id	sid	tid	token	lemma	pos
cana-4017	1	1	communications	communication	NOUN
cana-4017	1	2	on	on	ADP
cana-4017	1	3	applied	apply	VERB
cana-4017	1	4	nonlinear	nonlinear	ADJ
cana-4017	1	5	analysis	analysis	NOUN
cana-4017	1	6	issn	issn	NOUN
cana-4017	1	7	:	:	PUNCT
cana-4017	1	8	1074	1074	NUM
cana-4017	1	9	-	-	PUNCT
cana-4017	1	10	133x	133x	NUM
cana-4017	1	11	vol	vol	NOUN
cana-4017	1	12	32	32	NUM
cana-4017	1	13	no	no	NOUN
cana-4017	1	14	.	.	PUNCT
cana-4017	2	1	9s	9s	NUM
cana-4017	2	2	(	(	PUNCT
cana-4017	2	3	2025	2025	NUM
cana-4017	2	4	)	)	PUNCT
cana-4017	2	5	836	836	NUM
cana-4017	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4017	2	7	cryptographic	cryptographic	ADJ
cana-4017	2	8	application	application	NOUN
cana-4017	2	9	of	of	ADP
cana-4017	2	10	elliptic	elliptic	ADJ
cana-4017	2	11	curve	curve	NOUN
cana-4017	2	12	generated	generate	VERB
cana-4017	2	13	through	through	ADP
cana-4017	2	14	the	the	DET
cana-4017	2	15	formation	formation	NOUN
cana-4017	2	16	of	of	ADP
cana-4017	2	17	diophantine	diophantine	NOUN
cana-4017	2	18	triples	triple	NOUN
cana-4017	2	19	using	use	VERB
cana-4017	2	20	hex	hex	PROPN
cana-4017	2	21	numbers	number	NOUN
cana-4017	2	22	and	and	CCONJ
cana-4017	2	23	pronic	pronic	ADJ
cana-4017	2	24	numbers	number	NOUN
cana-4017	2	25	1	1	NUM
cana-4017	2	26	t.	t.	NOUN
cana-4017	2	27	anupreethi	anupreethi	PROPN
cana-4017	2	28	,	,	PUNCT
cana-4017	2	29	2vinmol	2vinmol	NUM
cana-4017	2	30	.	.	PUNCT
cana-4017	3	1	k.	k.	PROPN
cana-4017	3	2	jesudas	jesudas	PROPN
cana-4017	3	3	,	,	PUNCT
cana-4017	3	4	3manju	3manju	NUM
cana-4017	3	5	somanath	somanath	NOUN
cana-4017	3	6	,	,	PUNCT
cana-4017	3	7	4	4	NUM
cana-4017	3	8	*	*	PROPN
cana-4017	3	9	v.	v.	ADP
cana-4017	3	10	sangeetha	sangeetha	PROPN
cana-4017	3	11	,	,	PUNCT
cana-4017	3	12	5j	5j	NUM
cana-4017	3	13	.	.	PUNCT
cana-4017	4	1	kannan	kannan	PROPN
cana-4017	4	2	and	and	CCONJ
cana-4017	4	3	6p	6p	PROPN
cana-4017	4	4	.	.	PUNCT
cana-4017	5	1	vijaya	vijaya	PROPN
cana-4017	5	2	shanthi	shanthi	PROPN
cana-4017	5	3	1	1	NUM
cana-4017	5	4	ph	ph	PROPN
cana-4017	5	5	.	.	PROPN
cana-4017	5	6	d.	d.	PROPN
cana-4017	5	7	research	research	PROPN
cana-4017	5	8	scholar	scholar	NOUN
cana-4017	5	9	,	,	PUNCT
cana-4017	5	10	pg	pg	PROPN
cana-4017	5	11	and	and	CCONJ
cana-4017	5	12	research	research	PROPN
cana-4017	5	13	department	department	PROPN
cana-4017	5	14	of	of	ADP
cana-4017	5	15	mathematics	mathematics	PROPN
cana-4017	5	16	,	,	PUNCT
cana-4017	5	17	national	national	PROPN
cana-4017	5	18	college	college	PROPN
cana-4017	5	19	(	(	PUNCT
cana-4017	5	20	autonomous	autonomous	ADJ
cana-4017	5	21	,	,	PUNCT
cana-4017	5	22	affiliated	affiliate	VERB
cana-4017	5	23	to	to	PART
cana-4017	5	24	bharathidasan	bharathidasan	VERB
cana-4017	5	25	university	university	NOUN
cana-4017	5	26	)	)	PUNCT
cana-4017	5	27	,	,	PUNCT
cana-4017	5	28	trichy	trichy	NOUN
cana-4017	5	29	620	620	NUM
cana-4017	5	30	001	001	NUM
cana-4017	5	31	,	,	PUNCT
cana-4017	5	32	tamil	tamil	PROPN
cana-4017	5	33	nadu	nadu	PROPN
cana-4017	5	34	,	,	PUNCT
cana-4017	5	35	india	india	PROPN
cana-4017	5	36	.	.	PROPN
cana-4017	5	37	2	2	NUM
cana-4017	5	38	assistant	assistant	NOUN
cana-4017	5	39	professor	professor	NOUN
cana-4017	5	40	,	,	PUNCT
cana-4017	5	41	department	department	NOUN
cana-4017	5	42	of	of	ADP
cana-4017	5	43	mathematics	mathematic	NOUN
cana-4017	5	44	,	,	PUNCT
cana-4017	5	45	rajagiri	rajagiri	NOUN
cana-4017	5	46	school	school	NOUN
cana-4017	5	47	of	of	ADP
cana-4017	5	48	engineering	engineering	NOUN
cana-4017	5	49	and	and	CCONJ
cana-4017	5	50	technology	technology	NOUN
cana-4017	5	51	,	,	PUNCT
cana-4017	5	52	kerala	kerala	PROPN
cana-4017	5	53	.	.	PUNCT
cana-4017	6	1	(	(	PUNCT
cana-4017	6	2	research	research	NOUN
cana-4017	6	3	scholar	scholar	NOUN
cana-4017	6	4	,	,	PUNCT
cana-4017	6	5	pg	pg	PROPN
cana-4017	6	6	and	and	CCONJ
cana-4017	6	7	research	research	PROPN
cana-4017	6	8	department	department	PROPN
cana-4017	6	9	of	of	ADP
cana-4017	6	10	mathematics	mathematics	PROPN
cana-4017	6	11	,	,	PUNCT
cana-4017	6	12	national	national	PROPN
cana-4017	6	13	college	college	PROPN
cana-4017	6	14	(	(	PUNCT
cana-4017	6	15	autonomous	autonomous	ADJ
cana-4017	6	16	,	,	PUNCT
cana-4017	6	17	affiliated	affiliate	VERB
cana-4017	6	18	to	to	PART
cana-4017	6	19	bharathidasan	bharathidasan	VERB
cana-4017	6	20	university	university	NOUN
cana-4017	6	21	)	)	PUNCT
cana-4017	6	22	,	,	PUNCT
cana-4017	6	23	trichy	trichy	NOUN
cana-4017	6	24	620	620	NUM
cana-4017	6	25	001	001	NUM
cana-4017	6	26	,	,	PUNCT
cana-4017	6	27	tamil	tamil	PROPN
cana-4017	6	28	nadu	nadu	PROPN
cana-4017	6	29	,	,	PUNCT
cana-4017	6	30	india	india	PROPN
cana-4017	6	31	.	.	PUNCT
cana-4017	6	32	)	)	PUNCT
cana-4017	6	33	.	.	PUNCT
cana-4017	7	1	3associate	3associate	NUM
cana-4017	7	2	professor	professor	NOUN
cana-4017	7	3	,	,	PUNCT
cana-4017	7	4	pg	pg	NOUN
cana-4017	7	5	and	and	CCONJ
cana-4017	7	6	research	research	PROPN
cana-4017	7	7	department	department	PROPN
cana-4017	7	8	of	of	ADP
cana-4017	7	9	mathematics	mathematics	PROPN
cana-4017	7	10	,	,	PUNCT
cana-4017	7	11	national	national	PROPN
cana-4017	7	12	college	college	PROPN
cana-4017	7	13	(	(	PUNCT
cana-4017	7	14	autonomous	autonomous	ADJ
cana-4017	7	15	,	,	PUNCT
cana-4017	7	16	affiliated	affiliate	VERB
cana-4017	7	17	to	to	PART
cana-4017	7	18	bharathidasan	bharathidasan	VERB
cana-4017	7	19	university	university	NOUN
cana-4017	7	20	)	)	PUNCT
cana-4017	7	21	,	,	PUNCT
cana-4017	7	22	trichy	trichy	NOUN
cana-4017	7	23	620	620	NUM
cana-4017	7	24	001	001	NUM
cana-4017	7	25	,	,	PUNCT
cana-4017	7	26	tamil	tamil	PROPN
cana-4017	7	27	nadu	nadu	PROPN
cana-4017	7	28	,	,	PUNCT
cana-4017	7	29	india	india	PROPN
cana-4017	7	30	.	.	PROPN
cana-4017	7	31	4	4	NUM
cana-4017	7	32	assistant	assistant	NOUN
cana-4017	7	33	professor	professor	NOUN
cana-4017	7	34	,	,	PUNCT
cana-4017	7	35	pg	pg	NOUN
cana-4017	7	36	and	and	CCONJ
cana-4017	7	37	research	research	PROPN
cana-4017	7	38	department	department	PROPN
cana-4017	7	39	of	of	ADP
cana-4017	7	40	mathematics	mathematics	PROPN
cana-4017	7	41	,	,	PUNCT
cana-4017	7	42	national	national	PROPN
cana-4017	7	43	college	college	PROPN
cana-4017	7	44	(	(	PUNCT
cana-4017	7	45	autonomous	autonomous	ADJ
cana-4017	7	46	,	,	PUNCT
cana-4017	7	47	affiliated	affiliate	VERB
cana-4017	7	48	to	to	PART
cana-4017	7	49	bharathidasan	bharathidasan	VERB
cana-4017	7	50	university	university	NOUN
cana-4017	7	51	)	)	PUNCT
cana-4017	7	52	,	,	PUNCT
cana-4017	7	53	trichy	trichy	NOUN
cana-4017	7	54	620	620	NUM
cana-4017	7	55	001	001	NUM
cana-4017	7	56	,	,	PUNCT
cana-4017	7	57	tamil	tamil	PROPN
cana-4017	7	58	nadu	nadu	PROPN
cana-4017	7	59	,	,	PUNCT
cana-4017	7	60	india	india	PROPN
cana-4017	7	61	.	.	PROPN
cana-4017	7	62	5	5	NUM
cana-4017	7	63	assistant	assistant	NOUN
cana-4017	7	64	professor	professor	NOUN
cana-4017	7	65	,	,	PUNCT
cana-4017	7	66	department	department	NOUN
cana-4017	7	67	of	of	ADP
cana-4017	7	68	mathematics	mathematics	PROPN
cana-4017	7	69	,	,	PUNCT
cana-4017	7	70	ayya	ayya	PROPN
cana-4017	7	71	nadar	nadar	PROPN
cana-4017	7	72	janaki	janaki	PROPN
cana-4017	7	73	ammal	ammal	PROPN
cana-4017	7	74	college	college	PROPN
cana-4017	7	75	(	(	PUNCT
cana-4017	7	76	autonomous	autonomous	ADJ
cana-4017	7	77	,	,	PUNCT
cana-4017	7	78	affiliated	affiliate	VERB
cana-4017	7	79	to	to	PART
cana-4017	7	80	madurai	madurai	VERB
cana-4017	7	81	kamaraj	kamaraj	ADJ
cana-4017	7	82	university	university	NOUN
cana-4017	7	83	)	)	PUNCT
cana-4017	7	84	,	,	PUNCT
cana-4017	7	85	sivakasi	sivakasi	NOUN
cana-4017	7	86	–	–	PUNCT
cana-4017	7	87	626	626	NUM
cana-4017	7	88	124	124	NUM
cana-4017	7	89	,	,	PUNCT
cana-4017	7	90	tamil	tamil	PROPN
cana-4017	7	91	nadu	nadu	PROPN
cana-4017	7	92	,	,	PUNCT
cana-4017	7	93	india	india	PROPN
cana-4017	7	94	.	.	PROPN
cana-4017	7	95	6	6	NUM
cana-4017	7	96	assistant	assistant	NOUN
cana-4017	7	97	professor	professor	NOUN
cana-4017	7	98	,	,	PUNCT
cana-4017	7	99	pg	pg	NOUN
cana-4017	7	100	and	and	CCONJ
cana-4017	7	101	research	research	PROPN
cana-4017	7	102	department	department	PROPN
cana-4017	7	103	of	of	ADP
cana-4017	7	104	mathematics	mathematic	NOUN
cana-4017	7	105	,	,	PUNCT
cana-4017	7	106	a.p.c	a.p.c	PROPN
cana-4017	7	107	.	.	PUNCT
cana-4017	7	108	mahalaxmi	mahalaxmi	PROPN
cana-4017	7	109	college	college	NOUN
cana-4017	7	110	for	for	ADP
cana-4017	7	111	women	woman	NOUN
cana-4017	7	112	(	(	PUNCT
cana-4017	7	113	affiliated	affiliate	VERB
cana-4017	7	114	to	to	ADP
cana-4017	7	115	manonmaniam	manonmaniam	PROPN
cana-4017	7	116	sundaranar	sundaranar	PROPN
cana-4017	7	117	university	university	PROPN
cana-4017	7	118	)	)	PUNCT
cana-4017	7	119	,	,	PUNCT
cana-4017	7	120	thoothukudi	thoothukudi	PROPN
cana-4017	7	121	–	–	PUNCT
cana-4017	7	122	628	628	NUM
cana-4017	7	123	002	002	NUM
cana-4017	7	124	,	,	PUNCT
cana-4017	7	125	tamil	tamil	PROPN
cana-4017	7	126	nadu	nadu	PROPN
cana-4017	7	127	,	,	PUNCT
cana-4017	7	128	india	india	PROPN
cana-4017	7	129	.	.	PUNCT
cana-4017	8	1	email	email	NOUN
cana-4017	9	1	i	i	PROPN
cana-4017	9	2	d	d	PROPN
cana-4017	9	3	:	:	PUNCT
cana-4017	9	4	(	(	PUNCT
cana-4017	9	5	anupreethitamil@gmail.com	anupreethitamil@gmail.com	NOUN
cana-4017	9	6	,	,	PUNCT
cana-4017	9	7	vinmolk@rajagiritech.edu.in	vinmolk@rajagiritech.edu.in	NOUN
cana-4017	9	8	,	,	PUNCT
cana-4017	9	9	manjuajil@yahoo.com	manjuajil@yahoo.com	X
cana-4017	9	10	,	,	PUNCT
cana-4017	9	11	*	*	PUNCT
cana-4017	10	1	prasansangee@gmail.com	prasansangee@gmail.com	PROPN
cana-4017	10	2	,	,	PUNCT
cana-4017	10	3	jayram.kannan@gmail.com	jayram.kannan@gmail.com	PROPN
