	ADJ
cana-6328	32	3	polynomials	polynomial	NOUN
cana-6328	32	4	given	give	VERB
cana-6328	32	5	in	in	ADP
cana-6328	32	6	j.	j.	PROPN
cana-6328	32	7	silverman	silverman	PROPN
cana-6328	32	8	[	[	X
cana-6328	32	9	9	9	NUM
cana-6328	32	10	]	]	PUNCT
cana-6328	32	11	,	,	PUNCT
cana-6328	32	12	p.prapoorna	p.prapoorna	PROPN
cana-6328	33	1	[	[	X
cana-6328	33	2	5	5	NUM
cana-6328	33	3	]	]	PUNCT
cana-6328	33	4	in	in	ADP
cana-6328	33	5	the	the	DET
cana-6328	33	6	ring	ring	NOUN
cana-6328	33	7	r	r	NOUN
cana-6328	33	8	=	=	SYM
cana-6328	33	9	z[x]/	z[x]/	PROPN
cana-6328	33	10	(	(	PUNCT
cana-6328	33	11	x	x	NOUN
cana-6328	33	12	n	n	CCONJ
cana-6328	33	13	-1)are	-1)are	ADP
cana-6328	33	14	basic	basic	ADJ
cana-6328	33	15	objects	object	NOUN
cana-6328	33	16	and	and	CCONJ
cana-6328	33	17	the	the	DET
cana-6328	33	18	reduction	reduction	NOUN
cana-6328	33	19	of	of	ADP
cana-6328	33	20	polynomials	polynomial	NOUN
cana-6328	33	21	with	with	ADP
cana-6328	33	22	respect	respect	NOUN
cana-6328	33	23	to	to	ADP
cana-6328	33	24	relatively	relatively	ADV
cana-6328	33	25	prime	prime	ADJ
cana-6328	33	26	moduli	modulus	NOUN
cana-6328	33	27	i.e.	i.e.	X
cana-6328	33	28	,	,	PUNCT
cana-6328	33	29	p	p	NOUN
cana-6328	33	30	and	and	CCONJ
cana-6328	33	31	q	q	NOUN
cana-6328	33	32	are	be	AUX
cana-6328	33	33	the	the	DET
cana-6328	33	34	basic	basic	ADJ
cana-6328	33	35	tools	tool	NOUN
cana-6328	33	36	.	.	PUNCT
cana-6328	34	1	recently	recently	ADV
cana-6328	34	2	,	,	PUNCT
cana-6328	34	3	nayak	nayak	PROPN
cana-6328	34	4	et	et	PROPN
cana-6328	34	5	al	al	PROPN
cana-6328	34	6	.	.	PUNCT
cana-6328	35	1	[	[	X
cana-6328	35	2	8	8	NUM
cana-6328	35	3	]	]	PUNCT
cana-6328	35	4	have	have	AUX
cana-6328	35	5	proposed	propose	VERB
cana-6328	35	6	taking	take	VERB
cana-6328	35	7	invertible	invertible	ADJ
cana-6328	35	8	or	or	CCONJ
cana-6328	35	9	non	non	ADJ
cana-6328	35	10	singular	singular	ADJ
cana-6328	35	11	matrix	matrix	NOUN
cana-6328	35	12	in	in	ADP
cana-6328	35	13	ntru	ntru	ADJ
cana-6328	35	14	cryptosystem	cryptosystem	NOUN
cana-6328	35	15	[	[	X
cana-6328	35	16	4	4	NUM
cana-6328	35	17	]	]	PUNCT
cana-6328	35	18	.	.	PUNCT
cana-6328	36	1	they	they	PRON
cana-6328	36	2	have	have	AUX
cana-6328	36	3	given	give	VERB
cana-6328	36	4	a	a	DET
cana-6328	36	5	pkc	pkc	NOUN
cana-6328	36	6	by	by	ADP
cana-6328	36	7	method	method	NOUN
cana-6328	36	8	,	,	PUNCT
cana-6328	36	9	which	which	PRON
cana-6328	36	10	is	be	AUX
cana-6328	36	11	suitable	suitable	ADJ
cana-6328	36	12	to	to	PART
cana-6328	36	13	send	send	VERB
cana-6328	36	14	in	in	ADP
cana-6328	36	15	the	the	DET
cana-6328	36	16	key	key	ADJ
cana-6328	36	17	generation	generation	NOUN
cana-6328	36	18	phase	phase	NOUN
cana-6328	36	19	of	of	ADP
cana-6328	36	20	large	large	ADJ
cana-6328	36	21	message	message	NOUN
cana-6328	36	22	in	in	ADP
cana-6328	36	23	the	the	DET
cana-6328	36	24	form	form	NOUN
cana-6328	36	25	of	of	ADP
cana-6328	36	26	matrices	matrix	NOUN
cana-6328	36	27	.	.	PUNCT
cana-6328	37	1	now	now	ADV
cana-6328	37	2	in	in	ADP
cana-6328	37	3	this	this	DET
cana-6328	37	4	paper	paper	NOUN
cana-6328	37	5	,	,	PUNCT
cana-6328	37	6	mailto:1%20swati.verma@opju.ac.in	mailto:1%20swati.verma@opju.ac.in	PROPN
cana-6328	37	7	mailto:debasmita.samal@opju.ac.in	mailto:debasmita.samal@opju.ac.in	PROPN
cana-6328	37	8	mailto:3khushboo.thakur784@gmail.com	mailto:3khushboo.thakur784@gmail.com	PROPN
cana-6328	37	9	mailto:4priyavermatanu15@gmail.com	mailto:4priyavermatanu15@gmail.com	PROPN
cana-6328	37	10	communications	communication	NOUN
cana-6328	37	11	on	on	ADP
cana-6328	37	12	applied	apply	VERB
cana-6328	37	13	nonlinear	nonlinear	ADJ
cana-6328	37	14	analysis	analysis	NOUN
cana-6328	37	15	issn	issn	NOUN
cana-6328	37	16	:	:	PUNCT
cana-6328	37	17	1074	1074	NUM
cana-6328	37	18	-	-	PUNCT
cana-6328	37	19	133x	133x	NUM
cana-6328	37	20	vol	vol	NOUN
cana-6328	37	21	32	32	NUM
cana-6328	37	22	no	no	NOUN
cana-6328	37	23	.	.	PUNCT
cana-6328	38	1	1s	1s	NUM
cana-6328	38	2	(	(	PUNCT
cana-6328	38	3	2025	2025	NUM
cana-6328	38	4	)	)	PUNCT
cana-6328	38	5	776	776	NUM
cana-6328	38	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	38	7	we	we	PRON
cana-6328	38	8	consider	consider	VERB
cana-6328	38	9	gall	gall	NOUN
cana-6328	38	10	maan	maan	PROPN
cana-6328	38	11	matrix	matrix	NOUN
cana-6328	38	12	[	[	X
cana-6328	38	13	13	13	NUM
cana-6328	38	14	]	]	PUNCT
cana-6328	38	15	during	during	ADP
cana-6328	38	16	key	key	ADJ
cana-6328	38	17	generation	generation	NOUN
cana-6328	38	18	replacing	replace	VERB
cana-6328	38	19	the	the	DET
cana-6328	38	20	invertible	invertible	ADJ
cana-6328	38	21	matrix	matrix	NOUN
cana-6328	38	22	of	of	ADP
cana-6328	38	23	nayak	nayak	PROPN
cana-6328	38	24	et	et	PROPN
cana-6328	38	25	al	al	PROPN
cana-6328	38	26	.	.	PUNCT
cana-6328	39	1	[	[	X
cana-6328	39	2	8	8	NUM
cana-6328	39	3	]	]	PUNCT
cana-6328	39	4	design	design	NOUN
cana-6328	39	5	.	.	PUNCT
cana-6328	40	1	in	in	ADP
cana-6328	40	2	our	our	PRON
cana-6328	40	3	opinion	opinion	NOUN
cana-6328	40	4	,	,	PUNCT
cana-6328	40	5	gall	gall	PROPN
cana-6328	40	6	maan	maan	PROPN
cana-6328	40	7	matrix	matrix	PROPN
cana-6328	40	8	makes	make	VERB
cana-6328	40	9	the	the	DET
cana-6328	40	10	pkc	pkc	NOUN
cana-6328	40	11	more	more	ADV
cana-6328	40	12	efficient	efficient	ADJ
cana-6328	40	13	as	as	SCONJ
cana-6328	40	14	compare	compare	VERB
cana-6328	40	15	to	to	ADP
cana-6328	40	16	invertible	invertible	ADJ
cana-6328	40	17	matrix	matrix	NOUN
cana-6328	40	18	because	because	SCONJ
cana-6328	40	19	gell	gell	PROPN
cana-6328	40	20	maan	maan	PROPN
cana-6328	40	21	matrix	matrix	NOUN
cana-6328	40	22	is	be	AUX
cana-6328	40	23	traceless	traceless	ADJ
cana-6328	40	24	hermitian	hermitian	ADJ
cana-6328	40	25	matrices	matrix	NOUN
cana-6328	40	26	consequently	consequently	ADV
cana-6328	40	27	easily	easily	ADV
cana-6328	40	28	reducible	reducible	ADJ
cana-6328	40	29	.	.	PUNCT
cana-6328	41	1	2	2	X
cana-6328	41	2	.	.	X
cana-6328	41	3	review	review	NOUN
cana-6328	41	4	of	of	ADP
cana-6328	41	5	nayak	nayak	PROPN
cana-6328	41	6	et	et	PROPN
cana-6328	41	7	al	al	PROPN
cana-6328	41	8	.	.	PUNCT
cana-6328	42	1	[	[	X
cana-6328	42	2	8	8	NUM
cana-6328	42	3	]	]	PUNCT
cana-6328	42	4	system	system	NOUN
cana-6328	42	5	the	the	DET
cana-6328	42	6	nayak	nayak	PROPN
cana-6328	42	7	et	et	PROPN
cana-6328	42	8	al	al	PROPN
cana-6328	42	9	.	.	PUNCT
cana-6328	43	1	[	[	X
cana-6328	43	2	8	8	NUM
cana-6328	43	3	]	]	PUNCT
cana-6328	43	4	give	give	VERB
cana-6328	43	5	the	the	DET
cana-6328	43	6	key	key	ADJ
cana-6328	43	7	generation	generation	NOUN
cana-6328	43	8	,	,	PUNCT
cana-6328	43	9	encryption	encryption	NOUN
cana-6328	43	10	and	and	CCONJ
cana-6328	43	11	decryption	decryption	NOUN
cana-6328	43	12	for	for	ADP
cana-6328	43	13	their	their	PRON
cana-6328	43	14	cryptosystem	cryptosystem	NOUN
cana-6328	43	15	as	as	ADP
cana-6328	43	16	below	below	ADV
cana-6328	43	17	:	:	PUNCT
cana-6328	43	18	2.1	2.1	NUM
cana-6328	43	19	key	key	ADJ
cana-6328	43	20	generation	generation	NOUN
cana-6328	43	21	bob	bob	PROPN
cana-6328	43	22	(	(	PUNCT
cana-6328	43	23	receiver	receiver	NOUN
cana-6328	43	24	)	)	PUNCT
cana-6328	43	25	creates	create	VERB
cana-6328	43	26	a	a	DET
cana-6328	43	27	public	public	ADJ
cana-6328	43	28	and	and	CCONJ
cana-6328	43	29	private	private	ADJ
cana-6328	43	30	key	key	ADJ
cana-6328	43	31	pair	pair	NOUN
cana-6328	43	32	.	.	PUNCT
cana-6328	44	1	for	for	ADP
cana-6328	44	2	this	this	DET
cana-6328	44	3	purpose	purpose	NOUN
cana-6328	44	4	he	he	PRON
cana-6328	44	5	first	first	ADV
cana-6328	44	6	randomly	randomly	ADV
cana-6328	44	7	chooses	choose	VERB
cana-6328	44	8	two	two	NUM
cana-6328	44	9	matrices	matrix	NOUN
cana-6328	44	10	f	f	PROPN
cana-6328	44	11	and	and	CCONJ
cana-6328	44	12	g	g	NOUN
cana-6328	44	13	,	,	PUNCT
cana-6328	44	14	where	where	SCONJ
cana-6328	44	15	matrix	matrix	NOUN
cana-6328	44	16	f	f	AUX
cana-6328	44	17	be	be	AUX
cana-6328	44	18	an	an	DET
cana-6328	44	19	invertible	invertible	ADJ
cana-6328	44	20	matrix	matrix	NOUN
cana-6328	44	21	(	(	PUNCT
cana-6328	44	22	modulo	modulo	PROPN
cana-6328	44	23	p	p	X
cana-6328	44	24	)	)	PUNCT
cana-6328	44	25	.	.	PUNCT
cana-6328	45	1	bob	bob	PROPN
cana-6328	45	2	keeps	keep	VERB
cana-6328	45	3	the	the	DET
cana-6328	45	4	matrices	matrix	NOUN
cana-6328	45	5	f	f	PROPN
cana-6328	45	6	and	and	CCONJ
cana-6328	45	7	g	g	PROPN
cana-6328	45	8	private	private	ADJ
cana-6328	45	9	,	,	PUNCT
cana-6328	45	10	since	since	SCONJ
cana-6328	45	11	anyone	anyone	PRON
cana-6328	45	12	who	who	PRON
cana-6328	45	13	knows	know	VERB
cana-6328	45	14	any	any	DET
cana-6328	45	15	one	one	NUM
cana-6328	45	16	of	of	ADP
cana-6328	45	17	them	they	PRON
cana-6328	45	18	will	will	AUX
cana-6328	45	19	be	be	AUX
cana-6328	45	20	able	able	ADJ
cana-6328	45	21	to	to	PART
cana-6328	45	22	decrypt	decrypt	VERB
cana-6328	45	23	messages	message	NOUN
cana-6328	45	24	sent	send	VERB
cana-6328	45	25	to	to	ADP
cana-6328	45	26	bob	bob	PROPN
cana-6328	45	27	.	.	PUNCT
cana-6328	46	1	bob	bob	PROPN
cana-6328	46	2	's	's	PART
cana-6328	46	3	next	next	ADJ
cana-6328	46	4	step	step	NOUN
cana-6328	46	5	is	be	AUX
cana-6328	46	6	to	to	PART
cana-6328	46	7	compute	compute	VERB
cana-6328	46	8	the	the	DET
cana-6328	46	9	inverse	inverse	NOUN
cana-6328	46	10	of	of	ADP
cana-6328	46	11	f	f	PROPN
cana-6328	46	12	modulo	modulo	PROPN
cana-6328	46	13	q	q	NOUN
cana-6328	46	14	and	and	CCONJ
cana-6328	46	15	the	the	DET
cana-6328	46	16	inverse	inverse	NOUN
cana-6328	46	17	of	of	ADP
cana-6328	46	18	f	f	PROPN
cana-6328	46	19	modulo	modulo	PROPN
cana-6328	46	20	p.	p.	NOUN
cana-6328	46	21	thus	thus	ADV
cana-6328	46	22	he	he	PRON
cana-6328	46	23	computes	compute	VERB
cana-6328	46	24	matrix	matrix	NOUN
cana-6328	46	25	fq	fq	NOUN
cana-6328	46	26	and	and	CCONJ
cana-6328	46	27	fp	fp	PROPN
cana-6328	46	28	which	which	PRON
cana-6328	46	29	satisfies	satisfy	VERB
cana-6328	46	30	f	f	PROPN
cana-6328	46	31	*	*	PUNCT
cana-6328	46	32	fq=	fq=	NOUN
cana-6328	47	1	i	i	PRON
cana-6328	47	2	(	(	PUNCT
cana-6328	47	3	modulo	modulo	PROPN
cana-6328	47	4	q	q	X
cana-6328	47	5	)	)	PUNCT
cana-6328	47	6	and	and	CCONJ
cana-6328	47	7	f	f	PROPN
cana-6328	47	8	*	*	PUNCT
cana-6328	47	9	fp=	fp=	PROPN
cana-6328	47	10	i	i	PRON
cana-6328	47	11	(	(	PUNCT
cana-6328	47	12	modulo	modulo	PROPN
cana-6328	47	13	p	p	X
cana-6328	47	14	)	)	PUNCT
cana-6328	47	15	.	.	PUNCT
cana-6328	48	1	bob	bob	PROPN
cana-6328	48	2	then	then	ADV
cana-6328	48	3	ensures	ensure	VERB
cana-6328	48	4	the	the	DET
cana-6328	48	5	existence	existence	NOUN
cana-6328	48	6	of	of	ADP
cana-6328	48	7	inverse	inverse	NOUN
cana-6328	48	8	of	of	ADP
cana-6328	48	9	matrix	matrix	NOUN
cana-6328	48	10	f	f	NOUN
cana-6328	48	11	by	by	ADP
cana-6328	48	12	checking	check	VERB
cana-6328	48	13	f	f	PROPN
cana-6328	48	14	is	be	AUX
cana-6328	48	15	nonsingular	nonsingular	ADJ
cana-6328	48	16	and	and	CCONJ
cana-6328	48	17	f	f	PROPN
cana-6328	48	18	is	be	AUX
cana-6328	48	19	invertible	invertible	ADJ
cana-6328	48	20	mod	mod	PROPN
cana-6328	48	21	p	p	PROPN
cana-6328	48	22	(	(	PUNCT
cana-6328	48	23	mod	mod	PROPN
cana-6328	48	24	p	p	X
cana-6328	48	25	ntru	ntru	ADJ
cana-6328	48	26	cryptosystem	cryptosystem	NOUN
cana-6328	48	27	with	with	ADP
