id	sid	tid	token	lemma	pos
ejpam-5659	1	1	european	european	PROPN
ejpam-5659	1	2	journal	journal	PROPN
ejpam-5659	1	3	of	of	ADP
ejpam-5659	1	4	pure	pure	ADJ
ejpam-5659	1	5	and	and	CCONJ
ejpam-5659	1	6	applied	applied	ADJ
ejpam-5659	1	7	mathematics	mathematic	NOUN
ejpam-5659	1	8	2025	2025	NUM
ejpam-5659	1	9	,	,	PUNCT
ejpam-5659	1	10	vol	vol	NOUN
ejpam-5659	1	11	.	.	PROPN
ejpam-5659	1	12	18	18	NUM
ejpam-5659	1	13	,	,	PUNCT
ejpam-5659	1	14	issue	issue	NOUN
ejpam-5659	1	15	2	2	NUM
ejpam-5659	1	16	,	,	PUNCT
ejpam-5659	1	17	article	article	NOUN
ejpam-5659	1	18	number	number	NOUN
ejpam-5659	1	19	5659	5659	NUM
ejpam-5659	1	20	issn	issn	PROPN
ejpam-5659	1	21	1307	1307	NUM
ejpam-5659	1	22	-	-	SYM
ejpam-5659	1	23	5543	5543	NUM
ejpam-5659	1	24	–	–	PUNCT
ejpam-5659	1	25	ejpam.com	ejpam.com	X
ejpam-5659	1	26	published	publish	VERB
ejpam-5659	1	27	by	by	ADP
ejpam-5659	1	28	new	new	PROPN
ejpam-5659	1	29	york	york	PROPN
ejpam-5659	1	30	business	business	PROPN
ejpam-5659	1	31	global	global	PROPN
ejpam-5659	1	32	a	a	DET
ejpam-5659	1	33	new	new	ADJ
ejpam-5659	1	34	septupling	septupling	NOUN
ejpam-5659	1	35	point	point	NOUN
ejpam-5659	1	36	7p	7p	NUM
ejpam-5659	1	37	arithmetic	arithmetic	ADJ
ejpam-5659	1	38	formula	formula	NOUN
ejpam-5659	1	39	for	for	ADP
ejpam-5659	1	40	lópez	lópez	ADV
ejpam-5659	1	41	-	-	PUNCT
ejpam-5659	1	42	dahab	dahab	NOUN
ejpam-5659	1	43	coordinate	coordinate	NOUN
ejpam-5659	1	44	and	and	CCONJ
ejpam-5659	1	45	affine	affine	VERB
ejpam-5659	1	46	over	over	ADP
ejpam-5659	1	47	binary	binary	ADJ
ejpam-5659	1	48	elliptic	elliptic	ADJ
ejpam-5659	1	49	curve	curve	NOUN
ejpam-5659	1	50	cryptosystem	cryptosystem	NOUN
ejpam-5659	1	51	waleed	waleed	PROPN
ejpam-5659	1	52	k.	k.	PROPN
ejpam-5659	1	53	abdulraheem	abdulraheem	PROPN
ejpam-5659	1	54	department	department	PROPN
ejpam-5659	1	55	of	of	ADP
ejpam-5659	1	56	information	information	NOUN
ejpam-5659	1	57	system	system	NOUN
ejpam-5659	1	58	and	and	CCONJ
ejpam-5659	1	59	network	network	NOUN
ejpam-5659	1	60	,	,	PUNCT
ejpam-5659	1	61	the	the	DET
ejpam-5659	1	62	world	world	NOUN
ejpam-5659	1	63	islamic	islamic	PROPN
ejpam-5659	1	64	sciences	sciences	PROPN
ejpam-5659	1	65	and	and	CCONJ
ejpam-5659	1	66	education	education	PROPN
ejpam-5659	1	67	university	university	PROPN
ejpam-5659	1	68	,	,	PUNCT
ejpam-5659	1	69	amman	amman	PROPN
ejpam-5659	1	70	,	,	PUNCT
ejpam-5659	1	71	jordan	jordan	PROPN
ejpam-5659	1	72	abstract	abstract	PROPN
ejpam-5659	1	73	.	.	PUNCT
ejpam-5659	2	1	the	the	DET
ejpam-5659	2	2	elliptic	elliptic	ADJ
ejpam-5659	2	3	curve	curve	NOUN
ejpam-5659	2	4	cryptography	cryptography	NOUN
ejpam-5659	2	5	(	(	PUNCT
ejpam-5659	2	6	ecc	ecc	PROPN
ejpam-5659	2	7	)	)	PUNCT
ejpam-5659	2	8	is	be	AUX
ejpam-5659	2	9	one	one	NUM
ejpam-5659	2	10	of	of	ADP
ejpam-5659	2	11	the	the	DET
ejpam-5659	2	12	most	most	ADV
ejpam-5659	2	13	prominent	prominent	ADJ
ejpam-5659	2	14	asymmetricbased	asymmetricbase	VERB
ejpam-5659	2	15	cryptosystems	cryptosystem	NOUN
ejpam-5659	2	16	as	as	SCONJ
ejpam-5659	2	17	it	it	PRON
ejpam-5659	2	18	affords	afford	VERB
ejpam-5659	2	19	a	a	DET
ejpam-5659	2	20	higher	high	ADJ
ejpam-5659	2	21	level	level	NOUN
ejpam-5659	2	22	of	of	ADP
ejpam-5659	2	23	security	security	NOUN
ejpam-5659	2	24	with	with	ADP
ejpam-5659	2	25	small	small	ADJ
ejpam-5659	2	26	keys	key	NOUN
ejpam-5659	2	27	.	.	PUNCT
ejpam-5659	3	1	according	accord	VERB
ejpam-5659	3	2	to	to	ADP
ejpam-5659	3	3	national	national	PROPN
ejpam-5659	3	4	institute	institute	PROPN
ejpam-5659	3	5	of	of	ADP
ejpam-5659	3	6	standards	standard	NOUN
ejpam-5659	3	7	and	and	CCONJ
ejpam-5659	3	8	technology	technology	NOUN
ejpam-5659	3	9	(	(	PUNCT
ejpam-5659	3	10	nist	nist	NOUN
ejpam-5659	3	11	)	)	PUNCT
ejpam-5659	3	12	,	,	PUNCT
ejpam-5659	3	13	ecc	ecc	PROPN
ejpam-5659	3	14	gains	gain	VERB
ejpam-5659	3	15	the	the	DET
ejpam-5659	3	16	smallest	small	ADJ
ejpam-5659	3	17	secure	secure	ADJ
ejpam-5659	3	18	key	key	NOUN
ejpam-5659	3	19	over	over	ADP
ejpam-5659	3	20	the	the	DET
ejpam-5659	3	21	binary	binary	ADJ
ejpam-5659	3	22	curve	curve	NOUN
ejpam-5659	3	23	.	.	PUNCT
ejpam-5659	4	1	in	in	ADP
ejpam-5659	4	2	literature	literature	NOUN
ejpam-5659	4	3	,	,	PUNCT
ejpam-5659	4	4	the	the	DET
ejpam-5659	4	5	best	good	ADJ
ejpam-5659	4	6	field	field	NOUN
ejpam-5659	4	7	over	over	ADP
ejpam-5659	4	8	binary	binary	ADJ
ejpam-5659	4	9	curves	curve	NOUN
ejpam-5659	4	10	is	be	AUX
ejpam-5659	4	11	lopez	lopez	ADJ
ejpam-5659	4	12	-	-	PUNCT
ejpam-5659	4	13	dahab	dahab	PROPN
ejpam-5659	4	14	(	(	PUNCT
ejpam-5659	4	15	ld	ld	PROPN
ejpam-5659	4	16	)	)	PUNCT
ejpam-5659	4	17	and	and	CCONJ
ejpam-5659	4	18	affine	affine	NOUN
ejpam-5659	4	19	coordinates	coordinate	NOUN
ejpam-5659	4	20	,	,	PUNCT
ejpam-5659	4	21	and	and	CCONJ
ejpam-5659	4	22	it	it	PRON
ejpam-5659	4	23	considered	consider	VERB
ejpam-5659	4	24	fit	fit	ADJ
ejpam-5659	4	25	for	for	ADP
ejpam-5659	4	26	lightweight	lightweight	ADJ
ejpam-5659	4	27	cryptography	cryptography	NOUN
ejpam-5659	4	28	in	in	ADP
ejpam-5659	4	29	resource	resource	NOUN
ejpam-5659	4	30	-	-	PUNCT
ejpam-5659	4	31	constrained	constrain	VERB
ejpam-5659	4	32	devices	device	NOUN
ejpam-5659	4	33	such	such	ADJ
ejpam-5659	4	34	as	as	ADP
ejpam-5659	4	35	internet	internet	NOUN
ejpam-5659	4	36	of	of	ADP
ejpam-5659	4	37	things	thing	NOUN
ejpam-5659	4	38	(	(	PUNCT
ejpam-5659	4	39	iots	iot	NOUN
ejpam-5659	4	40	)	)	PUNCT
ejpam-5659	4	41	.	.	PUNCT
ejpam-5659	5	1	ecc	ecc	PROPN
ejpam-5659	5	2	consists	consist	VERB
ejpam-5659	5	3	of	of	ADP
ejpam-5659	5	4	three	three	NUM
ejpam-5659	5	5	operational	operational	ADJ
ejpam-5659	5	6	levels	level	NOUN
ejpam-5659	5	7	;	;	PUNCT
ejpam-5659	5	8	scalar	scalar	ADJ
ejpam-5659	5	9	multiplication	multiplication	NOUN
ejpam-5659	5	10	,	,	PUNCT
ejpam-5659	5	11	point	point	NOUN
ejpam-5659	5	12	arithmetic	arithmetic	ADJ
ejpam-5659	5	13	and	and	CCONJ
ejpam-5659	5	14	field	field	NOUN
ejpam-5659	5	15	arithmetic	arithmetic	ADJ
ejpam-5659	5	16	.	.	PUNCT
ejpam-5659	6	1	this	this	DET
ejpam-5659	6	2	research	research	NOUN
ejpam-5659	6	3	focuses	focus	VERB
ejpam-5659	6	4	on	on	ADP
ejpam-5659	6	5	point	point	NOUN
ejpam-5659	6	6	arithmetic	arithmetic	ADJ
ejpam-5659	6	7	precomputation	precomputation	NOUN
ejpam-5659	6	8	useful	useful	ADJ
ejpam-5659	6	9	in	in	ADP
ejpam-5659	6	10	scalar	scalar	ADJ
ejpam-5659	6	11	multiplication	multiplication	NOUN
ejpam-5659	6	12	and	and	CCONJ
ejpam-5659	6	13	then	then	ADV
ejpam-5659	6	14	for	for	SCONJ
ejpam-5659	6	15	field	field	NOUN
ejpam-5659	6	16	arithmetic	arithmetic	ADJ
ejpam-5659	6	17	.	.	PUNCT
ejpam-5659	7	1	there	there	PRON
ejpam-5659	7	2	is	be	VERB
ejpam-5659	7	3	no	no	DET
ejpam-5659	7	4	existing	exist	VERB
ejpam-5659	7	5	formula	formula	NOUN
ejpam-5659	7	6	for	for	ADP
ejpam-5659	7	7	septupling	septuple	VERB
ejpam-5659	7	8	point	point	NOUN
ejpam-5659	7	9	7p	7p	NOUN
ejpam-5659	7	10	over	over	ADP
ejpam-5659	7	11	binary	binary	ADJ
ejpam-5659	7	12	curves	curve	NOUN
ejpam-5659	7	13	in	in	ADP
ejpam-5659	7	14	ld	ld	PROPN
ejpam-5659	7	15	and	and	CCONJ
ejpam-5659	7	16	affine	affine	PROPN
ejpam-5659	7	17	coordinates	coordinate	NOUN
ejpam-5659	7	18	.	.	PUNCT
ejpam-5659	8	1	a	a	DET
ejpam-5659	8	2	new	new	ADJ
ejpam-5659	8	3	precomputed	precompute	VERB
ejpam-5659	8	4	septupling	septupling	NOUN
ejpam-5659	8	5	point	point	NOUN
ejpam-5659	8	6	7p	7p	NUM
ejpam-5659	8	7	is	be	AUX
ejpam-5659	8	8	introduced	introduce	VERB
ejpam-5659	8	9	in	in	ADP
ejpam-5659	8	10	this	this	DET
ejpam-5659	8	11	paper	paper	NOUN
ejpam-5659	8	12	using	use	VERB
ejpam-5659	8	13	ld	ld	PROPN
ejpam-5659	8	14	and	and	CCONJ
ejpam-5659	8	15	non	non	ADJ
ejpam-5659	8	16	-	-	ADJ
ejpam-5659	8	17	supersingular	supersingular	ADJ
ejpam-5659	8	18	affine	affine	NOUN
ejpam-5659	8	19	coordinate	coordinate	NOUN
ejpam-5659	8	20	over	over	ADP
ejpam-5659	8	21	the	the	DET
ejpam-5659	8	22	binary	binary	ADJ
ejpam-5659	8	23	field	field	NOUN
ejpam-5659	8	24	e(f2	e(f2	PROPN
ejpam-5659	8	25	m	m	PROPN
ejpam-5659	8	26	)	)	PUNCT
ejpam-5659	8	27	.	.	PUNCT
ejpam-5659	9	1	this	this	DET
ejpam-5659	9	2	paper	paper	NOUN
ejpam-5659	9	3	uses	use	VERB
ejpam-5659	9	4	the	the	DET
ejpam-5659	9	5	form	form	NOUN
ejpam-5659	9	6	7p	7p	NOUN
ejpam-5659	9	7	=	=	SYM
ejpam-5659	9	8	2(3p	2(3p	NUM
ejpam-5659	9	9	)	)	PUNCT
ejpam-5659	10	1	+	+	CCONJ
ejpam-5659	10	2	p	p	X
ejpam-5659	10	3	,	,	PUNCT
ejpam-5659	10	4	consisting	consist	VERB
ejpam-5659	10	5	of	of	ADP
ejpam-5659	10	6	doubling	double	VERB
ejpam-5659	10	7	point	point	NOUN
ejpam-5659	10	8	,	,	PUNCT
ejpam-5659	10	9	tripling	triple	VERB
ejpam-5659	10	10	point	point	NOUN
ejpam-5659	10	11	and	and	CCONJ
ejpam-5659	10	12	the	the	DET
ejpam-5659	10	13	point	point	NOUN
ejpam-5659	10	14	addition	addition	NOUN
ejpam-5659	10	15	.	.	PUNCT
ejpam-5659	11	1	also	also	ADV
ejpam-5659	11	2	,	,	PUNCT
ejpam-5659	11	3	the	the	DET
ejpam-5659	11	4	form	form	NOUN
ejpam-5659	11	5	2(3p	2(3p	NUM
ejpam-5659	11	6	)	)	PUNCT
ejpam-5659	11	7	means	mean	VERB
ejpam-5659	11	8	the	the	DET
ejpam-5659	11	9	sixtupling	sixtupling	NOUN
ejpam-5659	11	10	point	point	NOUN
ejpam-5659	11	11	is	be	AUX
ejpam-5659	11	12	also	also	ADV
ejpam-5659	11	13	proposed	propose	VERB
ejpam-5659	11	14	.	.	PUNCT
ejpam-5659	12	1	results	result	NOUN
ejpam-5659	12	2	show	show	VERB
ejpam-5659	12	3	that	that	SCONJ
ejpam-5659	12	4	the	the	DET
ejpam-5659	12	5	7p	7p	NUM
ejpam-5659	12	6	is	be	AUX
ejpam-5659	12	7	characterized	characterize	VERB
ejpam-5659	12	8	by	by	ADP
ejpam-5659	12	9	a	a	DET
ejpam-5659	12	10	cost	cost	NOUN
ejpam-5659	12	11	of	of	ADP
ejpam-5659	12	12	19	19	NUM
ejpam-5659	12	13	s	s	PART
ejpam-5659	12	14	+	+	NUM
ejpam-5659	12	15	28	28	NUM
ejpam-5659	12	16	m	m	NOUN
ejpam-5659	12	17	,	,	PUNCT
ejpam-5659	12	18	while	while	SCONJ
ejpam-5659	12	19	the	the	DET
ejpam-5659	12	20	cost	cost	NOUN
ejpam-5659	12	21	of	of	ADP
ejpam-5659	12	22	sixtupling	sixtupling	NOUN
ejpam-5659	12	23	point	point	NOUN
ejpam-5659	12	24	6p	6p	NUM
ejpam-5659	12	25	is	be	AUX
ejpam-5659	12	26	14	14	NUM
ejpam-5659	12	27	s	s	NOUN
ejpam-5659	12	28	+	+	NUM
ejpam-5659	12	29	19	19	NUM
ejpam-5659	12	30	m	m	NOUN
ejpam-5659	12	31	.	.	PUNCT
ejpam-5659	13	1	the	the	DET
ejpam-5659	13	2	point	point	NOUN
ejpam-5659	13	3	is	be	AUX
ejpam-5659	13	4	mathematically	mathematically	ADV
ejpam-5659	13	5	proved	prove	VERB
ejpam-5659	13	6	as	as	ADP
ejpam-5659	13	7	valid	valid	ADJ
ejpam-5659	13	8	.	.	PUNCT
ejpam-5659	14	1	the	the	DET
ejpam-5659	14	2	proposed	propose	VERB
ejpam-5659	14	3	point	point	NOUN
ejpam-5659	14	4	can	can	AUX
ejpam-5659	14	5	be	be	AUX
ejpam-5659	14	6	implemented	implement	VERB
ejpam-5659	14	7	for	for	ADP
ejpam-5659	14	8	different	different	ADJ
ejpam-5659	14	9	scalar	scalar	ADJ
ejpam-5659	14	10	multiplication	multiplication	NOUN
ejpam-5659	14	11	such	such	ADJ
ejpam-5659	14	12	as	as	ADP
ejpam-5659	14	13	w−naf	w−naf	NOUN
ejpam-5659	14	14	for	for	ADP
ejpam-5659	14	15	w	w	NOUN
ejpam-5659	14	16	=	=	SYM
ejpam-5659	14	17	4	4	NUM
ejpam-5659	14	18	,	,	PUNCT
ejpam-5659	14	19	and	and	CCONJ
ejpam-5659	14	20	multi	multi	ADJ
ejpam-5659	14	21	-	-	ADJ
ejpam-5659	14	22	based	base	VERB
ejpam-5659	14	23	scalar	scalar	NOUN
ejpam-5659	14	24	such	such	ADJ
ejpam-5659	14	25	as	as	ADP
ejpam-5659	14	26	{	{	PUNCT
ejpam-5659	14	27	2	2	NUM
ejpam-5659	14	28	,	,	PUNCT
ejpam-5659	14	29	3	3	NUM
ejpam-5659	14	30	,	,	PUNCT
ejpam-5659	14	31	7}-based	7}-based	NUM
ejpam-5659	14	32	scalar	scalar	ADJ
ejpam-5659	14	33	multiplication	multiplication	NOUN
ejpam-5659	14	34	method	method	NOUN
ejpam-5659	14	35	.	.	PUNCT
ejpam-5659	15	1	2020	2020	NUM
ejpam-5659	15	2	mathematics	mathematic	NOUN
ejpam-5659	15	3	subject	subject	NOUN
ejpam-5659	15	4	classifications	classification	NOUN
ejpam-5659	15	5	:	:	PUNCT
ejpam-5659	15	6	94a60	94a60	NUM
ejpam-5659	15	7	,	,	PUNCT
ejpam-5659	15	8	11t71	11t71	NUM
ejpam-5659	15	9	,	,	PUNCT
ejpam-5659	15	10	14g50	14g50	NUM
ejpam-5659	15	11	,	,	PUNCT
ejpam-5659	15	12	68p25	68p25	NUM
ejpam-5659	15	13	key	key	ADJ
ejpam-5659	15	14	words	word	NOUN
ejpam-5659	15	15	and	and	CCONJ
ejpam-5659	15	16	phrases	phrase	NOUN
ejpam-5659	15	17	:	:	PUNCT
ejpam-5659	15	18	elliptic	elliptic	ADJ
ejpam-5659	15	19	curve	curve	NOUN
ejpam-5659	15	20	cryptography	cryptography	NOUN
ejpam-5659	15	21	,	,	PUNCT
ejpam-5659	15	22	information	information	NOUN
ejpam-5659	15	23	security	security	NOUN
ejpam-5659	15	24	,	,	PUNCT
ejpam-5659	15	25	binary	binary	ADJ
ejpam-5659	15	26	curves	curve	NOUN
ejpam-5659	15	27	,	,	PUNCT
ejpam-5659	15	28	affine	affine	NOUN
ejpam-5659	15	29	coordinates	coordinate	NOUN
ejpam-5659	15	30	,	,	PUNCT
ejpam-5659	15	31	point	point	NOUN
ejpam-5659	15	32	septupling	septuple	VERB
ejpam-5659	15	33	arithmetic	arithmetic	ADJ
ejpam-5659	15	34	,	,	PUNCT
ejpam-5659	15	35	lightweight	lightweight	ADJ
ejpam-5659	15	36	cryptography	cryptography	NOUN
ejpam-5659	15	37	1	1	NUM
ejpam-5659	15	38	.	.	PUNCT
ejpam-5659	16	1	introduction	introduction	NOUN
ejpam-5659	16	2	recently	recently	ADV
ejpam-5659	16	3	,	,	PUNCT
ejpam-5659	16	4	information	information	NOUN
ejpam-5659	16	5	security	security	NOUN
ejpam-5659	16	6	has	have	AUX
ejpam-5659	16	7	become	become	VERB
ejpam-5659	16	8	one	one	NUM
ejpam-5659	16	9	of	of	ADP
ejpam-5659	16	10	the	the	DET
ejpam-5659	16	11	most	most	ADV
ejpam-5659	16	12	important	important	ADJ
ejpam-5659	16	13	research	research	NOUN
ejpam-5659	16	14	topics	topic	NOUN
ejpam-5659	16	15	affecting	affect	VERB
ejpam-5659	16	16	,	,	PUNCT
ejpam-5659	16	17	organizations	organization	NOUN
ejpam-5659	16	18	,	,	PUNCT
ejpam-5659	16	19	countries	country	NOUN
ejpam-5659	16	20	[	[	X
ejpam-5659	16	21	1	1	NUM
ejpam-5659	16	22	]	]	PUNCT
ejpam-5659	16	23	.	.	PUNCT
ejpam-5659	17	1	cryptography	cryptography	NOUN
ejpam-5659	17	2	is	be	AUX
ejpam-5659	17	3	considered	consider	VERB
ejpam-5659	17	4	the	the	DET
ejpam-5659	17	5	most	most	ADV
ejpam-5659	17	6	fundamental	fundamental	ADJ
ejpam-5659	17	7	method	method	NOUN
ejpam-5659	17	8	used	use	VERB
ejpam-5659	17	9	to	to	PART
ejpam-5659	17	10	ensure	ensure	VERB
ejpam-5659	17	11	the	the	DET
ejpam-5659	17	12	information	information	NOUN
ejpam-5659	17	13	and	and	CCONJ
ejpam-5659	17	14	cyber	cyber	NOUN
ejpam-5659	17	15	security	security	NOUN
ejpam-5659	17	16	[	[	X
ejpam-5659	17	17	2	2	NUM
ejpam-5659	17	18	]	]	PUNCT
ejpam-5659	17	19	.	.	PUNCT
ejpam-5659	18	1	as	as	ADP
ejpam-5659	18	2	a	a	DET
ejpam-5659	18	3	mechanism	mechanism	NOUN
ejpam-5659	18	4	for	for	ADP
ejpam-5659	18	5	achieving	achieve	VERB
ejpam-5659	18	6	security	security	NOUN
ejpam-5659	18	7	,	,	PUNCT
ejpam-5659	18	8	cryptography	cryptography	NOUN
ejpam-5659	18	9	is	be	AUX
ejpam-5659	18	10	vital	vital	ADJ
ejpam-5659	18	11	to	to	PART
ejpam-5659	18	12	protect	protect	VERB
ejpam-5659	18	13	our	our	PRON
ejpam-5659	18	14	data	data	NOUN
ejpam-5659	18	15	,	,	PUNCT
ejpam-5659	18	16	information	information	NOUN
ejpam-5659	18	17	,	,	PUNCT
ejpam-5659	18	18	and	and	CCONJ
ejpam-5659	18	19	communication	communication	NOUN
ejpam-5659	18	20	from	from	ADP
ejpam-5659	18	21	threats	threat	NOUN
ejpam-5659	18	22	,	,	PUNCT
ejpam-5659	18	23	intruders	intruder	NOUN
ejpam-5659	18	24	,	,	PUNCT
ejpam-5659	18	25	and	and	CCONJ
ejpam-5659	18	26	attackers	attacker	NOUN
ejpam-5659	18	27	[	[	X
ejpam-5659	18	28	3	3	NUM
ejpam-5659	18	29	]	]	PUNCT
ejpam-5659	18	30	.	.	PUNCT
ejpam-5659	19	1	cryptography	cryptography	NOUN
ejpam-5659	19	2	codes	code	VERB
ejpam-5659	19	3	the	the	DET
ejpam-5659	19	4	information	information	NOUN
ejpam-5659	19	5	to	to	PART
ejpam-5659	19	6	ensure	ensure	VERB
ejpam-5659	19	7	doi	doi	NOUN
ejpam-5659	19	8	:	:	PUNCT
ejpam-5659	19	9	https://doi.org/10.29020/nybg.ejpam.v18i2.5659	https://doi.org/10.29020/nybg.ejpam.v18i2.5659	NOUN
ejpam-5659	19	10	email	email	NOUN
ejpam-5659	19	11	address	address	NOUN
ejpam-5659	19	12	:	:	PUNCT
ejpam-5659	19	13	waleed.amin@wise.edu.jo	waleed.amin@wise.edu.jo	NOUN
ejpam-5659	19	14	(	(	PUNCT
ejpam-5659	19	15	w.	w.	PROPN
ejpam-5659	19	16	k.	k.	PROPN
ejpam-5659	19	17	abdulraheem	abdulraheem	PROPN
ejpam-5659	19	18	)	)	PUNCT
ejpam-5659	19	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5659	20	1	1	1	NUM
ejpam-5659	20	2	copyright	copyright	NOUN
ejpam-5659	20	3	:	:	PUNCT
ejpam-5659	20	4	©	©	PROPN
ejpam-5659	20	5	2025	2025	NUM
ejpam-5659	20	6	the	the	DET
ejpam-5659	20	7	author(s	author(s	NOUN
ejpam-5659	20	8	)	)	PUNCT
ejpam-5659	20	9	.	.	PUNCT
ejpam-5659	21	1	(	(	PUNCT
ejpam-5659	21	2	cc	cc	NOUN
ejpam-5659	21	3	by	by	ADP
ejpam-5659	21	4	-	-	PUNCT
ejpam-5659	21	5	nc	nc	PROPN
ejpam-5659	21	6	4.0	4.0	NUM
ejpam-5659	21	7	)	)	PUNCT
ejpam-5659	21	8	w.	w.	PROPN
ejpam-5659	21	9	k.	k.	PROPN
ejpam-5659	21	10	abdulraheem	abdulraheem	PROPN
ejpam-5659	21	11	/	/	SYM
ejpam-5659	21	12	eur	eur	PROPN
ejpam-5659	21	13	.	.	PUNCT
ejpam-5659	22	1	j.	j.	PROPN
ejpam-5659	22	2	pure	pure	PROPN
ejpam-5659	22	3	appl	appl	PROPN
ejpam-5659	22	4	.	.	PROPN
ejpam-5659	22	5	math	math	PROPN
ejpam-5659	22	6	,	,	PUNCT
ejpam-5659	22	7	18	18	NUM
ejpam-5659	22	8	(	(	PUNCT
ejpam-5659	22	9	2	2	NUM
ejpam-5659	22	10	)	)	PUNCT
ejpam-5659	22	11	(	(	PUNCT
ejpam-5659	22	12	2025	2025	NUM
ejpam-5659	22	13	)	)	PUNCT
ejpam-5659	22	14	,	,	PUNCT
ejpam-5659	22	15	5659	5659	NUM
ejpam-5659	22	16	2	2	NUM
ejpam-5659	22	17	of	of	ADP
ejpam-5659	22	18	13	13	NUM
ejpam-5659	22	19	the	the	DET
ejpam-5659	22	20	main	main	ADJ
ejpam-5659	22	21	three	three	NUM
ejpam-5659	22	22	security	security	NOUN
ejpam-5659	22	23	services	service	NOUN
ejpam-5659	22	24	which	which	PRON
ejpam-5659	22	25	are	be	AUX
ejpam-5659	22	26	confidentiality	confidentiality	NOUN
ejpam-5659	22	27	,	,	PUNCT
ejpam-5659	22	28	integrity	integrity	NOUN
ejpam-5659	22	29	and	and	CCONJ
ejpam-5659	22	30	authenticity	authenticity	NOUN
ejpam-5659	22	31	,	,	PUNCT
ejpam-5659	22	32	[	[	X
ejpam-5659	22	33	4	4	NUM
ejpam-5659	22	34	]	]	PUNCT
ejpam-5659	22	35	,	,	PUNCT
ejpam-5659	22	36	[	[	X
ejpam-5659	22	37	5	5	NUM
ejpam-5659	22	38	]	]	PUNCT
ejpam-5659	22	39	,	,	PUNCT
ejpam-5659	22	40	and	and	CCONJ
ejpam-5659	22	41	[	[	X
ejpam-5659	22	42	6	6	NUM
ejpam-5659	22	43	]	]	PUNCT
ejpam-5659	22	44	as	as	SCONJ
ejpam-5659	22	45	shown	show	VERB
ejpam-5659	22	46	in	in	ADP
ejpam-5659	22	47	fig	fig	NOUN
ejpam-5659	22	48	.	.	PUNCT
ejpam-5659	23	1	1	1	X
ejpam-5659	23	2	.	.	X
ejpam-5659	23	3	confidentiality	confidentiality	NOUN
ejpam-5659	23	4	ensures	ensure	VERB
ejpam-5659	23	5	the	the	DET
ejpam-5659	23	6	data	datum	NOUN
ejpam-5659	23	7	is	be	AUX
ejpam-5659	23	8	secret	secret	ADJ
ejpam-5659	23	9	,	,	PUNCT
ejpam-5659	23	10	integrity	integrity	NOUN
ejpam-5659	23	11	ensures	ensure	VERB
ejpam-5659	23	12	that	that	SCONJ
ejpam-5659	23	13	the	the	DET
ejpam-5659	23	14	data	data	NOUN
ejpam-5659	23	15	is	be	AUX
ejpam-5659	23	16	not	not	PART
ejpam-5659	23	17	changed	change	VERB
ejpam-5659	23	18	,	,	PUNCT
ejpam-5659	23	19	while	while	SCONJ
ejpam-5659	23	20	authentication	authentication	NOUN
ejpam-5659	23	21	verifies	verify	VERB
ejpam-5659	23	22	the	the	DET
ejpam-5659	23	23	message	message	NOUN
ejpam-5659	23	24	origin	origin	NOUN
ejpam-5659	23	25	[	[	X
ejpam-5659	23	26	7	7	NUM
ejpam-5659	23	27	]	]	PUNCT
ejpam-5659	23	28	,	,	PUNCT
ejpam-5659	23	29	[	[	X
ejpam-5659	23	30	8	8	NUM
ejpam-5659	23	31	]	]	PUNCT
ejpam-5659	23	32	and	and	CCONJ
ejpam-5659	23	33	[	[	X
ejpam-5659	23	34	9	9	NUM
ejpam-5659	23	35	]	]	PUNCT
ejpam-5659	23	36	.	.	PUNCT
ejpam-5659	24	1	figure	figure	NOUN
ejpam-5659	24	2	1	1	NUM
ejpam-5659	24	3	:	:	PUNCT
ejpam-5659	24	4	c.i.a	c.i.a	NOUN
ejpam-5659	24	5	triad	triad	NOUN
ejpam-5659	25	1	[	[	X
ejpam-5659	25	2	7	7	NUM
ejpam-5659	25	3	]	]	X
ejpam-5659	25	4	cryptography	cryptography	NOUN
ejpam-5659	25	5	can	can	AUX
ejpam-5659	25	6	be	be	AUX
ejpam-5659	25	7	divided	divide	VERB
ejpam-5659	25	8	into	into	ADP
ejpam-5659	25	9	three	three	NUM
ejpam-5659	25	10	types	type	NOUN
ejpam-5659	25	11	;	;	PUNCT
ejpam-5659	25	12	symmetric	symmetric	ADJ
ejpam-5659	25	13	,	,	PUNCT
ejpam-5659	25	14	asymmetric	asymmetric	ADJ
ejpam-5659	25	15	,	,	PUNCT
ejpam-5659	25	16	and	and	CCONJ
ejpam-5659	25	17	hashing	hash	VERB
ejpam-5659	25	18	algorithms	algorithm	NOUN
ejpam-5659	25	19	[	[	X
ejpam-5659	25	20	10	10	NUM
ejpam-5659	25	21	]	]	PUNCT
ejpam-5659	25	22	and	and	CCONJ
ejpam-5659	25	23	[	[	X
ejpam-5659	25	24	11	11	NUM
ejpam-5659	25	25	]	]	PUNCT
ejpam-5659	25	26	.	.	PUNCT
ejpam-5659	26	1	according	accord	VERB
ejpam-5659	26	2	to	to	ADP
ejpam-5659	26	3	national	national	PROPN
ejpam-5659	26	4	institute	institute	PROPN
ejpam-5659	26	5	of	of	ADP
ejpam-5659	26	6	standards	standard	NOUN
ejpam-5659	26	7	and	and	CCONJ
ejpam-5659	26	8	technology	technology	NOUN
ejpam-5659	26	9	nist	nist	NOUN
ejpam-5659	26	10	,	,	PUNCT
ejpam-5659	26	11	symmetric	symmetric	ADJ
ejpam-5659	26	12	key	key	ADJ
ejpam-5659	26	13	cryptography	cryptography	NOUN
ejpam-5659	26	14	or	or	CCONJ
ejpam-5659	26	15	private	private	ADJ
ejpam-5659	26	16	key	key	NOUN
ejpam-5659	26	17	refers	refer	VERB
ejpam-5659	26	18	to	to	ADP
ejpam-5659	26	19	cryptographic	cryptographic	ADJ
ejpam-5659	26	20	algorithms	algorithm	NOUN
ejpam-5659	26	21	that	that	PRON
ejpam-5659	26	22	uses	use	VERB
ejpam-5659	26	23	the	the	DET
ejpam-5659	26	24	same	same	ADJ
ejpam-5659	26	25	key	key	NOUN
ejpam-5659	26	26	for	for	ADP
ejpam-5659	26	27	encryption	encryption	NOUN
ejpam-5659	26	28	and	and	CCONJ
ejpam-5659	26	29	decryption	decryption	NOUN
ejpam-5659	26	30	operation	operation	NOUN
ejpam-5659	26	31	,	,	PUNCT
ejpam-5659	26	32	while	while	SCONJ
ejpam-5659	26	33	asymmetric	asymmetric	ADJ
ejpam-5659	26	34	or	or	CCONJ
ejpam-5659	26	35	public	public	ADJ
ejpam-5659	26	36	cryptography	cryptography	NOUN
ejpam-5659	26	37	refers	refer	VERB
ejpam-5659	26	38	to	to	ADP
ejpam-5659	26	39	algorithms	algorithm	NOUN
ejpam-5659	26	40	that	that	PRON
ejpam-5659	26	41	uses	use	VERB
ejpam-5659	26	42	two	two	NUM
ejpam-5659	26	43	different	different	ADJ
ejpam-5659	26	44	keys	key	NOUN
ejpam-5659	26	45	to	to	PART
ejpam-5659	26	46	exchange	exchange	VERB
ejpam-5659	26	47	information	information	NOUN
ejpam-5659	26	48	,	,	PUNCT
ejpam-5659	26	49	one	one	NUM
ejpam-5659	26	50	to	to	ADP
ejpam-5659	26	51	digital	digital	ADJ
ejpam-5659	26	52	sign	sign	NOUN
ejpam-5659	26	53	or	or	CCONJ
ejpam-5659	26	54	encrypt	encrypt	VERB
ejpam-5659	26	55	information	information	NOUN
ejpam-5659	26	56	and	and	CCONJ
ejpam-5659	26	57	the	the	DET
ejpam-5659	26	58	other	other	ADJ
ejpam-5659	26	59	to	to	PART
ejpam-5659	26	60	decrypt	decrypt	VERB
ejpam-5659	26	61	it	it	PRON
ejpam-5659	26	62	or	or	CCONJ
ejpam-5659	26	63	to	to	PART
ejpam-5659	26	64	verify	verify	VERB
ejpam-5659	26	65	the	the	DET
ejpam-5659	26	66	digital	digital	ADJ
ejpam-5659	26	67	signature	signature	NOUN
ejpam-5659	27	1	[	[	X
ejpam-5659	27	2	12	12	NUM
ejpam-5659	27	3	]	]	PUNCT