cana-4017	10	4	,	,	PUNCT
cana-4017	10	5	vijayashanthi26892@gmail.com	vijayashanthi26892@gmail.com	X
cana-4017	10	6	)	)	PUNCT
cana-4017	11	1	article	article	NOUN
cana-4017	11	2	history	history	NOUN
cana-4017	11	3	:	:	PUNCT
cana-4017	11	4	received	receive	VERB
cana-4017	11	5	:	:	PUNCT
cana-4017	11	6	12	12	NUM
cana-4017	11	7	-	-	SYM
cana-4017	11	8	11	11	NUM
cana-4017	11	9	-	-	PUNCT
cana-4017	11	10	2024	2024	NUM
cana-4017	11	11	revised	revise	VERB
cana-4017	11	12	:	:	PUNCT
cana-4017	11	13	22	22	NUM
cana-4017	11	14	-	-	SYM
cana-4017	11	15	12	12	NUM
cana-4017	11	16	-	-	PUNCT
cana-4017	11	17	2024	2024	NUM
cana-4017	11	18	accepted	accept	VERB
cana-4017	11	19	:	:	PUNCT
cana-4017	11	20	18	18	NUM
cana-4017	11	21	-	-	SYM
cana-4017	11	22	01	01	NUM
cana-4017	11	23	-	-	PUNCT
cana-4017	11	24	2025	2025	NUM
cana-4017	11	25	abstract	abstract	NOUN
cana-4017	11	26	:	:	PUNCT
cana-4017	11	27	a	a	DET
cana-4017	11	28	public	public	ADJ
cana-4017	11	29	-	-	PUNCT
cana-4017	11	30	key	key	NOUN
cana-4017	11	31	encryption	encryption	NOUN
cana-4017	11	32	technique	technique	NOUN
cana-4017	11	33	akin	akin	ADJ
cana-4017	11	34	to	to	ADP
cana-4017	11	35	rsa	rsa	PROPN
cana-4017	11	36	can	can	AUX
cana-4017	11	37	be	be	AUX
cana-4017	11	38	referred	refer	VERB
cana-4017	11	39	to	to	ADP
cana-4017	11	40	as	as	ADP
cana-4017	11	41	elliptic	elliptic	ADJ
cana-4017	11	42	curve	curve	NOUN
cana-4017	11	43	cryptography	cryptography	NOUN
cana-4017	11	44	(	(	PUNCT
cana-4017	11	45	ecc	ecc	PROPN
cana-4017	11	46	)	)	PUNCT
cana-4017	11	47	.	.	PUNCT
cana-4017	12	1	while	while	SCONJ
cana-4017	12	2	rsa	rsa	PROPN
cana-4017	12	3	's	's	PART
cana-4017	12	4	security	security	NOUN
cana-4017	12	5	relies	rely	VERB
cana-4017	12	6	on	on	ADP
cana-4017	12	7	huge	huge	ADJ
cana-4017	12	8	prime	prime	ADJ
cana-4017	12	9	numbers	number	NOUN
cana-4017	12	10	,	,	PUNCT
cana-4017	12	11	ecc	ecc	NOUN
cana-4017	12	12	leverages	leverage	VERB
cana-4017	12	13	the	the	DET
cana-4017	12	14	mathematical	mathematical	ADJ
cana-4017	12	15	idea	idea	NOUN
cana-4017	12	16	of	of	ADP
cana-4017	12	17	elliptic	elliptic	ADJ
cana-4017	12	18	curves	curve	NOUN
cana-4017	12	19	to	to	PART
cana-4017	12	20	offer	offer	VERB
cana-4017	12	21	the	the	DET
cana-4017	12	22	same	same	ADJ
cana-4017	12	23	level	level	NOUN
cana-4017	12	24	of	of	ADP
cana-4017	12	25	security	security	NOUN
cana-4017	12	26	with	with	ADP
cana-4017	12	27	much	much	ADV
cana-4017	12	28	smaller	small	ADJ
cana-4017	12	29	keys	key	NOUN
cana-4017	12	30	.	.	PUNCT
cana-4017	13	1	in	in	ADP
cana-4017	13	2	this	this	DET
cana-4017	13	3	paper	paper	NOUN
cana-4017	13	4	,	,	PUNCT
cana-4017	13	5	we	we	PRON
cana-4017	13	6	will	will	AUX
cana-4017	13	7	discuss	discuss	VERB
cana-4017	13	8	elliptic	elliptic	ADJ
cana-4017	13	9	curves	curve	NOUN
cana-4017	13	10	and	and	CCONJ
cana-4017	13	11	examine	examine	VERB
cana-4017	13	12	their	their	PRON
cana-4017	13	13	applications	application	NOUN
cana-4017	13	14	in	in	ADP
cana-4017	13	15	cryptography	cryptography	NOUN
cana-4017	13	16	.	.	PUNCT
cana-4017	14	1	a	a	DET
cana-4017	14	2	diophantine	diophantine	NOUN
cana-4017	14	3	pair	pair	NOUN
cana-4017	14	4	of	of	ADP
cana-4017	14	5	hex	hex	PROPN
cana-4017	14	6	numbers	number	NOUN
cana-4017	14	7	and	and	CCONJ
cana-4017	14	8	pronic	pronic	ADJ
cana-4017	14	9	numbers	number	NOUN
cana-4017	14	10	is	be	AUX
cana-4017	14	11	extended	extend	VERB
cana-4017	14	12	to	to	ADP
cana-4017	14	13	a	a	DET
cana-4017	14	14	diophantine	diophantine	NOUN
cana-4017	14	15	triple	triple	ADV
cana-4017	14	16	with	with	ADP
cana-4017	14	17	appropriate	appropriate	ADJ
cana-4017	14	18	property	property	NOUN
cana-4017	14	19	,	,	PUNCT
cana-4017	14	20	that	that	PRON
cana-4017	14	21	generates	generate	VERB
cana-4017	14	22	the	the	DET
cana-4017	14	23	elliptic	elliptic	ADJ
cana-4017	14	24	curve	curve	NOUN
cana-4017	14	25	and	and	CCONJ
cana-4017	14	26	perform	perform	VERB
cana-4017	14	27	the	the	DET
cana-4017	14	28	encryption	encryption	NOUN
cana-4017	14	29	-	-	PUNCT
cana-4017	14	30	decryption	decryption	NOUN
cana-4017	14	31	process	process	NOUN
cana-4017	14	32	.	.	PUNCT
cana-4017	15	1	keywords	keyword	NOUN
cana-4017	15	2	:	:	PUNCT
cana-4017	15	3	elliptic	elliptic	ADJ
cana-4017	15	4	curve	curve	NOUN
cana-4017	15	5	cryptography	cryptography	NOUN
cana-4017	15	6	,	,	PUNCT
cana-4017	15	7	hex	hex	PROPN
cana-4017	15	8	numbers	number	NOUN
cana-4017	15	9	,	,	PUNCT
cana-4017	15	10	pronic	pronic	ADJ
cana-4017	15	11	numbers	number	NOUN
cana-4017	15	12	,	,	PUNCT
cana-4017	15	13	diophantine	diophantine	VERB
cana-4017	15	14	triples	triple	NOUN
cana-4017	15	15	,	,	PUNCT
cana-4017	15	16	encryption	encryption	NOUN
cana-4017	15	17	,	,	PUNCT
cana-4017	15	18	decryption	decryption	NOUN
cana-4017	15	19	.	.	PUNCT
cana-4017	16	1	1	1	X
cana-4017	16	2	.	.	X
cana-4017	16	3	introduction	introduction	NOUN
cana-4017	16	4	ecc	ecc	PROPN
cana-4017	16	5	is	be	AUX
cana-4017	16	6	a	a	DET
cana-4017	16	7	public	public	ADJ
cana-4017	16	8	-	-	PUNCT
cana-4017	16	9	key	key	NOUN
cana-4017	16	10	cryptographic	cryptographic	ADJ
cana-4017	16	11	system	system	NOUN
cana-4017	16	12	that	that	PRON
cana-4017	16	13	utilizes	utilize	VERB
cana-4017	16	14	the	the	DET
cana-4017	16	15	algebraic	algebraic	ADJ
cana-4017	16	16	structure	structure	NOUN
cana-4017	16	17	of	of	ADP
cana-4017	16	18	elliptic	elliptic	ADJ
cana-4017	16	19	curves	curve	NOUN
cana-4017	16	20	over	over	ADP
cana-4017	16	21	finite	finite	ADJ
cana-4017	16	22	fields	field	NOUN
cana-4017	16	23	.	.	PUNCT
cana-4017	17	1	its	its	PRON
cana-4017	17	2	primary	primary	ADJ
cana-4017	17	3	advantage	advantage	NOUN
cana-4017	17	4	lies	lie	VERB
cana-4017	17	5	in	in	ADP
cana-4017	17	6	achieving	achieve	VERB
cana-4017	17	7	comparable	comparable	ADJ
cana-4017	17	8	security	security	NOUN
cana-4017	17	9	to	to	ADP
cana-4017	17	10	traditional	traditional	ADJ
cana-4017	17	11	systems	system	NOUN
cana-4017	17	12	like	like	ADP
cana-4017	17	13	rsa	rsa	PROPN
cana-4017	17	14	but	but	CCONJ
cana-4017	17	15	with	with	ADP
cana-4017	17	16	significantly	significantly	ADV
cana-4017	17	17	smaller	small	ADJ
cana-4017	17	18	key	key	ADJ
cana-4017	17	19	sizes	size	NOUN
cana-4017	17	20	,	,	PUNCT
cana-4017	17	21	leading	lead	VERB
cana-4017	17	22	to	to	ADP
cana-4017	17	23	efficiency	efficiency	NOUN
cana-4017	17	24	in	in	ADP
cana-4017	17	25	computation	computation	NOUN
cana-4017	17	26	and	and	CCONJ
cana-4017	17	27	storage	storage	NOUN
cana-4017	17	28	.	.	PUNCT
cana-4017	18	1	the	the	DET
cana-4017	18	2	mailto:jayram.kannan@gmail.com	mailto:jayram.kannan@gmail.com	X
cana-4017	18	3	communications	communication	NOUN
cana-4017	18	4	on	on	ADP
cana-4017	18	5	applied	apply	VERB
cana-4017	18	6	nonlinear	nonlinear	ADJ
cana-4017	18	7	analysis	analysis	NOUN
cana-4017	18	8	issn	issn	NOUN
cana-4017	18	9	:	:	PUNCT
cana-4017	18	10	1074	1074	NUM
cana-4017	18	11	-	-	PUNCT
cana-4017	18	12	133x	133x	NUM
cana-4017	18	13	vol	vol	NOUN
cana-4017	18	14	32	32	NUM
cana-4017	18	15	no	no	NOUN
cana-4017	18	16	.	.	PUNCT
cana-4017	19	1	9s	9s	NUM
cana-4017	19	2	(	(	PUNCT
cana-4017	19	3	2025	2025	NUM
cana-4017	19	4	)	)	PUNCT
cana-4017	19	5	837	837	NUM
cana-4017	19	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4017	19	7	security	security	NOUN
cana-4017	19	8	of	of	ADP
cana-4017	19	9	ecc	ecc	PROPN
cana-4017	19	10	is	be	AUX
cana-4017	19	11	based	base	VERB
cana-4017	19	12	on	on	ADP
cana-4017	19	13	the	the	DET
cana-4017	19	14	difficulty	difficulty	NOUN
cana-4017	19	15	of	of	ADP
cana-4017	19	16	the	the	DET
cana-4017	19	17	elliptic	elliptic	ADJ
cana-4017	19	18	curve	curve	NOUN
cana-4017	19	19	discrete	discrete	ADJ
cana-4017	19	20	logarithm	logarithm	NOUN
cana-4017	19	21	problem	problem	NOUN
cana-4017	19	22	(	(	PUNCT
cana-4017	19	23	ecdlp	ecdlp	NOUN
cana-4017	19	24	)	)	PUNCT
cana-4017	19	25	.	.	PUNCT
cana-4017	20	1	elliptic	elliptic	ADJ
cana-4017	20	2	curve	curve	NOUN
cana-4017	20	3	cryptography	cryptography	NOUN
cana-4017	20	4	algorithms	algorithm	NOUN
cana-4017	20	5	entered	enter	VERB
cana-4017	20	6	wide	wide	ADJ
cana-4017	20	7	use	use	NOUN
cana-4017	20	8	in	in	ADP
cana-4017	20	9	2004	2004	NUM
cana-4017	20	10	to	to	ADP
cana-4017	20	11	2005[1	2005[1	NUM
cana-4017	20	12	-	-	SYM
cana-4017	20	13	5	5	NUM
cana-4017	20	14	]	]	PUNCT
cana-4017	20	15	.	.	PUNCT
cana-4017	21	1	this	this	DET
cana-4017	21	2	research	research	NOUN
cana-4017	21	3	paper	paper	NOUN
cana-4017	21	4	delves	delf	NOUN
cana-4017	21	5	into	into	ADP
cana-4017	21	6	the	the	DET
cana-4017	21	7	innovative	innovative	ADJ
cana-4017	21	8	construction	construction	NOUN
cana-4017	21	9	of	of	ADP
cana-4017	21	10	elliptic	elliptic	ADJ
cana-4017	21	11	curves	curve	NOUN
cana-4017	21	12	for	for	ADP
cana-4017	21	13	cryptographic	cryptographic	ADJ
cana-4017	21	14	applications	application	NOUN
cana-4017	21	15	by	by	ADP
cana-4017	21	16	leveraging	leverage	VERB
cana-4017	21	17	diophantine	diophantine	NOUN
cana-4017	21	18	triples	triple	NOUN
cana-4017	21	19	derived	derive	VERB
cana-4017	21	20	from	from	ADP
cana-4017	21	21	specific	specific	ADJ
cana-4017	21	22	polynomial	polynomial	ADJ
cana-4017	21	23	sequences	sequence	NOUN
cana-4017	21	24	,	,	PUNCT
cana-4017	21	25	notably	notably	ADV
cana-4017	21	26	hex	hex	X
cana-4017	22	1	[	[	X
cana-4017	22	2	a003215]and	a003215]and	X
cana-4017	22	3	pronic	pronic	ADJ
cana-4017	22	4	numbers[a002378	numbers[a002378	NOUN
cana-4017	22	5	]	]	X
cana-4017	23	1	[	[	X
cana-4017	23	2	6].this	6].this	NUM
cana-4017	23	3	approach	approach	NOUN
cana-4017	23	4	is	be	AUX
cana-4017	23	5	part	part	NOUN
