id	sid	tid	token	lemma	pos
ejpam-3972	1	1	european	european	PROPN
ejpam-3972	1	2	journal	journal	PROPN
ejpam-3972	1	3	of	of	ADP
ejpam-3972	1	4	pure	pure	ADJ
ejpam-3972	1	5	and	and	CCONJ
ejpam-3972	1	6	applied	apply	VERB
ejpam-3972	1	7	mathematics	mathematic	NOUN
ejpam-3972	1	8	vol	vol	NOUN
ejpam-3972	1	9	.	.	PUNCT
ejpam-3972	2	1	14	14	NUM
ejpam-3972	2	2	,	,	PUNCT
ejpam-3972	2	3	no	no	INTJ
ejpam-3972	2	4	.	.	NOUN
ejpam-3972	2	5	2	2	NUM
ejpam-3972	2	6	,	,	PUNCT
ejpam-3972	2	7	2021	2021	NUM
ejpam-3972	2	8	,	,	PUNCT
ejpam-3972	2	9	521	521	NUM
ejpam-3972	2	10	-	-	SYM
ejpam-3972	2	11	536	536	NUM
ejpam-3972	2	12	issn	issn	PROPN
ejpam-3972	2	13	1307	1307	NUM
ejpam-3972	2	14	-	-	SYM
ejpam-3972	2	15	5543	5543	NUM
ejpam-3972	2	16	–	–	PUNCT
ejpam-3972	3	1	ejpam.com	ejpam.com	X
ejpam-3972	3	2	published	publish	VERB
ejpam-3972	3	3	by	by	ADP
ejpam-3972	3	4	new	new	PROPN
ejpam-3972	3	5	york	york	PROPN
ejpam-3972	3	6	business	business	PROPN
ejpam-3972	3	7	global	global	ADJ
ejpam-3972	3	8	group	group	NOUN
ejpam-3972	3	9	and	and	CCONJ
ejpam-3972	3	10	cipher	cipher	ADJ
ejpam-3972	3	11	in	in	ADP
ejpam-3972	3	12	wormhole	wormhole	NOUN
ejpam-3972	3	13	and	and	CCONJ
ejpam-3972	3	14	quantum	quantum	NOUN
ejpam-3972	3	15	entanglement	entanglement	NOUN
ejpam-3972	3	16	yonghong	yonghong	NOUN
ejpam-3972	3	17	liu	liu	PROPN
ejpam-3972	3	18	school	school	PROPN
ejpam-3972	3	19	of	of	ADP
ejpam-3972	3	20	automation	automation	NOUN
ejpam-3972	3	21	,	,	PUNCT
ejpam-3972	3	22	wuhan	wuhan	PROPN
ejpam-3972	3	23	university	university	PROPN
ejpam-3972	3	24	of	of	ADP
ejpam-3972	3	25	technology	technology	NOUN
ejpam-3972	3	26	,	,	PUNCT
ejpam-3972	3	27	205	205	NUM
ejpam-3972	3	28	luoshi	luoshi	PROPN
ejpam-3972	3	29	road	road	NOUN
ejpam-3972	3	30	,	,	PUNCT
ejpam-3972	3	31	wuhan	wuhan	PROPN
ejpam-3972	3	32	,	,	PUNCT
ejpam-3972	3	33	china	china	PROPN
ejpam-3972	3	34	abstract	abstract	NOUN
ejpam-3972	3	35	.	.	PUNCT
ejpam-3972	4	1	in	in	ADP
ejpam-3972	4	2	this	this	DET
ejpam-3972	4	3	article	article	NOUN
ejpam-3972	4	4	,	,	PUNCT
ejpam-3972	4	5	we	we	PRON
ejpam-3972	4	6	present	present	VERB
ejpam-3972	4	7	wormholes	wormhole	NOUN
ejpam-3972	4	8	cryptosystems	cryptosystem	NOUN
ejpam-3972	4	9	(	(	PUNCT
ejpam-3972	4	10	wcs	wcs	PROPN
ejpam-3972	4	11	)	)	PUNCT
ejpam-3972	4	12	.	.	PUNCT
ejpam-3972	5	1	the	the	DET
ejpam-3972	5	2	first	first	ADJ
ejpam-3972	5	3	is	be	AUX
ejpam-3972	5	4	the	the	DET
ejpam-3972	5	5	wormhole	wormhole	NOUN
ejpam-3972	5	6	key	key	ADJ
ejpam-3972	5	7	distribution	distribution	NOUN
ejpam-3972	5	8	centre	centre	NOUN
ejpam-3972	5	9	theorem	theorem	VERB
ejpam-3972	5	10	,	,	PUNCT
ejpam-3972	5	11	which	which	PRON
ejpam-3972	5	12	asserts	assert	VERB
ejpam-3972	5	13	that	that	SCONJ
ejpam-3972	5	14	the	the	DET
ejpam-3972	5	15	wcs	wcs	NOUN
ejpam-3972	5	16	is	be	AUX
ejpam-3972	5	17	a	a	DET
ejpam-3972	5	18	public	public	ADJ
ejpam-3972	5	19	key	key	ADJ
ejpam-3972	5	20	group	group	NOUN
ejpam-3972	5	21	.	.	PUNCT
ejpam-3972	6	1	the	the	DET
ejpam-3972	6	2	second	second	ADJ
ejpam-3972	6	3	is	be	AUX
ejpam-3972	6	4	the	the	DET
ejpam-3972	6	5	security	security	NOUN
ejpam-3972	6	6	theorem	theorem	VERB
ejpam-3972	6	7	,	,	PUNCT
ejpam-3972	6	8	which	which	PRON
ejpam-3972	6	9	asserts	assert	VERB
ejpam-3972	6	10	that	that	SCONJ
ejpam-3972	6	11	the	the	DET
ejpam-3972	6	12	wcs	wcs	NOUN
ejpam-3972	6	13	are	be	AUX
ejpam-3972	6	14	a	a	DET
ejpam-3972	6	15	one	one	NUM
ejpam-3972	6	16	-	-	PUNCT
ejpam-3972	6	17	way	way	NOUN
ejpam-3972	6	18	function	function	NOUN
ejpam-3972	6	19	.	.	PUNCT
ejpam-3972	7	1	the	the	DET
ejpam-3972	7	2	third	third	NOUN
ejpam-3972	7	3	is	be	AUX
ejpam-3972	7	4	new	new	ADJ
ejpam-3972	7	5	version	version	NOUN
ejpam-3972	7	6	of	of	ADP
ejpam-3972	7	7	the	the	DET
ejpam-3972	7	8	definition	definition	NOUN
ejpam-3972	7	9	for	for	ADP
ejpam-3972	7	10	the	the	DET
ejpam-3972	7	11	wcs	wcs	NOUN
ejpam-3972	7	12	,	,	PUNCT
ejpam-3972	7	13	and	and	CCONJ
ejpam-3972	7	14	we	we	PRON
ejpam-3972	7	15	introduce	introduce	VERB
ejpam-3972	7	16	the	the	DET
ejpam-3972	7	17	notion	notion	NOUN
ejpam-3972	7	18	of	of	ADP
ejpam-3972	7	19	groups	group	NOUN
ejpam-3972	7	20	of	of	ADP
ejpam-3972	7	21	wcs	wcs	PROPN
ejpam-3972	7	22	.	.	PUNCT
ejpam-3972	8	1	the	the	DET
ejpam-3972	8	2	fourth	fourth	ADJ
ejpam-3972	8	3	ingredient	ingredient	NOUN
ejpam-3972	8	4	is	be	AUX
ejpam-3972	8	5	the	the	DET
ejpam-3972	8	6	encryption	encryption	NOUN
ejpam-3972	8	7	algorithm	algorithm	NOUN
ejpam-3972	8	8	and	and	CCONJ
ejpam-3972	8	9	decryption	decryption	NOUN
ejpam-3972	8	10	algorithm	algorithm	NOUN
ejpam-3972	8	11	,	,	PUNCT
ejpam-3972	8	12	and	and	CCONJ
ejpam-3972	8	13	design	design	NOUN
ejpam-3972	8	14	principle	principle	NOUN
ejpam-3972	8	15	.	.	PUNCT
ejpam-3972	9	1	here	here	ADV
ejpam-3972	9	2	,	,	PUNCT
ejpam-3972	9	3	we	we	PRON
ejpam-3972	9	4	present	present	VERB
ejpam-3972	9	5	a	a	DET
ejpam-3972	9	6	toy	toy	NOUN
ejpam-3972	9	7	example	example	NOUN
ejpam-3972	9	8	to	to	PART
ejpam-3972	9	9	illustrate	illustrate	VERB
ejpam-3972	9	10	the	the	DET
ejpam-3972	9	11	computation	computation	NOUN
ejpam-3972	9	12	of	of	ADP
ejpam-3972	9	13	these	these	DET
ejpam-3972	9	14	encryptions	encryption	NOUN
ejpam-3972	9	15	and	and	CCONJ
ejpam-3972	9	16	decryptions	decryption	NOUN
ejpam-3972	9	17	.	.	PUNCT
ejpam-3972	10	1	the	the	DET
ejpam-3972	10	2	finally	finally	ADV
ejpam-3972	10	3	we	we	PRON
ejpam-3972	10	4	present	present	VERB
ejpam-3972	10	5	the	the	DET
ejpam-3972	10	6	unsymmetrical	unsymmetrical	ADJ
ejpam-3972	10	7	wcs	wcs	PROPN
ejpam-3972	10	8	theorem	theorem	NOUN
ejpam-3972	10	9	.	.	PROPN
ejpam-3972	10	10	2020	2020	NUM
ejpam-3972	10	11	mathematics	mathematics	PROPN
ejpam-3972	10	12	subject	subject	NOUN
ejpam-3972	10	13	classifications	classification	NOUN
ejpam-3972	10	14	:	:	PUNCT
ejpam-3972	10	15	94a60	94a60	NUM
ejpam-3972	10	16	,	,	PUNCT
ejpam-3972	10	17	81r12	81r12	NUM
ejpam-3972	10	18	,	,	PUNCT
ejpam-3972	10	19	81p40	81p40	NUM
ejpam-3972	10	20	key	key	ADJ
ejpam-3972	10	21	words	word	NOUN
ejpam-3972	10	22	and	and	CCONJ
ejpam-3972	10	23	phrases	phrase	NOUN
ejpam-3972	10	24	:	:	PUNCT
ejpam-3972	10	25	groups	group	NOUN
ejpam-3972	10	26	,	,	PUNCT
ejpam-3972	10	27	cryptography	cryptography	NOUN
ejpam-3972	10	28	,	,	PUNCT
ejpam-3972	10	29	one	one	NUM
ejpam-3972	10	30	-	-	PUNCT
ejpam-3972	10	31	way	way	NOUN
ejpam-3972	10	32	function	function	NOUN
ejpam-3972	10	33	,	,	PUNCT
ejpam-3972	10	34	zero	zero	NUM
ejpam-3972	10	35	-	-	PUNCT
ejpam-3972	10	36	knowledge	knowledge	NOUN
ejpam-3972	10	37	proof	proof	NOUN
ejpam-3972	10	38	,	,	PUNCT
ejpam-3972	10	39	quantum	quantum	ADJ
ejpam-3972	10	40	entanglement	entanglement	NOUN
ejpam-3972	10	41	,	,	PUNCT
ejpam-3972	10	42	wormhole	wormhole	NOUN
ejpam-3972	10	43	1	1	NUM
ejpam-3972	10	44	.	.	PUNCT
ejpam-3972	11	1	introduction	introduction	NOUN
ejpam-3972	11	2	quantum	quantum	NOUN
ejpam-3972	11	3	information	information	NOUN
ejpam-3972	11	4	science	science	NOUN
ejpam-3972	11	5	is	be	AUX
ejpam-3972	11	6	an	an	DET
ejpam-3972	11	7	area	area	NOUN
ejpam-3972	11	8	of	of	ADP
ejpam-3972	11	9	study	study	NOUN
ejpam-3972	11	10	based	base	VERB
ejpam-3972	11	11	on	on	ADP
ejpam-3972	11	12	the	the	DET
ejpam-3972	11	13	idea	idea	NOUN
ejpam-3972	11	14	that	that	SCONJ
ejpam-3972	11	15	information	information	NOUN
ejpam-3972	11	16	science	science	NOUN
ejpam-3972	11	17	depends	depend	VERB
ejpam-3972	11	18	on	on	ADP
ejpam-3972	11	19	quantum	quantum	ADJ
ejpam-3972	11	20	effects	effect	NOUN
ejpam-3972	11	21	in	in	ADP
ejpam-3972	11	22	physics	physics	NOUN
ejpam-3972	11	23	.	.	PUNCT
ejpam-3972	12	1	the	the	DET
ejpam-3972	12	2	wormhole	wormhole	NOUN
ejpam-3972	12	3	is	be	AUX
ejpam-3972	12	4	a	a	DET
ejpam-3972	12	5	subject	subject	NOUN
ejpam-3972	12	6	of	of	ADP
ejpam-3972	12	7	fascination	fascination	NOUN
ejpam-3972	12	8	for	for	ADP
ejpam-3972	12	9	the	the	DET
ejpam-3972	12	10	scientific	scientific	ADJ
ejpam-3972	12	11	community	community	NOUN
ejpam-3972	12	12	.	.	PUNCT
ejpam-3972	13	1	it	it	PRON
ejpam-3972	13	2	is	be	AUX
ejpam-3972	13	3	interesting	interesting	ADJ
ejpam-3972	13	4	to	to	PART
ejpam-3972	13	5	note	note	VERB
ejpam-3972	13	6	that	that	SCONJ
ejpam-3972	13	7	the	the	DET
ejpam-3972	13	8	quantum	quantum	ADJ
ejpam-3972	13	9	entanglement	entanglement	NOUN
ejpam-3972	13	10	has	have	VERB
ejpam-3972	13	11	that	that	DET
ejpam-3972	13	12	honor	honor	NOUN
ejpam-3972	13	13	that	that	PRON
ejpam-3972	13	14	has	have	AUX
ejpam-3972	13	15	put	put	VERB
ejpam-3972	13	16	it	it	PRON
ejpam-3972	13	17	in	in	ADP
ejpam-3972	13	18	wormhole	wormhole	NOUN
ejpam-3972	13	19	.	.	PUNCT
ejpam-3972	14	1	van	van	PROPN
ejpam-3972	14	2	raamsdonk	raamsdonk	PROPN
ejpam-3972	14	3	’s	’s	PART
ejpam-3972	14	4	essay	essay	NOUN
ejpam-3972	14	5	originally	originally	ADV
ejpam-3972	14	6	published	publish	VERB
ejpam-3972	14	7	in	in	ADP
ejpam-3972	14	8	the	the	DET
ejpam-3972	14	9	general	general	ADJ
ejpam-3972	14	10	relativity	relativity	NOUN
ejpam-3972	14	11	and	and	CCONJ
ejpam-3972	14	12	gravitation	gravitation	NOUN
ejpam-3972	14	13	[	[	X
ejpam-3972	14	14	1	1	X
ejpam-3972	14	15	]	]	PUNCT
ejpam-3972	14	16	has	have	AUX
ejpam-3972	14	17	been	be	AUX
ejpam-3972	14	18	concerned	concern	VERB
ejpam-3972	14	19	;	;	PUNCT
ejpam-3972	14	20	this	this	PRON
ejpam-3972	14	21	illustrates	illustrate	VERB
ejpam-3972	14	22	the	the	DET
ejpam-3972	14	23	wormhole	wormhole	NOUN
ejpam-3972	14	24	compatibility	compatibility	NOUN
ejpam-3972	14	25	with	with	ADP
ejpam-3972	14	26	the	the	DET
ejpam-3972	14	27	quantum	quantum	ADJ
ejpam-3972	14	28	entanglement	entanglement	NOUN
ejpam-3972	14	29	.	.	PUNCT
ejpam-3972	15	1	maldacena	maldacena	NOUN
ejpam-3972	15	2	and	and	CCONJ
ejpam-3972	15	3	susskind	susskind	NOUN
ejpam-3972	15	4	[	[	X
ejpam-3972	15	5	2	2	NUM
ejpam-3972	15	6	]	]	PUNCT
ejpam-3972	15	7	,	,	PUNCT
ejpam-3972	15	8	cowen	cowen	PROPN
ejpam-3972	16	1	[	[	X
ejpam-3972	16	2	3	3	NUM
ejpam-3972	16	3	]	]	PUNCT
ejpam-3972	16	4	and	and	CCONJ
ejpam-3972	16	5	others	other	NOUN
ejpam-3972	16	6	considered	consider	VERB
ejpam-3972	16	7	the	the	DET
ejpam-3972	16	8	problem	problem	NOUN
ejpam-3972	16	9	of	of	ADP
ejpam-3972	16	10	a	a	DET
ejpam-3972	16	11	related	related	ADJ
ejpam-3972	16	12	conjecture	conjecture	NOUN
ejpam-3972	16	13	,	,	PUNCT
ejpam-3972	16	14	i.e.	i.e.	X
ejpam-3972	16	15	,	,	PUNCT
ejpam-3972	16	16	er	er	INTJ
ejpam-3972	16	17	=	=	SYM
ejpam-3972	16	18	epr	epr	PROPN
ejpam-3972	17	1	[	[	X
ejpam-3972	17	2	4	4	NUM
ejpam-3972	17	3	]	]	PUNCT
ejpam-3972	17	4	;	;	PUNCT
ejpam-3972	17	5	it	it	PRON
ejpam-3972	17	6	is	be	AUX
ejpam-3972	17	7	a	a	DET
ejpam-3972	17	8	conjecture	conjecture	NOUN
ejpam-3972	17	9	in	in	ADP
ejpam-3972	17	10	physics	physics	NOUN
ejpam-3972	17	11	stating	state	VERB
ejpam-3972	17	12	that	that	SCONJ
ejpam-3972	17	13	entangled	entangle	VERB
ejpam-3972	17	14	particles	particle	NOUN
ejpam-3972	17	15	are	be	AUX
ejpam-3972	17	16	connected	connect	VERB
ejpam-3972	17	17	by	by	ADP
ejpam-3972	17	18	a	a	DET
ejpam-3972	17	19	wormhole	wormhole	NOUN
ejpam-3972	17	20	(	(	PUNCT
ejpam-3972	17	21	or	or	CCONJ
ejpam-3972	17	22	known	know	VERB
ejpam-3972	17	23	as	as	ADP
ejpam-3972	17	24	einstein	einstein	PROPN
ejpam-3972	17	25	-	-	PUNCT
ejpam-3972	17	26	rosen	rosen	PROPN
ejpam-3972	17	27	bridge	bridge	PROPN
ejpam-3972	17	28	)	)	PUNCT
ejpam-3972	18	1	[	[	X
ejpam-3972	18	2	3	3	NUM
ejpam-3972	18	3	]	]	PUNCT
ejpam-3972	18	4	;	;	PUNCT
ejpam-3972	18	5	the	the	DET
ejpam-3972	18	6	conjecture	conjecture	NOUN
ejpam-3972	18	7	was	be	AUX
ejpam-3972	18	8	proposed	propose	VERB
ejpam-3972	18	9	by	by	ADP
ejpam-3972	18	10	maldacena	maldacena	NOUN
ejpam-3972	18	11	and	and	CCONJ
ejpam-3972	18	12	susskind	susskind	NOUN
ejpam-3972	18	13	[	[	X
ejpam-3972	18	14	2	2	NUM
ejpam-3972	18	15	]	]	PUNCT
ejpam-3972	18	16	.	.	PUNCT
ejpam-3972	19	1	testing	test	VERB
ejpam-3972	19	2	the	the	DET
ejpam-3972	19	3	er	er	INTJ
ejpam-3972	19	4	=	=	PUNCT
ejpam-3972	19	5	epr	epr	PROPN
ejpam-3972	19	6	hypothesis	hypothesis	NOUN
ejpam-3972	19	7	to	to	PART
ejpam-3972	19	8	see	see	VERB
ejpam-3972	19	9	if	if	SCONJ
ejpam-3972	19	10	it	it	PRON
ejpam-3972	19	11	is	be	AUX
ejpam-3972	19	12	mathematically	mathematically	ADV
ejpam-3972	19	13	consistent	consistent	ADJ
ejpam-3972	19	14	with	with	ADP
ejpam-3972	19	15	everything	everything	PRON
ejpam-3972	19	16	else	else	ADV
ejpam-3972	19	17	that	that	PRON
ejpam-3972	19	18	is	be	AUX
ejpam-3972	19	19	known	know	VERB
ejpam-3972	19	20	about	about	ADP
ejpam-3972	19	21	entanglement	entanglement	NOUN
ejpam-3972	19	22	and	and	CCONJ
ejpam-3972	19	23	wormholes	wormhole	NOUN
ejpam-3972	19	24	,	,	PUNCT
ejpam-3972	19	25	because	because	SCONJ
ejpam-3972	19	26	it	it	PRON
ejpam-3972	19	27	involves	involve	VERB
ejpam-3972	19	28	the	the	DET
ejpam-3972	19	29	establishment	establishment	NOUN
ejpam-3972	19	30	of	of	ADP
ejpam-3972	19	31	new	new	ADJ
ejpam-3972	19	32	scheme	scheme	NOUN
ejpam-3972	19	33	for	for	ADP
ejpam-3972	19	34	cryptography	cryptography	NOUN
ejpam-3972	19	35	.	.	PUNCT
ejpam-3972	20	1	besides	besides	SCONJ
ejpam-3972	20	2	,	,	PUNCT
ejpam-3972	20	3	it	it	PRON
ejpam-3972	20	4	has	have	AUX
ejpam-3972	20	5	long	long	ADV
ejpam-3972	20	6	been	be	AUX
ejpam-3972	20	7	theorized	theorize	VERB
ejpam-3972	20	8	that	that	SCONJ
ejpam-3972	20	9	secure	secure	ADJ
ejpam-3972	20	10	asymmetric	asymmetric	ADJ
ejpam-3972	20	11	cipher	cipher	NOUN
ejpam-3972	20	12	all	all	PRON
ejpam-3972	20	13	use	use	VERB
ejpam-3972	20	14	the	the	DET
ejpam-3972	20	15	number	number	NOUN
ejpam-3972	20	16	theory	theory	NOUN
ejpam-3972	20	17	.	.	PUNCT
ejpam-3972	21	1	but	but	CCONJ
ejpam-3972	21	2	one	one	NUM
ejpam-3972	21	3	thing	thing	NOUN
ejpam-3972	21	4	that	that	PRON
ejpam-3972	21	5	is	be	AUX
ejpam-3972	21	6	certain	certain	ADJ
ejpam-3972	21	7	,	,	PUNCT
ejpam-3972	21	8	it	it	PRON
ejpam-3972	21	9	seems	seem	VERB
ejpam-3972	21	10	to	to	PART
ejpam-3972	21	11	be	be	AUX
ejpam-3972	21	12	very	very	ADV
ejpam-3972	21	13	difficult	difficult	ADJ
ejpam-3972	21	14	to	to	PART
ejpam-3972	21	15	prove	prove	VERB
ejpam-3972	21	16	anything	anything	PRON
ejpam-3972	21	17	about	about	ADP
ejpam-3972	21	18	the	the	DET
ejpam-3972	21	19	security	security	NOUN
ejpam-3972	21	20	of	of	ADP
ejpam-3972	21	21	a	a	DET
ejpam-3972	21	22	system	system	NOUN
ejpam-3972	21	23	if	if	SCONJ
ejpam-3972	21	24	the	the	DET
ejpam-3972	21	25	encryption	encryption	NOUN
ejpam-3972	21	26	is	be	AUX
ejpam-3972	21	27	deterministic	deterministic	ADJ
ejpam-3972	21	28	.	.	PUNCT
ejpam-3972	22	1	shor	shor	PROPN
ejpam-3972	23	1	[	[	X
ejpam-3972	23	2	5	5	NUM
ejpam-3972	23	3	]	]	PUNCT
ejpam-3972	23	4	stated	state	VERB
ejpam-3972	23	5	in	in	ADP
ejpam-3972	23	6	1994	1994	NUM
ejpam-3972	23	7	that	that	SCONJ
ejpam-3972	23	8	the	the	DET
ejpam-3972	23	9	discrete	discrete	ADJ
ejpam-3972	23	10	logarithms	logarithm	NOUN
ejpam-3972	23	11	problem	problem	NOUN
ejpam-3972	23	12	and	and	CCONJ
ejpam-3972	23	13	factoring	factoring	NOUN
ejpam-3972	23	14	doi	doi	NOUN
ejpam-3972	23	15	:	:	PUNCT
ejpam-3972	23	16	https://doi.org/10.29020/nybg.ejpam.v14i2.3972	https://doi.org/10.29020/nybg.ejpam.v14i2.3972	PROPN
ejpam-3972	23	17	email	email	NOUN
ejpam-3972	23	18	address	address	NOUN
ejpam-3972	23	19	:	:	PUNCT
ejpam-3972	23	20	hylinin@whut.edu.cn	hylinin@whut.edu.cn	NOUN
ejpam-3972	23	21	(	(	PUNCT
ejpam-3972	23	22	y.	y.	PROPN
ejpam-3972	23	23	liu	liu	PROPN
ejpam-3972	23	24	)	)	PUNCT
ejpam-3972	23	25	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3972	23	26	521	521	NUM
ejpam-3972	23	27	c	c	X
ejpam-3972	23	28	©	©	PROPN
ejpam-3972	23	29	2021	2021	NUM
ejpam-3972	23	30	ejpam	ejpam	VERB
ejpam-3972	23	31	all	all	DET
ejpam-3972	23	32	rights	right	NOUN
ejpam-3972	23	33	reserved	reserve	VERB
ejpam-3972	23	34	.	.	PUNCT
ejpam-3972	24	1	y.	y.	PROPN
ejpam-3972	24	2	liu	liu	PROPN
ejpam-3972	24	3	/	/	SYM
ejpam-3972	24	4	eur	eur	PROPN
ejpam-3972	24	5	.	.	PUNCT
ejpam-3972	25	1	j.	j.	PROPN
ejpam-3972	25	2	pure	pure	PROPN
ejpam-3972	25	3	appl	appl	PROPN
ejpam-3972	25	4	.	.	PROPN
ejpam-3972	25	5	math	math	PROPN
ejpam-3972	25	6	,	,	PUNCT
ejpam-3972	25	7	14	14	NUM
ejpam-3972	25	8	(	(	PUNCT
ejpam-3972	25	9	2	2	NUM
ejpam-3972	25	10	)	)	PUNCT
ejpam-3972	25	11	(	(	PUNCT
ejpam-3972	25	12	2021	2021	NUM
ejpam-3972	25	13	)	)	PUNCT
ejpam-3972	25	14	,	,	PUNCT
ejpam-3972	25	15	521	521	NUM
ejpam-3972	25	16	-	-	SYM
ejpam-3972	25	17	536	536	NUM
ejpam-3972	25	18	522	522	NUM
ejpam-3972	25	19	problem	problem	NOUN
ejpam-3972	25	20	by	by	ADP
ejpam-3972	25	21	the	the	DET
ejpam-3972	25	22	quantum	quantum	ADJ
ejpam-3972	25	23	algorithm	algorithm	NOUN
ejpam-3972	25	24	can	can	AUX
ejpam-3972	25	25	be	be	AUX
ejpam-3972	25	26	solved	solve	VERB
ejpam-3972	25	27	in	in	ADP
ejpam-3972	25	28	polynomial	polynomial	ADJ
ejpam-3972	25	29	time	time	NOUN
ejpam-3972	25	30	.	.	PUNCT
ejpam-3972	26	1	the	the	DET
ejpam-3972	26	2	quantum	quantum	ADJ
ejpam-3972	26	3	computers	computer	NOUN
ejpam-3972	26	4	should	should	AUX
ejpam-3972	26	5	be	be	AUX
ejpam-3972	26	6	able	able	ADJ
ejpam-3972	26	7	to	to	PART
ejpam-3972	26	8	defeat	defeat	VERB
ejpam-3972	26	9	encryption	encryption	NOUN
ejpam-3972	26	10	that	that	PRON
ejpam-3972	26	11	is	be	AUX
ejpam-3972	26	12	unbreakable	unbreakable	ADJ
ejpam-3972	26	13	in	in	ADP
ejpam-3972	26	14	practice	practice	NOUN
ejpam-3972	26	15	today	today	NOUN
ejpam-3972	26	16	,	,	PUNCT
ejpam-3972	26	17	with	with	ADP
ejpam-3972	26	18	people	people	NOUN
ejpam-3972	26	19	in	in	ADP
ejpam-3972	26	20	desperate	desperate	ADJ
ejpam-3972	26	21	need	need	NOUN
ejpam-3972	26	22	of	of	ADP
ejpam-3972	26	23	practical	practical	ADJ
ejpam-3972	26	24	and	and	CCONJ
ejpam-3972	26	25	secure	secure	ADJ
ejpam-3972	26	26	public	public	ADJ
ejpam-3972	26	27	-	-	PUNCT
ejpam-3972	26	28	key	key	NOUN
ejpam-3972	26	29	cryptosystems	cryptosystem	NOUN
ejpam-3972	26	30	.	.	PUNCT
ejpam-3972	27	1	in	in	ADP
ejpam-3972	27	2	this	this	DET
ejpam-3972	27	3	paper	paper	NOUN
ejpam-3972	27	4	,	,	PUNCT
ejpam-3972	27	5	the	the	DET
ejpam-3972	27	6	wormholes	wormhole	NOUN
ejpam-3972	27	7	cryptosystems	cryptosystem	NOUN
ejpam-3972	27	8	(	(	PUNCT
ejpam-3972	27	9	wcs	wcs	PROPN
ejpam-3972	27	10	)	)	PUNCT
ejpam-3972	27	11	is	be	AUX
ejpam-3972	27	12	a	a	DET
ejpam-3972	27	13	new	new	ADJ
ejpam-3972	27	14	public	public	ADJ
ejpam-3972	27	15	-	-	PUNCT
ejpam-3972	27	16	key	key	NOUN
ejpam-3972	27	17	cryptosystem	cryptosystem	NOUN
ejpam-3972	27	18	and	and	CCONJ
ejpam-3972	27	19	wormhole	wormhole	NOUN
ejpam-3972	27	20	key	key	ADJ
ejpam-3972	27	21	distribution	distribution	NOUN
ejpam-3972	27	22	(	(	PUNCT
ejpam-3972	27	23	wkd	wkd	NOUN
ejpam-3972	27	24	)	)	PUNCT
ejpam-3972	27	25	would	would	AUX
ejpam-3972	27	26	be	be	AUX
ejpam-3972	27	27	at	at	ADP
ejpam-3972	27	28	the	the	DET
ejpam-3972	27	29	very	very	ADJ
ejpam-3972	27	30	heart	heart	NOUN
ejpam-3972	27	31	of	of	ADP
ejpam-3972	27	32	it	it	PRON
ejpam-3972	27	33	.	.	PUNCT
ejpam-3972	28	1	the	the	DET
ejpam-3972	28	2	wcs	wcs	PROPN
ejpam-3972	28	3	and	and	CCONJ
ejpam-3972	28	4	the	the	DET
ejpam-3972	28	5	well	well	ADV
ejpam-3972	28	6	-	-	PUNCT
ejpam-3972	28	7	known	know	VERB
ejpam-3972	28	8	rsa	rsa	NOUN
ejpam-3972	28	9	[	[	X
ejpam-3972	28	10	6	6	NUM
ejpam-3972	28	11	]	]	PUNCT
ejpam-3972	28	12	are	be	AUX
ejpam-3972	28	13	very	very	ADV
ejpam-3972	28	14	different	different	ADJ
ejpam-3972	28	15	theories	theory	NOUN
ejpam-3972	28	16	.	.	PUNCT
ejpam-3972	29	1	wcs	wcs	PROPN
ejpam-3972	29	2	is	be	AUX
ejpam-3972	29	3	a	a	DET
ejpam-3972	29	4	new	new	ADJ
ejpam-3972	29	5	public	public	ADJ
ejpam-3972	29	6	-	-	PUNCT
ejpam-3972	29	7	key	key	NOUN
ejpam-3972	29	8	cryptosystem	cryptosystem	NOUN
ejpam-3972	29	9	and	and	CCONJ
ejpam-3972	29	10	wormhole	wormhole	NOUN
ejpam-3972	29	11	key	key	ADJ
ejpam-3972	29	12	distribution	distribution	NOUN
ejpam-3972	29	13	(	(	PUNCT
ejpam-3972	29	14	wkd	wkd	NOUN
ejpam-3972	29	15	)	)	PUNCT
ejpam-3972	29	16	would	would	AUX
ejpam-3972	29	17	be	be	AUX
ejpam-3972	29	18	at	at	ADP
ejpam-3972	29	19	the	the	DET
ejpam-3972	29	20	very	very	ADJ
ejpam-3972	29	21	heart	heart	NOUN
ejpam-3972	29	22	of	of	ADP
ejpam-3972	29	23	it	it	PRON
ejpam-3972	29	24	.	.	PUNCT