ejpam-5659	27	4	and	and	CCONJ
ejpam-5659	27	5	[	[	X
ejpam-5659	27	6	13	13	NUM
ejpam-5659	27	7	]	]	PUNCT
ejpam-5659	27	8	as	as	ADP
ejpam-5659	27	9	in	in	ADP
ejpam-5659	27	10	fig	fig	NOUN
ejpam-5659	27	11	.	.	PUNCT
ejpam-5659	28	1	2	2	X
ejpam-5659	28	2	.	.	X
ejpam-5659	28	3	although	although	SCONJ
ejpam-5659	28	4	symmetric	symmetric	ADJ
ejpam-5659	28	5	cryptosystems	cryptosystem	NOUN
ejpam-5659	28	6	are	be	AUX
ejpam-5659	28	7	very	very	ADV
ejpam-5659	28	8	effective	effective	ADJ
ejpam-5659	28	9	with	with	ADP
ejpam-5659	28	10	respect	respect	NOUN
ejpam-5659	28	11	to	to	ADP
ejpam-5659	28	12	consumed	consume	VERB
ejpam-5659	28	13	time	time	NOUN
ejpam-5659	28	14	and	and	CCONJ
ejpam-5659	28	15	resources	resource	NOUN
ejpam-5659	28	16	,	,	PUNCT
ejpam-5659	28	17	they	they	PRON
ejpam-5659	28	18	still	still	ADV
ejpam-5659	28	19	suffer	suffer	VERB
ejpam-5659	28	20	from	from	ADP
ejpam-5659	28	21	inherent	inherent	ADJ
ejpam-5659	28	22	problems	problem	NOUN
ejpam-5659	28	23	in	in	ADP
ejpam-5659	28	24	key	key	ADJ
ejpam-5659	28	25	distribution	distribution	NOUN
ejpam-5659	28	26	through	through	ADP
ejpam-5659	28	27	the	the	DET
ejpam-5659	28	28	unsecure	unsecure	NOUN
ejpam-5659	28	29	channels	channel	NOUN
ejpam-5659	28	30	[	[	X
ejpam-5659	28	31	14	14	NUM
ejpam-5659	28	32	]	]	PUNCT
ejpam-5659	28	33	and	and	CCONJ
ejpam-5659	28	34	[	[	X
ejpam-5659	28	35	15	15	NUM
ejpam-5659	28	36	]	]	PUNCT
ejpam-5659	28	37	.	.	PUNCT
ejpam-5659	29	1	asymmetric	asymmetric	ADJ
ejpam-5659	29	2	cryptosystem	cryptosystem	NOUN
ejpam-5659	29	3	mechanisms	mechanism	NOUN
ejpam-5659	29	4	facilitate	facilitate	VERB
ejpam-5659	29	5	key	key	ADJ
ejpam-5659	29	6	distribution	distribution	NOUN
ejpam-5659	29	7	over	over	ADP
ejpam-5659	29	8	unsecure	unsecure	NOUN
ejpam-5659	29	9	channels	channel	NOUN
ejpam-5659	29	10	which	which	PRON
ejpam-5659	29	11	assures	assure	VERB
ejpam-5659	29	12	both	both	DET
ejpam-5659	29	13	confidentiality	confidentiality	NOUN
ejpam-5659	29	14	and	and	CCONJ
ejpam-5659	29	15	non	non	NOUN
ejpam-5659	29	16	-	-	NOUN
ejpam-5659	29	17	repudiation	repudiation	NOUN
ejpam-5659	29	18	,	,	PUNCT
ejpam-5659	29	19	however	however	ADV
ejpam-5659	29	20	,	,	PUNCT
ejpam-5659	29	21	the	the	DET
ejpam-5659	29	22	performance	performance	NOUN
ejpam-5659	29	23	expectations	expectation	NOUN
ejpam-5659	29	24	are	be	AUX
ejpam-5659	29	25	lower	low	ADJ
ejpam-5659	29	26	compared	compare	VERB
ejpam-5659	29	27	to	to	ADP
ejpam-5659	29	28	symmetric	symmetric	ADJ
ejpam-5659	29	29	cryptosystem	cryptosystem	NOUN
ejpam-5659	29	30	[	[	X
ejpam-5659	29	31	16	16	NUM
ejpam-5659	29	32	]	]	PUNCT
ejpam-5659	29	33	and	and	CCONJ
ejpam-5659	29	34	[	[	X
ejpam-5659	29	35	17	17	NUM
ejpam-5659	29	36	]	]	PUNCT
ejpam-5659	29	37	.	.	PUNCT
ejpam-5659	30	1	w.	w.	PROPN
ejpam-5659	30	2	k.	k.	PROPN
ejpam-5659	30	3	abdulraheem	abdulraheem	PROPN
ejpam-5659	30	4	/	/	SYM
ejpam-5659	30	5	eur	eur	PROPN
ejpam-5659	30	6	.	.	PUNCT
ejpam-5659	31	1	j.	j.	PROPN
ejpam-5659	31	2	pure	pure	PROPN
ejpam-5659	31	3	appl	appl	PROPN
ejpam-5659	31	4	.	.	PROPN
ejpam-5659	31	5	math	math	PROPN
ejpam-5659	31	6	,	,	PUNCT
ejpam-5659	31	7	18	18	NUM
ejpam-5659	31	8	(	(	PUNCT
ejpam-5659	31	9	2	2	NUM
ejpam-5659	31	10	)	)	PUNCT
ejpam-5659	31	11	(	(	PUNCT
ejpam-5659	31	12	2025	2025	NUM
ejpam-5659	31	13	)	)	PUNCT
ejpam-5659	31	14	,	,	PUNCT
ejpam-5659	31	15	5659	5659	NUM
ejpam-5659	31	16	3	3	NUM
ejpam-5659	31	17	of	of	ADP
ejpam-5659	31	18	13	13	NUM
ejpam-5659	31	19	figure	figure	NOUN
ejpam-5659	31	20	2	2	NUM
ejpam-5659	31	21	:	:	PUNCT
ejpam-5659	31	22	symmetric	symmetric	ADJ
ejpam-5659	31	23	and	and	CCONJ
ejpam-5659	31	24	asymmetric	asymmetric	ADJ
ejpam-5659	31	25	cryptosystems	cryptosystem	NOUN
ejpam-5659	32	1	[	[	X
ejpam-5659	32	2	18	18	NUM
ejpam-5659	32	3	]	]	PUNCT
ejpam-5659	32	4	elliptic	elliptic	ADJ
ejpam-5659	32	5	curve	curve	NOUN
ejpam-5659	32	6	cryptography	cryptography	NOUN
ejpam-5659	32	7	ecc	ecc	PROPN
ejpam-5659	32	8	is	be	AUX
ejpam-5659	32	9	a	a	DET
ejpam-5659	32	10	public	public	ADJ
ejpam-5659	32	11	key	key	ADJ
ejpam-5659	32	12	cryptosystem	cryptosystem	NOUN
ejpam-5659	32	13	which	which	PRON
ejpam-5659	32	14	has	have	AUX
ejpam-5659	32	15	recently	recently	ADV
ejpam-5659	32	16	gained	gain	VERB
ejpam-5659	32	17	higher	high	ADJ
ejpam-5659	32	18	acceptance	acceptance	NOUN
ejpam-5659	32	19	and	and	CCONJ
ejpam-5659	32	20	popularity	popularity	NOUN
ejpam-5659	32	21	within	within	ADP
ejpam-5659	32	22	the	the	DET
ejpam-5659	32	23	research	research	NOUN
ejpam-5659	32	24	community	community	NOUN
ejpam-5659	32	25	.	.	PUNCT
ejpam-5659	33	1	this	this	PRON
ejpam-5659	33	2	is	be	AUX
ejpam-5659	33	3	because	because	SCONJ
ejpam-5659	33	4	it	it	PRON
ejpam-5659	33	5	achieves	achieve	VERB
ejpam-5659	33	6	a	a	DET
ejpam-5659	33	7	significantly	significantly	ADV
ejpam-5659	33	8	higher	high	ADJ
ejpam-5659	33	9	security	security	NOUN
ejpam-5659	33	10	level	level	NOUN
ejpam-5659	33	11	using	use	VERB
ejpam-5659	33	12	short	short	ADJ
ejpam-5659	33	13	keys	key	NOUN
ejpam-5659	33	14	compared	compare	VERB
ejpam-5659	33	15	to	to	ADP
ejpam-5659	33	16	other	other	ADJ
ejpam-5659	33	17	asymmetric	asymmetric	ADJ
ejpam-5659	33	18	cryptosystems	cryptosystem	NOUN
ejpam-5659	34	1	[	[	X
ejpam-5659	34	2	19	19	NUM
ejpam-5659	34	3	]	]	PUNCT
ejpam-5659	34	4	and	and	CCONJ
ejpam-5659	34	5	[	[	X
ejpam-5659	34	6	20	20	NUM
ejpam-5659	34	7	]	]	PUNCT
ejpam-5659	34	8	.	.	PUNCT
ejpam-5659	35	1	as	as	ADP
ejpam-5659	35	2	in	in	ADP
ejpam-5659	35	3	fig	fig	NOUN
ejpam-5659	35	4	.	.	PUNCT
ejpam-5659	36	1	3	3	NUM
ejpam-5659	36	2	,	,	PUNCT
ejpam-5659	36	3	the	the	DET
ejpam-5659	36	4	ecc	ecc	PROPN
ejpam-5659	36	5	scalar	scalar	ADJ
ejpam-5659	36	6	multiplication	multiplication	NOUN
ejpam-5659	36	7	is	be	AUX
ejpam-5659	36	8	composed	compose	VERB
ejpam-5659	36	9	of	of	ADP
ejpam-5659	36	10	three	three	NUM
ejpam-5659	36	11	computational	computational	ADJ
ejpam-5659	36	12	levels	level	NOUN
ejpam-5659	36	13	;	;	PUNCT
ejpam-5659	37	1	scalar	scalar	ADJ
ejpam-5659	37	2	arithmetic	arithmetic	ADJ
ejpam-5659	37	3	,	,	PUNCT
ejpam-5659	37	4	point	point	NOUN
ejpam-5659	37	5	arithmetic	arithmetic	ADJ
ejpam-5659	37	6	and	and	CCONJ
ejpam-5659	37	7	finally	finally	ADV
ejpam-5659	37	8	field	field	VERB
ejpam-5659	37	9	arithmetic	arithmetic	ADJ
ejpam-5659	37	10	.	.	PUNCT
ejpam-5659	38	1	scalar	scalar	ADJ
ejpam-5659	38	2	multiplication	multiplication	NOUN
ejpam-5659	38	3	is	be	AUX
ejpam-5659	38	4	to	to	PART
ejpam-5659	38	5	find	find	VERB
ejpam-5659	38	6	the	the	DET
ejpam-5659	38	7	result	result	NOUN
ejpam-5659	38	8	of	of	ADP
ejpam-5659	38	9	the	the	DET
ejpam-5659	38	10	operation	operation	NOUN
ejpam-5659	38	11	q	q	NOUN
ejpam-5659	39	1	=	=	PUNCT
ejpam-5659	39	2	kp	kp	NOUN
ejpam-5659	39	3	such	such	ADJ
ejpam-5659	39	4	that	that	SCONJ
ejpam-5659	39	5	k	k	PROPN
ejpam-5659	39	6	∈	∈	PROPN
ejpam-5659	39	7	n	n	PRON
ejpam-5659	39	8	,	,	PUNCT
ejpam-5659	39	9	p	p	NOUN
ejpam-5659	39	10	and	and	CCONJ
ejpam-5659	39	11	q	q	NOUN
ejpam-5659	39	12	are	be	AUX
ejpam-5659	39	13	two	two	NUM
ejpam-5659	39	14	points	point	NOUN
ejpam-5659	39	15	on	on	ADP
ejpam-5659	39	16	the	the	DET
ejpam-5659	39	17	curve	curve	NOUN
ejpam-5659	39	18	.	.	PUNCT
ejpam-5659	40	1	on	on	ADP
ejpam-5659	40	2	the	the	DET
ejpam-5659	40	3	other	other	ADJ
ejpam-5659	40	4	hand	hand	NOUN
ejpam-5659	40	5	,	,	PUNCT
ejpam-5659	40	6	point	point	NOUN
ejpam-5659	40	7	arithmetic	arithmetic	ADJ
ejpam-5659	40	8	is	be	AUX
ejpam-5659	40	9	adding	add	VERB
ejpam-5659	40	10	two	two	NUM
ejpam-5659	40	11	points	point	NOUN
ejpam-5659	40	12	on	on	ADP
ejpam-5659	40	13	the	the	DET
ejpam-5659	40	14	curve	curve	NOUN
ejpam-5659	40	15	p	p	PROPN
ejpam-5659	41	1	+	+	NOUN
ejpam-5659	41	2	q	q	NOUN
ejpam-5659	41	3	or	or	CCONJ
ejpam-5659	41	4	p	p	X
ejpam-5659	42	1	+	+	X
ejpam-5659	42	2	p	p	X
ejpam-5659	42	3	(	(	PUNCT
ejpam-5659	42	4	for	for	ADP
ejpam-5659	42	5	point	point	NOUN
ejpam-5659	42	6	doubling	doubling	NOUN
ejpam-5659	42	7	)	)	PUNCT
ejpam-5659	42	8	.	.	PUNCT
ejpam-5659	43	1	field	field	NOUN
ejpam-5659	43	2	arithmetic	arithmetic	NOUN
ejpam-5659	43	3	are	be	AUX
ejpam-5659	43	4	related	relate	VERB
ejpam-5659	43	5	to	to	ADP
ejpam-5659	43	6	coordinates	coordinate	NOUN
ejpam-5659	43	7	where	where	SCONJ
ejpam-5659	43	8	the	the	DET
ejpam-5659	43	9	point	point	NOUN
ejpam-5659	43	10	operations	operation	NOUN
ejpam-5659	43	11	are	be	AUX
ejpam-5659	43	12	performed	perform	VERB
ejpam-5659	43	13	[	[	PUNCT
ejpam-5659	43	14	21	21	NUM
ejpam-5659	43	15	]	]	PUNCT
ejpam-5659	43	16	.	.	PUNCT
ejpam-5659	44	1	figure	figure	VERB
ejpam-5659	44	2	3	3	NUM
ejpam-5659	44	3	:	:	PUNCT
ejpam-5659	44	4	operations	operation	NOUN
ejpam-5659	44	5	in	in	ADP
ejpam-5659	44	6	ecc	ecc	PROPN
ejpam-5659	44	7	divided	divide	VERB
ejpam-5659	44	8	by	by	ADP
ejpam-5659	44	9	levels.[21	levels.[21	PROPN
ejpam-5659	44	10	]	]	PUNCT
ejpam-5659	45	1	precomputing	precompute	VERB
ejpam-5659	45	2	the	the	DET
ejpam-5659	45	3	points	point	NOUN
ejpam-5659	45	4	will	will	AUX
ejpam-5659	45	5	help	help	VERB
ejpam-5659	45	6	faster	fast	ADJ
ejpam-5659	45	7	computation	computation	NOUN
ejpam-5659	45	8	at	at	ADP
ejpam-5659	45	9	level	level	NOUN
ejpam-5659	45	10	2	2	NUM
ejpam-5659	45	11	.	.	PUNCT
ejpam-5659	45	12	instead	instead	ADV
ejpam-5659	45	13	of	of	ADP
ejpam-5659	45	14	repeating	repeat	VERB
ejpam-5659	45	15	the	the	DET
ejpam-5659	45	16	addition	addition	NOUN
ejpam-5659	45	17	and	and	CCONJ
ejpam-5659	45	18	doubling	double	VERB
ejpam-5659	45	19	many	many	ADJ
ejpam-5659	45	20	times	time	NOUN
ejpam-5659	45	21	,	,	PUNCT
ejpam-5659	45	22	precomputation	precomputation	NOUN
ejpam-5659	45	23	will	will	AUX
ejpam-5659	45	24	increase	increase	VERB
ejpam-5659	45	25	the	the	DET
ejpam-5659	45	26	overall	overall	ADJ
ejpam-5659	45	27	performance	performance	NOUN
ejpam-5659	45	28	of	of	ADP
ejpam-5659	45	29	the	the	DET
ejpam-5659	45	30	scalar	scalar	ADJ
ejpam-5659	45	31	and	and	CCONJ
ejpam-5659	45	32	ecc	ecc	PROPN
ejpam-5659	45	33	protocols	protocol	NOUN
ejpam-5659	45	34	.	.	PUNCT
ejpam-5659	46	1	this	this	PRON
ejpam-5659	46	2	include	include	VERB
ejpam-5659	46	3	point	point	NOUN
ejpam-5659	46	4	tripling	triple	VERB
ejpam-5659	46	5	3p	3p	NUM
ejpam-5659	46	6	,	,	PUNCT
ejpam-5659	46	7	point	point	VERB
ejpam-5659	46	8	quintupling	quintuple	VERB
ejpam-5659	46	9	5p	5p	NUM
ejpam-5659	46	10	,	,	PUNCT
ejpam-5659	46	11	and	and	CCONJ
ejpam-5659	46	12	point	point	NOUN
ejpam-5659	46	13	septupling	septuple	VERB
ejpam-5659	46	14	7p	7p	NOUN
ejpam-5659	46	15	in	in	ADP
ejpam-5659	46	16	addition	addition	NOUN
ejpam-5659	46	17	to	to	ADP
ejpam-5659	46	18	other	other	ADJ
ejpam-5659	46	19	precomputed	precompute	VERB
ejpam-5659	46	20	points	point	NOUN
ejpam-5659	47	1	[	[	X
ejpam-5659	47	2	22	22	NUM
ejpam-5659	47	3	]	]	PUNCT
ejpam-5659	47	4	and	and	CCONJ
ejpam-5659	47	5	[	[	X
ejpam-5659	47	6	23	23	NUM
ejpam-5659	47	7	]	]	PUNCT
ejpam-5659	47	8	.	.	PUNCT
ejpam-5659	48	1	point	point	NOUN
ejpam-5659	48	2	septupling	septuple	VERB
ejpam-5659	48	3	7p	7p	NUM
ejpam-5659	48	4	is	be	AUX
ejpam-5659	48	5	to	to	PART
ejpam-5659	48	6	find	find	VERB
ejpam-5659	48	7	(	(	PUNCT
ejpam-5659	48	8	x7	x7	NOUN
ejpam-5659	48	9	,	,	PUNCT
ejpam-5659	48	10	y7	y7	PROPN
ejpam-5659	48	11	)	)	PUNCT
ejpam-5659	48	12	by	by	ADP
ejpam-5659	48	13	calculating	calculate	VERB
ejpam-5659	48	14	the	the	DET
ejpam-5659	48	15	7	7	NUM
ejpam-5659	48	16	-	-	NOUN
ejpam-5659	48	17	fold	fold	NOUN
ejpam-5659	48	18	of	of	ADP
ejpam-5659	48	19	the	the	DET
ejpam-5659	48	20	point	point	NOUN
ejpam-5659	48	21	p	p	X
ejpam-5659	48	22	=	=	SYM
ejpam-5659	48	23	(	(	PUNCT
ejpam-5659	48	24	x	x	PROPN
ejpam-5659	48	25	,	,	PUNCT
ejpam-5659	48	26	y	y	PROPN
ejpam-5659	48	27	)	)	PUNCT
ejpam-5659	48	28	.	.	PUNCT
ejpam-5659	49	1	according	accord	VERB
ejpam-5659	49	2	to	to	ADP
ejpam-5659	49	3	[	[	X
ejpam-5659	49	4	24	24	NUM
ejpam-5659	49	5	]	]	PUNCT
ejpam-5659	49	6	who	who	PRON
ejpam-5659	49	7	proposed	propose	VERB
ejpam-5659	49	8	the	the	DET
ejpam-5659	49	9	first	first	ADJ
ejpam-5659	49	10	septupling	septupling	NOUN
ejpam-5659	49	11	formula	formula	NOUN
ejpam-5659	49	12	of	of	ADP
ejpam-5659	49	13	the	the	DET
ejpam-5659	49	14	point	point	NOUN
ejpam-5659	49	15	introduced	introduce	VERB
ejpam-5659	49	16	by	by	ADP
ejpam-5659	49	17	[	[	X
ejpam-5659	49	18	25	25	NUM
ejpam-5659	49	19	]	]	PUNCT
ejpam-5659	49	20	,	,	PUNCT
ejpam-5659	49	21	the	the	DET
ejpam-5659	49	22	septupling	septupling	NOUN
ejpam-5659	49	23	is	be	AUX
ejpam-5659	49	24	calculated	calculate	VERB
ejpam-5659	49	25	over	over	ADP
ejpam-5659	49	26	the	the	DET
ejpam-5659	49	27	affine	affine	ADJ
ejpam-5659	49	28	binary	binary	ADJ
ejpam-5659	49	29	field	field	NOUN
ejpam-5659	49	30	to	to	PART
ejpam-5659	49	31	be	be	AUX
ejpam-5659	49	32	used	use	VERB
ejpam-5659	49	33	for	for	ADP
ejpam-5659	49	34	multi	multi	ADJ
ejpam-5659	49	35	-	-	ADJ
ejpam-5659	49	36	base	base	ADJ
ejpam-5659	49	37	number	number	NOUN
ejpam-5659	49	38	(	(	PUNCT
ejpam-5659	49	39	mtb	mtb	NOUN
ejpam-5659	49	40	)	)	PUNCT
ejpam-5659	49	41	as	as	ADP
ejpam-5659	49	42	a	a	DET
ejpam-5659	49	43	scalar	scalar	ADJ
ejpam-5659	49	44	recoding	recoding	NOUN
ejpam-5659	49	45	.	.	PUNCT
ejpam-5659	50	1	its	its	PRON
ejpam-5659	50	2	cost	cost	NOUN
ejpam-5659	50	3	is	be	AUX
ejpam-5659	50	4	3i+7s+18	3i+7s+18	NUM
ejpam-5659	50	5	m	m	NOUN
ejpam-5659	50	6	,	,	PUNCT
ejpam-5659	50	7	where	where	SCONJ
ejpam-5659	50	8	i	i	PRON
ejpam-5659	50	9	,	,	PUNCT
ejpam-5659	50	10	s	s	PROPN
ejpam-5659	50	11	,	,	PUNCT
ejpam-5659	50	12	and	and	CCONJ
ejpam-5659	50	13	m	m	PROPN
ejpam-5659	50	14	is	be	AUX
ejpam-5659	50	15	denote	denote	VERB
ejpam-5659	50	16	the	the	DET
ejpam-5659	50	17	cost	cost	NOUN
ejpam-5659	50	18	of	of	ADP
ejpam-5659	50	19	inversion	inversion	NOUN
ejpam-5659	50	20	,	,	PUNCT
ejpam-5659	50	21	squaring	squaring	NOUN
ejpam-5659	50	22	,	,	PUNCT
ejpam-5659	50	23	and	and	CCONJ
ejpam-5659	50	24	multiplication	multiplication	NOUN
ejpam-5659	50	25	respectively	respectively	ADV
ejpam-5659	50	26	.	.	PUNCT
ejpam-5659	51	1	later	later	ADV
ejpam-5659	51	2	,	,	PUNCT
ejpam-5659	51	3	[	[	X
ejpam-5659	51	4	26	26	NUM
ejpam-5659	51	5	]	]	PUNCT
ejpam-5659	51	6	proposed	propose	VERB
ejpam-5659	51	7	a	a	DET
ejpam-5659	51	8	new	new	ADJ
ejpam-5659	51	9	7p	7p	NUM
ejpam-5659	51	10	calculation	calculation	NOUN
ejpam-5659	51	11	over	over	ADP
ejpam-5659	51	12	binary	binary	ADJ
ejpam-5659	51	13	field	field	NOUN
ejpam-5659	51	14	in	in	ADP
ejpam-5659	51	15	terms	term	NOUN
ejpam-5659	51	16	of	of	ADP
ejpam-5659	51	17	affine	affine	NOUN
ejpam-5659	51	18	coordinates	coordinate	NOUN
ejpam-5659	51	19	,	,	PUNCT
ejpam-5659	51	20	the	the	DET
ejpam-5659	51	21	cost	cost	NOUN
ejpam-5659	51	22	of	of	ADP
ejpam-5659	51	23	the	the	DET
ejpam-5659	51	24	proposed	propose	VERB
ejpam-5659	51	25	w.	w.	PROPN
ejpam-5659	51	26	k.	k.	PROPN
ejpam-5659	51	27	abdulraheem	abdulraheem	PROPN
ejpam-5659	51	28	/	/	SYM
ejpam-5659	51	29	eur	eur	PROPN
ejpam-5659	51	30	.	.	PUNCT
ejpam-5659	52	1	j.	j.	PROPN
ejpam-5659	52	2	pure	pure	PROPN
ejpam-5659	52	3	appl	appl	PROPN
ejpam-5659	52	4	.	.	PROPN
ejpam-5659	52	5	math	math	PROPN
ejpam-5659	52	6	,	,	PUNCT
ejpam-5659	52	7	18	18	NUM
ejpam-5659	52	8	(	(	PUNCT
ejpam-5659	52	9	2	2	NUM
ejpam-5659	52	10	)	)	PUNCT
ejpam-5659	52	11	(	(	PUNCT
ejpam-5659	52	12	2025	2025	NUM
ejpam-5659	52	13	)	)	PUNCT
ejpam-5659	52	14	,	,	PUNCT
ejpam-5659	52	15	5659	5659	NUM
ejpam-5659	52	16	4	4	NUM
ejpam-5659	52	17	of	of	ADP
ejpam-5659	52	18	13	13	NUM
ejpam-5659	52	19	algorithm	algorithm	NOUN
ejpam-5659	52	20	is	be	AUX
ejpam-5659	52	21	2i	2i	NUM
ejpam-5659	52	22	+	+	CCONJ
ejpam-5659	52	23	7s	7	NOUN
ejpam-5659	52	24	+	+	CCONJ
ejpam-5659	52	25	14	14	NUM
ejpam-5659	52	26	m.	m.	NOUN
ejpam-5659	52	27	in	in	ADP
ejpam-5659	52	28	[	[	X
ejpam-5659	52	29	27	27	NUM
ejpam-5659	52	30	]	]	PUNCT
ejpam-5659	52	31	,	,	PUNCT
ejpam-5659	52	32	the	the	DET
ejpam-5659	52	33	authors	author	NOUN
ejpam-5659	52	34	studied	study	VERB
ejpam-5659	52	35	the	the	DET
ejpam-5659	52	36	literature	literature	NOUN
ejpam-5659	52	37	on	on	ADP
ejpam-5659	52	38	multiplying	multiply	VERB
ejpam-5659	52	39	an	an	DET
ejpam-5659	52	40	odd	odd	ADJ
ejpam-5659	52	41	scalar	scalar	NOUN
ejpam-5659	52	42	to	to	ADP
ejpam-5659	52	43	the	the	DET
ejpam-5659	52	44	point	point	NOUN
ejpam-5659	52	45	p	p	NOUN
ejpam-5659	52	46	over	over	ADP
ejpam-5659	52	47	prime	prime	ADJ
ejpam-5659	52	48	field	field	NOUN
ejpam-5659	52	49	.	.	PUNCT
ejpam-5659	53	1	they	they	PRON
ejpam-5659	53	2	found	find	VERB
ejpam-5659	53	3	that	that	SCONJ
ejpam-5659	53	4	sakai	sakai	PROPN
ejpam-5659	53	5	’s	’s	PART
ejpam-5659	53	6	method	method	NOUN
ejpam-5659	53	7	which	which	PRON
ejpam-5659	53	8	uses	use	VERB
ejpam-5659	53	9	the	the	DET
ejpam-5659	53	10	formula	formula	NOUN
ejpam-5659	54	1	[	[	X
ejpam-5659	54	2	α	α	X
ejpam-5659	54	3	+	+	NOUN
ejpam-5659	54	4	4d	4d	NUM
ejpam-5659	54	5	+	+	CCONJ
ejpam-5659	54	6	1	1	NUM
ejpam-5659	54	7	+	+	NUM
ejpam-5659	54	8	4d	4d	NUM
ejpam-5659	55	1	+	+	CCONJ
ejpam-5659	55	2	1	1	NUM
ejpam-5659	55	3	β	β	NOUN
ejpam-5659	55	4	]	]	PUNCT
ejpam-5659	55	5	to	to	PART
ejpam-5659	55	6	calculate	calculate	VERB
ejpam-5659	55	7	the	the	DET
ejpam-5659	55	8	cost	cost	NOUN
ejpam-5659	55	9	gives	give	VERB
ejpam-5659	55	10	the	the	DET
ejpam-5659	55	11	best	good	ADJ
ejpam-5659	55	12	performance	performance	NOUN
ejpam-5659	55	13	with	with	ADP
ejpam-5659	55	14	an	an	DET
ejpam-5659	55	15	overall	overall	ADJ
ejpam-5659	55	16	cost	cost	NOUN
ejpam-5659	55	17	of	of	ADP
ejpam-5659	55	18	67	67	NUM
ejpam-5659	55	19	operations	operation	NOUN
ejpam-5659	55	20	.	.	PUNCT
ejpam-5659	56	1	in	in	ADP
ejpam-5659	56	2	[	[	X
ejpam-5659	56	3	28	28	NUM
ejpam-5659	56	4	]	]	PUNCT
ejpam-5659	56	5	,	,	PUNCT
ejpam-5659	56	6	the	the	DET
ejpam-5659	56	7	authors	author	NOUN
ejpam-5659	56	8	proposed	propose	VERB
ejpam-5659	56	9	a	a	DET
ejpam-5659	56	10	new	new	ADJ
ejpam-5659	56	11	septupling	septupling	NOUN
ejpam-5659	56	12	point	point	NOUN
ejpam-5659	56	13	7p	7p	NUM
ejpam-5659	56	14	formula	formula	NOUN
ejpam-5659	56	15	in	in	ADP
ejpam-5659	56	16	jacobian	jacobian	ADJ
ejpam-5659	56	17	coordinates	coordinate	NOUN
ejpam-5659	56	18	and	and	CCONJ
ejpam-5659	56	19	used	use	VERB
ejpam-5659	56	20	it	it	PRON
ejpam-5659	56	21	in	in	ADP
ejpam-5659	56	22	the	the	DET
ejpam-5659	56	23	multi	multi	ADJ
ejpam-5659	56	24	-	-	ADJ
ejpam-5659	56	25	base	base	ADJ
ejpam-5659	56	26	non	non	ADJ
ejpam-5659	56	27	-	-	ADJ
ejpam-5659	56	28	adjacent	adjacent	ADJ
ejpam-5659	56	29	form	form	NOUN
ejpam-5659	56	30	(	(	PUNCT
ejpam-5659	56	31	mbnaf	mbnaf	PROPN
ejpam-5659	56	32	)	)	PUNCT
ejpam-5659	56	33	and	and	CCONJ
ejpam-5659	56	34	window	window	NOUN
ejpam-5659	56	35	-	-	PUNCT
ejpam-5659	56	36	based	base	VERB
ejpam-5659	56	37	(	(	PUNCT
ejpam-5659	56	38	wmbnaf	wmbnaf	NOUN
ejpam-5659	56	39	)	)	PUNCT
ejpam-5659	56	40	methods	method	NOUN
ejpam-5659	56	41	.	.	PUNCT
ejpam-5659	57	1	the	the	DET
ejpam-5659	57	2	cost	cost	NOUN
ejpam-5659	57	3	over	over	ADP
ejpam-5659	57	4	jacobian	jacobian	PROPN
ejpam-5659	57	5	is	be	AUX
ejpam-5659	57	6	14	14	NUM
ejpam-5659	57	7	m	m	NOUN
ejpam-5659	57	8	+	+	NOUN
ejpam-5659	57	9	15s	15	NOUN
ejpam-5659	57	10	.	.	PUNCT
ejpam-5659	58	1	similarly	similarly	ADV
ejpam-5659	58	2	in	in	ADP
ejpam-5659	58	3	[	[	X
ejpam-5659	58	4	24	24	NUM
ejpam-5659	58	5	]	]	PUNCT
ejpam-5659	58	6	,	,	PUNCT
ejpam-5659	58	7	they	they	PRON
ejpam-5659	58	8	proposed	propose	VERB
ejpam-5659	58	9	a	a	DET
ejpam-5659	58	10	new	new	ADJ
ejpam-5659	58	11	point	point	NOUN
ejpam-5659	58	12	septupling	septuple	VERB
ejpam-5659	58	13	7p	7p	NUM
ejpam-5659	58	14	formula	formula	NOUN
ejpam-5659	58	15	for	for	ADP
ejpam-5659	58	16	triple	triple	ADV
ejpam-5659	58	17	-	-	PUNCT
ejpam-5659	58	18	based	base	VERB
ejpam-5659	58	19	chain	chain	NOUN
ejpam-5659	58	20	(	(	PUNCT
ejpam-5659	58	21	tbc	tbc	NOUN
ejpam-5659	58	22	)	)	PUNCT
ejpam-5659	58	23	representation	representation	NOUN
ejpam-5659	58	24	of	of	ADP
ejpam-5659	58	25	the	the	DET
ejpam-5659	58	26	scalar	scalar	ADJ
ejpam-5659	58	27	using	use	VERB
ejpam-5659	58	28	{	{	PUNCT
ejpam-5659	58	29	2	2	NUM
ejpam-5659	58	30	,	,	PUNCT
ejpam-5659	58	31	3	3	NUM
ejpam-5659	58	32	,	,	PUNCT
ejpam-5659	58	33	7}-basis	7}-basis	NUM
ejpam-5659	58	34	over	over	ADP
ejpam-5659	58	35	prime	prime	ADJ
ejpam-5659	58	36	field	field	NOUN
ejpam-5659	58	37	.	.	PUNCT
ejpam-5659	59	1	similarly	similarly	ADV
ejpam-5659	59	2	,	,	PUNCT
ejpam-5659	59	3	they	they	PRON
ejpam-5659	59	4	used	use	VERB
ejpam-5659	59	5	co	co	NOUN
ejpam-5659	59	6	z	z	NOUN
ejpam-5659	59	7	operation	operation	NOUN
ejpam-5659	59	8	method	method	NOUN
ejpam-5659	59	9	and	and	CCONJ
ejpam-5659	59	10	calculate	calculate	VERB
ejpam-5659	59	11	the	the	DET
ejpam-5659	59	12	overall	overall	ADJ
ejpam-5659	59	13	cost	cost	NOUN
ejpam-5659	59	14	of	of	ADP
ejpam-5659	59	15	the	the	DET
ejpam-5659	59	16	triple	triple	ADV
ejpam-5659	59	17	-	-	PUNCT
ejpam-5659	59	18	based	base	VERB
ejpam-5659	59	19	together	together	ADV
ejpam-5659	59	20	.	.	PUNCT
ejpam-5659	60	1	2	2	X
ejpam-5659	60	2	.	.	X
ejpam-5659	60	3	motivation	motivation	NOUN
ejpam-5659	60	4	according	accord	VERB
ejpam-5659	60	5	to	to	ADP
ejpam-5659	60	6	nist	nist	NOUN
ejpam-5659	60	7	report	report	NOUN
ejpam-5659	60	8	[	[	X
ejpam-5659	60	9	29	29	NUM
ejpam-5659	60	10	]	]	SYM
ejpam-5659	60	11	page	page	NOUN
ejpam-5659	60	12	88	88	NUM
ejpam-5659	60	13	,	,	PUNCT
ejpam-5659	60	14	using	use	VERB
ejpam-5659	60	15	binary	binary	ADJ
ejpam-5659	60	16	field	field	NOUN
ejpam-5659	60	17	in	in	ADP
ejpam-5659	60	18	ecc	ecc	PROPN
ejpam-5659	60	19	is	be	AUX
ejpam-5659	60	20	outperforms	outperform	NOUN
ejpam-5659	60	21	the	the	DET
ejpam-5659	60	22	prime	prime	ADJ
ejpam-5659	60	23	field	field	NOUN
ejpam-5659	60	24	since	since	SCONJ
ejpam-5659	60	25	it	it	PRON
ejpam-5659	60	26	yields	yield	VERB
ejpam-5659	60	27	the	the	DET
ejpam-5659	60	28	same	same	ADJ
ejpam-5659	60	29	level	level	NOUN
ejpam-5659	60	30	of	of	ADP
ejpam-5659	60	31	security	security	NOUN
ejpam-5659	60	32	with	with	ADP
ejpam-5659	60	33	smaller	small	ADJ
ejpam-5659	60	34	key	key	ADJ
ejpam-5659	60	35	size	size	NOUN
ejpam-5659	60	36	(	(	PUNCT
ejpam-5659	60	37	163	163	NUM
ejpam-5659	60	38	vs.	vs.	ADP
ejpam-5659	60	39	192	192	NUM
ejpam-5659	60	40	)	)	PUNCT
ejpam-5659	60	41	.	.	PUNCT
ejpam-5659	61	1	in	in	ADP
ejpam-5659	61	2	addition	addition	NOUN
ejpam-5659	61	3	,	,	PUNCT
ejpam-5659	61	4	using	use	VERB
ejpam-5659	61	5	lopez	lopez	NOUN
ejpam-5659	61	6	-	-	PUNCT
ejpam-5659	61	7	dahan	dahan	PROPN
ejpam-5659	61	8	ld	ld	PROPN
ejpam-5659	61	9	coordinate	coordinate	NOUN
ejpam-5659	61	10	over	over	ADP
ejpam-5659	61	11	the	the	DET
ejpam-5659	61	12	binary	binary	ADJ
ejpam-5659	61	13	curve	curve	NOUN