cana-4017	23	6	of	of	ADP
cana-4017	23	7	a	a	DET
cana-4017	23	8	broader	broad	ADJ
cana-4017	23	9	exploration	exploration	NOUN
cana-4017	23	10	into	into	ADP
cana-4017	23	11	the	the	DET
cana-4017	23	12	intersection	intersection	NOUN
cana-4017	23	13	of	of	ADP
cana-4017	23	14	number	number	NOUN
cana-4017	23	15	theory	theory	NOUN
cana-4017	23	16	and	and	CCONJ
cana-4017	23	17	cryptography	cryptography	NOUN
cana-4017	23	18	,	,	PUNCT
cana-4017	23	19	aiming	aim	VERB
cana-4017	23	20	to	to	PART
cana-4017	23	21	enhance	enhance	VERB
cana-4017	23	22	security	security	NOUN
cana-4017	23	23	mechanisms	mechanism	NOUN
cana-4017	23	24	through	through	ADP
cana-4017	23	25	mathematical	mathematical	ADJ
cana-4017	23	26	rigor	rigor	NOUN
cana-4017	23	27	.	.	PUNCT
cana-4017	24	1	a	a	DET
cana-4017	24	2	diophantine	diophantine	NOUN
cana-4017	24	3	triple	triple	ADJ
cana-4017	24	4	consists	consist	NOUN
cana-4017	24	5	of	of	ADP
cana-4017	24	6	three	three	NUM
cana-4017	24	7	positive	positive	ADJ
cana-4017	24	8	integers	integer	NOUN
cana-4017	24	9	(	(	PUNCT
cana-4017	24	10	a	a	DET
cana-4017	24	11	,	,	PUNCT
cana-4017	24	12	b	b	NOUN
cana-4017	24	13	,	,	PUNCT
cana-4017	24	14	c	c	NOUN
cana-4017	24	15	)	)	PUNCT
cana-4017	24	16	such	such	ADJ
cana-4017	24	17	that	that	SCONJ
cana-4017	24	18	the	the	DET
cana-4017	24	19	product	product	NOUN
cana-4017	24	20	of	of	ADP
cana-4017	24	21	any	any	DET
cana-4017	24	22	two	two	NUM
cana-4017	24	23	,	,	PUNCT
cana-4017	24	24	increased	increase	VERB
cana-4017	24	25	by	by	ADP
cana-4017	24	26	one	one	NUM
cana-4017	24	27	,	,	PUNCT
cana-4017	24	28	yields	yield	VERB
cana-4017	24	29	a	a	DET
cana-4017	24	30	perfect	perfect	ADJ
cana-4017	24	31	square	square	NOUN
cana-4017	24	32	:	:	PUNCT
cana-4017	25	1	𝑎𝑏	𝑎𝑏	PROPN
cana-4017	25	2	+	+	CCONJ
cana-4017	25	3	1	1	NUM
cana-4017	25	4	=	=	SYM
cana-4017	25	5	𝑥2	𝑥2	NOUN
cana-4017	25	6	,	,	PUNCT
cana-4017	25	7	𝑏𝑐	𝑏𝑐	PROPN
cana-4017	25	8	+	+	NOUN
cana-4017	25	9	1	1	NUM
cana-4017	25	10	=	=	SYM
cana-4017	25	11	𝑦2	𝑦2	NOUN
cana-4017	25	12	,	,	PUNCT
cana-4017	25	13	𝑐𝑎	𝑐𝑎	NOUN
cana-4017	25	14	+	+	NOUN
cana-4017	25	15	1	1	NUM
cana-4017	25	16	=	=	NOUN
cana-4017	25	17	𝑧2	𝑧2	NOUN
cana-4017	25	18	these	these	DET
cana-4017	25	19	triples	triple	NOUN
cana-4017	25	20	can	can	AUX
cana-4017	25	21	be	be	AUX
cana-4017	25	22	utilized	utilize	VERB
cana-4017	25	23	to	to	PART
cana-4017	25	24	construct	construct	VERB
cana-4017	25	25	elliptic	elliptic	ADJ
cana-4017	25	26	curves	curve	NOUN
cana-4017	25	27	with	with	ADP
cana-4017	25	28	specific	specific	ADJ
cana-4017	25	29	properties	property	NOUN
cana-4017	25	30	.	.	PUNCT
cana-4017	26	1	for	for	ADP
cana-4017	26	2	instance	instance	NOUN
cana-4017	26	3	,	,	PUNCT
cana-4017	26	4	research	research	NOUN
cana-4017	26	5	has	have	AUX
cana-4017	26	6	demonstrated	demonstrate	VERB
cana-4017	26	7	that	that	SCONJ
cana-4017	26	8	certain	certain	ADJ
cana-4017	26	9	diophantine	diophantine	NOUN
cana-4017	26	10	triples	triple	NOUN
cana-4017	26	11	can	can	AUX
cana-4017	26	12	induce	induce	VERB
cana-4017	26	13	elliptic	elliptic	ADJ
cana-4017	26	14	curves	curve	NOUN
cana-4017	26	15	with	with	ADP
cana-4017	26	16	high	high	ADJ
cana-4017	26	17	ranks	rank	NOUN
cana-4017	26	18	,	,	PUNCT
cana-4017	26	19	which	which	PRON
cana-4017	26	20	are	be	AUX
cana-4017	26	21	beneficial	beneficial	ADJ
cana-4017	26	22	for	for	ADP
cana-4017	26	23	cryptographic	cryptographic	ADJ
cana-4017	26	24	applications	application	NOUN
cana-4017	26	25	.	.	PUNCT
cana-4017	27	1	the	the	DET
cana-4017	27	2	choice	choice	NOUN
cana-4017	27	3	of	of	ADP
cana-4017	27	4	specific	specific	ADJ
cana-4017	27	5	elliptic	elliptic	ADJ
cana-4017	27	6	curves	curve	NOUN
cana-4017	27	7	,	,	PUNCT
cana-4017	27	8	especially	especially	ADV
cana-4017	27	9	those	those	PRON
cana-4017	27	10	derived	derive	VERB
cana-4017	27	11	from	from	ADP
cana-4017	27	12	diophantine	diophantine	NOUN
cana-4017	27	13	triples	triple	NOUN
cana-4017	27	14	of	of	ADP
cana-4017	27	15	hex	hex	NOUN
cana-4017	27	16	and	and	CCONJ
cana-4017	27	17	pronic	pronic	ADJ
cana-4017	27	18	numbers	number	NOUN
cana-4017	27	19	,	,	PUNCT
cana-4017	27	20	can	can	AUX
cana-4017	27	21	influence	influence	VERB
cana-4017	27	22	the	the	DET
cana-4017	27	23	security	security	NOUN
cana-4017	27	24	and	and	CCONJ
cana-4017	27	25	efficiency	efficiency	NOUN
cana-4017	27	26	of	of	ADP
cana-4017	27	27	these	these	DET
cana-4017	27	28	cryptographic	cryptographic	ADJ
cana-4017	27	29	operations	operation	NOUN
cana-4017	27	30	.	.	PUNCT
cana-4017	28	1	recent	recent	ADJ
cana-4017	28	2	researchers	researcher	NOUN
cana-4017	28	3	work	work	VERB
cana-4017	28	4	on	on	ADP
cana-4017	28	5	transforming	transform	VERB
cana-4017	28	6	a	a	DET
cana-4017	28	7	diophantine	diophantine	NOUN
cana-4017	28	8	equation	equation	NOUN
cana-4017	28	9	to	to	ADP
cana-4017	28	10	an	an	DET
cana-4017	28	11	elliptic	elliptic	ADJ
cana-4017	28	12	curve	curve	NOUN
cana-4017	28	13	and	and	CCONJ
cana-4017	28	14	frame	frame	VERB
cana-4017	28	15	the	the	DET
cana-4017	28	16	algorithm	algorithm	NOUN
cana-4017	28	17	for	for	ADP
cana-4017	28	18	encryption	encryption	NOUN
cana-4017	28	19	-	-	PUNCT
cana-4017	28	20	decryption	decryption	NOUN
cana-4017	28	21	process	process	NOUN
cana-4017	28	22	[	[	X
cana-4017	28	23	7	7	NUM
cana-4017	28	24	,	,	PUNCT
cana-4017	28	25	8	8	NUM
cana-4017	28	26	]	]	PUNCT
cana-4017	28	27	.	.	PUNCT
cana-4017	29	1	as	as	ADP
cana-4017	29	2	a	a	DET
cana-4017	29	3	part	part	NOUN
cana-4017	29	4	of	of	ADP
cana-4017	29	5	recent	recent	ADJ
cana-4017	29	6	research	research	NOUN
cana-4017	29	7	,	,	PUNCT
cana-4017	29	8	we	we	PRON
cana-4017	29	9	form	form	VERB
cana-4017	29	10	an	an	DET
cana-4017	29	11	elliptic	elliptic	ADJ
cana-4017	29	12	curve	curve	NOUN
cana-4017	29	13	using	use	VERB
cana-4017	29	14	diophantine	diophantine	NOUN
cana-4017	29	15	triples	triple	NOUN
cana-4017	29	16	which	which	PRON
cana-4017	29	17	were	be	AUX
cana-4017	29	18	extended	extend	VERB
cana-4017	29	19	from	from	ADP
cana-4017	29	20	a	a	DET
cana-4017	29	21	pair	pair	NOUN
cana-4017	29	22	of	of	ADP
cana-4017	29	23	polynomials	polynomial	NOUN
cana-4017	29	24	namely	namely	ADV
cana-4017	29	25	hex	hex	VERB
cana-4017	29	26	number	number	NOUN
cana-4017	29	27	and	and	CCONJ
cana-4017	29	28	pronic	pronic	ADJ
cana-4017	29	29	number	number	NOUN
cana-4017	29	30	with	with	ADP
cana-4017	29	31	suitable	suitable	ADJ
cana-4017	29	32	property	property	NOUN
cana-4017	29	33	[	[	X
cana-4017	29	34	9	9	NUM
cana-4017	29	35	-	-	SYM
cana-4017	29	36	12	12	NUM
cana-4017	29	37	]	]	PUNCT
cana-4017	29	38	.	.	PUNCT
cana-4017	30	1	2	2	X
cana-4017	30	2	.	.	X
cana-4017	30	3	methods	method	NOUN
cana-4017	30	4	let	let	VERB
cana-4017	30	5	𝐻𝑁	𝐻𝑁	PROPN
cana-4017	30	6	=	=	SYM
cana-4017	30	7	3𝑛2	3𝑛2	NUM
cana-4017	30	8	+	+	NUM
cana-4017	30	9	3𝑛	3𝑛	NUM
cana-4017	30	10	+	+	CCONJ
cana-4017	30	11	1	1	NUM
cana-4017	30	12	and	and	CCONJ
cana-4017	30	13	𝑃𝑁	𝑃𝑁	PROPN
cana-4017	30	14	=	=	PUNCT
cana-4017	30	15	𝑛2	𝑛2	NOUN
cana-4017	30	16	+	+	CCONJ
cana-4017	30	17	𝑛	𝑛	PRON
cana-4017	30	18	be	be	VERB
cana-4017	30	19	hex	hex	PROPN
cana-4017	30	20	number	number	NOUN
cana-4017	30	21	and	and	CCONJ
cana-4017	30	22	pronic	pronic	ADJ
cana-4017	30	23	number	number	NOUN
cana-4017	30	24	respectively	respectively	ADV
cana-4017	30	25	,	,	PUNCT
cana-4017	30	26	so	so	SCONJ
cana-4017	30	27	that	that	SCONJ
cana-4017	30	28	𝐻𝑁𝑃𝑁	𝐻𝑁𝑃𝑁	PROPN
cana-4017	30	29	+	+	CCONJ
cana-4017	30	30	(	(	PUNCT
cana-4017	30	31	𝑛4	𝑛4	NOUN
cana-4017	30	32	−	−	PROPN
cana-4017	30	33	2𝑛3	2𝑛3	NUM
cana-4017	30	34	+	+	NUM
cana-4017	30	35	𝑛2	𝑛2	NOUN
cana-4017	30	36	+	+	CCONJ
cana-4017	30	37	𝑛	𝑛	PROPN
cana-4017	30	38	+	+	NOUN
cana-4017	30	39	1	1	NUM
cana-4017	30	40	)	)	PUNCT
cana-4017	30	41	is	be	AUX
cana-4017	30	42	a	a	DET
cana-4017	30	43	perfect	perfect	ADJ
cana-4017	30	44	square	square	NOUN
cana-4017	30	45	,	,	PUNCT
cana-4017	30	46	that	that	PRON
cana-4017	30	47	is	be	AUX
cana-4017	30	48	𝛼2	𝛼2	ADJ
cana-4017	30	49	=	=	SYM
cana-4017	30	50	(	(	PUNCT
cana-4017	30	51	2𝑛2	2𝑛2	NUM
cana-4017	30	52	+	+	CCONJ
cana-4017	30	53	𝑛	𝑛	DET
cana-4017	30	54	+	+	NOUN
cana-4017	30	55	1)2	1)2	NUM
cana-4017	30	56	.	.	PUNCT
cana-4017	31	1	let	let	VERB
cana-4017	31	2	𝐴𝑁	𝐴𝑁	PROPN
cana-4017	31	3	be	be	AUX
cana-4017	31	4	any	any	DET
cana-4017	31	5	non	non	ADJ
cana-4017	31	6	-	-	ADJ
cana-4017	31	7	zero	zero	ADJ
cana-4017	31	8	integer	integer	NOUN
cana-4017	31	9	such	such	ADJ
cana-4017	31	10	that	that	SCONJ
cana-4017	31	11	it	it	PRON
cana-4017	31	12	satisfies	satisfy	VERB
cana-4017	31	13	the	the	DET
cana-4017	31	14	following	follow	VERB
cana-4017	31	15	conditions	condition	NOUN
cana-4017	31	16	:	:	PUNCT
cana-4017	31	17	𝐻𝑁𝐴𝑁	𝐻𝑁𝐴𝑁	NOUN
cana-4017	31	18	+	+	CCONJ
cana-4017	31	19	(	(	PUNCT
cana-4017	31	20	𝑛4	𝑛4	NOUN
cana-4017	31	21	−	−	PROPN
cana-4017	31	22	2𝑛3	2𝑛3	NUM
cana-4017	32	1	+	+	NUM
cana-4017	32	2	𝑛2	𝑛2	NOUN
cana-4017	32	3	+	+	CCONJ
cana-4017	32	4	𝑛	𝑛	PROPN
cana-4017	32	5	+	+	NOUN
cana-4017	32	6	1	1	NUM
cana-4017	32	7	)	)	PUNCT
cana-4017	32	8	=	=	NOUN
cana-4017	32	9	𝛽2	𝛽2	NOUN
cana-4017	32	10	𝑃𝑁𝐴𝑁	𝑃𝑁𝐴𝑁	VERB
cana-4017	32	11	+	+	CCONJ
cana-4017	32	12	(	(	PUNCT
cana-4017	32	13	𝑛4	𝑛4	NOUN
cana-4017	32	14	−	−	PROPN
cana-4017	32	15	2𝑛3	2𝑛3	NUM
cana-4017	33	1	+	+	NUM
cana-4017	33	2	𝑛2	𝑛2	NOUN
cana-4017	33	3	+	+	CCONJ
cana-4017	33	4	𝑛	𝑛	PROPN
cana-4017	33	5	+	+	NOUN
cana-4017	33	6	1	1	NUM
cana-4017	33	7	)	)	PUNCT
cana-4017	33	8	=	=	NOUN
cana-4017	33	9	𝛾2	𝛾2	NOUN
cana-4017	33	10	.	.	PUNCT
cana-4017	34	1	by	by	ADP
cana-4017	34	2	using	use	VERB
cana-4017	34	3	the	the	DET