cana-6328	48	28	companion	companion	NOUN
cana-6328	48	29	matrix	matrix	NOUN
cana-6328	48	30	36=	36=	NUM
cana-6328	48	31	0	0	NUM
cana-6328	48	32	)	)	PUNCT
cana-6328	48	33	.	.	PUNCT
cana-6328	49	1	otherwise	otherwise	ADV
cana-6328	49	2	he	he	PRON
cana-6328	49	3	needs	need	VERB
cana-6328	49	4	to	to	PART
cana-6328	49	5	go	go	VERB
cana-6328	49	6	back	back	ADV
cana-6328	49	7	and	and	CCONJ
cana-6328	49	8	choose	choose	VERB
cana-6328	49	9	another	another	DET
cana-6328	49	10	matrix	matrix	NOUN
cana-6328	49	11	f.	f.	PROPN
cana-6328	49	12	now	now	ADV
cana-6328	49	13	bob	bob	PROPN
cana-6328	49	14	computes	compute	VERB
cana-6328	49	15	the	the	DET
cana-6328	49	16	product	product	NOUN
cana-6328	49	17	h	h	NOUN
cana-6328	49	18	=	=	SYM
cana-6328	49	19	p*fq*g	p*fq*g	PROPN
cana-6328	49	20	(	(	PUNCT
cana-6328	49	21	modulo	modulo	PROPN
cana-6328	49	22	q	q	NOUN
cana-6328	49	23	)	)	PUNCT
cana-6328	49	24	.	.	PUNCT
cana-6328	50	1	bob	bob	PROPN
cana-6328	50	2	's	's	PART
cana-6328	50	3	private	private	ADJ
cana-6328	50	4	key	key	NOUN
cana-6328	50	5	become	become	VERB
cana-6328	50	6	the	the	DET
cana-6328	50	7	pair	pair	NOUN
cana-6328	50	8	of	of	ADP
cana-6328	50	9	matrices	matrix	NOUN
cana-6328	50	10	f	f	PROPN
cana-6328	50	11	and	and	CCONJ
cana-6328	50	12	fp	fp	PROPN
cana-6328	50	13	and	and	CCONJ
cana-6328	50	14	his	his	PRON
cana-6328	50	15	public	public	ADJ
cana-6328	50	16	key	key	NOUN
cana-6328	50	17	is	be	AUX
cana-6328	50	18	the	the	DET
cana-6328	50	19	matrix	matrix	NOUN
cana-6328	50	20	h.	h.	NOUN
cana-6328	50	21	2.2	2.2	NUM
cana-6328	50	22	encryption	encryption	NOUN
cana-6328	50	23	sender	sender	NOUN
cana-6328	50	24	wants	want	VERB
cana-6328	50	25	to	to	PART
cana-6328	50	26	send	send	VERB
cana-6328	50	27	a	a	DET
cana-6328	50	28	message	message	NOUN
cana-6328	50	29	to	to	ADP
cana-6328	50	30	bob	bob	NOUN
cana-6328	50	31	using	use	VERB
cana-6328	50	32	bob	bob	PROPN
cana-6328	50	33	's	's	PART
cana-6328	50	34	public	public	ADJ
cana-6328	50	35	key	key	ADJ
cana-6328	50	36	h.	h.	NOUN
cana-6328	50	37	for	for	ADP
cana-6328	50	38	this	this	PRON
cana-6328	50	39	she	she	PRON
cana-6328	50	40	first	first	ADV
cana-6328	50	41	put	put	VERB
cana-6328	50	42	her	her	PRON
cana-6328	50	43	message	message	NOUN
cana-6328	50	44	in	in	ADP
cana-6328	50	45	the	the	DET
cana-6328	50	46	form	form	NOUN
cana-6328	50	47	of	of	ADP
cana-6328	50	48	binary	binary	ADJ
cana-6328	50	49	matrix	matrix	NOUN
cana-6328	50	50	m	m	PROPN
cana-6328	50	51	,	,	PUNCT
cana-6328	50	52	(	(	PUNCT
cana-6328	50	53	which	which	PRON
cana-6328	50	54	is	be	AUX
cana-6328	50	55	a	a	DET
cana-6328	50	56	matrix	matrix	NOUN
cana-6328	50	57	of	of	ADP
cana-6328	50	58	same	same	ADJ
cana-6328	50	59	order	order	NOUN
cana-6328	50	60	as	as	ADP
cana-6328	50	61	f	f	PROPN
cana-6328	50	62	and	and	CCONJ
cana-6328	50	63	g	g	NOUN
cana-6328	50	64	)	)	PUNCT
cana-6328	50	65	and	and	CCONJ
cana-6328	50	66	whose	whose	DET
cana-6328	50	67	elements	element	NOUN
cana-6328	50	68	are	be	AUX
cana-6328	50	69	chosen	choose	VERB
cana-6328	50	70	with	with	ADP
cana-6328	50	71	modulo	modulo	PROPN
cana-6328	50	72	p.	p.	NOUN
cana-6328	50	73	next	next	ADV
cana-6328	50	74	,	,	PUNCT
cana-6328	50	75	she	she	PRON
cana-6328	50	76	randomly	randomly	ADV
cana-6328	50	77	chooses	choose	VERB
cana-6328	50	78	another	another	DET
cana-6328	50	79	matrix	matrix	NOUN
cana-6328	50	80	r	r	NOUN
cana-6328	50	81	of	of	ADP
cana-6328	50	82	the	the	DET
cana-6328	50	83	same	same	ADJ
cana-6328	50	84	order	order	NOUN
cana-6328	50	85	as	as	SCONJ
cana-6328	50	86	f.	f.	PROPN
cana-6328	50	87	this	this	PRON
cana-6328	50	88	and	and	CCONJ
cana-6328	50	89	its	its	PRON
cana-6328	50	90	size	size	NOUN
cana-6328	50	91	is	be	AUX
cana-6328	50	92	same	same	ADJ
cana-6328	50	93	as	as	ADP
cana-6328	50	94	private	private	ADJ
cana-6328	50	95	key	key	ADJ
cana-6328	50	96	f	f	PROPN
cana-6328	50	97	and	and	CCONJ
cana-6328	50	98	g.	g.	PROPN
cana-6328	50	99	to	to	PART
cana-6328	50	100	create	create	VERB
cana-6328	50	101	a	a	DET
cana-6328	50	102	encrypted	encrypt	VERB
cana-6328	50	103	message	message	NOUN
cana-6328	50	104	she	she	PRON
cana-6328	50	105	then	then	ADV
cana-6328	50	106	chooses	choose	VERB
cana-6328	50	107	a	a	DET
cana-6328	50	108	random	random	ADJ
cana-6328	50	109	matrix	matrix	NOUN
cana-6328	50	110	r	r	NOUN
cana-6328	50	111	of	of	ADP
cana-6328	50	112	size	size	NOUN
cana-6328	50	113	f	f	PROPN
cana-6328	50	114	and	and	CCONJ
cana-6328	50	115	g.	g.	PROPN
cana-6328	50	116	this	this	DET
cana-6328	50	117	matrix	matrix	NOUN
cana-6328	50	118	is	be	AUX
cana-6328	50	119	based	base	VERB
cana-6328	50	120	on	on	ADP
cana-6328	50	121	blind	blind	ADJ
cana-6328	50	122	value	value	NOUN
cana-6328	50	123	,	,	PUNCT
cana-6328	50	124	which	which	PRON
cana-6328	50	125	is	be	AUX
cana-6328	50	126	used	use	VERB
cana-6328	50	127	to	to	PART
cana-6328	50	128	obscure	obscure	VERB
cana-6328	50	129	the	the	DET
cana-6328	50	130	message	message	NOUN
cana-6328	50	131	(	(	PUNCT
cana-6328	50	132	similar	similar	ADJ
cana-6328	50	133	to	to	ADP
cana-6328	50	134	the	the	DET
cana-6328	50	135	elgamal	elgamal	ADJ
cana-6328	50	136	algorithm	algorithm	NOUN
cana-6328	50	137	which	which	PRON
cana-6328	50	138	uses	use	VERB
cana-6328	50	139	a	a	DET
cana-6328	50	140	onetime	onetime	ADJ
cana-6328	50	141	random	random	ADJ
cana-6328	50	142	value	value	NOUN
cana-6328	50	143	when	when	SCONJ
cana-6328	50	144	encrypting).to	encrypting).to	NOUN
cana-6328	50	145	send	send	VERB
cana-6328	50	146	message	message	NOUN
cana-6328	50	147	m	m	PROPN
cana-6328	50	148	,	,	PUNCT
cana-6328	50	149	alice	alice	PROPN
cana-6328	50	150	chooses	choose	VERB
cana-6328	50	151	a	a	DET
cana-6328	50	152	random	random	ADJ
cana-6328	50	153	matrix	matrix	NOUN
cana-6328	50	154	r	r	NOUN
cana-6328	50	155	(	(	PUNCT
cana-6328	50	156	which	which	PRON
cana-6328	50	157	is	be	AUX
cana-6328	50	158	of	of	ADP
cana-6328	50	159	same	same	ADJ
cana-6328	50	160	order	order	NOUN
cana-6328	50	161	as	as	ADP
cana-6328	50	162	matrix	matrix	NOUN
cana-6328	50	163	x	x	NOUN
cana-6328	50	164	)	)	PUNCT
cana-6328	50	165	,	,	PUNCT
cana-6328	50	166	and	and	CCONJ
cana-6328	50	167	bob	bob	PROPN
cana-6328	50	168	's	's	PART
cana-6328	50	169	public	public	ADJ
cana-6328	50	170	key	key	ADJ
cana-6328	50	171	h	h	NOUN
cana-6328	50	172	to	to	PART
cana-6328	50	173	compute	compute	VERB
cana-6328	50	174	the	the	DET
cana-6328	50	175	matrix	matrix	NOUN
cana-6328	50	176	.	.	PUNCT
cana-6328	51	1	e	e	X
cana-6328	52	1	=	=	PUNCT
cana-6328	53	1	r	r	NOUN
cana-6328	53	2	*	*	PUNCT
cana-6328	53	3	h	h	NOUN
cana-6328	54	1	+	+	NOUN
cana-6328	54	2	m	m	PROPN
cana-6328	54	3	(	(	PUNCT
cana-6328	54	4	modulo	modulo	PROPN
cana-6328	54	5	q	q	NOUN
cana-6328	54	6	)	)	PUNCT
cana-6328	54	7	.	.	PUNCT
cana-6328	55	1	the	the	DET
cana-6328	55	2	matrix	matrix	NOUN
cana-6328	55	3	e	e	NOUN
cana-6328	55	4	is	be	AUX
cana-6328	55	5	the	the	DET
cana-6328	55	6	encrypted	encrypt	VERB
cana-6328	55	7	message	message	NOUN
cana-6328	55	8	which	which	PRON
cana-6328	55	9	alice	alice	PROPN
cana-6328	55	10	sends	send	VERB
cana-6328	55	11	to	to	ADP
cana-6328	55	12	bob	bob	PROPN
cana-6328	55	13	.	.	PROPN
cana-6328	56	1	2.3	2.3	NUM
cana-6328	56	2	decryption	decryption	NOUN
cana-6328	56	3	bob	bob	PROPN
cana-6328	56	4	has	have	AUX
cana-6328	56	5	received	receive	VERB
cana-6328	56	6	alice	alice	PROPN
cana-6328	56	7	's	's	PART
cana-6328	56	8	encrypted	encrypt	VERB
cana-6328	56	9	message	message	NOUN
cana-6328	56	10	e	e	NOUN
cana-6328	56	11	and	and	CCONJ
cana-6328	56	12	thus	thus	ADV
cana-6328	56	13	he	he	PRON
cana-6328	56	14	can	can	AUX
cana-6328	56	15	decrypt	decrypt	VERB
cana-6328	56	16	it	it	PRON
cana-6328	56	17	.	.	PUNCT
cana-6328	57	1	he	he	PRON
cana-6328	57	2	begins	begin	VERB
cana-6328	57	3	to	to	PART
cana-6328	57	4	decrypt	decrypt	VERB
cana-6328	57	5	the	the	DET
cana-6328	57	6	encrypted	encrypt	VERB
cana-6328	57	7	message	message	NOUN
cana-6328	57	8	by	by	ADP
cana-6328	57	9	using	use	VERB
cana-6328	57	10	his	his	PRON
cana-6328	57	11	private	private	ADJ
cana-6328	57	12	matrix	matrix	NOUN
cana-6328	57	13	f	f	X
cana-6328	57	14	to	to	PART
cana-6328	57	15	compute	compute	VERB
cana-6328	57	16	the	the	DET
cana-6328	57	17	matrix	matrix	NOUN
cana-6328	57	18	.	.	PUNCT
cana-6328	58	1	a	a	PRON
cana-6328	58	2	=	=	SYM
cana-6328	58	3	f	f	X
cana-6328	58	4	*	*	PUNCT
cana-6328	58	5	e	e	X
cana-6328	58	6	(	(	PUNCT
cana-6328	58	7	modulo	modulo	PROPN
cana-6328	58	8	q).bob	q).bob	AUX
cana-6328	58	9	next	next	ADJ
cana-6328	58	10	computes	compute	VERB
cana-6328	58	11	the	the	DET
cana-6328	58	12	matrix	matrix	NOUN
cana-6328	58	13	b	b	NOUN
cana-6328	58	14	=	=	SYM
cana-6328	58	15	a	a	DET
cana-6328	58	16	(	(	PUNCT
cana-6328	58	17	modulo	modulo	NOUN
cana-6328	58	18	p).this	p).this	DET
cana-6328	58	19	way	way	NOUN
cana-6328	58	20	he	he	PRON
cana-6328	58	21	reduces	reduce	VERB
cana-6328	58	22	each	each	PRON
cana-6328	58	23	of	of	ADP
cana-6328	58	24	the	the	DET
cana-6328	58	25	coefficients	coefficient	NOUN
cana-6328	58	26	of	of	ADP
cana-6328	58	27	a	a	DET
cana-6328	58	28	(	(	PUNCT
cana-6328	58	29	modulo	modulo	PROPN
cana-6328	58	30	p	p	X
cana-6328	58	31	)	)	PUNCT
cana-6328	58	32	.	.	PUNCT
cana-6328	59	1	finally	finally	ADV
cana-6328	59	2	bob	bob	PROPN
cana-6328	59	3	uses	use	VERB
cana-6328	59	4	his	his	PRON
cana-6328	59	5	other	other	ADJ
cana-6328	59	6	private	private	ADJ
cana-6328	59	7	matrix	matrix	NOUN
cana-6328	59	8	fp	fp	X
cana-6328	59	9	to	to	PART
cana-6328	59	10	compute	compute	VERB
cana-6328	59	11	c	c	NOUN
cana-6328	59	12	=	=	SYM
cana-6328	59	13	fp*b(modulo	fp*b(modulo	NUM
cana-6328	59	14	p	p	NOUN
cana-6328	59	15	)	)	PUNCT
cana-6328	59	16	in	in	ADP
cana-6328	59	17	order	order	NOUN
cana-6328	59	18	to	to	PART
cana-6328	59	19	get	get	VERB
cana-6328	59	20	the	the	DET
cana-6328	59	21	matrix	matrix	NOUN
cana-6328	59	22	c	c	NOUN
cana-6328	59	23	which	which	PRON
cana-6328	59	24	is	be	AUX
cana-6328	59	25	alice	alice	PROPN
cana-6328	59	26	's	's	PART
cana-6328	59	27	original	original	ADJ
cana-6328	59	28	message	message	NOUN
cana-6328	59	29	m.	m.	NOUN
cana-6328	59	30	3	3	NUM
cana-6328	59	31	.	.	PUNCT
cana-6328	59	32	proposed	propose	VERB
cana-6328	59	33	ntru	ntru	NOUN
cana-6328	59	34	with	with	ADP
cana-6328	59	35	gell	gell	NOUN
cana-6328	59	36	-	-	PUNCT
cana-6328	59	37	mann	mann	NOUN
cana-6328	59	38	matrix	matrix	NOUN
cana-6328	59	39	integration	integration	NOUN
cana-6328	59	40	the	the	DET
cana-6328	59	41	required	require	VERB
cana-6328	59	42	definition	definition	NOUN
cana-6328	59	43	and	and	CCONJ
cana-6328	59	44	ntru	ntru	ADJ
cana-6328	59	45	operation	operation	NOUN
cana-6328	59	46	for	for	ADP
cana-6328	59	47	proposed	propose	VERB
cana-6328	59	48	scheme	scheme	NOUN
cana-6328	59	49	as	as	ADP
cana-6328	59	50	below	below	ADV
cana-6328	59	51	:	:	PUNCT
cana-6328	59	52	communications	communication	NOUN
cana-6328	59	53	on	on	ADP
cana-6328	59	54	applied	apply	VERB
cana-6328	59	55	nonlinear	nonlinear	ADJ
cana-6328	59	56	analysis	analysis	NOUN
cana-6328	59	57	issn	issn	NOUN
cana-6328	59	58	:	:	PUNCT
cana-6328	59	59	1074	1074	NUM
cana-6328	59	60	-	-	PUNCT
cana-6328	59	61	133x	133x	NUM
cana-6328	59	62	vol	vol	NOUN
cana-6328	59	63	32	32	NUM