ejpam-5659	61	14	yields	yield	VERB
ejpam-5659	61	15	the	the	DET
ejpam-5659	61	16	best	good	ADJ
ejpam-5659	61	17	performance	performance	NOUN
ejpam-5659	61	18	for	for	ADP
ejpam-5659	61	19	ecc	ecc	PROPN
ejpam-5659	61	20	[	[	X
ejpam-5659	61	21	30	30	NUM
ejpam-5659	61	22	]	]	PUNCT
ejpam-5659	61	23	,	,	PUNCT
ejpam-5659	61	24	[	[	X
ejpam-5659	61	25	22	22	NUM
ejpam-5659	61	26	]	]	PUNCT
ejpam-5659	61	27	,	,	PUNCT
ejpam-5659	61	28	[	[	X
ejpam-5659	61	29	23	23	NUM
ejpam-5659	61	30	]	]	PUNCT
ejpam-5659	61	31	and	and	CCONJ
ejpam-5659	62	1	[	[	X
ejpam-5659	62	2	31	31	NUM
ejpam-5659	62	3	]	]	PUNCT
ejpam-5659	62	4	.	.	PUNCT
ejpam-5659	63	1	over	over	ADP
ejpam-5659	63	2	the	the	DET
ejpam-5659	63	3	binary	binary	ADJ
ejpam-5659	63	4	curves	curve	NOUN
ejpam-5659	63	5	,	,	PUNCT
ejpam-5659	63	6	most	most	ADV
ejpam-5659	63	7	known	know	VERB
ejpam-5659	63	8	formulas	formula	NOUN
ejpam-5659	63	9	for	for	ADP
ejpam-5659	63	10	adding	add	VERB
ejpam-5659	63	11	points	point	NOUN
ejpam-5659	63	12	together	together	ADV
ejpam-5659	63	13	are	be	AUX
ejpam-5659	63	14	incomplete	incomplete	ADJ
ejpam-5659	63	15	[	[	X
ejpam-5659	63	16	32	32	NUM
ejpam-5659	63	17	]	]	PUNCT
ejpam-5659	63	18	.	.	PUNCT
ejpam-5659	64	1	also	also	ADV
ejpam-5659	64	2	,	,	PUNCT
ejpam-5659	64	3	in	in	ADP
ejpam-5659	64	4	literature	literature	NOUN
ejpam-5659	64	5	,	,	PUNCT
ejpam-5659	64	6	the	the	DET
ejpam-5659	64	7	precomputed	precompute	VERB
ejpam-5659	64	8	formula	formula	NOUN
ejpam-5659	64	9	of	of	ADP
ejpam-5659	64	10	the	the	DET
ejpam-5659	64	11	point	point	NOUN
ejpam-5659	64	12	septupling	septuple	VERB
ejpam-5659	64	13	7p	7p	NUM
ejpam-5659	64	14	is	be	AUX
ejpam-5659	64	15	not	not	PART
ejpam-5659	64	16	available	available	ADJ
ejpam-5659	64	17	[	[	X
ejpam-5659	64	18	31	31	NUM
ejpam-5659	64	19	]	]	PUNCT
ejpam-5659	64	20	and	and	CCONJ
ejpam-5659	64	21	[	[	X
ejpam-5659	64	22	33	33	NUM
ejpam-5659	64	23	]	]	PUNCT
ejpam-5659	64	24	.	.	PUNCT
ejpam-5659	65	1	thus	thus	ADV
ejpam-5659	65	2	,	,	PUNCT
ejpam-5659	65	3	the	the	DET
ejpam-5659	65	4	point	point	NOUN
ejpam-5659	65	5	septupling	septuple	VERB
ejpam-5659	65	6	can	can	AUX
ejpam-5659	65	7	be	be	AUX
ejpam-5659	65	8	efficiently	efficiently	ADV
ejpam-5659	65	9	implemented	implement	VERB
ejpam-5659	65	10	by	by	ADP
ejpam-5659	65	11	scalar	scalar	ADJ
ejpam-5659	65	12	multiplication	multiplication	NOUN
ejpam-5659	65	13	such	such	ADJ
ejpam-5659	65	14	as	as	ADP
ejpam-5659	65	15	w−naf	w−naf	NOUN
ejpam-5659	65	16	,	,	PUNCT
ejpam-5659	65	17	double	double	ADJ
ejpam-5659	65	18	or	or	CCONJ
ejpam-5659	65	19	multi	multi	ADJ
ejpam-5659	65	20	-	-	ADJ
ejpam-5659	65	21	base	base	ADJ
ejpam-5659	65	22	numbering	numbering	NOUN
ejpam-5659	65	23	system	system	NOUN
ejpam-5659	65	24	.	.	PUNCT
ejpam-5659	66	1	in	in	ADP
ejpam-5659	66	2	view	view	NOUN
ejpam-5659	66	3	of	of	ADP
ejpam-5659	66	4	the	the	DET
ejpam-5659	66	5	aforementioned	aforementione	VERB
ejpam-5659	66	6	,	,	PUNCT
ejpam-5659	66	7	the	the	DET
ejpam-5659	66	8	contributions	contribution	NOUN
ejpam-5659	66	9	of	of	ADP
ejpam-5659	66	10	this	this	PRON
ejpam-5659	66	11	are	be	AUX
ejpam-5659	66	12	as	as	SCONJ
ejpam-5659	66	13	follows	follow	VERB
ejpam-5659	66	14	:	:	PUNCT
ejpam-5659	66	15	•	•	ADP
ejpam-5659	66	16	a	a	DET
ejpam-5659	66	17	new	new	ADJ
ejpam-5659	66	18	precomputed	precompute	VERB
ejpam-5659	66	19	septupling	septupling	NOUN
ejpam-5659	66	20	point	point	NOUN
ejpam-5659	66	21	7p	7p	NOUN
ejpam-5659	66	22	arithmetic	arithmetic	ADJ
ejpam-5659	66	23	formula	formula	NOUN
ejpam-5659	66	24	is	be	AUX
ejpam-5659	66	25	proposed	propose	VERB
ejpam-5659	66	26	for	for	ADP
ejpam-5659	66	27	ld	ld	PROPN
ejpam-5659	66	28	coordinate	coordinate	NOUN
ejpam-5659	66	29	over	over	ADP
ejpam-5659	66	30	the	the	DET
ejpam-5659	66	31	binary	binary	ADJ
ejpam-5659	66	32	curve	curve	NOUN
ejpam-5659	66	33	using	use	VERB
ejpam-5659	66	34	the	the	DET
ejpam-5659	66	35	form	form	NOUN
ejpam-5659	66	36	7p	7p	NOUN
ejpam-5659	66	37	=	=	SYM
ejpam-5659	67	1	6p	6p	NUM
ejpam-5659	68	1	+	+	ADP
ejpam-5659	68	2	p	p	NOUN
ejpam-5659	68	3	using	use	VERB
ejpam-5659	68	4	mixed	mixed	ADJ
ejpam-5659	68	5	addition	addition	NOUN
ejpam-5659	68	6	.	.	PUNCT
ejpam-5659	69	1	•	•	CCONJ
ejpam-5659	69	2	a	a	DET
ejpam-5659	69	3	new	new	ADJ
ejpam-5659	69	4	precomputed	precompute	VERB
ejpam-5659	69	5	sixtupling	sixtupling	NOUN
ejpam-5659	69	6	point	point	NOUN
ejpam-5659	69	7	6p	6p	NUM
ejpam-5659	69	8	arithmetic	arithmetic	ADJ
ejpam-5659	69	9	formula	formula	NOUN
ejpam-5659	69	10	is	be	AUX
ejpam-5659	69	11	proposed	propose	VERB
ejpam-5659	69	12	for	for	ADP
ejpam-5659	69	13	ld	ld	PROPN
ejpam-5659	69	14	coordinate	coordinate	NOUN
ejpam-5659	69	15	over	over	ADP
ejpam-5659	69	16	the	the	DET
ejpam-5659	69	17	binary	binary	ADJ
ejpam-5659	69	18	curve	curve	NOUN
ejpam-5659	69	19	using	use	VERB
ejpam-5659	69	20	the	the	DET
ejpam-5659	69	21	form	form	NOUN
ejpam-5659	69	22	6p	6p	NUM
ejpam-5659	69	23	=	=	SYM
ejpam-5659	69	24	3(2p	3(2p	NUM
ejpam-5659	69	25	)	)	PUNCT
ejpam-5659	69	26	using	use	VERB
ejpam-5659	69	27	mixed	mixed	ADJ
ejpam-5659	69	28	addition	addition	NOUN
ejpam-5659	69	29	which	which	PRON
ejpam-5659	69	30	is	be	AUX
ejpam-5659	69	31	to	to	PART
ejpam-5659	69	32	be	be	AUX
ejpam-5659	69	33	deployed	deploy	VERB
ejpam-5659	69	34	in	in	ADP
ejpam-5659	69	35	the	the	DET
ejpam-5659	69	36	septupling	septupling	NOUN
ejpam-5659	69	37	precomputed	precompute	VERB
ejpam-5659	69	38	formula	formula	NOUN
ejpam-5659	69	39	.	.	PUNCT
ejpam-5659	70	1	the	the	DET
ejpam-5659	70	2	remaining	remain	VERB
ejpam-5659	70	3	sections	section	NOUN
ejpam-5659	70	4	of	of	ADP
ejpam-5659	70	5	this	this	DET
ejpam-5659	70	6	paper	paper	NOUN
ejpam-5659	70	7	are	be	AUX
ejpam-5659	70	8	organized	organize	VERB
ejpam-5659	70	9	as	as	SCONJ
ejpam-5659	70	10	follows	follow	VERB
ejpam-5659	70	11	:	:	PUNCT
ejpam-5659	70	12	section	section	NOUN
ejpam-5659	70	13	2	2	NUM
ejpam-5659	70	14	introduces	introduce	VERB
ejpam-5659	70	15	the	the	DET
ejpam-5659	70	16	literature	literature	NOUN
ejpam-5659	70	17	and	and	CCONJ
ejpam-5659	70	18	related	related	ADJ
ejpam-5659	70	19	work	work	NOUN
ejpam-5659	70	20	.	.	PUNCT
ejpam-5659	71	1	section	section	NOUN
ejpam-5659	71	2	3	3	NUM
ejpam-5659	71	3	presents	present	VERB
ejpam-5659	71	4	the	the	DET
ejpam-5659	71	5	proposed	propose	VERB
ejpam-5659	71	6	formulas	formula	NOUN
ejpam-5659	71	7	,	,	PUNCT
ejpam-5659	71	8	and	and	CCONJ
ejpam-5659	71	9	finally	finally	ADV
ejpam-5659	71	10	section	section	NOUN
ejpam-5659	71	11	4	4	NUM
ejpam-5659	71	12	concludes	conclude	VERB
ejpam-5659	71	13	the	the	DET
ejpam-5659	71	14	paper	paper	NOUN
ejpam-5659	71	15	and	and	CCONJ
ejpam-5659	71	16	highlights	highlight	NOUN
ejpam-5659	71	17	suggestions	suggestion	NOUN
ejpam-5659	71	18	for	for	ADP
ejpam-5659	71	19	future	future	ADJ
ejpam-5659	71	20	work	work	NOUN
ejpam-5659	71	21	.	.	PUNCT
ejpam-5659	72	1	3	3	X
ejpam-5659	72	2	.	.	X
ejpam-5659	72	3	literature	literature	NOUN
ejpam-5659	72	4	review	review	VERB
ejpam-5659	72	5	elliptic	elliptic	ADJ
ejpam-5659	72	6	curve	curve	NOUN
ejpam-5659	72	7	cryptography	cryptography	NOUN
ejpam-5659	72	8	ecc	ecc	PROPN
ejpam-5659	72	9	utilizes	utilize	VERB
ejpam-5659	72	10	the	the	DET
ejpam-5659	72	11	elliptic	elliptic	ADJ
ejpam-5659	72	12	curve	curve	NOUN
ejpam-5659	72	13	over	over	ADP
ejpam-5659	72	14	a	a	DET
ejpam-5659	72	15	finite	finite	ADJ
ejpam-5659	72	16	field	field	NOUN
ejpam-5659	72	17	fq	fq	NOUN
ejpam-5659	72	18	,	,	PUNCT
ejpam-5659	72	19	denoted	denote	VERB
ejpam-5659	72	20	by	by	ADP
ejpam-5659	72	21	e(fq	e(fq	PROPN
ejpam-5659	72	22	)	)	PUNCT
ejpam-5659	72	23	which	which	PRON
ejpam-5659	72	24	contains	contain	VERB
ejpam-5659	72	25	the	the	DET
ejpam-5659	72	26	points	point	NOUN
ejpam-5659	72	27	(	(	PUNCT
ejpam-5659	72	28	x	x	X
ejpam-5659	72	29	,	,	PUNCT
ejpam-5659	72	30	y	y	NOUN
ejpam-5659	72	31	)	)	PUNCT
ejpam-5659	72	32	∈	∈	PROPN
ejpam-5659	72	33	fq	fq	NOUN
ejpam-5659	72	34	x	x	PROPN
ejpam-5659	72	35	fq	fq	PROPN
ejpam-5659	72	36	that	that	PRON
ejpam-5659	72	37	is	be	AUX
ejpam-5659	72	38	in	in	ADP
ejpam-5659	72	39	affine	affine	NOUN
ejpam-5659	72	40	coordinates	coordinate	NOUN
ejpam-5659	72	41	and	and	CCONJ
ejpam-5659	72	42	satisfy	satisfy	VERB
ejpam-5659	72	43	weierstrass	weierstrass	NOUN
ejpam-5659	72	44	as	as	SCONJ
ejpam-5659	72	45	provided	provide	VERB
ejpam-5659	72	46	in	in	ADP
ejpam-5659	72	47	equation	equation	NOUN
ejpam-5659	72	48	(	(	PUNCT
ejpam-5659	72	49	1	1	NUM
ejpam-5659	72	50	)	)	PUNCT
ejpam-5659	72	51	.	.	PUNCT
ejpam-5659	73	1	y2	y2	PROPN
ejpam-5659	74	1	+	+	CCONJ
ejpam-5659	74	2	a1xy	a1xy	X
ejpam-5659	75	1	+	+	CCONJ
ejpam-5659	75	2	a3y	a3y	X
ejpam-5659	75	3	=	=	SYM
ejpam-5659	75	4	x3	x3	PROPN
ejpam-5659	75	5	+	+	CCONJ
ejpam-5659	75	6	a2x	a2x	PROPN
ejpam-5659	75	7	2	2	NUM
ejpam-5659	75	8	+	+	NOUN
ejpam-5659	75	9	a4x+	a4x+	PROPN
ejpam-5659	75	10	a5	a5	NOUN
ejpam-5659	75	11	(	(	PUNCT
ejpam-5659	75	12	1	1	X
ejpam-5659	75	13	)	)	PUNCT
ejpam-5659	75	14	where	where	SCONJ
ejpam-5659	75	15	ai	ai	VERB
ejpam-5659	75	16	∈	∈	PROPN
ejpam-5659	75	17	fq	fq	NOUN
ejpam-5659	75	18	the	the	DET
ejpam-5659	75	19	point	point	NOUN
ejpam-5659	75	20	at	at	ADP
ejpam-5659	75	21	infinity	infinity	NOUN
ejpam-5659	75	22	o	o	NOUN
ejpam-5659	75	23	is	be	AUX
ejpam-5659	75	24	a	a	DET
ejpam-5659	75	25	special	special	ADJ
ejpam-5659	75	26	point	point	NOUN
ejpam-5659	75	27	that	that	PRON
ejpam-5659	75	28	form	form	NOUN
ejpam-5659	75	29	abelian	abelian	PROPN
ejpam-5659	75	30	group	group	NOUN
ejpam-5659	75	31	with	with	ADP
ejpam-5659	75	32	the	the	DET
ejpam-5659	75	33	finite	finite	ADJ
ejpam-5659	75	34	field	field	NOUN
ejpam-5659	75	35	e(fq	e(fq	PROPN
ejpam-5659	75	36	)	)	PUNCT
ejpam-5659	75	37	,	,	PUNCT
ejpam-5659	75	38	where	where	SCONJ
ejpam-5659	75	39	o	o	NOUN
ejpam-5659	75	40	is	be	AUX
ejpam-5659	75	41	a	a	DET
ejpam-5659	75	42	neutral	neutral	ADJ
ejpam-5659	75	43	element	element	NOUN
ejpam-5659	75	44	in	in	ADP
ejpam-5659	75	45	the	the	DET
ejpam-5659	75	46	group	group	NOUN
ejpam-5659	75	47	operation	operation	NOUN
ejpam-5659	76	1	[	[	X
ejpam-5659	76	2	7	7	NUM
ejpam-5659	76	3	]	]	PUNCT
ejpam-5659	76	4	.	.	PUNCT
ejpam-5659	77	1	w.	w.	PROPN
ejpam-5659	77	2	k.	k.	PROPN
ejpam-5659	77	3	abdulraheem	abdulraheem	PROPN
ejpam-5659	77	4	/	/	SYM
ejpam-5659	77	5	eur	eur	PROPN
ejpam-5659	77	6	.	.	PUNCT
ejpam-5659	78	1	j.	j.	PROPN
ejpam-5659	78	2	pure	pure	PROPN
ejpam-5659	78	3	appl	appl	PROPN
ejpam-5659	78	4	.	.	PROPN
ejpam-5659	78	5	math	math	PROPN
ejpam-5659	78	6	,	,	PUNCT
ejpam-5659	78	7	18	18	NUM
ejpam-5659	78	8	(	(	PUNCT
ejpam-5659	78	9	2	2	NUM
ejpam-5659	78	10	)	)	PUNCT
ejpam-5659	78	11	(	(	PUNCT
ejpam-5659	78	12	2025	2025	NUM
ejpam-5659	78	13	)	)	PUNCT
ejpam-5659	78	14	,	,	PUNCT
ejpam-5659	78	15	5659	5659	NUM
ejpam-5659	78	16	5	5	NUM
ejpam-5659	78	17	of	of	ADP
ejpam-5659	78	18	13	13	NUM
ejpam-5659	78	19	over	over	ADP
ejpam-5659	78	20	ecc	ecc	PROPN
ejpam-5659	78	21	,	,	PUNCT
ejpam-5659	78	22	different	different	ADJ
ejpam-5659	78	23	forms	form	NOUN
ejpam-5659	78	24	for	for	ADP
ejpam-5659	78	25	ai	ai	NOUN
ejpam-5659	78	26	will	will	AUX
ejpam-5659	78	27	represent	represent	VERB
ejpam-5659	78	28	different	different	ADJ
ejpam-5659	78	29	curves	curve	NOUN
ejpam-5659	78	30	.	.	PUNCT
ejpam-5659	79	1	some	some	DET
ejpam-5659	79	2	curves	curve	NOUN
ejpam-5659	79	3	are	be	AUX
ejpam-5659	79	4	suitable	suitable	ADJ
ejpam-5659	79	5	for	for	ADP
ejpam-5659	79	6	use	use	NOUN
ejpam-5659	79	7	in	in	ADP
ejpam-5659	79	8	the	the	DET
ejpam-5659	79	9	prime	prime	ADJ
ejpam-5659	79	10	field	field	NOUN
ejpam-5659	79	11	such	such	ADJ
ejpam-5659	79	12	as	as	ADP
ejpam-5659	79	13	short	short	ADJ
ejpam-5659	79	14	weierstrass	weierstrass	NOUN
ejpam-5659	79	15	curve	curve	NOUN
ejpam-5659	79	16	which	which	PRON
ejpam-5659	79	17	uses	use	VERB
ejpam-5659	79	18	the	the	DET
ejpam-5659	79	19	form	form	NOUN
ejpam-5659	79	20	in	in	ADP
ejpam-5659	79	21	equation	equation	NOUN
ejpam-5659	79	22	(	(	PUNCT
ejpam-5659	79	23	2	2	NUM
ejpam-5659	79	24	)	)	PUNCT
ejpam-5659	79	25	,	,	PUNCT
ejpam-5659	79	26	barreto	barreto	NOUN
ejpam-5659	79	27	-	-	PUNCT
ejpam-5659	79	28	naehrig	naehrig	PROPN
ejpam-5659	79	29	curve	curve	NOUN
ejpam-5659	79	30	which	which	PRON
ejpam-5659	79	31	uses	use	VERB
ejpam-5659	79	32	the	the	DET
ejpam-5659	79	33	form	form	NOUN
ejpam-5659	79	34	in	in	ADP
ejpam-5659	79	35	equation	equation	NOUN
ejpam-5659	79	36	(	(	PUNCT
ejpam-5659	79	37	3	3	NUM
ejpam-5659	79	38	)	)	PUNCT
ejpam-5659	79	39	below	below	ADV
ejpam-5659	79	40	,	,	PUNCT
ejpam-5659	79	41	as	as	ADV
ejpam-5659	79	42	well	well	ADV
ejpam-5659	79	43	as	as	ADP
ejpam-5659	79	44	other	other	ADJ
ejpam-5659	79	45	curves	curve	NOUN
ejpam-5659	79	46	.	.	PUNCT
ejpam-5659	80	1	although	although	SCONJ
ejpam-5659	80	2	there	there	PRON
ejpam-5659	80	3	are	be	VERB
ejpam-5659	80	4	several	several	ADJ
ejpam-5659	80	5	applicable	applicable	ADJ
ejpam-5659	80	6	formulas	formula	NOUN
ejpam-5659	80	7	within	within	ADP
ejpam-5659	80	8	the	the	DET
ejpam-5659	80	9	family	family	NOUN
ejpam-5659	80	10	of	of	ADP
ejpam-5659	80	11	binary	binary	ADJ
ejpam-5659	80	12	curves	curve	NOUN
ejpam-5659	80	13	,	,	PUNCT
ejpam-5659	80	14	the	the	DET
ejpam-5659	80	15	most	most	ADV
ejpam-5659	80	16	suitable	suitable	ADJ
ejpam-5659	80	17	curve	curve	NOUN
ejpam-5659	80	18	for	for	ADP
ejpam-5659	80	19	the	the	DET
ejpam-5659	80	20	binary	binary	ADJ
ejpam-5659	80	21	field	field	NOUN
ejpam-5659	80	22	is	be	AUX
ejpam-5659	80	23	koblitz	koblitz	ADJ
ejpam-5659	80	24	curve	curve	NOUN
ejpam-5659	80	25	as	as	SCONJ
ejpam-5659	80	26	shown	show	VERB
ejpam-5659	80	27	in	in	ADP
ejpam-5659	80	28	equation	equation	NOUN
ejpam-5659	80	29	(	(	PUNCT
ejpam-5659	80	30	4	4	NUM
ejpam-5659	80	31	)	)	PUNCT
ejpam-5659	80	32	,	,	PUNCT
ejpam-5659	80	33	where	where	SCONJ
ejpam-5659	80	34	a	a	DET
ejpam-5659	80	35	∈	∈	NOUN
ejpam-5659	80	36	{	{	PUNCT
ejpam-5659	80	37	0	0	NUM
ejpam-5659	80	38	,	,	PUNCT
ejpam-5659	80	39	1	1	NUM
ejpam-5659	80	40	}	}	PUNCT
ejpam-5659	80	41	.	.	PUNCT
ejpam-5659	81	1	y2	y2	NOUN
ejpam-5659	82	1	=	=	SYM
ejpam-5659	83	1	x3	x3	ADJ
ejpam-5659	83	2	+	+	CCONJ
ejpam-5659	83	3	ax+	ax+	ADJ
ejpam-5659	83	4	b	b	SYM
ejpam-5659	83	5	(	(	PUNCT
ejpam-5659	83	6	2	2	NUM
ejpam-5659	83	7	)	)	PUNCT
ejpam-5659	83	8	y2	y2	NOUN
ejpam-5659	83	9	=	=	PUNCT
ejpam-5659	84	1	x3	x3	PROPN
ejpam-5659	84	2	+	+	CCONJ
ejpam-5659	84	3	b	b	X
ejpam-5659	84	4	(	(	PUNCT
ejpam-5659	84	5	3	3	NUM
ejpam-5659	84	6	)	)	PUNCT
ejpam-5659	84	7	y2	y2	NOUN
ejpam-5659	85	1	+	+	CCONJ
ejpam-5659	85	2	xy	xy	NOUN
ejpam-5659	85	3	=	=	SYM
ejpam-5659	86	1	x3	x3	VERB
ejpam-5659	86	2	+	+	CCONJ
ejpam-5659	86	3	ax2	ax2	NOUN
ejpam-5659	86	4	+	+	CCONJ
ejpam-5659	86	5	1	1	NUM
ejpam-5659	86	6	(	(	PUNCT
ejpam-5659	86	7	4	4	NUM
ejpam-5659	86	8	)	)	PUNCT
ejpam-5659	86	9	anomalous	anomalous	ADJ
ejpam-5659	86	10	binary	binary	NOUN
ejpam-5659	86	11	curve	curve	NOUN
ejpam-5659	86	12	(	(	PUNCT
ejpam-5659	86	13	abc	abc	PROPN
ejpam-5659	86	14	)	)	PUNCT
ejpam-5659	86	15	or	or	CCONJ
ejpam-5659	86	16	koblitz	koblitz	ADJ
ejpam-5659	86	17	curve	curve	NOUN
ejpam-5659	86	18	is	be	AUX
ejpam-5659	86	19	recommended	recommend	VERB
ejpam-5659	86	20	by	by	ADP
ejpam-5659	86	21	nist	nist	NOUN
ejpam-5659	86	22	standard	standard	NOUN
ejpam-5659	86	23	[	[	X
ejpam-5659	86	24	29	29	NUM
ejpam-5659	86	25	]	]	PUNCT
ejpam-5659	86	26	for	for	ADP
ejpam-5659	86	27	the	the	DET
ejpam-5659	86	28	curve	curve	NOUN
ejpam-5659	86	29	k−163	k−163	PROPN
ejpam-5659	86	30	where	where	SCONJ
ejpam-5659	86	31	a	a	DET
ejpam-5659	86	32	=	=	NOUN
ejpam-5659	86	33	1	1	X
ejpam-5659	86	34	.	.	PUNCT
ejpam-5659	87	1	it	it	PRON
ejpam-5659	87	2	allows	allow	VERB
ejpam-5659	87	3	for	for	ADP
ejpam-5659	87	4	fast	fast	ADJ
ejpam-5659	87	5	and	and	CCONJ
ejpam-5659	87	6	efficient	efficient	ADJ
ejpam-5659	87	7	scalar	scalar	ADJ
ejpam-5659	87	8	multiplication	multiplication	NOUN
ejpam-5659	87	9	while	while	SCONJ
ejpam-5659	87	10	efficiently	efficiently	ADV
ejpam-5659	87	11	using	use	VERB
ejpam-5659	87	12	both	both	CCONJ
ejpam-5659	87	13	hardware	hardware	NOUN
ejpam-5659	87	14	and	and	CCONJ
ejpam-5659	87	15	software	software	NOUN
ejpam-5659	87	16	.	.	PUNCT
ejpam-5659	88	1	particularly	particularly	ADV
ejpam-5659	88	2	,	,	PUNCT
ejpam-5659	88	3	it	it	PRON
ejpam-5659	88	4	is	be	AUX
ejpam-5659	88	5	attractive	attractive	ADJ
ejpam-5659	88	6	because	because	SCONJ
ejpam-5659	88	7	of	of	ADP
ejpam-5659	88	8	its	its	PRON
ejpam-5659	88	9	lightweight	lightweight	ADJ
ejpam-5659	88	10	implementation	implementation	NOUN
ejpam-5659	88	11	[	[	X
ejpam-5659	88	12	34	34	NUM
ejpam-5659	88	13	]	]	PUNCT
ejpam-5659	88	14	.	.	PUNCT
ejpam-5659	89	1	over	over	ADP
ejpam-5659	89	2	ld	ld	PROPN
ejpam-5659	89	3	projective	projective	PROPN
ejpam-5659	89	4	coordinates	coordinate	NOUN
ejpam-5659	89	5	,	,	PUNCT
ejpam-5659	89	6	the	the	DET
ejpam-5659	89	7	equation	equation	NOUN
ejpam-5659	89	8	of	of	ADP
ejpam-5659	89	9	the	the	DET
ejpam-5659	89	10	projective	projective	ADJ
ejpam-5659	89	11	point	point	NOUN
ejpam-5659	89	12	(	(	PUNCT
ejpam-5659	89	13	x	x	X
ejpam-5659	89	14	:	:	PUNCT
ejpam-5659	89	15	y	y	NOUN
ejpam-5659	89	16	:	:	PUNCT
ejpam-5659	89	17	z	z	X
ejpam-5659	89	18	)	)	PUNCT
ejpam-5659	89	19	where	where	SCONJ
ejpam-5659	89	20	z	z	NOUN
ejpam-5659	89	21	̸=	̸=	PROPN
ejpam-5659	89	22	0	0	NUM
ejpam-5659	89	23	has	have	VERB
ejpam-5659	89	24	its	its	PRON
ejpam-5659	89	25	equation	equation	NOUN
ejpam-5659	89	26	as	as	SCONJ
ejpam-5659	89	27	shown	show	VERB
ejpam-5659	89	28	in	in	ADP
ejpam-5659	89	29	(	(	PUNCT
ejpam-5659	89	30	5	5	NUM
ejpam-5659	89	31	)	)	PUNCT
ejpam-5659	89	32	[	[	X
ejpam-5659	89	33	35	35	NUM
ejpam-5659	89	34	]	]	PUNCT
ejpam-5659	89	35	.	.	PUNCT
ejpam-5659	90	1	y	y	PROPN
ejpam-5659	90	2	2	2	NUM
ejpam-5659	91	1	+	+	NOUN
ejpam-5659	91	2	xy	xy	NOUN
ejpam-5659	91	3	z	z	NOUN
ejpam-5659	91	4	=	=	PUNCT
ejpam-5659	91	5	x3	x3	ADJ
ejpam-5659	92	1	+	+	CCONJ
ejpam-5659	92	2	ax2z2	ax2z2	PROPN
ejpam-5659	92	3	+	+	NUM
ejpam-5659	92	4	bz6	bz6	NOUN
ejpam-5659	92	5	(	(	PUNCT
ejpam-5659	92	6	5	5	X
ejpam-5659	92	7	)	)	PUNCT
ejpam-5659	92	8	the	the	DET
ejpam-5659	92	9	first	first	ADJ
ejpam-5659	92	10	proposed	propose	VERB
ejpam-5659	92	11	point	point	NOUN
ejpam-5659	92	12	addition	addition	NOUN
ejpam-5659	92	13	over	over	ADP
ejpam-5659	92	14	ld	ld	PROPN
ejpam-5659	92	15	by	by	ADP
ejpam-5659	92	16	[	[	X
ejpam-5659	92	17	36	36	NUM
ejpam-5659	92	18	]	]	PUNCT
ejpam-5659	92	19	costs	cost	VERB
ejpam-5659	92	20	6s+14	6s+14	NOUN
ejpam-5659	92	21	m	m	VERB
ejpam-5659	92	22	+8a	+8a	NUM
ejpam-5659	92	23	as	as	SCONJ
ejpam-5659	92	24	provided	provide	VERB
ejpam-5659	92	25	in	in	ADP
ejpam-5659	92	26	the	the	DET
ejpam-5659	92	27	formula	formula	NOUN
ejpam-5659	92	28	in	in	ADP
ejpam-5659	92	29	equation	equation	NOUN
ejpam-5659	92	30	(	(	PUNCT
ejpam-5659	92	31	6	6	NUM
ejpam-5659	92	32	)	)	PUNCT
ejpam-5659	92	33	below	below	ADV
ejpam-5659	92	34	.	.	PUNCT
ejpam-5659	93	1	(	(	PUNCT
ejpam-5659	93	2	x0	x0	PROPN
ejpam-5659	93	3	,	,	PUNCT
ejpam-5659	93	4	y0	y0	PROPN
ejpam-5659	93	5	,	,	PUNCT
ejpam-5659	93	6	z0	z0	PROPN
ejpam-5659	93	7	)	)	PUNCT
ejpam-5659	93	8	+	+	CCONJ
ejpam-5659	93	9	(	(	PUNCT
ejpam-5659	93	10	x1	x1	PROPN
ejpam-5659	93	11	,	,	PUNCT
ejpam-5659	93	12	y1	y1	PROPN
ejpam-5659	93	13	,	,	PUNCT
ejpam-5659	93	14	z1	z1	NOUN
ejpam-5659	93	15	)	)	PUNCT
ejpam-5659	93	16	=	=	SYM
ejpam-5659	93	17	(	(	PUNCT
ejpam-5659	93	18	x2	x2	PROPN
ejpam-5659	93	19	,	,	PUNCT
ejpam-5659	93	20	y2	y2	PROPN
ejpam-5659	93	21	,	,	PUNCT
ejpam-5659	93	22	z2	z2	PROPN
ejpam-5659	93	23	)	)	PUNCT
ejpam-5659	94	1	where	where	SCONJ
ejpam-5659	94	2	:	:	PUNCT
ejpam-5659	94	3	a0	a0	PROPN
ejpam-5659	94	4	=	=	PUNCT
ejpam-5659	94	5	y1.z0	y1.z0	PROPN
ejpam-5659	94	6	a1	a1	NOUN
ejpam-5659	94	7	=	=	SYM
ejpam-5659	94	8	y0.z	y0.z	NUM
ejpam-5659	94	9	2	2	NUM
ejpam-5659	94	10	1	1	NUM
ejpam-5659	94	11	b0	b0	NOUN
ejpam-5659	94	12	=	=	SYM
ejpam-5659	94	13	x1.z0	x1.z0	PROPN
ejpam-5659	94	14	b1	b1	NOUN
ejpam-5659	94	15	=	=	SYM
ejpam-5659	94	16	x0.z1	x0.z1	PROPN
ejpam-5659	94	17	c	c	NOUN
ejpam-5659	94	18	=	=	SYM
ejpam-5659	94	19	a0	a0	PROPN
ejpam-5659	94	20	+	+	NOUN
ejpam-5659	94	21	a1	a1	PROPN
ejpam-5659	94	22	d	d	NOUN
ejpam-5659	94	23	=	=	SYM
ejpam-5659	94	24	b0	b0	PROPN
ejpam-5659	94	25	+	+	NOUN
ejpam-5659	94	26	b1	b1	NOUN
ejpam-5659	94	27	e	e	NOUN
ejpam-5659	94	28	=	=	PUNCT
ejpam-5659	94	29	z0.z1	z0.z1	X
ejpam-5659	94	30	f	f	X
ejpam-5659	94	31	=	=	SYM
ejpam-5659	94	32	d.e	d.e	PROPN
ejpam-5659	94	33	z2	z2	PROPN
ejpam-5659	94	34	=	=	SYM
ejpam-5659	94	35	f	f	PROPN
ejpam-5659	94	36	2	2	NUM
ejpam-5659	94	37	g	g	NOUN
ejpam-5659	94	38	=	=	PROPN
ejpam-5659	94	39	d2.(f	d2.(f	PROPN
ejpam-5659	94	40	+	+	CCONJ
ejpam-5659	94	41	ae2	ae2	ADJ
ejpam-5659	94	42	)	)	PUNCT
ejpam-5659	94	43	h	h	NOUN
ejpam-5659	94	44	=	=	PROPN
ejpam-5659	94	45	c.f	c.f	PROPN
ejpam-5659	94	46	w.	w.	PROPN
ejpam-5659	94	47	k.	k.	PROPN
ejpam-5659	94	48	abdulraheem	abdulraheem	PROPN
ejpam-5659	94	49	/	/	SYM
ejpam-5659	94	50	eur	eur	PROPN
ejpam-5659	94	51	.	.	PUNCT
ejpam-5659	95	1	j.	j.	PROPN
ejpam-5659	95	2	pure	pure	PROPN
ejpam-5659	95	3	appl	appl	PROPN
ejpam-5659	95	4	.	.	PROPN
ejpam-5659	95	5	math	math	PROPN
ejpam-5659	95	6	,	,	PUNCT
ejpam-5659	95	7	18	18	NUM
ejpam-5659	95	8	(	(	PUNCT
ejpam-5659	95	9	2	2	NUM
ejpam-5659	95	10	)	)	PUNCT
ejpam-5659	95	11	(	(	PUNCT
ejpam-5659	95	12	2025	2025	NUM
ejpam-5659	95	13	)	)	PUNCT
ejpam-5659	95	14	,	,	PUNCT
ejpam-5659	95	15	5659	5659	NUM
ejpam-5659	95	16	6	6	NUM
ejpam-5659	95	17	of	of	ADP
ejpam-5659	95	18	13	13	NUM
ejpam-5659	95	19	x2	x2	NOUN
ejpam-5659	95	20	=	=	SYM
ejpam-5659	95	21	c2	c2	PROPN
ejpam-5659	96	1	+	+	NOUN
ejpam-5659	96	2	h	h	VERB
ejpam-5659	97	1	+	+	NOUN
ejpam-5659	97	2	g	g	NOUN
ejpam-5659	97	3	i	i	NOUN
ejpam-5659	97	4	=	=	PUNCT
ejpam-5659	97	5	d2.a0	d2.a0	PROPN
ejpam-5659	98	1	+	+	PROPN
ejpam-5659	98	2	x2	x2	PROPN
ejpam-5659	98	3	j	j	PROPN
ejpam-5659	98	4	=	=	SYM
ejpam-5659	98	5	d2.a0	d2.a0	PROPN
ejpam-5659	99	1	+	+	PROPN
ejpam-5659	100	1	x2	x2	PROPN
ejpam-5659	101	1	y2	y2	NOUN
ejpam-5659	102	1	=	=	PUNCT
ejpam-5659	103	1	h.i	h.i	PROPN
ejpam-5659	103	2	+	+	X
ejpam-5659	103	3	z2.j	z2.j	PROPN
ejpam-5659	103	4	(	(	PUNCT
ejpam-5659	103	5	6	6	NUM
ejpam-5659	103	6	)	)	PUNCT
ejpam-5659	103	7	to	to	PART
ejpam-5659	103	8	reduce	reduce	VERB
ejpam-5659	103	9	the	the	DET
ejpam-5659	103	10	cost	cost	NOUN
ejpam-5659	103	11	,	,	PUNCT
ejpam-5659	103	12	the	the	DET
ejpam-5659	103	13	formula	formula	NOUN
ejpam-5659	103	14	in	in	ADP
ejpam-5659	103	15	(	(	PUNCT
ejpam-5659	103	16	6	6	NUM
ejpam-5659	103	17	)	)	PUNCT
ejpam-5659	103	18	can	can	AUX
ejpam-5659	103	19	be	be	AUX
ejpam-5659	103	20	improved	improve	VERB
ejpam-5659	103	21	when	when	SCONJ