cana-4017	34	4	linear	linear	ADJ
cana-4017	34	5	transformations	transformation	NOUN
cana-4017	34	6	𝛽	𝛽	NOUN
cana-4017	34	7	=	=	SYM
cana-4017	34	8	𝑋	𝑋	PROPN
cana-4017	34	9	+	+	CCONJ
cana-4017	34	10	𝐻𝑁𝑦	𝐻𝑁𝑦	NOUN
cana-4017	34	11	;	;	PUNCT
cana-4017	34	12	𝛾	𝛾	X
cana-4017	34	13	=	=	SYM
cana-4017	34	14	𝑋	𝑋	NOUN
cana-4017	34	15	+	+	NUM
cana-4017	34	16	𝑃𝑁𝑦	𝑃𝑁𝑦	NOUN
cana-4017	34	17	,	,	PUNCT
cana-4017	34	18	these	these	DET
cana-4017	34	19	equations	equation	NOUN
cana-4017	34	20	can	can	AUX
cana-4017	34	21	be	be	AUX
cana-4017	34	22	reduced	reduce	VERB
cana-4017	34	23	to	to	ADP
cana-4017	34	24	a	a	DET
cana-4017	34	25	pellian	pellian	ADJ
cana-4017	34	26	equation	equation	NOUN
cana-4017	34	27	𝑋2	𝑋2	VERB
cana-4017	34	28	−	−	PROPN
cana-4017	34	29	𝐻𝑁𝑃𝑁𝑦2	𝐻𝑁𝑃𝑁𝑦2	NOUN
cana-4017	34	30	=	=	PUNCT
cana-4017	34	31	𝑛4	𝑛4	NOUN
cana-4017	35	1	−	−	PROPN
cana-4017	35	2	2𝑛3	2𝑛3	NUM
cana-4017	36	1	+	+	NUM
cana-4017	36	2	𝑛2	𝑛2	NOUN
cana-4017	36	3	+	+	CCONJ
cana-4017	36	4	𝑛	𝑛	PROPN
cana-4017	37	1	+	+	CCONJ
cana-4017	37	2	1,with	1,with	NUM
cana-4017	37	3	a	a	DET
cana-4017	37	4	basic	basic	ADJ
cana-4017	37	5	solution	solution	NOUN
cana-4017	37	6	(	(	PUNCT
cana-4017	37	7	(	(	PUNCT
cana-4017	37	8	2𝑛2	2𝑛2	NUM
cana-4017	37	9	+	+	CCONJ
cana-4017	37	10	𝑛	𝑛	PRON
cana-4017	37	11	+	+	NOUN
cana-4017	37	12	1	1	NUM
cana-4017	37	13	)	)	PUNCT
cana-4017	37	14	,	,	PUNCT
cana-4017	37	15	1	1	NUM
cana-4017	37	16	)	)	PUNCT
cana-4017	37	17	.	.	PUNCT
cana-4017	38	1	therefore	therefore	ADV
cana-4017	38	2	,	,	PUNCT
cana-4017	38	3	from	from	ADP
cana-4017	38	4	the	the	DET
cana-4017	38	5	infinite	infinite	ADJ
cana-4017	38	6	number	number	NOUN
cana-4017	38	7	of	of	ADP
cana-4017	38	8	solutions	solution	NOUN
cana-4017	38	9	to	to	ADP
cana-4017	38	10	the	the	DET
cana-4017	38	11	aforementioned	aforementioned	ADJ
cana-4017	38	12	pell	pell	PROPN
cana-4017	38	13	's	's	PART
cana-4017	38	14	equation	equation	NOUN
cana-4017	38	15	,	,	PUNCT
cana-4017	38	16	a	a	DET
cana-4017	38	17	diophantine	diophantine	NOUN
cana-4017	38	18	triple	triple	ADV
cana-4017	38	19	(	(	PUNCT
cana-4017	38	20	𝐻𝑁	𝐻𝑁	PROPN
cana-4017	38	21	,	,	PUNCT
cana-4017	38	22	𝑃𝑁	𝑃𝑁	PROPN
cana-4017	38	23	,	,	PUNCT
cana-4017	38	24	𝐴𝑁	𝐴𝑁	PROPN
cana-4017	38	25	)	)	PUNCT
cana-4017	38	26	=	=	PUNCT
cana-4017	38	27	(	(	PUNCT
cana-4017	38	28	3𝑛2	3𝑛2	NUM
cana-4017	38	29	+	+	NUM
cana-4017	38	30	3𝑛	3𝑛	NUM
cana-4017	38	31	+	+	CCONJ
cana-4017	38	32	1	1	NUM
cana-4017	38	33	,	,	PUNCT
cana-4017	38	34	𝑛2	𝑛2	NOUN
cana-4017	38	35	+	+	CCONJ
cana-4017	38	36	𝑛	𝑛	PROPN
cana-4017	38	37	,	,	PUNCT
cana-4017	38	38	8𝑛2	8𝑛2	NUM
cana-4017	38	39	+	+	CCONJ
cana-4017	38	40	6𝑛	6𝑛	NOUN
cana-4017	38	41	+	+	CCONJ
cana-4017	38	42	3	3	X
cana-4017	38	43	)	)	PUNCT
cana-4017	38	44	can	can	AUX
cana-4017	38	45	be	be	AUX
cana-4017	38	46	produced	produce	VERB
cana-4017	38	47	.	.	PUNCT
cana-4017	39	1	our	our	PRON
cana-4017	39	2	goal	goal	NOUN
cana-4017	39	3	in	in	ADP
cana-4017	39	4	this	this	DET
cana-4017	39	5	paper	paper	NOUN
cana-4017	39	6	is	be	AUX
cana-4017	39	7	to	to	PART
cana-4017	39	8	find	find	VERB
cana-4017	39	9	diophantine	diophantine	VERB
cana-4017	39	10	triples	triple	NOUN
cana-4017	39	11	(	(	PUNCT
cana-4017	39	12	𝐻𝑁	𝐻𝑁	PROPN
cana-4017	39	13	,	,	PUNCT
cana-4017	39	14	𝑃𝑁	𝑃𝑁	PROPN
cana-4017	39	15	,	,	PUNCT
cana-4017	39	16	𝐴𝑁	𝐴𝑁	PROPN
cana-4017	39	17	)	)	PUNCT
cana-4017	39	18	and	and	CCONJ
cana-4017	39	19	to	to	PART
cana-4017	39	20	illustrate	illustrate	VERB
cana-4017	39	21	them	they	PRON
cana-4017	39	22	.	.	PUNCT
cana-4017	40	1	firstly	firstly	ADV
cana-4017	40	2	,	,	PUNCT
cana-4017	40	3	let	let	VERB
cana-4017	40	4	us	we	PRON
cana-4017	40	5	look	look	VERB
cana-4017	40	6	at	at	ADP
cana-4017	40	7	the	the	DET
cana-4017	40	8	fundamental	fundamental	ADJ
cana-4017	40	9	formulae	formulae	NOUN
cana-4017	40	10	:	:	PUNCT
cana-4017	40	11	𝐻𝑁	𝐻𝑁	PROPN
cana-4017	40	12	=	=	SYM
cana-4017	40	13	3𝑛2	3𝑛2	NUM
cana-4017	40	14	+	+	NUM
cana-4017	40	15	3𝑛	3𝑛	NUM
cana-4017	40	16	+	+	CCONJ
cana-4017	40	17	1	1	NUM
cana-4017	40	18	,	,	PUNCT
cana-4017	40	19	𝑃𝑁	𝑃𝑁	PROPN
cana-4017	40	20	=	=	SYM
cana-4017	40	21	𝑛2	𝑛2	NOUN
cana-4017	40	22	+	+	CCONJ
cana-4017	40	23	𝑛	𝑛	PROPN
cana-4017	40	24	and	and	CCONJ
cana-4017	40	25	𝐴𝑁	𝐴𝑁	PROPN
cana-4017	40	26	=	=	SYM
cana-4017	40	27	8𝑛2	8𝑛2	NUM
cana-4017	41	1	+	+	CCONJ
cana-4017	41	2	6𝑛	6𝑛	NOUN
cana-4017	41	3	+	+	CCONJ
cana-4017	41	4	3	3	X
cana-4017	41	5	.	.	X
cana-4017	41	6	a	a	DET
cana-4017	41	7	recurrent	recurrent	ADJ
cana-4017	41	8	pattern	pattern	NOUN
cana-4017	41	9	emerges	emerge	VERB
cana-4017	41	10	as	as	SCONJ
cana-4017	41	11	we	we	PRON
cana-4017	41	12	begin	begin	VERB
cana-4017	41	13	to	to	PART
cana-4017	41	14	solve	solve	VERB
cana-4017	41	15	these	these	DET
cana-4017	41	16	equations	equation	NOUN
cana-4017	41	17	.	.	PUNCT
cana-4017	42	1	going	go	VERB
cana-4017	42	2	ahead	ahead	ADV
cana-4017	42	3	,	,	PUNCT
cana-4017	42	4	the	the	DET
cana-4017	42	5	idea	idea	NOUN
cana-4017	42	6	is	be	AUX
cana-4017	42	7	that	that	SCONJ
cana-4017	42	8	the	the	DET
cana-4017	42	9	existence	existence	NOUN
cana-4017	42	10	of	of	ADP
cana-4017	42	11	diophantine	diophantine	NOUN
cana-4017	42	12	3	3	NUM
cana-4017	42	13	-	-	PUNCT
cana-4017	42	14	tuples	tuple	NOUN
cana-4017	42	15	and	and	CCONJ
cana-4017	42	16	the	the	DET
cana-4017	42	17	characteristics	characteristic	NOUN
cana-4017	42	18	of	of	ADP
cana-4017	42	19	the	the	DET
cana-4017	42	20	elliptic	elliptic	ADJ
cana-4017	42	21	curves	curve	NOUN
cana-4017	42	22	associated	associate	VERB
cana-4017	42	23	with	with	ADP
cana-4017	42	24	them	they	PRON
cana-4017	42	25	are	be	AUX
cana-4017	42	26	closely	closely	ADV
cana-4017	42	27	communications	communication	NOUN
cana-4017	42	28	on	on	ADP
cana-4017	42	29	applied	apply	VERB
cana-4017	42	30	nonlinear	nonlinear	ADJ
cana-4017	42	31	analysis	analysis	NOUN
cana-4017	42	32	issn	issn	NOUN
cana-4017	42	33	:	:	PUNCT
cana-4017	42	34	1074	1074	NUM
cana-4017	42	35	-	-	PUNCT
cana-4017	42	36	133x	133x	NUM
cana-4017	42	37	vol	vol	NOUN
cana-4017	42	38	32	32	NUM
cana-4017	42	39	no	no	NOUN
cana-4017	42	40	.	.	PUNCT
cana-4017	43	1	9s	9s	NUM
cana-4017	43	2	(	(	PUNCT
cana-4017	43	3	2025	2025	NUM
cana-4017	43	4	)	)	PUNCT
cana-4017	43	5	838	838	NUM
cana-4017	43	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4017	43	7	related	related	ADJ
cana-4017	43	8	.	.	PUNCT
cana-4017	44	1	with	with	ADP
cana-4017	44	2	respect	respect	NOUN
cana-4017	44	3	to	to	ADP
cana-4017	44	4	the	the	DET
cana-4017	44	5	diophantine	diophantine	NOUN
cana-4017	44	6	triple	triple	ADV
cana-4017	44	7	(	(	PUNCT
cana-4017	44	8	𝐻𝑁	𝐻𝑁	PROPN
cana-4017	44	9	,	,	PUNCT
cana-4017	44	10	𝑃𝑁	𝑃𝑁	PROPN
cana-4017	44	11	,	,	PUNCT
cana-4017	44	12	𝐴𝑁	𝐴𝑁	PROPN
cana-4017	44	13	)	)	PUNCT
cana-4017	44	14	,	,	PUNCT
cana-4017	44	15	let	let	VERB
cana-4017	44	16	us	we	PRON
cana-4017	44	17	consider	consider	VERB
cana-4017	44	18	its	its	PRON
cana-4017	44	19	property	property	NOUN
cana-4017	44	20	𝐷(𝑛).for	𝐷(𝑛).for	ADP
cana-4017	44	21	all	all	DET
cana-4017	44	22	non	non	ADJ
cana-4017	44	23	-	-	ADJ
cana-4017	44	24	negative	negative	ADJ
cana-4017	44	25	integer	integer	NOUN
cana-4017	44	26	numbers	number	NOUN
cana-4017	44	27	δ	δ	PROPN
cana-4017	44	28	,	,	PUNCT
cana-4017	44	29	𝜓	𝜓	PROPN
cana-4017	44	30	and	and	CCONJ
cana-4017	44	31	γ	γ	X
cana-4017	44	32	,	,	PUNCT
cana-4017	44	33	there	there	PRON
cana-4017	44	34	exist	exist	VERB
cana-4017	44	35	the	the	DET
cana-4017	44	36	formulas	formula	NOUN
cana-4017	44	37	(	(	PUNCT
cana-4017	44	38	𝐻𝑁𝐴𝑁	𝐻𝑁𝐴𝑁	NOUN
cana-4017	44	39	+	+	CCONJ
cana-4017	44	40	𝑥	𝑥	X
cana-4017	44	41	)	)	PUNCT
cana-4017	44	42	=	=	SYM
cana-4017	44	43	δ2	δ2	VERB
cana-4017	44	44	,	,	PUNCT
cana-4017	44	45	(	(	PUNCT
cana-4017	44	46	𝑃𝑁𝐴𝑁	𝑃𝑁𝐴𝑁	VERB
cana-4017	44	47	+	+	NOUN
cana-4017	44	48	𝑥	𝑥	NOUN
cana-4017	44	49	)	)	PUNCT
cana-4017	44	50	=	=	SYM
cana-4017	44	51	ψ2	ψ2	NOUN
cana-4017	44	52	,	,	PUNCT
cana-4017	44	53	(	(	PUNCT
cana-4017	44	54	𝐻𝑁𝑃𝑁	𝐻𝑁𝑃𝑁	PROPN
cana-4017	44	55	+	+	NOUN
cana-4017	44	56	𝑥	𝑥	NOUN
cana-4017	44	57	)	)	PUNCT
cana-4017	45	1	=	=	SYM
cana-4017	45	2	γ2.when	γ2.when	ADV
cana-4017	45	3	δ𝜓γ	δ𝜓γ	X
cana-4017	45	4	=	=	SYM
cana-4017	45	5	y	y	NOUN
cana-4017	45	6	,	,	PUNCT
cana-4017	45	7	then	then	ADV
cana-4017	45	8	(	(	PUNCT
cana-4017	45	9	𝐻𝑁𝐴𝑁	𝐻𝑁𝐴𝑁	NOUN
cana-4017	45	10	+	+	CCONJ
cana-4017	45	11	𝑥)(𝑃𝑁𝐴𝑁	𝑥)(𝑃𝑁𝐴𝑁	NOUN
cana-4017	45	12	+	+	NUM
cana-4017	45	13	𝑥)(𝐻𝑁𝑃𝑁	𝑥)(𝐻𝑁𝑃𝑁	PROPN
cana-4017	45	14	+	+	CCONJ
cana-4017	45	15	𝑥	𝑥	X
cana-4017	45	16	)	)	PUNCT
cana-4017	45	17	=	=	SYM
cana-4017	46	1	(	(	PUNCT
cana-4017	46	2	δ𝜓γ)2	δ𝜓γ)2	ADV
cana-4017	46	3	.when	.when	ADP
cana-4017	46	4	we	we	PRON
cana-4017	46	5	substitute	substitute	VERB
cana-4017	46	6	𝐻𝑁	𝐻𝑁	PROPN
cana-4017	46	7	=	=	SYM
cana-4017	46	8	19,𝑃𝑁	19,𝑃𝑁	PROPN
cana-4017	46	9	=	=	SYM
cana-4017	46	10	6	6	NUM
cana-4017	46	11	and	and	CCONJ
cana-4017	46	12	𝐴𝑁	𝐴𝑁	PROPN
cana-4017	46	13	=	=	SYM
cana-4017	46	14	47,which	47,which	PROPN
cana-4017	46	15	are	be	AUX
cana-4017	46	16	obtained	obtain	VERB
cana-4017	46	17	from	from	ADP
cana-4017	46	18	the	the	DET
cana-4017	46	19	choice	choice	NOUN
cana-4017	46	20	𝑛	𝑛	NOUN
cana-4017	46	21	=	=	SYM
cana-4017	46	22	2	2	NUM
cana-4017	46	23	,	,	PUNCT
cana-4017	46	24	we	we	PRON
cana-4017	46	25	get	get	VERB
cana-4017	46	26	an	an	DET
cana-4017	46	27	elliptic	elliptic	ADJ
cana-4017	46	28	curve	curve	NOUN
cana-4017	46	29	(	(	PUNCT
cana-4017	46	30	114	114	NUM
cana-4017	46	31	+	+	NUM
cana-4017	46	32	𝑥)(893	𝑥)(893	NOUN
cana-4017	46	33	+	+	CCONJ
cana-4017	46	34	𝑥)(282	𝑥)(282	ADJ
cana-4017	46	35	+	+	PUNCT
cana-4017	46	36	𝑥	𝑥	X
cana-4017	46	37	)	)	PUNCT