cana-6328	59	64	no	no	NOUN
cana-6328	59	65	.	.	PUNCT
cana-6328	60	1	1s	1s	NUM
cana-6328	60	2	(	(	PUNCT
cana-6328	60	3	2025	2025	NUM
cana-6328	60	4	)	)	PUNCT
cana-6328	60	5	777	777	NUM
cana-6328	60	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	60	7	3.1	3.1	NUM
cana-6328	60	8	definition	definition	NOUN
cana-6328	60	9	of	of	ADP
cana-6328	60	10	gell	gell	NOUN
cana-6328	60	11	-	-	PUNCT
cana-6328	60	12	mann	mann	NOUN
cana-6328	60	13	matrix	matrix	NOUN
cana-6328	60	14	the	the	DET
cana-6328	60	15	gell	gell	NOUN
cana-6328	60	16	-	-	PUNCT
cana-6328	60	17	mann	mann	NOUN
cana-6328	60	18	matrices	matrix	NOUN
cana-6328	60	19	,	,	PUNCT
cana-6328	60	20	developed	develop	VERB
cana-6328	60	21	by	by	ADP
cana-6328	60	22	murray	murray	PROPN
cana-6328	60	23	gell	gell	PROPN
cana-6328	60	24	-	-	PUNCT
cana-6328	60	25	mann	mann	NOUN
cana-6328	60	26	,	,	PUNCT
cana-6328	60	27	are	be	AUX
cana-6328	60	28	a	a	DET
cana-6328	60	29	set	set	NOUN
cana-6328	60	30	of	of	ADP
cana-6328	60	31	eight	eight	NUM
cana-6328	60	32	linearly	linearly	ADV
cana-6328	60	33	independent	independent	ADJ
cana-6328	60	34	3×3	3×3	NUM
cana-6328	60	35	traceless	traceless	NOUN
cana-6328	60	36	hermitian	hermitian	ADJ
cana-6328	60	37	matrices	matrix	NOUN
cana-6328	60	38	used	use	VERB
cana-6328	60	39	in	in	ADP
cana-6328	60	40	the	the	DET
cana-6328	60	41	study	study	NOUN
cana-6328	60	42	of	of	ADP
cana-6328	60	43	the	the	DET
cana-6328	60	44	strong	strong	ADJ
cana-6328	60	45	interaction	interaction	NOUN
cana-6328	60	46	in	in	ADP
cana-6328	60	47	particle	particle	NOUN
cana-6328	60	48	physics	physics	NOUN
cana-6328	60	49	.	.	PUNCT
cana-6328	61	1	they	they	PRON
cana-6328	61	2	span	span	VERB
cana-6328	61	3	the	the	DET
cana-6328	61	4	lie	lie	NOUN
cana-6328	61	5	algebra	algebra	NOUN
cana-6328	61	6	of	of	ADP
cana-6328	61	7	the	the	DET
cana-6328	61	8	su(3	su(3	PROPN
cana-6328	61	9	)	)	PUNCT
cana-6328	61	10	group	group	NOUN
cana-6328	61	11	in	in	ADP
cana-6328	61	12	the	the	DET
cana-6328	61	13	defining	define	VERB
cana-6328	61	14	representation	representation	NOUN
cana-6328	61	15	.	.	PUNCT
cana-6328	62	1	these	these	DET
cana-6328	62	2	matrices	matrix	NOUN
cana-6328	62	3	are	be	AUX
cana-6328	62	4	traceless	traceless	NOUN
cana-6328	62	5	,	,	PUNCT
cana-6328	62	6	hermitian	hermitian	ADJ
cana-6328	62	7	,	,	PUNCT
cana-6328	62	8	and	and	CCONJ
cana-6328	62	9	obey	obey	VERB
cana-6328	62	10	the	the	DET
cana-6328	62	11	extra	extra	ADJ
cana-6328	62	12	trace	trace	NOUN
cana-6328	62	13	orthonormality	orthonormality	NOUN
cana-6328	62	14	relation	relation	NOUN
cana-6328	62	15	,	,	PUNCT
cana-6328	62	16	so	so	SCONJ
cana-6328	62	17	they	they	PRON
cana-6328	62	18	can	can	AUX
cana-6328	62	19	generate	generate	VERB
cana-6328	62	20	unitary	unitary	ADJ
cana-6328	62	21	matrix	matrix	NOUN
cana-6328	62	22	group	group	NOUN
cana-6328	62	23	elements	element	NOUN
cana-6328	62	24	of	of	ADP
cana-6328	62	25	su(3	su(3	PROPN
cana-6328	62	26	)	)	PUNCT
cana-6328	62	27	through	through	ADP
cana-6328	62	28	exponentiation[1	exponentiation[1	PROPN
cana-6328	62	29	]	]	X
cana-6328	62	30	.	.	PUNCT
cana-6328	63	1	these	these	DET
cana-6328	63	2	properties	property	NOUN
cana-6328	63	3	were	be	AUX
cana-6328	63	4	chosen	choose	VERB
cana-6328	63	5	by	by	ADP
cana-6328	63	6	gell	gell	NOUN
cana-6328	63	7	-	-	PUNCT
cana-6328	63	8	mann	mann	NOUN
cana-6328	63	9	because	because	SCONJ
cana-6328	63	10	they	they	PRON
cana-6328	63	11	then	then	ADV
cana-6328	63	12	naturally	naturally	ADV
cana-6328	63	13	generalize	generalize	VERB
cana-6328	63	14	the	the	DET
cana-6328	63	15	pauli	pauli	PROPN
cana-6328	63	16	matrices	matrix	NOUN
cana-6328	63	17	for	for	ADP
cana-6328	63	18	su(2	su(2	NOUN
cana-6328	63	19	)	)	PUNCT
cana-6328	63	20	to	to	ADP
cana-6328	63	21	su(3	su(3	PROPN
cana-6328	63	22	)	)	PUNCT
cana-6328	63	23	,	,	PUNCT
cana-6328	63	24	which	which	PRON
cana-6328	63	25	formed	form	VERB
cana-6328	63	26	the	the	DET
cana-6328	63	27	basis	basis	NOUN
cana-6328	63	28	for	for	ADP
cana-6328	63	29	gell	gell	NOUN
cana-6328	63	30	-	-	PUNCT
cana-6328	63	31	mann	mann	NOUN
cana-6328	63	32	's	's	PART
cana-6328	63	33	quark	quark	NOUN
cana-6328	63	34	model[2	model[2	NOUN
cana-6328	63	35	]	]	PUNCT
cana-6328	63	36	.	.	PUNCT
cana-6328	64	1	gellmann	gellmann	PROPN
cana-6328	64	2	's	's	PART
cana-6328	64	3	generalization	generalization	NOUN
cana-6328	64	4	further	far	ADV
cana-6328	64	5	extends	extend	VERB
cana-6328	64	6	to	to	ADP
cana-6328	64	7	general	general	ADJ
cana-6328	64	8	su(n	su(n	PROPN
cana-6328	64	9	)	)	PUNCT
cana-6328	64	10	.	.	PUNCT
cana-6328	65	1	gell	gell	NOUN
cana-6328	65	2	-	-	PUNCT
cana-6328	65	3	mann	mann	NOUN
cana-6328	65	4	matrices	matrix	NOUN
cana-6328	65	5	,	,	PUNCT
cana-6328	65	6	denoted	denote	VERB
cana-6328	65	7	as	as	ADP
cana-6328	65	8	λi	λi	NOUN
cana-6328	65	9	,	,	PUNCT
cana-6328	65	10	are	be	AUX
cana-6328	65	11	the	the	DET
cana-6328	65	12	generators	generator	NOUN
cana-6328	65	13	of	of	ADP
cana-6328	65	14	the	the	DET
cana-6328	65	15	su(3	su(3	PROPN
cana-6328	65	16	)	)	PUNCT
cana-6328	65	17	lie	lie	NOUN
cana-6328	65	18	algebra	algebra	NOUN
cana-6328	65	19	and	and	CCONJ
cana-6328	65	20	are	be	AUX
cana-6328	65	21	widely	widely	ADV
cana-6328	65	22	used	use	VERB
cana-6328	65	23	in	in	ADP
cana-6328	65	24	quantum	quantum	ADJ
cana-6328	65	25	mechanics	mechanic	NOUN
cana-6328	65	26	for	for	ADP
cana-6328	65	27	their	their	PRON
cana-6328	65	28	algebraic	algebraic	ADJ
cana-6328	65	29	and	and	CCONJ
cana-6328	65	30	symmetry	symmetry	NOUN
cana-6328	65	31	properties	property	NOUN
cana-6328	65	32	.	.	PUNCT
cana-6328	66	1	their	their	PRON
cana-6328	66	2	noncommutativity	noncommutativity	NOUN
cana-6328	66	3	and	and	CCONJ
cana-6328	66	4	orthogonality	orthogonality	NOUN
cana-6328	66	5	properties	property	NOUN
cana-6328	66	6	can	can	AUX
cana-6328	66	7	be	be	AUX
cana-6328	66	8	utilized	utilize	VERB
cana-6328	66	9	to	to	PART
cana-6328	66	10	introduce	introduce	VERB
cana-6328	66	11	additional	additional	ADJ
cana-6328	66	12	mixing	mixing	NOUN
cana-6328	66	13	in	in	ADP
cana-6328	66	14	polynomial	polynomial	ADJ
cana-6328	66	15	coefficients	coefficient	NOUN
cana-6328	66	16	during	during	ADP
cana-6328	66	17	encryption	encryption	NOUN
cana-6328	66	18	and	and	CCONJ
cana-6328	66	19	key	key	ADJ
cana-6328	66	20	generation	generation	NOUN
cana-6328	66	21	.	.	PUNCT
cana-6328	67	1	example	example	NOUN
cana-6328	67	2	:	:	PUNCT
cana-6328	68	1			PROPN
cana-6328	68	2			PROPN
cana-6328	68	3			PROPN
cana-6328	68	4			PROPN
cana-6328	68	5			X
cana-6328	68	6			NOUN
cana-6328	68	7			NOUN
cana-6328	68	8			NOUN
cana-6328	68	9			NOUN
cana-6328	68	10			PROPN
cana-6328	68	11	=	=	NOUN
cana-6328	68	12	000	000	NUM
cana-6328	68	13	001	001	NUM
cana-6328	68	14	010	010	NUM
cana-6328	68	15	1	1	NUM
cana-6328	68	16			PROPN
cana-6328	69	1			PROPN
cana-6328	69	2			PROPN
cana-6328	69	3			PROPN
cana-6328	69	4			X
cana-6328	69	5			NOUN
cana-6328	69	6			NOUN
cana-6328	69	7			NOUN
cana-6328	69	8			VERB
cana-6328	69	9			NOUN
cana-6328	69	10	−	−	NOUN
cana-6328	69	11	=	=	SYM
cana-6328	69	12	000	000	NUM
cana-6328	69	13	00	00	NUM
cana-6328	69	14	00	00	NUM
cana-6328	69	15	2	2	NUM
cana-6328	70	1	i	i	PRON
cana-6328	70	2	i	i	PRON
cana-6328	70	3			VERB
cana-6328	70	4			ADJ
cana-6328	70	5			PROPN
cana-6328	70	6			PROPN
cana-6328	70	7			PROPN
cana-6328	70	8			X
cana-6328	70	9			NOUN
cana-6328	70	10			NOUN
cana-6328	70	11			NOUN
cana-6328	70	12			NOUN
cana-6328	70	13			PROPN
cana-6328	70	14	−=	−=	NUM
cana-6328	70	15	000	000	NUM
cana-6328	70	16	010	010	NUM
cana-6328	70	17	001	001	NUM
cana-6328	70	18	3	3	NUM
cana-6328	70	19			NOUN
cana-6328	71	1			NOUN
cana-6328	71	2			NOUN
cana-6328	71	3			PROPN
cana-6328	71	4			PROPN
cana-6328	71	5			X
cana-6328	71	6			NOUN
cana-6328	71	7			NOUN
cana-6328	71	8			NOUN
cana-6328	71	9			NOUN
cana-6328	71	10			NOUN
cana-6328	71	11			PROPN
cana-6328	71	12	=	=	SYM
cana-6328	71	13	0	0	NUM
cana-6328	71	14	001	001	NUM
cana-6328	71	15	000	000	NUM
cana-6328	71	16	100	100	NUM
cana-6328	71	17	4	4	NUM
cana-6328	71	18			NOUN
cana-6328	71	19			PROPN
cana-6328	72	1			PROPN
cana-6328	72	2			PROPN
cana-6328	72	3			X
cana-6328	72	4			NOUN
cana-6328	72	5			NOUN
cana-6328	72	6			NOUN
cana-6328	72	7			VERB
cana-6328	72	8			NOUN
cana-6328	72	9	−	−	NOUN
cana-6328	73	1	=	=	SYM
cana-6328	73	2	00	00	NUM
cana-6328	73	3	000	000	NUM
cana-6328	73	4	00	00	NUM
cana-6328	73	5	5	5	NUM
cana-6328	74	1	i	i	PRON
cana-6328	74	2	i	i	PRON
cana-6328	74	3			VERB
cana-6328	74	4			ADJ
cana-6328	74	5			PROPN
cana-6328	74	6			PROPN
cana-6328	74	7			PROPN
cana-6328	74	8			X
cana-6328	74	9			NOUN
cana-6328	74	10			NOUN
cana-6328	74	11			NOUN
cana-6328	74	12			VERB
cana-6328	74	13			PROPN
cana-6328	74	14	=	=	SYM
cana-6328	74	15	010	010	NUM
cana-6328	74	16	100	100	NUM
cana-6328	74	17	000	000	NUM
cana-6328	74	18	6	6	NUM
cana-6328	74	19			PROPN
cana-6328	75	1			PROPN
cana-6328	75	2			PROPN
cana-6328	75	3			PROPN
cana-6328	75	4			X
cana-6328	75	5			NOUN
cana-6328	75	6			NOUN
cana-6328	75	7			NOUN
cana-6328	75	8			NOUN
cana-6328	75	9			PROPN
cana-6328	75	10	−=	−=	NOUN
cana-6328	75	11	00	00	NUM
cana-6328	75	12	00	00	NUM
cana-6328	75	13	000	000	NUM
cana-6328	75	14	7	7	NUM
cana-6328	76	1	i	i	NOUN
cana-6328	76	2	i	i	PROPN
cana-6328	76	3	.	.	PUNCT
cana-6328	77	1	200	200	NUM
cana-6328	77	2	010	010	NUM
cana-6328	77	3	001	001	NUM
cana-6328	77	4	3	3	NUM
cana-6328	77	5	1	1	NUM
cana-6328	77	6	8	8	NUM
cana-6328	77	7			NOUN
cana-6328	77	8			PROPN
cana-6328	77	9			PROPN
cana-6328	77	10			PROPN
cana-6328	77	11			X
cana-6328	77	12			NOUN
cana-6328	77	13			NOUN
cana-6328	77	14			NOUN
cana-6328	77	15			VERB
cana-6328	77	16			PROPN
cana-6328	77	17	−	−	PROPN
cana-6328	77	18	=	=	SYM
cana-6328	77	19			X
cana-6328	77	20	trace	trace	NOUN
cana-6328	77	21	orthonormality	orthonormality	NOUN
cana-6328	77	22	an	an	DET
cana-6328	77	23	orthonormality	orthonormality	NOUN
cana-6328	77	24	typically	typically	ADV
cana-6328	77	25	implies	imply	VERB
cana-6328	77	26	a	a	DET
cana-6328	77	27	norm	norm	NOUN
cana-6328	77	28	which	which	PRON
cana-6328	77	29	has	have	VERB
cana-6328	77	30	a	a	DET
cana-6328	77	31	value	value	NOUN
cana-6328	77	32	of	of	ADP
cana-6328	77	33	unity	unity	NOUN
cana-6328	77	34	(	(	PUNCT
cana-6328	77	35	1	1	NUM
cana-6328	77	36	)	)	PUNCT
cana-6328	77	37	.	.	PUNCT
cana-6328	78	1	gell	gell	NOUN
cana-6328	78	2	-	-	PUNCT
cana-6328	78	3	mann	mann	NOUN
cana-6328	78	4	matrices	matrix	NOUN
cana-6328	78	5	,	,	PUNCT
cana-6328	78	6	however	however	ADV
cana-6328	78	7	,	,	PUNCT
cana-6328	78	8	are	be	AUX
cana-6328	78	9	normalized	normalize	VERB
cana-6328	78	10	to	to	ADP
cana-6328	78	11	a	a	DET
cana-6328	78	12	value	value	NOUN
cana-6328	78	13	of	of	ADP
cana-6328	78	14	2	2	NUM
cana-6328	78	15	.	.	PUNCT
cana-6328	79	1	thus	thus	ADV
cana-6328	79	2	,	,	PUNCT
cana-6328	79	3	the	the	DET
cana-6328	79	4	trace	trace	NOUN
cana-6328	79	5	of	of	ADP
cana-6328	79	6	the	the	DET
cana-6328	79	7	pair	pair	NOUN
cana-6328	79	8	wise	wise	ADJ
cana-6328	79	9	product	product	NOUN
cana-6328	79	10	results	result	NOUN
cana-6328	79	11	in	in	ADP
cana-6328	79	12	the	the	DET
cana-6328	79	13	ortho	ortho	PROPN
cana-6328	79	14	-	-	PUNCT