ejpam-5659	103	22	z	z	NOUN
ejpam-5659	103	23	=	=	SYM
ejpam-5659	103	24	1	1	NUM
ejpam-5659	103	25	for	for	ADP
ejpam-5659	103	26	its	its	PRON
ejpam-5659	103	27	special	special	ADJ
ejpam-5659	103	28	case	case	NOUN
ejpam-5659	103	29	as	as	SCONJ
ejpam-5659	103	30	shown	show	VERB
ejpam-5659	103	31	in	in	ADP
ejpam-5659	103	32	the	the	DET
ejpam-5659	103	33	formula	formula	NOUN
ejpam-5659	103	34	provided	provide	VERB
ejpam-5659	103	35	in	in	ADP
ejpam-5659	103	36	equation	equation	NOUN
ejpam-5659	103	37	(	(	PUNCT
ejpam-5659	103	38	7	7	NUM
ejpam-5659	103	39	)	)	PUNCT
ejpam-5659	103	40	.	.	PUNCT
ejpam-5659	104	1	(	(	PUNCT
ejpam-5659	104	2	x0	x0	PROPN
ejpam-5659	104	3	,	,	PUNCT
ejpam-5659	104	4	y0	y0	PROPN
ejpam-5659	104	5	,	,	PUNCT
ejpam-5659	104	6	z0	z0	PROPN
ejpam-5659	104	7	)	)	PUNCT
ejpam-5659	104	8	+	+	CCONJ
ejpam-5659	104	9	(	(	PUNCT
ejpam-5659	104	10	x1	x1	PROPN
ejpam-5659	104	11	,	,	PUNCT
ejpam-5659	104	12	y1	y1	NOUN
ejpam-5659	104	13	,	,	PUNCT
ejpam-5659	104	14	1	1	NUM
ejpam-5659	104	15	)	)	PUNCT
ejpam-5659	104	16	=	=	SYM
ejpam-5659	104	17	(	(	PUNCT
ejpam-5659	104	18	x2	x2	PROPN
ejpam-5659	104	19	,	,	PUNCT
ejpam-5659	104	20	y2	y2	PROPN
ejpam-5659	104	21	,	,	PUNCT
ejpam-5659	104	22	z2	z2	PROPN
ejpam-5659	104	23	)	)	PUNCT
ejpam-5659	104	24	such	such	ADJ
ejpam-5659	104	25	that	that	SCONJ
ejpam-5659	104	26	:	:	PUNCT
ejpam-5659	104	27	a	a	PRON
ejpam-5659	104	28	=	=	SYM
ejpam-5659	104	29	y1.z	y1.z	ADJ
ejpam-5659	104	30	2	2	NUM
ejpam-5659	104	31	0	0	NUM
ejpam-5659	104	32	+	+	CCONJ
ejpam-5659	105	1	y0	y0	PROPN
ejpam-5659	105	2	b	b	NOUN
ejpam-5659	105	3	=	=	PUNCT
ejpam-5659	105	4	x1.z0	x1.z0	PROPN
ejpam-5659	106	1	+	+	NOUN
ejpam-5659	106	2	x0	x0	PROPN
ejpam-5659	106	3	c	c	NOUN
ejpam-5659	106	4	=	=	SYM
ejpam-5659	106	5	z0.b	z0.b	PUNCT
ejpam-5659	106	6	d	d	X
ejpam-5659	106	7	=	=	SYM
ejpam-5659	106	8	b2.(c	b2.(c	PROPN
ejpam-5659	106	9	+	+	NUM
ejpam-5659	106	10	az2	az2	PROPN
ejpam-5659	106	11	)	)	PUNCT
ejpam-5659	106	12	z2	z2	PROPN
ejpam-5659	106	13	=	=	SYM
ejpam-5659	106	14	c2	c2	PROPN
ejpam-5659	106	15	e	e	X
ejpam-5659	106	16	=	=	NOUN
ejpam-5659	106	17	a.c	a.c	PROPN
ejpam-5659	106	18	x2	x2	NOUN
ejpam-5659	106	19	=	=	PROPN
ejpam-5659	106	20	a2	a2	PROPN
ejpam-5659	106	21	+	+	PROPN
ejpam-5659	107	1	d	d	PROPN
ejpam-5659	107	2	+	+	X
ejpam-5659	107	3	e	e	X
ejpam-5659	107	4	f	f	NOUN
ejpam-5659	107	5	=	=	SYM
ejpam-5659	108	1	x2	x2	PROPN
ejpam-5659	109	1	+	+	PROPN
ejpam-5659	109	2	x1.z2	x1.z2	PROPN
ejpam-5659	109	3	g	g	NOUN
ejpam-5659	109	4	=	=	SYM
ejpam-5659	109	5	x2	x2	PROPN
ejpam-5659	110	1	+	+	NUM
ejpam-5659	110	2	y1.z2	y1.z2	NOUN
ejpam-5659	110	3	y2	y2	NOUN
ejpam-5659	110	4	=	=	PUNCT
ejpam-5659	110	5	e.f	e.f	PROPN
ejpam-5659	110	6	+	+	X
ejpam-5659	110	7	z2.g	z2.g	NUM
ejpam-5659	110	8	(	(	PUNCT
ejpam-5659	110	9	7	7	NUM
ejpam-5659	110	10	)	)	PUNCT
ejpam-5659	110	11	the	the	DET
ejpam-5659	110	12	cost	cost	NOUN
ejpam-5659	110	13	was	be	AUX
ejpam-5659	110	14	reduced	reduce	VERB
ejpam-5659	110	15	later	later	ADV
ejpam-5659	110	16	by	by	ADP
ejpam-5659	110	17	[	[	X
ejpam-5659	110	18	37	37	NUM
ejpam-5659	110	19	]	]	PUNCT
ejpam-5659	110	20	who	who	PRON
ejpam-5659	110	21	introduced	introduce	VERB
ejpam-5659	110	22	a	a	DET
ejpam-5659	110	23	new	new	ADJ
ejpam-5659	110	24	formula	formula	NOUN
ejpam-5659	110	25	with	with	ADP
ejpam-5659	110	26	cost	cost	NOUN
ejpam-5659	110	27	4s	4s	NUM
ejpam-5659	110	28	+	+	NUM
ejpam-5659	110	29	13	13	NUM
ejpam-5659	110	30	m	m	NOUN
ejpam-5659	110	31	+	+	NOUN
ejpam-5659	110	32	9a	9a	NOUN
ejpam-5659	110	33	.	.	PUNCT
ejpam-5659	111	1	afterwards	afterwards	ADV
ejpam-5659	111	2	,	,	PUNCT
ejpam-5659	111	3	[	[	X
ejpam-5659	111	4	38	38	NUM
ejpam-5659	111	5	]	]	PUNCT
ejpam-5659	111	6	proposed	propose	VERB
ejpam-5659	111	7	a	a	DET
ejpam-5659	111	8	new	new	ADJ
ejpam-5659	111	9	formula	formula	NOUN
ejpam-5659	111	10	which	which	PRON
ejpam-5659	111	11	reduces	reduce	VERB
ejpam-5659	111	12	the	the	DET
ejpam-5659	111	13	cost	cost	NOUN
ejpam-5659	111	14	of	of	ADP
ejpam-5659	111	15	the	the	DET
ejpam-5659	111	16	point	point	NOUN
ejpam-5659	111	17	addition	addition	NOUN
ejpam-5659	111	18	using	use	VERB
ejpam-5659	111	19	mix	mix	NOUN
ejpam-5659	111	20	addition	addition	NOUN
ejpam-5659	111	21	techniques	technique	NOUN
ejpam-5659	111	22	in	in	ADP
ejpam-5659	111	23	the	the	DET
ejpam-5659	111	24	projective	projective	NOUN
ejpam-5659	111	25	as	as	SCONJ
ejpam-5659	111	26	shown	show	VERB
ejpam-5659	111	27	in	in	ADP
ejpam-5659	111	28	the	the	DET
ejpam-5659	111	29	formula	formula	NOUN
ejpam-5659	111	30	provided	provide	VERB
ejpam-5659	111	31	in	in	ADP
ejpam-5659	111	32	equation	equation	NOUN
ejpam-5659	111	33	(	(	PUNCT
ejpam-5659	111	34	8)	8)	NUM
ejpam-5659	111	35	below	below	ADV
ejpam-5659	111	36	.	.	PUNCT
ejpam-5659	112	1	(	(	PUNCT
ejpam-5659	112	2	x1	x1	PROPN
ejpam-5659	112	3	,	,	PUNCT
ejpam-5659	112	4	y1	y1	NOUN
ejpam-5659	112	5	,	,	PUNCT
ejpam-5659	112	6	1	1	NUM
ejpam-5659	112	7	)	)	PUNCT
ejpam-5659	112	8	+	+	CCONJ
ejpam-5659	112	9	(	(	PUNCT
ejpam-5659	112	10	x2	x2	PROPN
ejpam-5659	112	11	,	,	PUNCT
ejpam-5659	112	12	y2	y2	PROPN
ejpam-5659	112	13	,	,	PUNCT
ejpam-5659	112	14	z2	z2	PROPN
ejpam-5659	112	15	)	)	PUNCT
ejpam-5659	112	16	=	=	SYM
ejpam-5659	112	17	(	(	PUNCT
ejpam-5659	112	18	x3	x3	ADJ
ejpam-5659	112	19	,	,	PUNCT
ejpam-5659	112	20	y3	y3	NOUN
ejpam-5659	112	21	,	,	PUNCT
ejpam-5659	112	22	z3	z3	PROPN
ejpam-5659	112	23	)	)	PUNCT
ejpam-5659	112	24	where	where	SCONJ
ejpam-5659	112	25	:	:	PUNCT
ejpam-5659	112	26	u	u	NOUN
ejpam-5659	112	27	=	=	PROPN
ejpam-5659	112	28	z2	z2	PROPN
ejpam-5659	112	29	2	2	NUM
ejpam-5659	112	30	y1	y1	NOUN
ejpam-5659	112	31	s	s	PART
ejpam-5659	112	32	=	=	SYM
ejpam-5659	112	33	z2	z2	PROPN
ejpam-5659	112	34	x1	x1	PROPN
ejpam-5659	113	1	+	+	PROPN
ejpam-5659	113	2	x2	x2	PROPN
ejpam-5659	113	3	t	t	NOUN
ejpam-5659	113	4	=	=	SYM
ejpam-5659	113	5	z2	z2	PROPN
ejpam-5659	113	6	s	s	PART
ejpam-5659	113	7	z3	z3	PROPN
ejpam-5659	113	8	=	=	SYM
ejpam-5659	113	9	t	t	PROPN
ejpam-5659	113	10	2	2	NUM
ejpam-5659	113	11	v	v	NOUN
ejpam-5659	113	12	=	=	SYM
ejpam-5659	113	13	z3	z3	PROPN
ejpam-5659	113	14	x1	x1	NUM
ejpam-5659	113	15	x3	x3	NOUN
ejpam-5659	113	16	=	=	SYM
ejpam-5659	114	1	u2	u2	PROPN
ejpam-5659	114	2	+	+	PROPN
ejpam-5659	114	3	t	t	PROPN
ejpam-5659	114	4	(	(	PUNCT
ejpam-5659	114	5	u	u	NOUN
ejpam-5659	114	6	+	+	CCONJ
ejpam-5659	114	7	s2	s2	PROPN
ejpam-5659	114	8	+	+	CCONJ
ejpam-5659	114	9	a2	a2	PROPN
ejpam-5659	114	10	t	t	PROPN
ejpam-5659	114	11	)	)	PUNCT
ejpam-5659	114	12	w.	w.	PROPN
ejpam-5659	114	13	k.	k.	PROPN
ejpam-5659	114	14	abdulraheem	abdulraheem	PROPN
ejpam-5659	114	15	/	/	SYM
ejpam-5659	114	16	eur	eur	PROPN
ejpam-5659	114	17	.	.	PUNCT
ejpam-5659	115	1	j.	j.	PROPN
ejpam-5659	115	2	pure	pure	PROPN
ejpam-5659	115	3	appl	appl	PROPN
ejpam-5659	115	4	.	.	PROPN
ejpam-5659	115	5	math	math	PROPN
ejpam-5659	115	6	,	,	PUNCT
ejpam-5659	115	7	18	18	NUM
ejpam-5659	115	8	(	(	PUNCT
ejpam-5659	115	9	2	2	NUM
ejpam-5659	115	10	)	)	PUNCT
ejpam-5659	115	11	(	(	PUNCT
ejpam-5659	115	12	2025	2025	NUM
ejpam-5659	115	13	)	)	PUNCT
ejpam-5659	115	14	,	,	PUNCT
ejpam-5659	115	15	5659	5659	NUM
ejpam-5659	115	16	7	7	NUM
ejpam-5659	115	17	of	of	ADP
ejpam-5659	115	18	13	13	NUM
ejpam-5659	115	19	y3(v	y3(v	PROPN
ejpam-5659	115	20	+	+	PROPN
ejpam-5659	115	21	x3)(tu	x3)(tu	PROPN
ejpam-5659	115	22	+	+	CCONJ
ejpam-5659	115	23	z3	z3	PROPN
ejpam-5659	115	24	)	)	PUNCT
ejpam-5659	116	1	+	+	CCONJ
ejpam-5659	116	2	z2	z2	NOUN
ejpam-5659	116	3	3	3	NUM
ejpam-5659	116	4	(	(	PUNCT
ejpam-5659	116	5	y1	y1	VERB
ejpam-5659	116	6	+	+	PROPN
ejpam-5659	116	7	x1	x1	NUM
ejpam-5659	116	8	)	)	PUNCT
ejpam-5659	116	9	(	(	PUNCT
ejpam-5659	116	10	8)	8)	NUM
ejpam-5659	116	11	the	the	DET
ejpam-5659	116	12	point	point	NOUN
ejpam-5659	116	13	doubling	double	VERB
ejpam-5659	116	14	2p	2p	NUM
ejpam-5659	116	15	implies	imply	VERB
ejpam-5659	116	16	adding	add	VERB
ejpam-5659	116	17	the	the	DET
ejpam-5659	116	18	point	point	NOUN
ejpam-5659	116	19	p	p	X
ejpam-5659	116	20	to	to	ADP
ejpam-5659	116	21	itself	itself	PRON
ejpam-5659	116	22	such	such	ADJ
ejpam-5659	116	23	that	that	SCONJ
ejpam-5659	116	24	2p	2p	NUM
ejpam-5659	116	25	=	=	PUNCT
ejpam-5659	117	1	p	p	X
ejpam-5659	117	2	+	+	NOUN
ejpam-5659	117	3	p	p	NOUN
ejpam-5659	117	4	.	.	PUNCT
ejpam-5659	118	1	the	the	DET
ejpam-5659	118	2	first	first	ADJ
ejpam-5659	118	3	proposed	propose	VERB
ejpam-5659	118	4	2p	2p	NOUN
ejpam-5659	118	5	over	over	ADP
ejpam-5659	118	6	ld	ld	PROPN
ejpam-5659	118	7	coordinate	coordinate	NOUN
ejpam-5659	118	8	as	as	SCONJ
ejpam-5659	118	9	the	the	DET
ejpam-5659	118	10	projected	project	VERB
ejpam-5659	118	11	form	form	NOUN
ejpam-5659	118	12	is	be	AUX
ejpam-5659	118	13	as	as	SCONJ
ejpam-5659	118	14	shown	show	VERB
ejpam-5659	118	15	in	in	ADP
ejpam-5659	118	16	the	the	DET
ejpam-5659	118	17	following	follow	VERB
ejpam-5659	118	18	formula	formula	NOUN
ejpam-5659	118	19	provided	provide	VERB
ejpam-5659	118	20	in	in	ADP
ejpam-5659	118	21	equation	equation	NOUN
ejpam-5659	118	22	(	(	PUNCT
ejpam-5659	118	23	9	9	NUM
ejpam-5659	118	24	)	)	PUNCT
ejpam-5659	118	25	below	below	ADP
ejpam-5659	118	26	with	with	ADP
ejpam-5659	118	27	the	the	DET
ejpam-5659	118	28	cost	cost	NOUN
ejpam-5659	118	29	4s	4s	NUM
ejpam-5659	118	30	+	+	NUM
ejpam-5659	118	31	5	5	NUM
ejpam-5659	118	32	m	m	NOUN
ejpam-5659	118	33	+	+	NUM
ejpam-5659	118	34	5a	5a	NUM
ejpam-5659	118	35	[	[	X
ejpam-5659	118	36	36	36	NUM
ejpam-5659	118	37	]	]	PUNCT
ejpam-5659	118	38	.	.	PUNCT
ejpam-5659	119	1	2(x1.y1	2(x1.y1	NUM
ejpam-5659	119	2	,	,	PUNCT
ejpam-5659	119	3	z1	z1	NOUN
ejpam-5659	119	4	)	)	PUNCT
ejpam-5659	119	5	=	=	SYM
ejpam-5659	119	6	(	(	PUNCT
ejpam-5659	119	7	x3	x3	ADJ
ejpam-5659	119	8	,	,	PUNCT
ejpam-5659	119	9	y3	y3	NOUN
ejpam-5659	119	10	,	,	PUNCT
ejpam-5659	119	11	z3	z3	PROPN
ejpam-5659	119	12	)	)	PUNCT
ejpam-5659	120	1	where	where	SCONJ
ejpam-5659	120	2	a	a	DET
ejpam-5659	120	3	=	=	SYM
ejpam-5659	120	4	z2	z2	PROPN
ejpam-5659	120	5	1	1	NUM
ejpam-5659	120	6	b	b	PROPN
ejpam-5659	120	7	=	=	SYM
ejpam-5659	120	8	ba2	ba2	PROPN
ejpam-5659	120	9	c	c	X
ejpam-5659	120	10	=	=	SYM
ejpam-5659	120	11	x2	x2	PROPN
ejpam-5659	120	12	1	1	NUM
ejpam-5659	120	13	z3	z3	NOUN
ejpam-5659	120	14	=	=	PUNCT
ejpam-5659	120	15	ac	ac	PROPN
ejpam-5659	120	16	x3	x3	NOUN
ejpam-5659	120	17	=	=	SYM
ejpam-5659	121	1	c2	c2	PROPN
ejpam-5659	121	2	+	+	PROPN
ejpam-5659	121	3	b	b	NOUN
ejpam-5659	121	4	y3	y3	NOUN
ejpam-5659	121	5	=	=	SYM
ejpam-5659	121	6	(	(	PUNCT
ejpam-5659	121	7	y	y	NOUN
ejpam-5659	121	8	2	2	NUM
ejpam-5659	121	9	1	1	NUM
ejpam-5659	121	10	+	+	ADP
ejpam-5659	121	11	az3	az3	ADJ
ejpam-5659	121	12	+	+	ADJ
ejpam-5659	121	13	b	b	NOUN
ejpam-5659	121	14	)	)	PUNCT
ejpam-5659	121	15	x3	x3	PROPN
ejpam-5659	122	1	+	+	CCONJ
ejpam-5659	122	2	z3	z3	PROPN
ejpam-5659	122	3	b	b	PROPN
ejpam-5659	122	4	(	(	PUNCT
ejpam-5659	122	5	9	9	NUM
ejpam-5659	122	6	)	)	PUNCT
ejpam-5659	122	7	later	later	ADV
ejpam-5659	122	8	,	,	PUNCT
ejpam-5659	122	9	[	[	X
ejpam-5659	122	10	39	39	NUM
ejpam-5659	122	11	]	]	PUNCT
ejpam-5659	122	12	improved	improve	VERB
ejpam-5659	122	13	the	the	DET
ejpam-5659	122	14	cost	cost	NOUN
ejpam-5659	122	15	of	of	ADP
ejpam-5659	122	16	the	the	DET
ejpam-5659	122	17	point	point	NOUN
ejpam-5659	122	18	doubling	double	VERB
ejpam-5659	122	19	to	to	ADP
ejpam-5659	122	20	4s	4s	NUM
ejpam-5659	122	21	+	+	CCONJ
ejpam-5659	122	22	5	5	NUM
ejpam-5659	122	23	m	m	NOUN
ejpam-5659	122	24	+	+	NOUN
ejpam-5659	122	25	5a	5a	NUM
ejpam-5659	122	26	.	.	PUNCT
ejpam-5659	123	1	the	the	DET
ejpam-5659	123	2	proposed	propose	VERB
ejpam-5659	123	3	projective	projective	ADJ
ejpam-5659	123	4	form	form	NOUN
ejpam-5659	123	5	is	be	AUX
ejpam-5659	123	6	as	as	SCONJ
ejpam-5659	123	7	shown	show	VERB
ejpam-5659	123	8	in	in	ADP
ejpam-5659	123	9	in	in	ADP
ejpam-5659	123	10	the	the	DET
ejpam-5659	123	11	formula	formula	NOUN
ejpam-5659	123	12	provided	provide	VERB
ejpam-5659	123	13	in	in	ADP
ejpam-5659	123	14	equation	equation	NOUN
ejpam-5659	123	15	(	(	PUNCT
ejpam-5659	123	16	10	10	NUM
ejpam-5659	123	17	)	)	PUNCT
ejpam-5659	123	18	below	below	ADP
ejpam-5659	123	19	:	:	PUNCT
ejpam-5659	123	20	2(x1	2(x1	NUM
ejpam-5659	123	21	,	,	PUNCT
ejpam-5659	123	22	y1	y1	NOUN
ejpam-5659	123	23	,	,	PUNCT
ejpam-5659	123	24	z1	z1	NOUN
ejpam-5659	123	25	)	)	PUNCT
ejpam-5659	124	1	=	=	SYM
ejpam-5659	124	2	(	(	PUNCT
ejpam-5659	124	3	x3	x3	ADJ
ejpam-5659	124	4	,	,	PUNCT
ejpam-5659	124	5	y3	y3	NOUN
ejpam-5659	124	6	,	,	PUNCT
ejpam-5659	124	7	z3	z3	PROPN
ejpam-5659	124	8	)	)	PUNCT
ejpam-5659	124	9	where	where	SCONJ
ejpam-5659	124	10	s	s	VERB
ejpam-5659	124	11	=	=	SYM
ejpam-5659	124	12	x2	x2	PROPN
ejpam-5659	124	13	1	1	NUM
ejpam-5659	124	14	u	u	NOUN
ejpam-5659	124	15	=	=	PROPN
ejpam-5659	124	16	s	s	PART
ejpam-5659	124	17	+	+	NUM
ejpam-5659	124	18	y1	y1	NOUN
ejpam-5659	124	19	t	t	NOUN
ejpam-5659	124	20	=	=	PUNCT
ejpam-5659	124	21	x1z1	x1z1	X
ejpam-5659	124	22	z3	z3	PROPN
ejpam-5659	124	23	=	=	SYM
ejpam-5659	124	24	t	t	PROPN
ejpam-5659	124	25	2	2	NUM
ejpam-5659	124	26	t	t	NOUN
ejpam-5659	124	27	=	=	SYM
ejpam-5659	124	28	ut	ut	PROPN
ejpam-5659	124	29	x3	x3	PROPN
ejpam-5659	124	30	=	=	SYM
ejpam-5659	124	31	u2	u2	PROPN
ejpam-5659	124	32	+	+	PROPN
ejpam-5659	124	33	t	t	NOUN
ejpam-5659	124	34	+	+	CCONJ
ejpam-5659	124	35	a2z3	a2z3	ADP
ejpam-5659	124	36	y3	y3	NOUN
ejpam-5659	124	37	=	=	PUNCT
ejpam-5659	124	38	(	(	PUNCT
ejpam-5659	124	39	z3	z3	PROPN
ejpam-5659	124	40	+	+	CCONJ
ejpam-5659	124	41	t	t	PROPN
ejpam-5659	124	42	)	)	PUNCT
ejpam-5659	125	1	x3	x3	PROPN
ejpam-5659	126	1	+	+	CCONJ
ejpam-5659	126	2	s2z3	s2z3	X
ejpam-5659	126	3	(	(	PUNCT
ejpam-5659	126	4	10	10	NUM
ejpam-5659	126	5	)	)	PUNCT
ejpam-5659	126	6	using	use	VERB
ejpam-5659	126	7	these	these	DET
ejpam-5659	126	8	formulas	formula	NOUN
ejpam-5659	126	9	,	,	PUNCT
ejpam-5659	126	10	different	different	ADJ
ejpam-5659	126	11	point	point	NOUN
ejpam-5659	126	12	compositions	composition	NOUN
ejpam-5659	126	13	have	have	AUX
ejpam-5659	126	14	been	be	AUX
ejpam-5659	126	15	implemented	implement	VERB
ejpam-5659	126	16	such	such	ADJ
ejpam-5659	126	17	as	as	ADP
ejpam-5659	126	18	point	point	NOUN
ejpam-5659	126	19	tripling	triple	VERB
ejpam-5659	126	20	3p	3p	NUM
ejpam-5659	126	21	using	use	VERB
ejpam-5659	126	22	the	the	DET
ejpam-5659	126	23	mixed	mixed	ADJ
ejpam-5659	126	24	addition	addition	NOUN
ejpam-5659	126	25	,	,	PUNCT
ejpam-5659	126	26	and	and	CCONJ
ejpam-5659	126	27	using	use	VERB
ejpam-5659	126	28	the	the	DET
ejpam-5659	126	29	projective	projective	ADJ
ejpam-5659	126	30	form	form	NOUN
ejpam-5659	126	31	for	for	ADP
ejpam-5659	126	32	ld	ld	PROPN
ejpam-5659	126	33	coordinate	coordinate	NOUN
ejpam-5659	126	34	over	over	ADP
ejpam-5659	126	35	binary	binary	ADJ
ejpam-5659	126	36	coordinates	coordinate	NOUN
ejpam-5659	126	37	.	.	PUNCT
ejpam-5659	127	1	the	the	DET
ejpam-5659	127	2	best	good	ADJ
ejpam-5659	127	3	cost	cost	NOUN
ejpam-5659	127	4	point	point	NOUN
ejpam-5659	127	5	tripling	tripling	NOUN
ejpam-5659	127	6	uses	use	VERB
ejpam-5659	127	7	the	the	DET
ejpam-5659	127	8	form	form	NOUN
ejpam-5659	127	9	3p	3p	NUM
ejpam-5659	127	10	=	=	NOUN
ejpam-5659	127	11	2p	2p	NOUN
ejpam-5659	128	1	+	+	ADV
ejpam-5659	128	2	p	p	NOUN
ejpam-5659	128	3	proposed	propose	VERB
ejpam-5659	128	4	by	by	ADP
ejpam-5659	128	5	[	[	X
ejpam-5659	128	6	22	22	NUM
ejpam-5659	128	7	]	]	PUNCT
ejpam-5659	128	8	,	,	PUNCT
ejpam-5659	128	9	with	with	ADP
ejpam-5659	128	10	a	a	DET
ejpam-5659	128	11	cost	cost	NOUN
ejpam-5659	128	12	of	of	ADP
ejpam-5659	128	13	7s+12	7s+12	NOUN
ejpam-5659	128	14	m	m	VERB
ejpam-5659	128	15	where	where	SCONJ
ejpam-5659	128	16	the	the	DET
ejpam-5659	128	17	addition	addition	NOUN
ejpam-5659	128	18	were	be	AUX
ejpam-5659	128	19	neglected	neglect	VERB
ejpam-5659	128	20	.	.	PUNCT
ejpam-5659	129	1	a	a	DET
ejpam-5659	129	2	new	new	ADJ
ejpam-5659	129	3	two	two	NUM
ejpam-5659	129	4	quintupling	quintupling	NOUN
ejpam-5659	129	5	points	point	NOUN
ejpam-5659	129	6	5p	5p	NUM
ejpam-5659	129	7	was	be	AUX
ejpam-5659	129	8	also	also	ADV
ejpam-5659	129	9	proposed	propose	VERB
ejpam-5659	129	10	by	by	ADP
ejpam-5659	129	11	[	[	X
ejpam-5659	129	12	23	23	NUM
ejpam-5659	129	13	]	]	PUNCT
ejpam-5659	129	14	using	use	VERB
ejpam-5659	129	15	two	two	NUM
ejpam-5659	129	16	forms	form	NOUN
ejpam-5659	129	17	;	;	PUNCT
ejpam-5659	129	18	5p	5p	NUM
ejpam-5659	129	19	=	=	SYM
ejpam-5659	129	20	3p	3p	NUM
ejpam-5659	129	21	+	+	CCONJ
ejpam-5659	129	22	2p	2p	NOUN
ejpam-5659	129	23	and	and	CCONJ
ejpam-5659	129	24	the	the	DET
ejpam-5659	129	25	form	form	NOUN
ejpam-5659	129	26	5p	5p	NUM
ejpam-5659	129	27	=	=	SYM
ejpam-5659	129	28	2(2p	2(2p	NUM
ejpam-5659	129	29	)	)	PUNCT
ejpam-5659	130	1	+	+	CCONJ
ejpam-5659	130	2	p	p	NOUN
ejpam-5659	130	3	with	with	ADP
ejpam-5659	130	4	cost	cost	NOUN
ejpam-5659	130	5	of	of	ADP
ejpam-5659	130	6	13s	13	NOUN
ejpam-5659	130	7	+	+	CCONJ
ejpam-5659	130	8	23	23	NUM
ejpam-5659	130	9	m	m	NOUN
ejpam-5659	130	10	and	and	CCONJ
ejpam-5659	130	11	12s	12	NOUN
ejpam-5659	130	12	+	+	CCONJ
ejpam-5659	130	13	17	17	NUM
ejpam-5659	130	14	m	m	NOUN
ejpam-5659	130	15	respectively	respectively	ADV
ejpam-5659	130	16	outperforming	outperform	VERB
ejpam-5659	130	17	the	the	DET
ejpam-5659	130	18	former	former	ADJ
ejpam-5659	130	19	with	with	ADP
ejpam-5659	130	20	respect	respect	NOUN
ejpam-5659	130	21	to	to	ADP
ejpam-5659	130	22	the	the	DET
ejpam-5659	130	23	second	second	ADJ
ejpam-5659	130	24	form	form	NOUN
ejpam-5659	130	25	.	.	PUNCT
ejpam-5659	131	1	w.	w.	PROPN
ejpam-5659	131	2	k.	k.	PROPN
ejpam-5659	131	3	abdulraheem	abdulraheem	PROPN
ejpam-5659	131	4	/	/	SYM
ejpam-5659	131	5	eur	eur	PROPN
ejpam-5659	131	6	.	.	PUNCT
ejpam-5659	132	1	j.	j.	PROPN
ejpam-5659	132	2	pure	pure	PROPN
ejpam-5659	132	3	appl	appl	PROPN
ejpam-5659	132	4	.	.	PROPN
ejpam-5659	132	5	math	math	PROPN
ejpam-5659	132	6	,	,	PUNCT
ejpam-5659	132	7	18	18	NUM
ejpam-5659	132	8	(	(	PUNCT
ejpam-5659	132	9	2	2	NUM
ejpam-5659	132	10	)	)	PUNCT
ejpam-5659	132	11	(	(	PUNCT
ejpam-5659	132	12	2025	2025	NUM
ejpam-5659	132	13	)	)	PUNCT
ejpam-5659	132	14	,	,	PUNCT
ejpam-5659	132	15	5659	5659	NUM
ejpam-5659	132	16	8	8	NUM
ejpam-5659	132	17	of	of	ADP
ejpam-5659	132	18	13	13	NUM
ejpam-5659	132	19	4	4	NUM
ejpam-5659	132	20	.	.	PUNCT
ejpam-5659	132	21	proposed	propose	VERB
ejpam-5659	132	22	algorithm	algorithm	NOUN
ejpam-5659	132	23	this	this	DET
ejpam-5659	132	24	paper	paper	NOUN
ejpam-5659	132	25	introduces	introduce	VERB
ejpam-5659	132	26	a	a	DET
ejpam-5659	132	27	new	new	ADJ
ejpam-5659	132	28	formula	formula	NOUN
ejpam-5659	132	29	for	for	ADP
ejpam-5659	132	30	point	point	NOUN
ejpam-5659	132	31	septupling	septuple	VERB
ejpam-5659	132	32	7p	7p	NUM
ejpam-5659	132	33	for	for	ADP
ejpam-5659	132	34	the	the	DET
ejpam-5659	132	35	projective	projective	ADJ
ejpam-5659	132	36	coordinates	coordinate	NOUN
ejpam-5659	132	37	using	use	VERB
ejpam-5659	132	38	affine	affine	NOUN
ejpam-5659	132	39	ld	ld	PROPN
ejpam-5659	132	40	over	over	ADP
ejpam-5659	132	41	short	short	ADJ
ejpam-5659	132	42	weiestrass	weiestrass	NOUN
ejpam-5659	132	43	curve	curve	NOUN
ejpam-5659	132	44	.	.	PUNCT
ejpam-5659	133	1	to	to	PART
ejpam-5659	133	2	achieve	achieve	VERB
ejpam-5659	133	3	a	a	DET
ejpam-5659	133	4	higher	high	ADJ
ejpam-5659	133	5	performance	performance	NOUN
ejpam-5659	133	6	,	,	PUNCT
ejpam-5659	133	7	the	the	DET
ejpam-5659	133	8	mixed	mixed	ADJ
ejpam-5659	133	9	formula	formula	NOUN
ejpam-5659	133	10	is	be	AUX
ejpam-5659	133	11	used	use	VERB
ejpam-5659	133	12	for	for	ADP
ejpam-5659	133	13	addition	addition	NOUN
ejpam-5659	133	14	in	in	ADP
ejpam-5659	133	15	the	the	DET
ejpam-5659	133	16	affine	affine	NOUN
ejpam-5659	133	17	.	.	PUNCT
ejpam-5659	134	1	the	the	DET
ejpam-5659	134	2	proposed	propose	VERB
ejpam-5659	134	3	point	point	NOUN
ejpam-5659	134	4	septupling	septuple	VERB
ejpam-5659	134	5	used	use	VERB
ejpam-5659	134	6	the	the	DET
ejpam-5659	134	7	form	form	NOUN
ejpam-5659	134	8	7p	7p	NOUN
ejpam-5659	134	9	=	=	SYM
ejpam-5659	134	10	2(3p	2(3p	NUM
ejpam-5659	134	11	)	)	PUNCT
ejpam-5659	135	1	+	+	CCONJ
ejpam-5659	135	2	p	p	NOUN
ejpam-5659	135	3	.with	.with	ADP
ejpam-5659	135	4	details	detail	NOUN
ejpam-5659	135	5	shown	show	VERB
ejpam-5659	135	6	in	in	ADP
ejpam-5659	135	7	algorithm	algorithm	NOUN
ejpam-5659	135	8	1	1	NUM
ejpam-5659	135	9	.	.	PUNCT
ejpam-5659	135	10	algorithm	algorithm	NOUN
ejpam-5659	135	11	1	1	NUM
ejpam-5659	135	12	:	:	PUNCT
ejpam-5659	135	13	a	a	DET
ejpam-5659	135	14	new	new	ADJ
ejpam-5659	135	15	septupling	septupling	NOUN
ejpam-5659	135	16	point	point	NOUN
ejpam-5659	135	17	of	of	ADP
ejpam-5659	135	18	the	the	DET
ejpam-5659	135	19	form	form	NOUN
ejpam-5659	135	20	7p	7p	NOUN
ejpam-5659	135	21	=	=	SYM
ejpam-5659	135	22	2(3p	2(3p	NUM
ejpam-5659	135	23	)	)	PUNCT
ejpam-5659	136	1	+	+	SCONJ
ejpam-5659	136	2	p	p	NOUN
ejpam-5659	136	3	using	use	VERB
ejpam-5659	136	4	ld	ld	PROPN
ejpam-5659	136	5	coordinate	coordinate	NOUN
ejpam-5659	136	6	in	in	ADP
ejpam-5659	136	7	affine	affine	NOUN
ejpam-5659	136	8	and	and	CCONJ
ejpam-5659	136	9	mixed	mixed	ADJ
ejpam-5659	136	10	addition	addition	NOUN
ejpam-5659	136	11	over	over	ADP
ejpam-5659	136	12	binary	binary	ADJ
ejpam-5659	136	13	curve	curve	NOUN
ejpam-5659	136	14	.	.	PUNCT
ejpam-5659	137	1	let	let	VERB
ejpam-5659	137	2	the	the	DET
ejpam-5659	137	3	point	point	NOUN
ejpam-5659	137	4	p	p	X
ejpam-5659	137	5	=	=	X
ejpam-5659	137	6	(	(	PUNCT
ejpam-5659	137	7	x1	x1	PROPN
ejpam-5659	137	8	,	,	PUNCT
ejpam-5659	137	9	y1	y1	PROPN
ejpam-5659	137	10	,	,	PUNCT
ejpam-5659	137	11	z1	z1	PROPN
ejpam-5659	137	12	)	)	PUNCT
ejpam-5659	137	13	be	be	VERB
ejpam-5659	137	14	a	a	DET
ejpam-5659	137	15	point	point	NOUN
ejpam-5659	137	16	on	on	ADP
ejpam-5659	137	17	the	the	DET
ejpam-5659	137	18	weiestrass	weiestrass	NOUN
ejpam-5659	137	19	curve	curve	NOUN
ejpam-5659	137	20	as	as	ADP
ejpam-5659	137	21	y	y	PROPN
ejpam-5659	137	22	2	2	NUM
ejpam-5659	138	1	+	+	CCONJ
ejpam-5659	138	2	x	x	SYM
ejpam-5659	138	3	y	y	NOUN
ejpam-5659	138	4	=	=	PUNCT
ejpam-5659	138	5	x3	x3	PROPN
ejpam-5659	138	6	+	+	CCONJ
ejpam-5659	138	7	ax2	ax2	NOUN
ejpam-5659	138	8	+	+	CCONJ
ejpam-5659	138	9	b	b	NOUN
ejpam-5659	138	10	using	use	VERB
ejpam-5659	138	11	ld	ld	NOUN
ejpam-5659	138	12	coordinate	coordinate	NOUN
ejpam-5659	138	13	,	,	PUNCT
ejpam-5659	138	14	let	let	VERB
ejpam-5659	138	15	the	the	DET
ejpam-5659	138	16	points	point	NOUN
ejpam-5659	138	17	2p	2p	NUM
ejpam-5659	138	18	,	,	PUNCT
ejpam-5659	138	19	3p	3p	NUM
ejpam-5659	138	20	,	,	PUNCT
ejpam-5659	138	21	and	and	CCONJ
ejpam-5659	138	22	6p	6p	NUM
ejpam-5659	138	23	is	be	AUX
ejpam-5659	138	24	(	(	PUNCT
ejpam-5659	138	25	x2	x2	PROPN
ejpam-5659	138	26	,	,	PUNCT