ejpam-3972	30	1	emphasis	emphasis	NOUN
ejpam-3972	30	2	here	here	ADV
ejpam-3972	30	3	is	be	AUX
ejpam-3972	30	4	on	on	ADP
ejpam-3972	30	5	a	a	DET
ejpam-3972	30	6	rigorous	rigorous	ADJ
ejpam-3972	30	7	algebraic	algebraic	ADJ
ejpam-3972	30	8	approach	approach	NOUN
ejpam-3972	30	9	to	to	ADP
ejpam-3972	30	10	the	the	DET
ejpam-3972	30	11	wcs	wcs	NOUN
ejpam-3972	30	12	.	.	PUNCT
ejpam-3972	31	1	it	it	PRON
ejpam-3972	31	2	is	be	AUX
ejpam-3972	31	3	based	base	VERB
ejpam-3972	31	4	on	on	ADP
ejpam-3972	31	5	a	a	DET
ejpam-3972	31	6	new	new	ADJ
ejpam-3972	31	7	group	group	NOUN
ejpam-3972	31	8	of	of	ADP
ejpam-3972	31	9	the	the	DET
ejpam-3972	31	10	product	product	NOUN
ejpam-3972	31	11	of	of	ADP
ejpam-3972	31	12	two	two	NUM
ejpam-3972	31	13	large	large	ADJ
ejpam-3972	31	14	primes	prime	NOUN
ejpam-3972	31	15	(	(	PUNCT
ejpam-3972	31	16	p	p	X
ejpam-3972	31	17	,	,	PUNCT
ejpam-3972	31	18	q	q	NOUN
ejpam-3972	31	19	)	)	PUNCT
ejpam-3972	31	20	and	and	CCONJ
ejpam-3972	31	21	is	be	AUX
ejpam-3972	31	22	a	a	DET
ejpam-3972	31	23	multiplication	multiplication	NOUN
ejpam-3972	31	24	function	function	NOUN
ejpam-3972	31	25	h(x	h(x	PROPN
ejpam-3972	31	26	,	,	PUNCT
ejpam-3972	31	27	y	y	PROPN
ejpam-3972	31	28	,	,	PUNCT
ejpam-3972	31	29	z	z	NOUN
ejpam-3972	31	30	)	)	PUNCT
ejpam-3972	31	31	of	of	ADP
ejpam-3972	31	32	wormholes	wormhole	NOUN
ejpam-3972	31	33	,	,	PUNCT
ejpam-3972	31	34	which	which	PRON
ejpam-3972	31	35	is	be	AUX
ejpam-3972	31	36	a	a	DET
ejpam-3972	31	37	one	one	NUM
ejpam-3972	31	38	-	-	PUNCT
ejpam-3972	31	39	way	way	NOUN
ejpam-3972	31	40	function	function	NOUN
ejpam-3972	31	41	.	.	PUNCT
ejpam-3972	32	1	the	the	DET
ejpam-3972	32	2	product	product	NOUN
ejpam-3972	32	3	of	of	ADP
ejpam-3972	32	4	these	these	DET
ejpam-3972	32	5	primes	prime	NOUN
ejpam-3972	32	6	is	be	AUX
ejpam-3972	32	7	a	a	DET
ejpam-3972	32	8	number	number	NOUN
ejpam-3972	32	9	of	of	ADP
ejpam-3972	32	10	between	between	ADP
ejpam-3972	32	11	about	about	ADV
ejpam-3972	32	12	200	200	NUM
ejpam-3972	32	13	and	and	CCONJ
ejpam-3972	32	14	600	600	NUM
ejpam-3972	32	15	decimal	decimal	ADJ
ejpam-3972	32	16	digits	digit	NOUN
ejpam-3972	32	17	,	,	PUNCT
ejpam-3972	32	18	can	can	AUX
ejpam-3972	32	19	not	not	PART
ejpam-3972	32	20	be	be	AUX
ejpam-3972	32	21	factored	factor	VERB
ejpam-3972	32	22	in	in	ADP
ejpam-3972	32	23	a	a	DET
ejpam-3972	32	24	reasonable	reasonable	ADJ
ejpam-3972	32	25	length	length	NOUN
ejpam-3972	32	26	of	of	ADP
ejpam-3972	32	27	time	time	NOUN
ejpam-3972	32	28	.	.	PUNCT
ejpam-3972	33	1	in	in	ADP
ejpam-3972	33	2	other	other	ADJ
ejpam-3972	33	3	words	word	NOUN
ejpam-3972	33	4	,	,	PUNCT
ejpam-3972	33	5	the	the	DET
ejpam-3972	33	6	wkd	wkd	NOUN
ejpam-3972	33	7	encryption	encryption	NOUN
ejpam-3972	33	8	algorithm	algorithm	NOUN
ejpam-3972	33	9	,	,	PUNCT
ejpam-3972	33	10	there	there	PRON
ejpam-3972	33	11	are	be	VERB
ejpam-3972	33	12	from	from	ADP
ejpam-3972	33	13	2200	2200	NUM
ejpam-3972	33	14	to	to	ADP
ejpam-3972	33	15	2600	2600	NUM
ejpam-3972	33	16	mappings	mapping	NOUN
ejpam-3972	33	17	.	.	PUNCT
ejpam-3972	34	1	therefore	therefore	ADV
ejpam-3972	34	2	,	,	PUNCT
ejpam-3972	34	3	the	the	DET
ejpam-3972	34	4	wcs	wcs	NOUN
ejpam-3972	34	5	as	as	ADP
ejpam-3972	34	6	a	a	DET
ejpam-3972	34	7	public	public	ADJ
ejpam-3972	34	8	-	-	PUNCT
ejpam-3972	34	9	key	key	NOUN
ejpam-3972	34	10	cryptosystem	cryptosystem	NOUN
ejpam-3972	34	11	are	be	AUX
ejpam-3972	34	12	computational	computational	ADJ
ejpam-3972	34	13	security	security	NOUN
ejpam-3972	34	14	.	.	PUNCT
ejpam-3972	35	1	we	we	PRON
ejpam-3972	35	2	can	can	AUX
ejpam-3972	35	3	now	now	ADV
ejpam-3972	35	4	establish	establish	VERB
ejpam-3972	35	5	the	the	DET
ejpam-3972	35	6	fact	fact	NOUN
ejpam-3972	35	7	that	that	PRON
ejpam-3972	35	8	makes	make	VERB
ejpam-3972	35	9	the	the	DET
ejpam-3972	35	10	key	key	ADJ
ejpam-3972	35	11	distribution	distribution	NOUN
ejpam-3972	35	12	centre	centre	NOUN
ejpam-3972	35	13	(	(	PUNCT
ejpam-3972	35	14	kdc	kdc	PROPN
ejpam-3972	35	15	)	)	PUNCT
ejpam-3972	35	16	interesting	interesting	ADJ
ejpam-3972	35	17	because	because	SCONJ
ejpam-3972	35	18	we	we	PRON
ejpam-3972	35	19	can	can	AUX
ejpam-3972	35	20	give	give	VERB
ejpam-3972	35	21	the	the	DET
ejpam-3972	35	22	physical	physical	ADJ
ejpam-3972	35	23	explanation	explanation	NOUN
ejpam-3972	35	24	on	on	ADP
ejpam-3972	35	25	rapid	rapid	ADJ
ejpam-3972	35	26	particles	particle	NOUN
ejpam-3972	35	27	,	,	PUNCT
ejpam-3972	35	28	and	and	CCONJ
ejpam-3972	35	29	the	the	DET
ejpam-3972	35	30	wormhole	wormhole	NOUN
ejpam-3972	35	31	key	key	ADJ
ejpam-3972	35	32	distribution	distribution	NOUN
ejpam-3972	35	33	centre	centre	NOUN
ejpam-3972	35	34	(	(	PUNCT
ejpam-3972	35	35	wkdc	wkdc	PROPN
ejpam-3972	35	36	)	)	PUNCT
ejpam-3972	35	37	is	be	AUX
ejpam-3972	35	38	considered	consider	VERB
ejpam-3972	35	39	sufficiently	sufficiently	ADV
ejpam-3972	35	40	secure	secure	ADJ
ejpam-3972	35	41	in	in	ADP
ejpam-3972	35	42	most	most	ADJ
ejpam-3972	35	43	situations	situation	NOUN
ejpam-3972	35	44	.	.	PUNCT
ejpam-3972	36	1	2	2	X
ejpam-3972	36	2	.	.	X
ejpam-3972	36	3	preliminaries	preliminary	NOUN
ejpam-3972	36	4	let	let	VERB
ejpam-3972	36	5	ω	ω	NOUN
ejpam-3972	36	6	be	be	AUX
ejpam-3972	36	7	an	an	DET
ejpam-3972	36	8	arbitrary	arbitrary	ADJ
ejpam-3972	36	9	nonempty	nonempty	NOUN
ejpam-3972	36	10	set	set	VERB
ejpam-3972	36	11	.	.	PUNCT
ejpam-3972	37	1	we	we	PRON
ejpam-3972	37	2	denote	denote	VERB
ejpam-3972	37	3	by	by	ADP
ejpam-3972	37	4	pas	pas	PROPN
ejpam-3972	37	5	(	(	PUNCT
ejpam-3972	37	6	ω	ω	NOUN
ejpam-3972	37	7	)	)	PUNCT
ejpam-3972	37	8	the	the	DET
ejpam-3972	37	9	set	set	NOUN
ejpam-3972	37	10	of	of	ADP
ejpam-3972	37	11	all	all	DET
ejpam-3972	37	12	bijections	bijection	NOUN
ejpam-3972	37	13	from	from	ADP
ejpam-3972	37	14	ω	ω	NUM
ejpam-3972	37	15	to	to	ADP
ejpam-3972	37	16	itself	itself	PRON
ejpam-3972	37	17	.	.	PUNCT
ejpam-3972	38	1	these	these	DET
ejpam-3972	38	2	bijections	bijection	NOUN
ejpam-3972	38	3	on	on	ADP
ejpam-3972	38	4	ω	ω	NUM
ejpam-3972	38	5	are	be	AUX
ejpam-3972	38	6	also	also	ADV
ejpam-3972	38	7	so	so	ADV
ejpam-3972	38	8	-	-	PUNCT
ejpam-3972	38	9	called	call	VERB
ejpam-3972	38	10	pseudo	pseudo	NOUN
ejpam-3972	38	11	-	-	NOUN
ejpam-3972	38	12	associations	association	NOUN
ejpam-3972	38	13	,	,	PUNCT
ejpam-3972	38	14	and	and	CCONJ
ejpam-3972	38	15	if	if	SCONJ
ejpam-3972	38	16	ω	ω	PROPN
ejpam-3972	38	17	finite	finite	VERB
ejpam-3972	38	18	,	,	PUNCT
ejpam-3972	38	19	this	this	PRON
ejpam-3972	38	20	is	be	AUX
ejpam-3972	38	21	,	,	PUNCT
ejpam-3972	38	22	of	of	ADP
ejpam-3972	38	23	course	course	NOUN
ejpam-3972	38	24	,	,	PUNCT
ejpam-3972	38	25	the	the	DET
ejpam-3972	38	26	new	new	ADJ
ejpam-3972	38	27	term	term	NOUN
ejpam-3972	38	28	.	.	PUNCT
ejpam-3972	39	1	the	the	DET
ejpam-3972	39	2	object	object	NOUN
ejpam-3972	39	3	pas	pas	NOUN
ejpam-3972	39	4	(	(	PUNCT
ejpam-3972	39	5	ω	ω	NOUN
ejpam-3972	39	6	)	)	PUNCT
ejpam-3972	39	7	is	be	AUX
ejpam-3972	39	8	called	call	VERB
ejpam-3972	39	9	the	the	DET
ejpam-3972	39	10	group	group	NOUN
ejpam-3972	39	11	[	[	X
ejpam-3972	39	12	4	4	X
ejpam-3972	39	13	]	]	PUNCT
ejpam-3972	39	14	on	on	ADP
ejpam-3972	39	15	ω	ω	NUM
ejpam-3972	39	16	,	,	PUNCT
ejpam-3972	39	17	and	and	CCONJ
ejpam-3972	39	18	subgroup	subgroup	NOUN
ejpam-3972	39	19	of	of	ADP
ejpam-3972	39	20	pas	pas	PROPN
ejpam-3972	39	21	(	(	PUNCT
ejpam-3972	39	22	ω	ω	NOUN
ejpam-3972	39	23	)	)	PUNCT
ejpam-3972	39	24	,	,	PUNCT
ejpam-3972	39	25	denoted	denote	VERB
ejpam-3972	39	26	by	by	ADP
ejpam-3972	39	27	pas	pas	PROPN
ejpam-3972	39	28	(	(	PUNCT
ejpam-3972	39	29	〈	〈	PROPN
ejpam-3972	39	30	ω	ω	PROPN
ejpam-3972	39	31	〉	〉	PROPN
ejpam-3972	39	32	)	)	PUNCT
ejpam-3972	39	33	,	,	PUNCT
ejpam-3972	39	34	which	which	PRON
ejpam-3972	39	35	we	we	PRON
ejpam-3972	39	36	are	be	AUX
ejpam-3972	39	37	about	about	ADJ
ejpam-3972	39	38	to	to	PART
ejpam-3972	39	39	define	define	VERB
ejpam-3972	39	40	.	.	PUNCT
ejpam-3972	40	1	definition	definition	NOUN
ejpam-3972	40	2	1	1	NUM
ejpam-3972	40	3	.	.	PUNCT
ejpam-3972	41	1	[	[	X
ejpam-3972	41	2	4	4	X
ejpam-3972	41	3	]	]	PUNCT
ejpam-3972	41	4	let	let	VERB
ejpam-3972	41	5	ω	ω	PRON
ejpam-3972	41	6	be	be	AUX
ejpam-3972	41	7	an	an	DET
ejpam-3972	41	8	arbitrary	arbitrary	ADJ
ejpam-3972	41	9	set	set	NOUN
ejpam-3972	41	10	and	and	CCONJ
ejpam-3972	41	11	let	let	VERB
ejpam-3972	41	12	g	g	PRON
ejpam-3972	41	13	be	be	AUX
ejpam-3972	41	14	a	a	DET
ejpam-3972	41	15	group	group	NOUN
ejpam-3972	41	16	.	.	PUNCT
ejpam-3972	42	1	we	we	PRON
ejpam-3972	42	2	say	say	VERB
ejpam-3972	42	3	that	that	SCONJ
ejpam-3972	42	4	g	g	PROPN
ejpam-3972	42	5	is	be	AUX
ejpam-3972	42	6	a	a	DET
ejpam-3972	42	7	pas	pas	NOUN
ejpam-3972	42	8	(	(	PUNCT
ejpam-3972	42	9	ω	ω	NOUN
ejpam-3972	42	10	)	)	PUNCT
ejpam-3972	42	11	on	on	ADP
ejpam-3972	42	12	ω	ω	PROPN
ejpam-3972	42	13	is	be	AUX
ejpam-3972	42	14	any	any	DET
ejpam-3972	42	15	nonempty	nonempty	NOUN
ejpam-3972	42	16	subset	subset	VERB
ejpam-3972	42	17	p	p	VERB
ejpam-3972	42	18	⊆	⊆	NUM
ejpam-3972	42	19	pas	pas	NOUN
ejpam-3972	42	20	(	(	PUNCT
ejpam-3972	42	21	ω	ω	NOUN
ejpam-3972	42	22	)	)	PUNCT
ejpam-3972	42	23	with	with	ADP
ejpam-3972	42	24	the	the	DET
ejpam-3972	42	25	following	follow	VERB
ejpam-3972	42	26	properties	property	NOUN
ejpam-3972	42	27	:	:	PUNCT
ejpam-3972	42	28	(	(	PUNCT
ejpam-3972	42	29	pag1	pag1	NOUN
ejpam-3972	42	30	)	)	PUNCT
ejpam-3972	42	31	p	p	NOUN
ejpam-3972	42	32	is	be	AUX
ejpam-3972	42	33	closed	close	VERB
ejpam-3972	42	34	under	under	ADP
ejpam-3972	42	35	a	a	DET
ejpam-3972	42	36	pseudo	pseudo	NOUN
ejpam-3972	42	37	associative	associative	ADJ
ejpam-3972	42	38	binary	binary	ADJ
ejpam-3972	42	39	operation	operation	NOUN
ejpam-3972	42	40	•.	•.	NOUN
ejpam-3972	42	41	(	(	PUNCT
ejpam-3972	42	42	pag2	pag2	NOUN
ejpam-3972	42	43	)	)	PUNCT
ejpam-3972	42	44	for	for	ADP
ejpam-3972	42	45	each	each	DET
ejpam-3972	42	46	x	x	SYM
ejpam-3972	42	47	∈	∈	PROPN
ejpam-3972	42	48	p	p	X
ejpam-3972	42	49	,	,	PUNCT
ejpam-3972	42	50	1	1	NUM
ejpam-3972	42	51	•	•	NOUN
ejpam-3972	42	52	x	x	X
ejpam-3972	42	53	=	=	PUNCT
ejpam-3972	42	54	x	x	SYM
ejpam-3972	42	55	=	=	PUNCT
ejpam-3972	42	56	x	x	SYM
ejpam-3972	42	57	•	•	NUM
ejpam-3972	42	58	1	1	NUM
ejpam-3972	42	59	.	.	PUNCT
ejpam-3972	43	1	(	(	PUNCT
ejpam-3972	43	2	pag3	pag3	PROPN
ejpam-3972	43	3	)	)	PUNCT
ejpam-3972	43	4	for	for	ADP
ejpam-3972	43	5	each	each	DET
ejpam-3972	43	6	x	x	SYM
ejpam-3972	43	7	∈	∈	PROPN
ejpam-3972	43	8	p	p	NOUN
ejpam-3972	43	9	,	,	PUNCT
ejpam-3972	43	10	there	there	PRON
ejpam-3972	43	11	exists	exist	VERB
ejpam-3972	43	12	x−1	x−1	PROPN
ejpam-3972	43	13	∈	∈	PROPN
ejpam-3972	43	14	p	p	NOUN
ejpam-3972	44	1	such	such	ADJ
ejpam-3972	44	2	that	that	SCONJ
ejpam-3972	44	3	x	x	PROPN
ejpam-3972	44	4	•	•	X
ejpam-3972	44	5	x−1	x−1	X
ejpam-3972	44	6	=	=	NOUN
ejpam-3972	44	7	1	1	NUM
ejpam-3972	44	8	=	=	SYM
ejpam-3972	44	9	x−1	x−1	PROPN
ejpam-3972	44	10	•	•	NUM
ejpam-3972	44	11	x.	x.	NOUN
ejpam-3972	44	12	(	(	PUNCT
ejpam-3972	44	13	pag4	pag4	PROPN
ejpam-3972	44	14	)	)	PUNCT
ejpam-3972	44	15	for	for	ADP
ejpam-3972	44	16	all	all	DET
ejpam-3972	44	17	x	x	NOUN
ejpam-3972	44	18	,	,	PUNCT
ejpam-3972	44	19	y	y	PROPN
ejpam-3972	44	20	,	,	PUNCT
ejpam-3972	44	21	z	z	PROPN
ejpam-3972	44	22	∈	∈	PROPN
ejpam-3972	44	23	p	p	X
ejpam-3972	44	24	,	,	PUNCT
ejpam-3972	44	25	(	(	PUNCT
ejpam-3972	44	26	x	x	SYM
ejpam-3972	44	27	•	•	NUM
ejpam-3972	44	28	y	y	NOUN
ejpam-3972	44	29	)	)	PUNCT
ejpam-3972	44	30	•	•	NOUN
ejpam-3972	44	31	z	z	NOUN
ejpam-3972	44	32	=	=	PUNCT
ejpam-3972	44	33	x	x	SYM
ejpam-3972	44	34	•	•	X
ejpam-3972	44	35	(	(	PUNCT
ejpam-3972	44	36	z	z	NOUN
ejpam-3972	44	37	•	•	PROPN
ejpam-3972	44	38	y	y	PROPN
ejpam-3972	44	39	)	)	PUNCT
ejpam-3972	44	40	.	.	PUNCT
ejpam-3972	45	1	definition	definition	NOUN
ejpam-3972	45	2	2	2	NUM
ejpam-3972	45	3	.	.	PUNCT
ejpam-3972	46	1	[	[	X
ejpam-3972	46	2	4	4	X
ejpam-3972	46	3	]	]	PUNCT
ejpam-3972	46	4	a	a	DET
ejpam-3972	46	5	mirror	mirror	NOUN
ejpam-3972	46	6	is	be	AUX
ejpam-3972	46	7	called	call	VERB
ejpam-3972	46	8	quasi	quasi	NOUN
ejpam-3972	46	9	-	-	NOUN
ejpam-3972	46	10	group	group	ADJ
ejpam-3972	46	11	g	g	NOUN
ejpam-3972	46	12	with	with	ADP
ejpam-3972	46	13	an	an	DET
ejpam-3972	46	14	identity	identity	NOUN
ejpam-3972	46	15	element	element	NOUN
ejpam-3972	46	16	1	1	NUM
ejpam-3972	46	17	with	with	ADP
ejpam-3972	46	18	an	an	DET
ejpam-3972	46	19	associative	associative	ADJ
ejpam-3972	46	20	binary	binary	ADJ
ejpam-3972	46	21	operation	operation	NOUN
ejpam-3972	46	22	•	•	ADP
ejpam-3972	46	23	defined	define	VERB
ejpam-3972	46	24	on	on	ADP
ejpam-3972	46	25	g	g	PROPN
ejpam-3972	46	26	such	such	ADJ
ejpam-3972	46	27	that	that	SCONJ
ejpam-3972	46	28	there	there	PRON
ejpam-3972	46	29	exists	exist	VERB
ejpam-3972	46	30	1	1	NUM
ejpam-3972	46	31	∈	∈	NOUN
ejpam-3972	46	32	g	g	NOUN
ejpam-3972	46	33	if	if	SCONJ
ejpam-3972	46	34	it	it	PRON
ejpam-3972	46	35	satisfies	satisfy	VERB
ejpam-3972	46	36	the	the	DET
ejpam-3972	46	37	axioms	axiom	NOUN
ejpam-3972	46	38	:	:	PUNCT
ejpam-3972	46	39	(	(	PUNCT
ejpam-3972	46	40	qug1	qug1	PROPN
ejpam-3972	46	41	)	)	PUNCT
ejpam-3972	46	42	1	1	NUM
ejpam-3972	46	43	•	•	NOUN
ejpam-3972	46	44	x	x	X
ejpam-3972	47	1	=	=	PUNCT
ejpam-3972	47	2	x	x	SYM
ejpam-3972	47	3	=	=	PUNCT
ejpam-3972	47	4	x	x	SYM
ejpam-3972	47	5	•	•	NUM
ejpam-3972	47	6	1	1	NUM
ejpam-3972	47	7	for	for	ADP
ejpam-3972	47	8	all	all	DET
ejpam-3972	47	9	x	x	SYM
ejpam-3972	47	10	∈	∈	PROPN
ejpam-3972	47	11	g	g	NOUN
ejpam-3972	47	12	and	and	CCONJ
ejpam-3972	47	13	(	(	PUNCT
ejpam-3972	47	14	qug2	qug2	PROPN
ejpam-3972	47	15	)	)	PUNCT
ejpam-3972	47	16	1	1	NUM
ejpam-3972	47	17	•	•	NOUN
ejpam-3972	47	18	(	(	PUNCT
ejpam-3972	47	19	x	x	SYM
ejpam-3972	47	20	•	•	NUM
ejpam-3972	47	21	y	y	NOUN
ejpam-3972	47	22	)	)	PUNCT
ejpam-3972	47	23	=	=	PUNCT
ejpam-3972	47	24	(	(	PUNCT
ejpam-3972	47	25	1	1	NUM
ejpam-3972	47	26	•	•	NUM
ejpam-3972	47	27	y	y	NOUN
ejpam-3972	47	28	)	)	PUNCT
ejpam-3972	47	29	•	•	NOUN
ejpam-3972	47	30	x	x	X
ejpam-3972	47	31	=	=	SYM
ejpam-3972	47	32	y	y	PROPN
ejpam-3972	47	33	•	•	NUM
ejpam-3972	47	34	x	x	PUNCT
ejpam-3972	47	35	for	for	ADP
ejpam-3972	47	36	all	all	DET
ejpam-3972	47	37	x	x	NOUN
ejpam-3972	47	38	,	,	PUNCT
ejpam-3972	47	39	y	y	PROPN
ejpam-3972	47	40	∈	∈	PROPN
ejpam-3972	47	41	g.	g.	NOUN
ejpam-3972	47	42	definition	definition	NOUN
ejpam-3972	47	43	3	3	NUM
ejpam-3972	47	44	.	.	PUNCT
ejpam-3972	48	1	[	[	X
ejpam-3972	48	2	7	7	X
ejpam-3972	48	3	]	]	X
ejpam-3972	48	4	a	a	DET
ejpam-3972	48	5	bcl+	bcl+	PROPN
ejpam-3972	48	6	algebra	algebra	NOUN
ejpam-3972	48	7	is	be	AUX
ejpam-3972	48	8	a	a	DET
ejpam-3972	48	9	triple	triple	ADJ
ejpam-3972	48	10	(	(	PUNCT
ejpam-3972	48	11	x	x	NOUN
ejpam-3972	48	12	;	;	PUNCT
ejpam-3972	48	13	•	•	NUM
ejpam-3972	48	14	,	,	PUNCT
ejpam-3972	48	15	1	1	NUM
ejpam-3972	48	16	)	)	PUNCT
ejpam-3972	48	17	,	,	PUNCT
ejpam-3972	48	18	where	where	SCONJ
ejpam-3972	48	19	x	x	PRON
ejpam-3972	48	20	is	be	AUX
ejpam-3972	48	21	a	a	DET
ejpam-3972	48	22	nonempty	nonempty	ADJ
ejpam-3972	48	23	set	set	VERB
ejpam-3972	48	24	,	,	PUNCT
ejpam-3972	48	25	•	•	PRON
ejpam-3972	48	26	is	be	AUX
ejpam-3972	48	27	a	a	DET
ejpam-3972	48	28	binary	binary	ADJ
ejpam-3972	48	29	operation	operation	NOUN
ejpam-3972	48	30	on	on	ADP
ejpam-3972	48	31	x	x	NOUN
ejpam-3972	48	32	,	,	PUNCT
ejpam-3972	48	33	and	and	CCONJ
ejpam-3972	48	34	1	1	NUM
ejpam-3972	48	35	∈	∈	NOUN
ejpam-3972	48	36	x	x	PUNCT
ejpam-3972	48	37	is	be	AUX
ejpam-3972	48	38	an	an	DET
ejpam-3972	48	39	element	element	NOUN
ejpam-3972	48	40	such	such	ADJ
ejpam-3972	48	41	that	that	SCONJ
ejpam-3972	48	42	the	the	DET
ejpam-3972	48	43	following	follow	VERB
ejpam-3972	48	44	three	three	NUM
ejpam-3972	48	45	axioms	axiom	NOUN
ejpam-3972	48	46	hold	hold	VERB
ejpam-3972	48	47	for	for	ADP
ejpam-3972	48	48	any	any	DET
ejpam-3972	48	49	x	x	NOUN
ejpam-3972	48	50	,	,	PUNCT
ejpam-3972	48	51	y	y	PROPN
ejpam-3972	48	52	,	,	PUNCT
ejpam-3972	48	53	z	z	PROPN
ejpam-3972	48	54	∈	∈	PROPN
ejpam-3972	48	55	x.	x.	NOUN
ejpam-3972	48	56	(	(	PUNCT
ejpam-3972	48	57	bcl+1	bcl+1	X
ejpam-3972	48	58	)	)	PUNCT
ejpam-3972	48	59	x	x	PUNCT
ejpam-3972	49	1	•	•	NUM
ejpam-3972	49	2	x	x	SYM
ejpam-3972	49	3	=	=	SYM
ejpam-3972	49	4	1	1	X
ejpam-3972	49	5	.	.	PUNCT
ejpam-3972	49	6	(	(	PUNCT
ejpam-3972	49	7	bcl+2	bcl+2	X
ejpam-3972	49	8	)	)	PUNCT
ejpam-3972	49	9	x	x	SYM
ejpam-3972	49	10	•	•	NUM
ejpam-3972	49	11	y	y	NOUN
ejpam-3972	49	12	=	=	SYM
ejpam-3972	49	13	1	1	NUM
ejpam-3972	49	14	and	and	CCONJ
ejpam-3972	49	15	y	y	PROPN
ejpam-3972	49	16	•	•	NOUN
ejpam-3972	49	17	x	x	X
ejpam-3972	49	18	=	=	SYM
ejpam-3972	49	19	1	1	NUM
ejpam-3972	49	20	imply	imply	VERB
ejpam-3972	49	21	x	x	X
ejpam-3972	49	22	=	=	SYM
ejpam-3972	49	23	y.	y.	NOUN
ejpam-3972	49	24	(	(	PUNCT
ejpam-3972	49	25	bcl+3	bcl+3	PROPN
ejpam-3972	49	26	)	)	PUNCT
ejpam-3972	49	27	(	(	PUNCT
ejpam-3972	49	28	(	(	PUNCT
ejpam-3972	49	29	x	x	SYM
ejpam-3972	49	30	•	•	NUM
ejpam-3972	49	31	y	y	NOUN
ejpam-3972	49	32	)	)	PUNCT
ejpam-3972	49	33	•	•	NUM
ejpam-3972	49	34	z	z	NOUN
ejpam-3972	49	35	)	)	PUNCT
ejpam-3972	49	36	•	•	NOUN
ejpam-3972	49	37	(	(	PUNCT
ejpam-3972	49	38	(	(	PUNCT
ejpam-3972	49	39	x	x	SYM
ejpam-3972	49	40	•	•	NUM
ejpam-3972	49	41	z	z	NOUN
ejpam-3972	49	42	)	)	PUNCT
ejpam-3972	49	43	•	•	NUM
ejpam-3972	49	44	y	y	NOUN
ejpam-3972	49	45	)	)	PUNCT
ejpam-3972	49	46	=	=	PUNCT
ejpam-3972	50	1	(	(	PUNCT
ejpam-3972	50	2	z	z	NOUN
ejpam-3972	50	3	•	•	NUM
ejpam-3972	50	4	y	y	NOUN
ejpam-3972	50	5	)	)	PUNCT
ejpam-3972	50	6	•	•	NOUN
ejpam-3972	50	7	x.	x.	PROPN
ejpam-3972	51	1	y.	y.	PROPN
ejpam-3972	51	2	liu	liu	PROPN
ejpam-3972	51	3	/	/	SYM
ejpam-3972	51	4	eur	eur	PROPN
ejpam-3972	51	5	.	.	PUNCT
ejpam-3972	52	1	j.	j.	PROPN
ejpam-3972	52	2	pure	pure	PROPN
ejpam-3972	52	3	appl	appl	PROPN
ejpam-3972	52	4	.	.	PROPN
ejpam-3972	52	5	math	math	PROPN
ejpam-3972	52	6	,	,	PUNCT
ejpam-3972	52	7	14	14	NUM
ejpam-3972	52	8	(	(	PUNCT
ejpam-3972	52	9	2	2	NUM
ejpam-3972	52	10	)	)	PUNCT
ejpam-3972	52	11	(	(	PUNCT
ejpam-3972	52	12	2021	2021	NUM
ejpam-3972	52	13	)	)	PUNCT
ejpam-3972	52	14	,	,	PUNCT
ejpam-3972	52	15	521	521	NUM
ejpam-3972	52	16	-	-	SYM
ejpam-3972	52	17	536	536	NUM
ejpam-3972	52	18	523	523	NUM
ejpam-3972	52	19	definition	definition	NOUN
ejpam-3972	52	20	4	4	NUM
ejpam-3972	52	21	.	.	PUNCT
ejpam-3972	53	1	[	[	X
ejpam-3972	53	2	8	8	NUM
ejpam-3972	53	3	]	]	X
ejpam-3972	53	4	if	if	SCONJ
ejpam-3972	53	5	(	(	PUNCT
ejpam-3972	53	6	f(x	f(x	PROPN
ejpam-3972	53	7	,	,	PUNCT
ejpam-3972	53	8	y	y	PROPN
ejpam-3972	53	9	,	,	PUNCT
ejpam-3972	53	10	z	z	NOUN
ejpam-3972	53	11	)	)	PUNCT
ejpam-3972	53	12	,	,	PUNCT
ejpam-3972	53	13	g(x	g(x	PROPN
ejpam-3972	53	14	,	,	PUNCT
ejpam-3972	53	15	y	y	PROPN
ejpam-3972	53	16	,	,	PUNCT
ejpam-3972	53	17	z	z	NOUN
ejpam-3972	53	18	)	)	PUNCT
ejpam-3972	53	19	)	)	PUNCT
ejpam-3972	54	1	=	=	SYM
ejpam-3972	54	2	1	1	NUM
ejpam-3972	54	3	,	,	PUNCT
ejpam-3972	54	4	then	then	ADV
ejpam-3972	54	5	we	we	PRON
ejpam-3972	54	6	say	say	VERB
ejpam-3972	54	7	that	that	SCONJ
ejpam-3972	54	8	f(x	f(x	PROPN
ejpam-3972	54	9	,	,	PUNCT
ejpam-3972	54	10	y	y	PROPN
ejpam-3972	54	11	,	,	PUNCT
ejpam-3972	54	12	z	z	NOUN
ejpam-3972	54	13	)	)	PUNCT
ejpam-3972	54	14	and	and	CCONJ
ejpam-3972	54	15	g(x	g(x	PROPN
ejpam-3972	54	16	,	,	PUNCT
ejpam-3972	54	17	y	y	PROPN
ejpam-3972	54	18	,	,	PUNCT
ejpam-3972	54	19	z	z	NOUN
ejpam-3972	54	20	)	)	PUNCT
ejpam-3972	54	21	are	be	AUX
ejpam-3972	54	22	coprime	coprime	ADJ
ejpam-3972	54	23	topological	topological	ADJ
ejpam-3972	54	24	groups	group	NOUN
ejpam-3972	54	25	(	(	PUNCT
ejpam-3972	54	26	y	y	NOUN
ejpam-3972	54	27	,	,	PUNCT
ejpam-3972	54	28	=	=	NOUN
ejpam-3972	54	29	,	,	PUNCT
ejpam-3972	54	30	•	•	NUM
ejpam-3972	54	31	)	)	PUNCT
ejpam-3972	54	32	for	for	ADP
ejpam-3972	54	33	all	all	DET
ejpam-3972	54	34	x	x	NOUN
ejpam-3972	54	35	,	,	PUNCT
ejpam-3972	54	36	y	y	PROPN
ejpam-3972	54	37	,	,	PUNCT
ejpam-3972	54	38	z	z	PROPN
ejpam-3972	54	39	∈	∈	PROPN
ejpam-3972	54	40	y.	y.	NOUN
ejpam-3972	54	41	let	let	VERB
ejpam-3972	54	42	h(x	h(x	PROPN
ejpam-3972	54	43	,	,	PUNCT
ejpam-3972	54	44	y	y	PROPN
ejpam-3972	54	45	,	,	PUNCT
ejpam-3972	54	46	z	z	NOUN
ejpam-3972	54	47	)	)	PUNCT
ejpam-3972	54	48	,	,	PUNCT
ejpam-3972	54	49	f(x	f(x	PROPN