cana-6328	79	15	normalization	normalization	NOUN
cana-6328	79	16	condition	condition	NOUN
cana-6328	79	17	.	.	PUNCT
cana-6328	79	18	)	)	PUNCT
cana-6328	80	1	(	(	PUNCT
cana-6328	80	2	ijjitr	ijjitr	NOUN
cana-6328	80	3			PROPN
cana-6328	80	4	=	=	SYM
cana-6328	80	5	where	where	SCONJ
cana-6328	80	6	.ij	.ij	PROPN
cana-6328	80	7	is	be	AUX
cana-6328	80	8	the	the	DET
cana-6328	80	9	kronecker	kronecker	NOUN
cana-6328	80	10	delta	delta	NOUN
cana-6328	80	11	.	.	PUNCT
cana-6328	81	1	this	this	PRON
cana-6328	81	2	is	be	AUX
cana-6328	81	3	so	so	ADV
cana-6328	81	4	the	the	DET
cana-6328	81	5	embedded	embed	VERB
cana-6328	81	6	pauli	pauli	PROPN
cana-6328	81	7	matrices	matrix	NOUN
cana-6328	81	8	corresponding	correspond	VERB
cana-6328	81	9	to	to	ADP
cana-6328	81	10	the	the	DET
cana-6328	81	11	three	three	NUM
cana-6328	81	12	embedded	embed	VERB
cana-6328	81	13	subalgebras	subalgebra	NOUN
cana-6328	81	14	of	of	ADP
cana-6328	81	15	su(2	su(2	NOUN
cana-6328	81	16	)	)	PUNCT
cana-6328	81	17	are	be	AUX
cana-6328	81	18	conventionally	conventionally	ADV
cana-6328	81	19	normalized	normalize	VERB
cana-6328	81	20	.	.	PUNCT
cana-6328	82	1	in	in	ADP
cana-6328	82	2	this	this	DET
cana-6328	82	3	three	three	NUM
cana-6328	82	4	-	-	PUNCT
cana-6328	82	5	dimensional	dimensional	ADJ
cana-6328	82	6	matrix	matrix	NOUN
cana-6328	82	7	representation	representation	NOUN
cana-6328	82	8	,	,	PUNCT
cana-6328	82	9	the	the	DET
cana-6328	82	10	cartan	cartan	ADJ
cana-6328	82	11	subalgebra	subalgebra	NOUN
cana-6328	82	12	is	be	AUX
cana-6328	82	13	the	the	DET
cana-6328	82	14	set	set	NOUN
cana-6328	82	15	of	of	ADP
cana-6328	82	16	linear	linear	PROPN
cana-6328	82	17	combinations	combination	NOUN
cana-6328	82	18	(	(	PUNCT
cana-6328	82	19	with	with	ADP
cana-6328	82	20	real	real	ADJ
cana-6328	82	21	coefficients	coefficient	NOUN
cana-6328	82	22	)	)	PUNCT
cana-6328	82	23	of	of	ADP
cana-6328	82	24	the	the	DET
cana-6328	82	25	two	two	NUM
cana-6328	82	26	matrices	matrix	NOUN
cana-6328	82	27	λ3	λ3	PROPN
cana-6328	82	28	and	and	CCONJ
cana-6328	82	29	λ8	λ8	VERB
cana-6328	82	30	which	which	PRON
cana-6328	82	31	commute	commute	NOUN
cana-6328	82	32	with	with	ADP
cana-6328	82	33	each	each	DET
cana-6328	82	34	other	other	ADJ
cana-6328	82	35	.	.	PUNCT
cana-6328	83	1	there	there	PRON
cana-6328	83	2	are	be	VERB
cana-6328	83	3	three	three	NUM
cana-6328	83	4	significant	significant	ADJ
cana-6328	83	5	su(2	su(2	NOUN
cana-6328	83	6	)	)	PUNCT
cana-6328	83	7	sub	sub	NOUN
cana-6328	83	8	algebras	algebra	NOUN
cana-6328	83	9	:	:	PUNCT
cana-6328	83	10	•	•	PRON
cana-6328	83	11	{	{	PUNCT
cana-6328	83	12	λ1	λ1	ADJ
cana-6328	83	13	,	,	PUNCT
cana-6328	83	14	λ2	λ2	PROPN
cana-6328	83	15	,	,	PUNCT
cana-6328	83	16	λ3	λ3	PROPN
cana-6328	83	17	,	,	PUNCT
cana-6328	83	18	}	}	PUNCT
cana-6328	83	19	•	•	X
cana-6328	83	20	{	{	PUNCT
cana-6328	83	21	λ4	λ4	PROPN
cana-6328	83	22	,	,	PUNCT
cana-6328	83	23	λ5	λ5	NOUN
cana-6328	83	24	,	,	PUNCT
cana-6328	83	25	x	x	NOUN
cana-6328	83	26	}	}	PUNCT
cana-6328	83	27	•	•	PRON
cana-6328	83	28	{	{	PUNCT
cana-6328	83	29	λ6	λ6	NOUN
cana-6328	83	30	,	,	PUNCT
cana-6328	83	31	λ7	λ7	PROPN
cana-6328	83	32	,	,	PUNCT
cana-6328	83	33	y	y	PROPN
cana-6328	83	34	}	}	PUNCT
cana-6328	83	35	https://en.wikipedia.org/wiki/murray_gell-mann	https://en.wikipedia.org/wiki/murray_gell-mann	VERB
cana-6328	83	36	https://en.wikipedia.org/wiki/linear_independence	https://en.wikipedia.org/wiki/linear_independence	NOUN
cana-6328	83	37	https://en.wikipedia.org/wiki/linear_independence	https://en.wikipedia.org/wiki/linear_independence	NOUN
cana-6328	83	38	https://en.wikipedia.org/wiki/matrix_trace	https://en.wikipedia.org/wiki/matrix_trace	NOUN
cana-6328	83	39	https://en.wikipedia.org/wiki/hermitian_matrices	https://en.wikipedia.org/wiki/hermitian_matrice	NOUN
cana-6328	83	40	https://en.wikipedia.org/wiki/strong_interaction	https://en.wikipedia.org/wiki/strong_interaction	PROPN
cana-6328	83	41	https://en.wikipedia.org/wiki/strong_interaction	https://en.wikipedia.org/wiki/strong_interaction	PROPN
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cana-6328	83	43	https://en.wikipedia.org/wiki/lie_group#the_lie_algebra_associated_with_a_lie_group	https://en.wikipedia.org/wiki/lie_group#the_lie_algebra_associated_with_a_lie_group	PROPN
cana-6328	83	44	https://en.wikipedia.org/wiki/special_unitary_group#su(3	https://en.wikipedia.org/wiki/special_unitary_group#su(3	NOUN
cana-6328	83	45	)	)	PUNCT
cana-6328	84	1	https://en.wikipedia.org/wiki/traceless	https://en.wikipedia.org/wiki/traceless	ADV
cana-6328	84	2	https://en.wikipedia.org/wiki/hermitian_matrix	https://en.wikipedia.org/wiki/hermitian_matrix	NOUN
cana-6328	84	3	https://en.wikipedia.org/wiki/unitary_matrix	https://en.wikipedia.org/wiki/unitary_matrix	VERB
cana-6328	84	4	https://en.wikipedia.org/wiki/su(3	https://en.wikipedia.org/wiki/su(3	NUM
cana-6328	84	5	)	)	PUNCT
cana-6328	84	6	https://en.wikipedia.org/wiki/matrix_exponential	https://en.wikipedia.org/wiki/matrix_exponential	ADJ
cana-6328	84	7	https://en.wikipedia.org/wiki/pauli_matrices	https://en.wikipedia.org/wiki/pauli_matrice	NOUN
cana-6328	84	8	https://en.wikipedia.org/wiki/pauli_matrices	https://en.wikipedia.org/wiki/pauli_matrice	NOUN
cana-6328	84	9	https://en.wikipedia.org/wiki/su(2	https://en.wikipedia.org/wiki/su(2	NUM
cana-6328	84	10	)	)	PUNCT
cana-6328	84	11	https://en.wikipedia.org/wiki/quark_model	https://en.wikipedia.org/wiki/quark_model	NOUN
cana-6328	84	12	https://en.wikipedia.org/wiki/generalizations_of_pauli_matrices#construction	https://en.wikipedia.org/wiki/generalizations_of_pauli_matrices#construction	PROPN
cana-6328	84	13	https://en.wikipedia.org/wiki/trace_(linear_algebra	https://en.wikipedia.org/wiki/trace_(linear_algebra	PROPN
cana-6328	84	14	)	)	PUNCT
cana-6328	84	15	https://en.wikipedia.org/wiki/kronecker_delta	https://en.wikipedia.org/wiki/kronecker_delta	NOUN
cana-6328	84	16	https://en.wikipedia.org/wiki/cartan_subalgebra	https://en.wikipedia.org/wiki/cartan_subalgebra	NOUN
cana-6328	84	17	https://en.wikipedia.org/wiki/clebsch%e2%80%93gordan_coefficients_for_su(3)#standard_basis	https://en.wikipedia.org/wiki/clebsch%e2%80%93gordan_coefficients_for_su(3)#standard_basis	NOUN
cana-6328	84	18	https://en.wikipedia.org/wiki/su(2	https://en.wikipedia.org/wiki/su(2	NOUN
cana-6328	84	19	)	)	PUNCT
cana-6328	84	20	communications	communication	NOUN
cana-6328	84	21	on	on	ADP
cana-6328	84	22	applied	apply	VERB
cana-6328	84	23	nonlinear	nonlinear	ADJ
cana-6328	84	24	analysis	analysis	NOUN
cana-6328	84	25	issn	issn	NOUN
cana-6328	84	26	:	:	PUNCT
cana-6328	84	27	1074	1074	NUM
cana-6328	84	28	-	-	PUNCT
cana-6328	84	29	133x	133x	NUM
cana-6328	84	30	vol	vol	NOUN
cana-6328	84	31	32	32	NUM
cana-6328	84	32	no	no	NOUN
cana-6328	84	33	.	.	PUNCT
cana-6328	85	1	1s	1s	NUM
cana-6328	85	2	(	(	PUNCT
cana-6328	85	3	2025	2025	NUM
cana-6328	85	4	)	)	PUNCT
cana-6328	85	5	778	778	NUM
cana-6328	85	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	85	7	where	where	SCONJ
cana-6328	85	8	the	the	DET
cana-6328	85	9	x	x	X
cana-6328	85	10	and	and	CCONJ
cana-6328	85	11	y	y	PROPN
cana-6328	85	12	are	be	AUX
cana-6328	85	13	linear	linear	ADJ
cana-6328	85	14	combinations	combination	NOUN
cana-6328	85	15	of	of	ADP
cana-6328	85	16	λ3	λ3	PROPN
cana-6328	85	17	and	and	CCONJ
cana-6328	85	18	λ8	λ8	ADJ
cana-6328	85	19	.	.	PUNCT
cana-6328	86	1	the	the	DET
cana-6328	86	2	su(2	su(2	NOUN
cana-6328	86	3	)	)	PUNCT
cana-6328	86	4	casimirs	casimir	NOUN
cana-6328	86	5	of	of	ADP
cana-6328	86	6	these	these	DET
cana-6328	86	7	subalgebras	subalgebras	PROPN
cana-6328	86	8	mutually	mutually	ADV
cana-6328	86	9	commute	commute	PROPN
cana-6328	86	10	.	.	PUNCT
cana-6328	87	1	however	however	ADV
cana-6328	87	2	,	,	PUNCT
cana-6328	87	3	any	any	DET
cana-6328	87	4	unitary	unitary	ADJ
cana-6328	87	5	similarity	similarity	NOUN
cana-6328	87	6	transformation	transformation	NOUN
cana-6328	87	7	of	of	ADP
cana-6328	87	8	these	these	DET
cana-6328	87	9	subalgebras	subalgebra	NOUN
cana-6328	87	10	will	will	AUX
cana-6328	87	11	yield	yield	VERB
cana-6328	87	12	su(2	su(2	NOUN
cana-6328	87	13	)	)	PUNCT
cana-6328	87	14	subalgebras	subalgebra	NOUN
cana-6328	87	15	.	.	PUNCT
cana-6328	88	1	there	there	PRON
cana-6328	88	2	is	be	VERB
cana-6328	88	3	an	an	DET
cana-6328	88	4	uncountable	uncountable	ADJ
cana-6328	88	5	number	number	NOUN
cana-6328	88	6	of	of	ADP
cana-6328	88	7	such	such	ADJ
cana-6328	88	8	transformations	transformation	NOUN
cana-6328	88	9	.	.	PUNCT
cana-6328	89	1	casimir	casimir	PROPN
cana-6328	89	2	operators	operator	NOUN
cana-6328	89	3	and	and	CCONJ
cana-6328	89	4	invariants	invariant	VERB
cana-6328	89	5	the	the	DET
cana-6328	89	6	squared	square	VERB
cana-6328	89	7	sum	sum	NOUN
cana-6328	89	8	of	of	ADP
cana-6328	89	9	the	the	DET
cana-6328	89	10	gell	gell	NOUN
cana-6328	89	11	-	-	PUNCT
cana-6328	89	12	mann	mann	NOUN
cana-6328	89	13	matrices	matrix	NOUN
cana-6328	89	14	gives	give	VERB
cana-6328	89	15	the	the	DET
cana-6328	89	16	quadratic	quadratic	ADJ
cana-6328	89	17	casimir	casimir	NOUN
cana-6328	89	18	operator	operator	NOUN
cana-6328	89	19	,	,	PUNCT
cana-6328	89	20	a	a	DET
cana-6328	89	21	group	group	NOUN
cana-6328	89	22	invariant	invariant	NOUN
cana-6328	89	23	,	,	PUNCT
cana-6328	89	24			X
cana-6328	89	25	=	=	PUNCT
cana-6328	90	1	=	=	SYM
cana-6328	90	2	=	=	SYM
cana-6328	90	3	8	8	NUM
cana-6328	90	4	0	0	NUM
cana-6328	90	5	.	.	PUNCT
cana-6328	91	1	3	3	NUM
cana-6328	91	2	16	16	NUM
cana-6328	92	1	i	i	PRON
cana-6328	92	2	ji	ji	INTJ
cana-6328	92	3	ic	ic	PROPN
cana-6328	92	4			VERB
cana-6328	92	5	where	where	SCONJ
cana-6328	92	6	i	i	PRON
cana-6328	92	7	is	be	AUX
cana-6328	92	8	3×3	3×3	NUM
cana-6328	92	9	identity	identity	NOUN
cana-6328	92	10	matrix	matrix	NOUN
cana-6328	92	11	.	.	PUNCT
cana-6328	93	1	there	there	PRON
cana-6328	93	2	is	be	VERB
cana-6328	93	3	another	another	DET
cana-6328	93	4	,	,	PUNCT
cana-6328	93	5	independent	independent	ADJ
cana-6328	93	6	,	,	PUNCT
cana-6328	93	7	cubic	cubic	ADJ
cana-6328	93	8	casimir	casimir	NOUN
cana-6328	93	9	operator	operator	NOUN
cana-6328	93	10	,	,	PUNCT
cana-6328	93	11	as	as	ADV
cana-6328	93	12	well	well	ADV
cana-6328	93	13	.	.	PUNCT
cana-6328	94	1	3.2	3.2	NUM
cana-6328	94	2	ntru	ntru	PROPN
cana-6328	94	3	operations	operation	NOUN
cana-6328	94	4	traditional	traditional	ADJ
cana-6328	94	5	ntru	ntru	PROPN
cana-6328	94	6	’s	’s	PART
cana-6328	94	7	polynomial	polynomial	ADJ
cana-6328	94	8	structure	structure	NOUN
cana-6328	94	9	can	can	AUX
cana-6328	94	10	be	be	AUX
cana-6328	94	11	predictable	predictable	ADJ
cana-6328	94	12	,	,	PUNCT
cana-6328	94	13	allowing	allow	VERB
cana-6328	94	14	lattice	lattice	NOUN
cana-6328	94	15	reduction	reduction	NOUN
cana-6328	94	16	attacks	attack	NOUN
cana-6328	94	17	to	to	PART
cana-6328	94	18	target	target	VERB
cana-6328	94	19	weak	weak	ADJ
cana-6328	94	20	instances	instance	NOUN
cana-6328	94	21	.	.	PUNCT
cana-6328	95	1	by	by	ADP
cana-6328	95	2	integrating	integrate	VERB
cana-6328	95	3	gell	gell	NOUN
cana-6328	95	4	-	-	PUNCT
cana-6328	95	5	mann	mann	NOUN
cana-6328	95	6	matrices	matrix	NOUN