ejpam-5659	138	27	y2	y2	PROPN
ejpam-5659	138	28	,	,	PUNCT
ejpam-5659	138	29	z2	z2	PROPN
ejpam-5659	138	30	)	)	PUNCT
ejpam-5659	138	31	,	,	PUNCT
ejpam-5659	138	32	(	(	PUNCT
ejpam-5659	138	33	x3	x3	ADJ
ejpam-5659	138	34	,	,	PUNCT
ejpam-5659	138	35	y3	y3	NOUN
ejpam-5659	138	36	,	,	PUNCT
ejpam-5659	138	37	z3	z3	PROPN
ejpam-5659	138	38	)	)	PUNCT
ejpam-5659	138	39	and	and	CCONJ
ejpam-5659	138	40	(	(	PUNCT
ejpam-5659	138	41	x6	x6	PROPN
ejpam-5659	138	42	,	,	PUNCT
ejpam-5659	138	43	y6	y6	ADJ
ejpam-5659	138	44	,	,	PUNCT
ejpam-5659	138	45	z6	z6	PROPN
ejpam-5659	138	46	)	)	PUNCT
ejpam-5659	138	47	respectively	respectively	ADV
ejpam-5659	138	48	.	.	PUNCT
ejpam-5659	139	1	then	then	ADV
ejpam-5659	139	2	the	the	DET
ejpam-5659	139	3	7p	7p	NOUN
ejpam-5659	139	4	formula	formula	NOUN
ejpam-5659	139	5	is	be	AUX
ejpam-5659	139	6	formulated	formulate	VERB
ejpam-5659	139	7	as	as	SCONJ
ejpam-5659	139	8	shown	show	VERB
ejpam-5659	139	9	below	below	ADV
ejpam-5659	139	10	:	:	PUNCT
ejpam-5659	139	11	first	first	ADV
ejpam-5659	139	12	,	,	PUNCT
ejpam-5659	139	13	the	the	DET
ejpam-5659	139	14	doubling	double	VERB
ejpam-5659	139	15	point	point	NOUN
ejpam-5659	139	16	2p	2p	NUM
ejpam-5659	139	17	is	be	AUX
ejpam-5659	139	18	found	find	VERB
ejpam-5659	139	19	using	use	VERB
ejpam-5659	139	20	the	the	DET
ejpam-5659	139	21	formula	formula	NOUN
ejpam-5659	139	22	in	in	ADP
ejpam-5659	139	23	(	(	PUNCT
ejpam-5659	139	24	10	10	NUM
ejpam-5659	139	25	)	)	PUNCT
ejpam-5659	139	26	as	as	SCONJ
ejpam-5659	139	27	shown	show	VERB
ejpam-5659	139	28	in	in	ADP
ejpam-5659	139	29	(	(	PUNCT
ejpam-5659	139	30	11	11	NUM
ejpam-5659	139	31	)	)	PUNCT
ejpam-5659	139	32	below	below	ADP
ejpam-5659	139	33	:	:	PUNCT
ejpam-5659	140	1	2(x1	2(x1	NUM
ejpam-5659	140	2	,	,	PUNCT
ejpam-5659	140	3	y1	y1	NOUN
ejpam-5659	140	4	,	,	PUNCT
ejpam-5659	140	5	z1	z1	NOUN
ejpam-5659	140	6	)	)	PUNCT
ejpam-5659	140	7	=	=	SYM
ejpam-5659	140	8	(	(	PUNCT
ejpam-5659	140	9	x2	x2	PROPN
ejpam-5659	140	10	,	,	PUNCT
ejpam-5659	140	11	y2	y2	PROPN
ejpam-5659	140	12	,	,	PUNCT
ejpam-5659	140	13	z2	z2	PROPN
ejpam-5659	140	14	)	)	PUNCT
ejpam-5659	140	15	a2	a2	PROPN
ejpam-5659	140	16	←−	←−	INTJ
ejpam-5659	140	17	x2	x2	PROPN
ejpam-5659	140	18	1	1	NUM
ejpam-5659	140	19	b2	b2	NOUN
ejpam-5659	140	20	←−	←−	PROPN
ejpam-5659	140	21	a2	a2	PROPN
ejpam-5659	140	22	+	+	CCONJ
ejpam-5659	140	23	y1	y1	PROPN
ejpam-5659	140	24	c2	c2	PROPN
ejpam-5659	140	25	←−	←−	NUM
ejpam-5659	140	26	x1	x1	PROPN
ejpam-5659	140	27	z1	z1	PROPN
ejpam-5659	140	28	d2	d2	PROPN
ejpam-5659	140	29	←−	←−	PUNCT
ejpam-5659	140	30	b2	b2	NOUN
ejpam-5659	140	31	c2	c2	PROPN
ejpam-5659	140	32	z2	z2	PROPN
ejpam-5659	140	33	←−	←−	PROPN
ejpam-5659	140	34	c2	c2	PROPN
ejpam-5659	140	35	2	2	NUM
ejpam-5659	140	36	x2	x2	PROPN
ejpam-5659	140	37	←−	←−	PROPN
ejpam-5659	140	38	b2	b2	NOUN
ejpam-5659	140	39	+	+	NOUN
ejpam-5659	140	40	d2	d2	NOUN
ejpam-5659	140	41	+	+	CCONJ
ejpam-5659	140	42	a	a	DET
ejpam-5659	140	43	z2	z2	NOUN
ejpam-5659	140	44	y2	y2	PROPN
ejpam-5659	140	45	←−	←−	PROPN
ejpam-5659	140	46	(	(	PUNCT
ejpam-5659	140	47	z2	z2	PROPN
ejpam-5659	140	48	+	+	NOUN
ejpam-5659	140	49	d2	d2	PROPN
ejpam-5659	140	50	)	)	PUNCT
ejpam-5659	140	51	x2	x2	PROPN
ejpam-5659	141	1	+	+	PROPN
ejpam-5659	141	2	a2	a2	PROPN
ejpam-5659	141	3	2	2	NUM
ejpam-5659	141	4	z2	z2	PROPN
ejpam-5659	141	5	cost	cost	NOUN
ejpam-5659	141	6	of	of	ADP
ejpam-5659	141	7	doubling	double	VERB
ejpam-5659	141	8	point	point	NOUN
ejpam-5659	141	9	is	be	AUX
ejpam-5659	141	10	:	:	PUNCT
ejpam-5659	141	11	4s	4s	NUM
ejpam-5659	141	12	+	+	NUM
ejpam-5659	141	13	5	5	NUM
ejpam-5659	141	14	m	m	NOUN
ejpam-5659	141	15	(	(	PUNCT
ejpam-5659	141	16	11	11	NUM
ejpam-5659	141	17	)	)	PUNCT
ejpam-5659	141	18	then	then	ADV
ejpam-5659	141	19	,	,	PUNCT
ejpam-5659	141	20	finding	find	VERB
ejpam-5659	141	21	the	the	DET
ejpam-5659	141	22	tripling	triple	VERB
ejpam-5659	141	23	point	point	NOUN
ejpam-5659	141	24	3p	3p	NUM
ejpam-5659	141	25	using	use	VERB
ejpam-5659	141	26	(	(	PUNCT
ejpam-5659	141	27	8)	8)	NUM
ejpam-5659	141	28	yields	yield	VERB
ejpam-5659	141	29	the	the	DET
ejpam-5659	141	30	formula	formula	NOUN
ejpam-5659	141	31	in	in	ADP
ejpam-5659	141	32	(	(	PUNCT
ejpam-5659	141	33	12	12	NUM
ejpam-5659	141	34	)	)	PUNCT
ejpam-5659	141	35	below	below	ADV
ejpam-5659	141	36	:	:	PUNCT
ejpam-5659	141	37	(	(	PUNCT
ejpam-5659	141	38	x3	x3	ADJ
ejpam-5659	141	39	,	,	PUNCT
ejpam-5659	141	40	y3	y3	NOUN
ejpam-5659	141	41	,	,	PUNCT
ejpam-5659	141	42	z3	z3	PROPN
ejpam-5659	141	43	)	)	PUNCT
ejpam-5659	141	44	=	=	PUNCT
ejpam-5659	141	45	(	(	PUNCT
ejpam-5659	141	46	x1	x1	PROPN
ejpam-5659	141	47	,	,	PUNCT
ejpam-5659	141	48	y1	y1	PROPN
ejpam-5659	141	49	,	,	PUNCT
ejpam-5659	141	50	z1	z1	NOUN
ejpam-5659	141	51	)	)	PUNCT
ejpam-5659	142	1	+	+	CCONJ
ejpam-5659	142	2	(	(	PUNCT
ejpam-5659	142	3	x2	x2	PROPN
ejpam-5659	142	4	,	,	PUNCT
ejpam-5659	142	5	y2	y2	PROPN
ejpam-5659	142	6	,	,	PUNCT
ejpam-5659	142	7	z2	z2	PROPN
ejpam-5659	142	8	)	)	PUNCT
ejpam-5659	142	9	such	such	ADJ
ejpam-5659	142	10	that	that	DET
ejpam-5659	142	11	z1	z1	PROPN
ejpam-5659	142	12	=	=	SYM
ejpam-5659	142	13	1	1	NUM
ejpam-5659	142	14	a3	a3	NOUN
ejpam-5659	142	15	←−	←−	PROPN
ejpam-5659	142	16	y2	y2	NOUN
ejpam-5659	142	17	+	+	CCONJ
ejpam-5659	142	18	y1	y1	PROPN
ejpam-5659	142	19	z2	z2	PROPN
ejpam-5659	142	20	2	2	NUM
ejpam-5659	142	21	b3	b3	PROPN
ejpam-5659	142	22	←−	←−	NUM
ejpam-5659	142	23	x2	x2	PROPN
ejpam-5659	143	1	+	+	PROPN
ejpam-5659	143	2	x1	x1	PROPN
ejpam-5659	143	3	z2	z2	PROPN
ejpam-5659	143	4	c3	c3	PROPN
ejpam-5659	143	5	←−	←−	PROPN
ejpam-5659	143	6	b3	b3	PROPN
ejpam-5659	143	7	z2	z2	PROPN
ejpam-5659	143	8	z3	z3	PROPN
ejpam-5659	143	9	←−	←−	PROPN
ejpam-5659	143	10	c2	c2	PROPN
ejpam-5659	143	11	3	3	NUM
ejpam-5659	143	12	d3	d3	PROPN
ejpam-5659	143	13	←−	←−	PROPN
ejpam-5659	143	14	x1	x1	PROPN
ejpam-5659	143	15	z3	z3	PROPN
ejpam-5659	143	16	x3	x3	PROPN
ejpam-5659	143	17	←−	←−	PROPN
ejpam-5659	143	18	a2	a2	PROPN
ejpam-5659	143	19	3	3	NUM
ejpam-5659	143	20	+	+	CCONJ
ejpam-5659	143	21	c3(a3	c3(a3	NOUN
ejpam-5659	143	22	+	+	NOUN
ejpam-5659	143	23	b2	b2	NOUN
ejpam-5659	143	24	3	3	NUM
ejpam-5659	143	25	+	+	CCONJ
ejpam-5659	143	26	a	a	DET
ejpam-5659	143	27	c3	c3	NOUN
ejpam-5659	143	28	)	)	PUNCT
ejpam-5659	143	29	y3	y3	PROPN
ejpam-5659	143	30	←−	←−	PROPN
ejpam-5659	143	31	(	(	PUNCT
ejpam-5659	143	32	d3	d3	PROPN
ejpam-5659	143	33	+	+	PROPN
ejpam-5659	143	34	x3)(a3	x3)(a3	PROPN
ejpam-5659	143	35	c3	c3	PROPN
ejpam-5659	143	36	+	+	CCONJ
ejpam-5659	143	37	z3	z3	PROPN
ejpam-5659	143	38	)	)	PUNCT
ejpam-5659	144	1	+	+	CCONJ
ejpam-5659	144	2	(	(	PUNCT
ejpam-5659	144	3	y1	y1	INTJ
ejpam-5659	144	4	+	+	PROPN
ejpam-5659	144	5	x1	x1	ADJ
ejpam-5659	144	6	)	)	PUNCT
ejpam-5659	144	7	z	z	NOUN
ejpam-5659	144	8	2	2	NUM
ejpam-5659	144	9	3	3	NUM
ejpam-5659	144	10	cost	cost	NOUN
ejpam-5659	144	11	of	of	ADP
ejpam-5659	144	12	doubling	double	VERB
ejpam-5659	144	13	point	point	NOUN
ejpam-5659	144	14	is	be	AUX
ejpam-5659	144	15	:	:	PUNCT
ejpam-5659	144	16	5s	5s	NUM
ejpam-5659	145	1	+	+	NOUN
ejpam-5659	145	2	9	9	NUM
ejpam-5659	145	3	m	m	NOUN
ejpam-5659	145	4	(	(	PUNCT
ejpam-5659	145	5	12	12	NUM
ejpam-5659	145	6	)	)	PUNCT
ejpam-5659	145	7	w.	w.	PROPN
ejpam-5659	145	8	k.	k.	PROPN
ejpam-5659	145	9	abdulraheem	abdulraheem	PROPN
ejpam-5659	145	10	/	/	SYM
ejpam-5659	145	11	eur	eur	PROPN
ejpam-5659	145	12	.	.	PUNCT
ejpam-5659	146	1	j.	j.	PROPN
ejpam-5659	146	2	pure	pure	PROPN
ejpam-5659	146	3	appl	appl	PROPN
ejpam-5659	146	4	.	.	PROPN
ejpam-5659	146	5	math	math	PROPN
ejpam-5659	146	6	,	,	PUNCT
ejpam-5659	146	7	18	18	NUM
ejpam-5659	146	8	(	(	PUNCT
ejpam-5659	146	9	2	2	NUM
ejpam-5659	146	10	)	)	PUNCT
ejpam-5659	146	11	(	(	PUNCT
ejpam-5659	146	12	2025	2025	NUM
ejpam-5659	146	13	)	)	PUNCT
ejpam-5659	146	14	,	,	PUNCT
ejpam-5659	146	15	5659	5659	NUM
ejpam-5659	146	16	9	9	NUM
ejpam-5659	146	17	of	of	ADP
ejpam-5659	146	18	13	13	NUM
ejpam-5659	146	19	both	both	CCONJ
ejpam-5659	146	20	the	the	DET
ejpam-5659	146	21	formulas	formula	NOUN
ejpam-5659	146	22	in	in	ADP
ejpam-5659	146	23	(	(	PUNCT
ejpam-5659	146	24	11	11	NUM
ejpam-5659	146	25	)	)	PUNCT
ejpam-5659	146	26	and	and	CCONJ
ejpam-5659	146	27	(	(	PUNCT
ejpam-5659	146	28	12	12	NUM
ejpam-5659	146	29	)	)	PUNCT
ejpam-5659	146	30	can	can	AUX
ejpam-5659	146	31	be	be	AUX
ejpam-5659	146	32	used	use	VERB
ejpam-5659	146	33	to	to	PART
ejpam-5659	146	34	find	find	VERB
ejpam-5659	146	35	the	the	DET
ejpam-5659	146	36	sixtupling	sixtupling	NOUN
ejpam-5659	146	37	point	point	NOUN
ejpam-5659	146	38	6p	6p	NUM
ejpam-5659	146	39	as	as	SCONJ
ejpam-5659	146	40	shown	show	VERB
ejpam-5659	146	41	in	in	ADP
ejpam-5659	146	42	(	(	PUNCT
ejpam-5659	146	43	13	13	NUM
ejpam-5659	146	44	)	)	PUNCT
ejpam-5659	146	45	below	below	ADP
ejpam-5659	146	46	:	:	PUNCT
ejpam-5659	146	47	6p	6p	NUM
ejpam-5659	146	48	=	=	SYM
ejpam-5659	146	49	2(3p	2(3p	PROPN
ejpam-5659	146	50	)	)	PUNCT
ejpam-5659	146	51	=	=	SYM
ejpam-5659	146	52	(	(	PUNCT
ejpam-5659	146	53	x6	x6	PROPN
ejpam-5659	146	54	,	,	PUNCT
ejpam-5659	146	55	y6	y6	ADJ
ejpam-5659	146	56	,	,	PUNCT
ejpam-5659	146	57	z6	z6	PROPN
ejpam-5659	146	58	)	)	PUNCT
ejpam-5659	146	59	=	=	SYM
ejpam-5659	146	60	2	2	NUM
ejpam-5659	146	61	∗	∗	NOUN
ejpam-5659	146	62	(	(	PUNCT
ejpam-5659	146	63	x3	x3	ADJ
ejpam-5659	146	64	,	,	PUNCT
ejpam-5659	146	65	y3	y3	NOUN
ejpam-5659	146	66	,	,	PUNCT
ejpam-5659	146	67	z3	z3	PROPN
ejpam-5659	146	68	)	)	PUNCT
ejpam-5659	146	69	a6	a6	PROPN
ejpam-5659	146	70	←−	←−	PROPN
ejpam-5659	146	71	x2	x2	PROPN
ejpam-5659	146	72	3	3	NUM
ejpam-5659	146	73	b6	b6	NOUN
ejpam-5659	146	74	←−	←−	NOUN
ejpam-5659	146	75	a6	a6	NOUN
ejpam-5659	146	76	+	+	CCONJ
ejpam-5659	146	77	y3	y3	PROPN
ejpam-5659	146	78	c6	c6	PROPN
ejpam-5659	146	79	←−	←−	VERB
ejpam-5659	146	80	x3	x3	PROPN
ejpam-5659	146	81	z3	z3	PROPN
ejpam-5659	146	82	d6	d6	PROPN
ejpam-5659	146	83	←−	←−	PROPN
ejpam-5659	146	84	b6	b6	NOUN
ejpam-5659	146	85	c6	c6	PROPN
ejpam-5659	146	86	z6	z6	PROPN
ejpam-5659	147	1	←−	←−	PROPN
ejpam-5659	147	2	c2	c2	PROPN
ejpam-5659	147	3	6	6	NUM
ejpam-5659	147	4	x6	x6	PROPN
ejpam-5659	147	5	←−	←−	PROPN
ejpam-5659	147	6	b2	b2	NOUN
ejpam-5659	147	7	6	6	NUM
ejpam-5659	147	8	+	+	NOUN
ejpam-5659	147	9	d6	d6	NOUN
ejpam-5659	147	10	+	+	CCONJ
ejpam-5659	147	11	a	a	DET
ejpam-5659	147	12	z6	z6	NOUN
ejpam-5659	147	13	y6	y6	PROPN
ejpam-5659	147	14	←−	←−	PROPN
ejpam-5659	147	15	(	(	PUNCT
ejpam-5659	147	16	z6	z6	PROPN
ejpam-5659	147	17	+	+	NOUN
ejpam-5659	147	18	d6	d6	NOUN
ejpam-5659	147	19	)	)	PUNCT
ejpam-5659	147	20	x6	x6	PROPN
ejpam-5659	148	1	+	+	SYM
ejpam-5659	148	2	a2	a2	PROPN
ejpam-5659	148	3	6	6	NUM
ejpam-5659	148	4	z6	z6	PROPN
ejpam-5659	148	5	cost	cost	NOUN
ejpam-5659	148	6	of	of	ADP
ejpam-5659	148	7	doubling	double	VERB
ejpam-5659	148	8	point	point	NOUN
ejpam-5659	148	9	is	be	AUX
ejpam-5659	148	10	:	:	PUNCT
ejpam-5659	148	11	4s	4s	NUM
ejpam-5659	148	12	+	+	NUM
ejpam-5659	148	13	5	5	NUM
ejpam-5659	148	14	m	m	NOUN
ejpam-5659	148	15	(	(	PUNCT
ejpam-5659	148	16	13	13	NUM
ejpam-5659	148	17	)	)	PUNCT
ejpam-5659	148	18	finally	finally	ADV
ejpam-5659	148	19	,	,	PUNCT
ejpam-5659	148	20	the	the	DET
ejpam-5659	148	21	septupling	septupling	NOUN
ejpam-5659	148	22	point	point	NOUN
ejpam-5659	148	23	7p	7p	NUM
ejpam-5659	148	24	is	be	AUX
ejpam-5659	148	25	found	find	VERB
ejpam-5659	148	26	using	use	VERB
ejpam-5659	148	27	the	the	DET
ejpam-5659	148	28	form	form	NOUN
ejpam-5659	148	29	7p	7p	NOUN
ejpam-5659	148	30	=	=	SYM
ejpam-5659	148	31	6p	6p	NUM
ejpam-5659	148	32	+	+	CCONJ
ejpam-5659	148	33	p	p	NOUN
ejpam-5659	148	34	using	use	VERB
ejpam-5659	148	35	the	the	DET
ejpam-5659	148	36	formulas	formula	NOUN
ejpam-5659	148	37	in	in	ADP
ejpam-5659	148	38	(	(	PUNCT
ejpam-5659	148	39	10	10	NUM
ejpam-5659	148	40	)	)	PUNCT
ejpam-5659	148	41	and	and	CCONJ
ejpam-5659	148	42	(	(	PUNCT
ejpam-5659	148	43	13	13	NUM
ejpam-5659	148	44	)	)	PUNCT
ejpam-5659	148	45	as	as	SCONJ
ejpam-5659	148	46	shown	show	VERB
ejpam-5659	148	47	in	in	ADP
ejpam-5659	148	48	(	(	PUNCT
ejpam-5659	148	49	14	14	NUM
ejpam-5659	148	50	)	)	PUNCT
ejpam-5659	148	51	below	below	ADV
ejpam-5659	148	52	:	:	PUNCT
ejpam-5659	148	53	(	(	PUNCT
ejpam-5659	148	54	x7	x7	NOUN
ejpam-5659	148	55	,	,	PUNCT
ejpam-5659	148	56	y7	y7	PROPN
ejpam-5659	148	57	,	,	PUNCT
ejpam-5659	148	58	z7	z7	PROPN
ejpam-5659	148	59	)	)	PUNCT
ejpam-5659	148	60	=	=	PUNCT
ejpam-5659	148	61	(	(	PUNCT
ejpam-5659	148	62	x1	x1	PROPN
ejpam-5659	148	63	,	,	PUNCT
ejpam-5659	148	64	y1	y1	PROPN
ejpam-5659	148	65	,	,	PUNCT
ejpam-5659	148	66	z1	z1	NOUN
ejpam-5659	148	67	)	)	PUNCT
ejpam-5659	149	1	+	+	CCONJ
ejpam-5659	149	2	(	(	PUNCT
ejpam-5659	149	3	x6	x6	PROPN
ejpam-5659	149	4	,	,	PUNCT
ejpam-5659	149	5	y6	y6	ADJ
ejpam-5659	149	6	,	,	PUNCT
ejpam-5659	149	7	z6	z6	PROPN
ejpam-5659	149	8	)	)	PUNCT
ejpam-5659	149	9	such	such	ADJ
ejpam-5659	149	10	that	that	DET
ejpam-5659	149	11	z1	z1	NOUN
ejpam-5659	149	12	=	=	SYM
ejpam-5659	149	13	1	1	NUM
ejpam-5659	149	14	a7	a7	PROPN
ejpam-5659	149	15	←−	←−	NUM
ejpam-5659	149	16	y6	y6	NOUN
ejpam-5659	149	17	+	+	CCONJ
ejpam-5659	149	18	y1	y1	PROPN
ejpam-5659	149	19	z2	z2	PROPN
ejpam-5659	149	20	6	6	NUM
ejpam-5659	149	21	b7	b7	PROPN
ejpam-5659	149	22	←−	←−	PROPN
ejpam-5659	149	23	x6	x6	PROPN
ejpam-5659	149	24	+	+	PROPN
ejpam-5659	149	25	x1	x1	PROPN
ejpam-5659	149	26	z6	z6	PROPN
ejpam-5659	149	27	c7	c7	PROPN
ejpam-5659	149	28	←−	←−	PROPN
ejpam-5659	149	29	b7	b7	PROPN
ejpam-5659	149	30	z6	z6	PROPN
ejpam-5659	149	31	z7	z7	PROPN
ejpam-5659	149	32	←−	←−	PROPN
ejpam-5659	149	33	c2	c2	PROPN
ejpam-5659	149	34	7	7	NUM
ejpam-5659	149	35	d7	d7	PROPN
ejpam-5659	149	36	←−	←−	PROPN
ejpam-5659	149	37	x1	x1	PROPN
ejpam-5659	149	38	z7	z7	PROPN
ejpam-5659	149	39	x7	x7	PROPN
ejpam-5659	149	40	←−	←−	PROPN
ejpam-5659	149	41	a2	a2	PROPN
ejpam-5659	149	42	7	7	NUM
ejpam-5659	149	43	+	+	CCONJ
ejpam-5659	149	44	c7(a7	c7(a7	NOUN
ejpam-5659	149	45	+	+	NOUN
ejpam-5659	149	46	b2	b2	NOUN
ejpam-5659	149	47	7	7	NUM
ejpam-5659	149	48	+	+	CCONJ
ejpam-5659	149	49	c7	c7	PROPN
ejpam-5659	149	50	a	a	PRON
ejpam-5659	149	51	)	)	PUNCT
ejpam-5659	149	52	y7	y7	PROPN
ejpam-5659	149	53	←−	←−	PROPN
ejpam-5659	149	54	(	(	PUNCT
ejpam-5659	149	55	d7	d7	PROPN
ejpam-5659	149	56	+	+	PROPN
ejpam-5659	149	57	x7)(a7	x7)(a7	PROPN
ejpam-5659	149	58	c7	c7	PROPN
ejpam-5659	149	59	+	+	PROPN
ejpam-5659	149	60	z7	z7	PROPN
ejpam-5659	149	61	)	)	PUNCT
ejpam-5659	150	1	+	+	CCONJ
ejpam-5659	150	2	(	(	PUNCT
ejpam-5659	150	3	y1	y1	INTJ
ejpam-5659	150	4	+	+	PROPN
ejpam-5659	150	5	x1	x1	ADJ
ejpam-5659	150	6	)	)	PUNCT
ejpam-5659	150	7	z	z	NOUN
ejpam-5659	150	8	2	2	NUM
ejpam-5659	150	9	7	7	NUM
ejpam-5659	150	10	cost	cost	NOUN
ejpam-5659	150	11	of	of	ADP
ejpam-5659	150	12	doubling	double	VERB
ejpam-5659	150	13	point	point	NOUN
ejpam-5659	150	14	is	be	AUX
ejpam-5659	150	15	:	:	PUNCT
ejpam-5659	150	16	5s	5s	NUM
ejpam-5659	151	1	+	+	NOUN
ejpam-5659	151	2	9	9	NUM
ejpam-5659	151	3	m	m	NOUN
ejpam-5659	151	4	(	(	PUNCT
ejpam-5659	151	5	14	14	NUM
ejpam-5659	151	6	)	)	PUNCT
ejpam-5659	151	7	the	the	DET
ejpam-5659	151	8	cost	cost	NOUN
ejpam-5659	151	9	of	of	ADP
ejpam-5659	151	10	the	the	DET
ejpam-5659	151	11	point	point	NOUN
ejpam-5659	151	12	is	be	AUX
ejpam-5659	151	13	obtained	obtain	VERB
ejpam-5659	151	14	by	by	ADP
ejpam-5659	151	15	adding	add	VERB
ejpam-5659	151	16	the	the	DET
ejpam-5659	151	17	number	number	NOUN
ejpam-5659	151	18	of	of	ADP
ejpam-5659	151	19	squaring	square	VERB
ejpam-5659	151	20	to	to	ADP
ejpam-5659	151	21	number	number	NOUN
ejpam-5659	151	22	of	of	ADP
ejpam-5659	151	23	multiplications	multiplication	NOUN
ejpam-5659	151	24	.	.	PUNCT
ejpam-5659	152	1	so	so	ADV
ejpam-5659	152	2	,	,	PUNCT
ejpam-5659	152	3	the	the	DET
ejpam-5659	152	4	septupling	septupling	NOUN
ejpam-5659	152	5	point	point	NOUN
ejpam-5659	152	6	cost	cost	NOUN
ejpam-5659	152	7	is	be	AUX
ejpam-5659	152	8	the	the	DET
ejpam-5659	152	9	total	total	NOUN
ejpam-5659	152	10	of	of	ADP
ejpam-5659	152	11	cost	cost	NOUN
ejpam-5659	152	12	of	of	ADP
ejpam-5659	152	13	formulas	formula	NOUN
ejpam-5659	152	14	(	(	PUNCT
ejpam-5659	152	15	11	11	NUM
ejpam-5659	152	16	)	)	PUNCT
ejpam-5659	152	17	,	,	PUNCT
ejpam-5659	152	18	(	(	PUNCT
ejpam-5659	152	19	12	12	NUM
ejpam-5659	152	20	)	)	PUNCT
ejpam-5659	152	21	,	,	PUNCT
ejpam-5659	152	22	(	(	PUNCT
ejpam-5659	152	23	13	13	NUM
ejpam-5659	152	24	)	)	PUNCT
ejpam-5659	152	25	,	,	PUNCT
ejpam-5659	152	26	and	and	CCONJ
ejpam-5659	152	27	(	(	PUNCT
ejpam-5659	152	28	14	14	NUM
ejpam-5659	152	29	)	)	PUNCT
ejpam-5659	152	30	;	;	PUNCT
ejpam-5659	152	31	which	which	PRON
ejpam-5659	152	32	19	19	NUM
ejpam-5659	152	33	s	s	NOUN
ejpam-5659	152	34	+	+	NUM
ejpam-5659	152	35	28	28	NUM
ejpam-5659	152	36	m	m	NOUN
ejpam-5659	152	37	,	,	PUNCT
ejpam-5659	152	38	while	while	SCONJ
ejpam-5659	152	39	the	the	DET
ejpam-5659	152	40	sixtupling	sixtupling	NOUN
ejpam-5659	152	41	point	point	NOUN
ejpam-5659	152	42	’s	’s	PART
ejpam-5659	152	43	cost	cost	NOUN
ejpam-5659	152	44	is	be	AUX
ejpam-5659	152	45	the	the	DET
ejpam-5659	152	46	total	total	ADJ
ejpam-5659	152	47	cost	cost	NOUN
ejpam-5659	152	48	of	of	ADP
ejpam-5659	152	49	(	(	PUNCT
ejpam-5659	152	50	11	11	NUM
ejpam-5659	152	51	)	)	PUNCT
ejpam-5659	152	52	,	,	PUNCT
ejpam-5659	152	53	(	(	PUNCT
ejpam-5659	152	54	12	12	NUM
ejpam-5659	152	55	)	)	PUNCT
ejpam-5659	152	56	and	and	CCONJ
ejpam-5659	152	57	(	(	PUNCT
ejpam-5659	152	58	13	13	NUM
ejpam-5659	152	59	)	)	PUNCT
ejpam-5659	152	60	;	;	PUNCT
ejpam-5659	152	61	which	which	PRON
ejpam-5659	152	62	14	14	NUM
ejpam-5659	152	63	s	s	NOUN
ejpam-5659	152	64	+	+	NUM
ejpam-5659	152	65	19	19	NUM
ejpam-5659	152	66	m	m	NOUN
ejpam-5659	152	67	.	.	PUNCT
ejpam-5659	153	1	to	to	PART
ejpam-5659	153	2	prove	prove	VERB
ejpam-5659	153	3	the	the	DET
ejpam-5659	153	4	septupling	septupling	NOUN
ejpam-5659	153	5	point	point	NOUN
ejpam-5659	153	6	,	,	PUNCT
ejpam-5659	153	7	a	a	DET
ejpam-5659	153	8	non	non	ADJ
ejpam-5659	153	9	-	-	ADJ
ejpam-5659	153	10	supersingular	supersingular	ADJ
ejpam-5659	153	11	affine	affine	NOUN
ejpam-5659	153	12	coordinate	coordinate	NOUN
ejpam-5659	153	13	is	be	AUX
ejpam-5659	153	14	used	use	VERB
ejpam-5659	153	15	over	over	ADP
ejpam-5659	153	16	the	the	DET
ejpam-5659	153	17	binary	binary	ADJ
ejpam-5659	153	18	field	field	NOUN
ejpam-5659	153	19	e(f2	e(f2	PROPN
ejpam-5659	153	20	m	m	VERB
ejpam-5659	153	21	)	)	PUNCT
ejpam-5659	153	22	for	for	ADP
ejpam-5659	153	23	the	the	DET
ejpam-5659	153	24	equation	equation	NOUN
ejpam-5659	153	25	y2+xy	y2+xy	X
ejpam-5659	154	1	=	=	PUNCT
ejpam-5659	155	1	x3+ax2+b	x3+ax2+b	X
ejpam-5659	155	2	which	which	PRON
ejpam-5659	155	3	includes	include	VERB
ejpam-5659	155	4	the	the	DET
ejpam-5659	155	5	set	set	NOUN
ejpam-5659	155	6	of	of	ADP
ejpam-5659	155	7	points	point	NOUN
ejpam-5659	155	8	p	p	X
ejpam-5659	155	9	(	(	PUNCT
ejpam-5659	155	10	x	x	NOUN
ejpam-5659	155	11	,	,	PUNCT
ejpam-5659	155	12	y	y	NOUN
ejpam-5659	155	13	)	)	PUNCT
ejpam-5659	155	14	such	such	ADJ
ejpam-5659	155	15	that	that	SCONJ
ejpam-5659	155	16	x	x	NOUN
ejpam-5659	155	17	,	,	PUNCT
ejpam-5659	155	18	y	y	PROPN
ejpam-5659	155	19	∈	∈	PROPN
ejpam-5659	155	20	f2	f2	PROPN
ejpam-5659	155	21	m	m	NOUN
ejpam-5659	155	22	.	.	PUNCT
ejpam-5659	156	1	proof	proof	NOUN
ejpam-5659	156	2	of	of	ADP
ejpam-5659	156	3	the	the	DET
ejpam-5659	156	4	used	use	VERB
ejpam-5659	156	5	method	method	NOUN
ejpam-5659	156	6	follows	follow	VERB
ejpam-5659	156	7	from	from	ADP
ejpam-5659	156	8	[	[	X
ejpam-5659	156	9	38	38	NUM
ejpam-5659	156	10	]	]	PUNCT
ejpam-5659	156	11	,	,	PUNCT
ejpam-5659	157	1	[	[	X
ejpam-5659	157	2	22	22	NUM
ejpam-5659	157	3	]	]	PUNCT
ejpam-5659	157	4	,	,	PUNCT
ejpam-5659	158	1	[	[	X
ejpam-5659	158	2	40	40	NUM
ejpam-5659	158	3	]	]	PUNCT
ejpam-5659	158	4	,	,	PUNCT
ejpam-5659	159	1	[	[	X
ejpam-5659	159	2	23	23	NUM
ejpam-5659	159	3	]	]	PUNCT
ejpam-5659	159	4	and	and	CCONJ
ejpam-5659	160	1	[	[	X
ejpam-5659	160	2	31	31	NUM
ejpam-5659	160	3	]	]	PUNCT
ejpam-5659	160	4	and	and	CCONJ
ejpam-5659	160	5	proposed	propose	VERB
ejpam-5659	160	6	as	as	ADP
ejpam-5659	160	7	in	in	ADP
ejpam-5659	160	8	lemma	lemma	PROPN
ejpam-5659	160	9	(	(	PUNCT
ejpam-5659	160	10	1	1	NUM
ejpam-5659	160	11	)	)	PUNCT
ejpam-5659	160	12	below	below	ADV
ejpam-5659	160	13	.	.	PUNCT
ejpam-5659	161	1	lemma	lemma	PROPN
ejpam-5659	161	2	1	1	NUM
ejpam-5659	161	3	:	:	PUNCT
ejpam-5659	161	4	the	the	DET
ejpam-5659	161	5	proposed	propose	VERB
ejpam-5659	161	6	septupling	septupling	NOUN
ejpam-5659	161	7	point	point	NOUN
ejpam-5659	161	8	of	of	ADP
ejpam-5659	161	9	form	form	NOUN
ejpam-5659	161	10	7p	7p	NOUN
ejpam-5659	161	11	=	=	SYM
ejpam-5659	161	12	2(3p	2(3p	NUM
ejpam-5659	161	13	)	)	PUNCT
ejpam-5659	162	1	+	+	CCONJ
ejpam-5659	162	2	p	p	NOUN
ejpam-5659	162	3	has	have	VERB
ejpam-5659	162	4	a	a	DET
ejpam-5659	162	5	valid	valid	ADJ
ejpam-5659	162	6	formula	formula	NOUN
ejpam-5659	162	7	.	.	PUNCT
ejpam-5659	163	1	proof	proof	NOUN
ejpam-5659	163	2	:	:	PUNCT
ejpam-5659	163	3	w.	w.	PROPN
ejpam-5659	163	4	k.	k.	PROPN
ejpam-5659	163	5	abdulraheem	abdulraheem	PROPN
ejpam-5659	163	6	/	/	SYM
ejpam-5659	163	7	eur	eur	PROPN
ejpam-5659	163	8	.	.	PUNCT
ejpam-5659	164	1	j.	j.	PROPN
ejpam-5659	164	2	pure	pure	PROPN
ejpam-5659	164	3	appl	appl	PROPN
ejpam-5659	164	4	.	.	PROPN
ejpam-5659	164	5	math	math	PROPN
ejpam-5659	164	6	,	,	PUNCT
ejpam-5659	164	7	18	18	NUM
ejpam-5659	164	8	(	(	PUNCT
ejpam-5659	164	9	2	2	NUM
ejpam-5659	164	10	)	)	PUNCT
ejpam-5659	164	11	(	(	PUNCT
ejpam-5659	164	12	2025	2025	NUM
ejpam-5659	164	13	)	)	PUNCT
ejpam-5659	164	14	,	,	PUNCT
ejpam-5659	164	15	5659	5659	NUM
ejpam-5659	164	16	10	10	NUM
ejpam-5659	164	17	of	of	ADP
ejpam-5659	164	18	13	13	NUM
ejpam-5659	164	19	to	to	PART
ejpam-5659	164	20	prove	prove	VERB
ejpam-5659	164	21	the	the	DET
ejpam-5659	164	22	formulas	formula	NOUN
ejpam-5659	164	23	in	in	ADP
ejpam-5659	164	24	algorithm	algorithm	NOUN
ejpam-5659	164	25	1	1	NUM
ejpam-5659	164	26	,	,	PUNCT
ejpam-5659	164	27	the	the	DET
ejpam-5659	164	28	affine	affine	NOUN
ejpam-5659	164	29	coordinate	coordinate	NOUN
ejpam-5659	164	30	is	be	AUX
ejpam-5659	164	31	used	use	VERB
ejpam-5659	164	32	.	.	PUNCT
ejpam-5659	165	1	in	in	ADP
ejpam-5659	165	2	affine	affine	NOUN
ejpam-5659	165	3	coordinates	coordinate	NOUN
ejpam-5659	165	4	,	,	PUNCT
ejpam-5659	165	5	for	for	ADP
ejpam-5659	165	6	adding	add	VERB
ejpam-5659	165	7	the	the	DET
ejpam-5659	165	8	two	two	NUM
ejpam-5659	165	9	points	point	NOUN
ejpam-5659	165	10	(	(	PUNCT
ejpam-5659	165	11	x7	x7	NOUN
ejpam-5659	165	12	,	,	PUNCT
ejpam-5659	165	13	y7	y7	PROPN
ejpam-5659	165	14	,	,	PUNCT
ejpam-5659	165	15	z7	z7	PROPN
ejpam-5659	165	16	)	)	PUNCT
ejpam-5659	165	17	=	=	PUNCT
ejpam-5659	165	18	(	(	PUNCT
ejpam-5659	165	19	x1	x1	PROPN