ejpam-3972	54	50	,	,	PUNCT
ejpam-3972	54	51	y	y	PROPN
ejpam-3972	54	52	,	,	PUNCT
ejpam-3972	54	53	z	z	NOUN
ejpam-3972	54	54	)	)	PUNCT
ejpam-3972	54	55	and	and	CCONJ
ejpam-3972	54	56	g(x	g(x	PROPN
ejpam-3972	54	57	,	,	PUNCT
ejpam-3972	54	58	y	y	PROPN
ejpam-3972	54	59	,	,	PUNCT
ejpam-3972	54	60	z	z	NOUN
ejpam-3972	54	61	)	)	PUNCT
ejpam-3972	54	62	be	be	AUX
ejpam-3972	54	63	ternary	ternary	ADJ
ejpam-3972	54	64	polynomial	polynomial	ADJ
ejpam-3972	54	65	.	.	PUNCT
ejpam-3972	55	1	suppose	suppose	VERB
ejpam-3972	55	2	the	the	DET
ejpam-3972	55	3	following	follow	VERB
ejpam-3972	55	4	conditions	condition	NOUN
ejpam-3972	55	5	hold	hold	VERB
ejpam-3972	55	6	:	:	PUNCT
ejpam-3972	55	7	(	(	PUNCT
ejpam-3972	55	8	wht1	wht1	PROPN
ejpam-3972	55	9	)	)	PUNCT
ejpam-3972	55	10	h(x	h(x	PROPN
ejpam-3972	55	11	,	,	PUNCT
ejpam-3972	55	12	y	y	PROPN
ejpam-3972	55	13	,	,	PUNCT
ejpam-3972	55	14	z	z	NOUN
ejpam-3972	55	15	)	)	PUNCT
ejpam-3972	55	16	=	=	PUNCT
ejpam-3972	56	1	(	(	PUNCT
ejpam-3972	56	2	z	z	NOUN
ejpam-3972	56	3	•	•	NUM
ejpam-3972	56	4	y	y	NOUN
ejpam-3972	56	5	)	)	PUNCT
ejpam-3972	56	6	•	•	NOUN
ejpam-3972	56	7	x.	x.	NOUN
ejpam-3972	56	8	(	(	PUNCT
ejpam-3972	56	9	wht2	wht2	PROPN
ejpam-3972	56	10	)	)	PUNCT
ejpam-3972	56	11	f(x	f(x	PROPN
ejpam-3972	56	12	,	,	PUNCT
ejpam-3972	56	13	y	y	PROPN
ejpam-3972	56	14	,	,	PUNCT
ejpam-3972	56	15	z	z	NOUN
ejpam-3972	56	16	)	)	PUNCT
ejpam-3972	56	17	=	=	SYM
ejpam-3972	57	1	(	(	PUNCT
ejpam-3972	57	2	x	x	SYM
ejpam-3972	57	3	•	•	NUM
ejpam-3972	57	4	y	y	NOUN
ejpam-3972	57	5	)	)	PUNCT
ejpam-3972	57	6	•	•	NOUN
ejpam-3972	57	7	z.	z.	PROPN
ejpam-3972	57	8	(	(	PUNCT
ejpam-3972	57	9	wht3	wht3	NOUN
ejpam-3972	57	10	)	)	PUNCT
ejpam-3972	58	1	g(x	g(x	PROPN
ejpam-3972	58	2	,	,	PUNCT
ejpam-3972	58	3	y	y	PROPN
ejpam-3972	58	4	,	,	PUNCT
ejpam-3972	58	5	z	z	NOUN
ejpam-3972	58	6	)	)	PUNCT
ejpam-3972	58	7	=	=	SYM
ejpam-3972	59	1	(	(	PUNCT
ejpam-3972	59	2	x	x	SYM
ejpam-3972	59	3	•	•	NUM
ejpam-3972	59	4	z	z	NOUN
ejpam-3972	59	5	)	)	PUNCT
ejpam-3972	59	6	•	•	NOUN
ejpam-3972	59	7	y.	y.	NOUN
ejpam-3972	59	8	definition	definition	NOUN
ejpam-3972	59	9	5	5	NUM
ejpam-3972	59	10	.	.	PUNCT
ejpam-3972	60	1	[	[	X
ejpam-3972	60	2	7	7	X
ejpam-3972	60	3	]	]	X
ejpam-3972	60	4	if	if	SCONJ
ejpam-3972	60	5	(	(	PUNCT
ejpam-3972	60	6	h(x	h(x	PROPN
ejpam-3972	60	7	,	,	PUNCT
ejpam-3972	60	8	y	y	PROPN
ejpam-3972	60	9	,	,	PUNCT
ejpam-3972	60	10	z	z	NOUN
ejpam-3972	60	11	)	)	PUNCT
ejpam-3972	60	12	,	,	PUNCT
ejpam-3972	60	13	f(x	f(x	PROPN
ejpam-3972	60	14	,	,	PUNCT
ejpam-3972	60	15	y	y	PROPN
ejpam-3972	60	16	,	,	PUNCT
ejpam-3972	60	17	z	z	NOUN
ejpam-3972	60	18	)	)	PUNCT
ejpam-3972	60	19	)	)	PUNCT
ejpam-3972	61	1	=	=	SYM
ejpam-3972	61	2	1	1	NUM
ejpam-3972	61	3	(	(	PUNCT
ejpam-3972	61	4	1	1	NUM
ejpam-3972	61	5	)	)	PUNCT
ejpam-3972	61	6	and	and	CCONJ
ejpam-3972	61	7	(	(	PUNCT
ejpam-3972	61	8	h(x	h(x	PROPN
ejpam-3972	61	9	,	,	PUNCT
ejpam-3972	61	10	y	y	PROPN
ejpam-3972	61	11	,	,	PUNCT
ejpam-3972	61	12	z	z	NOUN
ejpam-3972	61	13	)	)	PUNCT
ejpam-3972	61	14	,	,	PUNCT
ejpam-3972	61	15	g(x	g(x	PROPN
ejpam-3972	61	16	,	,	PUNCT
ejpam-3972	61	17	y	y	PROPN
ejpam-3972	61	18	,	,	PUNCT
ejpam-3972	61	19	z	z	NOUN
ejpam-3972	61	20	)	)	PUNCT
ejpam-3972	61	21	)	)	PUNCT
ejpam-3972	62	1	=	=	SYM
ejpam-3972	62	2	1	1	NUM
ejpam-3972	62	3	,	,	PUNCT
ejpam-3972	62	4	(	(	PUNCT
ejpam-3972	62	5	2	2	NUM
ejpam-3972	62	6	)	)	PUNCT
ejpam-3972	62	7	then	then	ADV
ejpam-3972	62	8	(	(	PUNCT
ejpam-3972	62	9	h(x	h(x	PROPN
ejpam-3972	62	10	,	,	PUNCT
ejpam-3972	62	11	y	y	PROPN
ejpam-3972	62	12	,	,	PUNCT
ejpam-3972	62	13	z	z	NOUN
ejpam-3972	62	14	)	)	PUNCT
ejpam-3972	62	15	,	,	PUNCT
ejpam-3972	62	16	f(x	f(x	PROPN
ejpam-3972	62	17	,	,	PUNCT
ejpam-3972	62	18	y	y	PROPN
ejpam-3972	62	19	,	,	PUNCT
ejpam-3972	62	20	z	z	NOUN
ejpam-3972	62	21	)	)	PUNCT
ejpam-3972	62	22	•	•	ADV
ejpam-3972	62	23	g(x	g(x	PROPN
ejpam-3972	62	24	,	,	PUNCT
ejpam-3972	62	25	y	y	PROPN
ejpam-3972	62	26	,	,	PUNCT
ejpam-3972	62	27	z	z	NOUN
ejpam-3972	62	28	)	)	PUNCT
ejpam-3972	62	29	)	)	PUNCT
ejpam-3972	63	1	=	=	PUNCT
ejpam-3972	63	2	1	1	X
ejpam-3972	63	3	.	.	PUNCT
ejpam-3972	63	4	(	(	PUNCT
ejpam-3972	63	5	3	3	X
ejpam-3972	63	6	)	)	PUNCT
ejpam-3972	63	7	theorem	theorem	NOUN
ejpam-3972	63	8	1	1	NUM
ejpam-3972	63	9	.	.	PUNCT
ejpam-3972	64	1	[	[	X
ejpam-3972	64	2	4	4	X
ejpam-3972	64	3	]	]	PUNCT
ejpam-3972	64	4	let	let	VERB
ejpam-3972	64	5	g	g	PRON
ejpam-3972	64	6	be	be	AUX
ejpam-3972	64	7	a	a	DET
ejpam-3972	64	8	group	group	NOUN
ejpam-3972	64	9	with	with	ADP
ejpam-3972	64	10	an	an	DET
ejpam-3972	64	11	associative	associative	ADJ
ejpam-3972	64	12	multiplication	multiplication	NOUN
ejpam-3972	64	13	and	and	CCONJ
ejpam-3972	64	14	suppose	suppose	VERB
ejpam-3972	64	15	there	there	PRON
ejpam-3972	64	16	exist	exist	VERB
ejpam-3972	64	17	unique	unique	ADJ
ejpam-3972	64	18	element	element	NOUN
ejpam-3972	64	19	x	x	NOUN
ejpam-3972	64	20	,	,	PUNCT
ejpam-3972	64	21	y	y	PROPN
ejpam-3972	64	22	∈	∈	PROPN
ejpam-3972	64	23	g	g	ADP
ejpam-3972	64	24	such	such	ADJ
ejpam-3972	64	25	that	that	SCONJ
ejpam-3972	64	26	x	x	PROPN
ejpam-3972	64	27	•	•	NUM
ejpam-3972	64	28	y	y	NOUN
ejpam-3972	64	29	=	=	SYM
ejpam-3972	64	30	1	1	NUM
ejpam-3972	64	31	•	•	NOUN
ejpam-3972	64	32	(	(	PUNCT
ejpam-3972	64	33	y	y	NOUN
ejpam-3972	64	34	•	•	NUM
ejpam-3972	64	35	x	x	NOUN
ejpam-3972	64	36	)	)	PUNCT
ejpam-3972	64	37	.	.	PUNCT
ejpam-3972	65	1	(	(	PUNCT
ejpam-3972	65	2	4	4	X
ejpam-3972	65	3	)	)	PUNCT
ejpam-3972	65	4	then	then	ADV
ejpam-3972	65	5	g	g	PROPN
ejpam-3972	65	6	is	be	AUX
ejpam-3972	65	7	a	a	DET
ejpam-3972	65	8	commutative	commutative	ADJ
ejpam-3972	65	9	group	group	NOUN
ejpam-3972	65	10	or	or	CCONJ
ejpam-3972	65	11	abelian	abelian	NOUN
ejpam-3972	65	12	.	.	PUNCT
ejpam-3972	66	1	we	we	PRON
ejpam-3972	66	2	think	think	VERB
ejpam-3972	66	3	of	of	ADP
ejpam-3972	66	4	a	a	DET
ejpam-3972	66	5	public	public	ADJ
ejpam-3972	66	6	-	-	PUNCT
ejpam-3972	66	7	key	key	NOUN
ejpam-3972	66	8	system	system	NOUN
ejpam-3972	66	9	in	in	ADP
ejpam-3972	66	10	terms	term	NOUN
ejpam-3972	66	11	of	of	ADP
ejpam-3972	66	12	an	an	DET
ejpam-3972	66	13	abstraction	abstraction	NOUN
ejpam-3972	66	14	called	call	VERB
ejpam-3972	66	15	a	a	DET
ejpam-3972	66	16	one	one	NUM
ejpam-3972	66	17	-	-	PUNCT
ejpam-3972	66	18	way	way	NOUN
ejpam-3972	66	19	function	function	NOUN
ejpam-3972	66	20	more	more	ADV
ejpam-3972	66	21	precise	precise	ADJ
ejpam-3972	66	22	,	,	PUNCT
ejpam-3972	66	23	as	as	SCONJ
ejpam-3972	66	24	follows	follow	VERB
ejpam-3972	66	25	.	.	PUNCT
ejpam-3972	67	1	definition	definition	NOUN
ejpam-3972	67	2	6	6	NUM
ejpam-3972	67	3	.	.	PUNCT
ejpam-3972	68	1	a	a	DET
ejpam-3972	68	2	function	function	NOUN
ejpam-3972	68	3	f	f	PROPN
ejpam-3972	68	4	is	be	AUX
ejpam-3972	68	5	a	a	DET
ejpam-3972	68	6	one	one	NUM
ejpam-3972	68	7	-	-	PUNCT
ejpam-3972	68	8	way	way	NOUN
ejpam-3972	68	9	function	function	NOUN
ejpam-3972	68	10	if	if	SCONJ
ejpam-3972	68	11	(	(	PUNCT
ejpam-3972	68	12	owf1	owf1	NOUN
ejpam-3972	68	13	)	)	PUNCT
ejpam-3972	68	14	the	the	DET
ejpam-3972	68	15	description	description	NOUN
ejpam-3972	68	16	of	of	ADP
ejpam-3972	68	17	f	f	PROPN
ejpam-3972	68	18	is	be	AUX
ejpam-3972	68	19	publicly	publicly	ADV
ejpam-3972	68	20	known	know	VERB
ejpam-3972	68	21	and	and	CCONJ
ejpam-3972	68	22	does	do	AUX
ejpam-3972	68	23	not	not	PART
ejpam-3972	68	24	require	require	VERB
ejpam-3972	68	25	any	any	DET
ejpam-3972	68	26	secret	secret	ADJ
ejpam-3972	68	27	information	information	NOUN
ejpam-3972	68	28	for	for	ADP
ejpam-3972	68	29	its	its	PRON
ejpam-3972	68	30	operation	operation	NOUN
ejpam-3972	68	31	.	.	PUNCT
ejpam-3972	69	1	(	(	PUNCT
ejpam-3972	69	2	owf2	owf2	PROPN
ejpam-3972	69	3	)	)	PUNCT
ejpam-3972	69	4	given	give	VERB
ejpam-3972	69	5	x	x	NOUN
ejpam-3972	69	6	,	,	PUNCT
ejpam-3972	69	7	it	it	PRON
ejpam-3972	69	8	is	be	AUX
ejpam-3972	69	9	easy	easy	ADJ
ejpam-3972	69	10	to	to	PART
ejpam-3972	69	11	compute	compute	VERB
ejpam-3972	69	12	f(x	f(x	PROPN
ejpam-3972	69	13	)	)	PUNCT
ejpam-3972	69	14	.	.	PUNCT
ejpam-3972	70	1	(	(	PUNCT
ejpam-3972	70	2	owf3	owf3	PROPN
ejpam-3972	70	3	)	)	PUNCT
ejpam-3972	70	4	given	give	VERB
ejpam-3972	70	5	y	y	PRON
ejpam-3972	70	6	,	,	PUNCT
ejpam-3972	70	7	in	in	ADP
ejpam-3972	70	8	the	the	DET
ejpam-3972	70	9	range	range	NOUN
ejpam-3972	70	10	of	of	ADP
ejpam-3972	70	11	f	f	PROPN
ejpam-3972	70	12	,	,	PUNCT
ejpam-3972	70	13	it	it	PRON
ejpam-3972	70	14	is	be	AUX
ejpam-3972	70	15	hard	hard	ADJ
ejpam-3972	70	16	to	to	PART
ejpam-3972	70	17	find	find	VERB
ejpam-3972	70	18	an	an	DET
ejpam-3972	70	19	x	x	NOUN
ejpam-3972	70	20	such	such	ADJ
ejpam-3972	70	21	that	that	SCONJ
ejpam-3972	70	22	f(x	f(x	NOUN
ejpam-3972	70	23	)	)	PUNCT
ejpam-3972	71	1	=	=	VERB
ejpam-3972	71	2	y.	y.	NOUN
ejpam-3972	71	3	any	any	DET
ejpam-3972	71	4	efficient	efficient	ADJ
ejpam-3972	71	5	algorithm	algorithm	NOUN
ejpam-3972	71	6	solving	solve	VERB
ejpam-3972	71	7	a	a	DET
ejpam-3972	71	8	p	p	NOUN
ejpam-3972	71	9	-	-	PUNCT
ejpam-3972	71	10	problem	problem	NOUN
ejpam-3972	71	11	succeeds	succeed	VERB
ejpam-3972	71	12	in	in	ADP
ejpam-3972	71	13	inverting	invert	VERB
ejpam-3972	71	14	f	f	PROPN
ejpam-3972	71	15	with	with	ADP
ejpam-3972	71	16	negligible	negligible	ADJ
ejpam-3972	71	17	probability	probability	NOUN
ejpam-3972	71	18	.	.	PUNCT
ejpam-3972	72	1	zero	zero	NUM
ejpam-3972	72	2	-	-	PUNCT
ejpam-3972	72	3	knowledge	knowledge	NOUN
ejpam-3972	72	4	techniques	technique	NOUN
ejpam-3972	72	5	[	[	X
ejpam-3972	72	6	9	9	NUM
ejpam-3972	72	7	]	]	PUNCT
ejpam-3972	72	8	are	be	AUX
ejpam-3972	72	9	mathematical	mathematical	ADJ
ejpam-3972	72	10	methods	method	NOUN
ejpam-3972	72	11	used	use	VERB
ejpam-3972	72	12	to	to	PART
ejpam-3972	72	13	verify	verify	VERB
ejpam-3972	72	14	things	thing	NOUN
ejpam-3972	72	15	without	without	ADP
ejpam-3972	72	16	sharing	share	VERB
ejpam-3972	72	17	or	or	CCONJ
ejpam-3972	72	18	revealing	reveal	VERB
ejpam-3972	72	19	underlying	underlie	VERB
ejpam-3972	72	20	data	datum	NOUN
ejpam-3972	72	21	,	,	PUNCT
ejpam-3972	72	22	and	and	CCONJ
ejpam-3972	72	23	zero	zero	NUM
ejpam-3972	72	24	-	-	PUNCT
ejpam-3972	72	25	knowledge	knowledge	NOUN
ejpam-3972	72	26	protocols	protocol	NOUN
ejpam-3972	72	27	are	be	AUX
ejpam-3972	72	28	probabilistic	probabilistic	ADJ
ejpam-3972	72	29	assessments	assessment	NOUN
ejpam-3972	72	30	.	.	PUNCT
ejpam-3972	73	1	the	the	DET
ejpam-3972	73	2	goal	goal	NOUN
ejpam-3972	73	3	is	be	AUX
ejpam-3972	73	4	to	to	PART
ejpam-3972	73	5	prove	prove	VERB
ejpam-3972	73	6	a	a	DET
ejpam-3972	73	7	statement	statement	NOUN
ejpam-3972	73	8	without	without	ADP
ejpam-3972	73	9	leaking	leak	VERB
ejpam-3972	73	10	extra	extra	ADJ
ejpam-3972	73	11	information	information	NOUN
ejpam-3972	73	12	,	,	PUNCT
ejpam-3972	73	13	for	for	ADP
ejpam-3972	73	14	example	example	NOUN
ejpam-3972	73	15	,	,	PUNCT
ejpam-3972	73	16	for	for	ADP
ejpam-3972	73	17	some	some	DET
ejpam-3972	73	18	n	n	NOUN
ejpam-3972	73	19	,	,	PUNCT
ejpam-3972	73	20	x	x	X
ejpam-3972	73	21	,	,	PUNCT
ejpam-3972	73	22	prove	prove	VERB
ejpam-3972	73	23	x	x	SYM
ejpam-3972	73	24	is	be	AUX
ejpam-3972	73	25	a	a	DET
ejpam-3972	73	26	quadratic	quadratic	ADJ
ejpam-3972	73	27	residue	residue	NOUN
ejpam-3972	73	28	in	in	ADP
ejpam-3972	73	29	z∗n	z∗n	NUM
ejpam-3972	73	30	.	.	PUNCT
ejpam-3972	74	1	definition	definition	NOUN
ejpam-3972	74	2	7	7	NUM
ejpam-3972	74	3	.	.	PUNCT
ejpam-3972	75	1	let	let	VERB
ejpam-3972	75	2	l	l	NOUN
ejpam-3972	75	3	⊆	⊆	NUM
ejpam-3972	75	4	σ∗.	σ∗.	NOUN
ejpam-3972	75	5	a	a	DET
ejpam-3972	75	6	zero	zero	NUM
ejpam-3972	75	7	-	-	PUNCT
ejpam-3972	75	8	knowledge	knowledge	NOUN
ejpam-3972	75	9	proof	proof	NOUN
ejpam-3972	75	10	system	system	NOUN
ejpam-3972	75	11	for	for	ADP
ejpam-3972	75	12	l	l	NOUN
ejpam-3972	75	13	is	be	AUX
ejpam-3972	75	14	a	a	DET
ejpam-3972	75	15	pair	pair	NOUN
ejpam-3972	75	16	(	(	PUNCT
ejpam-3972	75	17	p	p	X
ejpam-3972	75	18	,	,	PUNCT
ejpam-3972	75	19	v	v	NOUN
ejpam-3972	75	20	)	)	PUNCT
ejpam-3972	75	21	satisfying	satisfying	NOUN
ejpam-3972	75	22	(	(	PUNCT
ejpam-3972	75	23	zk1	zk1	NOUN
ejpam-3972	75	24	)	)	PUNCT
ejpam-3972	75	25	for	for	ADP
ejpam-3972	75	26	all	all	DET
ejpam-3972	75	27	x	x	SYM
ejpam-3972	75	28	∈	∈	PROPN
ejpam-3972	75	29	l	l	NOUN
ejpam-3972	75	30	,	,	PUNCT
ejpam-3972	75	31	a	a	DET
ejpam-3972	75	32	verifier	verifier	NOUN
ejpam-3972	75	33	says	say	VERB
ejpam-3972	75	34	“	"	PUNCT
ejpam-3972	75	35	yes	yes	INTJ
ejpam-3972	75	36	”	"	PUNCT
ejpam-3972	75	37	after	after	ADP
ejpam-3972	75	38	interacting	interact	VERB
ejpam-3972	75	39	with	with	ADP
ejpam-3972	75	40	the	the	DET
ejpam-3972	75	41	prover	prover	NOUN
ejpam-3972	75	42	(	(	PUNCT
ejpam-3972	75	43	complete	complete	ADJ
ejpam-3972	75	44	)	)	PUNCT
ejpam-3972	75	45	;	;	PUNCT
ejpam-3972	75	46	(	(	PUNCT
ejpam-3972	75	47	zk2	zk2	NOUN
ejpam-3972	75	48	)	)	PUNCT
ejpam-3972	75	49	for	for	ADP
ejpam-3972	75	50	all	all	DET
ejpam-3972	75	51	x	x	NOUN
ejpam-3972	75	52	/∈	/∈	PUNCT
ejpam-3972	76	1	l	l	NOUN
ejpam-3972	76	2	,	,	PUNCT
ejpam-3972	76	3	and	and	CCONJ
ejpam-3972	76	4	for	for	ADP
ejpam-3972	76	5	all	all	DET
ejpam-3972	76	6	provers	prover	NOUN
ejpam-3972	76	7	p	p	NOUN
ejpam-3972	76	8	∗	∗	NOUN
ejpam-3972	76	9	,	,	PUNCT
ejpam-3972	76	10	a	a	DET
ejpam-3972	76	11	verifier	verifier	NOUN
ejpam-3972	76	12	says	say	VERB
ejpam-3972	76	13	“	"	PUNCT
ejpam-3972	76	14	no	no	INTJ
ejpam-3972	76	15	”	"	PUNCT
ejpam-3972	76	16	after	after	ADP
ejpam-3972	76	17	interacting	interact	VERB
ejpam-3972	76	18	with	with	ADP
ejpam-3972	76	19	p	p	NOUN
ejpam-3972	76	20	∗	∗	NOUN
ejpam-3972	76	21	with	with	ADP
ejpam-3972	76	22	probability	probability	NOUN
ejpam-3972	76	23	at	at	ADP
ejpam-3972	76	24	least	least	ADJ
ejpam-3972	76	25	1/2	1/2	NUM
ejpam-3972	76	26	(	(	PUNCT
ejpam-3972	76	27	sound	sound	NOUN
ejpam-3972	76	28	)	)	PUNCT
ejpam-3972	76	29	;	;	PUNCT
ejpam-3972	76	30	(	(	PUNCT
ejpam-3972	76	31	zk3	zk3	NOUN
ejpam-3972	76	32	)	)	PUNCT
ejpam-3972	76	33	for	for	ADP
ejpam-3972	76	34	all	all	DET
ejpam-3972	76	35	verifiers	verifier	NOUN
ejpam-3972	76	36	v	v	ADP
ejpam-3972	76	37	∗	∗	NOUN
ejpam-3972	76	38	,	,	PUNCT
ejpam-3972	76	39	there	there	PRON
ejpam-3972	76	40	exists	exist	VERB
ejpam-3972	76	41	a	a	DET
ejpam-3972	76	42	simulator	simulator	NOUN
ejpam-3972	76	43	s∗	s∗	NOUN
ejpam-3972	76	44	that	that	PRON
ejpam-3972	76	45	is	be	AUX
ejpam-3972	76	46	a	a	DET
ejpam-3972	76	47	randomized	randomized	ADJ
ejpam-3972	76	48	polynomial	polynomial	ADJ
ejpam-3972	76	49	time	time	NOUN
ejpam-3972	76	50	algorithm	algorithm	NOUN
ejpam-3972	76	51	such	such	ADJ
ejpam-3972	76	52	that	that	SCONJ
ejpam-3972	76	53	for	for	ADP
ejpam-3972	76	54	all	all	DET
ejpam-3972	76	55	x	x	SYM
ejpam-3972	76	56	∈	∈	PROPN
ejpam-3972	76	57	l	l	NOUN
ejpam-3972	76	58	,	,	PUNCT
ejpam-3972	76	59	{	{	PUNCT
ejpam-3972	76	60	transcript((p	transcript((p	NOUN
ejpam-3972	76	61	,	,	PUNCT
ejpam-3972	76	62	v	v	ADP
ejpam-3972	76	63	∗)(x	∗)(x	NOUN
ejpam-3972	76	64	)	)	PUNCT
ejpam-3972	76	65	)	)	PUNCT
ejpam-3972	76	66	}	}	PUNCT
ejpam-3972	76	67	=	=	SYM
ejpam-3972	76	68	{	{	PUNCT
ejpam-3972	76	69	s∗(x	s∗(x	NOUN
ejpam-3972	76	70	)	)	PUNCT
ejpam-3972	76	71	}	}	PUNCT
ejpam-3972	76	72	(	(	PUNCT
ejpam-3972	76	73	perfect	perfect	ADJ
ejpam-3972	76	74	)	)	PUNCT
ejpam-3972	76	75	.	.	PUNCT
ejpam-3972	77	1	(	(	PUNCT
ejpam-3972	77	2	5	5	X
ejpam-3972	77	3	)	)	PUNCT
ejpam-3972	77	4	y.	y.	PROPN
ejpam-3972	77	5	liu	liu	PROPN
ejpam-3972	77	6	/	/	SYM
ejpam-3972	77	7	eur	eur	PROPN
ejpam-3972	77	8	.	.	PUNCT
ejpam-3972	78	1	j.	j.	PROPN
ejpam-3972	78	2	pure	pure	PROPN
ejpam-3972	78	3	appl	appl	PROPN
ejpam-3972	78	4	.	.	PROPN
ejpam-3972	78	5	math	math	PROPN
ejpam-3972	78	6	,	,	PUNCT
ejpam-3972	78	7	14	14	NUM
ejpam-3972	78	8	(	(	PUNCT
ejpam-3972	78	9	2	2	NUM
ejpam-3972	78	10	)	)	PUNCT
ejpam-3972	78	11	(	(	PUNCT
ejpam-3972	78	12	2021	2021	NUM
ejpam-3972	78	13	)	)	PUNCT
ejpam-3972	78	14	,	,	PUNCT
ejpam-3972	78	15	521	521	NUM
ejpam-3972	78	16	-	-	SYM
ejpam-3972	78	17	536	536	NUM
ejpam-3972	78	18	524	524	NUM
ejpam-3972	78	19	3	3	NUM
ejpam-3972	78	20	.	.	PUNCT
ejpam-3972	78	21	main	main	ADJ
ejpam-3972	78	22	results	result	NOUN
ejpam-3972	78	23	theorem	theorem	VERB
ejpam-3972	78	24	2	2	NUM
ejpam-3972	78	25	.	.	PUNCT
ejpam-3972	79	1	(	(	PUNCT
ejpam-3972	79	2	wkdc	wkdc	NOUN
ejpam-3972	79	3	law	law	NOUN
ejpam-3972	79	4	)	)	PUNCT
ejpam-3972	79	5	let	let	VERB
ejpam-3972	79	6	g	g	NOUN
ejpam-3972	79	7	=	=	PUNCT
ejpam-3972	79	8	{	{	PUNCT
ejpam-3972	79	9	p	p	X
ejpam-3972	79	10	,	,	PUNCT
ejpam-3972	79	11	q	q	ADJ
ejpam-3972	79	12	,	,	PUNCT
ejpam-3972	79	13	x	x	NOUN
ejpam-3972	79	14	}	}	PUNCT
ejpam-3972	79	15	and	and	CCONJ
ejpam-3972	79	16	let	let	VERB
ejpam-3972	79	17	(	(	PUNCT
ejpam-3972	79	18	g	g	NOUN
ejpam-3972	79	19	,	,	PUNCT
ejpam-3972	79	20	•	•	NUM
ejpam-3972	79	21	)	)	PUNCT
ejpam-3972	79	22	is	be	AUX
ejpam-3972	79	23	a	a	DET
ejpam-3972	79	24	public	public	ADJ
ejpam-3972	79	25	key	key	ADJ
ejpam-3972	79	26	group	group	NOUN
ejpam-3972	79	27	.	.	PUNCT
ejpam-3972	80	1	then	then	ADV
ejpam-3972	80	2	(	(	PUNCT
ejpam-3972	80	3	wkdc1	wkdc1	X
ejpam-3972	80	4	)	)	PUNCT
ejpam-3972	80	5	x	x	X
ejpam-3972	81	1	=	=	PUNCT
ejpam-3972	81	2	x	x	SYM
ejpam-3972	81	3	•	•	NUM
ejpam-3972	81	4	x	x	X
ejpam-3972	81	5	=	=	PUNCT
ejpam-3972	81	6	p	p	NOUN
ejpam-3972	81	7	•	•	NUM
ejpam-3972	81	8	q	q	NOUN
ejpam-3972	81	9	and	and	CCONJ
ejpam-3972	81	10	(	(	PUNCT
ejpam-3972	81	11	wkdc2	wkdc2	NOUN
ejpam-3972	81	12	)	)	PUNCT
ejpam-3972	81	13	q	q	NOUN
ejpam-3972	82	1	=	=	PUNCT
ejpam-3972	82	2	x	x	SYM
ejpam-3972	82	3	•	•	NUM
ejpam-3972	82	4	q	q	X
ejpam-3972	82	5	iff	iff	PROPN
ejpam-3972	82	6	x	x	X
ejpam-3972	82	7	=	=	NOUN
ejpam-3972	82	8	1	1	X
ejpam-3972	82	9	.	.	PUNCT
ejpam-3972	82	10	proof	proof	NOUN
ejpam-3972	82	11	.	.	PUNCT
ejpam-3972	83	1	assume	assume	VERB
ejpam-3972	83	2	(	(	PUNCT
ejpam-3972	83	3	wkdc2	wkdc2	NOUN
ejpam-3972	83	4	)	)	PUNCT
ejpam-3972	83	5	and	and	CCONJ
ejpam-3972	83	6	prove	prove	VERB
ejpam-3972	83	7	(	(	PUNCT
ejpam-3972	83	8	wkdc1	wkdc1	PROPN
ejpam-3972	83	9	)	)	PUNCT
ejpam-3972	83	10	.	.	PUNCT
ejpam-3972	84	1	let	let	VERB
ejpam-3972	84	2	p	p	PRON
ejpam-3972	84	3	,	,	PUNCT
ejpam-3972	84	4	q	q	INTJ
ejpam-3972	84	5	,	,	PUNCT
ejpam-3972	84	6	x	x	SYM
ejpam-3972	84	7	∈	∈	NOUN
ejpam-3972	84	8	g.	g.	NOUN
ejpam-3972	84	9	use	use	VERB
ejpam-3972	84	10	the	the	DET
ejpam-3972	84	11	identities	identity	NOUN
ejpam-3972	84	12	of	of	ADP
ejpam-3972	84	13	group	group	NOUN
ejpam-3972	84	14	.	.	PUNCT
ejpam-3972	85	1	the	the	DET
ejpam-3972	85	2	steps	step	NOUN
ejpam-3972	85	3	used	use	VERB
ejpam-3972	85	4	to	to	PART
ejpam-3972	85	5	derive	derive	VERB
ejpam-3972	85	6	this	this	DET
ejpam-3972	85	7	identity	identity	NOUN
ejpam-3972	85	8	(	(	PUNCT
ejpam-3972	85	9	p	p	NOUN
ejpam-3972	85	10	•	•	NUM
ejpam-3972	85	11	q	q	NOUN
ejpam-3972	85	12	)	)	PUNCT
ejpam-3972	85	13	•	•	NOUN
ejpam-3972	85	14	x	x	X
ejpam-3972	86	1	=	=	PUNCT
ejpam-3972	86	2	p	p	NOUN
ejpam-3972	86	3	•	•	NOUN
ejpam-3972	86	4	(	(	PUNCT
ejpam-3972	86	5	x	x	SYM
ejpam-3972	86	6	•	•	NUM
ejpam-3972	86	7	q	q	NOUN
ejpam-3972	86	8	)	)	PUNCT
ejpam-3972	87	1	=	=	SYM
ejpam-3972	88	1	p	p	ADJ
ejpam-3972	88	2	•	•	NUM
ejpam-3972	88	3	q	q	NOUN
ejpam-3972	88	4	,	,	PUNCT
ejpam-3972	88	5	(	(	PUNCT
ejpam-3972	88	6	6	6	NUM
ejpam-3972	88	7	)	)	PUNCT
ejpam-3972	88	8	and	and	CCONJ
ejpam-3972	88	9	x	x	SYM
ejpam-3972	88	10	•	•	X
ejpam-3972	88	11	(	(	PUNCT
ejpam-3972	88	12	p	p	NOUN
ejpam-3972	88	13	•	•	NUM
ejpam-3972	88	14	q	q	NOUN
ejpam-3972	88	15	)	)	PUNCT
ejpam-3972	88	16	=	=	SYM
ejpam-3972	89	1	(	(	PUNCT
ejpam-3972	89	2	x	x	SYM
ejpam-3972	89	3	•	•	NUM
ejpam-3972	89	4	q	q	NOUN
ejpam-3972	89	5	)	)	PUNCT
ejpam-3972	89	6	•	•	NOUN
ejpam-3972	90	1	p	p	NOUN
ejpam-3972	90	2	=	=	X
ejpam-3972	90	3	q	q	NOUN
ejpam-3972	90	4	•	•	NUM
ejpam-3972	90	5	p.	p.	NOUN
ejpam-3972	90	6	(	(	PUNCT
ejpam-3972	90	7	7	7	NUM
ejpam-3972	90	8	)	)	PUNCT
ejpam-3972	90	9	by	by	ADP
ejpam-3972	90	10	theorem	theorem	NOUN
ejpam-3972	90	11	1	1	NUM
ejpam-3972	90	12	,	,	PUNCT
ejpam-3972	90	13	we	we	PRON
ejpam-3972	90	14	have	have	VERB
ejpam-3972	90	15	.	.	PUNCT
ejpam-3972	91	1	p	p	NOUN
ejpam-3972	91	2	•	•	NUM
ejpam-3972	91	3	q	q	NOUN