cana-6328	95	7	into	into	ADP
cana-6328	95	8	the	the	DET
cana-6328	95	9	key	key	ADJ
cana-6328	95	10	generation	generation	NOUN
cana-6328	95	11	and	and	CCONJ
cana-6328	95	12	encryption	encryption	NOUN
cana-6328	95	13	phases	phase	NOUN
cana-6328	95	14	,	,	PUNCT
cana-6328	95	15	we	we	PRON
cana-6328	95	16	induce	induce	VERB
cana-6328	95	17	additional	additional	ADJ
cana-6328	95	18	algebraic	algebraic	ADJ
cana-6328	95	19	diversity	diversity	NOUN
cana-6328	95	20	.	.	PUNCT
cana-6328	96	1	1	1	X
cana-6328	96	2	.	.	X
cana-6328	96	3	star	star	PROPN
cana-6328	96	4	multiply	multiply	NOUN
cana-6328	96	5	.	.	PUNCT
cana-6328	97	1	2	2	X
cana-6328	97	2	.	.	X
cana-6328	97	3	rand	rand	NOUN
cana-6328	97	4	poly	poly	NOUN
cana-6328	97	5	.	.	PUNCT
cana-6328	98	1	3	3	X
cana-6328	98	2	.	.	X
cana-6328	98	3	inverse	inverse	NOUN
cana-6328	98	4	poly	poly	PROPN
cana-6328	98	5	-	-	PUNCT
cana-6328	98	6	fq	fq	NOUN
cana-6328	98	7	.	.	PROPN
cana-6328	98	8	4	4	NUM
cana-6328	98	9	.	.	NOUN
cana-6328	98	10	inverse	inverse	NOUN
cana-6328	98	11	poly	poly	PROPN
cana-6328	98	12	fp	fp	PROPN
cana-6328	98	13	.	.	PROPN
cana-6328	98	14	5	5	NUM
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cana-6328	98	18	.	.	PUNCT
cana-6328	99	1	6	6	NUM
cana-6328	99	2	.	.	X
cana-6328	99	3	encode	encode	ADJ
cana-6328	99	4	.	.	PUNCT
cana-6328	100	1	7	7	X
cana-6328	100	2	.	.	X
cana-6328	100	3	decode	decode	PROPN
cana-6328	100	4	.	.	PUNCT
cana-6328	101	1	following	follow	VERB
cana-6328	101	2	the	the	DET
cana-6328	101	3	modular	modular	ADJ
cana-6328	101	4	arithmetic	arithmetic	NOUN
cana-6328	101	5	on	on	ADP
cana-6328	101	6	companion	companion	NOUN
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cana-6328	101	8	give	give	VERB
cana-6328	101	9	the	the	DET
cana-6328	101	10	key	key	ADJ
cana-6328	101	11	generation	generation	NOUN
cana-6328	101	12	,	,	PUNCT
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cana-6328	101	14	and	and	CCONJ
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cana-6328	101	21	3.3	3.3	NUM
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cana-6328	101	26	:	:	PUNCT
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cana-6328	101	30	choose	choose	VERB
cana-6328	101	31	small	small	ADJ
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cana-6328	101	33	f	f	NOUN
cana-6328	101	34	,	,	PUNCT
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cana-6328	101	36	∈	∈	PROPN
cana-6328	101	37	r	r	NOUN
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cana-6328	101	39	invertibility	invertibility	NOUN
cana-6328	101	40	modulo	modulo	NOUN
cana-6328	101	41	p	p	NOUN
cana-6328	101	42	and	and	CCONJ
cana-6328	101	43	q.	q.	PROPN
cana-6328	101	44	•	•	NUM
cana-6328	101	45	construct	construct	VERB
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cana-6328	102	3	⋅	⋅	PROPN
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cana-6328	102	7	=	=	NOUN
cana-6328	102	8	λj⋅g	λj⋅g	X
cana-6328	102	9	where	where	SCONJ
cana-6328	102	10	λi	λi	X
cana-6328	102	11	,	,	PUNCT
cana-6328	102	12	λj	λj	PROPN
cana-6328	102	13	are	be	AUX
cana-6328	102	14	selected	select	VERB
cana-6328	102	15	gell	gell	NOUN
cana-6328	102	16	-	-	PUNCT
cana-6328	102	17	mann	mann	NOUN
cana-6328	102	18	matrices	matrix	NOUN
cana-6328	102	19	,	,	PUNCT
cana-6328	102	20	operating	operate	VERB
cana-6328	102	21	on	on	ADP
cana-6328	102	22	the	the	DET
cana-6328	102	23	polynomial	polynomial	ADJ
cana-6328	102	24	coefficient	coefficient	NOUN
cana-6328	102	25	vectors	vector	NOUN
cana-6328	102	26	.	.	PUNCT
cana-6328	103	1	•	•	NUM
cana-6328	103	2	public	public	ADJ
cana-6328	103	3	key	key	NOUN
cana-6328	103	4	:	:	PUNCT
cana-6328	103	5	h	h	NOUN
cana-6328	103	6	=	=	VERB
cana-6328	103	7	p∗g∗f-1	p∗g∗f-1	NOUN
cana-6328	103	8	mod	mod	PROPN
cana-6328	103	9	 	 	SPACE
cana-6328	103	10	q.	q.	PROPN
cana-6328	103	11	•	•	NUM
cana-6328	103	12	private	private	ADJ
cana-6328	103	13	key	key	NOUN
cana-6328	103	14	:	:	PUNCT
cana-6328	103	15	f.	f.	NOUN
cana-6328	103	16	matrices	matrix	NOUN
cana-6328	103	17	f	f	PROPN
cana-6328	103	18	must	must	AUX
cana-6328	103	19	satisfy	satisfy	VERB
cana-6328	103	20	additional	additional	ADJ
cana-6328	103	21	requirement	requirement	NOUN
cana-6328	103	22	to	to	PART
cana-6328	103	23	have	have	VERB
cana-6328	103	24	inverse	inverse	NOUN
cana-6328	103	25	modulo	modulo	PROPN
cana-6328	103	26	p	p	PROPN
cana-6328	103	27	and	and	CCONJ
cana-6328	103	28	q.	q.	PROPN
cana-6328	103	29	matrices	matrix	NOUN
cana-6328	103	30	g	g	PROPN
cana-6328	103	31	and	and	CCONJ
cana-6328	103	32	c	c	PROPN
cana-6328	103	33	should	should	AUX
cana-6328	103	34	have	have	VERB
cana-6328	103	35	inverse	inverse	NOUN
cana-6328	103	36	modulo	modulo	NOUN
cana-6328	104	1	p.	p.	NOUN
cana-6328	104	2	we	we	PRON
cana-6328	104	3	denote	denote	VERB
cana-6328	104	4	these	these	DET
cana-6328	104	5	inverse	inverse	NOUN
cana-6328	104	6	by	by	ADP
cana-6328	104	7	notation	notation	PROPN
cana-6328	104	8	fp	fp	PROPN
cana-6328	104	9	,	,	PUNCT
cana-6328	104	10	fq	fq	PROPN
cana-6328	104	11	,	,	PUNCT
cana-6328	104	12	gp	gp	NOUN
cana-6328	104	13	,	,	PUNCT
cana-6328	104	14	cp	cp	X
cana-6328	104	15	respectively	respectively	ADV
cana-6328	104	16	.	.	PUNCT
cana-6328	105	1	f	f	PROPN
cana-6328	105	2			PROPN
cana-6328	105	3	fq=	fq=	NOUN
cana-6328	106	1	i	i	PRON
cana-6328	106	2	(	(	PUNCT
cana-6328	106	3	mod	mod	PROPN
cana-6328	106	4	q	q	PROPN
cana-6328	106	5	)	)	PUNCT
cana-6328	106	6	;	;	PUNCT
cana-6328	106	7	g	g	PROPN
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cana-6328	106	9	gp=	gp=	PROPN
cana-6328	107	1	i	i	PRON
cana-6328	107	2	(	(	PUNCT
cana-6328	107	3	mod	mod	PROPN
cana-6328	107	4	p	p	X
cana-6328	107	5	)	)	PUNCT
cana-6328	107	6	gq	gq	PROPN
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cana-6328	107	8	g	g	PROPN
cana-6328	107	9	=	=	PUNCT
cana-6328	107	10	i	i	PROPN
cana-6328	107	11	(	(	PUNCT
cana-6328	107	12	mod	mod	PROPN
cana-6328	107	13	q	q	NOUN
cana-6328	107	14	)	)	PUNCT
cana-6328	107	15	https://en.wikipedia.org/wiki/casimir_operator	https://en.wikipedia.org/wiki/casimir_operator	NOUN
cana-6328	107	16	https://en.wikipedia.org/wiki/clebsch%e2%80%93gordan_coefficients_for_su(3)#casimir_operators	https://en.wikipedia.org/wiki/clebsch%e2%80%93gordan_coefficients_for_su(3)#casimir_operator	NOUN
cana-6328	107	17	communications	communication	NOUN
cana-6328	107	18	on	on	ADP
cana-6328	107	19	applied	apply	VERB
cana-6328	107	20	nonlinear	nonlinear	ADJ
cana-6328	107	21	analysis	analysis	NOUN
cana-6328	107	22	issn	issn	NOUN
cana-6328	107	23	:	:	PUNCT
cana-6328	107	24	1074	1074	NUM
cana-6328	107	25	-	-	PUNCT
cana-6328	107	26	133x	133x	NUM
cana-6328	107	27	vol	vol	NOUN
cana-6328	107	28	32	32	NUM
cana-6328	107	29	no	no	NOUN
cana-6328	107	30	.	.	PUNCT
cana-6328	108	1	1s	1s	NUM
cana-6328	108	2	(	(	PUNCT
cana-6328	108	3	2025	2025	NUM
cana-6328	108	4	)	)	PUNCT
cana-6328	108	5	779	779	NUM
cana-6328	109	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	109	2	cp	cp	INTJ
cana-6328	110	1	*	*	PUNCT
cana-6328	110	2	c	c	PROPN
cana-6328	110	3	=	=	SYM
cana-6328	110	4	i	i	PROPN
cana-6328	110	5	(	(	PUNCT
cana-6328	110	6	mod	mod	PROPN
cana-6328	110	7	p	p	X
cana-6328	110	8	)	)	PUNCT
cana-6328	110	9	and	and	CCONJ
cana-6328	110	10	wq	wq	NOUN
cana-6328	110	11	*	*	PROPN
cana-6328	110	12	w	w	PROPN
cana-6328	110	13	=	=	PUNCT
cana-6328	110	14	i(mod	i(mod	PROPN
cana-6328	110	15	q	q	NOUN
cana-6328	110	16	)	)	PUNCT
cana-6328	110	17	bob	bob	PROPN
cana-6328	110	18	next	next	ADJ
cana-6328	110	19	compute	compute	NOUN
cana-6328	110	20	the	the	DET
cana-6328	110	21	companion	companion	NOUN
cana-6328	110	22	matrices	matrice	VERB
cana-6328	110	23	h	h	NOUN
cana-6328	111	1	=	=	NOUN
cana-6328	111	2	p*gq(mod	p*gq(mod	NOUN
cana-6328	111	3	q	q	NOUN
cana-6328	111	4	)	)	PUNCT
cana-6328	111	5	.	.	PUNCT
cana-6328	112	1	(	(	PUNCT
cana-6328	112	2	1	1	X
cana-6328	112	3	)	)	PUNCT
cana-6328	112	4	h	h	NOUN
cana-6328	113	1	=	=	NOUN
cana-6328	113	2	w	w	NOUN
cana-6328	113	3	*	*	PUNCT
cana-6328	113	4	fq*c(mod	fq*c(mod	PROPN
cana-6328	113	5	q	q	X
cana-6328	113	6	)	)	PUNCT
cana-6328	113	7	(	(	PUNCT
cana-6328	113	8	2	2	X
cana-6328	113	9	)	)	PUNCT
cana-6328	113	10	bob	bob	NOUN
cana-6328	113	11	publish	publish	VERB
cana-6328	113	12	the	the	DET
cana-6328	113	13	pair	pair	NOUN
cana-6328	113	14	of	of	ADP
cana-6328	113	15	matrices	matrix	NOUN
cana-6328	113	16	(	(	PUNCT
cana-6328	113	17	h	h	NOUN
cana-6328	113	18	,	,	PUNCT
cana-6328	113	19	h	h	NOUN
cana-6328	113	20	)	)	PUNCT
cana-6328	113	21	m	m	ADP
cana-6328	113	22	as	as	ADP
cana-6328	113	23	his	his	PRON
cana-6328	113	24	public	public	ADJ
cana-6328	113	25	key	key	NOUN
cana-6328	113	26	,	,	PUNCT
cana-6328	113	27	(	(	PUNCT
cana-6328	113	28	f	f	X
cana-6328	113	29	,	,	PUNCT
cana-6328	113	30	g	g	PROPN
cana-6328	113	31	,	,	PUNCT
cana-6328	113	32	c	c	NOUN
cana-6328	113	33	)	)	PUNCT
cana-6328	113	34	has	have	VERB
cana-6328	113	35	his	his	PRON
cana-6328	113	36	private	private	ADJ
cana-6328	113	37	key	key	NOUN
cana-6328	113	38	.	.	PUNCT
cana-6328	114	1	3.4	3.4	NUM
cana-6328	114	2	encryption	encryption	NOUN
cana-6328	114	3	suppose	suppose	VERB
cana-6328	114	4	alice	alice	PROPN
cana-6328	114	5	wants	want	VERB
cana-6328	114	6	to	to	PART
cana-6328	114	7	send	send	VERB
cana-6328	114	8	a	a	DET
cana-6328	114	9	message	message	NOUN
cana-6328	114	10	to	to	ADP
cana-6328	114	11	bob	bob	PROPN
cana-6328	114	12	.	.	PUNCT
cana-6328	115	1	alice	alice	PROPN
cana-6328	115	2	selects	select	VERB
cana-6328	115	3	a	a	DET
cana-6328	115	4	message	message	NOUN
cana-6328	115	5	m	m	VERB
cana-6328	115	6	from	from	ADP
cana-6328	115	7	the	the	DET
cana-6328	115	8	set	set	NOUN
cana-6328	115	9	of	of	ADP
cana-6328	115	10	plaintext	plaintext	NOUN
cana-6328	115	11	lm	lm	INTJ
cana-6328	115	12	.	.	PUNCT
cana-6328	116	1	next	next	ADV
cana-6328	116	2	,	,	PUNCT
cana-6328	116	3	alice	alice	PROPN
cana-6328	116	4	randomly	randomly	ADV
cana-6328	116	5	choose	choose	VERB
cana-6328	116	6	a	a	DET
cana-6328	116	7	matrices	matrix	NOUN
cana-6328	116	8	l	l	PROPN
cana-6328	116	9			NOUN
cana-6328	116	10	and	and	CCONJ
cana-6328	116	11	bob	bob	PROPN
cana-6328	116	12	's	's	PART
cana-6328	116	13	public	public	ADJ
cana-6328	116	14	key	key	NOUN
cana-6328	116	15	(	(	PUNCT
cana-6328	116	16	h	h	NOUN
cana-6328	116	17	,	,	PUNCT
cana-6328	116	18	h	h	NOUN
cana-6328	116	19	)	)	PUNCT
cana-6328	116	20	to	to	PART
cana-6328	116	21	compute	compute	VERB
cana-6328	116	22	,	,	PUNCT
cana-6328	116	23	for	for	ADP
cana-6328	116	24	message	message	NOUN
cana-6328	116	25	polynomial	polynomial	PROPN
cana-6328	116	26	m	m	PROPN
cana-6328	116	27	,	,	PUNCT
cana-6328	116	28	select	select	VERB
cana-6328	116	29	a	a	DET
cana-6328	116	30	random	random	ADJ
cana-6328	116	31	small	small	ADJ
cana-6328	116	32	polynomial	polynomial	PROPN
cana-6328	116	33	r.	r.	PROPN
cana-6328	116	34	compute	compute	PROPN
cana-6328	116	35	ciphertext	ciphertext	NOUN
cana-6328	116	36	:	:	PUNCT
cana-6328	116	37	c	c	X
cana-6328	116	38	=	=	ADJ
cana-6328	116	39	h∗r+m	h∗r+m	PROPN
cana-6328	116	40	mod	mod	PROPN
cana-6328	116	41	 	 	SPACE
cana-6328	116	42	q.	q.	PROPN
cana-6328	116	43	(	(	PUNCT
cana-6328	116	44	3	3	NUM
cana-6328	116	45	)	)	PUNCT