cana-4017	46	38	=	=	SYM
cana-4017	46	39	𝑦2	𝑦2	NOUN
cana-4017	46	40	simplifying	simplify	VERB
cana-4017	46	41	the	the	DET
cana-4017	46	42	expression	expression	NOUN
cana-4017	46	43	further	far	ADV
cana-4017	46	44	yields	yield	VERB
cana-4017	46	45	the	the	DET
cana-4017	46	46	following	follow	VERB
cana-4017	46	47	:	:	PUNCT
cana-4017	46	48	𝑥3	𝑥3	NOUN
cana-4017	46	49	+	+	CCONJ
cana-4017	46	50	1289𝑥2	1289𝑥2	NUM
cana-4017	46	51	+	+	NUM
cana-4017	46	52	385776𝑥	385776𝑥	NUM
cana-4017	46	53	+	+	CCONJ
cana-4017	46	54	28708164	28708164	NUM
cana-4017	46	55	=	=	SYM
cana-4017	46	56	𝑦2	𝑦2	NOUN
cana-4017	46	57	…	…	PUNCT
cana-4017	46	58	…	…	PUNCT
cana-4017	46	59	…	…	PUNCT
cana-4017	46	60	…	…	PUNCT
cana-4017	46	61	…	…	PUNCT
cana-4017	46	62	…	…	SYM
cana-4017	46	63	.(1	.(1	NUM
cana-4017	46	64	)	)	PUNCT
cana-4017	46	65	cubic	cubic	ADJ
cana-4017	46	66	equations	equation	NOUN
cana-4017	46	67	for	for	ADP
cana-4017	46	68	elliptic	elliptic	ADJ
cana-4017	46	69	curves	curve	NOUN
cana-4017	46	70	typically	typically	ADV
cana-4017	46	71	take	take	VERB
cana-4017	46	72	the	the	DET
cana-4017	46	73	form	form	NOUN
cana-4017	46	74	of	of	ADP
cana-4017	46	75	weierstrass	weierstrass	NOUN
cana-4017	46	76	equations	equation	NOUN
cana-4017	46	77	,	,	PUNCT
cana-4017	46	78	which	which	PRON
cana-4017	46	79	are	be	AUX
cana-4017	46	80	expressed	express	VERB
cana-4017	46	81	as	as	ADP
cana-4017	46	82	𝑦2	𝑦2	PROPN
cana-4017	46	83	+	+	CCONJ
cana-4017	46	84	𝑎𝑥𝑦	𝑎𝑥𝑦	NOUN
cana-4017	47	1	+	+	CCONJ
cana-4017	47	2	𝑏𝑦	𝑏𝑦	NOUN
cana-4017	47	3	=	=	SYM
cana-4017	47	4	𝑥3	𝑥3	NOUN
cana-4017	47	5	+	+	NUM
cana-4017	47	6	𝑐𝑥2	𝑐𝑥2	NOUN
cana-4017	47	7	+	+	CCONJ
cana-4017	47	8	𝑑𝑥	𝑑𝑥	X
cana-4017	47	9	+	+	NOUN
cana-4017	47	10	𝑒	𝑒	PROPN
cana-4017	47	11	where	where	SCONJ
cana-4017	47	12	𝑎	𝑎	NOUN
cana-4017	47	13	,	,	PUNCT
cana-4017	47	14	𝑏	𝑏	NOUN
cana-4017	47	15	,	,	PUNCT
cana-4017	47	16	𝑐	𝑐	PROPN
cana-4017	47	17	,	,	PUNCT
cana-4017	47	18	𝑑	𝑑	NOUN
cana-4017	47	19	,	,	PUNCT
cana-4017	47	20	𝑒	𝑒	PROPN
cana-4017	47	21	are	be	AUX
cana-4017	47	22	real	real	ADJ
cana-4017	47	23	numbers	number	NOUN
cana-4017	47	24	and	and	CCONJ
cana-4017	47	25	𝑥	𝑥	X
cana-4017	47	26	and	and	CCONJ
cana-4017	47	27	𝑦	𝑦	PRON
cana-4017	48	1	take	take	VERB
cana-4017	48	2	values	value	NOUN
cana-4017	48	3	in	in	ADP
cana-4017	48	4	the	the	DET
cana-4017	48	5	real	real	ADJ
cana-4017	48	6	numbers	number	NOUN
cana-4017	48	7	.	.	PUNCT
cana-4017	49	1	we	we	PRON
cana-4017	49	2	only	only	ADV
cana-4017	49	3	need	need	VERB
cana-4017	49	4	to	to	PART
cana-4017	49	5	consider	consider	VERB
cana-4017	49	6	equations	equation	NOUN
cana-4017	49	7	of	of	ADP
cana-4017	49	8	the	the	DET
cana-4017	49	9	type	type	NOUN
cana-4017	49	10	𝑦2	𝑦2	NOUN
cana-4017	49	11	=	=	SYM
cana-4017	49	12	𝑥3	𝑥3	NOUN
cana-4017	49	13	+	+	CCONJ
cana-4017	49	14	𝑎𝑥	𝑎𝑥	X
cana-4017	49	15	+	+	CCONJ
cana-4017	49	16	𝑏.	𝑏.	VERB
cana-4017	49	17	for	for	ADP
cana-4017	49	18	our	our	PRON
cana-4017	49	19	purposes	purpose	NOUN
cana-4017	49	20	.	.	PUNCT
cana-4017	50	1	reducing	reduce	VERB
cana-4017	50	2	(	(	PUNCT
cana-4017	50	3	1	1	NUM
cana-4017	50	4	)	)	PUNCT
cana-4017	50	5	over	over	ADP
cana-4017	50	6	𝐸𝑝	𝐸𝑝	PROPN
cana-4017	50	7	for	for	ADP
cana-4017	50	8	𝑝	𝑝	NOUN
cana-4017	50	9	=	=	SYM
cana-4017	50	10	1289	1289	NUM
cana-4017	50	11	yields	yield	VERB
cana-4017	50	12	an	an	DET
cana-4017	50	13	elliptic	elliptic	ADJ
cana-4017	50	14	curve	curve	NOUN
cana-4017	50	15	in	in	ADP
cana-4017	50	16	weierstrass	weierstrass	NOUN
cana-4017	50	17	form	form	NOUN
cana-4017	50	18	𝐸𝑝(𝑎	𝐸𝑝(𝑎	NOUN
cana-4017	50	19	,	,	PUNCT
cana-4017	50	20	𝑏	𝑏	NOUN
cana-4017	50	21	)	)	PUNCT
cana-4017	50	22	=	=	SYM
cana-4017	50	23	𝐸1289(365,845	𝐸1289(365,845	NOUN
cana-4017	50	24	)	)	PUNCT
cana-4017	50	25	.	.	PUNCT
cana-4017	51	1	therefore	therefore	ADV
cana-4017	51	2	,	,	PUNCT
cana-4017	51	3	(	(	PUNCT
cana-4017	51	4	𝑥3	𝑥3	NOUN
cana-4017	51	5	+	+	CCONJ
cana-4017	51	6	365𝑥	365𝑥	PROPN
cana-4017	51	7	+	+	CCONJ
cana-4017	51	8	845)(𝑚𝑜𝑑	845)(𝑚𝑜𝑑	NUM
cana-4017	51	9	1289	1289	NUM
cana-4017	51	10	)	)	PUNCT
cana-4017	52	1	=	=	SYM
cana-4017	52	2	𝑦2(𝑚𝑜𝑑	𝑦2(𝑚𝑜𝑑	NUM
cana-4017	52	3	1289	1289	NUM
cana-4017	52	4	)	)	PUNCT
cana-4017	52	5	…	…	PUNCT
cana-4017	52	6	…	…	PUNCT
cana-4017	52	7	…	…	PUNCT
cana-4017	52	8	…	…	PUNCT
cana-4017	52	9	…	…	PUNCT
cana-4017	52	10	…	…	PUNCT
cana-4017	52	11	..	..	PUNCT
cana-4017	52	12	(	(	PUNCT
cana-4017	52	13	2	2	X
cana-4017	52	14	)	)	PUNCT
cana-4017	52	15	when	when	SCONJ
cana-4017	52	16	congruence	congruence	NOUN
cana-4017	52	17	is	be	AUX
cana-4017	52	18	taken	take	VERB
cana-4017	52	19	modulo	modulo	NOUN
cana-4017	52	20	1289	1289	NUM
cana-4017	52	21	.	.	PUNCT
cana-4017	53	1	if	if	SCONJ
cana-4017	53	2	(	(	PUNCT
cana-4017	53	3	𝑥3	𝑥3	NOUN
cana-4017	53	4	+	+	CCONJ
cana-4017	53	5	𝑎𝑥	𝑎𝑥	X
cana-4017	53	6	+	+	CCONJ
cana-4017	53	7	𝑏	𝑏	NOUN
cana-4017	53	8	)	)	PUNCT
cana-4017	53	9	𝑚𝑜𝑑	𝑚𝑜𝑑	NOUN
cana-4017	53	10	𝑝	𝑝	PROPN
cana-4017	53	11	has	have	VERB
cana-4017	53	12	repeated	repeat	VERB
cana-4017	53	13	factors	factor	NOUN
cana-4017	53	14	,	,	PUNCT
cana-4017	53	15	then	then	ADV
cana-4017	53	16	the	the	DET
cana-4017	53	17	set	set	NOUN
cana-4017	53	18	𝐸𝑝(𝑎	𝐸𝑝(𝑎	NOUN
cana-4017	53	19	,	,	PUNCT
cana-4017	53	20	𝑏	𝑏	NOUN
cana-4017	53	21	)	)	PUNCT
cana-4017	53	22	can	can	AUX
cana-4017	53	23	be	be	AUX
cana-4017	53	24	used	use	VERB
cana-4017	53	25	to	to	PART
cana-4017	53	26	define	define	VERB
cana-4017	53	27	a	a	DET
cana-4017	53	28	finite	finite	ADJ
cana-4017	53	29	abelian	abelian	PROPN
cana-4017	53	30	group	group	NOUN
cana-4017	53	31	over	over	ADP
cana-4017	53	32	𝐸𝑝(𝑎	𝐸𝑝(𝑎	PROPN
cana-4017	53	33	,	,	PUNCT
cana-4017	53	34	𝑏).this	𝑏).this	PROPN
cana-4017	53	35	can	can	AUX
cana-4017	53	36	be	be	AUX
cana-4017	53	37	expressed	express	VERB
cana-4017	53	38	as	as	SCONJ
cana-4017	53	39	follows	follow	VERB
cana-4017	53	40	:	:	PUNCT
cana-4017	53	41	(	(	PUNCT
cana-4017	53	42	4𝑎3	4𝑎3	NUM
cana-4017	53	43	+	+	NUM
cana-4017	53	44	27𝑏2	27𝑏2	NUM
cana-4017	53	45	)	)	PUNCT
cana-4017	53	46	𝑚𝑜𝑑	𝑚𝑜𝑑	NOUN
cana-4017	53	47	𝑝	𝑝	NOUN
cana-4017	53	48	≠	≠	PROPN
cana-4017	53	49	0(𝑚𝑜𝑑	0(𝑚𝑜𝑑	ADJ
cana-4017	53	50	𝑝	𝑝	NOUN
cana-4017	53	51	)	)	PUNCT
cana-4017	53	52	.	.	PUNCT
cana-4017	54	1	4𝑎3	4𝑎3	NUM
cana-4017	55	1	+	+	NUM
cana-4017	55	2	27𝑏2	27𝑏2	NUM
cana-4017	55	3	≠	≠	NOUN
cana-4017	55	4	0	0	NUM
cana-4017	55	5	since	since	SCONJ
cana-4017	55	6	𝑎	𝑎	PROPN
cana-4017	55	7	=	=	SYM
cana-4017	55	8	365	365	NUM
cana-4017	55	9	,	,	PUNCT
cana-4017	55	10	𝑏	𝑏	PROPN
cana-4017	55	11	=	=	SYM
cana-4017	55	12	845	845	NUM
cana-4017	55	13	and	and	CCONJ
cana-4017	55	14	𝑝	𝑝	NOUN
cana-4017	55	15	=	=	SYM
cana-4017	55	16	1289.thus	1289.thus	NUM
cana-4017	55	17	,	,	PUNCT
cana-4017	55	18	elliptic	elliptic	ADJ
cana-4017	55	19	curve	curve	NOUN
cana-4017	55	20	cryptography	cryptography	NOUN
cana-4017	55	21	can	can	AUX
cana-4017	55	22	be	be	AUX
cana-4017	55	23	implemented	implement	VERB
cana-4017	55	24	using	use	VERB
cana-4017	55	25	equation	equation	NOUN
cana-4017	55	26	(	(	PUNCT
cana-4017	55	27	2	2	NUM
cana-4017	55	28	)	)	PUNCT
cana-4017	55	29	.	.	PUNCT
cana-4017	56	1	3	3	X
cana-4017	56	2	.	.	X
cana-4017	56	3	algorithm	algorithm	NOUN
cana-4017	56	4	for	for	ADP
cana-4017	56	5	elliptic	elliptic	ADJ
cana-4017	56	6	curve	curve	NOUN
cana-4017	56	7	cryptography	cryptography	NOUN
cana-4017	56	8	(	(	PUNCT
cana-4017	56	9	i	i	NOUN
cana-4017	56	10	)	)	PUNCT
cana-4017	56	11	𝐸𝑝(𝑎	𝐸𝑝(𝑎	NOUN
cana-4017	56	12	,	,	PUNCT
cana-4017	56	13	𝑏	𝑏	NOUN
cana-4017	56	14	)	)	PUNCT
cana-4017	56	15	∶	∶	NOUN
cana-4017	56	16	(	(	PUNCT
cana-4017	56	17	𝑥3	𝑥3	NOUN
cana-4017	56	18	+	+	CCONJ
cana-4017	56	19	365𝑥	365𝑥	NUM
cana-4017	56	20	+	+	CCONJ
cana-4017	56	21	845	845	NUM
cana-4017	56	22	)	)	PUNCT
cana-4017	57	1	=	=	NOUN
cana-4017	57	2	𝑦2	𝑦2	NOUN
cana-4017	57	3	is	be	AUX
cana-4017	57	4	the	the	DET
cana-4017	57	5	equation	equation	NOUN
cana-4017	57	6	for	for	ADP
cana-4017	57	7	an	an	DET
cana-4017	57	8	elliptic	elliptic	ADJ
cana-4017	57	9	curve	curve	NOUN
cana-4017	57	10	,	,	PUNCT
cana-4017	57	11	where	where	SCONJ
cana-4017	57	12	𝐸𝑝	𝐸𝑝	NOUN
cana-4017	57	13	is	be	AUX
cana-4017	57	14	an	an	DET
cana-4017	57	15	elliptic	elliptic	ADJ
cana-4017	57	16	curve	curve	NOUN
cana-4017	57	17	defined	define	VERB
cana-4017	57	18	over	over	ADP
cana-4017	57	19	the	the	DET
cana-4017	57	20	finite	finite	ADJ
cana-4017	57	21	field	field	NOUN
cana-4017	57	22	𝐸𝑝	𝐸𝑝	PROPN
cana-4017	57	23	for	for	ADP
cana-4017	57	24	a	a	DET
cana-4017	57	25	prime	prime	NOUN
cana-4017	57	26	𝑝	𝑝	NOUN
cana-4017	57	27	.	.	PUNCT
cana-4017	58	1	(	(	PUNCT
cana-4017	58	2	ii	ii	NOUN
cana-4017	58	3	)	)	PUNCT
cana-4017	58	4	key	key	NOUN
cana-4017	58	5	generating	generating	NOUN
cana-4017	58	6	:	:	PUNCT
cana-4017	58	7	the	the	DET
cana-4017	58	8	message	message	NOUN
cana-4017	58	9	will	will	AUX
cana-4017	58	10	be	be	AUX
cana-4017	58	11	encrypted	encrypt	VERB
cana-4017	58	12	by	by	ADP
cana-4017	58	13	the	the	DET
cana-4017	58	14	sender	sender	NOUN
cana-4017	58	15	using	use	VERB
cana-4017	58	16	the	the	DET
cana-4017	58	17	recipient	recipient	NOUN
cana-4017	58	18	's	's	PART
cana-4017	58	19	public	public	ADJ
cana-4017	58	20	key	key	NOUN
cana-4017	58	21	and	and	CCONJ
cana-4017	58	22	the	the	DET
cana-4017	58	23	recipient	recipient	NOUN
cana-4017	58	24	will	will	AUX
cana-4017	58	25	use	use	VERB
cana-4017	58	26	his	his	PRON
cana-4017	58	27	private	private	ADJ
cana-4017	58	28	key	key	NOUN
cana-4017	58	29	to	to	PART
cana-4017	58	30	decrypt	decrypt	VERB
cana-4017	58	31	it	it	PRON
cana-4017	58	32	.	.	PUNCT
cana-4017	59	1	(	(	PUNCT
cana-4017	59	2	i	i	NOUN