ejpam-3972	92	1	=	=	PUNCT
ejpam-3972	92	2	q	q	NOUN
ejpam-3972	92	3	•	•	NUM
ejpam-3972	92	4	p	p	X
ejpam-3972	92	5	,	,	PUNCT
ejpam-3972	92	6	(	(	PUNCT
ejpam-3972	92	7	8)	8)	NUM
ejpam-3972	92	8	and	and	CCONJ
ejpam-3972	92	9	so	so	ADV
ejpam-3972	92	10	(	(	PUNCT
ejpam-3972	92	11	p	p	NOUN
ejpam-3972	92	12	•	•	NUM
ejpam-3972	92	13	q	q	NOUN
ejpam-3972	92	14	)	)	PUNCT
ejpam-3972	92	15	•	•	NOUN
ejpam-3972	92	16	x	x	SYM
ejpam-3972	93	1	=	=	PUNCT
ejpam-3972	93	2	x	x	SYM
ejpam-3972	93	3	•	•	NOUN
ejpam-3972	93	4	(	(	PUNCT
ejpam-3972	93	5	p	p	NOUN
ejpam-3972	93	6	•	•	NUM
ejpam-3972	93	7	q	q	NOUN
ejpam-3972	93	8	)	)	PUNCT
ejpam-3972	93	9	,	,	PUNCT
ejpam-3972	93	10	(	(	PUNCT
ejpam-3972	93	11	9	9	X
ejpam-3972	93	12	)	)	PUNCT
ejpam-3972	93	13	we	we	PRON
ejpam-3972	93	14	deduce	deduce	VERB
ejpam-3972	93	15	that	that	SCONJ
ejpam-3972	93	16	p	p	NOUN
ejpam-3972	94	1	•	•	NOUN
ejpam-3972	94	2	q	q	NOUN
ejpam-3972	95	1	=	=	PUNCT
ejpam-3972	96	1	x.	x.	NOUN
ejpam-3972	97	1	(	(	PUNCT
ejpam-3972	98	1	10	10	NUM
ejpam-3972	98	2	)	)	PUNCT
ejpam-3972	98	3	since	since	SCONJ
ejpam-3972	98	4	x	x	X
ejpam-3972	98	5	=	=	PUNCT
ejpam-3972	98	6	p	p	PROPN
ejpam-3972	98	7	•	•	NUM
ejpam-3972	98	8	q	q	NOUN
ejpam-3972	99	1	=	=	PUNCT
ejpam-3972	99	2	p	p	NOUN
ejpam-3972	99	3	•	•	NOUN
ejpam-3972	99	4	(	(	PUNCT
ejpam-3972	99	5	(	(	PUNCT
ejpam-3972	99	6	p	p	NOUN
ejpam-3972	99	7	•	•	NUM
ejpam-3972	99	8	q	q	NOUN
ejpam-3972	99	9	)	)	PUNCT
ejpam-3972	99	10	•	•	NUM
ejpam-3972	99	11	q	q	NOUN
ejpam-3972	99	12	)	)	PUNCT
ejpam-3972	99	13	=	=	SYM
ejpam-3972	100	1	(	(	PUNCT
ejpam-3972	100	2	p	p	NOUN
ejpam-3972	100	3	•	•	NUM
ejpam-3972	100	4	q	q	NOUN
ejpam-3972	100	5	)	)	PUNCT
ejpam-3972	100	6	•	•	NOUN
ejpam-3972	100	7	(	(	PUNCT
ejpam-3972	100	8	p	p	NOUN
ejpam-3972	100	9	•	•	NUM
ejpam-3972	100	10	q	q	NOUN
ejpam-3972	100	11	)	)	PUNCT
ejpam-3972	100	12	=	=	SYM
ejpam-3972	101	1	x	x	PUNCT
ejpam-3972	101	2	•	•	NOUN
ejpam-3972	101	3	x.	x.	NOUN
ejpam-3972	101	4	(	(	PUNCT
ejpam-3972	101	5	11	11	NUM
ejpam-3972	101	6	)	)	PUNCT
ejpam-3972	101	7	for	for	ADP
ejpam-3972	101	8	(	(	PUNCT
ejpam-3972	101	9	wkdc2	wkdc2	NOUN
ejpam-3972	101	10	)	)	PUNCT
ejpam-3972	101	11	.	.	PUNCT
ejpam-3972	102	1	let	let	VERB
ejpam-3972	102	2	q	q	X
ejpam-3972	102	3	,	,	PUNCT
ejpam-3972	102	4	x	x	SYM
ejpam-3972	102	5	∈	∈	NOUN
ejpam-3972	102	6	g.	g.	NOUN
ejpam-3972	102	7	by	by	ADP
ejpam-3972	102	8	definition	definition	NOUN
ejpam-3972	102	9	1	1	NUM
ejpam-3972	102	10	.	.	PUNCT
ejpam-3972	103	1	define	define	NOUN
ejpam-3972	103	2	:	:	PUNCT
ejpam-3972	103	3	q	q	NOUN
ejpam-3972	103	4	•	•	NUM
ejpam-3972	103	5	q	q	NOUN
ejpam-3972	103	6	=	=	NOUN
ejpam-3972	103	7	1	1	NUM
ejpam-3972	103	8	,	,	PUNCT
ejpam-3972	103	9	(	(	PUNCT
ejpam-3972	103	10	12	12	NUM
ejpam-3972	103	11	)	)	PUNCT
ejpam-3972	103	12	we	we	PRON
ejpam-3972	103	13	have	have	VERB
ejpam-3972	103	14	(	(	PUNCT
ejpam-3972	103	15	x	x	SYM
ejpam-3972	103	16	•	•	NUM
ejpam-3972	103	17	q	q	NOUN
ejpam-3972	103	18	)	)	PUNCT
ejpam-3972	103	19	•	•	NOUN
ejpam-3972	103	20	q	q	NOUN
ejpam-3972	104	1	=	=	PUNCT
ejpam-3972	104	2	x	x	SYM
ejpam-3972	104	3	•	•	NOUN
ejpam-3972	104	4	(	(	PUNCT
ejpam-3972	104	5	q	q	NOUN
ejpam-3972	104	6	•	•	NUM
ejpam-3972	104	7	q	q	NOUN
ejpam-3972	104	8	)	)	PUNCT
ejpam-3972	104	9	=	=	SYM
ejpam-3972	105	1	x	x	SYM
ejpam-3972	105	2	•	•	NUM
ejpam-3972	105	3	1	1	NUM
ejpam-3972	105	4	,	,	PUNCT
ejpam-3972	105	5	(	(	PUNCT
ejpam-3972	105	6	13	13	NUM
ejpam-3972	105	7	)	)	PUNCT
ejpam-3972	105	8	and	and	CCONJ
ejpam-3972	105	9	q	q	NOUN
ejpam-3972	105	10	•	•	NOUN
ejpam-3972	105	11	(	(	PUNCT
ejpam-3972	105	12	x	x	SYM
ejpam-3972	105	13	•	•	NUM
ejpam-3972	105	14	q	q	NOUN
ejpam-3972	105	15	)	)	PUNCT
ejpam-3972	105	16	=	=	SYM
ejpam-3972	105	17	(	(	PUNCT
ejpam-3972	105	18	q	q	NOUN
ejpam-3972	105	19	•	•	NUM
ejpam-3972	105	20	q	q	NOUN
ejpam-3972	105	21	)	)	PUNCT
ejpam-3972	105	22	•	•	NOUN
ejpam-3972	105	23	x	x	SYM
ejpam-3972	105	24	=	=	SYM
ejpam-3972	105	25	1	1	NUM
ejpam-3972	105	26	•	•	NUM
ejpam-3972	105	27	x	x	NOUN
ejpam-3972	105	28	,	,	PUNCT
ejpam-3972	105	29	(	(	PUNCT
ejpam-3972	105	30	14	14	NUM
ejpam-3972	105	31	)	)	PUNCT
ejpam-3972	105	32	and	and	CCONJ
ejpam-3972	105	33	so	so	ADV
ejpam-3972	105	34	x	x	SYM
ejpam-3972	105	35	•	•	NUM
ejpam-3972	105	36	1	1	NUM
ejpam-3972	105	37	=	=	SYM
ejpam-3972	105	38	1	1	NUM
ejpam-3972	105	39	=	=	SYM
ejpam-3972	105	40	1	1	NUM
ejpam-3972	105	41	•	•	NUM
ejpam-3972	105	42	x	x	NOUN
ejpam-3972	105	43	,	,	PUNCT
ejpam-3972	105	44	(	(	PUNCT
ejpam-3972	105	45	15	15	X
ejpam-3972	105	46	)	)	PUNCT
ejpam-3972	105	47	y.	y.	PROPN
ejpam-3972	105	48	liu	liu	PROPN
ejpam-3972	105	49	/	/	SYM
ejpam-3972	105	50	eur	eur	PROPN
ejpam-3972	105	51	.	.	PUNCT
ejpam-3972	106	1	j.	j.	PROPN
ejpam-3972	106	2	pure	pure	PROPN
ejpam-3972	106	3	appl	appl	PROPN
ejpam-3972	106	4	.	.	PROPN
ejpam-3972	106	5	math	math	PROPN
ejpam-3972	106	6	,	,	PUNCT
ejpam-3972	106	7	14	14	NUM
ejpam-3972	106	8	(	(	PUNCT
ejpam-3972	106	9	2	2	NUM
ejpam-3972	106	10	)	)	PUNCT
ejpam-3972	106	11	(	(	PUNCT
ejpam-3972	106	12	2021	2021	NUM
ejpam-3972	106	13	)	)	PUNCT
ejpam-3972	106	14	,	,	PUNCT
ejpam-3972	106	15	521	521	NUM
ejpam-3972	106	16	-	-	SYM
ejpam-3972	106	17	536	536	NUM
ejpam-3972	106	18	525	525	NUM
ejpam-3972	106	19	table	table	NOUN
ejpam-3972	106	20	1	1	NUM
ejpam-3972	106	21	:	:	PUNCT
ejpam-3972	106	22	table	table	NOUN
ejpam-3972	106	23	for	for	ADP
ejpam-3972	106	24	(	(	PUNCT
ejpam-3972	106	25	g	g	NOUN
ejpam-3972	106	26	,	,	PUNCT
ejpam-3972	106	27	•	•	NOUN
ejpam-3972	106	28	)	)	PUNCT
ejpam-3972	106	29	.	.	PUNCT
ejpam-3972	107	1	•	•	NUM
ejpam-3972	108	1	p	p	X
ejpam-3972	108	2	q	q	NOUN
ejpam-3972	109	1	x	x	X
ejpam-3972	109	2	p	p	NOUN
ejpam-3972	109	3	—	—	PUNCT
ejpam-3972	109	4	x	x	X
ejpam-3972	109	5	—	—	PUNCT
ejpam-3972	109	6	q	q	NOUN
ejpam-3972	109	7	—	—	PUNCT
ejpam-3972	109	8	—	—	PUNCT
ejpam-3972	109	9	—	—	PUNCT
ejpam-3972	109	10	x	x	X
ejpam-3972	109	11	—	—	PUNCT
ejpam-3972	109	12	q	q	NOUN
ejpam-3972	109	13	x	x	PUNCT
ejpam-3972	109	14	figure	figure	NOUN
ejpam-3972	109	15	2	2	NUM
ejpam-3972	109	16	:	:	PUNCT
ejpam-3972	109	17	figure	figure	NOUN
ejpam-3972	109	18	1	1	NUM
ejpam-3972	109	19	.	.	X
ejpam-3972	109	20	zero	zero	NUM
ejpam-3972	109	21	-	-	PUNCT
ejpam-3972	109	22	knowledge	knowledge	NOUN
ejpam-3972	109	23	proofs	proof	NOUN
ejpam-3972	109	24	:	:	PUNCT
ejpam-3972	109	25	an	an	DET
ejpam-3972	109	26	illustrated	illustrated	ADJ
ejpam-3972	109	27	guide	guide	NOUN
ejpam-3972	109	28	.	.	PUNCT
ejpam-3972	110	1	since	since	SCONJ
ejpam-3972	110	2	x	x	PROPN
ejpam-3972	110	3	=	=	SYM
ejpam-3972	110	4	1	1	NUM
ejpam-3972	110	5	,	,	PUNCT
ejpam-3972	110	6	we	we	PRON
ejpam-3972	110	7	deduce	deduce	VERB
ejpam-3972	110	8	that	that	SCONJ
ejpam-3972	110	9	(	(	PUNCT
ejpam-3972	110	10	x	x	SYM
ejpam-3972	110	11	•	•	NUM
ejpam-3972	110	12	q	q	NOUN
ejpam-3972	110	13	)	)	PUNCT
ejpam-3972	110	14	•	•	NOUN
ejpam-3972	110	15	q	q	NOUN
ejpam-3972	110	16	=	=	PUNCT
ejpam-3972	110	17	q	q	NOUN
ejpam-3972	110	18	•	•	NOUN
ejpam-3972	110	19	(	(	PUNCT
ejpam-3972	110	20	x	x	SYM
ejpam-3972	110	21	•	•	NUM
ejpam-3972	110	22	q	q	NOUN
ejpam-3972	110	23	)	)	PUNCT
ejpam-3972	110	24	=	=	SYM
ejpam-3972	110	25	1	1	NUM
ejpam-3972	110	26	implies	imply	VERB
ejpam-3972	110	27	q	q	X
ejpam-3972	111	1	=	=	PUNCT
ejpam-3972	111	2	x	x	SYM
ejpam-3972	111	3	•	•	NUM
ejpam-3972	111	4	q	q	NOUN
ejpam-3972	111	5	.	.	PUNCT
ejpam-3972	112	1	(	(	PUNCT
ejpam-3972	112	2	16	16	NUM
ejpam-3972	112	3	)	)	PUNCT
ejpam-3972	112	4	the	the	DET
ejpam-3972	112	5	verification	verification	NOUN
ejpam-3972	112	6	of	of	ADP
ejpam-3972	112	7	this	this	DET
ejpam-3972	112	8	identity	identity	NOUN
ejpam-3972	112	9	is	be	AUX
ejpam-3972	112	10	show	show	NOUN
ejpam-3972	112	11	in	in	ADP
ejpam-3972	112	12	table	table	NOUN
ejpam-3972	112	13	1	1	NUM
ejpam-3972	112	14	.	.	PUNCT
ejpam-3972	112	15	table	table	NOUN
ejpam-3972	112	16	1	1	NUM
ejpam-3972	112	17	illustrates	illustrate	VERB
ejpam-3972	112	18	wkdc	wkdc	NOUN
ejpam-3972	112	19	is	be	AUX
ejpam-3972	112	20	a	a	DET
ejpam-3972	112	21	group	group	NOUN
ejpam-3972	112	22	and	and	CCONJ
ejpam-3972	112	23	is	be	AUX
ejpam-3972	112	24	to	to	PART
ejpam-3972	112	25	set	set	VERB
ejpam-3972	112	26	up	up	ADP
ejpam-3972	112	27	a	a	DET
ejpam-3972	112	28	stable	stable	ADJ
ejpam-3972	112	29	algebra	algebra	NOUN
ejpam-3972	112	30	structure	structure	NOUN
ejpam-3972	112	31	.	.	PUNCT
ejpam-3972	113	1	still	still	ADV
ejpam-3972	113	2	,	,	PUNCT
ejpam-3972	113	3	the	the	DET
ejpam-3972	113	4	outcome	outcome	NOUN
ejpam-3972	113	5	does	do	AUX
ejpam-3972	113	6	not	not	PART
ejpam-3972	113	7	meet	meet	VERB
ejpam-3972	113	8	the	the	DET
ejpam-3972	113	9	distributive	distributive	ADJ
ejpam-3972	113	10	law	law	NOUN
ejpam-3972	113	11	and	and	CCONJ
ejpam-3972	113	12	also	also	ADV
ejpam-3972	113	13	does	do	AUX
ejpam-3972	113	14	not	not	PART
ejpam-3972	113	15	meet	meet	VERB
ejpam-3972	113	16	associative	associative	ADJ
ejpam-3972	113	17	law	law	NOUN
ejpam-3972	113	18	.	.	PUNCT
ejpam-3972	114	1	it	it	PRON
ejpam-3972	114	2	is	be	AUX
ejpam-3972	114	3	this	this	DET
ejpam-3972	114	4	characteristic	characteristic	NOUN
ejpam-3972	114	5	that	that	PRON
ejpam-3972	114	6	provides	provide	VERB
ejpam-3972	114	7	a	a	DET
ejpam-3972	114	8	structure	structure	NOUN
ejpam-3972	114	9	of	of	ADP
ejpam-3972	114	10	security	security	NOUN
ejpam-3972	114	11	.	.	PUNCT
ejpam-3972	115	1	the	the	DET
ejpam-3972	115	2	secret	secret	ADJ
ejpam-3972	115	3	key	key	NOUN
ejpam-3972	115	4	is	be	AUX
ejpam-3972	115	5	the	the	DET
ejpam-3972	115	6	corresponding	correspond	VERB
ejpam-3972	115	7	value	value	NOUN
ejpam-3972	115	8	p	p	X
ejpam-3972	115	9	(	(	PUNCT
ejpam-3972	115	10	a	a	DET
ejpam-3972	115	11	large	large	ADJ
ejpam-3972	115	12	prime	prime	NOUN
ejpam-3972	115	13	)	)	PUNCT
ejpam-3972	115	14	such	such	ADJ
ejpam-3972	115	15	that	that	SCONJ
ejpam-3972	115	16	2200≤	2200≤	NUM
ejpam-3972	115	17	p	p	ADJ
ejpam-3972	115	18	≤	≤	NUM
ejpam-3972	115	19	2600	2600	NUM
ejpam-3972	115	20	.	.	PUNCT
ejpam-3972	116	1	this	this	PRON
ejpam-3972	116	2	should	should	AUX
ejpam-3972	116	3	go	go	VERB
ejpam-3972	116	4	without	without	ADP
ejpam-3972	116	5	saying	say	VERB
ejpam-3972	116	6	,	,	PUNCT
ejpam-3972	116	7	but	but	CCONJ
ejpam-3972	116	8	make	make	VERB
ejpam-3972	116	9	sure	sure	ADJ
ejpam-3972	116	10	you	you	PRON
ejpam-3972	116	11	have	have	VERB
ejpam-3972	116	12	a	a	DET
ejpam-3972	116	13	secure	secure	ADJ
ejpam-3972	116	14	password	password	NOUN
ejpam-3972	116	15	q.	q.	NOUN
ejpam-3972	116	16	to	to	PART
ejpam-3972	116	17	crack	crack	VERB
ejpam-3972	116	18	the	the	DET
ejpam-3972	116	19	code	code	NOUN
ejpam-3972	116	20	,	,	PUNCT
ejpam-3972	116	21	the	the	DET
ejpam-3972	116	22	lottery	lottery	NOUN
ejpam-3972	116	23	is	be	AUX
ejpam-3972	116	24	2−200	2−200	NUM
ejpam-3972	116	25	.	.	PUNCT
ejpam-3972	117	1	this	this	DET
ejpam-3972	117	2	h(x	h(x	PROPN
ejpam-3972	117	3	)	)	PUNCT
ejpam-3972	117	4	is	be	AUX
ejpam-3972	117	5	a	a	DET
ejpam-3972	117	6	candidate	candidate	NOUN
ejpam-3972	117	7	for	for	ADP
ejpam-3972	117	8	a	a	DET
ejpam-3972	117	9	one	one	NUM
ejpam-3972	117	10	-	-	PUNCT
ejpam-3972	117	11	way	way	NOUN
ejpam-3972	117	12	function	function	NOUN
ejpam-3972	117	13	.	.	PUNCT
ejpam-3972	118	1	but	but	CCONJ
ejpam-3972	118	2	until	until	ADP
ejpam-3972	118	3	now	now	ADV
ejpam-3972	118	4	,	,	PUNCT
ejpam-3972	118	5	no	no	DET
ejpam-3972	118	6	probabilistic	probabilistic	ADJ
ejpam-3972	118	7	polynomial	polynomial	ADJ
ejpam-3972	118	8	time	time	NOUN
ejpam-3972	118	9	algorithm	algorithm	NOUN
ejpam-3972	118	10	is	be	AUX
ejpam-3972	118	11	known	know	VERB
ejpam-3972	118	12	that	that	PRON
ejpam-3972	118	13	can	can	AUX
ejpam-3972	118	14	invert	invert	VERB
ejpam-3972	118	15	h(x	h(x	PROPN
ejpam-3972	118	16	)	)	PUNCT
ejpam-3972	118	17	,	,	PUNCT
ejpam-3972	118	18	ever	ever	ADV
ejpam-3972	118	19	on	on	ADP
ejpam-3972	118	20	a	a	DET
ejpam-3972	118	21	polynomial	polynomial	ADJ
ejpam-3972	118	22	fraction	fraction	NOUN
ejpam-3972	118	23	of	of	ADP
ejpam-3972	118	24	input	input	NOUN
ejpam-3972	118	25	.	.	PUNCT
ejpam-3972	119	1	it	it	PRON
ejpam-3972	119	2	’s	’	VERB
ejpam-3972	119	3	also	also	ADV
ejpam-3972	119	4	worth	worth	ADJ
ejpam-3972	119	5	mentioning	mention	VERB
ejpam-3972	119	6	that	that	SCONJ
ejpam-3972	119	7	the	the	DET
ejpam-3972	119	8	theorem	theorem	NOUN
ejpam-3972	119	9	2	2	NUM
ejpam-3972	119	10	gives	give	VERB
ejpam-3972	119	11	another	another	DET
ejpam-3972	119	12	internal	internal	ADJ
ejpam-3972	119	13	characterization	characterization	NOUN
ejpam-3972	119	14	of	of	ADP
ejpam-3972	119	15	the	the	DET
ejpam-3972	119	16	wkdc	wkdc	NOUN
ejpam-3972	119	17	law	law	NOUN
ejpam-3972	119	18	,	,	PUNCT
ejpam-3972	119	19	that	that	ADV
ejpam-3972	119	20	is	is	ADV
ejpam-3972	119	21	—	—	PUNCT
ejpam-3972	119	22	the	the	DET
ejpam-3972	119	23	problem	problem	NOUN
ejpam-3972	119	24	of	of	ADP
ejpam-3972	119	25	zero	zero	NUM
ejpam-3972	119	26	-	-	PUNCT
ejpam-3972	119	27	knowledge	knowledge	NOUN
ejpam-3972	119	28	proof	proof	NOUN
ejpam-3972	119	29	of	of	ADP
ejpam-3972	119	30	n	n	NOUN
ejpam-3972	119	31	=	=	SYM
ejpam-3972	119	32	p	p	PROPN
ejpam-3972	119	33	•	•	NUM
ejpam-3972	119	34	q.	q.	PROPN
ejpam-3972	119	35	zeroknowledge	zeroknowledge	PROPN
ejpam-3972	119	36	cave	cave	PROPN
ejpam-3972	119	37	,	,	PUNCT
ejpam-3972	119	38	as	as	SCONJ
ejpam-3972	119	39	shown	show	VERB
ejpam-3972	119	40	in	in	ADP
ejpam-3972	119	41	figure	figure	NOUN
ejpam-3972	119	42	1	1	NUM
ejpam-3972	119	43	.	.	PUNCT
ejpam-3972	120	1	of	of	ADP
ejpam-3972	120	2	course	course	NOUN
ejpam-3972	120	3	,	,	PUNCT
ejpam-3972	120	4	in	in	ADP
ejpam-3972	120	5	network	network	NOUN
ejpam-3972	120	6	to	to	PART
ejpam-3972	120	7	transmit	transmit	VERB
ejpam-3972	120	8	news	news	NOUN
ejpam-3972	120	9	,	,	PUNCT
ejpam-3972	120	10	except	except	SCONJ
ejpam-3972	120	11	secrecy	secrecy	NOUN
ejpam-3972	120	12	,	,	PUNCT
ejpam-3972	120	13	the	the	DET
ejpam-3972	120	14	authentication	authentication	NOUN
ejpam-3972	120	15	,	,	PUNCT
ejpam-3972	120	16	integrity	integrity	NOUN
ejpam-3972	120	17	and	and	CCONJ
ejpam-3972	120	18	nonrepudiation	nonrepudiation	NOUN
ejpam-3972	120	19	are	be	AUX
ejpam-3972	120	20	important	important	ADJ
ejpam-3972	120	21	to	to	ADP
ejpam-3972	120	22	us	we	PRON
ejpam-3972	120	23	.	.	PUNCT
ejpam-3972	121	1	here	here	ADV
ejpam-3972	121	2	,	,	PUNCT
ejpam-3972	121	3	we	we	PRON
ejpam-3972	121	4	describe	describe	VERB
ejpam-3972	121	5	the	the	DET
ejpam-3972	121	6	multiplication	multiplication	NOUN
ejpam-3972	121	7	function	function	NOUN
ejpam-3972	121	8	y.	y.	PROPN
ejpam-3972	121	9	liu	liu	PROPN
ejpam-3972	121	10	/	/	SYM
ejpam-3972	121	11	eur	eur	PROPN
ejpam-3972	121	12	.	.	PUNCT
ejpam-3972	122	1	j.	j.	PROPN
ejpam-3972	122	2	pure	pure	PROPN
ejpam-3972	122	3	appl	appl	PROPN
ejpam-3972	122	4	.	.	PROPN
ejpam-3972	122	5	math	math	PROPN
ejpam-3972	122	6	,	,	PUNCT
ejpam-3972	122	7	14	14	NUM
ejpam-3972	122	8	(	(	PUNCT
ejpam-3972	122	9	2	2	NUM
ejpam-3972	122	10	)	)	PUNCT
ejpam-3972	122	11	(	(	PUNCT
ejpam-3972	122	12	2021	2021	NUM
ejpam-3972	122	13	)	)	PUNCT
ejpam-3972	122	14	,	,	PUNCT
ejpam-3972	122	15	521	521	NUM
ejpam-3972	122	16	-	-	SYM
ejpam-3972	122	17	536	536	NUM
ejpam-3972	122	18	526	526	NUM
ejpam-3972	122	19	figure	figure	NOUN
ejpam-3972	122	20	4	4	NUM
ejpam-3972	122	21	:	:	PUNCT
ejpam-3972	122	22	figure	figure	NOUN
ejpam-3972	122	23	2	2	NUM
ejpam-3972	122	24	.	.	PUNCT
ejpam-3972	123	1	the	the	DET
ejpam-3972	123	2	entanglement	entanglement	PROPN
ejpam-3972	123	3	diagram	diagram	NOUN
ejpam-3972	123	4	of	of	ADP
ejpam-3972	123	5	(	(	PUNCT
ejpam-3972	123	6	{	{	PUNCT
ejpam-3972	123	7	z	z	NOUN
ejpam-3972	123	8	,	,	PUNCT
ejpam-3972	123	9	y	y	NOUN
ejpam-3972	123	10	}	}	PUNCT
ejpam-3972	123	11	,	,	PUNCT
ejpam-3972	123	12	•	•	NUM
ejpam-3972	123	13	)	)	PUNCT
ejpam-3972	123	14	.	.	PUNCT
ejpam-3972	124	1	that	that	PRON
ejpam-3972	124	2	underlies	underlie	VERB
ejpam-3972	124	3	the	the	DET
ejpam-3972	124	4	wcs	wcs	NOUN
ejpam-3972	124	5	.	.	PUNCT
ejpam-3972	125	1	the	the	DET
ejpam-3972	125	2	following	follow	VERB
ejpam-3972	125	3	proposition	proposition	NOUN
ejpam-3972	125	4	is	be	AUX
ejpam-3972	125	5	the	the	DET
ejpam-3972	125	6	“	"	PUNCT
ejpam-3972	125	7	constructive	constructive	ADJ
ejpam-3972	125	8	”	"	PUNCT
ejpam-3972	125	9	formulation	formulation	NOUN
ejpam-3972	125	10	of	of	ADP
ejpam-3972	125	11	the	the	DET
ejpam-3972	125	12	fundamental	fundamental	ADJ
ejpam-3972	125	13	theorem	theorem	NOUN
ejpam-3972	125	14	of	of	ADP
ejpam-3972	125	15	groups	group	NOUN
ejpam-3972	125	16	.	.	PUNCT
ejpam-3972	126	1	theorem	theorem	NOUN
ejpam-3972	126	2	3	3	NUM
ejpam-3972	126	3	.	.	PUNCT
ejpam-3972	127	1	(	(	PUNCT
ejpam-3972	127	2	security	security	NOUN
ejpam-3972	127	3	of	of	ADP
ejpam-3972	127	4	wcs	wcs	PROPN
ejpam-3972	127	5	)	)	PUNCT
ejpam-3972	127	6	a	a	DET
ejpam-3972	127	7	multiplication	multiplication	NOUN
ejpam-3972	127	8	function	function	VERB
ejpam-3972	127	9	h(x	h(x	PROPN
ejpam-3972	127	10	,	,	PUNCT
ejpam-3972	127	11	y	y	PROPN
ejpam-3972	127	12	,	,	PUNCT
ejpam-3972	127	13	z	z	NOUN
ejpam-3972	127	14	)	)	PUNCT
ejpam-3972	127	15	of	of	ADP
ejpam-3972	127	16	a	a	DET
ejpam-3972	127	17	wormhole	wormhole	NOUN
ejpam-3972	127	18	is	be	AUX
ejpam-3972	127	19	a	a	DET
ejpam-3972	127	20	one	one	NUM
ejpam-3972	127	21	-	-	PUNCT
ejpam-3972	127	22	way	way	NOUN
ejpam-3972	127	23	function	function	NOUN
ejpam-3972	127	24	.	.	PUNCT
ejpam-3972	128	1	proof	proof	NOUN
ejpam-3972	128	2	.	.	PUNCT
ejpam-3972	129	1	suppose	suppose	VERB
ejpam-3972	129	2	g	g	PROPN
ejpam-3972	129	3	is	be	AUX
ejpam-3972	129	4	a	a	DET
ejpam-3972	129	5	group	group	NOUN
ejpam-3972	129	6	of	of	ADP
ejpam-3972	129	7	pas	pas	PROPN
ejpam-3972	129	8	(	(	PUNCT
ejpam-3972	129	9	ω	ω	NOUN
ejpam-3972	129	10	)	)	PUNCT
ejpam-3972	129	11	for	for	ADP
ejpam-3972	129	12	all	all	DET
ejpam-3972	129	13	x	x	NOUN
ejpam-3972	129	14	,	,	PUNCT
ejpam-3972	129	15	y	y	PROPN
ejpam-3972	129	16	,	,	PUNCT
ejpam-3972	129	17	z	z	PROPN
ejpam-3972	129	18	∈	∈	PROPN
ejpam-3972	129	19	g.	g.	NOUN
ejpam-3972	129	20	formally	formally	ADV
ejpam-3972	129	21	,	,	PUNCT
ejpam-3972	129	22	h(x	h(x	PROPN
ejpam-3972	129	23	,	,	PUNCT
ejpam-3972	129	24	y	y	PROPN
ejpam-3972	129	25	,	,	PUNCT
ejpam-3972	129	26	z	z	NOUN
ejpam-3972	129	27	)	)	PUNCT
ejpam-3972	129	28	=	=	SYM
ejpam-3972	130	1	(	(	PUNCT
ejpam-3972	130	2	x	x	SYM
ejpam-3972	130	3	•	•	NUM
ejpam-3972	130	4	y	y	NOUN
ejpam-3972	130	5	)	)	PUNCT
ejpam-3972	130	6	•	•	NOUN
ejpam-3972	130	7	z.	z.	PROPN
ejpam-3972	130	8	(	(	PUNCT
ejpam-3972	130	9	17	17	NUM
ejpam-3972	130	10	)	)	PUNCT
ejpam-3972	130	11	h(x	h(x	PROPN
ejpam-3972	130	12	,	,	PUNCT
ejpam-3972	130	13	y	y	PROPN
ejpam-3972	130	14	,	,	PUNCT
ejpam-3972	130	15	z	z	NOUN
ejpam-3972	130	16	)	)	PUNCT
ejpam-3972	130	17	is	be	AUX
ejpam-3972	130	18	easy	easy	ADJ
ejpam-3972	130	19	to	to	PART
ejpam-3972	130	20	compute	compute	VERB
ejpam-3972	130	21	when	when	SCONJ
ejpam-3972	130	22	x	x	X
ejpam-3972	130	23	,	,	PUNCT
ejpam-3972	130	24	y	y	PROPN
ejpam-3972	130	25	and	and	CCONJ
ejpam-3972	130	26	z	z	PROPN
ejpam-3972	130	27	are	be	AUX
ejpam-3972	130	28	known	know	VERB
ejpam-3972	130	29	,	,	PUNCT
ejpam-3972	130	30	but	but	CCONJ
ejpam-3972	130	31	h(x	h(x	PROPN
ejpam-3972	130	32	,	,	PUNCT
ejpam-3972	130	33	y	y	PROPN
ejpam-3972	130	34	,	,	PUNCT
ejpam-3972	130	35	z	z	NOUN
ejpam-3972	130	36	)	)	PUNCT
ejpam-3972	130	37	is	be	AUX
ejpam-3972	130	38	hard	hard	ADJ
ejpam-3972	130	39	to	to	PART
ejpam-3972	130	40	invert	invert	VERB
ejpam-3972	130	41	in	in	ADP
ejpam-3972	130	42	the	the	DET
ejpam-3972	130	43	absence	absence	NOUN
ejpam-3972	130	44	of	of	ADP
ejpam-3972	130	45	x	x	PROPN
ejpam-3972	130	46	or	or	CCONJ
ejpam-3972	130	47	y	y	PROPN
ejpam-3972	130	48	,	,	PUNCT
ejpam-3972	130	49	or	or	CCONJ
ejpam-3972	130	50	z.	z.	PROPN
ejpam-3972	131	1	if	if	SCONJ
ejpam-3972	131	2	x′	x′	PROPN
ejpam-3972	131	3	,	,	PUNCT
ejpam-3972	131	4	y′	y′	NUM
ejpam-3972	131	5	,	,	PUNCT
ejpam-3972	131	6	z′	z′	PROPN
ejpam-3972	131	7	∈	∈	PROPN
ejpam-3972	131	8	g	g	NOUN
ejpam-3972	131	9	,	,	PUNCT
ejpam-3972	131	10	inversion	inversion	NOUN
ejpam-3972	131	11	formula	formula	NOUN
ejpam-3972	131	12	6	6	NUM