ejpam-5659	165	20	,	,	PUNCT
ejpam-5659	165	21	y1	y1	PROPN
ejpam-5659	165	22	,	,	PUNCT
ejpam-5659	165	23	z1	z1	NOUN
ejpam-5659	165	24	)	)	PUNCT
ejpam-5659	165	25	+	+	CCONJ
ejpam-5659	165	26	(	(	PUNCT
ejpam-5659	165	27	x6	x6	PROPN
ejpam-5659	165	28	,	,	PUNCT
ejpam-5659	165	29	y6	y6	ADJ
ejpam-5659	165	30	,	,	PUNCT
ejpam-5659	165	31	z6	z6	PROPN
ejpam-5659	165	32	)	)	PUNCT
ejpam-5659	165	33	the	the	DET
ejpam-5659	165	34	following	follow	VERB
ejpam-5659	165	35	equations	equation	NOUN
ejpam-5659	165	36	should	should	AUX
ejpam-5659	165	37	be	be	AUX
ejpam-5659	165	38	satisfied	satisfied	ADJ
ejpam-5659	165	39	:	:	PUNCT
ejpam-5659	165	40	λ	λ	X
ejpam-5659	165	41	=	=	SYM
ejpam-5659	165	42	(	(	PUNCT
ejpam-5659	165	43	y6	y6	PROPN
ejpam-5659	165	44	+	+	CCONJ
ejpam-5659	165	45	y1	y1	NOUN
ejpam-5659	165	46	)	)	PUNCT
ejpam-5659	165	47	(	(	PUNCT
ejpam-5659	165	48	x6	x6	PROPN
ejpam-5659	165	49	+	+	CCONJ
ejpam-5659	165	50	x1	x1	ADJ
ejpam-5659	165	51	)	)	PUNCT
ejpam-5659	166	1	x7	x7	NOUN
ejpam-5659	166	2	=	=	SYM
ejpam-5659	166	3	λ2	λ2	NOUN
ejpam-5659	166	4	+	+	CCONJ
ejpam-5659	166	5	λ+	λ+	NUM
ejpam-5659	166	6	x6	x6	PROPN
ejpam-5659	166	7	+	+	CCONJ
ejpam-5659	166	8	x1	x1	PROPN
ejpam-5659	167	1	+	+	CCONJ
ejpam-5659	167	2	a	a	DET
ejpam-5659	167	3	y7	y7	ADJ
ejpam-5659	167	4	=	=	PUNCT
ejpam-5659	167	5	λ(x1	λ(x1	NOUN
ejpam-5659	167	6	+	+	CCONJ
ejpam-5659	167	7	x7	x7	NOUN
ejpam-5659	167	8	)	)	PUNCT
ejpam-5659	168	1	+	+	NUM
ejpam-5659	168	2	x7	x7	NOUN
ejpam-5659	168	3	+	+	CCONJ
ejpam-5659	168	4	y1	y1	INTJ
ejpam-5659	168	5	(	(	PUNCT
ejpam-5659	168	6	15	15	NUM
ejpam-5659	168	7	)	)	PUNCT
ejpam-5659	168	8	using	use	VERB
ejpam-5659	168	9	formulas	formula	NOUN
ejpam-5659	168	10	(	(	PUNCT
ejpam-5659	168	11	11	11	NUM
ejpam-5659	168	12	)	)	PUNCT
ejpam-5659	168	13	,	,	PUNCT
ejpam-5659	168	14	(	(	PUNCT
ejpam-5659	168	15	12	12	NUM
ejpam-5659	168	16	)	)	PUNCT
ejpam-5659	168	17	,	,	PUNCT
ejpam-5659	168	18	(	(	PUNCT
ejpam-5659	168	19	13	13	NUM
ejpam-5659	168	20	)	)	PUNCT
ejpam-5659	168	21	,	,	PUNCT
ejpam-5659	168	22	and	and	CCONJ
ejpam-5659	168	23	(	(	PUNCT
ejpam-5659	168	24	14	14	NUM
ejpam-5659	168	25	)	)	PUNCT
ejpam-5659	168	26	,	,	PUNCT
ejpam-5659	168	27	the	the	DET
ejpam-5659	168	28	forms	form	NOUN
ejpam-5659	168	29	x7	x7	VERB
ejpam-5659	168	30	z7	z7	NOUN
ejpam-5659	168	31	=	=	PUNCT
ejpam-5659	169	1	x7	x7	NOUN
ejpam-5659	169	2	and	and	CCONJ
ejpam-5659	169	3	y7	y7	ADJ
ejpam-5659	169	4	z2	z2	NOUN
ejpam-5659	169	5	7	7	NUM
ejpam-5659	169	6	=	=	SYM
ejpam-5659	169	7	y7	y7	PROPN
ejpam-5659	169	8	needs	need	VERB
ejpam-5659	169	9	to	to	PART
ejpam-5659	169	10	be	be	AUX
ejpam-5659	169	11	proven	prove	VERB
ejpam-5659	169	12	.	.	PUNCT
ejpam-5659	170	1	the	the	DET
ejpam-5659	170	2	process	process	NOUN
ejpam-5659	170	3	is	be	AUX
ejpam-5659	170	4	:	:	PUNCT
ejpam-5659	170	5	x7	x7	NOUN
ejpam-5659	170	6	z7	z7	PROPN
ejpam-5659	170	7	=	=	SYM
ejpam-5659	170	8	a2	a2	PROPN
ejpam-5659	170	9	7	7	NUM
ejpam-5659	170	10	+	+	CCONJ
ejpam-5659	170	11	c7(a7	c7(a7	NOUN
ejpam-5659	170	12	+	+	NOUN
ejpam-5659	170	13	b2	b2	NOUN
ejpam-5659	170	14	7	7	NUM
ejpam-5659	170	15	+	+	CCONJ
ejpam-5659	170	16	ac7	ac7	PROPN
ejpam-5659	170	17	)	)	PUNCT
ejpam-5659	171	1	c2	c2	PROPN
ejpam-5659	171	2	7	7	NUM
ejpam-5659	171	3	=	=	SYM
ejpam-5659	171	4	a2	a2	PROPN
ejpam-5659	171	5	7	7	NUM
ejpam-5659	171	6	c2	c2	PROPN
ejpam-5659	171	7	7	7	NUM
ejpam-5659	171	8	+	+	CCONJ
ejpam-5659	171	9	a7	a7	PROPN
ejpam-5659	171	10	c7	c7	PROPN
ejpam-5659	171	11	+	+	CCONJ
ejpam-5659	171	12	b2	b2	PROPN
ejpam-5659	171	13	7	7	NUM
ejpam-5659	171	14	c7	c7	NOUN
ejpam-5659	171	15	+	+	CCONJ
ejpam-5659	171	16	a	a	PROPN
ejpam-5659	171	17	=	=	X
ejpam-5659	171	18	(	(	PUNCT
ejpam-5659	171	19	y6	y6	ADJ
ejpam-5659	171	20	+	+	CCONJ
ejpam-5659	171	21	y1z	y1z	VERB
ejpam-5659	171	22	2	2	NUM
ejpam-5659	171	23	6	6	NUM
ejpam-5659	171	24	)	)	PUNCT
ejpam-5659	171	25	2	2	NUM
ejpam-5659	171	26	(	(	PUNCT
ejpam-5659	171	27	b7z6)2	b7z6)2	NOUN
ejpam-5659	171	28	+	+	CCONJ
ejpam-5659	171	29	y6	y6	ADJ
ejpam-5659	171	30	+	+	CCONJ
ejpam-5659	171	31	y1z	y1z	VERB
ejpam-5659	171	32	2	2	NUM
ejpam-5659	171	33	6	6	NUM
ejpam-5659	171	34	b7z6	b7z6	NOUN
ejpam-5659	171	35	+	+	CCONJ
ejpam-5659	171	36	a	a	X
ejpam-5659	171	37	=	=	PUNCT
ejpam-5659	171	38	(	(	PUNCT
ejpam-5659	171	39	y6	y6	ADJ
ejpam-5659	171	40	+	+	CCONJ
ejpam-5659	171	41	y1z	y1z	VERB
ejpam-5659	171	42	2	2	NUM
ejpam-5659	171	43	6	6	NUM
ejpam-5659	171	44	)	)	PUNCT
ejpam-5659	171	45	2	2	NUM
ejpam-5659	171	46	(	(	PUNCT
ejpam-5659	171	47	x6	x6	NOUN
ejpam-5659	171	48	+	+	PROPN
ejpam-5659	171	49	x1z6)2(z6)2	x1z6)2(z6)2	PROPN
ejpam-5659	172	1	+	+	CCONJ
ejpam-5659	172	2	y6	y6	ADJ
ejpam-5659	172	3	+	+	CCONJ
ejpam-5659	172	4	y1z	y1z	VERB
ejpam-5659	172	5	2	2	NUM
ejpam-5659	172	6	6	6	NUM
ejpam-5659	172	7	(	(	PUNCT
ejpam-5659	172	8	x6	x6	NOUN
ejpam-5659	172	9	+	+	CCONJ
ejpam-5659	172	10	x1z6)z6	x1z6)z6	ADJ
ejpam-5659	172	11	+	+	CCONJ
ejpam-5659	172	12	x6	x6	PROPN
ejpam-5659	172	13	+	+	PROPN
ejpam-5659	172	14	x1z6	x1z6	PROPN
ejpam-5659	172	15	z6	z6	PROPN
ejpam-5659	172	16	+	+	CCONJ
ejpam-5659	172	17	a	a	DET
ejpam-5659	172	18	(	(	PUNCT
ejpam-5659	172	19	16	16	NUM
ejpam-5659	172	20	)	)	PUNCT
ejpam-5659	172	21	let	let	VERB
ejpam-5659	172	22	z6	z6	PROPN
ejpam-5659	172	23	=	=	SYM
ejpam-5659	172	24	1	1	NUM
ejpam-5659	172	25	=	=	SYM
ejpam-5659	172	26	(	(	PUNCT
ejpam-5659	172	27	y6	y6	PROPN
ejpam-5659	172	28	+	+	CCONJ
ejpam-5659	172	29	y1	y1	NOUN
ejpam-5659	172	30	)	)	PUNCT
ejpam-5659	172	31	2	2	NUM
ejpam-5659	172	32	(	(	PUNCT
ejpam-5659	172	33	x6	x6	NOUN
ejpam-5659	172	34	+	+	PROPN
ejpam-5659	172	35	x1)2	x1)2	VERB
ejpam-5659	173	1	+	+	CCONJ
ejpam-5659	173	2	y6	y6	ADJ
ejpam-5659	173	3	+	+	CCONJ
ejpam-5659	173	4	y1	y1	NOUN
ejpam-5659	173	5	x6	x6	PROPN
ejpam-5659	174	1	+	+	NOUN
ejpam-5659	174	2	x1	x1	PROPN
ejpam-5659	175	1	+	+	ADJ
ejpam-5659	175	2	x6	x6	PROPN
ejpam-5659	175	3	+	+	NOUN
ejpam-5659	175	4	x1	x1	PROPN
ejpam-5659	175	5	+	+	CCONJ
ejpam-5659	175	6	a	a	X
ejpam-5659	175	7	=	=	PUNCT
ejpam-5659	175	8	(	(	PUNCT
ejpam-5659	175	9	y6	y6	ADJ
ejpam-5659	175	10	+	+	CCONJ
ejpam-5659	175	11	y1	y1	NOUN
ejpam-5659	175	12	x6	x6	PROPN
ejpam-5659	175	13	+	+	NOUN
ejpam-5659	175	14	x1	x1	PROPN
ejpam-5659	175	15	)	)	PUNCT
ejpam-5659	175	16	2	2	NUM
ejpam-5659	175	17	+	+	CCONJ
ejpam-5659	175	18	y6	y6	ADJ
ejpam-5659	175	19	+	+	CCONJ
ejpam-5659	175	20	y1	y1	NOUN
ejpam-5659	175	21	x6	x6	PROPN
ejpam-5659	176	1	+	+	NOUN
ejpam-5659	176	2	x1	x1	PROPN
ejpam-5659	177	1	+	+	ADJ
ejpam-5659	177	2	x6	x6	PROPN
ejpam-5659	177	3	+	+	NOUN
ejpam-5659	177	4	x1	x1	PROPN
ejpam-5659	177	5	+	+	CCONJ
ejpam-5659	177	6	a	a	X
ejpam-5659	177	7	=	=	PUNCT
ejpam-5659	177	8	(	(	PUNCT
ejpam-5659	177	9	y6	y6	PROPN
ejpam-5659	177	10	+	+	CCONJ
ejpam-5659	177	11	y1	y1	ADJ
ejpam-5659	177	12	/	/	SYM
ejpam-5659	177	13	z	z	NOUN
ejpam-5659	177	14	2	2	NUM
ejpam-5659	177	15	1	1	NUM
ejpam-5659	177	16	x6	x6	NUM
ejpam-5659	177	17	+	+	NOUN
ejpam-5659	177	18	x1	x1	PROPN
ejpam-5659	177	19	/	/	SYM
ejpam-5659	177	20	z1	z1	ADJ
ejpam-5659	177	21	)	)	PUNCT
ejpam-5659	177	22	2	2	NUM
ejpam-5659	178	1	+	+	CCONJ
ejpam-5659	178	2	y6	y6	ADJ
ejpam-5659	178	3	+	+	CCONJ
ejpam-5659	178	4	y1	y1	ADJ
ejpam-5659	178	5	/	/	SYM
ejpam-5659	178	6	z	z	NOUN
ejpam-5659	178	7	2	2	NUM
ejpam-5659	178	8	1	1	NUM
ejpam-5659	178	9	x6	x6	NUM
ejpam-5659	178	10	+	+	NOUN
ejpam-5659	178	11	x1	x1	PROPN
ejpam-5659	178	12	/	/	SYM
ejpam-5659	178	13	z1	z1	PROPN
ejpam-5659	178	14	+	+	NOUN
ejpam-5659	178	15	x6	x6	PROPN
ejpam-5659	178	16	+	+	CCONJ
ejpam-5659	178	17	x1	x1	PROPN
ejpam-5659	178	18	z1	z1	NOUN
ejpam-5659	178	19	+	+	CCONJ
ejpam-5659	178	20	a	a	PRON
ejpam-5659	178	21	=	=	PUNCT
ejpam-5659	178	22	(	(	PUNCT
ejpam-5659	178	23	y6	y6	ADJ
ejpam-5659	179	1	+	+	CCONJ
ejpam-5659	179	2	y1	y1	PROPN
ejpam-5659	179	3	x6	x6	PROPN
ejpam-5659	179	4	+	+	CCONJ
ejpam-5659	179	5	x1	x1	NUM
ejpam-5659	179	6	)	)	PUNCT
ejpam-5659	179	7	2	2	NUM
ejpam-5659	180	1	+	+	CCONJ
ejpam-5659	180	2	y6	y6	ADJ
ejpam-5659	180	3	+	+	CCONJ
ejpam-5659	180	4	y1	y1	PROPN
ejpam-5659	180	5	x6	x6	PROPN
ejpam-5659	180	6	+	+	CCONJ
ejpam-5659	180	7	x1	x1	PROPN
ejpam-5659	181	1	+	+	NUM
ejpam-5659	181	2	x6	x6	PROPN
ejpam-5659	182	1	+	+	CCONJ
ejpam-5659	182	2	x1	x1	PROPN
ejpam-5659	182	3	+	+	CCONJ
ejpam-5659	182	4	a	a	DET
ejpam-5659	182	5	x7	x7	NOUN
ejpam-5659	182	6	=	=	SYM
ejpam-5659	182	7	λ2	λ2	NOUN
ejpam-5659	182	8	+	+	CCONJ
ejpam-5659	182	9	λ+	λ+	NUM
ejpam-5659	182	10	x6	x6	PROPN
ejpam-5659	182	11	+	+	CCONJ
ejpam-5659	182	12	x1	x1	PROPN
ejpam-5659	183	1	+	+	X
ejpam-5659	183	2	a	a	PRON
ejpam-5659	183	3	(	(	PUNCT
ejpam-5659	183	4	as	as	ADP
ejpam-5659	183	5	x7	x7	NOUN
ejpam-5659	183	6	form	form	NOUN
ejpam-5659	183	7	in	in	ADP
ejpam-5659	183	8	formula	formula	NOUN
ejpam-5659	183	9	(	(	PUNCT
ejpam-5659	183	10	15	15	NUM
ejpam-5659	183	11	)	)	PUNCT
ejpam-5659	183	12	)	)	PUNCT
ejpam-5659	184	1	y7	y7	PROPN
ejpam-5659	184	2	z2	z2	NOUN
ejpam-5659	184	3	7	7	NUM
ejpam-5659	184	4	=	=	SYM
ejpam-5659	184	5	(	(	PUNCT
ejpam-5659	184	6	d7	d7	PROPN
ejpam-5659	184	7	+	+	PROPN
ejpam-5659	184	8	x7)(a7c7	x7)(a7c7	PROPN
ejpam-5659	184	9	+	+	ADJ
ejpam-5659	184	10	z7	z7	PROPN
ejpam-5659	184	11	)	)	PUNCT
ejpam-5659	185	1	+	+	CCONJ
ejpam-5659	185	2	(	(	PUNCT
ejpam-5659	185	3	y1	y1	INTJ
ejpam-5659	185	4	+	+	PROPN
ejpam-5659	185	5	x1)z	x1)z	NOUN
ejpam-5659	185	6	2	2	NUM
ejpam-5659	185	7	7	7	NUM
ejpam-5659	185	8	c4	c4	NOUN
ejpam-5659	185	9	7	7	NUM
ejpam-5659	185	10	=	=	SYM
ejpam-5659	185	11	a7c7(x1z7	a7c7(x1z7	PROPN
ejpam-5659	185	12	+	+	NOUN
ejpam-5659	185	13	d7	d7	PROPN
ejpam-5659	185	14	)	)	PUNCT
ejpam-5659	186	1	+	+	CCONJ
ejpam-5659	186	2	(	(	PUNCT
ejpam-5659	186	3	y1	y1	INTJ
ejpam-5659	186	4	+	+	PROPN
ejpam-5659	186	5	x1)z	x1)z	NOUN
ejpam-5659	186	6	2	2	NUM
ejpam-5659	186	7	7	7	NUM
ejpam-5659	186	8	c4	c4	NOUN
ejpam-5659	186	9	7	7	NUM
ejpam-5659	186	10	=	=	SYM
ejpam-5659	186	11	(	(	PUNCT
ejpam-5659	186	12	y6	y6	ADJ
ejpam-5659	186	13	+	+	CCONJ
ejpam-5659	186	14	y1z	y1z	VERB
ejpam-5659	186	15	2	2	NUM
ejpam-5659	186	16	6	6	NUM
ejpam-5659	186	17	)	)	PUNCT
ejpam-5659	186	18	(	(	PUNCT
ejpam-5659	186	19	x1z7	x1z7	X
ejpam-5659	186	20	+	+	NOUN
ejpam-5659	186	21	x7	x7	NOUN
ejpam-5659	186	22	)	)	PUNCT
ejpam-5659	186	23	c3	c3	NOUN
ejpam-5659	186	24	7	7	NUM
ejpam-5659	187	1	+	+	CCONJ
ejpam-5659	187	2	x7	x7	NOUN
ejpam-5659	187	3	c2	c2	PROPN
ejpam-5659	187	4	7	7	NUM
ejpam-5659	187	5	+	+	NUM
ejpam-5659	187	6	y1	y1	NOUN
ejpam-5659	187	7	=	=	SYM
ejpam-5659	187	8	(	(	PUNCT
ejpam-5659	187	9	y1	y1	INTJ
ejpam-5659	187	10	+	+	CCONJ
ejpam-5659	187	11	y6	y6	ADJ
ejpam-5659	187	12	/	/	SYM
ejpam-5659	187	13	z	z	PROPN
ejpam-5659	187	14	2	2	NUM
ejpam-5659	187	15	6	6	NUM
ejpam-5659	187	16	)	)	PUNCT
ejpam-5659	187	17	(	(	PUNCT
ejpam-5659	187	18	x1	x1	PROPN
ejpam-5659	187	19	+	+	NOUN
ejpam-5659	187	20	x6	x6	PROPN
ejpam-5659	187	21	/	/	SYM
ejpam-5659	187	22	z6	z6	PROPN
ejpam-5659	187	23	)	)	PUNCT
ejpam-5659	187	24	(	(	PUNCT
ejpam-5659	187	25	x1	x1	PROPN
ejpam-5659	187	26	+	+	NOUN
ejpam-5659	187	27	x7z7	x7z7	X
ejpam-5659	187	28	)	)	PUNCT
ejpam-5659	188	1	+	+	CCONJ
ejpam-5659	188	2	x7	x7	X
ejpam-5659	188	3	z7	z7	NOUN
ejpam-5659	188	4	+	+	CCONJ
ejpam-5659	188	5	y1	y1	NOUN
ejpam-5659	188	6	=	=	SYM
ejpam-5659	188	7	(	(	PUNCT
ejpam-5659	188	8	y1	y1	INTJ
ejpam-5659	188	9	+	+	CCONJ
ejpam-5659	188	10	y6	y6	NOUN
ejpam-5659	188	11	)	)	PUNCT
ejpam-5659	188	12	(	(	PUNCT
ejpam-5659	188	13	x1	x1	PROPN
ejpam-5659	188	14	+	+	NUM
ejpam-5659	188	15	x6	x6	PROPN
ejpam-5659	188	16	)	)	PUNCT
ejpam-5659	188	17	(	(	PUNCT
ejpam-5659	188	18	x1	x1	PROPN
ejpam-5659	188	19	+	+	CCONJ
ejpam-5659	188	20	x7	x7	NOUN
ejpam-5659	188	21	)	)	PUNCT
ejpam-5659	188	22	+	+	NUM
ejpam-5659	188	23	x7	x7	NOUN
ejpam-5659	188	24	+	+	CCONJ
ejpam-5659	188	25	y1	y1	NOUN
ejpam-5659	188	26	y5	y5	NOUN
ejpam-5659	188	27	=	=	NOUN
ejpam-5659	188	28	λ(x1	λ(x1	NOUN
ejpam-5659	188	29	+	+	CCONJ
ejpam-5659	188	30	x7	x7	NOUN
ejpam-5659	188	31	)	)	PUNCT
ejpam-5659	189	1	+	+	NUM
ejpam-5659	189	2	x7	x7	NOUN
ejpam-5659	189	3	+	+	CCONJ
ejpam-5659	189	4	y1	y1	NOUN
ejpam-5659	189	5	(	(	PUNCT
ejpam-5659	189	6	proven	prove	VERB
ejpam-5659	189	7	as	as	ADP
ejpam-5659	189	8	in	in	ADP
ejpam-5659	189	9	formula	formula	NOUN
ejpam-5659	189	10	(	(	PUNCT
ejpam-5659	189	11	15	15	NUM
ejpam-5659	189	12	)	)	PUNCT
ejpam-5659	189	13	)	)	PUNCT
ejpam-5659	190	1	w.	w.	PROPN
ejpam-5659	190	2	k.	k.	PROPN
ejpam-5659	190	3	abdulraheem	abdulraheem	PROPN
ejpam-5659	190	4	/	/	SYM
ejpam-5659	190	5	eur	eur	PROPN
ejpam-5659	190	6	.	.	PUNCT
ejpam-5659	191	1	j.	j.	PROPN
ejpam-5659	191	2	pure	pure	PROPN
ejpam-5659	191	3	appl	appl	PROPN
ejpam-5659	191	4	.	.	PROPN
ejpam-5659	191	5	math	math	PROPN
ejpam-5659	191	6	,	,	PUNCT
ejpam-5659	191	7	18	18	NUM
ejpam-5659	191	8	(	(	PUNCT
ejpam-5659	191	9	2	2	NUM
ejpam-5659	191	10	)	)	PUNCT
ejpam-5659	191	11	(	(	PUNCT
ejpam-5659	191	12	2025	2025	NUM
ejpam-5659	191	13	)	)	PUNCT
ejpam-5659	191	14	,	,	PUNCT
ejpam-5659	191	15	5659	5659	NUM
ejpam-5659	191	16	11	11	NUM
ejpam-5659	191	17	of	of	ADP
ejpam-5659	191	18	13	13	NUM
ejpam-5659	191	19	5	5	NUM
ejpam-5659	191	20	.	.	PUNCT
ejpam-5659	191	21	conclusion	conclusion	NOUN
ejpam-5659	191	22	and	and	CCONJ
ejpam-5659	191	23	future	future	ADJ
ejpam-5659	191	24	work	work	NOUN
ejpam-5659	191	25	this	this	DET
ejpam-5659	191	26	paper	paper	NOUN
ejpam-5659	191	27	introduces	introduce	VERB
ejpam-5659	191	28	the	the	DET
ejpam-5659	191	29	formula	formula	NOUN
ejpam-5659	191	30	of	of	ADP
ejpam-5659	191	31	the	the	DET
ejpam-5659	191	32	septupling	septupling	NOUN
ejpam-5659	191	33	point	point	NOUN
ejpam-5659	191	34	7p	7p	NUM
ejpam-5659	191	35	,	,	PUNCT
ejpam-5659	191	36	using	use	VERB
ejpam-5659	191	37	ld	ld	PROPN
ejpam-5659	191	38	coordinates	coordinate	NOUN
ejpam-5659	191	39	and	and	CCONJ
ejpam-5659	191	40	a	a	DET
ejpam-5659	191	41	non	non	ADJ
ejpam-5659	191	42	-	-	ADJ
ejpam-5659	191	43	supersingular	supersingular	ADJ
ejpam-5659	191	44	affine	affine	NOUN
ejpam-5659	191	45	over	over	ADP
ejpam-5659	191	46	the	the	DET
ejpam-5659	191	47	binary	binary	ADJ
ejpam-5659	191	48	field	field	NOUN
ejpam-5659	191	49	e(f2	e(f2	PROPN
ejpam-5659	191	50	m	m	VERB
ejpam-5659	191	51	)	)	PUNCT
ejpam-5659	191	52	for	for	ADP
ejpam-5659	191	53	the	the	DET
ejpam-5659	191	54	equation	equation	NOUN
ejpam-5659	191	55	y2	y2	PROPN
ejpam-5659	192	1	+	+	CCONJ
ejpam-5659	192	2	xy	xy	X
ejpam-5659	192	3	=	=	SYM
ejpam-5659	193	1	x3	x3	VERB
ejpam-5659	193	2	+	+	CCONJ
ejpam-5659	193	3	ax2	ax2	NOUN
ejpam-5659	193	4	+	+	CCONJ
ejpam-5659	193	5	b	b	NOUN
ejpam-5659	193	6	which	which	PRON
ejpam-5659	193	7	includes	include	VERB
ejpam-5659	193	8	the	the	DET
ejpam-5659	193	9	set	set	NOUN
ejpam-5659	193	10	of	of	ADP
ejpam-5659	193	11	points	point	NOUN
ejpam-5659	193	12	p	p	X
ejpam-5659	193	13	(	(	PUNCT
ejpam-5659	193	14	x	x	NOUN
ejpam-5659	193	15	,	,	PUNCT
ejpam-5659	193	16	y	y	NOUN
ejpam-5659	193	17	)	)	PUNCT
ejpam-5659	193	18	such	such	ADJ
ejpam-5659	193	19	that	that	SCONJ
ejpam-5659	193	20	x	x	NOUN
ejpam-5659	193	21	,	,	PUNCT
ejpam-5659	193	22	y	y	PROPN
ejpam-5659	193	23	∈	∈	PROPN
ejpam-5659	193	24	f2	f2	PROPN
ejpam-5659	193	25	m	m	VERB
ejpam-5659	193	26	.	.	PUNCT
ejpam-5659	194	1	the	the	DET
ejpam-5659	194	2	point	point	NOUN
ejpam-5659	194	3	is	be	AUX
ejpam-5659	194	4	using	use	VERB
ejpam-5659	194	5	the	the	DET
ejpam-5659	194	6	form	form	NOUN
ejpam-5659	194	7	7p	7p	NOUN
ejpam-5659	194	8	=	=	SYM
ejpam-5659	194	9	2(3p	2(3p	NUM
ejpam-5659	194	10	)	)	PUNCT
ejpam-5659	195	1	+	+	CCONJ
ejpam-5659	195	2	p	p	X
ejpam-5659	195	3	where	where	SCONJ
ejpam-5659	195	4	the	the	DET
ejpam-5659	195	5	point	point	NOUN
ejpam-5659	195	6	p	p	NOUN
ejpam-5659	195	7	is	be	AUX
ejpam-5659	195	8	in	in	ADP
ejpam-5659	195	9	the	the	DET
ejpam-5659	195	10	affine	affine	NOUN
ejpam-5659	195	11	and	and	CCONJ
ejpam-5659	195	12	the	the	DET
ejpam-5659	195	13	sixtupling	sixtupling	NOUN
ejpam-5659	195	14	point	point	NOUN
ejpam-5659	195	15	2(3p	2(3p	NUM
ejpam-5659	195	16	)	)	PUNCT
ejpam-5659	196	1	=	=	SYM
ejpam-5659	196	2	6p	6p	NUM
ejpam-5659	196	3	form	form	NOUN
ejpam-5659	196	4	is	be	AUX
ejpam-5659	196	5	in	in	ADP
ejpam-5659	196	6	the	the	DET
ejpam-5659	196	7	projective	projective	ADJ
ejpam-5659	196	8	coordinates	coordinate	NOUN
ejpam-5659	196	9	.	.	PUNCT
ejpam-5659	197	1	the	the	DET
ejpam-5659	197	2	cost	cost	NOUN
ejpam-5659	197	3	of	of	ADP
ejpam-5659	197	4	the	the	DET
ejpam-5659	197	5	septupling	septupling	NOUN
ejpam-5659	197	6	point	point	NOUN
ejpam-5659	197	7	is	be	AUX
ejpam-5659	197	8	19	19	NUM
ejpam-5659	197	9	s	s	NOUN
ejpam-5659	197	10	+	+	NUM
ejpam-5659	197	11	28	28	NUM
ejpam-5659	197	12	m	m	NOUN
ejpam-5659	197	13	,	,	PUNCT
ejpam-5659	197	14	while	while	SCONJ
ejpam-5659	197	15	the	the	DET
ejpam-5659	197	16	cost	cost	NOUN
ejpam-5659	197	17	of	of	ADP
ejpam-5659	197	18	sixtupling	sixtupling	NOUN
ejpam-5659	197	19	point	point	NOUN
ejpam-5659	197	20	6p	6p	NUM
ejpam-5659	197	21	is	be	AUX
ejpam-5659	197	22	14	14	NUM
ejpam-5659	197	23	s	s	NOUN
ejpam-5659	197	24	+	+	NUM
ejpam-5659	197	25	19	19	NUM
ejpam-5659	197	26	m	m	NOUN
ejpam-5659	197	27	.	.	PUNCT
ejpam-5659	198	1	the	the	DET
ejpam-5659	198	2	point	point	NOUN
ejpam-5659	198	3	is	be	AUX
ejpam-5659	198	4	not	not	PART
ejpam-5659	198	5	comparable	comparable	ADJ
ejpam-5659	198	6	to	to	ADP
ejpam-5659	198	7	any	any	DET
ejpam-5659	198	8	septupling	septupling	NOUN
ejpam-5659	198	9	point	point	NOUN
ejpam-5659	198	10	since	since	SCONJ
ejpam-5659	198	11	it	it	PRON
ejpam-5659	198	12	is	be	AUX
ejpam-5659	198	13	the	the	DET
ejpam-5659	198	14	first	first	ADJ
ejpam-5659	198	15	formula	formula	NOUN
ejpam-5659	198	16	for	for	ADP
ejpam-5659	198	17	7p	7p	NUM
ejpam-5659	198	18	over	over	ADP
ejpam-5659	198	19	ld	ld	PROPN
ejpam-5659	198	20	coordinate	coordinate	NOUN
ejpam-5659	198	21	and	and	CCONJ
ejpam-5659	198	22	affine	affine	NOUN
ejpam-5659	198	23	.	.	PUNCT
ejpam-5659	199	1	since	since	SCONJ
ejpam-5659	199	2	it	it	PRON
ejpam-5659	199	3	is	be	AUX
ejpam-5659	199	4	precomputed	precompute	VERB
ejpam-5659	199	5	and	and	CCONJ
ejpam-5659	199	6	precalculated	precalculate	VERB
ejpam-5659	199	7	,	,	PUNCT
ejpam-5659	199	8	the	the	DET
ejpam-5659	199	9	point	point	NOUN
ejpam-5659	199	10	can	can	AUX
ejpam-5659	199	11	be	be	AUX
ejpam-5659	199	12	used	use	VERB
ejpam-5659	199	13	with	with	ADP
ejpam-5659	199	14	scalar	scalar	ADJ
ejpam-5659	199	15	multiplication	multiplication	NOUN
ejpam-5659	199	16	operation	operation	NOUN
ejpam-5659	199	17	in	in	ADP
ejpam-5659	199	18	ecc	ecc	PROPN
ejpam-5659	199	19	operation	operation	NOUN
ejpam-5659	199	20	methods	method	NOUN
ejpam-5659	199	21	such	such	ADJ
ejpam-5659	199	22	as	as	ADP
ejpam-5659	199	23	w	w	PROPN
ejpam-5659	199	24	−	−	PROPN
ejpam-5659	199	25	naf	naf	PROPN
ejpam-5659	199	26	where	where	SCONJ
ejpam-5659	199	27	w	w	NOUN
ejpam-5659	199	28	=	=	NOUN
ejpam-5659	199	29	4	4	NUM
ejpam-5659	199	30	or	or	CCONJ
ejpam-5659	199	31	multi	multi	ADJ
ejpam-5659	199	32	-	-	ADJ
ejpam-5659	199	33	base	base	ADJ
ejpam-5659	199	34	scalar	scalar	ADJ
ejpam-5659	199	35	multiplication	multiplication	NOUN
ejpam-5659	199	36	such	such	ADJ
ejpam-5659	199	37	as	as	ADP
ejpam-5659	199	38	{	{	PUNCT
ejpam-5659	199	39	2	2	NUM
ejpam-5659	199	40	3	3	NUM
ejpam-5659	199	41	,	,	PUNCT
ejpam-5659	199	42	7}-base	7}-base	NUM
ejpam-5659	199	43	methods	method	NOUN
ejpam-5659	199	44	.	.	PUNCT
ejpam-5659	200	1	this	this	DET
ejpam-5659	200	2	work	work	NOUN
ejpam-5659	200	3	can	can	AUX
ejpam-5659	200	4	also	also	ADV
ejpam-5659	200	5	be	be	AUX
ejpam-5659	200	6	improved	improve	VERB
ejpam-5659	200	7	using	use	VERB
ejpam-5659	200	8	other	other	ADJ
ejpam-5659	200	9	forms	form	NOUN
ejpam-5659	200	10	if	if	SCONJ
ejpam-5659	200	11	available	available	ADJ
ejpam-5659	200	12	,	,	PUNCT
ejpam-5659	200	13	and	and	CCONJ
ejpam-5659	200	14	higher	high	ADJ
ejpam-5659	200	15	point	point	NOUN
ejpam-5659	200	16	calculations	calculation	NOUN
ejpam-5659	200	17	can	can	AUX
ejpam-5659	200	18	be	be	AUX
ejpam-5659	200	19	precomputed	precompute	VERB
ejpam-5659	200	20	such	such	ADJ
ejpam-5659	200	21	as	as	ADP
ejpam-5659	200	22	nineupling	nineuple	VERB
ejpam-5659	200	23	9p	9p	NUM
ejpam-5659	200	24	or	or	CCONJ
ejpam-5659	200	25	much	much	ADV
ejpam-5659	200	26	higher	high	ADJ
ejpam-5659	200	27	degrees	degree	NOUN
ejpam-5659	200	28	.	.	PUNCT
ejpam-5659	201	1	references	reference	NOUN
ejpam-5659	201	2	[	[	X
ejpam-5659	201	3	1	1	NUM
ejpam-5659	201	4	]	]	X
ejpam-5659	201	5	n.	n.	PROPN
ejpam-5659	201	6	a.	a.	PROPN
ejpam-5659	201	7	karim	karim	PROPN
ejpam-5659	201	8	and	and	CCONJ
ejpam-5659	201	9	a.	a.	PROPN
ejpam-5659	201	10	h.	h.	PROPN
ejpam-5659	201	11	ali	ali	PROPN
ejpam-5659	201	12	.	.	PUNCT
ejpam-5659	202	1	e	e	X
ejpam-5659	202	2	-	-	ADJ
ejpam-5659	202	3	learning	learn	VERB
ejpam-5659	202	4	virtual	virtual	ADJ
ejpam-5659	202	5	meeting	meeting	NOUN
ejpam-5659	202	6	applications	application	NOUN
ejpam-5659	202	7	:	:	PUNCT
ejpam-5659	202	8	a	a	DET
ejpam-5659	202	9	comparative	comparative	ADJ
ejpam-5659	202	10	study	study	NOUN
ejpam-5659	202	11	from	from	ADP
ejpam-5659	202	12	a	a	DET
ejpam-5659	202	13	cybersecurity	cybersecurity	NOUN
ejpam-5659	202	14	perspective	perspective	NOUN
ejpam-5659	202	15	.	.	PUNCT
ejpam-5659	203	1	indones	indone	NOUN
ejpam-5659	203	2	.	.	PUNCT
ejpam-5659	204	1	j.	j.	PROPN
ejpam-5659	204	2	electr	electr	PROPN
ejpam-5659	204	3	.	.	PUNCT
ejpam-5659	205	1	eng	eng	PROPN
ejpam-5659	205	2	.	.	PUNCT
ejpam-5659	206	1	comput	comput	PROPN
ejpam-5659	206	2	.	.	PUNCT
ejpam-5659	207	1	sci	sci	PROPN
ejpam-5659	207	2	.	.	PROPN
ejpam-5659	207	3	,	,	PUNCT
ejpam-5659	207	4	24(2):1121–1129	24(2):1121–1129	NUM
ejpam-5659	207	5	,	,	PUNCT
ejpam-5659	207	6	2021	2021	NUM
ejpam-5659	207	7	.	.	PUNCT
ejpam-5659	208	1	[	[	X
ejpam-5659	208	2	2	2	NUM
ejpam-5659	208	3	]	]	PUNCT
ejpam-5659	208	4	m.	m.	NOUN
ejpam-5659	208	5	hijjawi	hijjawi	X
ejpam-5659	208	6	et	et	PROPN
ejpam-5659	208	7	al	al	PROPN
ejpam-5659	208	8	.	.	PUNCT
ejpam-5659	209	1	a	a	DET
ejpam-5659	209	2	novel	novel	ADJ
ejpam-5659	209	3	hybrid	hybrid	ADJ
ejpam-5659	209	4	prairie	prairie	ADJ
ejpam-5659	209	5	dog	dog	NOUN
ejpam-5659	209	6	algorithm	algorithm	NOUN
ejpam-5659	209	7	and	and	CCONJ
ejpam-5659	209	8	harris	harris	PROPN
ejpam-5659	209	9	hawks	hawks	PROPN
ejpam-5659	209	10	algorithm	algorithm	PROPN
ejpam-5659	209	11	for	for	ADP
ejpam-5659	209	12	resource	resource	NOUN
ejpam-5659	209	13	allocation	allocation	NOUN
ejpam-5659	209	14	of	of	ADP
ejpam-5659	209	15	wireless	wireless	ADJ
ejpam-5659	209	16	networks	network	NOUN
ejpam-5659	209	17	.	.	PUNCT
ejpam-5659	210	1	ieee	ieee	NOUN
ejpam-5659	210	2	access	access	NOUN
ejpam-5659	210	3	,	,	PUNCT
ejpam-5659	210	4	11(november):145146–145166	11(november):145146–145166	NUM