cana-4017	59	3	)	)	PUNCT
cana-4017	59	4	let	let	VERB
cana-4017	59	5	"	"	PUNCT
cana-4017	59	6	𝑀	𝑀	PROPN
cana-4017	59	7	"	"	PUNCT
cana-4017	59	8	be	be	AUX
cana-4017	59	9	the	the	DET
cana-4017	59	10	point	point	NOUN
cana-4017	59	11	on	on	ADP
cana-4017	59	12	the	the	DET
cana-4017	59	13	elliptic	elliptic	ADJ
cana-4017	59	14	curve	curve	NOUN
cana-4017	59	15	.	.	PUNCT
cana-4017	60	1	(	(	PUNCT
cana-4017	60	2	ii	ii	NOUN
cana-4017	60	3	)	)	PUNCT
cana-4017	60	4	select	select	ADJ
cana-4017	60	5	"	"	PUNCT
cana-4017	60	6	𝑀	𝑀	PROPN
cana-4017	60	7	"	"	PUNCT
cana-4017	60	8	as	as	ADP
cana-4017	60	9	the	the	DET
cana-4017	60	10	point	point	NOUN
cana-4017	60	11	from𝐸𝑝(𝑎	from𝐸𝑝(𝑎	PROPN
cana-4017	60	12	,	,	PUNCT
cana-4017	60	13	𝑏	𝑏	NOUN
cana-4017	60	14	)	)	PUNCT
cana-4017	60	15	.	.	PUNCT
cana-4017	61	1	(	(	PUNCT
cana-4017	61	2	iii	iii	X
cana-4017	61	3	)	)	PUNCT
cana-4017	61	4	choose	choose	VERB
cana-4017	61	5	generator	generator	NOUN
cana-4017	61	6	point	point	NOUN
cana-4017	61	7	𝐺	𝐺	PROPN
cana-4017	61	8	in	in	ADP
cana-4017	61	9	𝐸𝑝(𝑎	𝐸𝑝(𝑎	PROPN
cana-4017	61	10	,	,	PUNCT
cana-4017	61	11	𝑏	𝑏	NOUN
cana-4017	61	12	)	)	PUNCT
cana-4017	61	13	.	.	PUNCT
cana-4017	62	1	(	(	PUNCT
cana-4017	62	2	iv	iv	X
cana-4017	62	3	)	)	PUNCT
cana-4017	62	4	select	select	VERB
cana-4017	62	5	a	a	DET
cana-4017	62	6	private	private	ADJ
cana-4017	62	7	key	key	NOUN
cana-4017	62	8	𝑛	𝑛	PROPN
cana-4017	62	9	from	from	ADP
cana-4017	62	10	the	the	DET
cana-4017	62	11	interval	interval	NOUN
cana-4017	62	12	1	1	NUM
cana-4017	62	13	≤	≤	NOUN
cana-4017	62	14	𝑛	𝑛	DET
cana-4017	62	15	≤	≤	NUM
cana-4017	62	16	𝑝	𝑝	ADP
cana-4017	62	17	−	−	PROPN
cana-4017	62	18	1	1	NUM
cana-4017	62	19	and	and	CCONJ
cana-4017	62	20	utilize	utilize	VERB
cana-4017	62	21	it	it	PRON
cana-4017	62	22	to	to	PART
cana-4017	62	23	compute	compute	VERB
cana-4017	62	24	𝑃𝑈	𝑃𝑈	PROPN
cana-4017	62	25	=	=	SYM
cana-4017	62	26	𝑛	𝑛	PROPN
cana-4017	62	27	∗	∗	NOUN
cana-4017	62	28	𝐺	𝐺	PROPN
cana-4017	62	29	the	the	DET
cana-4017	62	30	public	public	ADJ
cana-4017	62	31	key	key	NOUN
cana-4017	62	32	.	.	PUNCT
cana-4017	63	1	(	(	PUNCT
cana-4017	63	2	v	v	NOUN
cana-4017	63	3	)	)	PUNCT
cana-4017	63	4	choose	choose	VERB
cana-4017	63	5	a	a	DET
cana-4017	63	6	number	number	NOUN
cana-4017	63	7	𝑘	𝑘	NOUN
cana-4017	63	8	that	that	PRON
cana-4017	63	9	falls	fall	VERB
cana-4017	63	10	between	between	ADP
cana-4017	63	11	1	1	NUM
cana-4017	63	12	≤	≤	NOUN
cana-4017	63	13	𝑘	𝑘	DET
cana-4017	63	14	≤	≤	NUM
cana-4017	63	15	𝑝	𝑝	ADV
cana-4017	63	16	−	−	PROPN
cana-4017	63	17	1	1	NUM
cana-4017	63	18	at	at	ADP
cana-4017	63	19	this	this	DET
cana-4017	63	20	point	point	NOUN
cana-4017	63	21	.	.	PUNCT
cana-4017	64	1	communications	communication	NOUN
cana-4017	64	2	on	on	ADP
cana-4017	64	3	applied	apply	VERB
cana-4017	64	4	nonlinear	nonlinear	ADJ
cana-4017	64	5	analysis	analysis	NOUN
cana-4017	64	6	issn	issn	NOUN
cana-4017	64	7	:	:	PUNCT
cana-4017	64	8	1074	1074	NUM
cana-4017	64	9	-	-	PUNCT
cana-4017	64	10	133x	133x	NUM
cana-4017	64	11	vol	vol	NOUN
cana-4017	64	12	32	32	NUM
cana-4017	64	13	no	no	NOUN
cana-4017	64	14	.	.	PUNCT
cana-4017	65	1	9s	9s	NUM
cana-4017	65	2	(	(	PUNCT
cana-4017	65	3	2025	2025	NUM
cana-4017	65	4	)	)	PUNCT
cana-4017	65	5	839	839	NUM
cana-4017	65	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4017	65	7	(	(	PUNCT
cana-4017	65	8	iii	iii	NOUN
cana-4017	65	9	)	)	PUNCT
cana-4017	65	10	encryption	encryption	NOUN
cana-4017	65	11	:	:	PUNCT
cana-4017	65	12	𝐶1and	𝐶1and	PROPN
cana-4017	65	13	𝐶2	𝐶2	X
cana-4017	65	14	are	be	AUX
cana-4017	65	15	the	the	DET
cana-4017	65	16	two	two	NUM
cana-4017	65	17	cipher	cipher	ADJ
cana-4017	65	18	texts	text	NOUN
cana-4017	65	19	that	that	PRON
cana-4017	65	20	will	will	AUX
cana-4017	65	21	be	be	AUX
cana-4017	65	22	generated	generate	VERB
cana-4017	65	23	.	.	PUNCT
cana-4017	66	1	𝐶1	𝐶1	PRON
cana-4017	66	2	=	=	SYM
cana-4017	66	3	𝑘	𝑘	PRON
cana-4017	66	4	∗	∗	NOUN
cana-4017	66	5	𝐺,𝐶2	𝐺,𝐶2	NOUN
cana-4017	67	1	=	=	SYM
cana-4017	67	2	𝑀	𝑀	PROPN
cana-4017	67	3	+	+	CCONJ
cana-4017	67	4	𝑘	𝑘	PRON
cana-4017	67	5	∗	∗	NOUN
cana-4017	67	6	𝑃𝑈.	𝑃𝑈.	NOUN
cana-4017	67	7	these	these	DET
cana-4017	67	8	𝐶1	𝐶1	NOUN
cana-4017	67	9	and	and	CCONJ
cana-4017	67	10	𝐶2will	𝐶2will	AUX
cana-4017	67	11	be	be	AUX
cana-4017	67	12	given	give	VERB
cana-4017	67	13	to	to	ADP
cana-4017	67	14	the	the	DET
cana-4017	67	15	recipient	recipient	NOUN
cana-4017	67	16	.	.	PUNCT
cana-4017	68	1	(	(	PUNCT
cana-4017	68	2	iv	iv	X
cana-4017	68	3	)	)	PUNCT
cana-4017	68	4	decryption	decryption	NOUN
cana-4017	68	5	:	:	PUNCT
cana-4017	68	6	the	the	DET
cana-4017	68	7	original	original	ADJ
cana-4017	68	8	point	point	NOUN
cana-4017	68	9	that	that	PRON
cana-4017	68	10	we	we	PRON
cana-4017	68	11	have	have	AUX
cana-4017	68	12	sent	send	VERB
cana-4017	68	13	,	,	PUNCT
cana-4017	68	14	point	point	VERB
cana-4017	68	15	"	"	PUNCT
cana-4017	68	16	𝑀	𝑀	PROPN
cana-4017	68	17	"	"	PUNCT
cana-4017	68	18	,	,	PUNCT
cana-4017	68	19	needs	need	VERB
cana-4017	68	20	to	to	PART
cana-4017	68	21	be	be	AUX
cana-4017	68	22	decrypted	decrypt	VERB
cana-4017	68	23	using	use	VERB
cana-4017	68	24	the	the	DET
cana-4017	68	25	formula	formula	NOUN
cana-4017	68	26	𝑀	𝑀	PROPN
cana-4017	68	27	=	=	PUNCT
cana-4017	69	1	𝐶2	𝐶2	PROPN
cana-4017	69	2	−	−	PROPN
cana-4017	69	3	𝑛	𝑛	PROPN
cana-4017	69	4	∗	∗	NOUN
cana-4017	69	5	𝐶1	𝐶1	NUM
cana-4017	69	6	,	,	PUNCT
cana-4017	69	7	as	as	SCONJ
cana-4017	69	8	it	it	PRON
cana-4017	69	9	was	be	AUX
cana-4017	69	10	sent	send	VERB
cana-4017	69	11	to	to	ADP
cana-4017	69	12	the	the	DET
cana-4017	69	13	recipient	recipient	NOUN
cana-4017	69	14	.	.	PUNCT
cana-4017	70	1	4	4	X
cana-4017	70	2	.	.	X
cana-4017	70	3	an	an	DET
cana-4017	70	4	example	example	NOUN
cana-4017	70	5	demonstrating	demonstrate	VERB
cana-4017	70	6	the	the	DET
cana-4017	70	7	encryption	encryption	NOUN
cana-4017	70	8	and	and	CCONJ
cana-4017	70	9	decryption	decryption	NOUN
cana-4017	70	10	of	of	ADP
cana-4017	70	11	an	an	DET
cana-4017	70	12	elliptic	elliptic	ADJ
cana-4017	70	13	curve	curve	NOUN
cana-4017	70	14	:	:	PUNCT
cana-4017	70	15	examine	examine	VERB
cana-4017	70	16	the	the	DET
cana-4017	70	17	following	follow	VERB
cana-4017	70	18	elliptic	elliptic	ADJ
cana-4017	70	19	curve	curve	NOUN
cana-4017	70	20	𝐸1289(365,845	𝐸1289(365,845	PROPN
cana-4017	70	21	):	):	PUNCT
cana-4017	70	22	𝑦2	𝑦2	PROPN
cana-4017	70	23	=	=	SYM
cana-4017	70	24	𝑥3	𝑥3	PROPN
cana-4017	70	25	+	+	CCONJ
cana-4017	70	26	365𝑥	365𝑥	PROPN
cana-4017	70	27	+	+	CCONJ
cana-4017	70	28	845	845	NUM
cana-4017	70	29	.	.	PUNCT
cana-4017	71	1	(	(	PUNCT
cana-4017	71	2	i)a	i)a	X
cana-4017	71	3	simple	simple	ADJ
cana-4017	71	4	text	text	NOUN
cana-4017	71	5	message	message	NOUN
cana-4017	71	6	can	can	AUX
cana-4017	71	7	be	be	AUX
cana-4017	71	8	encoded	encode	VERB
cana-4017	71	9	as	as	ADP
cana-4017	71	10	a	a	DET
cana-4017	71	11	point	point	NOUN
cana-4017	71	12	on	on	ADP
cana-4017	71	13	the	the	DET
cana-4017	71	14	elliptic	elliptic	ADJ
cana-4017	71	15	curve	curve	NOUN
cana-4017	71	16	𝐸1289(365,845	𝐸1289(365,845	PROPN
cana-4017	71	17	)	)	PUNCT
cana-4017	71	18	.	.	PUNCT
cana-4017	72	1	we	we	PRON
cana-4017	72	2	obtain	obtain	VERB
cana-4017	72	3	𝑀	𝑀	PROPN
cana-4017	72	4	=	=	SYM
cana-4017	72	5	(	(	PUNCT
cana-4017	72	6	188,1000	188,1000	NUM
cana-4017	72	7	)	)	PUNCT
cana-4017	72	8	∈	∈	PROPN
cana-4017	72	9	𝐸1289(365,845	𝐸1289(365,845	NOUN
cana-4017	72	10	)	)	PUNCT
cana-4017	72	11	from	from	ADP
cana-4017	72	12	the	the	DET
cana-4017	72	13	solution	solution	NOUN
cana-4017	72	14	of	of	ADP
cana-4017	72	15	(	(	PUNCT
cana-4017	72	16	2).this	2).this	NUM
cana-4017	72	17	study	study	NOUN
cana-4017	72	18	will	will	AUX
cana-4017	72	19	use	use	VERB
cana-4017	72	20	encryption	encryption	NOUN
cana-4017	72	21	to	to	PART
cana-4017	72	22	protect	protect	VERB
cana-4017	72	23	the	the	DET
cana-4017	72	24	point	point	NOUN
cana-4017	72	25	(	(	PUNCT
cana-4017	72	26	188,1000	188,1000	NUM
cana-4017	72	27	)	)	PUNCT
cana-4017	72	28	.	.	PUNCT
cana-4017	73	1	(	(	PUNCT
cana-4017	73	2	ii	ii	NOUN
cana-4017	73	3	)	)	PUNCT
cana-4017	73	4	a	a	DET
cana-4017	73	5	generator	generator	NOUN
cana-4017	73	6	point	point	NOUN
cana-4017	73	7	𝐺	𝐺	PROPN
cana-4017	73	8	=	=	SYM
cana-4017	73	9	(	(	PUNCT
cana-4017	73	10	8,446	8,446	NUM
cana-4017	73	11	)	)	PUNCT
cana-4017	73	12	∈	∈	PROPN
cana-4017	73	13	𝐸1289(365,845	𝐸1289(365,845	NOUN
cana-4017	73	14	)	)	PUNCT
cana-4017	73	15	should	should	AUX
cana-4017	73	16	be	be	AUX
cana-4017	73	17	selected	select	VERB
cana-4017	73	18	.	.	PUNCT
cana-4017	74	1	afterwards	afterwards	ADV
cana-4017	74	2	,	,	PUNCT
cana-4017	74	3	choose	choose	VERB
cana-4017	74	4	a	a	DET
cana-4017	74	5	private	private	ADJ
cana-4017	74	6	key	key	NOUN
cana-4017	74	7	𝑛	𝑛	NOUN
cana-4017	74	8	=	=	SYM
cana-4017	74	9	5	5	NUM
cana-4017	74	10	that	that	PRON
cana-4017	74	11	falls	fall	VERB
cana-4017	74	12	between	between	ADP
cana-4017	74	13	1	1	NUM
cana-4017	74	14	≤	≤	NUM
cana-4017	74	15	𝑛	𝑛	DET
cana-4017	74	16	≤	≤	NUM
cana-4017	74	17	1288	1288	NUM
cana-4017	74	18	and	and	CCONJ
cana-4017	74	19	calculate	calculate	VERB
cana-4017	74	20	𝑃𝑈	𝑃𝑈	PROPN
cana-4017	74	21	=	=	SYM
cana-4017	74	22	5	5	NUM
cana-4017	74	23	∗	∗	NOUN
cana-4017	74	24	𝐺.	𝐺.	NOUN
cana-4017	74	25	the	the	DET
cana-4017	74	26	algebraic	algebraic	ADJ
cana-4017	74	27	method	method	NOUN
cana-4017	74	28	for	for	ADP
cana-4017	74	29	elliptic	elliptic	ADJ
cana-4017	74	30	curves	curve	NOUN
cana-4017	74	31	defined	define	VERB
cana-4017	74	32	over	over	ADP
cana-4017	74	33	real	real	ADJ
cana-4017	74	34	numbers	number	NOUN
cana-4017	74	35	is	be	AUX