ejpam-3972	131	13	∃h(x′	∃h(x′	VERB
ejpam-3972	131	14	,	,	PUNCT
ejpam-3972	131	15	y′	y′	NUM
ejpam-3972	131	16	,	,	PUNCT
ejpam-3972	131	17	z′	z′	NUM
ejpam-3972	131	18	)	)	PUNCT
ejpam-3972	131	19	=	=	SYM
ejpam-3972	131	20	h(x	h(x	PROPN
ejpam-3972	131	21	,	,	PUNCT
ejpam-3972	131	22	y	y	PROPN
ejpam-3972	131	23	,	,	PUNCT
ejpam-3972	131	24	z	z	NOUN
ejpam-3972	131	25	)	)	PUNCT
ejpam-3972	131	26	(	(	PUNCT
ejpam-3972	131	27	or	or	CCONJ
ejpam-3972	131	28	computationally	computationally	ADV
ejpam-3972	131	29	hard	hard	ADJ
ejpam-3972	131	30	)	)	PUNCT
ejpam-3972	131	31	.	.	PUNCT
ejpam-3972	132	1	(	(	PUNCT
ejpam-3972	132	2	18	18	NUM
ejpam-3972	132	3	)	)	PUNCT
ejpam-3972	132	4	let	let	VERB
ejpam-3972	132	5	λ	λ	X
ejpam-3972	132	6	=	=	PUNCT
ejpam-3972	132	7	{	{	PUNCT
ejpam-3972	132	8	0	0	NUM
ejpam-3972	132	9	,	,	PUNCT
ejpam-3972	132	10	1	1	NUM
ejpam-3972	132	11	}	}	PUNCT
ejpam-3972	132	12	and	and	CCONJ
ejpam-3972	132	13	let	let	VERB
ejpam-3972	132	14	λ	λ	X
ejpam-3972	132	15	∈	∈	PROPN
ejpam-3972	132	16	λ′.	λ′.	AUX
ejpam-3972	132	17	define	define	VERB
ejpam-3972	132	18	:	:	PUNCT
ejpam-3972	132	19	h(λ	h(λ	PROPN
ejpam-3972	132	20	)	)	PUNCT
ejpam-3972	132	21	is	be	AUX
ejpam-3972	132	22	the	the	DET
ejpam-3972	132	23	string	string	NOUN
ejpam-3972	132	24	representing	represent	VERB
ejpam-3972	132	25	the	the	DET
ejpam-3972	132	26	product	product	NOUN
ejpam-3972	132	27	of	of	ADP
ejpam-3972	132	28	the	the	DET
ejpam-3972	132	29	first	first	ADJ
ejpam-3972	132	30	and	and	CCONJ
ejpam-3972	132	31	second	second	ADJ
ejpam-3972	132	32	halves	half	NOUN
ejpam-3972	132	33	of	of	ADP
ejpam-3972	132	34	λ	λ	NOUN
ejpam-3972	132	35	,	,	PUNCT
ejpam-3972	132	36	we	we	PRON
ejpam-3972	132	37	have	have	VERB
ejpam-3972	132	38	h(λ	h(λ	NOUN
ejpam-3972	132	39	)	)	PUNCT
ejpam-3972	133	1	=	=	SYM
ejpam-3972	133	2	λ1	λ1	ADJ
ejpam-3972	133	3	•	•	NUM
ejpam-3972	133	4	λ2	λ2	NOUN
ejpam-3972	133	5	,	,	PUNCT
ejpam-3972	133	6	(	(	PUNCT
ejpam-3972	133	7	19	19	NUM
ejpam-3972	133	8	)	)	PUNCT
ejpam-3972	133	9	where	where	SCONJ
ejpam-3972	133	10	λ1	λ1	PROPN
ejpam-3972	133	11	is	be	AUX
ejpam-3972	133	12	also	also	ADV
ejpam-3972	133	13	the	the	DET
ejpam-3972	133	14	string	string	NOUN
ejpam-3972	133	15	representing	represent	VERB
ejpam-3972	133	16	the	the	DET
ejpam-3972	133	17	product	product	NOUN
ejpam-3972	133	18	of	of	ADP
ejpam-3972	133	19	the	the	DET
ejpam-3972	133	20	first	first	ADJ
ejpam-3972	133	21	and	and	CCONJ
ejpam-3972	133	22	second	second	ADJ
ejpam-3972	133	23	halves	half	NOUN
ejpam-3972	133	24	,	,	PUNCT
ejpam-3972	133	25	that	that	PRON
ejpam-3972	133	26	is	be	AUX
ejpam-3972	133	27	λ1	λ1	ADJ
ejpam-3972	133	28	=	=	SYM
ejpam-3972	133	29	x	x	SYM
ejpam-3972	133	30	•	•	NUM
ejpam-3972	133	31	y	y	PROPN
ejpam-3972	133	32	,	,	PUNCT
ejpam-3972	133	33	(	(	PUNCT
ejpam-3972	133	34	20	20	NUM
ejpam-3972	133	35	)	)	PUNCT
ejpam-3972	133	36	the	the	DET
ejpam-3972	133	37	string	string	NOUN
ejpam-3972	133	38	λ	λ	X
ejpam-3972	133	39	=	=	PUNCT
ejpam-3972	133	40	x	x	SYM
ejpam-3972	133	41	•	•	NUM
ejpam-3972	133	42	y	y	PROPN
ejpam-3972	133	43	•	•	NUM
ejpam-3972	133	44	λ2	λ2	NOUN
ejpam-3972	133	45	(	(	PUNCT
ejpam-3972	133	46	21	21	NUM
ejpam-3972	133	47	)	)	PUNCT
ejpam-3972	133	48	y.	y.	PROPN
ejpam-3972	133	49	liu	liu	PROPN
ejpam-3972	133	50	/	/	SYM
ejpam-3972	133	51	eur	eur	PROPN
ejpam-3972	133	52	.	.	PUNCT
ejpam-3972	134	1	j.	j.	PROPN
ejpam-3972	134	2	pure	pure	PROPN
ejpam-3972	134	3	appl	appl	PROPN
ejpam-3972	134	4	.	.	PROPN
ejpam-3972	134	5	math	math	PROPN
ejpam-3972	134	6	,	,	PUNCT
ejpam-3972	134	7	14	14	NUM
ejpam-3972	134	8	(	(	PUNCT
ejpam-3972	134	9	2	2	NUM
ejpam-3972	134	10	)	)	PUNCT
ejpam-3972	134	11	(	(	PUNCT
ejpam-3972	134	12	2021	2021	NUM
ejpam-3972	134	13	)	)	PUNCT
ejpam-3972	134	14	,	,	PUNCT
ejpam-3972	134	15	521	521	NUM
ejpam-3972	134	16	-	-	SYM
ejpam-3972	134	17	536	536	NUM
ejpam-3972	134	18	527	527	NUM
ejpam-3972	134	19	as	as	SCONJ
ejpam-3972	134	20	binary	binary	ADJ
ejpam-3972	134	21	numbers	number	NOUN
ejpam-3972	134	22	are	be	AUX
ejpam-3972	134	23	{	{	PUNCT
ejpam-3972	134	24	b1	b1	NOUN
ejpam-3972	134	25	,	,	PUNCT
ejpam-3972	134	26	b2	b2	NOUN
ejpam-3972	134	27	,	,	PUNCT
ejpam-3972	134	28	·	·	PUNCT
ejpam-3972	134	29	·	·	PUNCT
ejpam-3972	134	30	·	·	PUNCT
ejpam-3972	134	31	,	,	PUNCT
ejpam-3972	134	32	bk	bk	ADP
ejpam-3972	134	33	}	}	PUNCT
ejpam-3972	134	34	.	.	PUNCT
ejpam-3972	135	1	if	if	SCONJ
ejpam-3972	135	2	|λ|	|λ|	PROPN
ejpam-3972	135	3	is	be	AUX
ejpam-3972	135	4	even	even	ADV
ejpam-3972	135	5	,	,	PUNCT
ejpam-3972	135	6	then	then	ADV
ejpam-3972	135	7	|λ1|	|λ1|	X
ejpam-3972	135	8	=	=	SYM
ejpam-3972	135	9	|x	|x	X
ejpam-3972	135	10	•	•	NOUN
ejpam-3972	135	11	y|	y|	NOUN
ejpam-3972	135	12	=	=	NOUN
ejpam-3972	135	13	|λ2|	|λ2|	NOUN
ejpam-3972	135	14	.	.	PUNCT
ejpam-3972	136	1	(	(	PUNCT
ejpam-3972	136	2	22	22	NUM
ejpam-3972	136	3	)	)	PUNCT
ejpam-3972	136	4	if	if	SCONJ
ejpam-3972	136	5	|λ|	|λ|	PROPN
ejpam-3972	136	6	is	be	AUX
ejpam-3972	136	7	odd	odd	ADJ
ejpam-3972	136	8	,	,	PUNCT
ejpam-3972	136	9	then	then	ADV
ejpam-3972	136	10	|λ1|	|λ1|	X
ejpam-3972	136	11	=	=	SYM
ejpam-3972	136	12	|x	|x	X
ejpam-3972	136	13	•	•	NOUN
ejpam-3972	136	14	y|	y|	NOUN
ejpam-3972	136	15	=	=	SYM
ejpam-3972	136	16	|λ2|+	|λ2|+	X
ejpam-3972	136	17	1	1	X
ejpam-3972	136	18	.	.	PUNCT
ejpam-3972	136	19	(	(	PUNCT
ejpam-3972	136	20	23	23	NUM
ejpam-3972	136	21	)	)	PUNCT
ejpam-3972	136	22	let	let	VERB
ejpam-3972	136	23	h(λ	h(λ	PROPN
ejpam-3972	136	24	)	)	PUNCT
ejpam-3972	136	25	is	be	AUX
ejpam-3972	136	26	a	a	DET
ejpam-3972	136	27	compression	compression	NOUN
ejpam-3972	136	28	function	function	NOUN
ejpam-3972	136	29	,	,	PUNCT
ejpam-3972	136	30	i.e.	i.e.	X
ejpam-3972	136	31	,	,	PUNCT
ejpam-3972	136	32	h(λ	h(λ	PROPN
ejpam-3972	136	33	)	)	PUNCT
ejpam-3972	136	34	is	be	AUX
ejpam-3972	136	35	a	a	DET
ejpam-3972	136	36	fixed	fix	VERB
ejpam-3972	136	37	length	length	NOUN
ejpam-3972	136	38	and	and	CCONJ
ejpam-3972	136	39	x	x	X
ejpam-3972	136	40	or	or	CCONJ
ejpam-3972	136	41	y	y	NOUN
ejpam-3972	136	42	,	,	PUNCT
ejpam-3972	136	43	or	or	CCONJ
ejpam-3972	136	44	λ2	λ2	NOUN
ejpam-3972	136	45	is	be	AUX
ejpam-3972	136	46	any	any	DET
ejpam-3972	136	47	finite	finite	ADJ
ejpam-3972	136	48	length	length	NOUN
ejpam-3972	136	49	.	.	PUNCT
ejpam-3972	137	1	then	then	ADV
ejpam-3972	137	2	we	we	PRON
ejpam-3972	137	3	need	need	VERB
ejpam-3972	137	4	to	to	PART
ejpam-3972	137	5	pad	pad	VERB
ejpam-3972	137	6	h(λ	h(λ	PROPN
ejpam-3972	137	7	)	)	PUNCT
ejpam-3972	137	8	with	with	ADP
ejpam-3972	137	9	leading	lead	VERB
ejpam-3972	137	10	0s	0s	NOUN
ejpam-3972	137	11	so	so	SCONJ
ejpam-3972	137	12	that	that	SCONJ
ejpam-3972	137	13	it	it	PRON
ejpam-3972	137	14	has	have	VERB
ejpam-3972	137	15	the	the	DET
ejpam-3972	137	16	same	same	ADJ
ejpam-3972	137	17	length	length	NOUN
ejpam-3972	137	18	as	as	ADP
ejpam-3972	137	19	λ	λ	X
ejpam-3972	137	20	.	.	PUNCT
ejpam-3972	138	1	we	we	PRON
ejpam-3972	138	2	deduce	deduce	VERB
ejpam-3972	138	3	that	that	PRON
ejpam-3972	138	4	can	can	AUX
ejpam-3972	138	5	not	not	PART
ejpam-3972	138	6	invert	invert	VERB
ejpam-3972	139	1	h(λ)(or	h(λ)(or	PRON
ejpam-3972	139	2	h(x	h(x	PROPN
ejpam-3972	139	3	,	,	PUNCT
ejpam-3972	139	4	y	y	PROPN
ejpam-3972	139	5	,	,	PUNCT
ejpam-3972	139	6	z	z	NOUN
ejpam-3972	139	7	)	)	PUNCT
ejpam-3972	139	8	)	)	PUNCT
ejpam-3972	139	9	.	.	PUNCT
ejpam-3972	140	1	but	but	CCONJ
ejpam-3972	140	2	it	it	PRON
ejpam-3972	140	3	would	would	AUX
ejpam-3972	140	4	technically	technically	ADV
ejpam-3972	140	5	—	—	PUNCT
ejpam-3972	140	6	the	the	DET
ejpam-3972	140	7	probabilities	probability	NOUN
ejpam-3972	140	8	of	of	ADP
ejpam-3972	140	9	cheating	cheat	VERB
ejpam-3972	140	10	by	by	ADP
ejpam-3972	140	11	one	one	NUM
ejpam-3972	140	12	of	of	ADP
ejpam-3972	140	13	the	the	DET
ejpam-3972	140	14	penetrator	penetrator	NOUN
ejpam-3972	140	15	are	be	AUX
ejpam-3972	140	16	very	very	ADV
ejpam-3972	140	17	small	small	ADJ
ejpam-3972	140	18	.	.	PUNCT
ejpam-3972	141	1	let	let	VERB
ejpam-3972	141	2	p	p	PRON
ejpam-3972	141	3	:	:	PUNCT
ejpam-3972	141	4	a	a	DET
ejpam-3972	141	5	→	→	SYM
ejpam-3972	141	6	b	b	PROPN
ejpam-3972	141	7	and	and	CCONJ
ejpam-3972	141	8	q	q	NOUN
ejpam-3972	141	9	:	:	PUNCT
ejpam-3972	141	10	b	b	X
ejpam-3972	141	11	→	→	SYM
ejpam-3972	141	12	c.	c.	NOUN
ejpam-3972	141	13	if	if	SCONJ
ejpam-3972	141	14	x	x	X
ejpam-3972	141	15	:	:	PUNCT
ejpam-3972	141	16	a	a	DET
ejpam-3972	141	17	→	→	SYM
ejpam-3972	141	18	c	c	NOUN
ejpam-3972	141	19	and	and	CCONJ
ejpam-3972	141	20	x	x	X
ejpam-3972	141	21	=	=	PUNCT
ejpam-3972	141	22	p	p	PROPN
ejpam-3972	141	23	•	•	NUM
ejpam-3972	141	24	q	q	NOUN
ejpam-3972	141	25	,	,	PUNCT
ejpam-3972	141	26	then	then	ADV
ejpam-3972	141	27	p	p	X
ejpam-3972	141	28	,	,	PUNCT
ejpam-3972	141	29	q	q	PUNCT
ejpam-3972	141	30	and	and	CCONJ
ejpam-3972	141	31	x	x	AUX
ejpam-3972	141	32	have	have	VERB
ejpam-3972	141	33	a	a	DET
ejpam-3972	141	34	commutative	commutative	ADJ
ejpam-3972	141	35	diagram	diagram	NOUN
ejpam-3972	141	36	.	.	PUNCT
ejpam-3972	142	1	show	show	VERB
ejpam-3972	142	2	that	that	DET
ejpam-3972	142	3	diagram	diagram	NOUN
ejpam-3972	142	4	is	be	AUX
ejpam-3972	142	5	a	a	DET
ejpam-3972	142	6	valid	valid	ADJ
ejpam-3972	142	7	commutative	commutative	ADJ
ejpam-3972	142	8	diagram	diagram	NOUN
ejpam-3972	142	9	(	(	PUNCT
ejpam-3972	142	10	x	x	NOUN
ejpam-3972	142	11	=	=	SYM
ejpam-3972	142	12	z•y	z•y	PROPN
ejpam-3972	142	13	)	)	PUNCT
ejpam-3972	142	14	,	,	PUNCT
ejpam-3972	142	15	i.e.	i.e.	X
ejpam-3972	142	16	,	,	PUNCT
ejpam-3972	142	17	quantum	quantum	ADJ
ejpam-3972	142	18	entanglement	entanglement	NOUN
ejpam-3972	142	19	in	in	ADP
ejpam-3972	142	20	wormhole	wormhole	NOUN
ejpam-3972	142	21	,	,	PUNCT
ejpam-3972	142	22	where	where	SCONJ
ejpam-3972	142	23	x	x	PRON
ejpam-3972	142	24	is	be	AUX
ejpam-3972	142	25	a	a	DET
ejpam-3972	142	26	composite	composite	ADJ
ejpam-3972	142	27	(	(	PUNCT
ejpam-3972	142	28	or	or	CCONJ
ejpam-3972	142	29	modulus	modulus	NOUN
ejpam-3972	142	30	)	)	PUNCT
ejpam-3972	142	31	,	,	PUNCT
ejpam-3972	142	32	z	z	PROPN
ejpam-3972	142	33	and	and	CCONJ
ejpam-3972	142	34	y	y	PROPN
ejpam-3972	142	35	be	be	VERB
ejpam-3972	142	36	two	two	NUM
ejpam-3972	142	37	large	large	ADJ
ejpam-3972	142	38	primes	prime	NOUN
ejpam-3972	142	39	in	in	ADP
ejpam-3972	142	40	figure	figure	NOUN
ejpam-3972	142	41	2	2	NUM
ejpam-3972	142	42	,	,	PUNCT
ejpam-3972	142	43	and	and	CCONJ
ejpam-3972	142	44	this	this	PRON
ejpam-3972	142	45	is	be	AUX
ejpam-3972	142	46	illustrated	illustrate	VERB
ejpam-3972	142	47	in	in	ADP
ejpam-3972	142	48	figure	figure	NOUN
ejpam-3972	142	49	a1	a1	NOUN
ejpam-3972	142	50	(	(	PUNCT
ejpam-3972	142	51	as	as	SCONJ
ejpam-3972	142	52	noted	note	VERB
ejpam-3972	142	53	in	in	ADP
ejpam-3972	142	54	appendix	appendix	NOUN
ejpam-3972	142	55	)	)	PUNCT
ejpam-3972	142	56	,	,	PUNCT
ejpam-3972	142	57	we	we	PRON
ejpam-3972	142	58	shows	show	VERB
ejpam-3972	142	59	that	that	SCONJ
ejpam-3972	142	60	the	the	DET
ejpam-3972	142	61	wormhole	wormhole	NOUN
ejpam-3972	142	62	computation	computation	NOUN
ejpam-3972	142	63	by	by	ADP
ejpam-3972	142	64	the	the	DET
ejpam-3972	142	65	quantum	quantum	ADJ
ejpam-3972	142	66	entanglement	entanglement	NOUN
ejpam-3972	142	67	method	method	NOUN
ejpam-3972	142	68	.	.	PUNCT
ejpam-3972	143	1	although	although	SCONJ
ejpam-3972	143	2	our	our	PRON
ejpam-3972	143	3	understanding	understanding	NOUN
ejpam-3972	143	4	of	of	ADP
ejpam-3972	143	5	the	the	DET
ejpam-3972	143	6	wormhole	wormhole	NOUN
ejpam-3972	143	7	of	of	ADP
ejpam-3972	143	8	calculate	calculate	NOUN
ejpam-3972	143	9	is	be	AUX
ejpam-3972	143	10	fairly	fairly	ADV
ejpam-3972	143	11	limited	limited	ADJ
ejpam-3972	143	12	,	,	PUNCT
ejpam-3972	143	13	we	we	PRON
ejpam-3972	143	14	use	use	VERB
ejpam-3972	143	15	the	the	DET
ejpam-3972	143	16	design	design	NOUN
ejpam-3972	143	17	methodologies	methodology	NOUN
ejpam-3972	143	18	of	of	ADP
ejpam-3972	143	19	algebra	algebra	NOUN
ejpam-3972	143	20	,	,	PUNCT
ejpam-3972	143	21	i.e.	i.e.	X
ejpam-3972	143	22	,	,	PUNCT
ejpam-3972	143	23	the	the	DET
ejpam-3972	143	24	group	group	NOUN
ejpam-3972	143	25	is	be	AUX
ejpam-3972	143	26	used	use	VERB
ejpam-3972	143	27	to	to	PART
ejpam-3972	143	28	model	model	VERB
ejpam-3972	143	29	the	the	DET
ejpam-3972	143	30	circuitry	circuitry	NOUN
ejpam-3972	143	31	of	of	ADP
ejpam-3972	143	32	electronic	electronic	ADJ
ejpam-3972	143	33	devices	device	NOUN
ejpam-3972	143	34	(	(	PUNCT
ejpam-3972	143	35	e.g.	e.g.	ADV
ejpam-3972	143	36	analog	analog	NOUN
ejpam-3972	143	37	multiplier	multiplier	ADV
ejpam-3972	143	38	)	)	PUNCT
ejpam-3972	143	39	for	for	ADP
ejpam-3972	143	40	simulates	simulate	NOUN
ejpam-3972	143	41	wormhole	wormhole	NOUN
ejpam-3972	143	42	operations	operation	NOUN
ejpam-3972	143	43	in	in	ADP
ejpam-3972	143	44	identity	identity	NOUN
ejpam-3972	143	45	(	(	PUNCT
ejpam-3972	143	46	wkdc1	wkdc1	PROPN
ejpam-3972	143	47	)	)	PUNCT
ejpam-3972	143	48	.	.	PUNCT
ejpam-3972	144	1	in	in	ADP
ejpam-3972	144	2	fact	fact	NOUN
ejpam-3972	144	3	,	,	PUNCT
ejpam-3972	144	4	the	the	DET
ejpam-3972	144	5	quantum	quantum	ADJ
ejpam-3972	144	6	computers	computer	NOUN
ejpam-3972	144	7	should	should	AUX
ejpam-3972	144	8	be	be	AUX
ejpam-3972	144	9	able	able	ADJ
ejpam-3972	144	10	to	to	PART
ejpam-3972	144	11	perform	perform	VERB
ejpam-3972	144	12	highly	highly	ADV
ejpam-3972	144	13	complex	complex	ADJ
ejpam-3972	144	14	simulations	simulation	NOUN
ejpam-3972	144	15	.	.	PUNCT
ejpam-3972	145	1	this	this	DET
ejpam-3972	145	2	identity	identity	NOUN
ejpam-3972	145	3	(	(	PUNCT
ejpam-3972	145	4	wkdc2	wkdc2	PROPN
ejpam-3972	145	5	)	)	PUNCT
ejpam-3972	145	6	is	be	AUX
ejpam-3972	145	7	implemented	implement	VERB
ejpam-3972	145	8	by	by	ADP
ejpam-3972	145	9	the	the	DET
ejpam-3972	145	10	sick	sick	ADJ
ejpam-3972	145	11	circuit	circuit	NOUN
ejpam-3972	145	12	,	,	PUNCT
ejpam-3972	145	13	so	so	SCONJ
ejpam-3972	145	14	it	it	PRON
ejpam-3972	145	15	makes	make	VERB
ejpam-3972	145	16	no	no	DET
ejpam-3972	145	17	operational	operational	ADJ
ejpam-3972	145	18	sense	sense	NOUN
ejpam-3972	145	19	.	.	PUNCT
ejpam-3972	146	1	obviously	obviously	ADV
ejpam-3972	146	2	,	,	PUNCT
ejpam-3972	146	3	this	this	PRON
ejpam-3972	146	4	is	be	AUX
ejpam-3972	146	5	an	an	DET
ejpam-3972	146	6	abstraction	abstraction	NOUN
ejpam-3972	146	7	of	of	ADP
ejpam-3972	146	8	mathematical	mathematical	ADJ
ejpam-3972	146	9	concepts	concept	NOUN
ejpam-3972	146	10	.	.	PUNCT
ejpam-3972	147	1	a	a	DET
ejpam-3972	147	2	public	public	ADJ
ejpam-3972	147	3	-	-	PUNCT
ejpam-3972	147	4	key	key	NOUN
ejpam-3972	147	5	cryptosystem	cryptosystem	NOUN
ejpam-3972	147	6	,	,	PUNCT
ejpam-3972	147	7	such	such	ADJ
ejpam-3972	147	8	as	as	ADP
ejpam-3972	147	9	rsa	rsa	PROPN
ejpam-3972	147	10	[	[	X
ejpam-3972	147	11	10	10	NUM
ejpam-3972	147	12	,	,	PUNCT
ejpam-3972	147	13	11	11	NUM
ejpam-3972	147	14	]	]	PUNCT
ejpam-3972	147	15	,	,	PUNCT
ejpam-3972	147	16	can	can	AUX
ejpam-3972	147	17	be	be	AUX
ejpam-3972	147	18	used	use	VERB
ejpam-3972	147	19	to	to	PART
ejpam-3972	147	20	distribute	distribute	VERB
ejpam-3972	147	21	private	private	ADJ
ejpam-3972	147	22	keys	key	NOUN
ejpam-3972	147	23	to	to	ADP
ejpam-3972	147	24	pairs	pair	NOUN
ejpam-3972	147	25	of	of	ADP
ejpam-3972	147	26	individuals	individual	NOUN
ejpam-3972	147	27	when	when	SCONJ
ejpam-3972	147	28	they	they	PRON
ejpam-3972	147	29	wish	wish	VERB
ejpam-3972	147	30	to	to	PART
ejpam-3972	147	31	communicate	communicate	VERB
ejpam-3972	147	32	,	,	PUNCT
ejpam-3972	147	33	and	and	CCONJ
ejpam-3972	147	34	then	then	ADV
ejpam-3972	147	35	use	use	VERB
ejpam-3972	147	36	a	a	DET
ejpam-3972	147	37	private	private	ADJ
ejpam-3972	147	38	key	key	ADJ
ejpam-3972	147	39	system	system	NOUN
ejpam-3972	147	40	,	,	PUNCT
ejpam-3972	147	41	such	such	ADJ
ejpam-3972	147	42	as	as	ADP
ejpam-3972	147	43	data	data	NOUN
ejpam-3972	147	44	encryption	encryption	NOUN
ejpam-3972	147	45	standard	standard	NOUN
ejpam-3972	147	46	(	(	PUNCT
ejpam-3972	147	47	des	des	PROPN
ejpam-3972	147	48	)	)	PUNCT
ejpam-3972	147	49	[	[	X
ejpam-3972	147	50	12	12	NUM
ejpam-3972	147	51	]	]	PUNCT
ejpam-3972	147	52	is	be	AUX
ejpam-3972	147	53	a	a	DET
ejpam-3972	147	54	block	block	NOUN
ejpam-3972	147	55	cipher	cipher	ADJ
ejpam-3972	147	56	algorithm	algorithm	NOUN
ejpam-3972	147	57	,	,	PUNCT
ejpam-3972	147	58	for	for	ADP
ejpam-3972	147	59	encryption	encryption	NOUN
ejpam-3972	147	60	and	and	CCONJ
ejpam-3972	147	61	decryption	decryption	NOUN
ejpam-3972	147	62	of	of	ADP
ejpam-3972	147	63	messages	message	NOUN
ejpam-3972	147	64	.	.	PUNCT
ejpam-3972	148	1	about	about	ADP
ejpam-3972	148	2	wkdc	wkdc	PROPN
ejpam-3972	148	3	,	,	PUNCT
ejpam-3972	148	4	it	it	PRON
ejpam-3972	148	5	is	be	AUX
ejpam-3972	148	6	best	good	ADJ
ejpam-3972	148	7	to	to	PART
ejpam-3972	148	8	use	use	VERB
ejpam-3972	148	9	the	the	DET
ejpam-3972	148	10	wkd	wkd	NOUN
ejpam-3972	148	11	to	to	PART
ejpam-3972	148	12	avoid	avoid	VERB
ejpam-3972	148	13	causing	cause	VERB
ejpam-3972	148	14	any	any	DET
ejpam-3972	148	15	damage	damage	NOUN
ejpam-3972	148	16	the	the	DET
ejpam-3972	148	17	message	message	NOUN
ejpam-3972	148	18	(	(	PUNCT
ejpam-3972	148	19	e.g.	e.g.	ADV
ejpam-3972	148	20	pion	pion	NOUN
ejpam-3972	148	21	)	)	PUNCT
ejpam-3972	148	22	,	,	PUNCT
ejpam-3972	148	23	just	just	ADV
ejpam-3972	148	24	like	like	ADP
ejpam-3972	148	25	a	a	DET
ejpam-3972	148	26	cloud	cloud	NOUN
ejpam-3972	148	27	storage	storage	NOUN
ejpam-3972	148	28	.	.	PUNCT
ejpam-3972	149	1	wormhole	wormhole	NOUN
ejpam-3972	149	2	computation	computation	NOUN
ejpam-3972	149	3	is	be	AUX
ejpam-3972	149	4	the	the	DET
ejpam-3972	149	5	basis	basis	NOUN
ejpam-3972	149	6	for	for	ADP
ejpam-3972	149	7	a	a	DET
ejpam-3972	149	8	method	method	NOUN
ejpam-3972	149	9	that	that	PRON
ejpam-3972	149	10	can	can	AUX
ejpam-3972	149	11	be	be	AUX
ejpam-3972	149	12	used	use	VERB
ejpam-3972	149	13	to	to	PART
ejpam-3972	149	14	perform	perform	VERB
ejpam-3972	149	15	arithmetic	arithmetic	ADJ
ejpam-3972	149	16	with	with	ADP
ejpam-3972	149	17	large	large	ADJ
ejpam-3972	149	18	integers	integer	NOUN
ejpam-3972	149	19	.	.	PUNCT
ejpam-3972	150	1	more	more	ADJ
ejpam-3972	150	2	than	than	ADP
ejpam-3972	150	3	that	that	PRON
ejpam-3972	150	4	,	,	PUNCT
ejpam-3972	150	5	wormhole	wormhole	NOUN
ejpam-3972	150	6	teleportation	teleportation	NOUN
ejpam-3972	150	7	is	be	AUX
ejpam-3972	150	8	a	a	DET
ejpam-3972	150	9	jumping	jumping	NOUN
ejpam-3972	150	10	window	window	NOUN
ejpam-3972	150	11	,	,	PUNCT
ejpam-3972	150	12	and	and	CCONJ
ejpam-3972	150	13	it	it	PRON
ejpam-3972	150	14	ensures	ensure	VERB
ejpam-3972	150	15	integrality	integrality	NOUN
ejpam-3972	150	16	of	of	ADP
ejpam-3972	150	17	messages	message	NOUN
ejpam-3972	150	18	,	,	PUNCT
ejpam-3972	150	19	in	in	ADP
ejpam-3972	150	20	particular	particular	ADJ
ejpam-3972	150	21	to	to	PART
ejpam-3972	150	22	ensure	ensure	VERB
ejpam-3972	150	23	opening	opening	NOUN
ejpam-3972	150	24	of	of	ADP
ejpam-3972	150	25	messages	message	NOUN
ejpam-3972	150	26	.	.	PUNCT
ejpam-3972	151	1	in	in	ADP
ejpam-3972	151	2	the	the	DET
ejpam-3972	151	3	wcs	wcs	NOUN
ejpam-3972	151	4	encryption	encryption	NOUN
ejpam-3972	151	5	method	method	NOUN
ejpam-3972	151	6	,	,	PUNCT
ejpam-3972	151	7	messages	message	NOUN
ejpam-3972	151	8	are	be	AUX
ejpam-3972	151	9	translated	translate	VERB
ejpam-3972	151	10	into	into	ADP
ejpam-3972	151	11	sequences	sequence	NOUN
ejpam-3972	151	12	of	of	ADP
ejpam-3972	151	13	integers	integer	NOUN
ejpam-3972	151	14	.	.	PUNCT
ejpam-3972	152	1	by	by	ADP
ejpam-3972	152	2	the	the	DET
ejpam-3972	152	3	function	function	NOUN
ejpam-3972	152	4	expression	expression	NOUN
ejpam-3972	152	5	of	of	ADP
ejpam-3972	152	6	wcs	wcs	PROPN
ejpam-3972	152	7	,	,	PUNCT
ejpam-3972	152	8	it	it	PRON
ejpam-3972	152	9	follows	follow	VERB
ejpam-3972	152	10	that	that	SCONJ
ejpam-3972	152	11	(	(	PUNCT
ejpam-3972	152	12	wcs1	wcs1	NOUN
ejpam-3972	152	13	)	)	PUNCT
ejpam-3972	152	14	h(x	h(x	PROPN
ejpam-3972	152	15	,	,	PUNCT
ejpam-3972	152	16	y	y	PROPN
ejpam-3972	152	17	,	,	PUNCT
ejpam-3972	152	18	z	z	NOUN
ejpam-3972	152	19	)	)	PUNCT
ejpam-3972	152	20	=	=	SYM
ejpam-3972	152	21	f(x	f(x	PROPN
ejpam-3972	152	22	,	,	PUNCT
ejpam-3972	152	23	y	y	PROPN