ejpam-5659	210	5	,	,	PUNCT
ejpam-5659	210	6	2023	2023	NUM
ejpam-5659	210	7	.	.	PUNCT
ejpam-5659	211	1	[	[	X
ejpam-5659	211	2	3	3	X
ejpam-5659	211	3	]	]	X
ejpam-5659	211	4	n.	n.	NOUN
ejpam-5659	211	5	a.	a.	NOUN
ejpam-5659	211	6	salameh	salameh	PROPN
ejpam-5659	211	7	,	,	PUNCT
ejpam-5659	211	8	a.	a.	NOUN
ejpam-5659	211	9	elias	elias	PROPN
ejpam-5659	211	10	,	,	PUNCT
ejpam-5659	211	11	and	and	CCONJ
ejpam-5659	211	12	n.	n.	PROPN
ejpam-5659	211	13	f.	f.	PROPN
ejpam-5659	211	14	karim	karim	PROPN
ejpam-5659	211	15	.	.	PUNCT
ejpam-5659	212	1	proposed	propose	VERB
ejpam-5659	212	2	model	model	NOUN
ejpam-5659	212	3	for	for	ADP
ejpam-5659	212	4	measuring	measure	VERB
ejpam-5659	212	5	acceptance	acceptance	NOUN
ejpam-5659	212	6	of	of	ADP
ejpam-5659	212	7	online	online	ADJ
ejpam-5659	212	8	ads	ad	NOUN
ejpam-5659	212	9	.	.	PUNCT
ejpam-5659	213	1	j.	j.	PROPN
ejpam-5659	213	2	eng	eng	PROPN
ejpam-5659	213	3	.	.	PROPN
ejpam-5659	213	4	appl	appl	PROPN
ejpam-5659	213	5	.	.	PUNCT
ejpam-5659	214	1	sci	sci	PROPN
ejpam-5659	214	2	.	.	PROPN
ejpam-5659	214	3	,	,	PUNCT
ejpam-5659	214	4	100(10):2181–2185	100(10):2181–2185	NUM
ejpam-5659	214	5	,	,	PUNCT
ejpam-5659	214	6	2016	2016	NUM
ejpam-5659	214	7	.	.	PUNCT
ejpam-5659	215	1	[	[	X
ejpam-5659	215	2	4	4	X
ejpam-5659	215	3	]	]	PUNCT
ejpam-5659	215	4	s.	s.	PROPN
ejpam-5659	215	5	d.	d.	PROPN
ejpam-5659	215	6	patil	patil	PROPN
ejpam-5659	215	7	,	,	PUNCT
ejpam-5659	215	8	a.	a.	PROPN
ejpam-5659	215	9	b.	b.	PROPN
ejpam-5659	215	10	kathole	kathole	PROPN
ejpam-5659	215	11	,	,	PUNCT
ejpam-5659	215	12	s.	s.	PROPN
ejpam-5659	215	13	kumbhare	kumbhare	PROPN
ejpam-5659	215	14	,	,	PUNCT
ejpam-5659	215	15	k.	k.	PROPN
ejpam-5659	215	16	vhatkar	vhatkar	PROPN
ejpam-5659	215	17	,	,	PUNCT
ejpam-5659	215	18	and	and	CCONJ
ejpam-5659	216	1	v.	v.	ADP
ejpam-5659	216	2	v.	v.	PROPN
ejpam-5659	216	3	kimbahune	kimbahune	PROPN
ejpam-5659	216	4	.	.	PUNCT
ejpam-5659	217	1	a	a	DET
ejpam-5659	217	2	blockchain	blockchain	NOUN
ejpam-5659	217	3	-	-	PUNCT
ejpam-5659	217	4	based	base	VERB
ejpam-5659	217	5	approach	approach	NOUN
ejpam-5659	217	6	to	to	ADP
ejpam-5659	217	7	ensuring	ensure	VERB
ejpam-5659	217	8	the	the	DET
ejpam-5659	217	9	security	security	NOUN
ejpam-5659	217	10	of	of	ADP
ejpam-5659	217	11	electronic	electronic	ADJ
ejpam-5659	217	12	data	datum	NOUN
ejpam-5659	217	13	.	.	PUNCT
ejpam-5659	218	1	int	int	NOUN
ejpam-5659	218	2	.	.	PUNCT
ejpam-5659	219	1	j.	j.	PROPN
ejpam-5659	219	2	intell	intell	PROPN
ejpam-5659	219	3	.	.	PUNCT
ejpam-5659	220	1	syst	syst	PROPN
ejpam-5659	220	2	.	.	PUNCT
ejpam-5659	221	1	appl	appl	PROPN
ejpam-5659	221	2	.	.	PUNCT
ejpam-5659	222	1	eng	eng	PROPN
ejpam-5659	222	2	.	.	PROPN
ejpam-5659	222	3	,	,	PUNCT
ejpam-5659	222	4	12(11):649–655	12(11):649–655	PROPN
ejpam-5659	222	5	,	,	PUNCT
ejpam-5659	222	6	2024	2024	NUM
ejpam-5659	222	7	.	.	PUNCT
ejpam-5659	223	1	[	[	X
ejpam-5659	223	2	5	5	X
ejpam-5659	223	3	]	]	PUNCT
ejpam-5659	223	4	k.	k.	PROPN
ejpam-5659	223	5	k.	k.	PROPN
ejpam-5659	223	6	kommineni	kommineni	PROPN
ejpam-5659	223	7	and	and	CCONJ
ejpam-5659	223	8	a.	a.	NOUN
ejpam-5659	223	9	prasad	prasad	PROPN
ejpam-5659	223	10	.	.	PUNCT
ejpam-5659	224	1	a	a	DET
ejpam-5659	224	2	review	review	NOUN
ejpam-5659	224	3	on	on	ADP
ejpam-5659	224	4	privacy	privacy	NOUN
ejpam-5659	224	5	and	and	CCONJ
ejpam-5659	224	6	security	security	NOUN
ejpam-5659	224	7	improvement	improvement	NOUN
ejpam-5659	224	8	mechanisms	mechanism	NOUN
ejpam-5659	224	9	in	in	ADP
ejpam-5659	224	10	manets	manet	NOUN
ejpam-5659	224	11	.	.	PUNCT
ejpam-5659	225	1	int	int	NOUN
ejpam-5659	225	2	.	.	PUNCT
ejpam-5659	226	1	j.	j.	PROPN
ejpam-5659	226	2	intell	intell	PROPN
ejpam-5659	226	3	.	.	PUNCT
ejpam-5659	227	1	syst	syst	PROPN
ejpam-5659	227	2	.	.	PUNCT
ejpam-5659	228	1	appl	appl	PROPN
ejpam-5659	228	2	.	.	PUNCT
ejpam-5659	229	1	eng	eng	PROPN
ejpam-5659	229	2	.	.	PROPN
ejpam-5659	229	3	,	,	PUNCT
ejpam-5659	229	4	12(2):90–99	12(2):90–99	NUM
ejpam-5659	229	5	,	,	PUNCT
ejpam-5659	229	6	2024	2024	NUM
ejpam-5659	229	7	.	.	PUNCT
ejpam-5659	230	1	[	[	X
ejpam-5659	230	2	6	6	NUM
ejpam-5659	230	3	]	]	PUNCT
ejpam-5659	230	4	w.	w.	PROPN
ejpam-5659	230	5	k.	k.	PROPN
ejpam-5659	230	6	abdulraheem	abdulraheem	PROPN
ejpam-5659	230	7	.	.	PUNCT
ejpam-5659	231	1	performance	performance	NOUN
ejpam-5659	231	2	comparison	comparison	NOUN
ejpam-5659	231	3	of	of	ADP
ejpam-5659	231	4	xen	xen	PROPN
ejpam-5659	231	5	and	and	CCONJ
ejpam-5659	231	6	hyper	hyper	NOUN
ejpam-5659	231	7	-	-	NOUN
ejpam-5659	231	8	v	v	NOUN
ejpam-5659	231	9	in	in	ADP
ejpam-5659	231	10	cloud	cloud	NOUN
ejpam-5659	231	11	computing	computing	NOUN
ejpam-5659	231	12	while	while	SCONJ
ejpam-5659	231	13	using	use	VERB
ejpam-5659	231	14	cryptosystems	cryptosystem	NOUN
ejpam-5659	231	15	.	.	PUNCT
ejpam-5659	232	1	int	int	NOUN
ejpam-5659	232	2	.	.	PUNCT
ejpam-5659	233	1	j.	j.	PROPN
ejpam-5659	233	2	adv	adv	PROPN
ejpam-5659	233	3	.	.	PUNCT
ejpam-5659	233	4	soft	soft	ADJ
ejpam-5659	233	5	comput	comput	NOUN
ejpam-5659	233	6	.	.	PUNCT
ejpam-5659	234	1	its	its	PRON
ejpam-5659	234	2	appl	appl	NOUN
ejpam-5659	234	3	.	.	PROPN
ejpam-5659	234	4	,	,	PUNCT
ejpam-5659	234	5	14(3):17–30	14(3):17–30	NUM
ejpam-5659	234	6	,	,	PUNCT
ejpam-5659	234	7	2022	2022	NUM
ejpam-5659	234	8	.	.	PUNCT
ejpam-5659	235	1	[	[	X
ejpam-5659	235	2	7	7	X
ejpam-5659	235	3	]	]	X
ejpam-5659	235	4	o.	o.	PROPN
ejpam-5659	235	5	m.	m.	PROPN
ejpam-5659	235	6	c.	c.	PROPN
ejpam-5659	235	7	osazuwa	osazuwa	PROPN
ejpam-5659	235	8	.	.	PUNCT
ejpam-5659	236	1	confidentiality	confidentiality	NOUN
ejpam-5659	236	2	,	,	PUNCT
ejpam-5659	236	3	integrity	integrity	NOUN
ejpam-5659	236	4	,	,	PUNCT
ejpam-5659	236	5	and	and	CCONJ
ejpam-5659	236	6	availability	availability	NOUN
ejpam-5659	236	7	in	in	ADP
ejpam-5659	236	8	network	network	NOUN
ejpam-5659	236	9	systems	system	NOUN
ejpam-5659	236	10	:	:	PUNCT
ejpam-5659	236	11	a	a	DET
ejpam-5659	236	12	review	review	NOUN
ejpam-5659	236	13	of	of	ADP
ejpam-5659	236	14	related	related	ADJ
ejpam-5659	236	15	literature	literature	NOUN
ejpam-5659	236	16	.	.	PUNCT
ejpam-5659	237	1	int	int	NOUN
ejpam-5659	237	2	.	.	PUNCT
ejpam-5659	238	1	j.	j.	PROPN
ejpam-5659	238	2	innov	innov	PROPN
ejpam-5659	238	3	.	.	PUNCT
ejpam-5659	239	1	sci	sci	PROPN
ejpam-5659	239	2	.	.	PUNCT
ejpam-5659	239	3	res	res	PROPN
ejpam-5659	239	4	.	.	PROPN
ejpam-5659	240	1	technol	technol	PROPN
ejpam-5659	240	2	.	.	PROPN
ejpam-5659	240	3	,	,	PUNCT
ejpam-5659	240	4	8(12):1946–1955	8(12):1946–1955	NUM
ejpam-5659	240	5	,	,	PUNCT
ejpam-5659	240	6	2024	2024	NUM
ejpam-5659	240	7	.	.	PUNCT
ejpam-5659	241	1	[	[	X
ejpam-5659	241	2	8	8	NUM
ejpam-5659	241	3	]	]	X
ejpam-5659	242	1	n.	n.	NOUN
ejpam-5659	242	2	a.	a.	PROPN
ejpam-5659	243	1	karim	karim	PROPN
ejpam-5659	243	2	et	et	PROPN
ejpam-5659	243	3	al	al	PROPN
ejpam-5659	243	4	.	.	PROPN
ejpam-5659	244	1	performance	performance	NOUN
ejpam-5659	244	2	comparison	comparison	NOUN
ejpam-5659	244	3	of	of	ADP
ejpam-5659	244	4	hyper	hyper	NOUN
ejpam-5659	244	5	-	-	NOUN
ejpam-5659	244	6	v	v	NOUN
ejpam-5659	244	7	and	and	CCONJ
ejpam-5659	244	8	kvm	kvm	NOUN
ejpam-5659	244	9	for	for	ADP
ejpam-5659	244	10	cryptographic	cryptographic	ADJ
ejpam-5659	244	11	tasks	task	NOUN
ejpam-5659	244	12	in	in	ADP
ejpam-5659	244	13	cloud	cloud	NOUN
ejpam-5659	244	14	computing	computing	NOUN
ejpam-5659	244	15	.	.	PUNCT
ejpam-5659	245	1	comput	comput	NOUN
ejpam-5659	245	2	.	.	PUNCT
ejpam-5659	246	1	mater	mater	NOUN
ejpam-5659	246	2	.	.	PUNCT
ejpam-5659	247	1	contin	contin	AUX
ejpam-5659	247	2	.	.	PUNCT
ejpam-5659	247	3	,	,	PUNCT
ejpam-5659	248	1	78(2):2023–2045	78(2):2023–2045	NUM
ejpam-5659	248	2	,	,	PUNCT
ejpam-5659	248	3	2024	2024	NUM
ejpam-5659	248	4	.	.	PUNCT
ejpam-5659	249	1	[	[	X
ejpam-5659	249	2	9	9	NUM
ejpam-5659	249	3	]	]	X
ejpam-5659	249	4	n.	n.	NOUN
ejpam-5659	249	5	a.	a.	PROPN
ejpam-5659	249	6	karim	karim	PROPN
ejpam-5659	249	7	et	et	PROPN
ejpam-5659	249	8	al	al	PROPN
ejpam-5659	249	9	.	.	PUNCT
ejpam-5659	250	1	using	use	VERB
ejpam-5659	250	2	interface	interface	NOUN
ejpam-5659	250	3	preferences	preference	NOUN
ejpam-5659	250	4	as	as	ADP
ejpam-5659	250	5	evidence	evidence	NOUN
ejpam-5659	250	6	of	of	ADP
ejpam-5659	250	7	user	user	NOUN
ejpam-5659	250	8	identity	identity	NOUN
ejpam-5659	250	9	:	:	PUNCT
ejpam-5659	250	10	a	a	DET
ejpam-5659	250	11	feasibility	feasibility	NOUN
ejpam-5659	250	12	study	study	NOUN
ejpam-5659	250	13	.	.	PUNCT
ejpam-5659	251	1	int	int	NOUN
ejpam-5659	251	2	.	.	PUNCT
ejpam-5659	252	1	j.	j.	PROPN
ejpam-5659	252	2	data	data	PROPN
ejpam-5659	252	3	netw	netw	PROPN
ejpam-5659	252	4	.	.	PUNCT
ejpam-5659	253	1	sci	sci	PROPN
ejpam-5659	253	2	.	.	PROPN
ejpam-5659	253	3	,	,	PUNCT
ejpam-5659	253	4	8(1):537–548	8(1):537–548	NUM
ejpam-5659	253	5	,	,	PUNCT
ejpam-5659	253	6	2024	2024	NUM
ejpam-5659	253	7	.	.	PUNCT
ejpam-5659	254	1	[	[	X
ejpam-5659	254	2	10	10	NUM
ejpam-5659	254	3	]	]	PUNCT
ejpam-5659	254	4	m.	m.	NOUN
ejpam-5659	254	5	i.	i.	PROPN
ejpam-5659	254	6	adawy	adawy	PROPN
ejpam-5659	254	7	,	,	PUNCT
ejpam-5659	254	8	m.	m.	NOUN
ejpam-5659	254	9	tahboush	tahboush	PROPN
ejpam-5659	254	10	,	,	PUNCT
ejpam-5659	254	11	o.	o.	PROPN
ejpam-5659	254	12	aloqaily	aloqaily	ADV
ejpam-5659	254	13	,	,	PUNCT
ejpam-5659	254	14	and	and	CCONJ
ejpam-5659	254	15	w.	w.	NOUN
ejpam-5659	254	16	abdulraheem	abdulraheem	NOUN
ejpam-5659	254	17	.	.	PUNCT
ejpam-5659	255	1	man	man	NOUN
ejpam-5659	255	2	-	-	PUNCT
ejpam-5659	255	3	in	in	ADP
ejpam-5659	255	4	-	-	PUNCT
ejpam-5659	255	5	the	the	DET
ejpam-5659	255	6	middle	middle	ADJ
ejpam-5659	255	7	attack	attack	NOUN
ejpam-5659	255	8	detection	detection	NOUN
ejpam-5659	255	9	scheme	scheme	NOUN
ejpam-5659	255	10	on	on	ADP
ejpam-5659	255	11	data	datum	NOUN
ejpam-5659	255	12	aggregation	aggregation	NOUN
ejpam-5659	255	13	in	in	ADP
ejpam-5659	255	14	wireless	wireless	ADJ
ejpam-5659	255	15	sensor	sensor	NOUN
ejpam-5659	255	16	networks	network	NOUN
ejpam-5659	255	17	.	.	PUNCT
ejpam-5659	256	1	int	int	NOUN
ejpam-5659	256	2	.	.	PUNCT
ejpam-5659	257	1	j.	j.	PROPN
ejpam-5659	257	2	adv	adv	PROPN
ejpam-5659	257	3	.	.	PUNCT
ejpam-5659	257	4	soft	soft	ADJ
ejpam-5659	257	5	comput	comput	NOUN
ejpam-5659	257	6	.	.	PUNCT
ejpam-5659	258	1	its	its	PRON
ejpam-5659	258	2	appl	appl	NOUN
ejpam-5659	258	3	.	.	PROPN
ejpam-5659	258	4	,	,	PUNCT
ejpam-5659	258	5	15(2):179–193	15(2):179–193	NUM
ejpam-5659	258	6	,	,	PUNCT
ejpam-5659	258	7	2023	2023	NUM
ejpam-5659	258	8	.	.	PUNCT
ejpam-5659	259	1	[	[	X
ejpam-5659	259	2	11	11	NUM
ejpam-5659	259	3	]	]	PUNCT
ejpam-5659	259	4	t.	t.	PROPN
ejpam-5659	259	5	koroglu	koroglu	PROPN
ejpam-5659	259	6	and	and	CCONJ
ejpam-5659	259	7	r.	r.	PROPN
ejpam-5659	259	8	samet	samet	PROPN
ejpam-5659	259	9	.	.	PUNCT
ejpam-5659	260	1	can	can	AUX
ejpam-5659	260	2	there	there	PRON
ejpam-5659	260	3	be	be	AUX
ejpam-5659	260	4	a	a	DET
ejpam-5659	260	5	two	two	NUM
ejpam-5659	260	6	way	way	NOUN
ejpam-5659	260	7	hash	hash	NOUN
ejpam-5659	260	8	function	function	NOUN
ejpam-5659	260	9	?	?	PUNCT
ejpam-5659	261	1	ieee	ieee	NOUN
ejpam-5659	261	2	access	access	NOUN
ejpam-5659	261	3	,	,	PUNCT
ejpam-5659	261	4	12(january):18358–18386	12(january):18358–18386	NUM
ejpam-5659	261	5	,	,	PUNCT
ejpam-5659	261	6	2024	2024	NUM
ejpam-5659	261	7	.	.	PUNCT
ejpam-5659	262	1	w.	w.	PROPN
ejpam-5659	262	2	k.	k.	PROPN
ejpam-5659	262	3	abdulraheem	abdulraheem	PROPN
ejpam-5659	262	4	/	/	SYM
ejpam-5659	262	5	eur	eur	PROPN
ejpam-5659	262	6	.	.	PUNCT
ejpam-5659	263	1	j.	j.	PROPN
ejpam-5659	263	2	pure	pure	PROPN
ejpam-5659	263	3	appl	appl	PROPN
ejpam-5659	263	4	.	.	PROPN
ejpam-5659	263	5	math	math	PROPN
ejpam-5659	263	6	,	,	PUNCT
ejpam-5659	263	7	18	18	NUM
ejpam-5659	263	8	(	(	PUNCT
ejpam-5659	263	9	2	2	NUM
ejpam-5659	263	10	)	)	PUNCT
ejpam-5659	263	11	(	(	PUNCT
ejpam-5659	263	12	2025	2025	NUM
ejpam-5659	263	13	)	)	PUNCT
ejpam-5659	263	14	,	,	PUNCT
ejpam-5659	263	15	5659	5659	NUM
ejpam-5659	263	16	12	12	NUM
ejpam-5659	263	17	of	of	ADP
ejpam-5659	263	18	13	13	NUM
ejpam-5659	263	19	[	[	X
ejpam-5659	263	20	12	12	NUM
ejpam-5659	263	21	]	]	X
ejpam-5659	263	22	e.	e.	PROPN
ejpam-5659	263	23	barker	barker	PROPN
ejpam-5659	263	24	,	,	PUNCT
ejpam-5659	263	25	q.	q.	PROPN
ejpam-5659	263	26	dang	dang	PROPN
ejpam-5659	263	27	,	,	PUNCT
ejpam-5659	263	28	f.	f.	PROPN
ejpam-5659	263	29	sheila	sheila	PROPN
ejpam-5659	263	30	,	,	PUNCT
ejpam-5659	263	31	k.	k.	PROPN
ejpam-5659	263	32	scarfone	scarfone	PROPN
ejpam-5659	263	33	,	,	PUNCT
ejpam-5659	263	34	and	and	CCONJ
ejpam-5659	263	35	p.	p.	NOUN
ejpam-5659	263	36	wouters	wouter	NOUN
ejpam-5659	263	37	.	.	PUNCT
ejpam-5659	264	1	guide	guide	VERB
ejpam-5659	264	2	to	to	ADP
ejpam-5659	264	3	ipsec	ipsec	PROPN
ejpam-5659	264	4	vpns	vpns	NOUN
ejpam-5659	264	5	.	.	PUNCT
ejpam-5659	265	1	2020	2020	NUM
ejpam-5659	265	2	.	.	PUNCT
ejpam-5659	266	1	[	[	X
ejpam-5659	266	2	13	13	NUM
ejpam-5659	266	3	]	]	PUNCT
ejpam-5659	266	4	m.	m.	NOUN
ejpam-5659	266	5	al	al	PROPN
ejpam-5659	266	6	-	-	PUNCT
ejpam-5659	266	7	shalabi	shalabi	PROPN
ejpam-5659	266	8	,	,	PUNCT
ejpam-5659	266	9	j.	j.	PROPN
ejpam-5659	266	10	ababneh	ababneh	PROPN
ejpam-5659	266	11	,	,	PUNCT
ejpam-5659	266	12	and	and	CCONJ
ejpam-5659	266	13	w.	w.	NOUN
ejpam-5659	266	14	abdulraheem	abdulraheem	NOUN
ejpam-5659	266	15	.	.	PUNCT
ejpam-5659	267	1	a	a	DET
ejpam-5659	267	2	novel	novel	ADJ
ejpam-5659	267	3	adjacent	adjacent	ADJ
ejpam-5659	267	4	sensors	sensor	NOUN
ejpam-5659	267	5	-	-	PUNCT
ejpam-5659	267	6	based	base	VERB
ejpam-5659	267	7	mechanism	mechanism	NOUN
ejpam-5659	267	8	to	to	PART
ejpam-5659	267	9	increase	increase	VERB
ejpam-5659	267	10	performance	performance	NOUN
ejpam-5659	267	11	of	of	ADP
ejpam-5659	267	12	wireless	wireless	ADJ
ejpam-5659	267	13	sensor	sensor	NOUN
ejpam-5659	267	14	networks	network	NOUN
ejpam-5659	267	15	.	.	PUNCT
ejpam-5659	268	1	int	int	NOUN
ejpam-5659	268	2	.	.	PUNCT
ejpam-5659	269	1	j.	j.	PROPN
ejpam-5659	269	2	antennas	antennas	PROPN
ejpam-5659	269	3	propag	propag	PROPN
ejpam-5659	269	4	.	.	PUNCT
ejpam-5659	269	5	,	,	PUNCT
ejpam-5659	269	6	2021:1–9	2021:1–9	NUM
ejpam-5659	269	7	,	,	PUNCT
ejpam-5659	269	8	2021	2021	NUM
ejpam-5659	269	9	.	.	PUNCT
ejpam-5659	270	1	[	[	X
ejpam-5659	270	2	14	14	NUM
ejpam-5659	270	3	]	]	X
ejpam-5659	270	4	o.	o.	PROPN
ejpam-5659	270	5	a.	a.	PROPN
ejpam-5659	270	6	khashan	khashan	PROPN
ejpam-5659	270	7	,	,	PUNCT
ejpam-5659	270	8	n.	n.	PROPN
ejpam-5659	270	9	m.	m.	PROPN
ejpam-5659	270	10	khafajah	khafajah	PROPN
ejpam-5659	270	11	,	,	PUNCT
ejpam-5659	270	12	w.	w.	PROPN
ejpam-5659	270	13	alomoush	alomoush	PROPN
ejpam-5659	270	14	,	,	PUNCT
ejpam-5659	270	15	and	and	CCONJ
ejpam-5659	270	16	m.	m.	NOUN
ejpam-5659	270	17	alshinwan	alshinwan	PROPN
ejpam-5659	270	18	.	.	PUNCT
ejpam-5659	271	1	innovative	innovative	ADJ
ejpam-5659	271	2	energyefficient	energyefficient	NOUN
ejpam-5659	271	3	proxy	proxy	NOUN
ejpam-5659	271	4	re	re	NOUN
ejpam-5659	272	1	-	-	NOUN
ejpam-5659	273	1	encryption	encryption	NOUN
ejpam-5659	273	2	for	for	ADP
ejpam-5659	273	3	secure	secure	ADJ
ejpam-5659	273	4	data	datum	NOUN
ejpam-5659	273	5	exchange	exchange	NOUN
ejpam-5659	273	6	in	in	ADP
ejpam-5659	273	7	wireless	wireless	ADJ
ejpam-5659	273	8	sensor	sensor	NOUN
ejpam-5659	273	9	networks	network	NOUN
ejpam-5659	273	10	.	.	PUNCT
ejpam-5659	274	1	ieee	ieee	NOUN
ejpam-5659	274	2	access	access	NOUN
ejpam-5659	274	3	,	,	PUNCT
ejpam-5659	274	4	12(february):23290–23304	12(february):23290–23304	NUM
ejpam-5659	274	5	,	,	PUNCT
ejpam-5659	274	6	2024	2024	NUM
ejpam-5659	274	7	.	.	PUNCT
ejpam-5659	275	1	[	[	X
ejpam-5659	275	2	15	15	NUM
ejpam-5659	275	3	]	]	X
ejpam-5659	275	4	n.	n.	PROPN
ejpam-5659	275	5	a.	a.	PROPN
ejpam-5659	275	6	karim	karim	PROPN
ejpam-5659	275	7	,	,	PUNCT
ejpam-5659	275	8	h.	h.	PROPN
ejpam-5659	275	9	kanaker	kanaker	PROPN
ejpam-5659	275	10	,	,	PUNCT
ejpam-5659	275	11	w.	w.	PROPN
ejpam-5659	275	12	k.	k.	PROPN
ejpam-5659	275	13	abdulraheem	abdulraheem	PROPN
ejpam-5659	275	14	,	,	PUNCT
ejpam-5659	275	15	m.	m.	NOUN
ejpam-5659	275	16	a.	a.	PROPN
ejpam-5659	275	17	ghaith	ghaith	PROPN
ejpam-5659	275	18	,	,	PUNCT
ejpam-5659	275	19	e.	e.	PROPN
ejpam-5659	275	20	alhroob	alhroob	PROPN
ejpam-5659	275	21	,	,	PUNCT
ejpam-5659	275	22	and	and	CCONJ
ejpam-5659	275	23	a.	a.	PROPN
ejpam-5659	275	24	m.	m.	PROPN
ejpam-5659	275	25	f.	f.	PROPN
ejpam-5659	275	26	alali	alali	PROPN
ejpam-5659	275	27	.	.	PUNCT
ejpam-5659	276	1	choosing	choose	VERB
ejpam-5659	276	2	the	the	DET
ejpam-5659	276	3	right	right	NOUN
ejpam-5659	276	4	mfa	mfa	PROPN
ejpam-5659	276	5	method	method	PROPN
ejpam-5659	276	6	for	for	ADP
ejpam-5659	276	7	online	online	ADJ
ejpam-5659	276	8	systems	system	NOUN
ejpam-5659	276	9	:	:	PUNCT
ejpam-5659	276	10	a	a	DET
ejpam-5659	276	11	comparative	comparative	ADJ
ejpam-5659	276	12	analysis	analysis	NOUN
ejpam-5659	276	13	.	.	PUNCT
ejpam-5659	277	1	int	int	NOUN
ejpam-5659	277	2	.	.	PUNCT
ejpam-5659	278	1	j.	j.	PROPN
ejpam-5659	278	2	data	data	PROPN
ejpam-5659	278	3	netw	netw	PROPN
ejpam-5659	278	4	.	.	PUNCT
ejpam-5659	279	1	sci	sci	PROPN
ejpam-5659	279	2	.	.	PROPN
ejpam-5659	279	3	,	,	PUNCT
ejpam-5659	279	4	8(1):201–212	8(1):201–212	NUM
ejpam-5659	279	5	,	,	PUNCT
ejpam-5659	279	6	2024	2024	NUM
ejpam-5659	279	7	.	.	PUNCT
ejpam-5659	280	1	[	[	X
ejpam-5659	280	2	16	16	NUM
ejpam-5659	280	3	]	]	X
ejpam-5659	280	4	r.	r.	PROPN
ejpam-5659	280	5	nadaf	nadaf	PROPN
ejpam-5659	280	6	,	,	PUNCT
ejpam-5659	280	7	n.	n.	PROPN
ejpam-5659	280	8	b.	b.	PROPN
ejpam-5659	280	9	sumangala	sumangala	PROPN
ejpam-5659	280	10	,	,	PUNCT
ejpam-5659	280	11	m.	m.	NOUN
ejpam-5659	280	12	mandi	mandi	PROPN
ejpam-5659	280	13	,	,	PUNCT
ejpam-5659	280	14	and	and	CCONJ
ejpam-5659	280	15	a.	a.	NOUN
ejpam-5659	280	16	konnur	konnur	PROPN
ejpam-5659	280	17	.	.	PUNCT
ejpam-5659	281	1	symmetric	symmetric	ADJ
ejpam-5659	281	2	and	and	CCONJ
ejpam-5659	281	3	asymmetric	asymmetric	ADJ
ejpam-5659	281	4	cryptographic	cryptographic	ADJ
ejpam-5659	281	5	approach	approach	NOUN
ejpam-5659	281	6	based	base	VERB
ejpam-5659	281	7	security	security	NOUN
ejpam-5659	281	8	protocol	protocol	NOUN
ejpam-5659	281	9	for	for	ADP
ejpam-5659	281	10	key	key	ADJ
ejpam-5659	281	11	exchange	exchange	NOUN
ejpam-5659	281	12	.	.	PUNCT
ejpam-5659	282	1	pages	page	NOUN
ejpam-5659	282	2	1–6	1–6	NUM
ejpam-5659	282	3	,	,	PUNCT
ejpam-5659	282	4	2023	2023	NUM
ejpam-5659	282	5	.	.	PUNCT
ejpam-5659	283	1	[	[	X
ejpam-5659	283	2	17	17	NUM
ejpam-5659	283	3	]	]	X
ejpam-5659	283	4	w.	w.	PROPN
ejpam-5659	283	5	k.	k.	PROPN
ejpam-5659	283	6	a.	a.	PROPN
ejpam-5659	283	7	abdulrahem	abdulrahem	PROPN
ejpam-5659	283	8	,	,	PUNCT
ejpam-5659	283	9	h.	h.	PROPN
ejpam-5659	283	10	h.	h.	PROPN
ejpam-5659	283	11	o.	o.	PROPN
ejpam-5659	283	12	nasereddin	nasereddin	PROPN
ejpam-5659	283	13	,	,	PUNCT
ejpam-5659	283	14	and	and	CCONJ
ejpam-5659	283	15	s.	s.	PROPN
ejpam-5659	283	16	m.	m.	PROPN
ejpam-5659	283	17	h.	h.	PROPN
ejpam-5659	283	18	fares	fare	NOUN
ejpam-5659	283	19	.	.	PUNCT
ejpam-5659	284	1	business	business	NOUN
ejpam-5659	284	2	continuity	continuity	NOUN
ejpam-5659	284	3	based	base	VERB
ejpam-5659	284	4	on	on	ADP
ejpam-5659	284	5	rfid	rfid	NOUN
ejpam-5659	284	6	.	.	PUNCT
ejpam-5659	284	7	am	be	AUX
ejpam-5659	284	8	.	.	PUNCT
ejpam-5659	285	1	acad	acad	PROPN
ejpam-5659	285	2	.	.	PUNCT
ejpam-5659	286	1	sch	sch	PROPN
ejpam-5659	286	2	.	.	PUNCT
ejpam-5659	287	1	res	res	PROPN
ejpam-5659	287	2	.	.	PUNCT
ejpam-5659	288	1	j.	j.	PROPN
ejpam-5659	288	2	,	,	PUNCT
ejpam-5659	288	3	5(3):223–228	5(3):223–228	NUM
ejpam-5659	288	4	,	,	PUNCT
ejpam-5659	288	5	2013	2013	NUM
ejpam-5659	288	6	.	.	PUNCT
ejpam-5659	289	1	[	[	X
ejpam-5659	289	2	18	18	NUM
ejpam-5659	289	3	]	]	PUNCT
ejpam-5659	289	4	a.	a.	NOUN
ejpam-5659	289	5	h.	h.	PROPN
ejpam-5659	289	6	alwan	alwan	PROPN
ejpam-5659	289	7	.	.	PUNCT
ejpam-5659	290	1	novel	novel	ADJ
ejpam-5659	290	2	design	design	NOUN
ejpam-5659	290	3	of	of	ADP
ejpam-5659	290	4	radg	radg	NOUN
ejpam-5659	290	5	automata	automata	NOUN
ejpam-5659	290	6	in	in	ADP
ejpam-5659	290	7	crns	crn	NOUN
ejpam-5659	290	8	.	.	PUNCT
ejpam-5659	291	1	2016	2016	NUM
ejpam-5659	291	2	.	.	PUNCT
ejpam-5659	292	1	[	[	X
ejpam-5659	292	2	19	19	NUM
ejpam-5659	292	3	]	]	X
ejpam-5659	292	4	s.	s.	PROPN
ejpam-5659	292	5	smadi	smadi	PROPN
ejpam-5659	292	6	,	,	PUNCT
ejpam-5659	292	7	o.	o.	PROPN
ejpam-5659	292	8	almomani	almomani	PROPN
ejpam-5659	292	9	,	,	PUNCT
ejpam-5659	292	10	a.	a.	NOUN
ejpam-5659	292	11	mohammad	mohammad	PROPN
ejpam-5659	292	12	,	,	PUNCT
ejpam-5659	292	13	m.	m.	NOUN
ejpam-5659	292	14	alauthman	alauthman	PROPN
ejpam-5659	292	15	,	,	PUNCT
ejpam-5659	292	16	and	and	CCONJ
ejpam-5659	292	17	a.	a.	PROPN
ejpam-5659	292	18	saaidah	saaidah	PROPN
ejpam-5659	292	19	.	.	PUNCT
ejpam-5659	293	1	vpn	vpn	NOUN
ejpam-5659	293	2	encrypted	encrypt	VERB
ejpam-5659	293	3	traffic	traffic	NOUN
ejpam-5659	293	4	classification	classification	NOUN
ejpam-5659	293	5	using	use	VERB
ejpam-5659	293	6	xgboost	xgboost	X
ejpam-5659	293	7	.	.	PUNCT
ejpam-5659	294	1	int	int	NOUN
ejpam-5659	294	2	.	.	PUNCT
ejpam-5659	295	1	j.	j.	PROPN
ejpam-5659	295	2	emerg	emerg	PROPN
ejpam-5659	295	3	.	.	PUNCT
ejpam-5659	296	1	trends	trend	NOUN
ejpam-5659	297	1	eng	eng	PROPN
ejpam-5659	297	2	.	.	PUNCT
ejpam-5659	298	1	res	res	PROPN
ejpam-5659	298	2	.	.	PROPN
ejpam-5659	298	3	,	,	PUNCT
ejpam-5659	298	4	9(7):960	9(7):960	NUM
ejpam-5659	298	5	–	–	PUNCT
ejpam-5659	298	6	966	966	NUM
ejpam-5659	298	7	,	,	PUNCT
ejpam-5659	298	8	2021	2021	NUM
ejpam-5659	298	9	.	.	PUNCT
ejpam-5659	299	1	[	[	X
ejpam-5659	299	2	20	20	NUM
ejpam-5659	299	3	]	]	X
ejpam-5659	299	4	n.	n.	PROPN
ejpam-5659	299	5	a.	a.	PROPN
ejpam-5659	299	6	karim	karim	PROPN
ejpam-5659	299	7	,	,	PUNCT
ejpam-5659	299	8	o.	o.	PROPN
ejpam-5659	299	9	a.	a.	PROPN
ejpam-5659	299	10	khashan	khashan	PROPN
ejpam-5659	299	11	,	,	PUNCT
ejpam-5659	299	12	h.	h.	PROPN
ejpam-5659	299	13	kanaker	kanaker	PROPN
ejpam-5659	299	14	,	,	PUNCT
ejpam-5659	299	15	w.	w.	PROPN
ejpam-5659	299	16	k.	k.	PROPN
ejpam-5659	299	17	abdulraheem	abdulraheem	PROPN
ejpam-5659	299	18	,	,	PUNCT
ejpam-5659	299	19	m.	m.	NOUN
ejpam-5659	299	20	alshinwan	alshinwan	PROPN
ejpam-5659	299	21	,	,	PUNCT
ejpam-5659	299	22	and	and	CCONJ
ejpam-5659	299	23	a.	a.	NOUN
ejpam-5659	299	24	albanna	albanna	NOUN
ejpam-5659	299	25	.	.	PUNCT
ejpam-5659	300	1	online	online	ADJ
ejpam-5659	300	2	banking	banking	NOUN
ejpam-5659	300	3	user	user	NOUN
ejpam-5659	300	4	authentication	authentication	NOUN
ejpam-5659	300	5	methods	method	NOUN
ejpam-5659	300	6	:	:	PUNCT
ejpam-5659	300	7	a	a	DET
ejpam-5659	300	8	systematic	systematic	ADJ
ejpam-5659	300	9	literature	literature	NOUN
ejpam-5659	300	10	review	review	NOUN