cana-6328	116	46	where	where	SCONJ
cana-6328	116	47	r	r	NOUN
cana-6328	116	48	is	be	AUX
cana-6328	116	49	premultiplied	premultiplie	VERB
cana-6328	116	50	by	by	ADP
cana-6328	116	51	a	a	DET
cana-6328	116	52	randomly	randomly	ADV
cana-6328	116	53	chosen	choose	VERB
cana-6328	116	54	gell	gell	NOUN
cana-6328	116	55	-	-	PUNCT
cana-6328	116	56	mann	mann	NOUN
cana-6328	116	57	matrix	matrix	NOUN
cana-6328	116	58	λk	λk	X
cana-6328	116	59	before	before	ADP
cana-6328	116	60	multiplication	multiplication	NOUN
cana-6328	116	61	with	with	ADP
cana-6328	116	62	h.	h.	PROPN
cana-6328	116	63	alice	alice	PROPN
cana-6328	116	64	then	then	ADV
cana-6328	116	65	transmit	transmit	VERB
cana-6328	116	66	c	c	PROPN
cana-6328	116	67	to	to	ADP
cana-6328	116	68	bob	bob	PROPN
cana-6328	116	69	.	.	PUNCT
cana-6328	117	1	a	a	DET
cana-6328	117	2	different	different	ADJ
cana-6328	117	3	random	random	ADJ
cana-6328	117	4	choice	choice	NOUN
cana-6328	117	5	of	of	ADP
cana-6328	117	6	blinding	blinding	ADJ
cana-6328	117	7	value	value	NOUN
cana-6328	117	8	is	be	AUX
cana-6328	117	9	made	make	VERB
cana-6328	117	10	for	for	ADP
cana-6328	117	11	each	each	DET
cana-6328	117	12	plaintext	plaintext	NOUN
cana-6328	117	13	m[12	m[12	PROPN
cana-6328	117	14	]	]	SYM
cana-6328	117	15	.	.	PUNCT
cana-6328	118	1	3.5	3.5	NUM
cana-6328	118	2	decryption	decryption	NOUN
cana-6328	118	3	compute	compute	NOUN
cana-6328	118	4	:	:	PUNCT
cana-6328	118	5	a	a	DET
cana-6328	118	6	=	=	ADJ
cana-6328	118	7	f∗c	f∗c	PROPN
cana-6328	118	8	mod	mod	NOUN
cana-6328	118	9	 	 	SPACE
cana-6328	118	10	q.	q.	NOUN
cana-6328	118	11	reduce	reduce	VERB
cana-6328	118	12	a	a	DET
cana-6328	118	13	modulo	modulo	NOUN
cana-6328	118	14	p	p	NOUN
cana-6328	118	15	to	to	PART
cana-6328	118	16	recover	recover	VERB
cana-6328	118	17	m.	m.	NOUN
cana-6328	118	18	to	to	PART
cana-6328	118	19	decrypt	decrypt	VERB
cana-6328	118	20	the	the	DET
cana-6328	118	21	ciphertext	ciphertext	NOUN
cana-6328	118	22	,	,	PUNCT
cana-6328	118	23	bob	bob	PROPN
cana-6328	118	24	first	first	PROPN
cana-6328	118	25	compute	compute	VERB
cana-6328	118	26	a	a	DET
cana-6328	118	27			PROPN
cana-6328	118	28	f	f	X
cana-6328	118	29	*	*	PUNCT
cana-6328	118	30	e	e	X
cana-6328	118	31	*	*	PUNCT
cana-6328	118	32	g(mod	g(mod	X
cana-6328	118	33	q	q	X
cana-6328	118	34	)	)	PUNCT
cana-6328	118	35	a	a	DET
cana-6328	118	36			PROPN
cana-6328	118	37	f	f	X
cana-6328	118	38	*	*	PUNCT
cana-6328	118	39	(	(	PUNCT
cana-6328	118	40			NOUN
cana-6328	118	41	*	*	PUNCT
cana-6328	118	42	h	h	NOUN
cana-6328	119	1	+	+	CCONJ
cana-6328	119	2	h	h	NOUN
cana-6328	119	3	*	*	NOUN
cana-6328	119	4	m	m	NOUN
cana-6328	119	5	)	)	PUNCT
cana-6328	120	1	*	*	PUNCT
cana-6328	120	2	g(mod	g(mod	PROPN
cana-6328	120	3	q	q	X
cana-6328	120	4	)	)	PUNCT
cana-6328	120	5	a	a	DET
cana-6328	120	6			PROPN
cana-6328	120	7	(	(	PUNCT
cana-6328	120	8	f*	f*	PROPN
cana-6328	120	9	*	*	PUNCT
cana-6328	121	1	h	h	NOUN
cana-6328	121	2	*	*	PUNCT
cana-6328	121	3	g	g	PROPN
cana-6328	122	1	+	+	CCONJ
cana-6328	122	2	f	f	X
cana-6328	123	1	*	*	PUNCT
cana-6328	123	2	h	h	NOUN
cana-6328	123	3	*	*	NOUN
cana-6328	123	4	m	m	VERB
cana-6328	123	5	*	*	PUNCT
cana-6328	123	6	g)(mod	g)(mod	PROPN
cana-6328	123	7	q	q	NOUN
cana-6328	123	8	)	)	PUNCT
cana-6328	123	9	a	a	DET
cana-6328	123	10			PROPN
cana-6328	123	11	(	(	PUNCT
cana-6328	123	12	f	f	NOUN
cana-6328	123	13	*	*	PUNCT
cana-6328	123	14			NOUN
cana-6328	123	15	*	*	PUNCT
cana-6328	123	16	(	(	PUNCT
cana-6328	123	17	p	p	X
cana-6328	123	18	*	*	PROPN
cana-6328	123	19	gq	gq	PROPN
cana-6328	123	20	)	)	PUNCT
cana-6328	123	21	*	*	PUNCT
cana-6328	124	1	g	g	PROPN
cana-6328	124	2	+	+	NOUN
cana-6328	124	3	f	f	X
cana-6328	124	4	*	*	PUNCT
cana-6328	124	5	(	(	PUNCT
cana-6328	124	6	w	w	PROPN
cana-6328	124	7	*	*	PUNCT
cana-6328	124	8	fq	fq	PROPN
cana-6328	124	9	*	*	PROPN
cana-6328	124	10	c	c	NOUN
cana-6328	124	11	)	)	PUNCT
cana-6328	124	12	*	*	PUNCT
cana-6328	124	13	m	m	VERB
cana-6328	124	14	*	*	PUNCT
cana-6328	124	15	g)(mod	g)(mod	PROPN
cana-6328	124	16	q	q	X
cana-6328	124	17	)	)	PUNCT
cana-6328	124	18	a	a	DET
cana-6328	124	19			PROPN
cana-6328	124	20	(	(	PUNCT
cana-6328	124	21	f	f	NOUN
cana-6328	124	22	*	*	PUNCT
cana-6328	124	23			X
cana-6328	124	24	*	*	PUNCT
cana-6328	125	1	p	p	X
cana-6328	125	2	*	*	PUNCT
cana-6328	125	3	gq*g	gq*g	X
cana-6328	125	4	+	+	ADP
cana-6328	125	5	f	f	X
cana-6328	125	6	*	*	PUNCT
cana-6328	125	7	w*fq*c	w*fq*c	PROPN
cana-6328	125	8	*	*	PUNCT
cana-6328	125	9	m*g)(mod	m*g)(mod	PROPN
cana-6328	125	10	q	q	NOUN
cana-6328	125	11	)	)	PUNCT
cana-6328	125	12	a	a	DET
cana-6328	125	13			PROPN
cana-6328	125	14	(	(	PUNCT
cana-6328	125	15	pf	pf	NOUN
cana-6328	125	16	*	*	PUNCT
cana-6328	125	17			NOUN
cana-6328	125	18	+	+	NOUN
cana-6328	125	19	w	w	NOUN
cana-6328	125	20	?	?	PUNCT
cana-6328	126	1	c	c	NOUN
cana-6328	126	2	?	?	PUNCT
cana-6328	127	1	m	m	VERB
cana-6328	127	2	?	?	PUNCT
cana-6328	128	1	g)(mod	g)(mod	INTJ
cana-6328	128	2	q	q	NOUN
cana-6328	128	3	)	)	PUNCT
cana-6328	128	4	where	where	SCONJ
cana-6328	128	5	he	he	PRON
cana-6328	128	6	choose	choose	VERB
cana-6328	128	7	the	the	DET
cana-6328	128	8	coefficients	coefficient	NOUN
cana-6328	128	9	of	of	ADP
cana-6328	128	10	the	the	DET
cana-6328	128	11	polynomial	polynomial	NOUN
cana-6328	128	12	of	of	ADP
cana-6328	128	13	the	the	DET
cana-6328	128	14	matrices	matrix	NOUN
cana-6328	129	1	a	a	PRON
cana-6328	129	2	to	to	PART
cana-6328	129	3	lie	lie	VERB
cana-6328	129	4	in	in	ADP
cana-6328	129	5	interval	interval	NOUN
cana-6328	129	6	of	of	ADP
cana-6328	129	7	-q/2	-q/2	NOUN
cana-6328	129	8	to	to	ADP
cana-6328	129	9	q/2	q/2	PROPN
cana-6328	129	10	.	.	PUNCT
cana-6328	130	1	matrices	matrix	NOUN
cana-6328	130	2			NOUN
cana-6328	130	3	,	,	PUNCT
cana-6328	130	4	g	g	PROPN
cana-6328	130	5	,	,	PUNCT
cana-6328	130	6	f	f	PROPN
cana-6328	130	7	,	,	PUNCT
cana-6328	130	8	m	m	PROPN
cana-6328	130	9	,	,	PUNCT
cana-6328	130	10	c	c	PROPN
cana-6328	130	11	and	and	CCONJ
cana-6328	130	12	w	w	PROPN
cana-6328	130	13	have	have	VERB
cana-6328	130	14	polynomial	polynomial	ADJ
cana-6328	130	15	with	with	ADP
cana-6328	130	16	small	small	ADJ
cana-6328	130	17	coefficients	coefficient	NOUN
cana-6328	130	18	and	and	CCONJ
cana-6328	130	19	p	p	NOUN
cana-6328	130	20	is	be	AUX
cana-6328	130	21	much	much	ADV
cana-6328	130	22	larger	large	ADJ
cana-6328	130	23	than	than	ADP
cana-6328	130	24	q	q	NOUN
cana-6328	130	25	[	[	X
cana-6328	130	26	11	11	NUM
cana-6328	130	27	]	]	PUNCT
cana-6328	130	28	.	.	PUNCT
cana-6328	131	1	now	now	ADV
cana-6328	131	2	bob	bob	PROPN
cana-6328	131	3	's	's	PART
cana-6328	131	4	next	next	ADJ
cana-6328	131	5	computes	compute	VERB
cana-6328	131	6	the	the	DET
cana-6328	131	7	matrices	matrix	NOUN
cana-6328	131	8	b	b	X
cana-6328	131	9			PROPN
cana-6328	131	10	a(mod	a(mod	PROPN
cana-6328	132	1	p	p	X
cana-6328	132	2	)	)	PUNCT
cana-6328	132	3	b	b	PROPN
cana-6328	132	4			PROPN
cana-6328	132	5	(	(	PUNCT
cana-6328	132	6	pf	pf	NOUN
cana-6328	132	7	*	*	PUNCT
cana-6328	132	8			NOUN
cana-6328	132	9	+	+	CCONJ
cana-6328	132	10	w	w	NOUN
cana-6328	132	11	*	*	PUNCT
cana-6328	132	12	c	c	X
cana-6328	132	13	*	*	PUNCT
cana-6328	132	14	m	m	VERB
cana-6328	132	15	*	*	PUNCT
cana-6328	132	16	g)(mod	g)(mod	PROPN
cana-6328	132	17	p	p	NOUN
cana-6328	132	18	)	)	PUNCT
cana-6328	132	19	b	b	PROPN
cana-6328	133	1			PROPN
cana-6328	133	2	pf	pf	NOUN
cana-6328	133	3	*	*	PUNCT
cana-6328	133	4			NOUN
cana-6328	133	5	(	(	PUNCT
cana-6328	133	6	mod	mod	PROPN
cana-6328	133	7	p	p	X
cana-6328	133	8	)	)	PUNCT
cana-6328	134	1	+	+	CCONJ
cana-6328	135	1	w	w	X
cana-6328	135	2	*	*	PUNCT
cana-6328	135	3	c	c	X
cana-6328	135	4	*	*	PUNCT
cana-6328	135	5	m	m	VERB
cana-6328	135	6	*	*	PUNCT
cana-6328	135	7	g(mod	g(mod	PROPN
cana-6328	135	8	p	p	NOUN
cana-6328	135	9	)	)	PUNCT
cana-6328	135	10	b	b	PROPN
cana-6328	135	11			PROPN
cana-6328	135	12	0	0	PUNCT
cana-6328	136	1	+	+	CCONJ
cana-6328	137	1	w	w	PROPN
cana-6328	137	2	*	*	PUNCT
cana-6328	137	3	c	c	X
cana-6328	137	4	*	*	PUNCT
cana-6328	137	5	m	m	VERB
cana-6328	137	6	*	*	PUNCT
cana-6328	137	7	g(mod	g(mod	PROPN
cana-6328	137	8	p	p	NOUN
cana-6328	137	9	)	)	PUNCT
cana-6328	137	10	b	b	PROPN
cana-6328	138	1			PROPN
cana-6328	138	2	w	w	PROPN
cana-6328	138	3	*	*	PUNCT
cana-6328	138	4	c	c	X
cana-6328	138	5	*	*	PUNCT
cana-6328	138	6	m	m	VERB
cana-6328	138	7	*	*	PUNCT
cana-6328	138	8	g(mod	g(mod	PROPN
cana-6328	138	9	p	p	NOUN
cana-6328	138	10	)	)	PUNCT
cana-6328	138	11	communications	communication	NOUN
cana-6328	138	12	on	on	ADP
cana-6328	138	13	applied	apply	VERB
cana-6328	138	14	nonlinear	nonlinear	ADJ
cana-6328	138	15	analysis	analysis	NOUN
cana-6328	138	16	issn	issn	NOUN
cana-6328	138	17	:	:	PUNCT
cana-6328	138	18	1074	1074	NUM
cana-6328	138	19	-	-	PUNCT
cana-6328	138	20	133x	133x	NUM
cana-6328	138	21	vol	vol	NOUN
cana-6328	138	22	32	32	NUM
cana-6328	138	23	no	no	NOUN
cana-6328	138	24	.	.	PUNCT
cana-6328	139	1	1s	1s	NUM
cana-6328	139	2	(	(	PUNCT
cana-6328	139	3	2025	2025	NUM
cana-6328	139	4	)	)	PUNCT
cana-6328	139	5	780	780	NUM
cana-6328	139	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	139	7	finally	finally	ADV
cana-6328	139	8	bob	bob	PROPN
cana-6328	139	9	uses	use	VERB
cana-6328	139	10	his	his	PRON
cana-6328	139	11	private	private	ADJ
cana-6328	139	12	matrix	matrix	NOUN
cana-6328	139	13	cp	cp	NOUN
cana-6328	139	14	,	,	PUNCT
cana-6328	139	15	gp	gp	NOUN
cana-6328	139	16	and	and	CCONJ
cana-6328	139	17	wp	wp	PROPN
cana-6328	139	18	to	to	PART
cana-6328	139	19	compute	compute	VERB
cana-6328	139	20	d	d	PROPN
cana-6328	139	21			PROPN
cana-6328	139	22	cp	cp	PROPN
cana-6328	139	23	*	*	PUNCT
cana-6328	139	24	b	b	PROPN
cana-6328	139	25	*	*	PUNCT
cana-6328	139	26	gp*wp(mod	gp*wp(mod	VERB
cana-6328	139	27	p	p	NOUN
cana-6328	139	28	)	)	PUNCT
cana-6328	139	29	(	(	PUNCT
cana-6328	139	30	4	4	X
cana-6328	139	31	)	)	PUNCT
cana-6328	139	32	the	the	DET
cana-6328	139	33	matrix	matrix	NOUN
cana-6328	140	1	d	d	NOUN
cana-6328	140	2	will	will	AUX
cana-6328	140	3	be	be	AUX
cana-6328	140	4	alice	alice	PROPN
cana-6328	140	5	's	's	PART
cana-6328	140	6	original	original	ADJ
cana-6328	140	7	message	message	NOUN
cana-6328	140	8	m.	m.	NOUN
cana-6328	140	9	3.6	3.6	NUM
cana-6328	140	10	correctness	correctness	NOUN
cana-6328	140	11	of	of	ADP
cana-6328	140	12	algorithm	algorithm	NOUN
cana-6328	140	13	theorem	theorem	VERB
cana-6328	140	14	1.the	1.the	DET
cana-6328	140	15	equation	equation	NOUN
cana-6328	141	1	d	d	NOUN
cana-6328	141	2	=	=	SYM
cana-6328	141	3	m	m	PROPN
cana-6328	141	4	(	(	PUNCT
cana-6328	141	5	mod	mod	PROPN
cana-6328	141	6	p	p	X
cana-6328	141	7	)	)	PUNCT
cana-6328	141	8	is	be	AUX
cana-6328	141	9	correct	correct	ADJ
cana-6328	141	10	.	.	PUNCT
cana-6328	142	1	proof	proof	NOUN
cana-6328	142	2	:	:	PUNCT
cana-6328	143	1	d	d	X
cana-6328	143	2			PROPN
cana-6328	143	3	cp	cp	PROPN
cana-6328	143	4	*	*	PUNCT
cana-6328	143	5	b	b	PROPN
cana-6328	143	6	*	*	PUNCT
cana-6328	143	7	gp*wp(mod	gp*wp(mod	VERB
cana-6328	143	8	p	p	NOUN
cana-6328	143	9	)	)	PUNCT
cana-6328	143	10	d	d	PROPN
cana-6328	143	11			PROPN
cana-6328	143	12	cp	cp	INTJ
cana-6328	143	13	*	*	PUNCT
cana-6328	143	14	(	(	PUNCT
cana-6328	143	15	w	w	NOUN