ejpam-3972	152	24	,	,	PUNCT
ejpam-3972	152	25	z	z	NOUN
ejpam-3972	152	26	)	)	PUNCT
ejpam-3972	152	27	•	•	ADV
ejpam-3972	152	28	g(x	g(x	PROPN
ejpam-3972	152	29	,	,	PUNCT
ejpam-3972	152	30	y	y	PROPN
ejpam-3972	152	31	,	,	PUNCT
ejpam-3972	152	32	z	z	NOUN
ejpam-3972	152	33	)	)	PUNCT
ejpam-3972	152	34	and	and	CCONJ
ejpam-3972	152	35	(	(	PUNCT
ejpam-3972	152	36	wcs2	wcs2	PROPN
ejpam-3972	152	37	)	)	PUNCT
ejpam-3972	152	38	(	(	PUNCT
ejpam-3972	152	39	(	(	PUNCT
ejpam-3972	152	40	x	x	SYM
ejpam-3972	152	41	•	•	NUM
ejpam-3972	152	42	y	y	NOUN
ejpam-3972	152	43	)	)	PUNCT
ejpam-3972	152	44	•	•	NUM
ejpam-3972	152	45	z	z	NOUN
ejpam-3972	152	46	)	)	PUNCT
ejpam-3972	152	47	•	•	NOUN
ejpam-3972	152	48	(	(	PUNCT
ejpam-3972	152	49	(	(	PUNCT
ejpam-3972	152	50	x	x	SYM
ejpam-3972	152	51	•	•	NUM
ejpam-3972	152	52	z	z	NOUN
ejpam-3972	152	53	)	)	PUNCT
ejpam-3972	152	54	•	•	NUM
ejpam-3972	152	55	y	y	NOUN
ejpam-3972	152	56	)	)	PUNCT
ejpam-3972	152	57	=	=	PUNCT
ejpam-3972	153	1	(	(	PUNCT
ejpam-3972	153	2	z	z	NOUN
ejpam-3972	153	3	•	•	NUM
ejpam-3972	153	4	y	y	NOUN
ejpam-3972	153	5	)	)	PUNCT
ejpam-3972	153	6	•	•	NOUN
ejpam-3972	153	7	x.	x.	NOUN
ejpam-3972	153	8	definition	definition	NOUN
ejpam-3972	153	9	8	8	NUM
ejpam-3972	153	10	.	.	PUNCT
ejpam-3972	154	1	(	(	PUNCT
ejpam-3972	154	2	polynomial	polynomial	NOUN
ejpam-3972	154	3	of	of	ADP
ejpam-3972	154	4	wcs	wcs	NOUN
ejpam-3972	154	5	)	)	PUNCT
ejpam-3972	155	1	let	let	VERB
ejpam-3972	155	2	(	(	PUNCT
ejpam-3972	155	3	x	x	NOUN
ejpam-3972	155	4	;	;	PUNCT
ejpam-3972	155	5	•	•	NUM
ejpam-3972	155	6	,	,	PUNCT
ejpam-3972	155	7	1	1	NUM
ejpam-3972	155	8	)	)	PUNCT
ejpam-3972	155	9	is	be	AUX
ejpam-3972	155	10	a	a	DET
ejpam-3972	155	11	bcl+	bcl+	PROPN
ejpam-3972	155	12	algebra	algebra	NOUN
ejpam-3972	155	13	.	.	PUNCT
ejpam-3972	156	1	assume	assume	VERB
ejpam-3972	156	2	that	that	SCONJ
ejpam-3972	156	3	for	for	ADP
ejpam-3972	156	4	an	an	DET
ejpam-3972	156	5	,	,	PUNCT
ejpam-3972	156	6	an−1	an−1	ADJ
ejpam-3972	156	7	,	,	PUNCT
ejpam-3972	156	8	·	·	PUNCT
ejpam-3972	156	9	·	·	PUNCT
ejpam-3972	156	10	·	·	PUNCT
ejpam-3972	156	11	,	,	PUNCT
ejpam-3972	156	12	a0	a0	PROPN
ejpam-3972	156	13	∈	∈	PROPN
ejpam-3972	156	14	x	x	PRON
ejpam-3972	156	15	,	,	PUNCT
ejpam-3972	156	16	there	there	PRON
ejpam-3972	156	17	is	be	VERB
ejpam-3972	156	18	defined	define	VERB
ejpam-3972	156	19	a	a	DET
ejpam-3972	156	20	coefficient	coefficient	NOUN
ejpam-3972	156	21	1xi	1xi	NOUN
ejpam-3972	156	22	=	=	SYM
ejpam-3972	156	23	1	1	NUM
ejpam-3972	156	24	,	,	PUNCT
ejpam-3972	156	25	and	and	CCONJ
ejpam-3972	156	26	let	let	VERB
ejpam-3972	156	27	f(x	f(x	PROPN
ejpam-3972	156	28	)	)	PUNCT
ejpam-3972	156	29	∈	∈	PROPN
ejpam-3972	157	1	x[x	x[x	X
ejpam-3972	157	2	]	]	X
ejpam-3972	157	3	is	be	AUX
ejpam-3972	157	4	a	a	DET
ejpam-3972	157	5	polynomial	polynomial	ADJ
ejpam-3972	157	6	such	such	ADJ
ejpam-3972	157	7	that	that	SCONJ
ejpam-3972	157	8	f(x	f(x	NOUN
ejpam-3972	157	9	)	)	PUNCT
ejpam-3972	158	1	=	=	PUNCT
ejpam-3972	159	1	anx	anx	ADJ
ejpam-3972	159	2	n	n	PROPN
ejpam-3972	159	3	+	+	CCONJ
ejpam-3972	159	4	an−1x	an−1x	PROPN
ejpam-3972	159	5	n−1	n−1	PROPN
ejpam-3972	159	6	+	+	CCONJ
ejpam-3972	159	7	·	·	PUNCT
ejpam-3972	159	8	·	·	PUNCT
ejpam-3972	159	9	·	·	PUNCT
ejpam-3972	159	10	+	+	NUM
ejpam-3972	159	11	a0	a0	PROPN
ejpam-3972	159	12	.	.	PUNCT
ejpam-3972	160	1	(	(	PUNCT
ejpam-3972	160	2	24	24	NUM
ejpam-3972	160	3	)	)	PUNCT
ejpam-3972	160	4	y.	y.	PROPN
ejpam-3972	160	5	liu	liu	PROPN
ejpam-3972	160	6	/	/	SYM
ejpam-3972	160	7	eur	eur	PROPN
ejpam-3972	160	8	.	.	PUNCT
ejpam-3972	161	1	j.	j.	PROPN
ejpam-3972	161	2	pure	pure	PROPN
ejpam-3972	161	3	appl	appl	PROPN
ejpam-3972	161	4	.	.	PROPN
ejpam-3972	161	5	math	math	PROPN
ejpam-3972	161	6	,	,	PUNCT
ejpam-3972	161	7	14	14	NUM
ejpam-3972	161	8	(	(	PUNCT
ejpam-3972	161	9	2	2	NUM
ejpam-3972	161	10	)	)	PUNCT
ejpam-3972	161	11	(	(	PUNCT
ejpam-3972	161	12	2021	2021	NUM
ejpam-3972	161	13	)	)	PUNCT
ejpam-3972	161	14	,	,	PUNCT
ejpam-3972	161	15	521	521	NUM
ejpam-3972	161	16	-	-	SYM
ejpam-3972	161	17	536	536	NUM
ejpam-3972	161	18	528	528	NUM
ejpam-3972	161	19	then	then	ADV
ejpam-3972	161	20	(	(	PUNCT
ejpam-3972	161	21	x[x	x[x	X
ejpam-3972	161	22	]	]	X
ejpam-3972	161	23	;	;	PUNCT
ejpam-3972	161	24	•	•	X
ejpam-3972	161	25	,	,	PUNCT
ejpam-3972	161	26	1	1	NUM
ejpam-3972	161	27	)	)	PUNCT
ejpam-3972	161	28	is	be	AUX
ejpam-3972	161	29	bcl+algebra	bcl+algebra	NOUN
ejpam-3972	161	30	.	.	PUNCT
ejpam-3972	162	1	definition	definition	NOUN
ejpam-3972	162	2	9	9	NUM
ejpam-3972	162	3	.	.	PUNCT
ejpam-3972	163	1	(	(	PUNCT
ejpam-3972	163	2	groups	group	NOUN
ejpam-3972	163	3	of	of	ADP
ejpam-3972	163	4	wcs	wcs	NOUN
ejpam-3972	163	5	)	)	PUNCT
ejpam-3972	163	6	.	.	PUNCT
ejpam-3972	164	1	let	let	VERB
ejpam-3972	164	2	g	g	PRON
ejpam-3972	164	3	be	be	AUX
ejpam-3972	164	4	a	a	DET
ejpam-3972	164	5	group	group	NOUN
ejpam-3972	164	6	for	for	ADP
ejpam-3972	164	7	all	all	DET
ejpam-3972	164	8	n	n	CCONJ
ejpam-3972	164	9	,	,	PUNCT
ejpam-3972	164	10	p	p	X
ejpam-3972	164	11	,	,	PUNCT
ejpam-3972	164	12	q	q	PROPN
ejpam-3972	164	13	∈	∈	PROPN
ejpam-3972	164	14	g.	g.	NOUN
ejpam-3972	165	1	if	if	SCONJ
ejpam-3972	165	2	(	(	PUNCT
ejpam-3972	165	3	f(p	f(p	PROPN
ejpam-3972	165	4	)	)	PUNCT
ejpam-3972	165	5	,	,	PUNCT
ejpam-3972	165	6	g(q	g(q	NOUN
ejpam-3972	165	7	)	)	PUNCT
ejpam-3972	165	8	)	)	PUNCT
ejpam-3972	165	9	=	=	SYM
ejpam-3972	166	1	1	1	X
ejpam-3972	166	2	.	.	PUNCT
ejpam-3972	166	3	(	(	PUNCT
ejpam-3972	166	4	25	25	NUM
ejpam-3972	166	5	)	)	PUNCT
ejpam-3972	166	6	then	then	ADV
ejpam-3972	166	7	(	(	PUNCT
ejpam-3972	166	8	h(n	h(n	PROPN
ejpam-3972	166	9	)	)	PUNCT
ejpam-3972	166	10	,	,	PUNCT
ejpam-3972	166	11	f(p	f(p	PROPN
ejpam-3972	166	12	)	)	PUNCT
ejpam-3972	166	13	•	•	ADP
ejpam-3972	166	14	g(q	g(q	NOUN
ejpam-3972	166	15	)	)	PUNCT
ejpam-3972	166	16	)	)	PUNCT
ejpam-3972	167	1	=	=	SYM
ejpam-3972	167	2	1	1	X
ejpam-3972	167	3	.	.	PUNCT
ejpam-3972	167	4	(	(	PUNCT
ejpam-3972	167	5	26	26	NUM
ejpam-3972	167	6	)	)	PUNCT
ejpam-3972	167	7	we	we	PRON
ejpam-3972	167	8	have	have	VERB
ejpam-3972	167	9	(	(	PUNCT
ejpam-3972	167	10	wht4	wht4	NOUN
ejpam-3972	167	11	)	)	PUNCT
ejpam-3972	167	12	h(n	h(n	PROPN
ejpam-3972	167	13	)	)	PUNCT
ejpam-3972	168	1	=	=	PUNCT
ejpam-3972	168	2	p	p	ADJ
ejpam-3972	169	1	•	•	NUM
ejpam-3972	169	2	q	q	NOUN
ejpam-3972	169	3	,	,	PUNCT
ejpam-3972	169	4	where	where	SCONJ
ejpam-3972	169	5	p	p	NOUN
ejpam-3972	169	6	and	and	CCONJ
ejpam-3972	169	7	q	q	NOUN
ejpam-3972	169	8	be	be	AUX
ejpam-3972	169	9	two	two	NUM
ejpam-3972	169	10	large	large	ADJ
ejpam-3972	169	11	primes	prime	NOUN
ejpam-3972	169	12	,	,	PUNCT
ejpam-3972	169	13	n	n	PRON
ejpam-3972	169	14	is	be	AUX
ejpam-3972	169	15	a	a	DET
ejpam-3972	169	16	composite	composite	ADJ
ejpam-3972	169	17	(	(	PUNCT
ejpam-3972	169	18	200	200	NUM
ejpam-3972	169	19	-	-	PUNCT
ejpam-3972	169	20	digit	digit	NOUN
ejpam-3972	169	21	for	for	ADP
ejpam-3972	169	22	security	security	NOUN
ejpam-3972	169	23	)	)	PUNCT
ejpam-3972	169	24	.	.	PUNCT
ejpam-3972	170	1	4	4	X
ejpam-3972	170	2	.	.	X
ejpam-3972	170	3	methods	method	NOUN
ejpam-3972	170	4	first	first	ADV
ejpam-3972	170	5	off	off	ADV
ejpam-3972	170	6	,	,	PUNCT
ejpam-3972	170	7	we	we	PRON
ejpam-3972	170	8	needs	need	VERB
ejpam-3972	170	9	to	to	PART
ejpam-3972	170	10	design	design	VERB
ejpam-3972	170	11	the	the	DET
ejpam-3972	170	12	algorithms	algorithm	NOUN
ejpam-3972	170	13	and	and	CCONJ
ejpam-3972	170	14	mathematical	mathematical	ADJ
ejpam-3972	170	15	details	detail	NOUN
ejpam-3972	170	16	in	in	ADP
ejpam-3972	170	17	order	order	NOUN
ejpam-3972	170	18	to	to	PART
ejpam-3972	170	19	further	further	VERB
ejpam-3972	170	20	research	research	VERB
ejpam-3972	170	21	about	about	ADP
ejpam-3972	170	22	wcs	wcs	PROPN
ejpam-3972	170	23	.	.	PUNCT
ejpam-3972	171	1	4.1	4.1	NUM
ejpam-3972	171	2	.	.	PUNCT
ejpam-3972	171	3	algorithm	algorithm	NOUN
ejpam-3972	171	4	(	(	PUNCT
ejpam-3972	171	5	a	a	X
ejpam-3972	171	6	)	)	PUNCT
ejpam-3972	171	7	//	//	NOUN
ejpam-3972	171	8	using	use	VERB
ejpam-3972	171	9	the	the	DET
ejpam-3972	171	10	current	current	ADJ
ejpam-3972	171	11	generation	generation	NOUN
ejpam-3972	171	12	of	of	ADP
ejpam-3972	171	13	computers	computer	NOUN
ejpam-3972	171	14	for	for	ADP
ejpam-3972	171	15	algorithm	algorithm	NOUN
ejpam-3972	171	16	(	(	PUNCT
ejpam-3972	171	17	a	a	NOUN
ejpam-3972	171	18	)	)	PUNCT
ejpam-3972	171	19	,	,	PUNCT
ejpam-3972	171	20	because	because	SCONJ
ejpam-3972	171	21	p	p	PROPN
ejpam-3972	171	22	and	and	CCONJ
ejpam-3972	171	23	q	q	NOUN
ejpam-3972	171	24	be	be	AUX
ejpam-3972	171	25	two	two	NUM
ejpam-3972	171	26	large	large	ADJ
ejpam-3972	171	27	primes	prime	NOUN
ejpam-3972	171	28	.	.	PUNCT
ejpam-3972	172	1	//	//	NUM
ejpam-3972	173	1	•	•	NUM
ejpam-3972	173	2	wcs	wcs	PROPN
ejpam-3972	173	3	parameter	parameter	NOUN
ejpam-3972	173	4	generation	generation	NOUN
ejpam-3972	173	5	step	step	NOUN
ejpam-3972	173	6	1	1	NUM
ejpam-3972	173	7	.	.	PUNCT
ejpam-3972	173	8	generate	generate	VERB
ejpam-3972	173	9	two	two	NUM
ejpam-3972	173	10	large	large	ADJ
ejpam-3972	173	11	primes	prime	NOUN
ejpam-3972	173	12	,	,	PUNCT
ejpam-3972	173	13	p	p	NOUN
ejpam-3972	173	14	and	and	CCONJ
ejpam-3972	173	15	q	q	NOUN
ejpam-3972	173	16	,	,	PUNCT
ejpam-3972	174	1	such	such	ADJ
ejpam-3972	174	2	that	that	SCONJ
ejpam-3972	174	3	p	p	PROPN
ejpam-3972	174	4	6=	6=	PROPN
ejpam-3972	174	5	q	q	X
ejpam-3972	174	6	,	,	PUNCT
ejpam-3972	174	7	and	and	CCONJ
ejpam-3972	174	8	generate	generate	VERB
ejpam-3972	174	9	one	one	NUM
ejpam-3972	174	10	large	large	ADJ
ejpam-3972	174	11	number	number	NOUN
ejpam-3972	174	12	x.	x.	NOUN
ejpam-3972	174	13	step	step	NOUN
ejpam-3972	174	14	2	2	NUM
ejpam-3972	174	15	.	.	PUNCT
ejpam-3972	174	16	λ←	λ←	PUNCT
ejpam-3972	174	17	pqx	pqx	NOUN
ejpam-3972	174	18	and	and	CCONJ
ejpam-3972	174	19	φ(λ)←	φ(λ)←	NOUN
ejpam-3972	174	20	(	(	PUNCT
ejpam-3972	174	21	p−	p−	NOUN
ejpam-3972	174	22	1)(q	1)(q	NUM
ejpam-3972	174	23	−	−	PROPN
ejpam-3972	174	24	1)(x−	1)(x−	NUM
ejpam-3972	174	25	1	1	NUM
ejpam-3972	174	26	)	)	PUNCT
ejpam-3972	175	1	.	.	PUNCT
ejpam-3972	176	1	step	step	NOUN
ejpam-3972	176	2	3	3	NUM
ejpam-3972	176	3	.	.	PUNCT
ejpam-3972	176	4	e←	e←	PROPN
ejpam-3972	177	1	pq	pq	PROPN
ejpam-3972	177	2	.	.	PROPN
ejpam-3972	177	3	step	step	NOUN
ejpam-3972	177	4	4	4	NUM
ejpam-3972	177	5	.	.	PUNCT
ejpam-3972	177	6	choose	choose	VERB
ejpam-3972	177	7	a	a	DET
ejpam-3972	177	8	random	random	ADJ
ejpam-3972	177	9	m	m	NOUN
ejpam-3972	177	10	,	,	PUNCT
ejpam-3972	177	11	such	such	ADJ
ejpam-3972	177	12	that	that	SCONJ
ejpam-3972	177	13	m∗	m∗	PROPN
ejpam-3972	177	14	←	←	PROPN
ejpam-3972	177	15	meλ	meλ	PROPN
ejpam-3972	177	16	,	,	PUNCT
ejpam-3972	177	17	gcd(m	gcd(m	PROPN
ejpam-3972	177	18	,	,	PUNCT
ejpam-3972	177	19	φ(λ	φ(λ	PROPN
ejpam-3972	177	20	)	)	PUNCT
ejpam-3972	177	21	)	)	PUNCT
ejpam-3972	178	1	=	=	PUNCT
ejpam-3972	178	2	1	1	X
ejpam-3972	178	3	.	.	X
ejpam-3972	178	4	step	step	NOUN
ejpam-3972	178	5	5	5	NUM
ejpam-3972	178	6	.	.	PUNCT
ejpam-3972	178	7	//	//	NOUN
ejpam-3972	179	1	it	it	PRON
ejpam-3972	179	2	is	be	AUX
ejpam-3972	179	3	certainly	certainly	ADV
ejpam-3972	179	4	necessary	necessary	ADJ
ejpam-3972	179	5	that	that	SCONJ
ejpam-3972	179	6	λ	λ	NOUN
ejpam-3972	179	7	must	must	AUX
ejpam-3972	179	8	be	be	AUX
ejpam-3972	179	9	large	large	ADJ
ejpam-3972	179	10	enough	enough	ADV
ejpam-3972	179	11	that	that	SCONJ
ejpam-3972	179	12	factoring	factoring	NOUN
ejpam-3972	179	13	it	it	PRON
ejpam-3972	179	14	will	will	AUX
ejpam-3972	179	15	be	be	AUX
ejpam-3972	179	16	computationally	computationally	ADV
ejpam-3972	179	17	infeasible	infeasible	ADJ
ejpam-3972	179	18	.	.	PUNCT
ejpam-3972	180	1	//	//	PUNCT
ejpam-3972	181	1	the	the	DET
ejpam-3972	181	2	public	public	ADJ
ejpam-3972	181	3	key	key	NOUN
ejpam-3972	181	4	is	be	AUX
ejpam-3972	181	5	(	(	PUNCT
ejpam-3972	181	6	λ	λ	INTJ
ejpam-3972	181	7	,	,	PUNCT
ejpam-3972	181	8	m∗	m∗	NOUN
ejpam-3972	181	9	)	)	PUNCT
ejpam-3972	181	10	and	and	CCONJ
ejpam-3972	181	11	the	the	DET
ejpam-3972	181	12	private	private	ADJ
ejpam-3972	181	13	key	key	NOUN
ejpam-3972	181	14	is	be	AUX
ejpam-3972	181	15	(	(	PUNCT
ejpam-3972	181	16	p	p	X
ejpam-3972	181	17	,	,	PUNCT
ejpam-3972	181	18	q	q	ADJ
ejpam-3972	181	19	,	,	PUNCT
ejpam-3972	181	20	x	x	NOUN
ejpam-3972	181	21	,	,	PUNCT
ejpam-3972	181	22	e	e	NOUN
ejpam-3972	181	23	)	)	PUNCT
ejpam-3972	181	24	.	.	PUNCT
ejpam-3972	182	1	•	•	NOUN
ejpam-3972	182	2	wcs	wcs	NOUN
ejpam-3972	182	3	encryption	encryption	NOUN
ejpam-3972	182	4	step	step	NOUN
ejpam-3972	182	5	1	1	NUM
ejpam-3972	182	6	.	.	PUNCT
ejpam-3972	182	7	//	//	NOUN
ejpam-3972	183	1	the	the	DET
ejpam-3972	183	2	encryption	encryption	NOUN
ejpam-3972	183	3	key	key	NOUN
ejpam-3972	183	4	is	be	AUX
ejpam-3972	183	5	kept	keep	VERB
ejpam-3972	183	6	secret	secret	ADJ
ejpam-3972	183	7	.	.	PUNCT
ejpam-3972	184	1	//	//	PUNCT
ejpam-3972	185	1	y.	y.	PROPN
ejpam-3972	185	2	liu	liu	PROPN
ejpam-3972	185	3	/	/	SYM
ejpam-3972	185	4	eur	eur	PROPN
ejpam-3972	185	5	.	.	PUNCT
ejpam-3972	186	1	j.	j.	PROPN
ejpam-3972	186	2	pure	pure	PROPN
ejpam-3972	186	3	appl	appl	PROPN
ejpam-3972	186	4	.	.	PROPN
ejpam-3972	186	5	math	math	PROPN
ejpam-3972	186	6	,	,	PUNCT
ejpam-3972	186	7	14	14	NUM
ejpam-3972	186	8	(	(	PUNCT
ejpam-3972	186	9	2	2	NUM
ejpam-3972	186	10	)	)	PUNCT
ejpam-3972	186	11	(	(	PUNCT
ejpam-3972	186	12	2021	2021	NUM
ejpam-3972	186	13	)	)	PUNCT
ejpam-3972	186	14	,	,	PUNCT
ejpam-3972	186	15	521	521	NUM
ejpam-3972	186	16	-	-	SYM
ejpam-3972	186	17	536	536	NUM
ejpam-3972	186	18	529	529	NUM
ejpam-3972	186	19	f(p	f(p	NOUN
ejpam-3972	186	20	,	,	PUNCT
ejpam-3972	186	21	q	q	NOUN
ejpam-3972	186	22	,	,	PUNCT
ejpam-3972	186	23	n	n	CCONJ
ejpam-3972	186	24	)	)	PUNCT
ejpam-3972	186	25	=	=	VERB
ejpam-3972	187	1	p.	p.	NOUN
ejpam-3972	187	2	step	step	NOUN
ejpam-3972	187	3	2	2	NUM
ejpam-3972	187	4	.	.	PUNCT
ejpam-3972	187	5	//	//	NOUN
ejpam-3972	188	1	the	the	DET
ejpam-3972	188	2	encryption	encryption	NOUN
ejpam-3972	188	3	key	key	NOUN
ejpam-3972	188	4	is	be	AUX
ejpam-3972	188	5	kept	keep	VERB
ejpam-3972	188	6	secret	secret	ADJ
ejpam-3972	188	7	and	and	CCONJ
ejpam-3972	188	8	send	send	VERB
ejpam-3972	188	9	the	the	DET
ejpam-3972	188	10	secret	secret	ADJ
ejpam-3972	188	11	message	message	NOUN
ejpam-3972	188	12	q	q	NOUN
ejpam-3972	188	13	of	of	ADP
ejpam-3972	188	14	compression	compression	NOUN
ejpam-3972	188	15	.	.	PUNCT
ejpam-3972	189	1	//	//	PUNCT
ejpam-3972	190	1	g(p	g(p	PROPN
ejpam-3972	190	2	,	,	PUNCT
ejpam-3972	190	3	q	q	NOUN
ejpam-3972	190	4	,	,	PUNCT
ejpam-3972	190	5	n	n	CCONJ
ejpam-3972	190	6	)	)	PUNCT
ejpam-3972	190	7	=	=	VERB
ejpam-3972	190	8	q.	q.	NOUN
ejpam-3972	190	9	step	step	NOUN
ejpam-3972	190	10	3	3	NUM
ejpam-3972	190	11	.	.	PUNCT
ejpam-3972	190	12	//	//	NOUN
ejpam-3972	191	1	the	the	DET
ejpam-3972	191	2	public	public	ADJ
ejpam-3972	191	3	-	-	PUNCT
ejpam-3972	191	4	key	key	NOUN
ejpam-3972	191	5	is	be	AUX
ejpam-3972	191	6	compression	compression	NOUN
ejpam-3972	191	7	n	n	NOUN
ejpam-3972	191	8	and	and	CCONJ
ejpam-3972	191	9	is	be	AUX
ejpam-3972	191	10	release	release	VERB
ejpam-3972	191	11	a	a	DET
ejpam-3972	191	12	in	in	ADP
ejpam-3972	191	13	figure	figure	NOUN
ejpam-3972	191	14	a1	a1	PROPN
ejpam-3972	191	15	.	.	PUNCT
ejpam-3972	191	16	//	//	SYM
ejpam-3972	191	17	h(p	h(p	PROPN
ejpam-3972	191	18	,	,	PUNCT
ejpam-3972	191	19	q	q	NOUN
ejpam-3972	191	20	,	,	PUNCT
ejpam-3972	191	21	n	n	CCONJ
ejpam-3972	191	22	)	)	PUNCT
ejpam-3972	191	23	=	=	VERB
ejpam-3972	192	1	n.	n.	NOUN
ejpam-3972	192	2	•	•	NUM
ejpam-3972	192	3	wcs	wcs	NOUN
ejpam-3972	192	4	decryption	decryption	NOUN
ejpam-3972	192	5	step	step	NOUN
ejpam-3972	192	6	1	1	NUM
ejpam-3972	192	7	.	.	PUNCT
ejpam-3972	192	8	//	//	X
ejpam-3972	192	9	receive	receive	VERB
ejpam-3972	192	10	the	the	DET
ejpam-3972	192	11	public	public	ADJ
ejpam-3972	192	12	-	-	PUNCT
ejpam-3972	192	13	key	key	NOUN
ejpam-3972	192	14	of	of	ADP
ejpam-3972	192	15	compression	compression	NOUN
ejpam-3972	192	16	.	.	PUNCT
ejpam-3972	193	1	//	//	X
ejpam-3972	193	2	h(p	h(p	PROPN
ejpam-3972	193	3	,	,	PUNCT
ejpam-3972	193	4	q	q	NOUN
ejpam-3972	193	5	,	,	PUNCT
ejpam-3972	193	6	n	n	CCONJ
ejpam-3972	193	7	)	)	PUNCT
ejpam-3972	193	8	=	=	VERB
ejpam-3972	193	9	n.	n.	NOUN
ejpam-3972	193	10	step	step	NOUN
ejpam-3972	193	11	2	2	NUM
ejpam-3972	193	12	.	.	PUNCT
ejpam-3972	193	13	//	//	X
ejpam-3972	193	14	receive	receive	VERB
ejpam-3972	193	15	the	the	DET
ejpam-3972	193	16	secret	secret	ADJ
ejpam-3972	193	17	message	message	NOUN
ejpam-3972	193	18	.	.	PUNCT
ejpam-3972	194	1	//	//	PUNCT
ejpam-3972	195	1	g(p	g(p	PROPN
ejpam-3972	195	2	,	,	PUNCT
ejpam-3972	195	3	q	q	NOUN
ejpam-3972	195	4	,	,	PUNCT
ejpam-3972	195	5	n	n	CCONJ
ejpam-3972	195	6	)	)	PUNCT
ejpam-3972	195	7	=	=	VERB
ejpam-3972	195	8	q.	q.	NOUN
ejpam-3972	195	9	step	step	NOUN
ejpam-3972	195	10	3	3	NUM
ejpam-3972	195	11	.	.	PUNCT
ejpam-3972	195	12	//	//	NOUN
ejpam-3972	196	1	the	the	DET
ejpam-3972	196	2	receiver	receiver	NOUN
ejpam-3972	196	3	uses	use	VERB
ejpam-3972	196	4	the	the	DET
ejpam-3972	196	5	function	function	NOUN
ejpam-3972	196	6	expression	expression	NOUN
ejpam-3972	196	7	to	to	PART
ejpam-3972	196	8	obtain	obtain	VERB
ejpam-3972	196	9	the	the	DET
ejpam-3972	196	10	original	original	ADJ
ejpam-3972	196	11	message	message	NOUN
ejpam-3972	196	12	from	from	ADP
ejpam-3972	196	13	its	its	PRON
ejpam-3972	196	14	encryption	encryption	NOUN
ejpam-3972	196	15	,	,	PUNCT
ejpam-3972	196	16	and	and	CCONJ
ejpam-3972	196	17	this	this	PRON
ejpam-3972	196	18	completes	complete	VERB
ejpam-3972	196	19	the	the	DET
ejpam-3972	196	20	algorithm	algorithm	NOUN
ejpam-3972	196	21	.	.	PUNCT
ejpam-3972	197	1	//	//	PUNCT
ejpam-3972	197	2	f(p	f(p	PROPN
ejpam-3972	197	3	,	,	PUNCT
ejpam-3972	197	4	q	q	NOUN
ejpam-3972	197	5	,	,	PUNCT
ejpam-3972	197	6	n	n	CCONJ
ejpam-3972	197	7	)	)	PUNCT
ejpam-3972	197	8	=	=	SYM
ejpam-3972	197	9	n	n	CCONJ
ejpam-3972	197	10	/	/	SYM
ejpam-3972	197	11	q	q	NOUN
ejpam-3972	197	12	=	=	PUNCT
ejpam-3972	198	1	p.	p.	NOUN
ejpam-3972	198	2	•	•	ADP
ejpam-3972	198	3	a	a	DET
ejpam-3972	198	4	ciphertext	ciphertext	NOUN
ejpam-3972	198	5	-	-	PUNCT
ejpam-3972	198	6	only	only	ADV
ejpam-3972	198	7	attack	attack	NOUN
ejpam-3972	198	8	//	//	PUNCT
ejpam-3972	198	9	some	some	DET
ejpam-3972	198	10	attacks	attack	NOUN
ejpam-3972	198	11	would	would	AUX
ejpam-3972	198	12	receive	receive	VERB
ejpam-3972	198	13	the	the	DET
ejpam-3972	198	14	public	public	ADJ
ejpam-3972	198	15	-	-	PUNCT
ejpam-3972	198	16	key	key	NOUN
ejpam-3972	198	17	n	n	NOUN
ejpam-3972	198	18	of	of	ADP
ejpam-3972	198	19	compression	compression	NOUN
ejpam-3972	198	20	.	.	PUNCT
ejpam-3972	199	1	//	//	PUNCT
ejpam-3972	199	2	design	design	VERB
ejpam-3972	199	3	a	a	DET
ejpam-3972	199	4	factorization	factorization	NOUN
ejpam-3972	199	5	algorithm	algorithm	NOUN
ejpam-3972	199	6	for	for	ADP
ejpam-3972	199	7	n	n	CCONJ
ejpam-3972	199	8	:	:	PUNCT
ejpam-3972	199	9	h(p	h(p	PROPN
ejpam-3972	199	10	,	,	PUNCT
ejpam-3972	199	11	q	q	NOUN
ejpam-3972	199	12	,	,	PUNCT
ejpam-3972	199	13	n	n	CCONJ
ejpam-3972	199	14	)	)	PUNCT
ejpam-3972	199	15	=	=	SYM
ejpam-3972	200	1	n	n	NOUN
ejpam-3972	200	2	=	=	SYM
ejpam-3972	200	3	p	p	NOUN
ejpam-3972	200	4	•	•	NUM
ejpam-3972	200	5	q.	q.	NOUN
ejpam-3972	200	6	as	as	ADP
ejpam-3972	200	7	an	an	DET
ejpam-3972	200	8	application	application	NOUN
ejpam-3972	200	9	of	of	ADP
ejpam-3972	200	10	group	group	NOUN
ejpam-3972	200	11	,	,	PUNCT
ejpam-3972	200	12	consider	consider	VERB
ejpam-3972	200	13	the	the	DET
ejpam-3972	200	14	general	general	ADJ
ejpam-3972	200	15	case	case	NOUN
ejpam-3972	200	16	,	,	PUNCT
ejpam-3972	200	17	the	the	DET
ejpam-3972	200	18	encryption	encryption	NOUN
ejpam-3972	200	19	and	and	CCONJ
ejpam-3972	200	20	decryption	decryption	NOUN
ejpam-3972	200	21	are	be	AUX
ejpam-3972	200	22	at	at	ADP
ejpam-3972	200	23	a	a	DET
ejpam-3972	200	24	more	more	ADV
ejpam-3972	200	25	complex	complex	ADJ
ejpam-3972	200	26	organization	organization	NOUN
ejpam-3972	200	27	than	than	ADP
ejpam-3972	200	28	algorithm	algorithm	NOUN
ejpam-3972	200	29	(	(	PUNCT
ejpam-3972	200	30	a	a	NOUN
ejpam-3972	200	31	)	)	PUNCT
ejpam-3972	200	32	.	.	PUNCT