ejpam-5659	300	11	.	.	PUNCT
ejpam-5659	301	1	ieee	ieee	NOUN
ejpam-5659	301	2	access	access	NOUN
ejpam-5659	301	3	,	,	PUNCT
ejpam-5659	301	4	12(november):741–757	12(november):741–757	NUM
ejpam-5659	301	5	,	,	PUNCT
ejpam-5659	301	6	2023	2023	NUM
ejpam-5659	301	7	.	.	PUNCT
ejpam-5659	302	1	[	[	X
ejpam-5659	302	2	21	21	NUM
ejpam-5659	302	3	]	]	X
ejpam-5659	302	4	c.	c.	PROPN
ejpam-5659	302	5	a.	a.	PROPN
ejpam-5659	302	6	lara	lara	PROPN
ejpam-5659	302	7	-	-	PUNCT
ejpam-5659	302	8	nino	nino	PROPN
ejpam-5659	302	9	,	,	PUNCT
ejpam-5659	302	10	a.	a.	PROPN
ejpam-5659	302	11	diaz	diaz	PROPN
ejpam-5659	302	12	-	-	PUNCT
ejpam-5659	302	13	perez	perez	PROPN
ejpam-5659	302	14	,	,	PUNCT
ejpam-5659	302	15	and	and	CCONJ
ejpam-5659	302	16	m.	m.	NOUN
ejpam-5659	302	17	morales	morales	PROPN
ejpam-5659	302	18	-	-	PUNCT
ejpam-5659	302	19	sandoval	sandoval	PROPN
ejpam-5659	302	20	.	.	PUNCT
ejpam-5659	303	1	elliptic	elliptic	ADJ
ejpam-5659	303	2	curve	curve	NOUN
ejpam-5659	303	3	lightweight	lightweight	ADJ
ejpam-5659	303	4	cryptography	cryptography	NOUN
ejpam-5659	303	5	:	:	PUNCT
ejpam-5659	303	6	a	a	DET
ejpam-5659	303	7	survey	survey	NOUN
ejpam-5659	303	8	.	.	PUNCT
ejpam-5659	304	1	ieee	ieee	NOUN
ejpam-5659	304	2	access	access	NOUN
ejpam-5659	304	3	,	,	PUNCT
ejpam-5659	304	4	6(november):72514–72550	6(november):72514–72550	NUM
ejpam-5659	304	5	,	,	PUNCT
ejpam-5659	304	6	2018	2018	NUM
ejpam-5659	304	7	.	.	PUNCT
ejpam-5659	305	1	[	[	X
ejpam-5659	305	2	22	22	NUM
ejpam-5659	305	3	]	]	PUNCT
ejpam-5659	305	4	s.	s.	PROPN
ejpam-5659	305	5	yasin	yasin	PROPN
ejpam-5659	305	6	and	and	CCONJ
ejpam-5659	305	7	z.	z.	PROPN
ejpam-5659	305	8	muda	muda	PROPN
ejpam-5659	305	9	.	.	PUNCT
ejpam-5659	305	10	tripling	triple	VERB
ejpam-5659	305	11	formulae	formulae	NOUN
ejpam-5659	305	12	of	of	ADP
ejpam-5659	305	13	elliptic	elliptic	ADJ
ejpam-5659	305	14	curve	curve	NOUN
ejpam-5659	305	15	over	over	ADP
ejpam-5659	305	16	binary	binary	ADJ
ejpam-5659	305	17	field	field	NOUN
ejpam-5659	305	18	in	in	ADP
ejpam-5659	305	19	lopezdahab	lopezdahab	PROPN
ejpam-5659	305	20	model	model	NOUN
ejpam-5659	305	21	.	.	PUNCT
ejpam-5659	306	1	j.	j.	PROPN
ejpam-5659	306	2	theor	theor	PROPN
ejpam-5659	306	3	.	.	PUNCT
ejpam-5659	307	1	appl	appl	PROPN
ejpam-5659	307	2	.	.	PROPN
ejpam-5659	307	3	inf	inf	PROPN
ejpam-5659	307	4	.	.	PUNCT
ejpam-5659	307	5	technol	technol	PROPN
ejpam-5659	307	6	.	.	PROPN
ejpam-5659	307	7	,	,	PUNCT
ejpam-5659	307	8	75(2):212–216	75(2):212–216	PROPN
ejpam-5659	307	9	,	,	PUNCT
ejpam-5659	307	10	2015	2015	NUM
ejpam-5659	307	11	.	.	PUNCT
ejpam-5659	308	1	[	[	X
ejpam-5659	308	2	23	23	NUM
ejpam-5659	308	3	]	]	PUNCT
ejpam-5659	308	4	w.	w.	PROPN
ejpam-5659	308	5	k.	k.	PROPN
ejpam-5659	308	6	abdulraheem	abdulraheem	PROPN
ejpam-5659	308	7	,	,	PUNCT
ejpam-5659	308	8	s.	s.	PROPN
ejpam-5659	308	9	b.	b.	PROPN
ejpam-5659	308	10	m.	m.	PROPN
ejpam-5659	308	11	yasin	yasin	PROPN
ejpam-5659	308	12	,	,	PUNCT
ejpam-5659	308	13	n.	n.	PROPN
ejpam-5659	308	14	i.	i.	PROPN
ejpam-5659	308	15	b.	b.	PROPN
ejpam-5659	308	16	udzir	udzir	PROPN
ejpam-5659	308	17	,	,	PUNCT
ejpam-5659	308	18	and	and	CCONJ
ejpam-5659	308	19	m.	m.	PROPN
ejpam-5659	308	20	r.	r.	PROPN
ejpam-5659	308	21	b.	b.	PROPN
ejpam-5659	308	22	k.	k.	PROPN
ejpam-5659	308	23	ariffin	ariffin	PROPN
ejpam-5659	308	24	.	.	PUNCT
ejpam-5659	309	1	new	new	ADJ
ejpam-5659	309	2	quintupling	quintupling	NOUN
ejpam-5659	309	3	point	point	NOUN
ejpam-5659	309	4	arithmetic	arithmetic	ADJ
ejpam-5659	309	5	5p	5p	NUM
ejpam-5659	309	6	formulas	formula	NOUN
ejpam-5659	309	7	for	for	ADP
ejpam-5659	309	8	lǒpez	lǒpez	NOUN
ejpam-5659	309	9	-	-	PUNCT
ejpam-5659	309	10	dahab	dahab	PROPN
ejpam-5659	309	11	coordinate	coordinate	NOUN
ejpam-5659	309	12	over	over	ADP
ejpam-5659	309	13	binary	binary	ADJ
ejpam-5659	309	14	elliptic	elliptic	ADJ
ejpam-5659	309	15	curve	curve	NOUN
ejpam-5659	309	16	cryptography	cryptography	NOUN
ejpam-5659	309	17	.	.	PUNCT
ejpam-5659	310	1	int	int	NOUN
ejpam-5659	310	2	.	.	PUNCT
ejpam-5659	311	1	j.	j.	PROPN
ejpam-5659	311	2	adv	adv	PROPN
ejpam-5659	311	3	.	.	PUNCT
ejpam-5659	312	1	comput	comput	PROPN
ejpam-5659	312	2	.	.	PUNCT
ejpam-5659	313	1	sci	sci	PROPN
ejpam-5659	313	2	.	.	PUNCT
ejpam-5659	313	3	appl	appl	PROPN
ejpam-5659	313	4	.	.	PROPN
ejpam-5659	313	5	,	,	PUNCT
ejpam-5659	313	6	10(7):397–401	10(7):397–401	PROPN
ejpam-5659	313	7	,	,	PUNCT
ejpam-5659	313	8	2019	2019	NUM
ejpam-5659	313	9	.	.	PUNCT
ejpam-5659	314	1	[	[	X
ejpam-5659	314	2	24	24	NUM
ejpam-5659	314	3	]	]	PUNCT
ejpam-5659	314	4	s.	s.	PROPN
ejpam-5659	314	5	liu	liu	PROPN
ejpam-5659	314	6	and	and	CCONJ
ejpam-5659	314	7	l.	l.	PROPN
ejpam-5659	314	8	zhang	zhang	PROPN
ejpam-5659	314	9	.	.	PUNCT
ejpam-5659	315	1	efficient	efficient	PROPN
ejpam-5659	315	2	septuple	septuple	PROPN
ejpam-5659	315	3	formula	formula	NOUN
ejpam-5659	315	4	for	for	ADP
ejpam-5659	315	5	elliptic	elliptic	ADJ
ejpam-5659	315	6	curve	curve	NOUN
ejpam-5659	315	7	and	and	CCONJ
ejpam-5659	315	8	efficient	efficient	ADJ
ejpam-5659	315	9	scalar	scalar	ADJ
ejpam-5659	315	10	multiplication	multiplication	NOUN
ejpam-5659	315	11	using	use	VERB
ejpam-5659	315	12	a	a	DET
ejpam-5659	315	13	triple	triple	ADJ
ejpam-5659	315	14	-	-	PUNCT
ejpam-5659	315	15	base	base	NOUN
ejpam-5659	315	16	chain	chain	NOUN
ejpam-5659	315	17	representation	representation	NOUN
ejpam-5659	315	18	.	.	PUNCT
ejpam-5659	316	1	ieee	ieee	NOUN
ejpam-5659	316	2	access	access	NOUN
ejpam-5659	316	3	,	,	PUNCT
ejpam-5659	316	4	9(4):129512	9(4):129512	NUM
ejpam-5659	316	5	–	–	PUNCT
ejpam-5659	316	6	129520	129520	NUM
ejpam-5659	316	7	,	,	PUNCT
ejpam-5659	316	8	2021	2021	NUM
ejpam-5659	316	9	.	.	PUNCT
ejpam-5659	317	1	[	[	X
ejpam-5659	317	2	25	25	NUM
ejpam-5659	317	3	]	]	X
ejpam-5659	317	4	g.	g.	PROPN
ejpam-5659	317	5	n.	n.	PROPN
ejpam-5659	317	6	purohit	purohit	PROPN
ejpam-5659	317	7	and	and	CCONJ
ejpam-5659	317	8	a.	a.	PROPN
ejpam-5659	317	9	singh	singh	PROPN
ejpam-5659	317	10	rawat	rawat	PROPN
ejpam-5659	317	11	.	.	PUNCT
ejpam-5659	318	1	fast	fast	ADJ
ejpam-5659	318	2	scalar	scalar	ADJ
ejpam-5659	318	3	multiplication	multiplication	NOUN
ejpam-5659	318	4	in	in	ADP
ejpam-5659	318	5	ecc	ecc	PROPN
ejpam-5659	318	6	using	use	VERB
ejpam-5659	318	7	the	the	DET
ejpam-5659	318	8	multi	multi	ADJ
ejpam-5659	318	9	base	base	NOUN
ejpam-5659	318	10	number	number	NOUN
ejpam-5659	318	11	system	system	NOUN
ejpam-5659	318	12	.	.	PUNCT
ejpam-5659	319	1	ijcsi	ijcsi	NOUN
ejpam-5659	319	2	int	int	NOUN
ejpam-5659	319	3	.	.	PUNCT
ejpam-5659	320	1	j.	j.	PROPN
ejpam-5659	320	2	comput	comput	PROPN
ejpam-5659	320	3	.	.	PUNCT
ejpam-5659	321	1	sci	sci	PROPN
ejpam-5659	321	2	.	.	PUNCT
ejpam-5659	321	3	issues	issue	NOUN
ejpam-5659	321	4	,	,	PUNCT
ejpam-5659	321	5	8(1):1–11	8(1):1–11	ADP
ejpam-5659	321	6	,	,	PUNCT
ejpam-5659	321	7	2011	2011	NUM
ejpam-5659	321	8	.	.	PUNCT
ejpam-5659	322	1	[	[	X
ejpam-5659	322	2	26	26	NUM
ejpam-5659	322	3	]	]	PUNCT
ejpam-5659	322	4	z.	z.	PROPN
ejpam-5659	322	5	lai	lai	PROPN
ejpam-5659	322	6	,	,	PUNCT
ejpam-5659	322	7	z.	z.	PROPN
ejpam-5659	322	8	zhang	zhang	PROPN
ejpam-5659	322	9	,	,	PUNCT
ejpam-5659	322	10	and	and	CCONJ
ejpam-5659	322	11	d.	d.	PROPN
ejpam-5659	322	12	tao	tao	PROPN
ejpam-5659	322	13	.	.	PUNCT
ejpam-5659	323	1	algorithm	algorithm	PROPN
ejpam-5659	323	2	for	for	ADP
ejpam-5659	323	3	directly	directly	ADV
ejpam-5659	323	4	computing	compute	VERB
ejpam-5659	323	5	7p	7p	NOUN
ejpam-5659	323	6	elliptic	elliptic	ADJ
ejpam-5659	323	7	curves	curve	NOUN
ejpam-5659	323	8	and	and	CCONJ
ejpam-5659	323	9	its	its	PRON
ejpam-5659	323	10	application	application	NOUN
ejpam-5659	323	11	.	.	PUNCT
ejpam-5659	324	1	j.	j.	PROPN
ejpam-5659	324	2	comput	comput	PROPN
ejpam-5659	324	3	.	.	PUNCT
ejpam-5659	325	1	appl	appl	PROPN
ejpam-5659	325	2	.	.	PROPN
ejpam-5659	325	3	,	,	PUNCT
ejpam-5659	325	4	33(7):1870–1874	33(7):1870–1874	NUM
ejpam-5659	325	5	,	,	PUNCT
ejpam-5659	325	6	2013	2013	NUM
ejpam-5659	325	7	.	.	PUNCT
ejpam-5659	326	1	[	[	X
ejpam-5659	326	2	27	27	NUM
ejpam-5659	326	3	]	]	X
ejpam-5659	326	4	m.	m.	NOUN
ejpam-5659	326	5	rasmi	rasmi	PROPN
ejpam-5659	326	6	,	,	PUNCT
ejpam-5659	326	7	h.	h.	PROPN
ejpam-5659	326	8	mimi	mimi	PROPN
ejpam-5659	326	9	,	,	PUNCT
ejpam-5659	326	10	and	and	CCONJ
ejpam-5659	326	11	m.	m.	PROPN
ejpam-5659	326	12	s.	s.	PROPN
ejpam-5659	326	13	daoud	daoud	PROPN
ejpam-5659	326	14	.	.	PUNCT
ejpam-5659	326	15	evaluating	evaluate	VERB
ejpam-5659	326	16	composite	composite	ADJ
ejpam-5659	326	17	ec	ec	PROPN
ejpam-5659	326	18	operations	operation	NOUN
ejpam-5659	326	19	and	and	CCONJ
ejpam-5659	326	20	their	their	PRON
ejpam-5659	326	21	applicability	applicability	NOUN
ejpam-5659	326	22	to	to	ADP
ejpam-5659	326	23	the	the	DET
ejpam-5659	326	24	on	on	ADP
ejpam-5659	326	25	-	-	PUNCT
ejpam-5659	326	26	the	the	DET
ejpam-5659	326	27	-	-	PUNCT
ejpam-5659	326	28	fly	fly	NOUN
ejpam-5659	326	29	and	and	CCONJ
ejpam-5659	326	30	non	non	ADJ
ejpam-5659	326	31	-	-	ADJ
ejpam-5659	326	32	window	window	ADJ
ejpam-5659	326	33	multiplication	multiplication	NOUN
ejpam-5659	326	34	methods	method	NOUN
ejpam-5659	326	35	.	.	PUNCT
ejpam-5659	327	1	int	int	NOUN
ejpam-5659	327	2	.	.	PUNCT
ejpam-5659	328	1	j.	j.	PROPN
ejpam-5659	328	2	comput	comput	PROPN
ejpam-5659	328	3	.	.	PUNCT
ejpam-5659	329	1	appl	appl	PROPN
ejpam-5659	329	2	.	.	PROPN
ejpam-5659	329	3	,	,	PUNCT
ejpam-5659	329	4	105(6):19–26	105(6):19–26	NUM
ejpam-5659	329	5	,	,	PUNCT
ejpam-5659	329	6	2014	2014	NUM
ejpam-5659	329	7	.	.	PUNCT
ejpam-5659	330	1	[	[	X
ejpam-5659	330	2	28	28	NUM
ejpam-5659	330	3	]	]	X
ejpam-5659	330	4	p.	p.	NOUN
ejpam-5659	330	5	longa	longa	NOUN
ejpam-5659	330	6	and	and	CCONJ
ejpam-5659	330	7	c.	c.	PROPN
ejpam-5659	330	8	gebotys	gebotys	PROPN
ejpam-5659	330	9	.	.	PUNCT
ejpam-5659	331	1	fast	fast	ADJ
ejpam-5659	331	2	multibase	multibase	ADJ
ejpam-5659	331	3	methods	method	NOUN
ejpam-5659	331	4	and	and	CCONJ
ejpam-5659	331	5	other	other	ADJ
ejpam-5659	331	6	several	several	ADJ
ejpam-5659	331	7	optimizations	optimization	NOUN
ejpam-5659	331	8	for	for	ADP
ejpam-5659	331	9	elliptic	elliptic	ADJ
ejpam-5659	331	10	curve	curve	NOUN
ejpam-5659	331	11	scalar	scalar	ADJ
ejpam-5659	331	12	multiplication	multiplication	NOUN
ejpam-5659	331	13	.	.	PUNCT
ejpam-5659	332	1	5443:443–462	5443:443–462	ADJ
ejpam-5659	332	2	,	,	PUNCT
ejpam-5659	332	3	2019	2019	NUM
ejpam-5659	332	4	.	.	PUNCT
ejpam-5659	333	1	[	[	X
ejpam-5659	333	2	29	29	NUM
ejpam-5659	333	3	]	]	SYM
ejpam-5659	333	4	nist	nist	NOUN
ejpam-5659	333	5	.	.	PUNCT
ejpam-5659	334	1	digital	digital	ADJ
ejpam-5659	334	2	signature	signature	NOUN
ejpam-5659	334	3	standard	standard	NOUN
ejpam-5659	334	4	(	(	PUNCT
ejpam-5659	334	5	dss	dss	NOUN
ejpam-5659	334	6	)	)	PUNCT
ejpam-5659	334	7	.	.	PUNCT
ejpam-5659	335	1	2013	2013	NUM
ejpam-5659	335	2	.	.	PUNCT
ejpam-5659	336	1	[	[	X
ejpam-5659	336	2	30	30	NUM
ejpam-5659	336	3	]	]	X
ejpam-5659	336	4	b.	b.	PROPN
ejpam-5659	336	5	rashidi	rashidi	PROPN
ejpam-5659	336	6	.	.	PUNCT
ejpam-5659	337	1	a	a	DET
ejpam-5659	337	2	survey	survey	NOUN
ejpam-5659	337	3	on	on	ADP
ejpam-5659	337	4	hardware	hardware	NOUN
ejpam-5659	337	5	implementations	implementation	NOUN
ejpam-5659	337	6	of	of	ADP
ejpam-5659	337	7	elliptic	elliptic	ADJ
ejpam-5659	337	8	curve	curve	NOUN
ejpam-5659	337	9	cryptosystems	cryptosystem	NOUN
ejpam-5659	337	10	.	.	PUNCT
ejpam-5659	338	1	w.	w.	PROPN
ejpam-5659	338	2	k.	k.	PROPN
ejpam-5659	338	3	abdulraheem	abdulraheem	PROPN
ejpam-5659	338	4	/	/	SYM
ejpam-5659	338	5	eur	eur	PROPN
ejpam-5659	338	6	.	.	PUNCT
ejpam-5659	339	1	j.	j.	PROPN
ejpam-5659	339	2	pure	pure	PROPN
ejpam-5659	339	3	appl	appl	PROPN
ejpam-5659	339	4	.	.	PROPN
ejpam-5659	339	5	math	math	PROPN
ejpam-5659	339	6	,	,	PUNCT
ejpam-5659	339	7	18	18	NUM
ejpam-5659	339	8	(	(	PUNCT
ejpam-5659	339	9	2	2	NUM
ejpam-5659	339	10	)	)	PUNCT
ejpam-5659	339	11	(	(	PUNCT
ejpam-5659	339	12	2025	2025	NUM
ejpam-5659	339	13	)	)	PUNCT
ejpam-5659	339	14	,	,	PUNCT
ejpam-5659	339	15	5659	5659	NUM
ejpam-5659	339	16	13	13	NUM
ejpam-5659	339	17	of	of	ADP
ejpam-5659	339	18	13	13	NUM
ejpam-5659	339	19	arxiv	arxiv	PROPN
ejpam-5659	339	20	prepr	prepr	NOUN
ejpam-5659	339	21	.	.	PUNCT
ejpam-5659	340	1	arxiv1710.08336	arxiv1710.08336	PROPN
ejpam-5659	340	2	,	,	PUNCT
ejpam-5659	340	3	2017	2017	NUM
ejpam-5659	340	4	.	.	PUNCT
ejpam-5659	341	1	[	[	X
ejpam-5659	341	2	31	31	NUM
ejpam-5659	341	3	]	]	PUNCT
ejpam-5659	341	4	z.	z.	PROPN
ejpam-5659	341	5	razali	razali	PROPN
ejpam-5659	341	6	,	,	PUNCT
ejpam-5659	341	7	n.	n.	PROPN
ejpam-5659	341	8	muslim	muslim	PROPN
ejpam-5659	341	9	,	,	PUNCT
ejpam-5659	341	10	s.	s.	PROPN
ejpam-5659	341	11	kahar	kahar	PROPN
ejpam-5659	341	12	,	,	PUNCT
ejpam-5659	341	13	and	and	CCONJ
ejpam-5659	341	14	f.	f.	PROPN
ejpam-5659	341	15	yunos	yunos	PROPN
ejpam-5659	341	16	.	.	PUNCT
ejpam-5659	342	1	implementation	implementation	NOUN
ejpam-5659	342	2	of	of	ADP
ejpam-5659	342	3	quintupling	quintuple	VERB
ejpam-5659	342	4	formula	formula	NOUN
ejpam-5659	342	5	in	in	ADP
ejpam-5659	342	6	q	q	PROPN
ejpam-5659	342	7	-	-	PUNCT
ejpam-5659	342	8	naf	naf	PROPN
ejpam-5659	342	9	.	.	PUNCT
ejpam-5659	342	10	neuroquantology	neuroquantology	NOUN
ejpam-5659	342	11	,	,	PUNCT
ejpam-5659	342	12	20(8):1339–1344	20(8):1339–1344	NUM
ejpam-5659	342	13	,	,	PUNCT
ejpam-5659	342	14	2022	2022	NUM
ejpam-5659	342	15	.	.	PUNCT
ejpam-5659	343	1	[	[	X
ejpam-5659	343	2	32	32	NUM
ejpam-5659	343	3	]	]	PUNCT
ejpam-5659	343	4	t.	t.	PROPN
ejpam-5659	343	5	pornin	pornin	PROPN
ejpam-5659	343	6	.	.	PUNCT
ejpam-5659	344	1	efficient	efficient	ADJ
ejpam-5659	344	2	and	and	CCONJ
ejpam-5659	344	3	complete	complete	ADJ
ejpam-5659	344	4	formulas	formula	NOUN
ejpam-5659	344	5	for	for	ADP
ejpam-5659	344	6	binary	binary	ADJ
ejpam-5659	344	7	curves	curve	NOUN
ejpam-5659	344	8	.	.	PUNCT
ejpam-5659	345	1	cryptol	cryptol	NOUN
ejpam-5659	345	2	.	.	PUNCT
ejpam-5659	346	1	eprint	eprint	NOUN
ejpam-5659	346	2	arch	arch	PROPN
ejpam-5659	346	3	.	.	PUNCT
ejpam-5659	346	4	,	,	PUNCT
ejpam-5659	346	5	9(4):1–29	9(4):1–29	NUM
ejpam-5659	346	6	,	,	PUNCT
ejpam-5659	346	7	2022	2022	NUM
ejpam-5659	346	8	.	.	PUNCT
ejpam-5659	347	1	[	[	X
ejpam-5659	347	2	33	33	NUM
ejpam-5659	347	3	]	]	PUNCT
ejpam-5659	347	4	z.	z.	PROPN
ejpam-5659	347	5	razali	razali	PROPN
ejpam-5659	347	6	,	,	PUNCT
ejpam-5659	347	7	n.	n.	PROPN
ejpam-5659	347	8	muslim	muslim	PROPN
ejpam-5659	347	9	,	,	PUNCT
ejpam-5659	347	10	s.	s.	PROPN
ejpam-5659	347	11	kahar	kahar	PROPN
ejpam-5659	347	12	,	,	PUNCT
ejpam-5659	347	13	f.	f.	PROPN
ejpam-5659	347	14	yunos	yunos	PROPN
ejpam-5659	347	15	,	,	PUNCT
ejpam-5659	347	16	and	and	CCONJ
ejpam-5659	347	17	k.	k.	PROPN
ejpam-5659	347	18	mohamed	mohamed	PROPN
ejpam-5659	347	19	.	.	PROPN
ejpam-5659	348	1	improved	improve	VERB
ejpam-5659	348	2	point	point	NOUN
ejpam-5659	348	3	5p	5p	NUM
ejpam-5659	348	4	formula	formula	NOUN
ejpam-5659	348	5	for	for	ADP
ejpam-5659	348	6	twisted	twisted	ADJ
ejpam-5659	348	7	edwards	edwards	PROPN
ejpam-5659	348	8	curve	curve	PROPN
ejpam-5659	348	9	in	in	ADP
ejpam-5659	348	10	projective	projective	ADJ
ejpam-5659	348	11	coordinate	coordinate	NOUN
ejpam-5659	348	12	over	over	ADP
ejpam-5659	348	13	prime	prime	ADJ
ejpam-5659	348	14	field	field	NOUN
ejpam-5659	348	15	.	.	PUNCT
ejpam-5659	349	1	pages	page	NOUN
ejpam-5659	349	2	498–502	498–502	NUM
ejpam-5659	349	3	,	,	PUNCT
ejpam-5659	349	4	2022	2022	NUM
ejpam-5659	349	5	.	.	PUNCT
ejpam-5659	350	1	[	[	X
ejpam-5659	350	2	34	34	NUM
ejpam-5659	350	3	]	]	X
ejpam-5659	350	4	s.	s.	PROPN
ejpam-5659	350	5	chowdhury	chowdhury	PROPN
ejpam-5659	350	6	,	,	PUNCT
ejpam-5659	350	7	d.	d.	PROPN
ejpam-5659	350	8	b.	b.	PROPN
ejpam-5659	350	9	roy	roy	PROPN
ejpam-5659	350	10	,	,	PUNCT
ejpam-5659	350	11	and	and	CCONJ
ejpam-5659	350	12	d.	d.	PROPN
ejpam-5659	350	13	mukhopadhyay	mukhopadhyay	PROPN
ejpam-5659	350	14	.	.	PUNCT
ejpam-5659	351	1	a	a	DET
ejpam-5659	351	2	minimalistic	minimalistic	ADJ
ejpam-5659	351	3	perspective	perspective	NOUN
ejpam-5659	351	4	on	on	ADP
ejpam-5659	351	5	koblitz	koblitz	ADJ
ejpam-5659	351	6	curve	curve	VERB
ejpam-5659	351	7	scalar	scalar	ADJ
ejpam-5659	351	8	multiplication	multiplication	NOUN
ejpam-5659	351	9	for	for	ADP
ejpam-5659	351	10	fpga	fpga	PROPN
ejpam-5659	351	11	platforms	platform	NOUN
ejpam-5659	351	12	.	.	PUNCT
ejpam-5659	352	1	2020	2020	NUM
ejpam-5659	352	2	-	-	SYM
ejpam-5659	352	3	octob:70–75	octob:70–75	ADJ
ejpam-5659	352	4	,	,	PUNCT
ejpam-5659	352	5	2020	2020	NUM
ejpam-5659	352	6	.	.	PUNCT
ejpam-5659	353	1	[	[	X
ejpam-5659	353	2	35	35	NUM
ejpam-5659	353	3	]	]	PUNCT
ejpam-5659	354	1	p.	p.	PROPN
ejpam-5659	354	2	k.	k.	PROPN
ejpam-5659	354	3	vishnubhai	vishnubhai	PROPN
ejpam-5659	354	4	.	.	PUNCT
ejpam-5659	355	1	design	design	NOUN
ejpam-5659	355	2	and	and	CCONJ
ejpam-5659	355	3	implementation	implementation	NOUN
ejpam-5659	355	4	of	of	ADP
ejpam-5659	355	5	efficient	efficient	ADJ
ejpam-5659	355	6	elliptic	elliptic	ADJ
ejpam-5659	355	7	curve	curve	NOUN
ejpam-5659	355	8	cryptography	cryptography	NOUN
ejpam-5659	355	9	on	on	ADP
ejpam-5659	355	10	reconfigurable	reconfigurable	ADJ
ejpam-5659	355	11	platforms	platform	NOUN
ejpam-5659	355	12	.	.	PUNCT
ejpam-5659	356	1	2023	2023	NUM
ejpam-5659	356	2	.	.	PUNCT
ejpam-5659	357	1	[	[	X
ejpam-5659	357	2	36	36	NUM
ejpam-5659	357	3	]	]	X
ejpam-5659	357	4	r.	r.	PROPN
ejpam-5659	357	5	lópez	lópez	PROPN
ejpam-5659	357	6	and	and	CCONJ
ejpam-5659	357	7	j.	j.	PROPN
ejpam-5659	357	8	dahab	dahab	PROPN
ejpam-5659	357	9	.	.	PUNCT
ejpam-5659	358	1	improved	improve	VERB
ejpam-5659	358	2	algorithms	algorithm	NOUN
ejpam-5659	358	3	for	for	ADP
ejpam-5659	358	4	elliptic	elliptic	ADJ
ejpam-5659	358	5	curve	curve	NOUN
ejpam-5659	358	6	arithmetic	arithmetic	ADJ
ejpam-5659	358	7	in	in	ADP
ejpam-5659	358	8	gf(2n	gf(2n	NOUN
ejpam-5659	358	9	)	)	PUNCT
ejpam-5659	358	10	.	.	PUNCT
ejpam-5659	359	1	97(107):201–212	97(107):201–212	PROPN
ejpam-5659	359	2	,	,	PUNCT
ejpam-5659	359	3	1999	1999	NUM
ejpam-5659	359	4	.	.	PUNCT
ejpam-5659	360	1	[	[	X
ejpam-5659	360	2	37	37	NUM
ejpam-5659	360	3	]	]	PUNCT
ejpam-5659	360	4	a.	a.	NOUN
ejpam-5659	360	5	higuchi	higuchi	PROPN
ejpam-5659	360	6	and	and	CCONJ
ejpam-5659	360	7	n.	n.	PROPN
ejpam-5659	360	8	takagi	takagi	PROPN
ejpam-5659	360	9	.	.	PUNCT
ejpam-5659	361	1	fast	fast	ADJ
ejpam-5659	361	2	addition	addition	NOUN
ejpam-5659	361	3	algorithm	algorithm	NOUN
ejpam-5659	361	4	for	for	ADP
ejpam-5659	361	5	elliptic	elliptic	ADJ
ejpam-5659	361	6	curve	curve	NOUN
ejpam-5659	361	7	arithmetic	arithmetic	ADJ
ejpam-5659	361	8	in	in	ADP
ejpam-5659	361	9	gf(2n	gf(2n	NOUN
ejpam-5659	361	10	)	)	PUNCT
ejpam-5659	361	11	using	use	VERB
ejpam-5659	361	12	projective	projective	ADJ
ejpam-5659	361	13	coordinates	coordinate	NOUN
ejpam-5659	361	14	.	.	PUNCT
ejpam-5659	362	1	inf	inf	PROPN
ejpam-5659	362	2	.	.	PUNCT
ejpam-5659	362	3	process	process	NOUN
ejpam-5659	362	4	.	.	PUNCT
ejpam-5659	363	1	lett	lett	PROPN
ejpam-5659	363	2	.	.	PROPN
ejpam-5659	363	3	,	,	PUNCT
ejpam-5659	363	4	76(3):101–103	76(3):101–103	PROPN
ejpam-5659	363	5	,	,	PUNCT
ejpam-5659	363	6	2000	2000	NUM
ejpam-5659	363	7	.	.	PUNCT
ejpam-5659	364	1	[	[	X
ejpam-5659	364	2	38	38	NUM
ejpam-5659	364	3	]	]	PUNCT
ejpam-5659	364	4	e.	e.	PROPN
ejpam-5659	364	5	al	al	PROPN
ejpam-5659	364	6	-	-	PUNCT
ejpam-5659	364	7	daoud	daoud	PROPN
ejpam-5659	364	8	,	,	PUNCT
ejpam-5659	364	9	r.	r.	PROPN
ejpam-5659	364	10	mahmod	mahmod	PROPN
ejpam-5659	364	11	,	,	PUNCT
ejpam-5659	364	12	m.	m.	NOUN
ejpam-5659	364	13	rushdan	rushdan	PROPN
ejpam-5659	364	14	,	,	PUNCT
ejpam-5659	364	15	and	and	CCONJ
ejpam-5659	364	16	a.	a.	NOUN
ejpam-5659	364	17	kilicman	kilicman	NOUN
ejpam-5659	364	18	.	.	PUNCT
ejpam-5659	365	1	a	a	DET
ejpam-5659	365	2	new	new	ADJ
ejpam-5659	365	3	addition	addition	NOUN
ejpam-5659	365	4	formula	formula	NOUN
ejpam-5659	365	5	for	for	ADP
ejpam-5659	365	6	elliptic	elliptic	ADJ
ejpam-5659	365	7	curves	curve	NOUN
ejpam-5659	365	8	over	over	ADP
ejpam-5659	365	9	gf(2n	gf(2n	NOUN
ejpam-5659	365	10	)	)	PUNCT
ejpam-5659	365	11	.	.	PUNCT
ejpam-5659	366	1	ieee	ieee	PROPN
ejpam-5659	366	2	trans	trans	PROPN
ejpam-5659	366	3	.	.	PUNCT
ejpam-5659	367	1	comput	comput	PROPN
ejpam-5659	367	2	.	.	PUNCT
ejpam-5659	367	3	,	,	PUNCT
ejpam-5659	367	4	51(8):972–975	51(8):972–975	NUM
ejpam-5659	367	5	,	,	PUNCT
ejpam-5659	367	6	2002	2002	NUM
ejpam-5659	367	7	.	.	PUNCT
ejpam-5659	368	1	[	[	X
ejpam-5659	368	2	39	39	NUM
ejpam-5659	368	3	]	]	PUNCT
ejpam-5659	368	4	t.	t.	NOUN
ejpam-5659	368	5	lange	lange	NOUN
ejpam-5659	368	6	.	.	PUNCT
ejpam-5659	369	1	a	a	DET
ejpam-5659	369	2	note	note	NOUN
ejpam-5659	369	3	on	on	ADP
ejpam-5659	369	4	lópez	lópez	PROPN
ejpam-5659	369	5	-	-	PUNCT
ejpam-5659	369	6	dahab	dahab	PROPN
ejpam-5659	369	7	coordinates	coordinate	NOUN
ejpam-5659	369	8	.	.	PUNCT
ejpam-5659	370	1	tatra	tatra	PROPN
ejpam-5659	370	2	mt	mt	PROPN
ejpam-5659	370	3	.	.	PROPN
ejpam-5659	370	4	math	math	PROPN
ejpam-5659	370	5	.	.	PUNCT
ejpam-5659	371	1	publ	publ	PROPN
ejpam-5659	371	2	.	.	PUNCT
ejpam-5659	371	3	,	,	PUNCT
ejpam-5659	371	4	24(33):1–7	24(33):1–7	NUM
ejpam-5659	371	5	,	,	PUNCT
ejpam-5659	371	6	2006	2006	NUM
ejpam-5659	371	7	.	.	PUNCT
ejpam-5659	372	1	[	[	X
ejpam-5659	372	2	40	40	NUM
ejpam-5659	372	3	]	]	PUNCT
ejpam-5659	372	4	m.	m.	NOUN
ejpam-5659	372	5	m.	m.	PROPN
ejpam-5659	372	6	ahmad	ahmad	PROPN
ejpam-5659	372	7	,	,	PUNCT
ejpam-5659	372	8	s.	s.	PROPN
ejpam-5659	372	9	m.	m.	PROPN
ejpam-5659	372	10	yasin	yasin	PROPN
ejpam-5659	372	11	,	,	PUNCT
ejpam-5659	372	12	r.	r.	PROPN
ejpam-5659	372	13	mahmod	mahmod	PROPN
ejpam-5659	372	14	,	,	PUNCT
ejpam-5659	372	15	and	and	CCONJ
ejpam-5659	372	16	m.	m.	PROPN
ejpam-5659	372	17	a.	a.	PROPN
ejpam-5659	372	18	mohamed	mohamed	PROPN
ejpam-5659	372	19	.	.	PUNCT
ejpam-5659	373	1	x	x	X
ejpam-5659	373	2	-	-	PUNCT
ejpam-5659	373	3	tract	tract	ADJ
ejpam-5659	373	4	recoding	recode	VERB
ejpam-5659	373	5	algorithm	algorithm	NOUN
ejpam-5659	373	6	for	for	ADP
ejpam-5659	373	7	minimal	minimal	ADJ
ejpam-5659	373	8	hamming	hamming	NOUN
ejpam-5659	373	9	weight	weight	NOUN
ejpam-5659	373	10	digit	digit	NOUN
ejpam-5659	373	11	set	set	NOUN
ejpam-5659	373	12	conversion	conversion	NOUN
ejpam-5659	373	13	.	.	PUNCT
ejpam-5659	374	1	j.	j.	PROPN
ejpam-5659	374	2	theor	theor	PROPN
ejpam-5659	374	3	.	.	PUNCT
ejpam-5659	375	1	appl	appl	PROPN
ejpam-5659	375	2	.	.	PROPN
ejpam-5659	375	3	inf	inf	PROPN
ejpam-5659	375	4	.	.	PUNCT
ejpam-5659	375	5	technol	technol	PROPN
ejpam-5659	375	6	.	.	PROPN
ejpam-5659	375	7	,	,	PUNCT
ejpam-5659	375	8	75(1):109–114	75(1):109–114	PROPN
ejpam-5659	375	9	,	,	PUNCT
ejpam-5659	375	10	2015	2015	NUM
ejpam-5659	375	11	.	.	PUNCT