cana-6328	143	16	*	*	PUNCT
cana-6328	143	17	c	c	X
cana-6328	143	18	*	*	PUNCT
cana-6328	143	19	m	m	VERB
cana-6328	143	20	*	*	ADJ
cana-6328	143	21	g	g	NOUN
cana-6328	143	22	)	)	PUNCT
cana-6328	143	23	*	*	PUNCT
cana-6328	143	24	gp*wp	gp*wp	X
cana-6328	143	25	(	(	PUNCT
cana-6328	143	26	mod	mod	NOUN
cana-6328	143	27	p	p	X
cana-6328	143	28	)	)	PUNCT
cana-6328	143	29	d	d	PROPN
cana-6328	143	30			PROPN
cana-6328	143	31	(	(	PUNCT
cana-6328	143	32	cp	cp	INTJ
cana-6328	143	33	*	*	PUNCT
cana-6328	143	34	c	c	NOUN
cana-6328	143	35	*	*	PUNCT
cana-6328	143	36	m	m	VERB
cana-6328	143	37	*	*	PUNCT
cana-6328	143	38	g	g	PROPN
cana-6328	143	39	*	*	PUNCT
cana-6328	143	40	gp	gp	NOUN
cana-6328	143	41	*	*	PUNCT
cana-6328	143	42	w	w	PROPN
cana-6328	143	43	*	*	PROPN
cana-6328	143	44	wp	wp	PROPN
cana-6328	143	45	)	)	PUNCT
cana-6328	143	46	(	(	PUNCT
cana-6328	143	47	mod	mod	PROPN
cana-6328	143	48	p	p	X
cana-6328	143	49	)	)	PUNCT
cana-6328	143	50	d	d	PROPN
cana-6328	143	51			PROPN
cana-6328	143	52	m.	m.	NOUN
cana-6328	143	53	4	4	NUM
cana-6328	143	54	.	.	PUNCT
cana-6328	144	1	security	security	NOUN
cana-6328	144	2	analysis	analysis	NOUN
cana-6328	144	3	•	•	ADP
cana-6328	144	4	lattice	lattice	NOUN
cana-6328	144	5	attack	attack	NOUN
cana-6328	144	6	resistance	resistance	NOUN
cana-6328	144	7	:	:	PUNCT
cana-6328	144	8	the	the	DET
cana-6328	144	9	gell	gell	NOUN
cana-6328	144	10	-	-	PUNCT
cana-6328	144	11	mann	mann	NOUN
cana-6328	144	12	matrix	matrix	NOUN
cana-6328	144	13	integration	integration	NOUN
cana-6328	144	14	randomizes	randomize	VERB
cana-6328	144	15	the	the	DET
cana-6328	144	16	structured	structured	ADJ
cana-6328	144	17	lattice	lattice	NOUN
cana-6328	144	18	,	,	PUNCT
cana-6328	144	19	increasing	increase	VERB
cana-6328	144	20	the	the	DET
cana-6328	144	21	difficulty	difficulty	NOUN
cana-6328	144	22	of	of	ADP
cana-6328	144	23	applying	apply	VERB
cana-6328	144	24	lattice	lattice	NOUN
cana-6328	144	25	reduction	reduction	NOUN
cana-6328	144	26	methods	method	NOUN
cana-6328	144	27	like	like	ADP
cana-6328	144	28	lll	lll	PROPN
cana-6328	144	29	and	and	CCONJ
cana-6328	144	30	bkz	bkz	NOUN
cana-6328	144	31	.	.	PROPN
cana-6328	144	32	•	•	ADJ
cana-6328	144	33	quantum	quantum	NOUN
cana-6328	144	34	security	security	NOUN
cana-6328	144	35	:	:	PUNCT
cana-6328	144	36	retains	retain	VERB
cana-6328	144	37	the	the	DET
cana-6328	144	38	underlying	underlie	VERB
cana-6328	144	39	hardness	hardness	NOUN
cana-6328	144	40	of	of	ADP
cana-6328	144	41	svp	svp	NOUN
cana-6328	144	42	and	and	CCONJ
cana-6328	144	43	ring	ring	NOUN
cana-6328	144	44	-	-	PUNCT
cana-6328	144	45	lwe	lwe	PROPN
cana-6328	144	46	assumptions	assumption	NOUN
cana-6328	144	47	,	,	PUNCT
cana-6328	144	48	providing	provide	VERB
cana-6328	144	49	post	post	ADJ
cana-6328	144	50	-	-	ADJ
cana-6328	144	51	quantum	quantum	ADJ
cana-6328	144	52	security	security	NOUN
cana-6328	144	53	.	.	PUNCT
cana-6328	145	1	•	•	NUM
cana-6328	145	2	side	side	NOUN
cana-6328	145	3	-	-	PUNCT
cana-6328	145	4	channel	channel	NOUN
cana-6328	145	5	resilience	resilience	NOUN
cana-6328	145	6	:	:	PUNCT
cana-6328	145	7	the	the	DET
cana-6328	145	8	added	add	VERB
cana-6328	145	9	randomness	randomness	NOUN
cana-6328	145	10	complicates	complicate	VERB
cana-6328	145	11	timing	timing	NOUN
cana-6328	145	12	and	and	CCONJ
cana-6328	145	13	power	power	NOUN
cana-6328	145	14	analysis	analysis	NOUN
cana-6328	145	15	attacks	attack	NOUN
cana-6328	145	16	due	due	ADP
cana-6328	145	17	to	to	ADP
cana-6328	145	18	unpredictable	unpredictable	ADJ
cana-6328	145	19	coefficient	coefficient	NOUN
cana-6328	145	20	manipulations	manipulation	NOUN
cana-6328	145	21	.	.	PUNCT
cana-6328	146	1	5	5	X
cana-6328	146	2	.	.	X
cana-6328	146	3	conclusion	conclusion	NOUN
cana-6328	146	4	this	this	DET
cana-6328	146	5	paper	paper	NOUN
cana-6328	146	6	propose	propose	VERB
cana-6328	146	7	a	a	DET
cana-6328	146	8	method	method	NOUN
cana-6328	146	9	,	,	PUNCT
cana-6328	146	10	which	which	PRON
cana-6328	146	11	is	be	AUX
cana-6328	146	12	suitable	suitable	ADJ
cana-6328	146	13	to	to	PART
cana-6328	146	14	send	send	VERB
cana-6328	146	15	large	large	ADJ
cana-6328	146	16	messages	message	NOUN
cana-6328	146	17	in	in	ADP
cana-6328	146	18	the	the	DET
cana-6328	146	19	form	form	NOUN
cana-6328	146	20	of	of	ADP
cana-6328	146	21	gell	gell	NOUN
cana-6328	146	22	maan	maan	PROPN
cana-6328	146	23	matrix	matrix	NOUN
cana-6328	146	24	and	and	CCONJ
cana-6328	146	25	this	this	DET
cana-6328	146	26	method	method	NOUN
cana-6328	146	27	is	be	AUX
cana-6328	146	28	more	more	ADV
cana-6328	146	29	secure	secure	ADJ
cana-6328	146	30	,	,	PUNCT
cana-6328	146	31	since	since	SCONJ
cana-6328	146	32	gell	gell	NOUN
cana-6328	146	33	maan	maan	PROPN
cana-6328	146	34	matrix	matrix	NOUN
cana-6328	146	35	is	be	AUX
cana-6328	146	36	easy	easy	ADJ
cana-6328	146	37	calculate	calculate	NOUN
cana-6328	146	38	for	for	ADP
cana-6328	146	39	large	large	ADJ
cana-6328	146	40	degree	degree	NOUN
cana-6328	146	41	of	of	ADP
cana-6328	146	42	polynomial	polynomial	ADJ
cana-6328	146	43	.	.	PUNCT
cana-6328	147	1	this	this	DET
cana-6328	147	2	method	method	NOUN
cana-6328	147	3	is	be	AUX
cana-6328	147	4	more	more	ADV
cana-6328	147	5	efficient	efficient	ADJ
cana-6328	147	6	and	and	CCONJ
cana-6328	147	7	more	more	ADV
cana-6328	147	8	secure	secure	ADJ
cana-6328	147	9	as	as	SCONJ
cana-6328	147	10	compare	compare	NOUN
cana-6328	147	11	to	to	ADP
cana-6328	147	12	the	the	DET
cana-6328	147	13	nayak	nayak	PROPN
cana-6328	147	14	et	et	PROPN
cana-6328	147	15	al	al	PROPN
cana-6328	148	1	[	[	X
cana-6328	148	2	8	8	NUM
cana-6328	148	3	]	]	PUNCT
cana-6328	148	4	.	.	PUNCT
cana-6328	149	1	this	this	DET
cana-6328	149	2	paper	paper	NOUN
cana-6328	149	3	also	also	ADV
cana-6328	149	4	introduces	introduce	VERB
cana-6328	149	5	a	a	DET
cana-6328	149	6	new	new	ADJ
cana-6328	149	7	variant	variant	NOUN
cana-6328	149	8	of	of	ADP
cana-6328	149	9	ntru	ntru	NOUN
cana-6328	149	10	by	by	ADP
cana-6328	149	11	integrating	integrate	VERB
cana-6328	149	12	gellmann	gellmann	ADJ
cana-6328	149	13	matrices	matrix	NOUN
cana-6328	149	14	to	to	PART
cana-6328	149	15	enhance	enhance	VERB
cana-6328	149	16	algebraic	algebraic	ADJ
cana-6328	149	17	randomness	randomness	NOUN
cana-6328	149	18	,	,	PUNCT
cana-6328	149	19	improving	improve	VERB
cana-6328	149	20	resistance	resistance	NOUN
cana-6328	149	21	against	against	ADP
cana-6328	149	22	advanced	advanced	ADJ
cana-6328	149	23	lattice	lattice	NOUN
cana-6328	149	24	attacks	attack	NOUN
cana-6328	149	25	while	while	SCONJ
cana-6328	149	26	preserving	preserve	VERB
cana-6328	149	27	the	the	DET
cana-6328	149	28	lightweight	lightweight	ADJ
cana-6328	149	29	nature	nature	NOUN
cana-6328	149	30	of	of	ADP
cana-6328	149	31	the	the	DET
cana-6328	149	32	ntru	ntru	ADJ
cana-6328	149	33	cryptosystem	cryptosystem	NOUN
cana-6328	149	34	.	.	PUNCT
cana-6328	150	1	this	this	DET
cana-6328	150	2	method	method	NOUN
cana-6328	150	3	contributes	contribute	VERB
cana-6328	150	4	towards	towards	ADP
cana-6328	150	5	practical	practical	ADJ
cana-6328	150	6	post	post	ADJ
cana-6328	150	7	-	-	ADJ
cana-6328	150	8	quantum	quantum	ADJ
cana-6328	150	9	cryptography	cryptography	NOUN
cana-6328	150	10	in	in	ADP
cana-6328	150	11	low	low	ADJ
cana-6328	150	12	-	-	PUNCT
cana-6328	150	13	resource	resource	NOUN
cana-6328	150	14	environments	environment	NOUN
cana-6328	150	15	.	.	PUNCT
cana-6328	151	1	references	reference	NOUN
cana-6328	151	2	[	[	X
cana-6328	151	3	1	1	NUM
cana-6328	151	4	]	]	PUNCT
cana-6328	151	5	brassard	brassard	PROPN
cana-6328	151	6	g.	g.	PROPN
cana-6328	151	7	and	and	CCONJ
cana-6328	151	8	bratley	bratley	PROPN
cana-6328	151	9	p.	p.	NOUN
cana-6328	151	10	“	"	PUNCT
cana-6328	151	11	fundamentals	fundamental	NOUN
cana-6328	151	12	of	of	ADP
cana-6328	151	13	algorithm	algorithm	NOUN
cana-6328	151	14	"	"	PUNCT
cana-6328	151	15	,	,	PUNCT
cana-6328	151	16	phi	phi	NOUN
cana-6328	151	17	,	,	PUNCT
cana-6328	151	18	1996	1996	NUM
cana-6328	151	19	.	.	PUNCT
cana-6328	152	1	[	[	X
cana-6328	152	2	2	2	NUM
cana-6328	152	3	]	]	X
cana-6328	152	4	cohen	cohen	PROPN
cana-6328	152	5	h.	h.	PROPN
cana-6328	152	6	,	,	PUNCT
cana-6328	152	7	“	"	PUNCT
cana-6328	152	8	a	a	DET
cana-6328	152	9	course	course	NOUN
cana-6328	152	10	in	in	ADP
cana-6328	152	11	computational	computational	ADJ
cana-6328	152	12	algebraic	algebraic	ADJ
cana-6328	152	13	number	number	NOUN
cana-6328	152	14	theory	theory	NOUN
cana-6328	152	15	"	"	PUNCT
cana-6328	152	16	,	,	PUNCT
cana-6328	152	17	springer	springer	NOUN
cana-6328	152	18	-	-	PUNCT
cana-6328	152	19	verlag	verlag	PROPN
cana-6328	152	20	,	,	PUNCT
cana-6328	152	21	berlin	berlin	PROPN
cana-6328	152	22	,	,	PUNCT
cana-6328	152	23	1993	1993	NUM
cana-6328	152	24	.	.	PUNCT
cana-6328	153	1	[	[	X
cana-6328	153	2	3	3	X
cana-6328	153	3	]	]	X
cana-6328	153	4	coppersmith	coppersmith	NOUN
cana-6328	153	5	and	and	CCONJ
cana-6328	153	6	a.	a.	NOUN
cana-6328	153	7	shamir	shamir	PROPN
cana-6328	153	8	,	,	PUNCT
cana-6328	153	9	”	"	PUNCT
cana-6328	153	10	lattice	lattice	NOUN
cana-6328	153	11	attacks	attack	NOUN
cana-6328	153	12	on	on	ADP
cana-6328	153	13	ntru	ntru	PROPN
cana-6328	153	14	,	,	PUNCT
cana-6328	153	15	in	in	ADP
cana-6328	153	16	proc	proc	NOUN
cana-6328	153	17	.	.	PUNCT
cana-6328	153	18	of	of	ADP
cana-6328	153	19	eurocrypt	eurocrypt	PROPN
cana-6328	153	20	97	97	NUM
cana-6328	153	21	"	"	PUNCT
cana-6328	153	22	,	,	PUNCT
cana-6328	153	23	lecture	lecture	NOUN
cana-6328	153	24	notes	note	NOUN
cana-6328	153	25	in	in	ADP
cana-6328	153	26	computer	computer	NOUN
cana-6328	153	27	science	science	NOUN
cana-6328	153	28	,	,	PUNCT
cana-6328	153	29	springer	springer	NOUN
cana-6328	153	30	-	-	PUNCT
cana-6328	153	31	verlag,1997	verlag,1997	NOUN
cana-6328	153	32	.	.	PUNCT
cana-6328	154	1	[	[	X
cana-6328	154	2	4	4	X
cana-6328	154	3	]	]	PUNCT
cana-6328	154	4	hoffstein	hoffstein	PROPN
cana-6328	154	5	j.	j.	PROPN
cana-6328	154	6	,	,	PUNCT
cana-6328	154	7	pipher	pipher	PROPN
cana-6328	154	8	j.	j.	PROPN
cana-6328	154	9	and	and	CCONJ
cana-6328	154	10	silverman	silverman	PROPN
cana-6328	154	11	j.h	j.h	PROPN
cana-6328	154	12	.	.	PROPN
cana-6328	154	13	,	,	PUNCT
cana-6328	154	14	silverman	silverman	NOUN
cana-6328	154	15	"	"	PUNCT
cana-6328	154	16	invertibility	invertibility	NOUN
cana-6328	154	17	in	in	ADP
cana-6328	154	18	truncated	truncated	ADJ
cana-6328	154	19	polynomial	polynomial	ADJ
cana-6328	154	20	rings	ring	NOUN
cana-6328	154	21	"	"	PUNCT
cana-6328	154	22	,	,	PUNCT
cana-6328	154	23	ntru	ntru	ADJ
cana-6328	154	24	cryptosystems	cryptosystem	NOUN
cana-6328	154	25	,	,	PUNCT
cana-6328	154	26	technical	technical	ADJ
cana-6328	154	27	report	report	NOUN
cana-6328	154	28	no.9	no.9	PROPN
cana-6328	154	29	.	.	PUNCT
cana-6328	154	30	available	available	ADJ
cana-6328	154	31	at	at	ADP
cana-6328	154	32	http://www.ntru.com	http://www.ntru.com	PROPN
cana-6328	154	33	,	,	PUNCT
cana-6328	154	34	(	(	PUNCT
cana-6328	154	35	1998	1998	NUM
cana-6328	154	36	)	)	PUNCT
cana-6328	154	37	.	.	PUNCT
cana-6328	155	1	[	[	X
cana-6328	155	2	5	5	NUM
cana-6328	155	3	]	]	PUNCT
cana-6328	155	4	hoffstein	hoffstein	PROPN
cana-6328	155	5	j.	j.	PROPN
cana-6328	155	6	,	,	PUNCT