ejpam-3972	201	1	we	we	PRON
ejpam-3972	201	2	give	give	VERB
ejpam-3972	201	3	the	the	DET
ejpam-3972	201	4	following	follow	VERB
ejpam-3972	201	5	algorithm	algorithm	NOUN
ejpam-3972	201	6	for	for	ADP
ejpam-3972	201	7	wcs	wcs	PROPN
ejpam-3972	201	8	.	.	PUNCT
ejpam-3972	202	1	4.2	4.2	NUM
ejpam-3972	202	2	.	.	PUNCT
ejpam-3972	203	1	algorithm	algorithm	NOUN
ejpam-3972	203	2	(	(	PUNCT
ejpam-3972	203	3	b	b	NOUN
ejpam-3972	203	4	)	)	PUNCT
ejpam-3972	203	5	//	//	NOUN
ejpam-3972	204	1	it	it	PRON
ejpam-3972	204	2	requires	require	VERB
ejpam-3972	204	3	multi	multi	ADJ
ejpam-3972	204	4	-	-	ADJ
ejpam-3972	204	5	multiplication	multiplication	ADJ
ejpam-3972	204	6	tables	table	NOUN
ejpam-3972	204	7	of	of	ADP
ejpam-3972	204	8	topological	topological	ADJ
ejpam-3972	204	9	group	group	NOUN
ejpam-3972	204	10	,	,	PUNCT
ejpam-3972	204	11	and	and	CCONJ
ejpam-3972	204	12	by	by	ADP
ejpam-3972	204	13	definition	definition	NOUN
ejpam-3972	204	14	4	4	NUM
ejpam-3972	204	15	and	and	CCONJ
ejpam-3972	204	16	definition	definition	NOUN
ejpam-3972	204	17	5	5	NUM
ejpam-3972	204	18	for	for	ADP
ejpam-3972	204	19	algorithm	algorithm	NOUN
ejpam-3972	204	20	(	(	PUNCT
ejpam-3972	204	21	b	b	NOUN
ejpam-3972	204	22	)	)	PUNCT
ejpam-3972	204	23	.	.	PUNCT
ejpam-3972	205	1	//	//	NUM
ejpam-3972	205	2	step	step	NOUN
ejpam-3972	205	3	1	1	NUM
ejpam-3972	205	4	.	.	PUNCT
ejpam-3972	205	5	//	//	NUM
ejpam-3972	205	6	encryption	encryption	NOUN
ejpam-3972	205	7	key	key	NOUN
ejpam-3972	205	8	of	of	ADP
ejpam-3972	205	9	wkdc	wkdc	PROPN
ejpam-3972	205	10	.	.	PUNCT
ejpam-3972	206	1	//	//	PUNCT
ejpam-3972	206	2	y.	y.	PROPN
ejpam-3972	206	3	liu	liu	PROPN
ejpam-3972	206	4	/	/	SYM
ejpam-3972	206	5	eur	eur	PROPN
ejpam-3972	206	6	.	.	PUNCT
ejpam-3972	207	1	j.	j.	PROPN
ejpam-3972	207	2	pure	pure	PROPN
ejpam-3972	207	3	appl	appl	PROPN
ejpam-3972	207	4	.	.	PROPN
ejpam-3972	207	5	math	math	PROPN
ejpam-3972	207	6	,	,	PUNCT
ejpam-3972	207	7	14	14	NUM
ejpam-3972	207	8	(	(	PUNCT
ejpam-3972	207	9	2	2	NUM
ejpam-3972	207	10	)	)	PUNCT
ejpam-3972	207	11	(	(	PUNCT
ejpam-3972	207	12	2021	2021	NUM
ejpam-3972	207	13	)	)	PUNCT
ejpam-3972	207	14	,	,	PUNCT
ejpam-3972	207	15	521	521	NUM
ejpam-3972	207	16	-	-	SYM
ejpam-3972	207	17	536	536	NUM
ejpam-3972	207	18	530	530	NUM
ejpam-3972	207	19	x	x	NOUN
ejpam-3972	207	20	,	,	PUNCT
ejpam-3972	207	21	y	y	PROPN
ejpam-3972	207	22	,	,	PUNCT
ejpam-3972	207	23	z.	z.	PROPN
ejpam-3972	207	24	step	step	NOUN
ejpam-3972	207	25	2	2	NUM
ejpam-3972	207	26	.	.	PUNCT
ejpam-3972	208	1	some	some	DET
ejpam-3972	208	2	random	random	ADJ
ejpam-3972	208	3	data	datum	NOUN
ejpam-3972	208	4	allocated	allocate	VERB
ejpam-3972	208	5	from	from	ADP
ejpam-3972	208	6	the	the	DET
ejpam-3972	208	7	wkdc	wkdc	NOUN
ejpam-3972	208	8	and	and	CCONJ
ejpam-3972	208	9	algebraic	algebraic	ADJ
ejpam-3972	208	10	manipulation	manipulation	NOUN
ejpam-3972	208	11	:	:	PUNCT
ejpam-3972	208	12	h(x	h(x	PROPN
ejpam-3972	208	13	,	,	PUNCT
ejpam-3972	208	14	y	y	PROPN
ejpam-3972	208	15	,	,	PUNCT
ejpam-3972	208	16	z	z	NOUN
ejpam-3972	208	17	)	)	PUNCT
ejpam-3972	208	18	=	=	PUNCT
ejpam-3972	208	19	(	(	PUNCT
ejpam-3972	208	20	z	z	NOUN
ejpam-3972	208	21	•	•	NUM
ejpam-3972	208	22	y	y	NOUN
ejpam-3972	208	23	)	)	PUNCT
ejpam-3972	208	24	•	•	NOUN
ejpam-3972	208	25	x	x	X
ejpam-3972	208	26	=	=	SYM
ejpam-3972	208	27	λ	λ	PROPN
ejpam-3972	208	28	.	.	PROPN
ejpam-3972	208	29	step	step	NOUN
ejpam-3972	208	30	3	3	NUM
ejpam-3972	208	31	.	.	PUNCT
ejpam-3972	208	32	//	//	SYM
ejpam-3972	208	33	public	public	ADJ
ejpam-3972	208	34	-	-	PUNCT
ejpam-3972	208	35	key	key	NOUN
ejpam-3972	208	36	λ	λ	PROPN
ejpam-3972	208	37	.	.	PROPN
ejpam-3972	208	38	//	//	PROPN
ejpam-3972	208	39	h	h	PROPN
ejpam-3972	208	40	(	(	PUNCT
ejpam-3972	208	41	λ	λ	NOUN
ejpam-3972	208	42	)	)	PUNCT
ejpam-3972	208	43	=	=	SYM
ejpam-3972	208	44	λ	λ	X
ejpam-3972	208	45	.	.	PROPN
ejpam-3972	208	46	step	step	NOUN
ejpam-3972	208	47	4	4	NUM
ejpam-3972	208	48	.	.	PUNCT
ejpam-3972	209	1	alice	alice	PROPN
ejpam-3972	209	2	and	and	CCONJ
ejpam-3972	209	3	bob	bob	PROPN
ejpam-3972	209	4	have	have	VERB
ejpam-3972	209	5	common	common	ADJ
ejpam-3972	209	6	encryption	encryption	NOUN
ejpam-3972	209	7	key	key	NOUN
ejpam-3972	209	8	:	:	PUNCT
ejpam-3972	209	9	h	h	NOUN
ejpam-3972	209	10	(	(	PUNCT
ejpam-3972	209	11	e	e	NOUN
ejpam-3972	209	12	)	)	PUNCT
ejpam-3972	209	13	=	=	SYM
ejpam-3972	210	1	(	(	PUNCT
ejpam-3972	210	2	x	x	SYM
ejpam-3972	210	3	•	•	NUM
ejpam-3972	210	4	z	z	NOUN
ejpam-3972	210	5	)	)	PUNCT
ejpam-3972	210	6	•	•	NOUN
ejpam-3972	210	7	y	y	PROPN
ejpam-3972	210	8	=	=	SYM
ejpam-3972	210	9	e.	e.	PROPN
ejpam-3972	210	10	step	step	PROPN
ejpam-3972	210	11	5	5	NUM
ejpam-3972	210	12	.	.	PUNCT
ejpam-3972	211	1	alice	alice	PROPN
ejpam-3972	211	2	’s	’s	PART
ejpam-3972	211	3	encryption	encryption	NOUN
ejpam-3972	211	4	key	key	NOUN
ejpam-3972	211	5	:	:	PUNCT
ejpam-3972	212	1	d	d	X
ejpam-3972	212	2	=	=	SYM
ejpam-3972	212	3	(	(	PUNCT
ejpam-3972	212	4	x	x	PROPN
ejpam-3972	212	5	•	•	NUM
ejpam-3972	212	6	y	y	NOUN
ejpam-3972	212	7	)	)	PUNCT
ejpam-3972	212	8	•	•	NOUN
ejpam-3972	212	9	z.	z.	PROPN
ejpam-3972	212	10	step	step	NOUN
ejpam-3972	212	11	6	6	NUM
ejpam-3972	212	12	.	.	PUNCT
ejpam-3972	212	13	//	//	NOUN
ejpam-3972	213	1	alice	alice	PROPN
ejpam-3972	213	2	and	and	CCONJ
ejpam-3972	213	3	bob	bob	PROPN
ejpam-3972	213	4	need	need	VERB
ejpam-3972	213	5	to	to	PART
ejpam-3972	213	6	be	be	AUX
ejpam-3972	213	7	assured	assure	VERB
ejpam-3972	213	8	that	that	SCONJ
ejpam-3972	213	9	the	the	DET
ejpam-3972	213	10	λ	λ	PROPN
ejpam-3972	213	11	is	be	AUX
ejpam-3972	213	12	true	true	ADJ
ejpam-3972	213	13	.	.	PUNCT
ejpam-3972	214	1	//	//	PUNCT
ejpam-3972	215	1	d	d	NOUN
ejpam-3972	215	2	•	•	NUM
ejpam-3972	215	3	e	e	X
ejpam-3972	215	4	=	=	SYM
ejpam-3972	215	5	λ	λ	PROPN
ejpam-3972	215	6	.	.	PROPN
ejpam-3972	215	7	step	step	NOUN
ejpam-3972	215	8	7	7	NUM
ejpam-3972	215	9	.	.	PUNCT
ejpam-3972	215	10	//	//	PUNCT
ejpam-3972	215	11	by	by	ADP
ejpam-3972	215	12	definition	definition	NOUN
ejpam-3972	215	13	5	5	NUM
ejpam-3972	215	14	and	and	CCONJ
ejpam-3972	215	15	(	(	PUNCT
ejpam-3972	215	16	wcs2	wcs2	PROPN
ejpam-3972	215	17	)	)	PUNCT
ejpam-3972	215	18	.	.	PUNCT
ejpam-3972	216	1	//	//	PUNCT
ejpam-3972	216	2	check	check	VERB
ejpam-3972	216	3	the	the	DET
ejpam-3972	216	4	encryption	encryption	NOUN
ejpam-3972	216	5	key	key	NOUN
ejpam-3972	216	6	:	:	PUNCT
ejpam-3972	216	7	(	(	PUNCT
ejpam-3972	216	8	(	(	PUNCT
ejpam-3972	216	9	x	x	SYM
ejpam-3972	216	10	•	•	NUM
ejpam-3972	216	11	y	y	NOUN
ejpam-3972	216	12	)	)	PUNCT
ejpam-3972	216	13	•	•	NUM
ejpam-3972	216	14	z	z	NOUN
ejpam-3972	216	15	)	)	PUNCT
ejpam-3972	216	16	•	•	NOUN
ejpam-3972	216	17	(	(	PUNCT
ejpam-3972	216	18	(	(	PUNCT
ejpam-3972	216	19	x	x	SYM
ejpam-3972	216	20	•	•	NUM
ejpam-3972	216	21	z	z	NOUN
ejpam-3972	216	22	)	)	PUNCT
ejpam-3972	216	23	•	•	NUM
ejpam-3972	216	24	y	y	NOUN
ejpam-3972	216	25	)	)	PUNCT
ejpam-3972	216	26	=	=	PUNCT
ejpam-3972	217	1	(	(	PUNCT
ejpam-3972	217	2	z	z	NOUN
ejpam-3972	217	3	•	•	NUM
ejpam-3972	217	4	y	y	NOUN
ejpam-3972	217	5	)	)	PUNCT
ejpam-3972	217	6	•	•	NOUN
ejpam-3972	217	7	x.	x.	NOUN
ejpam-3972	217	8	step	step	NOUN
ejpam-3972	217	9	8	8	NUM
ejpam-3972	217	10	.	.	PUNCT
ejpam-3972	218	1	a	a	DET
ejpam-3972	218	2	numeric	numeric	ADJ
ejpam-3972	218	3	λ	λ	NOUN
ejpam-3972	218	4	release	release	NOUN
ejpam-3972	218	5	by	by	ADP
ejpam-3972	218	6	alice	alice	PROPN
ejpam-3972	218	7	.	.	PUNCT
ejpam-3972	219	1	step	step	NOUN
ejpam-3972	219	2	9	9	NUM
ejpam-3972	219	3	.	.	PUNCT
ejpam-3972	219	4	//	//	SYM
ejpam-3972	219	5	non	non	ADJ
ejpam-3972	219	6	-	-	NOUN
ejpam-3972	219	7	repudiation	repudiation	NOUN
ejpam-3972	219	8	!	!	PUNCT
ejpam-3972	219	9	!	!	PUNCT
ejpam-3972	220	1	//	//	NUM
ejpam-3972	221	1	digital	digital	ADJ
ejpam-3972	221	2	signature	signature	NOUN
ejpam-3972	221	3	:	:	PUNCT
ejpam-3972	221	4	a	a	DET
ejpam-3972	221	5	numeric	numeric	ADJ
ejpam-3972	221	6	e	e	NOUN
ejpam-3972	221	7	transfer	transfer	NOUN
ejpam-3972	221	8	from	from	ADP
ejpam-3972	221	9	alice	alice	PROPN
ejpam-3972	221	10	to	to	ADP
ejpam-3972	221	11	bob	bob	PROPN
ejpam-3972	221	12	.	.	PROPN
ejpam-3972	222	1	step	step	NOUN
ejpam-3972	222	2	10	10	NUM
ejpam-3972	222	3	.	.	PUNCT
ejpam-3972	223	1	a	a	DET
ejpam-3972	223	2	plaintext	plaintext	NOUN
ejpam-3972	223	3	m	m	NOUN
ejpam-3972	223	4	by	by	ADP
ejpam-3972	223	5	bob	bob	PROPN
ejpam-3972	223	6	.	.	PROPN
ejpam-3972	223	7	step	step	NOUN
ejpam-3972	223	8	11	11	NUM
ejpam-3972	223	9	.	.	PUNCT
ejpam-3972	224	1	//	//	NUM
ejpam-3972	224	2	attack	attack	NOUN
ejpam-3972	224	3	,	,	PUNCT
ejpam-3972	224	4	this	this	DET
ejpam-3972	224	5	hope	hope	NOUN
ejpam-3972	224	6	is	be	AUX
ejpam-3972	224	7	forlorn	forlorn	ADJ
ejpam-3972	224	8	.	.	PUNCT
ejpam-3972	225	1	//	//	PUNCT
ejpam-3972	226	1	bob	bob	PROPN
ejpam-3972	226	2	’s	’s	PART
ejpam-3972	226	3	ciphertext	ciphertext	NOUN
ejpam-3972	226	4	:	:	PUNCT
ejpam-3972	226	5	m∗	m∗	PROPN
ejpam-3972	226	6	=	=	SYM
ejpam-3972	226	7	(	(	PUNCT
ejpam-3972	226	8	m	m	VERB
ejpam-3972	226	9	•	•	NUM
ejpam-3972	226	10	e	e	NOUN
ejpam-3972	226	11	)	)	PUNCT
ejpam-3972	226	12	•	•	NUM
ejpam-3972	226	13	λ	λ	PROPN
ejpam-3972	226	14	.	.	PROPN
ejpam-3972	226	15	step	step	NOUN
ejpam-3972	226	16	12	12	NUM
ejpam-3972	226	17	.	.	PUNCT
ejpam-3972	227	1	a	a	DET
ejpam-3972	227	2	ciphertext	ciphertext	PROPN
ejpam-3972	227	3	m∗	m∗	NOUN
ejpam-3972	227	4	transfer	transfer	NOUN
ejpam-3972	227	5	from	from	ADP
ejpam-3972	227	6	bob	bob	PROPN
ejpam-3972	227	7	to	to	ADP
ejpam-3972	227	8	alice	alice	PROPN
ejpam-3972	227	9	.	.	PUNCT
ejpam-3972	228	1	step	step	NOUN
ejpam-3972	228	2	13	13	NUM
ejpam-3972	228	3	.	.	PUNCT
ejpam-3972	229	1	alice	alice	PROPN
ejpam-3972	229	2	decryption	decryption	PROPN
ejpam-3972	229	3	:	:	PUNCT
ejpam-3972	229	4	m	m	VERB
ejpam-3972	229	5	=	=	SYM
ejpam-3972	229	6	(	(	PUNCT
ejpam-3972	229	7	m∗•	m∗•	PROPN
ejpam-3972	229	8	e	e	NOUN
ejpam-3972	229	9	)	)	PUNCT
ejpam-3972	229	10	•	•	ADP
ejpam-3972	229	11	d.	d.	PROPN
ejpam-3972	229	12	y.	y.	PROPN
ejpam-3972	229	13	liu	liu	PROPN
ejpam-3972	229	14	/	/	SYM
ejpam-3972	229	15	eur	eur	PROPN
ejpam-3972	229	16	.	.	PUNCT
ejpam-3972	230	1	j.	j.	PROPN
ejpam-3972	230	2	pure	pure	PROPN
ejpam-3972	230	3	appl	appl	PROPN
ejpam-3972	230	4	.	.	PROPN
ejpam-3972	230	5	math	math	PROPN
ejpam-3972	230	6	,	,	PUNCT
ejpam-3972	230	7	14	14	NUM
ejpam-3972	230	8	(	(	PUNCT
ejpam-3972	230	9	2	2	NUM
ejpam-3972	230	10	)	)	PUNCT
ejpam-3972	230	11	(	(	PUNCT
ejpam-3972	230	12	2021	2021	NUM
ejpam-3972	230	13	)	)	PUNCT
ejpam-3972	230	14	,	,	PUNCT
ejpam-3972	230	15	521	521	NUM
ejpam-3972	230	16	-	-	SYM
ejpam-3972	230	17	536	536	NUM
ejpam-3972	230	18	531	531	NUM
ejpam-3972	230	19	table	table	NOUN
ejpam-3972	230	20	2	2	NUM
ejpam-3972	230	21	:	:	PUNCT
ejpam-3972	230	22	bcl+	bcl+	NOUN
ejpam-3972	230	23	operations	operation	NOUN
ejpam-3972	230	24	•	•	ADV
ejpam-3972	230	25	of	of	ADP
ejpam-3972	230	26	(	(	PUNCT
ejpam-3972	230	27	{	{	PUNCT
ejpam-3972	230	28	1	1	NUM
ejpam-3972	230	29	,	,	PUNCT
ejpam-3972	230	30	x	x	NOUN
ejpam-3972	230	31	,	,	PUNCT
ejpam-3972	230	32	y	y	PROPN
ejpam-3972	230	33	,	,	PUNCT
ejpam-3972	230	34	z	z	NOUN
ejpam-3972	230	35	}	}	PUNCT
ejpam-3972	230	36	)	)	PUNCT
ejpam-3972	230	37	for	for	ADP
ejpam-3972	230	38	both	both	DET
ejpam-3972	230	39	encryption	encryption	NOUN
ejpam-3972	230	40	and	and	CCONJ
ejpam-3972	230	41	decryption	decryption	NOUN
ejpam-3972	230	42	.	.	PUNCT
ejpam-3972	231	1	•	•	NUM
ejpam-3972	231	2	1	1	NUM
ejpam-3972	231	3	x	x	SYM
ejpam-3972	231	4	y	y	PROPN
ejpam-3972	231	5	z	z	NOUN
ejpam-3972	231	6	1	1	NUM
ejpam-3972	231	7	1	1	NUM
ejpam-3972	231	8	1	1	NUM
ejpam-3972	231	9	1	1	NUM
ejpam-3972	231	10	1	1	NUM
ejpam-3972	231	11	x	x	SYM
ejpam-3972	231	12	x	x	SYM
ejpam-3972	231	13	1	1	NUM
ejpam-3972	231	14	1	1	NUM
ejpam-3972	231	15	z	z	NOUN
ejpam-3972	231	16	y	y	SYM
ejpam-3972	231	17	y	y	PROPN
ejpam-3972	231	18	1	1	NUM
ejpam-3972	231	19	1	1	NUM
ejpam-3972	232	1	z	z	NOUN
ejpam-3972	232	2	z	z	NOUN
ejpam-3972	232	3	z	z	NOUN
ejpam-3972	232	4	1	1	NUM
ejpam-3972	232	5	z	z	NOUN
ejpam-3972	232	6	1	1	NUM
ejpam-3972	232	7	remark	remark	NOUN
ejpam-3972	232	8	1	1	NUM
ejpam-3972	232	9	.	.	PUNCT
ejpam-3972	233	1	the	the	DET
ejpam-3972	233	2	relation	relation	NOUN
ejpam-3972	233	3	between	between	ADP
ejpam-3972	233	4	d	d	PROPN
ejpam-3972	233	5	and	and	CCONJ
ejpam-3972	233	6	λ	λ	PROPN
ejpam-3972	233	7	is	be	AUX
ejpam-3972	233	8	that	that	SCONJ
ejpam-3972	233	9	they	they	PRON
ejpam-3972	233	10	are	be	AUX
ejpam-3972	233	11	mutually	mutually	ADV
ejpam-3972	233	12	multiplicative	multiplicative	ADJ
ejpam-3972	233	13	bcl+	bcl+	PROPN
ejpam-3972	233	14	algebras	algebra	NOUN
ejpam-3972	233	15	,	,	PUNCT
ejpam-3972	233	16	meaning	mean	VERB
ejpam-3972	233	17	that	that	SCONJ
ejpam-3972	233	18	λ	λ	PROPN
ejpam-3972	233	19	•	•	NOUN
ejpam-3972	233	20	d	d	X
ejpam-3972	233	21	=	=	SYM
ejpam-3972	233	22	1	1	NUM
ejpam-3972	233	23	=	=	SYM
ejpam-3972	233	24	d	d	NOUN
ejpam-3972	233	25	•	•	NOUN
ejpam-3972	233	26	λ	λ	PROPN
ejpam-3972	233	27	implies	imply	VERB
ejpam-3972	233	28	m	m	PROPN
ejpam-3972	233	29	=	=	NOUN
ejpam-3972	233	30	m∗/e	m∗/e	NUM
ejpam-3972	233	31	•	•	NUM
ejpam-3972	233	32	λ	λ	X
ejpam-3972	233	33	.	.	PUNCT
ejpam-3972	234	1	(	(	PUNCT
ejpam-3972	234	2	27	27	NUM
ejpam-3972	234	3	)	)	PUNCT
ejpam-3972	234	4	remark	remark	NOUN
ejpam-3972	234	5	2	2	NUM
ejpam-3972	234	6	.	.	PUNCT
ejpam-3972	235	1	algorithm	algorithm	NOUN
ejpam-3972	235	2	(	(	PUNCT
ejpam-3972	235	3	b	b	NOUN
ejpam-3972	235	4	)	)	PUNCT
ejpam-3972	235	5	illustrates	illustrate	VERB
ejpam-3972	235	6	how	how	SCONJ
ejpam-3972	235	7	wcs	wcs	PROPN
ejpam-3972	235	8	based	base	VERB
ejpam-3972	235	9	on	on	ADP
ejpam-3972	235	10	the	the	DET
ejpam-3972	235	11	topological	topological	ADJ
ejpam-3972	235	12	group	group	NOUN
ejpam-3972	235	13	and	and	CCONJ
ejpam-3972	235	14	bcl+algebras	bcl+algebra	NOUN
ejpam-3972	235	15	encryption	encryption	NOUN
ejpam-3972	235	16	and	and	CCONJ
ejpam-3972	235	17	decrypt	decrypt	VERB
ejpam-3972	235	18	the	the	DET
ejpam-3972	235	19	messages	message	NOUN
ejpam-3972	235	20	are	be	AUX
ejpam-3972	235	21	performed	perform	VERB
ejpam-3972	235	22	.	.	PUNCT
ejpam-3972	236	1	and	and	CCONJ
ejpam-3972	236	2	most	most	ADJ
ejpam-3972	236	3	of	of	ADP
ejpam-3972	236	4	all	all	PRON
ejpam-3972	236	5	,	,	PUNCT
ejpam-3972	236	6	even	even	ADV
ejpam-3972	236	7	after	after	SCONJ
ejpam-3972	236	8	leaked	leak	VERB
ejpam-3972	236	9	three	three	NUM
ejpam-3972	236	10	numeric	numeric	ADJ
ejpam-3972	236	11	m	m	NOUN
ejpam-3972	236	12	*	*	NOUN
ejpam-3972	236	13	,	,	PUNCT
ejpam-3972	236	14	e	e	NOUN
ejpam-3972	236	15	and	and	CCONJ
ejpam-3972	236	16	d	d	PROPN
ejpam-3972	236	17	once	once	ADV
ejpam-3972	236	18	,	,	PUNCT
ejpam-3972	236	19	this	this	DET
ejpam-3972	236	20	result	result	NOUN
ejpam-3972	236	21	affect	affect	VERB
ejpam-3972	236	22	only	only	ADV
ejpam-3972	236	23	this	this	PRON
ejpam-3972	236	24	once	once	ADV
ejpam-3972	236	25	,	,	PUNCT
ejpam-3972	236	26	the	the	DET
ejpam-3972	236	27	system	system	NOUN
ejpam-3972	236	28	security	security	NOUN
ejpam-3972	236	29	remains	remain	VERB
ejpam-3972	236	30	the	the	DET
ejpam-3972	236	31	same	same	ADJ
ejpam-3972	236	32	because	because	SCONJ
ejpam-3972	236	33	wcs	wcs	PROPN
ejpam-3972	236	34	is	be	AUX
ejpam-3972	236	35	a	a	DET
ejpam-3972	236	36	formidable	formidable	ADJ
ejpam-3972	236	37	system	system	NOUN
ejpam-3972	236	38	.	.	PUNCT
ejpam-3972	237	1	in	in	ADP
ejpam-3972	237	2	the	the	DET
ejpam-3972	237	3	new	new	ADJ
ejpam-3972	237	4	algorithm	algorithm	NOUN
ejpam-3972	237	5	,	,	PUNCT
ejpam-3972	237	6	a	a	DET
ejpam-3972	237	7	central	central	ADJ
ejpam-3972	237	8	feature	feature	NOUN
ejpam-3972	237	9	is	be	AUX
ejpam-3972	237	10	multivariate	multivariate	VERB
ejpam-3972	237	11	wcs	wcs	NOUN
ejpam-3972	237	12	.	.	PUNCT
ejpam-3972	238	1	the	the	DET
ejpam-3972	238	2	algorithm	algorithm	NOUN
ejpam-3972	238	3	provides	provide	VERB
ejpam-3972	238	4	that	that	SCONJ
ejpam-3972	238	5	the	the	DET
ejpam-3972	238	6	algorithmic	algorithmic	ADJ
ejpam-3972	238	7	mechanism	mechanism	NOUN
ejpam-3972	238	8	for	for	ADP
ejpam-3972	238	9	identifying	identify	VERB
ejpam-3972	238	10	the	the	DET
ejpam-3972	238	11	invader	invader	NOUN
ejpam-3972	238	12	.	.	PUNCT
ejpam-3972	239	1	moreover	moreover	ADV
ejpam-3972	239	2	,	,	PUNCT
ejpam-3972	239	3	the	the	DET
ejpam-3972	239	4	quick	quick	ADJ
ejpam-3972	239	5	algorithm	algorithm	NOUN
ejpam-3972	239	6	(	(	PUNCT
ejpam-3972	239	7	b	b	NOUN
ejpam-3972	239	8	)	)	PUNCT
ejpam-3972	239	9	only	only	ADV
ejpam-3972	239	10	shows	show	VERB
ejpam-3972	239	11	how	how	SCONJ
ejpam-3972	239	12	to	to	PART
ejpam-3972	239	13	multiplication	multiplication	VERB
ejpam-3972	239	14	.	.	PUNCT
ejpam-3972	240	1	(	(	PUNCT
ejpam-3972	240	2	wormhole	wormhole	NOUN
ejpam-3972	240	3	computer	computer	NOUN
ejpam-3972	240	4	is	be	AUX
ejpam-3972	240	5	very	very	ADV
ejpam-3972	240	6	good	good	ADJ
ejpam-3972	240	7	at	at	ADP
ejpam-3972	240	8	,	,	PUNCT
ejpam-3972	240	9	but	but	CCONJ
ejpam-3972	240	10	with	with	ADP
ejpam-3972	240	11	that	that	PRON
ejpam-3972	240	12	also	also	ADV
ejpam-3972	240	13	lead	lead	VERB
ejpam-3972	240	14	to	to	ADP
ejpam-3972	240	15	headaches	headache	NOUN
ejpam-3972	240	16	of	of	ADP
ejpam-3972	240	17	god	god	PROPN
ejpam-3972	240	18	.	.	PUNCT
ejpam-3972	240	19	)	)	PUNCT
ejpam-3972	240	20	remark	remark	VERB
ejpam-3972	240	21	3	3	NUM
ejpam-3972	240	22	.	.	PUNCT
ejpam-3972	240	23	elementary	elementary	ADJ
ejpam-3972	240	24	aspects	aspect	NOUN
ejpam-3972	240	25	of	of	ADP
ejpam-3972	240	26	security	security	NOUN
ejpam-3972	240	27	.	.	PUNCT
ejpam-3972	241	1	the	the	DET
ejpam-3972	241	2	hard	hard	ADJ
ejpam-3972	241	3	task	task	NOUN
ejpam-3972	241	4	here	here	ADV
ejpam-3972	241	5	is	be	AUX
ejpam-3972	241	6	factorization	factorization	NOUN
ejpam-3972	241	7	of	of	ADP
ejpam-3972	241	8	large	large	ADJ
ejpam-3972	241	9	integers	integer	NOUN
ejpam-3972	241	10	λ	λ	VERB
ejpam-3972	241	11	into	into	ADP
ejpam-3972	241	12	primes	prime	NOUN
ejpam-3972	241	13	y	y	PROPN
ejpam-3972	241	14	,	,	PUNCT
ejpam-3972	241	15	z	z	PROPN
ejpam-3972	241	16	and	and	CCONJ
ejpam-3972	241	17	x	x	SYM
ejpam-3972	241	18	(	(	PUNCT
ejpam-3972	241	19	x	x	NOUN
ejpam-3972	241	20	need	need	AUX
ejpam-3972	241	21	not	not	PART
ejpam-3972	241	22	be	be	AUX
ejpam-3972	241	23	prime	prime	ADJ
ejpam-3972	241	24	)	)	PUNCT
ejpam-3972	241	25	.	.	PUNCT
ejpam-3972	242	1	wcs	wcs	PROPN
ejpam-3972	242	2	has	have	VERB
ejpam-3972	242	3	four	four	NUM
ejpam-3972	242	4	private	private	ADJ
ejpam-3972	242	5	keys	key	NOUN
ejpam-3972	242	6	,	,	PUNCT
ejpam-3972	242	7	that	that	PRON
ejpam-3972	242	8	is	is	ADV
ejpam-3972	242	9	y	y	PROPN
ejpam-3972	242	10	(	(	PUNCT
ejpam-3972	242	11	or	or	CCONJ
ejpam-3972	242	12	prime	prime	ADJ
ejpam-3972	242	13	p	p	NOUN
ejpam-3972	242	14	)	)	PUNCT
ejpam-3972	242	15	,	,	PUNCT
ejpam-3972	242	16	z	z	NOUN
ejpam-3972	242	17	(	(	PUNCT
ejpam-3972	242	18	or	or	CCONJ
ejpam-3972	242	19	prime	prime	ADJ
ejpam-3972	242	20	q	q	NOUN
ejpam-3972	242	21	)	)	PUNCT
ejpam-3972	242	22	,	,	PUNCT
ejpam-3972	242	23	x	x	X
ejpam-3972	242	24	,	,	PUNCT
ejpam-3972	242	25	and	and	CCONJ
ejpam-3972	242	26	e.	e.	PROPN
ejpam-3972	242	27	in	in	ADP
ejpam-3972	242	28	comparison	comparison	NOUN
ejpam-3972	242	29	,	,	PUNCT
ejpam-3972	242	30	rsa	rsa	PROPN
ejpam-3972	242	31	has	have	VERB
ejpam-3972	242	32	three	three	NUM
ejpam-3972	242	33	private	private	ADJ
ejpam-3972	242	34	keys	key	NOUN
ejpam-3972	242	35	,	,	PUNCT
ejpam-3972	242	36	that	that	PRON
ejpam-3972	242	37	is	be	AUX
ejpam-3972	242	38	p	p	NOUN
ejpam-3972	242	39	,	,	PUNCT
ejpam-3972	242	40	q	q	X
ejpam-3972	242	41	,	,	PUNCT
ejpam-3972	242	42	and	and	CCONJ
ejpam-3972	242	43	a.	a.	NOUN
ejpam-3972	242	44	remark	remark	NOUN
ejpam-3972	242	45	4	4	NUM
ejpam-3972	242	46	.	.	PUNCT
ejpam-3972	243	1	the	the	DET
ejpam-3972	243	2	most	most	ADV
ejpam-3972	243	3	obvious	obvious	ADJ
ejpam-3972	243	4	advantage	advantage	NOUN
ejpam-3972	243	5	of	of	ADP
ejpam-3972	243	6	speed	speed	NOUN
ejpam-3972	243	7	of	of	ADP
ejpam-3972	243	8	encryption	encryption	NOUN
ejpam-3972	243	9	/	/	SYM
ejpam-3972	243	10	decryption	decryption	NOUN