cana-4017	74	36	corresponding	correspond	VERB
cana-4017	74	37	to	to	ADP
cana-4017	74	38	the	the	DET
cana-4017	74	39	addition	addition	NOUN
cana-4017	74	40	rules	rule	NOUN
cana-4017	74	41	over	over	ADP
cana-4017	74	42	𝐸𝑝(𝑎	𝐸𝑝(𝑎	NOUN
cana-4017	74	43	,	,	PUNCT
cana-4017	74	44	𝑏	𝑏	NOUN
cana-4017	74	45	)	)	PUNCT
cana-4017	74	46	.	.	PUNCT
cana-4017	75	1	5	5	NUM
cana-4017	75	2	∗	∗	NOUN
cana-4017	75	3	𝐺	𝐺	NOUN
cana-4017	75	4	=	=	PUNCT
cana-4017	75	5	5(8,446	5(8,446	NUM
cana-4017	75	6	)	)	PUNCT
cana-4017	75	7	=	=	NOUN
cana-4017	75	8	(	(	PUNCT
cana-4017	75	9	8,446	8,446	NUM
cana-4017	75	10	)	)	PUNCT
cana-4017	75	11	+	+	CCONJ
cana-4017	75	12	(	(	PUNCT
cana-4017	75	13	8,446	8,446	NUM
cana-4017	75	14	)	)	PUNCT
cana-4017	75	15	+	+	CCONJ
cana-4017	75	16	(	(	PUNCT
cana-4017	75	17	8,446	8,446	NUM
cana-4017	75	18	)	)	PUNCT
cana-4017	75	19	+	+	CCONJ
cana-4017	75	20	(	(	PUNCT
cana-4017	75	21	8,446	8,446	NUM
cana-4017	75	22	)	)	PUNCT
cana-4017	75	23	+	+	CCONJ
cana-4017	75	24	(	(	PUNCT
cana-4017	75	25	8,446	8,446	NUM
cana-4017	75	26	)	)	PUNCT
cana-4017	75	27	when	when	SCONJ
cana-4017	75	28	we	we	PRON
cana-4017	75	29	first	first	ADV
cana-4017	75	30	compute	compute	VERB
cana-4017	75	31	5	5	NUM
cana-4017	75	32	∗	∗	NOUN
cana-4017	75	33	𝐺	𝐺	NOUN
cana-4017	75	34	=	=	SYM
cana-4017	75	35	(	(	PUNCT
cana-4017	75	36	1079,185	1079,185	NUM
cana-4017	75	37	)	)	PUNCT
cana-4017	75	38	,	,	PUNCT
cana-4017	75	39	we	we	PRON
cana-4017	75	40	obtain	obtain	VERB
cana-4017	75	41	𝑃𝑈	𝑃𝑈	NOUN
cana-4017	75	42	=	=	SYM
cana-4017	75	43	5	5	NUM
cana-4017	75	44	∗	∗	NOUN
cana-4017	75	45	𝐺	𝐺	NOUN
cana-4017	75	46	=	=	SYM
cana-4017	75	47	(	(	PUNCT
cana-4017	75	48	1079	1079	NUM
cana-4017	75	49	,	,	PUNCT
cana-4017	75	50	185	185	NUM
cana-4017	75	51	)	)	PUNCT
cana-4017	75	52	(	(	PUNCT
cana-4017	75	53	iii	iii	NOUN
cana-4017	75	54	)	)	PUNCT
cana-4017	75	55	for	for	ADP
cana-4017	75	56	𝑝	𝑝	NOUN
cana-4017	75	57	=	=	SYM
cana-4017	75	58	1289	1289	NUM
cana-4017	75	59	,	,	PUNCT
cana-4017	75	60	take	take	VERB
cana-4017	75	61	a	a	DET
cana-4017	75	62	random	random	ADJ
cana-4017	75	63	number	number	NOUN
cana-4017	75	64	𝑘	𝑘	ADP
cana-4017	75	65	such	such	ADJ
cana-4017	75	66	that	that	SCONJ
cana-4017	75	67	1	1	NUM
cana-4017	75	68	≤	≤	NOUN
cana-4017	76	1	𝑘	𝑘	DET
cana-4017	76	2	≤	≤	NUM
cana-4017	76	3	𝑝	𝑝	PROPN
cana-4017	76	4	−	−	PROPN
cana-4017	76	5	1.select	1.select	NUM
cana-4017	76	6	𝑘	𝑘	X
cana-4017	76	7	=	=	SYM
cana-4017	76	8	3	3	NUM
cana-4017	76	9	𝐶1	𝐶1	NOUN
cana-4017	76	10	=	=	SYM
cana-4017	76	11	𝑘	𝑘	PROPN
cana-4017	76	12	∗	∗	X
cana-4017	76	13	𝐺	𝐺	NOUN
cana-4017	76	14	=	=	PUNCT
cana-4017	76	15	(	(	PUNCT
cana-4017	76	16	868,435	868,435	NUM
cana-4017	76	17	)	)	PUNCT
cana-4017	76	18	𝐶2	𝐶2	PROPN
cana-4017	76	19	=	=	PUNCT
cana-4017	76	20	𝑀	𝑀	PROPN
cana-4017	76	21	+	+	CCONJ
cana-4017	76	22	𝑘	𝑘	PRON
cana-4017	76	23	∗	∗	NOUN
cana-4017	76	24	𝑃𝑈	𝑃𝑈	NOUN
cana-4017	76	25	=	=	SYM
cana-4017	76	26	(	(	PUNCT
cana-4017	76	27	188,1000	188,1000	NUM
cana-4017	76	28	)	)	PUNCT
cana-4017	76	29	+	+	CCONJ
cana-4017	76	30	3	3	NUM
cana-4017	76	31	∗	∗	NOUN
cana-4017	76	32	(	(	PUNCT
cana-4017	76	33	1079,185	1079,185	NUM
cana-4017	76	34	)	)	PUNCT
cana-4017	76	35	𝐶2	𝐶2	NOUN
cana-4017	76	36	=	=	PUNCT
cana-4017	76	37	(	(	PUNCT
cana-4017	76	38	1110,1232	1110,1232	NOUN
cana-4017	76	39	)	)	PUNCT
cana-4017	76	40	.	.	PUNCT
cana-4017	77	1	as	as	ADP
cana-4017	77	2	a	a	DET
cana-4017	77	3	result	result	NOUN
cana-4017	77	4	,	,	PUNCT
cana-4017	77	5	the	the	DET
cana-4017	77	6	cipher	cipher	ADJ
cana-4017	77	7	text	text	NOUN
cana-4017	77	8	or	or	CCONJ
cana-4017	77	9	encrypted	encrypt	VERB
cana-4017	77	10	message	message	NOUN
cana-4017	77	11	is	be	AUX
cana-4017	77	12	(	(	PUNCT
cana-4017	77	13	𝐶1	𝐶1	PROPN
cana-4017	77	14	,	,	PUNCT
cana-4017	77	15	𝐶2	𝐶2	PROPN
cana-4017	77	16	)	)	PUNCT
cana-4017	77	17	,	,	PUNCT
cana-4017	77	18	where	where	SCONJ
cana-4017	77	19	𝐶1	𝐶1	ADV
cana-4017	77	20	=	=	SYM
cana-4017	77	21	(	(	PUNCT
cana-4017	77	22	868,435	868,435	NUM
cana-4017	77	23	)	)	PUNCT
cana-4017	77	24	and	and	CCONJ
cana-4017	77	25	𝐶2	𝐶2	X
cana-4017	77	26	=	=	SYM
cana-4017	77	27	(	(	PUNCT
cana-4017	77	28	1110,1232	1110,1232	NOUN
cana-4017	77	29	)	)	PUNCT
cana-4017	77	30	.	.	PUNCT
cana-4017	78	1	(	(	PUNCT
cana-4017	78	2	iv	iv	X
cana-4017	78	3	)	)	PUNCT
cana-4017	78	4	to	to	PART
cana-4017	78	5	obtain	obtain	VERB
cana-4017	78	6	the	the	DET
cana-4017	78	7	elliptic	elliptic	ADJ
cana-4017	78	8	point	point	NOUN
cana-4017	78	9	,	,	PUNCT
cana-4017	78	10	the	the	DET
cana-4017	78	11	decryption	decryption	NOUN
cana-4017	78	12	process	process	NOUN
cana-4017	78	13	is	be	AUX
cana-4017	78	14	used	use	VERB
cana-4017	78	15	in	in	ADP
cana-4017	78	16	accordance	accordance	NOUN
cana-4017	78	17	with	with	ADP
cana-4017	78	18	the	the	DET
cana-4017	78	19	algorithm	algorithm	NOUN
cana-4017	78	20	,	,	PUNCT
cana-4017	78	21	𝑀	𝑀	PROPN
cana-4017	78	22	=	=	PUNCT
cana-4017	78	23	(	(	PUNCT
cana-4017	78	24	188,1000	188,1000	NUM
cana-4017	78	25	)	)	PUNCT
cana-4017	78	26	communications	communication	NOUN
cana-4017	78	27	on	on	ADP
cana-4017	78	28	applied	apply	VERB
cana-4017	78	29	nonlinear	nonlinear	ADJ
cana-4017	78	30	analysis	analysis	NOUN
cana-4017	78	31	issn	issn	NOUN
cana-4017	78	32	:	:	PUNCT
cana-4017	78	33	1074	1074	NUM
cana-4017	78	34	-	-	PUNCT
cana-4017	78	35	133x	133x	NUM
cana-4017	78	36	vol	vol	NOUN
cana-4017	78	37	32	32	NUM
cana-4017	79	1	no	no	NOUN
cana-4017	79	2	.	.	PUNCT
cana-4017	80	1	9s	9s	NUM
cana-4017	80	2	(	(	PUNCT
cana-4017	80	3	2025	2025	NUM
cana-4017	80	4	)	)	PUNCT
cana-4017	80	5	840	840	NUM
cana-4017	80	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4017	80	7	𝑀	𝑀	PROPN
cana-4017	80	8	=	=	PUNCT
cana-4017	81	1	𝐶2	𝐶2	PROPN
cana-4017	81	2	−	−	PROPN
cana-4017	82	1	𝑛	𝑛	PROPN
cana-4017	82	2	∗	∗	NOUN
cana-4017	82	3	𝐶1	𝐶1	NOUN
cana-4017	82	4	=	=	SYM
cana-4017	82	5	(	(	PUNCT
cana-4017	82	6	1110,1232	1110,1232	NUM
cana-4017	82	7	)	)	PUNCT
cana-4017	82	8	−	−	NOUN
cana-4017	82	9	5	5	NUM
cana-4017	82	10	∗	∗	NOUN
cana-4017	82	11	(	(	PUNCT
cana-4017	82	12	868,435	868,435	NUM
cana-4017	82	13	)	)	PUNCT
cana-4017	82	14	=	=	SYM
cana-4017	82	15	(	(	PUNCT
cana-4017	82	16	1110,1232	1110,1232	NOUN
cana-4017	82	17	)	)	PUNCT
cana-4017	82	18	−	−	PROPN
cana-4017	83	1	(	(	PUNCT
cana-4017	83	2	5,305	5,305	NUM
cana-4017	83	3	)	)	PUNCT
cana-4017	83	4	=	=	PRON
cana-4017	83	5	(	(	PUNCT
cana-4017	83	6	1110,1232	1110,1232	NOUN
cana-4017	83	7	)	)	PUNCT
cana-4017	83	8	+	+	CCONJ
cana-4017	83	9	(	(	PUNCT
cana-4017	83	10	5	5	NUM
cana-4017	83	11	,	,	PUNCT
cana-4017	83	12	−305(𝑚𝑜𝑑	−305(𝑚𝑜𝑑	ADJ
cana-4017	83	13	1289	1289	NUM
cana-4017	83	14	)	)	PUNCT
cana-4017	83	15	)	)	PUNCT
cana-4017	84	1	=	=	PRON
cana-4017	84	2	(	(	PUNCT
cana-4017	84	3	1110,1232	1110,1232	NOUN
cana-4017	84	4	)	)	PUNCT
cana-4017	84	5	+	+	CCONJ
cana-4017	84	6	(	(	PUNCT
cana-4017	84	7	5,984	5,984	NUM
cana-4017	84	8	)	)	PUNCT
cana-4017	84	9	𝑀	𝑀	PROPN
cana-4017	84	10	=	=	SYM
cana-4017	84	11	(	(	PUNCT
cana-4017	84	12	188,1000	188,1000	NUM
cana-4017	84	13	)	)	PUNCT
cana-4017	84	14	this	this	DET
cana-4017	84	15	verifies	verifie	NOUN
cana-4017	84	16	the	the	DET
cana-4017	84	17	process	process	NOUN
cana-4017	84	18	for	for	ADP
cana-4017	84	19	generating	generate	VERB
cana-4017	84	20	an	an	DET
cana-4017	84	21	elliptic	elliptic	ADJ
cana-4017	84	22	curve	curve	NOUN
cana-4017	84	23	for	for	ADP
cana-4017	84	24	cryptography	cryptography	NOUN
cana-4017	84	25	.	.	PUNCT
cana-4017	85	1	5	5	X
cana-4017	85	2	.	.	X
cana-4017	85	3	conclusion	conclusion	NOUN
cana-4017	85	4	in	in	ADP
cana-4017	85	5	summary	summary	NOUN
cana-4017	85	6	,	,	PUNCT
cana-4017	85	7	this	this	DET
cana-4017	85	8	research	research	NOUN
cana-4017	85	9	paper	paper	NOUN
cana-4017	85	10	contributes	contribute	VERB
cana-4017	85	11	to	to	ADP
cana-4017	85	12	the	the	DET
cana-4017	85	13	ongoing	ongoing	ADJ
cana-4017	85	14	efforts	effort	NOUN
cana-4017	85	15	to	to	PART
cana-4017	85	16	explore	explore	VERB
cana-4017	85	17	novel	novel	ADJ
cana-4017	85	18	mathematical	mathematical	ADJ
cana-4017	85	19	constructs	construct	NOUN
cana-4017	85	20	in	in	ADP
cana-4017	85	21	the	the	DET
cana-4017	85	22	design	design	NOUN
cana-4017	85	23	of	of	ADP
cana-4017	85	24	secure	secure	ADJ
cana-4017	85	25	and	and	CCONJ
cana-4017	85	26	efficient	efficient	ADJ
cana-4017	85	27	cryptographic	cryptographic	ADJ
cana-4017	85	28	systems	system	NOUN
cana-4017	85	29	.	.	PUNCT
cana-4017	86	1	by	by	ADP
cana-4017	86	2	harnessing	harness	VERB
cana-4017	86	3	the	the	DET
cana-4017	86	4	properties	property	NOUN
cana-4017	86	5	of	of	ADP
cana-4017	86	6	diophantine	diophantine	NOUN
cana-4017	86	7	triples	triple	NOUN
cana-4017	86	8	and	and	CCONJ
cana-4017	86	9	special	special	ADJ
cana-4017	86	10	polynomial	polynomial	ADJ
cana-4017	86	11	sequences	sequence	NOUN
cana-4017	86	12	,	,	PUNCT
cana-4017	86	13	it	it	PRON
cana-4017	86	14	's	be	AUX
cana-4017	86	15	possible	possible	ADJ
cana-4017	86	16	to	to	PART
cana-4017	86	17	develop	develop	VERB
cana-4017	86	18	elliptic	elliptic	ADJ
cana-4017	86	19	curves	curve	NOUN
cana-4017	86	20	that	that	PRON
cana-4017	86	21	offer	offer	VERB
cana-4017	86	22	robust	robust	ADJ
cana-4017	86	23	security	security	NOUN
cana-4017	86	24	features	feature	NOUN
cana-4017	86	25	for	for	ADP
cana-4017	86	26	modern	modern	ADJ
cana-4017	86	27	cryptographic	cryptographic	ADJ
cana-4017	86	28	applications	application	NOUN
cana-4017	86	29	references	reference	NOUN
cana-4017	86	30	[	[	X
cana-4017	86	31	1	1	NUM
cana-4017	86	32	]	]	X
cana-4017	86	33	dickson	dickson	PROPN
cana-4017	86	34	,	,	PUNCT