cana-6328	155	7	lieman	lieman	PROPN
cana-6328	155	8	d.	d.	PROPN
cana-6328	155	9	,	,	PUNCT
cana-6328	155	10	silverman	silverman	PROPN
cana-6328	155	11	j.	j.	PROPN
cana-6328	155	12	polynomial	polynomial	PROPN
cana-6328	155	13	rings	ring	NOUN
cana-6328	155	14	and	and	CCONJ
cana-6328	155	15	efficient	efficient	ADJ
cana-6328	155	16	public	public	ADJ
cana-6328	155	17	key	key	ADJ
cana-6328	155	18	authentication	authentication	NOUN
cana-6328	155	19	"	"	PUNCT
cana-6328	155	20	,	,	PUNCT
cana-6328	155	21	proceeding	proceed	VERB
cana-6328	155	22	of	of	ADP
cana-6328	155	23	the	the	DET
cana-6328	155	24	international	international	ADJ
cana-6328	155	25	workshopon	workshopon	ADV
cana-6328	155	26	cryptographic	cryptographic	ADJ
cana-6328	155	27	techniques	technique	NOUN
cana-6328	155	28	communications	communication	NOUN
cana-6328	155	29	on	on	ADP
cana-6328	155	30	applied	apply	VERB
cana-6328	155	31	nonlinear	nonlinear	ADJ
cana-6328	155	32	analysis	analysis	NOUN
cana-6328	155	33	issn	issn	NOUN
cana-6328	155	34	:	:	PUNCT
cana-6328	155	35	1074	1074	NUM
cana-6328	155	36	-	-	PUNCT
cana-6328	155	37	133x	133x	NUM
cana-6328	155	38	vol	vol	NOUN
cana-6328	155	39	32	32	NUM
cana-6328	155	40	no	no	NOUN
cana-6328	155	41	.	.	PUNCT
cana-6328	156	1	1s	1s	NUM
cana-6328	156	2	(	(	PUNCT
cana-6328	156	3	2025	2025	NUM
cana-6328	156	4	)	)	PUNCT
cana-6328	156	5	781	781	NUM
cana-6328	156	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6328	156	7	and	and	CCONJ
cana-6328	156	8	e	e	NOUN
cana-6328	156	9	-	-	NOUN
cana-6328	156	10	commerce	commerce	ADJ
cana-6328	156	11	(	(	PUNCT
cana-6328	156	12	cryptec	cryptec	ADJ
cana-6328	156	13	99	99	NUM
cana-6328	156	14	)	)	PUNCT
cana-6328	156	15	,	,	PUNCT
cana-6328	156	16	m.	m.	NOUN
cana-6328	156	17	blumand	blumand	PROPN
cana-6328	156	18	c.h.lee	c.h.lee	PROPN
cana-6328	156	19	,	,	PUNCT
cana-6328	156	20	eds	eds	PROPN
cana-6328	156	21	.	.	PROPN
cana-6328	156	22	,	,	PUNCT
cana-6328	156	23	city	city	PROPN
cana-6328	156	24	university	university	PROPN
cana-6328	156	25	of	of	ADP
cana-6328	156	26	hong	hong	PROPN
cana-6328	156	27	kong	kong	PROPN
cana-6328	156	28	press	press	PROPN
cana-6328	156	29	,	,	PUNCT
cana-6328	156	30	1999	1999	NUM
cana-6328	156	31	.	.	PUNCT
cana-6328	157	1	[	[	X
cana-6328	157	2	6	6	NUM
cana-6328	157	3	]	]	PUNCT
cana-6328	157	4	horowitz	horowitz	PROPN
cana-6328	157	5	e.	e.	PROPN
cana-6328	157	6	,	,	PUNCT
cana-6328	157	7	sahani	sahani	PROPN
cana-6328	157	8	s.	s.	PROPN
cana-6328	157	9	,	,	PUNCT
cana-6328	157	10	and	and	CCONJ
cana-6328	157	11	rajasekharan	rajasekharan	VERB
cana-6328	157	12	s.	s.	PROPN
cana-6328	157	13	“	"	PUNCT
cana-6328	157	14	fundamental	fundamental	ADJ
cana-6328	157	15	of	of	ADP
cana-6328	157	16	computer	computer	NOUN
cana-6328	157	17	algorithm	algorithm	NOUN
cana-6328	157	18	"	"	PUNCT
cana-6328	157	19	,	,	PUNCT
cana-6328	157	20	galgotia	galgotia	NOUN
cana-6328	157	21	,	,	PUNCT
cana-6328	157	22	1998	1998	NUM
cana-6328	157	23	.	.	PUNCT
cana-6328	158	1	[	[	X
cana-6328	158	2	7	7	X
cana-6328	158	3	]	]	PUNCT
cana-6328	158	4	j.	j.	PROPN
cana-6328	158	5	hoffstein	hoffstein	PROPN
cana-6328	158	6	,	,	PUNCT
cana-6328	158	7	j.	j.	PROPN
cana-6328	158	8	pipher	pipher	PROPN
cana-6328	158	9	and	and	CCONJ
cana-6328	158	10	j.	j.	PROPN
cana-6328	158	11	h.	h.	PROPN
cana-6328	158	12	silverman	silverman	PROPN
cana-6328	158	13	,	,	PUNCT
cana-6328	158	14	“	"	PUNCT
cana-6328	158	15	ntru	ntru	PROPN
cana-6328	158	16	:	:	PUNCT
cana-6328	158	17	a	a	DET
cana-6328	158	18	ring	ring	NOUN
cana-6328	158	19	-	-	PUNCT
cana-6328	158	20	based	base	VERB
cana-6328	158	21	public	public	ADJ
cana-6328	158	22	key	key	ADJ
cana-6328	158	23	cryptosystem	cryptosystem	NOUN
cana-6328	158	24	"	"	PUNCT
cana-6328	158	25	.	.	PUNCT
cana-6328	159	1	algorithmic	algorithmic	ADJ
cana-6328	159	2	number	number	NOUN
cana-6328	159	3	theory	theory	NOUN
cana-6328	159	4	(	(	PUNCT
cana-6328	159	5	ants	ants	PROPN
cana-6328	159	6	iii	iii	NUM
cana-6328	159	7	)	)	PUNCT
cana-6328	159	8	,	,	PUNCT
cana-6328	159	9	springerverlag	springerverlag	NOUN
cana-6328	159	10	,	,	PUNCT
cana-6328	159	11	1998	1998	NUM
cana-6328	159	12	,	,	PUNCT
cana-6328	159	13	pp	pp	ADV
cana-6328	159	14	.	.	PUNCT
cana-6328	160	1	267	267	NUM
cana-6328	160	2	288	288	NUM
cana-6328	160	3	.	.	PUNCT
cana-6328	161	1	[	[	X
cana-6328	161	2	8	8	NUM
cana-6328	161	3	]	]	X
cana-6328	161	4	nayak	nayak	PROPN
cana-6328	161	5	r.	r.	PROPN
cana-6328	161	6	,	,	PUNCT
cana-6328	161	7	sastry	sastry	PROPN
cana-6328	161	8	c.	c.	PROPN
cana-6328	161	9	v.	v.	PROPN
cana-6328	161	10	,	,	PUNCT
cana-6328	161	11	and	and	CCONJ
cana-6328	161	12	pradhan	pradhan	PROPN
cana-6328	161	13	j.	j.	PROPN
cana-6328	161	14	“	"	PUNCT
cana-6328	161	15	a	a	DET
cana-6328	161	16	matrix	matrix	NOUN
cana-6328	161	17	formulation	formulation	NOUN
cana-6328	161	18	for	for	ADP
cana-6328	161	19	ntru	ntru	ADJ
cana-6328	161	20	cryptosystems	cryptosystem	NOUN
cana-6328	161	21	"	"	PUNCT
cana-6328	161	22	,	,	PUNCT
cana-6328	161	23	proc	proc	NOUN
cana-6328	161	24	.	.	PUNCT
cana-6328	162	1	16th	16th	ADJ
cana-6328	162	2	ieee	ieee	PROPN
cana-6328	162	3	international	international	ADJ
cana-6328	162	4	conference	conference	NOUN
cana-6328	162	5	on	on	ADP
cana-6328	162	6	network(icon-2008	network(icon-2008	NOUN
cana-6328	162	7	)	)	PUNCT
cana-6328	162	8	,	,	PUNCT
cana-6328	162	9	new	new	PROPN
cana-6328	162	10	delhi	delhi	PROPN
cana-6328	162	11	,	,	PUNCT
cana-6328	162	12	india	india	PROPN
cana-6328	162	13	,	,	PUNCT
cana-6328	162	14	pp	pp	PROPN
cana-6328	162	15	.	.	PUNCT
cana-6328	163	1	12	12	NUM
cana-6328	163	2	-	-	SYM
cana-6328	163	3	14	14	NUM
cana-6328	163	4	,	,	PUNCT
cana-6328	163	5	2008	2008	NUM
cana-6328	163	6	.	.	PUNCT
cana-6328	164	1	[	[	X
cana-6328	164	2	9	9	NUM
cana-6328	164	3	]	]	SYM
cana-6328	164	4	peikert	peikert	NOUN
cana-6328	164	5	,	,	PUNCT
cana-6328	164	6	c.	c.	NOUN
cana-6328	164	7	(	(	PUNCT
cana-6328	164	8	2016	2016	NUM
cana-6328	164	9	)	)	PUNCT
cana-6328	164	10	.	.	PUNCT
cana-6328	165	1	a	a	DET
cana-6328	165	2	decade	decade	NOUN
cana-6328	165	3	of	of	ADP
cana-6328	165	4	lattice	lattice	ADJ
cana-6328	165	5	cryptography	cryptography	NOUN
cana-6328	165	6	.	.	PUNCT
cana-6328	166	1	foundations	foundation	NOUN
cana-6328	166	2	and	and	CCONJ
cana-6328	166	3	trends	trend	NOUN
cana-6328	166	4	®	®	NOUN
cana-6328	166	5	in	in	ADP
cana-6328	166	6	theoretical	theoretical	ADJ
cana-6328	166	7	computer	computer	NOUN
cana-6328	166	8	science	science	NOUN
cana-6328	166	9	.	.	PUNCT
cana-6328	167	1	[	[	X
cana-6328	167	2	10	10	NUM
cana-6328	167	3	]	]	X
cana-6328	168	1	roja	roja	PROPN
cana-6328	168	2	p.	p.	PROPN
cana-6328	168	3	p.	p.	PROPN
cana-6328	168	4	,	,	PUNCT
cana-6328	169	1	avadhani	avadhani	PROPN
cana-6328	169	2	p.	p.	PROPN
cana-6328	169	3	s.	s.	PROPN
cana-6328	169	4	and	and	CCONJ
cana-6328	169	5	prasand	prasand	PROPN
cana-6328	169	6	e.	e.	PROPN
cana-6328	170	1	v.	v.	PROPN
cana-6328	170	2	“	"	PUNCT
cana-6328	170	3	an	an	DET
cana-6328	170	4	efficient	efficient	ADJ
cana-6328	170	5	method	method	NOUN
cana-6328	170	6	of	of	ADP
cana-6328	170	7	shared	share	VERB
cana-6328	170	8	key	key	ADJ
cana-6328	170	9	generation	generation	NOUN
cana-6328	170	10	based	base	VERB
cana-6328	170	11	on	on	ADP
cana-6328	170	12	truncated	truncated	ADJ
cana-6328	170	13	polynomials	polynomial	NOUN
cana-6328	170	14	"	"	PUNCT
cana-6328	170	15	,	,	PUNCT
cana-6328	170	16	ijcsns	ijcsns	PROPN
cana-6328	170	17	international	international	ADJ
cana-6328	170	18	journal	journal	NOUN
cana-6328	170	19	of	of	ADP
cana-6328	170	20	computer	computer	NOUN
cana-6328	170	21	science	science	NOUN
cana-6328	170	22	and	and	CCONJ
cana-6328	170	23	network	network	NOUN
cana-6328	170	24	security	security	NOUN
cana-6328	170	25	,	,	PUNCT
cana-6328	170	26	vol.6	vol.6	PROPN
cana-6328	170	27	no	no	INTJ
cana-6328	170	28	.	.	PUNCT
cana-6328	171	1	8b	8b	NUM
cana-6328	171	2	,	,	PUNCT
cana-6328	171	3	pp	pp	ADJ
cana-6328	171	4	.	.	PUNCT
cana-6328	172	1	156	156	NUM
cana-6328	172	2	-	-	SYM
cana-6328	172	3	161	161	NUM
cana-6328	172	4	,	,	PUNCT
cana-6328	172	5	2006	2006	NUM
cana-6328	172	6	.	.	PUNCT
cana-6328	173	1	[	[	X
cana-6328	173	2	11	11	NUM
cana-6328	173	3	]	]	PUNCT
cana-6328	173	4	silverman	silverman	PROPN
cana-6328	173	5	j.	j.	PROPN
cana-6328	173	6	h.	h.	PROPN
cana-6328	173	7	,	,	PUNCT
cana-6328	173	8	“	"	PUNCT
cana-6328	173	9	ntru	ntru	PROPN
cana-6328	173	10	"	"	PUNCT
cana-6328	173	11	:	:	PUNCT
cana-6328	173	12	a	a	DET
cana-6328	173	13	ring	ring	NOUN
cana-6328	173	14	based	base	VERB
cana-6328	173	15	public	public	ADJ
cana-6328	173	16	key	key	ADJ
cana-6328	173	17	cryptosystem	cryptosystem	NOUN
cana-6328	173	18	,	,	PUNCT
cana-6328	173	19	in	in	ADP
cana-6328	173	20	proc	proc	NOUN
cana-6328	173	21	.	.	PUNCT
cana-6328	173	22	of	of	ADP
cana-6328	173	23	ants	ants	PROPN
cana-6328	173	24	iii	iii	PROPN
cana-6328	173	25	,	,	PUNCT
cana-6328	173	26	volume	volume	NOUN
cana-6328	173	27	1423	1423	NUM
cana-6328	173	28	of	of	ADP
cana-6328	173	29	lncs.springer	lncs.springer	NOUN
cana-6328	173	30	-	-	PUNCT
cana-6328	173	31	verlag	verlag	PROPN
cana-6328	173	32	,	,	PUNCT
cana-6328	173	33	available	available	ADJ
cana-6328	173	34	athttp://www.ntru.com	athttp://www.ntru.com	PROPN
cana-6328	173	35	,	,	PUNCT
cana-6328	173	36	pp	pp	ADJ
cana-6328	173	37	.	.	PUNCT
cana-6328	174	1	267288	267288	NUM
cana-6328	174	2	,	,	PUNCT
cana-6328	174	3	2001	2001	NUM
cana-6328	174	4	.	.	PUNCT
cana-6328	175	1	[	[	X
cana-6328	175	2	12	12	NUM
cana-6328	175	3	]	]	PUNCT
cana-6328	175	4	wells	wells	PROPN
cana-6328	175	5	a.	a.	PROPN
cana-6328	175	6	l.	l.	PROPN
cana-6328	175	7	,	,	PUNCT
cana-6328	175	8	“	"	PUNCT
cana-6328	175	9	a	a	DET
cana-6328	175	10	polynomial	polynomial	ADJ
cana-6328	175	11	form	form	NOUN
cana-6328	175	12	for	for	ADP
cana-6328	175	13	logarithms	logarithm	NOUN
cana-6328	175	14	modulo	modulo	VERB
cana-6328	175	15	a	a	DET
cana-6328	175	16	prime	prime	NOUN
cana-6328	175	17	"	"	PUNCT
cana-6328	175	18	,	,	PUNCT
cana-6328	175	19	ieee	ieee	NOUN
cana-6328	175	20	transactions	transaction	NOUN
cana-6328	175	21	on	on	ADP
cana-6328	175	22	information	information	NOUN
cana-6328	175	23	theory	theory	NOUN
cana-6328	175	24	,	,	PUNCT
cana-6328	175	25	pp	pp	PROPN
cana-6328	175	26	.	.	PUNCT
cana-6328	176	1	845	845	NUM
cana-6328	176	2	-	-	SYM
cana-6328	176	3	846	846	NUM
cana-6328	176	4	,	,	PUNCT
cana-6328	176	5	1984	1984	NUM
cana-6328	176	6	.	.	PUNCT
cana-6328	177	1	[	[	X
cana-6328	177	2	13	13	NUM
cana-6328	177	3	]	]	X
cana-6328	177	4	gell	gell	NOUN
cana-6328	177	5	-	-	PUNCT
cana-6328	177	6	mann	mann	NOUN
cana-6328	177	7	,	,	PUNCT
cana-6328	177	8	m.	m.	NOUN
cana-6328	177	9	(	(	PUNCT
cana-6328	177	10	1962	1962	NUM
cana-6328	177	11	)	)	PUNCT
cana-6328	177	12	.	.	PUNCT
cana-6328	178	1	symmetries	symmetry	NOUN
cana-6328	178	2	of	of	ADP
cana-6328	178	3	baryons	baryon	NOUN
cana-6328	178	4	and	and	CCONJ
cana-6328	178	5	mesons	meson	NOUN
cana-6328	178	6	.	.	PUNCT
cana-6328	179	1	physical	physical	PROPN
cana-6328	179	2	review	review	PROPN
cana-6328	179	3	,	,	PUNCT
cana-6328	179	4	125(3	125(3	NUM
cana-6328	179	5	)	)	PUNCT
cana-6328	179	6	,	,	PUNCT
cana-6328	179	7	1067–1084	1067–1084	NUM
cana-6328	179	8	.	.	PUNCT