cana-4017	86	35	l.e.(1952	l.e.(1952	PROPN
cana-4017	86	36	)	)	PUNCT
cana-4017	86	37	.	.	PUNCT
cana-4017	87	1	history	history	NOUN
cana-4017	87	2	of	of	ADP
cana-4017	87	3	theory	theory	NOUN
cana-4017	87	4	of	of	ADP
cana-4017	87	5	numbers	number	NOUN
cana-4017	87	6	,	,	PUNCT
cana-4017	87	7	chelsea	chelsea	PROPN
cana-4017	87	8	publishing	publishing	PROPN
cana-4017	87	9	company	company	NOUN
cana-4017	87	10	,	,	PUNCT
cana-4017	87	11	new	new	PROPN
cana-4017	87	12	york	york	PROPN
cana-4017	87	13	.	.	PUNCT
cana-4017	88	1	[	[	X
cana-4017	88	2	2	2	NUM
cana-4017	88	3	]	]	X
cana-4017	88	4	miret	miret	NOUN
cana-4017	88	5	,	,	PUNCT
cana-4017	88	6	j.m	j.m	PROPN
cana-4017	88	7	.	.	PROPN
cana-4017	88	8	,	,	PUNCT
cana-4017	88	9	sadornil	sadornil	PROPN
cana-4017	88	10	,	,	PUNCT
cana-4017	88	11	d.	d.	PROPN
cana-4017	88	12	,	,	PUNCT
cana-4017	88	13	and	and	CCONJ
cana-4017	88	14	tena	tena	PROPN
cana-4017	88	15	,	,	PUNCT
cana-4017	88	16	j.g	j.g	PROPN
cana-4017	88	17	.	.	PROPN
cana-4017	88	18	(	(	PUNCT
cana-4017	88	19	2018	2018	NUM
cana-4017	88	20	)	)	PUNCT
cana-4017	88	21	.	.	PUNCT
cana-4017	89	1	pairing	pairing	NOUN
cana-4017	89	2	-	-	PUNCT
cana-4017	89	3	based	base	VERB
cana-4017	89	4	cryptography	cryptography	NOUN
cana-4017	89	5	on	on	ADP
cana-4017	89	6	elliptic	elliptic	ADJ
cana-4017	89	7	curves	curve	NOUN
cana-4017	89	8	.	.	PUNCT
cana-4017	90	1	math	math	NOUN
cana-4017	90	2	.	.	PUNCT
cana-4017	91	1	comput	comput	NOUN
cana-4017	91	2	.	.	PUNCT
cana-4017	92	1	sci	sci	PROPN
cana-4017	92	2	.	.	PROPN
cana-4017	92	3	12	12	NUM
cana-4017	92	4	,	,	PUNCT
cana-4017	92	5	309	309	NUM
cana-4017	92	6	-	-	SYM
cana-4017	92	7	318	318	NUM
cana-4017	92	8	.	.	PUNCT
cana-4017	93	1	[	[	X
cana-4017	93	2	3	3	NUM
cana-4017	93	3	]	]	X
cana-4017	93	4	kannan	kannan	PROPN
cana-4017	93	5	,	,	PUNCT
cana-4017	93	6	j.	j.	PROPN
cana-4017	93	7	,	,	PUNCT
cana-4017	93	8	manju	manju	PROPN
cana-4017	93	9	,	,	PUNCT
cana-4017	93	10	s.(2023	s.(2023	PROPN
cana-4017	93	11	)	)	PUNCT
cana-4017	93	12	.	.	PUNCT
cana-4017	94	1	fundamental	fundamental	ADJ
cana-4017	94	2	perceptions	perception	NOUN
cana-4017	94	3	in	in	ADP
cana-4017	94	4	contemporary	contemporary	ADJ
cana-4017	94	5	number	number	NOUN
cana-4017	94	6	theory	theory	NOUN
cana-4017	94	7	,	,	PUNCT
cana-4017	94	8	nova	nova	PROPN
cana-4017	94	9	science	science	NOUN
cana-4017	94	10	publisher	publisher	PROPN
cana-4017	94	11	,	,	PUNCT
cana-4017	94	12	inc	inc	PROPN
cana-4017	94	13	,	,	PUNCT
cana-4017	94	14	ny,11788	ny,11788	VERB
cana-4017	94	15	usa.isbn:979	usa.isbn:979	NOUN
cana-4017	94	16	-	-	PUNCT
cana-4017	94	17	8	8	NUM
cana-4017	94	18	-	-	PUNCT
cana-4017	94	19	88697	88697	NUM
cana-4017	94	20	-	-	PUNCT
cana-4017	94	21	794	794	NUM
cana-4017	94	22	-	-	SYM
cana-4017	94	23	3	3	NUM
cana-4017	94	24	.	.	PUNCT
cana-4017	95	1	[	[	X
cana-4017	95	2	4	4	X
cana-4017	95	3	]	]	PUNCT
cana-4017	95	4	richard	richard	PROPN
cana-4017	95	5	michael	michael	PROPN
cana-4017	95	6	hill,(2020).introduction	hill,(2020).introduction	PROPN
cana-4017	95	7	to	to	ADP
cana-4017	95	8	number	number	NOUN
cana-4017	95	9	theory	theory	NOUN
cana-4017	95	10	,	,	PUNCT
cana-4017	95	11	world	world	NOUN
cana-4017	95	12	scientific	scientific	ADJ
cana-4017	95	13	,	,	PUNCT
cana-4017	95	14	publishing	publish	VERB
cana-4017	95	15	company	company	NOUN
cana-4017	95	16	.	.	PUNCT
cana-4017	96	1	[	[	X
cana-4017	96	2	5	5	NUM
cana-4017	96	3	]	]	X
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cana-4017	96	5	,	,	PUNCT
cana-4017	96	6	v.	v.	ADP
cana-4017	96	7	,	,	PUNCT
cana-4017	96	8	anupreethi	anupreethi	NOUN
cana-4017	96	9	,	,	PUNCT
cana-4017	96	10	t.	t.	PROPN
cana-4017	96	11	,	,	PUNCT
cana-4017	96	12	and	and	CCONJ
cana-4017	96	13	manju	manju	PROPN
cana-4017	96	14	,	,	PUNCT
cana-4017	96	15	s.(2023	s.(2023	PROPN
cana-4017	96	16	)	)	PUNCT
cana-4017	96	17	.	.	PUNCT
cana-4017	97	1	construction	construction	NOUN
cana-4017	97	2	of	of	ADP
cana-4017	97	3	special	special	ADJ
cana-4017	97	4	dio	dio	NOUN
cana-4017	97	5	-	-	PUNCT
cana-4017	97	6	triples	triple	NOUN
cana-4017	97	7	.	.	PUNCT
cana-4017	98	1	indian	indian	ADJ
cana-4017	98	2	journal	journal	PROPN
cana-4017	98	3	of	of	ADP
cana-4017	98	4	science	science	NOUN
cana-4017	98	5	and	and	CCONJ
cana-4017	98	6	technology.16(39),3440	technology.16(39),3440	NOUN
cana-4017	98	7	-	-	PUNCT
cana-4017	98	8	3442	3442	NUM
cana-4017	98	9	.	.	PUNCT
cana-4017	99	1	[	[	X
cana-4017	99	2	6	6	NUM
cana-4017	99	3	]	]	PUNCT
cana-4017	99	4	https://oeis.org	https://oeis.org	PROPN
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cana-4017	99	7	]	]	X
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cana-4017	99	9	,	,	PUNCT
cana-4017	99	10	m.	m.	NOUN
cana-4017	99	11	,	,	PUNCT
cana-4017	99	12	das	das	PROPN
cana-4017	99	13	,	,	PUNCT
cana-4017	99	14	r.	r.	PROPN
cana-4017	99	15	,	,	PUNCT
cana-4017	99	16	and	and	CCONJ
cana-4017	99	17	bindu	bindu	NOUN
cana-4017	99	18	,	,	PUNCT
cana-4017	99	19	v.a	v.a	PROPN
cana-4017	99	20	.	.	PROPN
cana-4017	100	1	(	(	PUNCT
cana-4017	100	2	2024).solution	2024).solution	NUM
cana-4017	100	3	of	of	ADP
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cana-4017	100	6	's	's	PART
cana-4017	100	7	equation	equation	NOUN
cana-4017	100	8	using	use	VERB
cana-4017	100	9	self	self	NOUN
cana-4017	100	10	primes	prime	NOUN
cana-4017	100	11	,	,	PUNCT
cana-4017	100	12	palestine	palestine	PROPN
cana-4017	100	13	journal	journal	PROPN
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cana-4017	100	15	mathematics,13(4),1005	mathematics,13(4),1005	PROPN
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cana-4017	100	18	.	.	PUNCT
cana-4017	101	1	[	[	X
cana-4017	101	2	8	8	NUM
cana-4017	101	3	]	]	SYM
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cana-4017	101	5	,	,	PUNCT
cana-4017	101	6	m.	m.	NOUN
cana-4017	101	7	,	,	PUNCT
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cana-4017	101	10	j.	j.	PROPN
cana-4017	101	11	,	,	PUNCT
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cana-4017	101	16	a	a	DET
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cana-4017	101	18	of	of	ADP
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cana-4017	101	20	for	for	ADP
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cana-4017	101	22	hyperbolic	hyperbolic	ADJ
cana-4017	101	23	diophantine	diophantine	NOUN
cana-4017	101	24	equation	equation	NOUN
cana-4017	101	25	.	.	PUNCT
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cana-4017	102	2	journal	journal	NOUN
cana-4017	102	3	of	of	ADP
cana-4017	102	4	applied	apply	VERB
cana-4017	102	5	mathematics,32(3),443	mathematics,32(3),443	NOUN
cana-4017	102	6	-	-	PUNCT
cana-4017	102	7	449	449	NUM
cana-4017	102	8	.	.	PUNCT
cana-4017	103	1	[	[	X
cana-4017	103	2	9	9	NUM
cana-4017	103	3	]	]	SYM
cana-4017	103	4	somanath	somanath	NOUN
cana-4017	103	5	,	,	PUNCT
cana-4017	103	6	m.	m.	NOUN
cana-4017	103	7	,	,	PUNCT
cana-4017	103	8	gopalan	gopalan	PROPN
cana-4017	103	9	,	,	PUNCT
cana-4017	103	10	m.a	m.a	PROPN
cana-4017	103	11	.	.	PROPN
cana-4017	103	12	,	,	PUNCT
cana-4017	103	13	sangeetha	sangeetha	PROPN
cana-4017	103	14	,	,	PUNCT
cana-4017	103	15	v.(2014).construction	v.(2014).construction	NOUN
cana-4017	103	16	of	of	ADP
cana-4017	103	17	strong	strong	ADJ
cana-4017	103	18	and	and	CCONJ
cana-4017	103	19	almost	almost	ADV
cana-4017	103	20	strong	strong	ADJ
cana-4017	103	21	rational	rational	ADJ
cana-4017	103	22	diophantine	diophantine	NOUN
cana-4017	103	23	quadruples.jp	quadruples.jp	PRON
cana-4017	103	24	journal	journal	NOUN
cana-4017	103	25	of	of	ADP
cana-4017	103	26	algebra	algebra	PROPN
cana-4017	103	27	,	,	PUNCT
cana-4017	103	28	number	number	NOUN
cana-4017	103	29	theory	theory	NOUN
cana-4017	103	30	and	and	CCONJ
cana-4017	103	31	applications,35(1),35	applications,35(1),35	PROPN
cana-4017	103	32	-	-	SYM
cana-4017	103	33	48	48	NUM
cana-4017	103	34	.	.	PUNCT
cana-4017	104	1	[	[	X
cana-4017	104	2	10	10	NUM
cana-4017	104	3	]	]	X
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cana-4017	104	8	security	security	NOUN
cana-4017	104	9	:	:	PUNCT
cana-4017	104	10	principles	principle	NOUN
cana-4017	104	11	and	and	CCONJ
cana-4017	104	12	practice	practice	NOUN
cana-4017	104	13	,	,	PUNCT
cana-4017	104	14	pearson	pearson	PROPN
cana-4017	104	15	education	education	PROPN
cana-4017	104	16	inc	inc	PROPN
cana-4017	104	17	.	.	PROPN
cana-4017	104	18	,	,	PUNCT
cana-4017	104	19	london	london	PROPN
cana-4017	104	20	,	,	PUNCT
cana-4017	104	21	8th	8th	ADJ
cana-4017	104	22	edition	edition	NOUN
cana-4017	104	23	.	.	PUNCT
cana-4017	105	1	[	[	X
cana-4017	105	2	11	11	NUM
cana-4017	105	3	]	]	X
cana-4017	105	4	yuhan	yuhan	ADP
cana-4017	105	5	yan,(2022).the	yan,(2022).the	DET
cana-4017	105	6	overview	overview	NOUN
cana-4017	105	7	of	of	ADP
cana-4017	105	8	elliptic	elliptic	ADJ
cana-4017	105	9	curve	curve	NOUN
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cana-4017	105	11	(	(	PUNCT
cana-4017	105	12	ecc),journal	ecc),journal	PROPN
cana-4017	105	13	of	of	ADP
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cana-4017	105	15	:	:	PUNCT
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cana-4017	105	18	.	.	PUNCT
cana-4017	106	1	[	[	X
cana-4017	106	2	12	12	NUM
cana-4017	106	3	]	]	PUNCT
cana-4017	106	4	https://www.researchgate.net/publication/343211676_high_rank_elliptic_curves_induced_by	https://www.researchgate.net/publication/343211676_high_rank_elliptic_curves_induced_by	X
cana-4017	106	5	_	_	PRON
cana-4017	106	6	rational_diophantine_triples	rational_diophantine_triple	VERB