ejpam-3972	243	11	algorithms	algorithms	NOUN
ejpam-3972	243	12	is	be	AUX
ejpam-3972	243	13	to	to	PART
ejpam-3972	243	14	calculate	calculate	VERB
ejpam-3972	243	15	very	very	ADV
ejpam-3972	243	16	quickly	quickly	ADV
ejpam-3972	243	17	.	.	PUNCT
ejpam-3972	244	1	in	in	ADP
ejpam-3972	244	2	comparison	comparison	NOUN
ejpam-3972	244	3	,	,	PUNCT
ejpam-3972	244	4	both	both	CCONJ
ejpam-3972	244	5	the	the	DET
ejpam-3972	244	6	encryption	encryption	NOUN
ejpam-3972	244	7	and	and	CCONJ
ejpam-3972	244	8	the	the	DET
ejpam-3972	244	9	decryption	decryption	NOUN
ejpam-3972	244	10	operations	operation	NOUN
ejpam-3972	244	11	in	in	ADP
ejpam-3972	244	12	the	the	DET
ejpam-3972	244	13	rsa	rsa	PROPN
ejpam-3972	244	14	cryptosystem	cryptosystem	NOUN
ejpam-3972	244	15	are	be	AUX
ejpam-3972	244	16	modular	modular	ADJ
ejpam-3972	244	17	exponentiations	exponentiation	NOUN
ejpam-3972	244	18	.	.	PUNCT
ejpam-3972	245	1	we	we	PRON
ejpam-3972	245	2	illustrate	illustrate	VERB
ejpam-3972	245	3	the	the	DET
ejpam-3972	245	4	application	application	NOUN
ejpam-3972	245	5	of	of	ADP
ejpam-3972	245	6	the	the	DET
ejpam-3972	245	7	above	above	ADJ
ejpam-3972	245	8	algorithm	algorithm	NOUN
ejpam-3972	245	9	with	with	ADP
ejpam-3972	245	10	an	an	DET
ejpam-3972	245	11	example	example	NOUN
ejpam-3972	245	12	.	.	PUNCT
ejpam-3972	246	1	example	example	NOUN
ejpam-3972	247	1	1	1	NUM
ejpam-3972	247	2	.	.	PUNCT
ejpam-3972	247	3	suppose	suppose	VERB
ejpam-3972	247	4	alice	alice	PROPN
ejpam-3972	247	5	chooses	choose	VERB
ejpam-3972	247	6	x	x	PUNCT
ejpam-3972	247	7	=	=	SYM
ejpam-3972	247	8	101	101	NUM
ejpam-3972	247	9	,	,	PUNCT
ejpam-3972	247	10	y	y	PROPN
ejpam-3972	247	11	=	=	SYM
ejpam-3972	247	12	113	113	NUM
ejpam-3972	247	13	and	and	CCONJ
ejpam-3972	247	14	z	z	NOUN
ejpam-3972	248	1	=	=	SYM
ejpam-3972	248	2	227	227	NUM
ejpam-3972	248	3	.	.	PUNCT
ejpam-3972	249	1	then	then	ADV
ejpam-3972	249	2	λ	λ	X
ejpam-3972	249	3	=	=	PUNCT
ejpam-3972	249	4	2590751	2590751	NUM
ejpam-3972	249	5	.	.	PUNCT
ejpam-3972	250	1	both	both	DET
ejpam-3972	250	2	y	y	PROPN
ejpam-3972	250	3	and	and	CCONJ
ejpam-3972	250	4	z	z	PROPN
ejpam-3972	250	5	are	be	AUX
ejpam-3972	250	6	primes	prime	NOUN
ejpam-3972	250	7	.	.	PUNCT
ejpam-3972	251	1	alice	alice	PROPN
ejpam-3972	251	2	publishes	publish	VERB
ejpam-3972	251	3	λ	λ	PROPN
ejpam-3972	251	4	=	=	SYM
ejpam-3972	251	5	2590751	2590751	NUM
ejpam-3972	251	6	and	and	CCONJ
ejpam-3972	251	7	keeps	keep	VERB
ejpam-3972	251	8	x	x	PROPN
ejpam-3972	251	9	,	,	PUNCT
ejpam-3972	251	10	y	y	PROPN
ejpam-3972	251	11	and	and	CCONJ
ejpam-3972	251	12	z	z	PROPN
ejpam-3972	251	13	secret	secret	ADJ
ejpam-3972	251	14	.	.	PUNCT
ejpam-3972	252	1	she	she	PRON
ejpam-3972	252	2	computes	compute	VERB
ejpam-3972	252	3	the	the	DET
ejpam-3972	252	4	encryption	encryption	NOUN
ejpam-3972	252	5	key	key	NOUN
ejpam-3972	252	6	e	e	NOUN
ejpam-3972	252	7	,	,	PUNCT
ejpam-3972	252	8	by	by	ADP
ejpam-3972	252	9	the	the	DET
ejpam-3972	252	10	following	following	ADJ
ejpam-3972	252	11	cayley	cayley	ADJ
ejpam-3972	252	12	table	table	NOUN
ejpam-3972	252	13	2	2	NUM
ejpam-3972	252	14	.	.	PUNCT
ejpam-3972	252	15	e	e	NOUN
ejpam-3972	252	16	=	=	SYM
ejpam-3972	252	17	227	227	NUM
ejpam-3972	252	18	×	×	NOUN
ejpam-3972	252	19	113	113	NUM
ejpam-3972	252	20	=	=	SYM
ejpam-3972	252	21	25651	25651	NUM
ejpam-3972	252	22	.	.	PUNCT
ejpam-3972	253	1	then	then	ADV
ejpam-3972	253	2	alice	alice	PROPN
ejpam-3972	253	3	transmits	transmit	VERB
ejpam-3972	253	4	to	to	ADP
ejpam-3972	253	5	bob	bob	PROPN
ejpam-3972	253	6	25651	25651	NUM
ejpam-3972	253	7	.	.	PUNCT
ejpam-3972	254	1	whenever	whenever	SCONJ
ejpam-3972	254	2	bob	bob	PROPN
ejpam-3972	254	3	wants	want	VERB
ejpam-3972	254	4	to	to	PART
ejpam-3972	254	5	send	send	VERB
ejpam-3972	254	6	alice	alice	PROPN
ejpam-3972	254	7	a	a	DET
ejpam-3972	254	8	secure	secure	ADJ
ejpam-3972	254	9	message	message	NOUN
ejpam-3972	254	10	,	,	PUNCT
ejpam-3972	254	11	for	for	ADP
ejpam-3972	254	12	example	example	NOUN
ejpam-3972	254	13	,	,	PUNCT
ejpam-3972	254	14	m	m	VERB
ejpam-3972	254	15	=	=	NOUN
ejpam-3972	254	16	9726	9726	NUM
ejpam-3972	254	17	,	,	PUNCT
ejpam-3972	254	18	he	he	PRON
ejpam-3972	254	19	computes	compute	VERB
ejpam-3972	254	20	the	the	DET
ejpam-3972	254	21	plaintext	plaintext	NOUN
ejpam-3972	254	22	m∗	m∗	NOUN
ejpam-3972	254	23	=	=	SYM
ejpam-3972	254	24	646344772041126	646344772041126	NUM
ejpam-3972	254	25	.	.	PUNCT
ejpam-3972	255	1	he	he	PRON
ejpam-3972	255	2	transmits	transmit	VERB
ejpam-3972	255	3	this	this	PRON
ejpam-3972	255	4	to	to	ADP
ejpam-3972	255	5	alice	alice	PROPN
ejpam-3972	255	6	.	.	PUNCT
ejpam-3972	256	1	when	when	SCONJ
ejpam-3972	256	2	alice	alice	PROPN
ejpam-3972	256	3	receives	receive	VERB
ejpam-3972	256	4	such	such	DET
ejpam-3972	256	5	a	a	DET
ejpam-3972	256	6	message	message	NOUN
ejpam-3972	256	7	,	,	PUNCT
ejpam-3972	256	8	she	she	PRON
ejpam-3972	256	9	decrypts	decrypt	NOUN
ejpam-3972	256	10	by	by	ADP
ejpam-3972	256	11	computing	compute	VERB
ejpam-3972	256	12	y.	y.	PROPN
ejpam-3972	256	13	liu	liu	PROPN
ejpam-3972	256	14	/	/	SYM
ejpam-3972	256	15	eur	eur	PROPN
ejpam-3972	256	16	.	.	PUNCT
ejpam-3972	257	1	j.	j.	PROPN
ejpam-3972	257	2	pure	pure	PROPN
ejpam-3972	257	3	appl	appl	PROPN
ejpam-3972	257	4	.	.	PROPN
ejpam-3972	257	5	math	math	PROPN
ejpam-3972	257	6	,	,	PUNCT
ejpam-3972	257	7	14	14	NUM
ejpam-3972	257	8	(	(	PUNCT
ejpam-3972	257	9	2	2	NUM
ejpam-3972	257	10	)	)	PUNCT
ejpam-3972	257	11	(	(	PUNCT
ejpam-3972	257	12	2021	2021	NUM
ejpam-3972	257	13	)	)	PUNCT
ejpam-3972	257	14	,	,	PUNCT
ejpam-3972	257	15	521	521	NUM
ejpam-3972	257	16	-	-	SYM
ejpam-3972	257	17	536	536	NUM
ejpam-3972	257	18	532	532	NUM
ejpam-3972	257	19	m	m	NOUN
ejpam-3972	257	20	=	=	NOUN
ejpam-3972	257	21	m∗	m∗	PROPN
ejpam-3972	257	22	e×	e×	PROPN
ejpam-3972	257	23	λ	λ	NOUN
ejpam-3972	257	24	=	=	SYM
ejpam-3972	257	25	9726	9726	NUM
ejpam-3972	257	26	.	.	PUNCT
ejpam-3972	258	1	(	(	PUNCT
ejpam-3972	258	2	28	28	NUM
ejpam-3972	258	3	)	)	PUNCT
ejpam-3972	258	4	we	we	PRON
ejpam-3972	258	5	conclude	conclude	VERB
ejpam-3972	258	6	that	that	SCONJ
ejpam-3972	258	7	we	we	PRON
ejpam-3972	258	8	have	have	AUX
ejpam-3972	258	9	determined	determine	VERB
ejpam-3972	258	10	the	the	DET
ejpam-3972	258	11	correct	correct	ADJ
ejpam-3972	258	12	key	key	NOUN
ejpam-3972	258	13	.	.	PUNCT
ejpam-3972	259	1	implementing	implement	VERB
ejpam-3972	259	2	the	the	DET
ejpam-3972	259	3	wcs	wcs	NOUN
ejpam-3972	259	4	,	,	PUNCT
ejpam-3972	259	5	let	let	VERB
ejpam-3972	259	6	’s	’s	PRON
ejpam-3972	259	7	now	now	ADV
ejpam-3972	259	8	do	do	VERB
ejpam-3972	259	9	an	an	DET
ejpam-3972	259	10	example	example	NOUN
ejpam-3972	259	11	to	to	PART
ejpam-3972	259	12	illustrate	illustrate	VERB
ejpam-3972	259	13	encryption	encryption	NOUN
ejpam-3972	259	14	and	and	CCONJ
ejpam-3972	259	15	decryption	decryption	NOUN
ejpam-3972	259	16	.	.	PUNCT
ejpam-3972	260	1	obviously	obviously	ADV
ejpam-3972	260	2	,	,	PUNCT
ejpam-3972	260	3	this	this	DET
ejpam-3972	260	4	construction	construction	NOUN
ejpam-3972	260	5	generalizes	generalize	VERB
ejpam-3972	260	6	example	example	NOUN
ejpam-3972	260	7	1	1	NUM
ejpam-3972	260	8	.	.	PUNCT
ejpam-3972	260	9	example	example	NOUN
ejpam-3972	261	1	2	2	NUM
ejpam-3972	261	2	.	.	PUNCT
ejpam-3972	261	3	here	here	ADV
ejpam-3972	261	4	,	,	PUNCT
ejpam-3972	261	5	we	we	PRON
ejpam-3972	261	6	describe	describe	VERB
ejpam-3972	261	7	the	the	DET
ejpam-3972	261	8	one	one	NUM
ejpam-3972	261	9	-	-	PUNCT
ejpam-3972	261	10	way	way	NOUN
ejpam-3972	261	11	function	function	NOUN
ejpam-3972	261	12	that	that	PRON
ejpam-3972	261	13	underlies	underlie	VERB
ejpam-3972	261	14	the	the	DET
ejpam-3972	261	15	wcs	wcs	NOUN
ejpam-3972	261	16	cryptosystem	cryptosystem	NOUN
ejpam-3972	261	17	.	.	PUNCT
ejpam-3972	262	1	we	we	PRON
ejpam-3972	262	2	give	give	VERB
ejpam-3972	262	3	its	its	PRON
ejpam-3972	262	4	associated	associated	ADJ
ejpam-3972	262	5	trio	trio	NOUN
ejpam-3972	262	6	f	f	PROPN
ejpam-3972	262	7	,	,	PUNCT
ejpam-3972	262	8	m	m	PROPN
ejpam-3972	262	9	,	,	PUNCT
ejpam-3972	262	10	and	and	CCONJ
ejpam-3972	262	11	h.	h.	PROPN
ejpam-3972	262	12	the	the	DET
ejpam-3972	262	13	generator	generator	NOUN
ejpam-3972	262	14	machine	machine	NOUN
ejpam-3972	263	1	m	m	VERB
ejpam-3972	263	2	operates	operate	VERB
ejpam-3972	263	3	this	this	DET
ejpam-3972	263	4	example	example	NOUN
ejpam-3972	263	5	1	1	NUM
ejpam-3972	263	6	.	.	PUNCT
ejpam-3972	264	1	doing	do	VERB
ejpam-3972	264	2	so	so	ADV
ejpam-3972	264	3	is	be	AUX
ejpam-3972	264	4	possible	possible	ADJ
ejpam-3972	264	5	because	because	SCONJ
ejpam-3972	264	6	the	the	DET
ejpam-3972	264	7	set	set	NOUN
ejpam-3972	264	8	of	of	ADP
ejpam-3972	264	9	numbers	number	NOUN
ejpam-3972	264	10	{	{	PUNCT
ejpam-3972	264	11	1	1	NUM
ejpam-3972	264	12	,	,	PUNCT
ejpam-3972	264	13	·	·	PUNCT
ejpam-3972	264	14	·	·	PUNCT
ejpam-3972	264	15	·	·	PUNCT
ejpam-3972	264	16	,	,	PUNCT
ejpam-3972	264	17	φ(λ	φ(λ	PROPN
ejpam-3972	264	18	)	)	PUNCT
ejpam-3972	264	19	}	}	PUNCT
ejpam-3972	264	20	that	that	PRON
ejpam-3972	264	21	are	be	AUX
ejpam-3972	264	22	relatively	relatively	ADV
ejpam-3972	264	23	primes	prime	NOUN
ejpam-3972	264	24	to	to	ADP
ejpam-3972	264	25	φ(λ	φ(λ	PROPN
ejpam-3972	264	26	)	)	PUNCT
ejpam-3972	264	27	form	form	VERB
ejpam-3972	264	28	a	a	DET
ejpam-3972	264	29	group	group	NOUN
ejpam-3972	264	30	under	under	ADP
ejpam-3972	264	31	the	the	DET
ejpam-3972	264	32	operation	operation	NOUN
ejpam-3972	264	33	of	of	ADP
ejpam-3972	264	34	bcl	bcl	NOUN
ejpam-3972	264	35	multiplication	multiplication	NOUN
ejpam-3972	264	36	φ(λ	φ(λ	PROPN
ejpam-3972	264	37	)	)	PUNCT
ejpam-3972	264	38	.	.	PUNCT
ejpam-3972	265	1	it	it	PRON
ejpam-3972	265	2	selects	select	VERB
ejpam-3972	265	3	a	a	DET
ejpam-3972	265	4	random	random	ADJ
ejpam-3972	265	5	number	number	NOUN
ejpam-3972	265	6	m	m	NOUN
ejpam-3972	265	7	,	,	PUNCT
ejpam-3972	265	8	and	and	CCONJ
ejpam-3972	265	9	he	he	PRON
ejpam-3972	265	10	index	index	NOUN
ejpam-3972	265	11	to	to	ADP
ejpam-3972	265	12	the	the	DET
ejpam-3972	265	13	function	function	NOUN
ejpam-3972	265	14	f	f	PROPN
ejpam-3972	265	15	consists	consist	VERB
ejpam-3972	265	16	of	of	ADP
ejpam-3972	265	17	the	the	DET
ejpam-3972	265	18	four	four	NUM
ejpam-3972	265	19	numbers	number	NOUN
ejpam-3972	265	20	x	x	NOUN
ejpam-3972	265	21	,	,	PUNCT
ejpam-3972	265	22	y	y	PROPN
ejpam-3972	265	23	,	,	PUNCT
ejpam-3972	265	24	z	z	PROPN
ejpam-3972	265	25	and	and	CCONJ
ejpam-3972	265	26	m.	m.	NOUN
ejpam-3972	265	27	finally	finally	ADV
ejpam-3972	265	28	,	,	PUNCT
ejpam-3972	265	29	the	the	DET
ejpam-3972	265	30	algorithm	algorithm	NOUN
ejpam-3972	265	31	computes	compute	VERB
ejpam-3972	265	32	the	the	DET
ejpam-3972	265	33	multiplicative	multiplicative	ADJ
ejpam-3972	265	34	inverse	inverse	NOUN
ejpam-3972	265	35	d.	d.	PROPN
ejpam-3972	265	36	m	m	PROPN
ejpam-3972	265	37	outputs	output	NOUN
ejpam-3972	265	38	(	(	PUNCT
ejpam-3972	265	39	(	(	PUNCT
ejpam-3972	265	40	λ	λ	INTJ
ejpam-3972	265	41	,	,	PUNCT
ejpam-3972	265	42	m	m	NOUN
ejpam-3972	265	43	)	)	PUNCT
ejpam-3972	265	44	,	,	PUNCT
ejpam-3972	265	45	d	d	NOUN
ejpam-3972	265	46	)	)	PUNCT
ejpam-3972	265	47	,	,	PUNCT
ejpam-3972	265	48	where	where	SCONJ
ejpam-3972	265	49	d	d	NOUN
ejpam-3972	265	50	=	=	PUNCT
ejpam-3972	265	51	e×λ	e×λ	PROPN
ejpam-3972	265	52	.	.	PUNCT
ejpam-3972	265	53	function	function	PROPN
ejpam-3972	265	54	h	h	NOUN
ejpam-3972	265	55	properly	properly	ADV
ejpam-3972	265	56	inverts	invert	VERB
ejpam-3972	265	57	because	because	SCONJ
ejpam-3972	265	58	h(d	h(d	PROPN
ejpam-3972	265	59	,	,	PUNCT
ejpam-3972	265	60	fλ	fλ	INTJ
ejpam-3972	265	61	,	,	PUNCT
ejpam-3972	265	62	m	m	NOUN
ejpam-3972	265	63	)	)	PUNCT
ejpam-3972	265	64	=	=	SYM
ejpam-3972	265	65	hd(fλ	hd(fλ	NOUN
ejpam-3972	265	66	,	,	PUNCT
ejpam-3972	265	67	m	m	PROPN
ejpam-3972	265	68	)	)	PUNCT
ejpam-3972	265	69	for	for	ADP
ejpam-3972	265	70	any	any	DET
ejpam-3972	265	71	m	m	NOUN
ejpam-3972	265	72	and	and	CCONJ
ejpam-3972	265	73	λ	λ	NOUN
ejpam-3972	265	74	.	.	PUNCT
ejpam-3972	266	1	so	so	ADV
ejpam-3972	266	2	,	,	PUNCT
ejpam-3972	266	3	h	h	NOUN
ejpam-3972	266	4	properly	properly	ADV
ejpam-3972	266	5	inverts	invert	VERB
ejpam-3972	266	6	f	f	NOUN
ejpam-3972	266	7	,	,	PUNCT
ejpam-3972	266	8	we	we	PRON
ejpam-3972	266	9	says	say	VERB
ejpam-3972	266	10	that	that	SCONJ
ejpam-3972	266	11	fλ	fλ	PROPN
ejpam-3972	266	12	,	,	PUNCT
ejpam-3972	266	13	m	m	VERB
ejpam-3972	266	14	is	be	AUX
ejpam-3972	266	15	hard	hard	ADJ
ejpam-3972	266	16	to	to	PART
ejpam-3972	266	17	invert	invert	VERB
ejpam-3972	266	18	in	in	ADP
ejpam-3972	266	19	the	the	DET
ejpam-3972	266	20	absence	absence	NOUN
ejpam-3972	266	21	of	of	ADP
ejpam-3972	266	22	e.	e.	PROPN
ejpam-3972	266	23	5	5	PROPN
ejpam-3972	266	24	.	.	PUNCT
ejpam-3972	267	1	principles	principle	NOUN
ejpam-3972	267	2	is	be	AUX
ejpam-3972	267	3	the	the	DET
ejpam-3972	267	4	wcs	wcs	PROPN
ejpam-3972	267	5	really	really	ADV
ejpam-3972	267	6	vernam	vernam	NOUN
ejpam-3972	267	7	(	(	PUNCT
ejpam-3972	267	8	or	or	CCONJ
ejpam-3972	267	9	one	one	NUM
ejpam-3972	267	10	-	-	PUNCT
ejpam-3972	267	11	time	time	NOUN
ejpam-3972	267	12	pad	pad	NOUN
ejpam-3972	267	13	(	(	PUNCT
ejpam-3972	267	14	otp	otp	NOUN
ejpam-3972	267	15	)	)	PUNCT
ejpam-3972	267	16	)	)	PUNCT
ejpam-3972	267	17	?	?	PUNCT
ejpam-3972	268	1	in	in	ADP
ejpam-3972	268	2	other	other	ADJ
ejpam-3972	268	3	words	word	NOUN
ejpam-3972	268	4	,	,	PUNCT
ejpam-3972	268	5	we	we	PRON
ejpam-3972	268	6	will	will	AUX
ejpam-3972	268	7	give	give	VERB
ejpam-3972	268	8	the	the	DET
ejpam-3972	268	9	security	security	NOUN
ejpam-3972	268	10	proof	proof	NOUN
ejpam-3972	268	11	for	for	ADP
ejpam-3972	268	12	wcs	wcs	PROPN
ejpam-3972	268	13	.	.	PUNCT
ejpam-3972	269	1	first	first	ADV
ejpam-3972	269	2	,	,	PUNCT
ejpam-3972	269	3	we	we	PRON
ejpam-3972	269	4	have	have	VERB
ejpam-3972	269	5	the	the	DET
ejpam-3972	269	6	following	follow	VERB
ejpam-3972	269	7	design	design	NOUN
ejpam-3972	269	8	principles	principle	NOUN
ejpam-3972	269	9	.	.	PUNCT
ejpam-3972	270	1	principle	principle	NOUN
ejpam-3972	270	2	1	1	NUM
ejpam-3972	270	3	.	.	PUNCT
ejpam-3972	271	1	the	the	DET
ejpam-3972	271	2	key	key	NOUN
ejpam-3972	271	3	not	not	PART
ejpam-3972	271	4	reuse	reuse	NOUN
ejpam-3972	271	5	and	and	CCONJ
ejpam-3972	271	6	wonderful	wonderful	ADJ
ejpam-3972	271	7	key	key	ADJ
ejpam-3972	271	8	quality	quality	NOUN
ejpam-3972	271	9	(	(	PUNCT
ejpam-3972	271	10	i.e.	i.e.	X
ejpam-3972	271	11	,	,	PUNCT
ejpam-3972	271	12	the	the	DET
ejpam-3972	271	13	wcs	wcs	NOUN
ejpam-3972	271	14	is	be	AUX
ejpam-3972	271	15	unbreakable	unbreakable	ADJ
ejpam-3972	271	16	when	when	SCONJ
ejpam-3972	271	17	used	use	VERB
ejpam-3972	271	18	properly	properly	ADV
ejpam-3972	271	19	)	)	PUNCT
ejpam-3972	271	20	.	.	PUNCT
ejpam-3972	272	1	principle	principle	NOUN
ejpam-3972	272	2	2	2	NUM
ejpam-3972	272	3	.	.	PUNCT
ejpam-3972	273	1	in	in	ADP
ejpam-3972	273	2	wcs	wcs	PROPN
ejpam-3972	273	3	,	,	PUNCT
ejpam-3972	273	4	the	the	DET
ejpam-3972	273	5	next	next	ADJ
ejpam-3972	273	6	random	random	ADJ
ejpam-3972	273	7	bit	bit	NOUN
ejpam-3972	273	8	is	be	AUX
ejpam-3972	273	9	inscrutable	inscrutable	ADJ
ejpam-3972	273	10	.	.	PUNCT
ejpam-3972	274	1	principle	principle	NOUN
ejpam-3972	274	2	3	3	NUM
ejpam-3972	274	3	.	.	PUNCT
ejpam-3972	275	1	the	the	DET
ejpam-3972	275	2	plaintext	plaintext	NOUN
ejpam-3972	275	3	of	of	ADP
ejpam-3972	275	4	wcs	wcs	PROPN
ejpam-3972	275	5	that	that	PRON
ejpam-3972	275	6	a	a	DET
ejpam-3972	275	7	same	same	ADJ
ejpam-3972	275	8	character	character	NOUN
ejpam-3972	275	9	uses	use	VERB
ejpam-3972	275	10	the	the	DET
ejpam-3972	275	11	multi	multi	ADJ
ejpam-3972	275	12	-	-	ADJ
ejpam-3972	275	13	multiplication	multiplication	ADJ
ejpam-3972	275	14	tables	table	NOUN
ejpam-3972	275	15	can	can	AUX
ejpam-3972	275	16	make	make	VERB
ejpam-3972	275	17	a	a	DET
ejpam-3972	275	18	significant	significant	ADJ
ejpam-3972	275	19	difference	difference	NOUN
ejpam-3972	275	20	in	in	ADP
ejpam-3972	275	21	the	the	DET
ejpam-3972	275	22	outcome	outcome	NOUN
ejpam-3972	275	23	of	of	ADP
ejpam-3972	275	24	the	the	DET
ejpam-3972	275	25	encryption	encryption	NOUN
ejpam-3972	275	26	.	.	PUNCT
ejpam-3972	276	1	principle	principle	NOUN
ejpam-3972	276	2	4	4	NUM
ejpam-3972	276	3	.	.	PUNCT
ejpam-3972	277	1	the	the	DET
ejpam-3972	277	2	ciphertext	ciphertext	NOUN
ejpam-3972	277	3	(	(	PUNCT
ejpam-3972	277	4	e.g.	e.g.	ADV
ejpam-3972	277	5	,	,	PUNCT
ejpam-3972	277	6	ciphertext	ciphertext	ADJ
ejpam-3972	277	7	m∗	m∗	NOUN
ejpam-3972	277	8	of	of	ADP
ejpam-3972	277	9	wcs	wcs	PROPN
ejpam-3972	277	10	in	in	ADP
ejpam-3972	277	11	algorithm	algorithm	NOUN
ejpam-3972	277	12	(	(	PUNCT
ejpam-3972	277	13	b	b	NOUN
ejpam-3972	277	14	)	)	PUNCT
ejpam-3972	277	15	)	)	PUNCT
ejpam-3972	277	16	does	do	AUX
ejpam-3972	277	17	not	not	PART
ejpam-3972	277	18	make	make	VERB
ejpam-3972	277	19	sense	sense	NOUN
ejpam-3972	277	20	and	and	CCONJ
ejpam-3972	277	21	random	random	ADJ
ejpam-3972	277	22	to	to	PART
ejpam-3972	277	23	put	put	VERB
ejpam-3972	277	24	a	a	DET
ejpam-3972	277	25	bunch	bunch	NOUN
ejpam-3972	277	26	of	of	ADP
ejpam-3972	277	27	text	text	NOUN
ejpam-3972	277	28	private	private	ADJ
ejpam-3972	277	29	menus	menu	NOUN
ejpam-3972	277	30	,	,	PUNCT
ejpam-3972	277	31	including	include	VERB
ejpam-3972	277	32	the	the	DET
ejpam-3972	277	33	nonprintable	nonprintable	ADJ
ejpam-3972	277	34	characters	character	NOUN
ejpam-3972	277	35	of	of	ADP
ejpam-3972	277	36	the	the	DET
ejpam-3972	277	37	ascii	ascii	NOUN
ejpam-3972	277	38	.	.	PUNCT
ejpam-3972	278	1	remark	remark	NOUN
ejpam-3972	278	2	5	5	NUM
ejpam-3972	278	3	.	.	PUNCT
ejpam-3972	279	1	in	in	ADP
ejpam-3972	279	2	fact	fact	NOUN
ejpam-3972	279	3	,	,	PUNCT
ejpam-3972	279	4	the	the	DET
ejpam-3972	279	5	opt	opt	NOUN
ejpam-3972	279	6	is	be	AUX
ejpam-3972	279	7	symmetrical	symmetrical	ADJ
ejpam-3972	279	8	.	.	PUNCT
ejpam-3972	280	1	but	but	CCONJ
ejpam-3972	280	2	wcs	wcs	PROPN
ejpam-3972	280	3	is	be	AUX
ejpam-3972	280	4	a	a	DET
ejpam-3972	280	5	brand	brand	NOUN
ejpam-3972	280	6	-	-	PUNCT
ejpam-3972	280	7	new	new	ADJ
ejpam-3972	280	8	opt	opt	NOUN
ejpam-3972	280	9	,	,	PUNCT
ejpam-3972	280	10	is	be	AUX
ejpam-3972	280	11	unsymmetrical	unsymmetrical	ADJ
ejpam-3972	280	12	.	.	PUNCT
ejpam-3972	281	1	theorem	theorem	ADJ
ejpam-3972	281	2	4	4	NUM
ejpam-3972	281	3	.	.	PUNCT
ejpam-3972	282	1	(	(	PUNCT
ejpam-3972	282	2	unsymmetrical	unsymmetrical	ADJ
ejpam-3972	282	3	wcs	wcs	PROPN
ejpam-3972	282	4	)	)	PUNCT
ejpam-3972	282	5	.	.	PUNCT
ejpam-3972	283	1	let	let	VERB
ejpam-3972	283	2	e	e	PRON
ejpam-3972	283	3	be	be	AUX
ejpam-3972	283	4	an	an	DET
ejpam-3972	283	5	encryption	encryption	NOUN
ejpam-3972	283	6	sets	set	NOUN
ejpam-3972	283	7	and	and	CCONJ
ejpam-3972	283	8	let	let	VERB
ejpam-3972	283	9	d	d	PRON
ejpam-3972	283	10	be	be	AUX
ejpam-3972	283	11	a	a	DET
ejpam-3972	283	12	decryption	decryption	NOUN
ejpam-3972	283	13	sets	set	NOUN
ejpam-3972	283	14	.	.	PUNCT
ejpam-3972	284	1	then	then	ADV
ejpam-3972	284	2	e	e	X
ejpam-3972	284	3	6⇔	6⇔	ADJ
ejpam-3972	284	4	d.	d.	PROPN
ejpam-3972	284	5	proof	proof	NOUN
ejpam-3972	284	6	.	.	PUNCT
ejpam-3972	285	1	let	let	VERB
ejpam-3972	285	2	λ	λ	X
ejpam-3972	285	3	is	be	AUX
ejpam-3972	285	4	the	the	DET
ejpam-3972	285	5	public	public	ADJ
ejpam-3972	285	6	-	-	PUNCT
ejpam-3972	285	7	key	key	NOUN
ejpam-3972	285	8	,	,	PUNCT
ejpam-3972	285	9	by	by	ADP
ejpam-3972	285	10	algorithm	algorithm	NOUN
ejpam-3972	285	11	(	(	PUNCT
ejpam-3972	285	12	b	b	NOUN
ejpam-3972	285	13	)	)	PUNCT
ejpam-3972	285	14	,	,	PUNCT
ejpam-3972	285	15	we	we	PRON
ejpam-3972	285	16	know	know	VERB
ejpam-3972	285	17	that	that	SCONJ
ejpam-3972	286	1	d	d	NOUN
ejpam-3972	286	2	•	•	NUM
ejpam-3972	286	3	e	e	X
ejpam-3972	286	4	=	=	SYM
ejpam-3972	286	5	λ	λ	X
ejpam-3972	286	6	(	(	PUNCT
ejpam-3972	286	7	29	29	NUM
ejpam-3972	286	8	)	)	PUNCT
ejpam-3972	286	9	y.	y.	PROPN
ejpam-3972	286	10	liu	liu	PROPN
ejpam-3972	286	11	/	/	SYM
ejpam-3972	286	12	eur	eur	PROPN
ejpam-3972	286	13	.	.	PUNCT
ejpam-3972	287	1	j.	j.	PROPN
ejpam-3972	287	2	pure	pure	PROPN
ejpam-3972	287	3	appl	appl	PROPN
ejpam-3972	287	4	.	.	PROPN
ejpam-3972	287	5	math	math	PROPN
ejpam-3972	287	6	,	,	PUNCT
ejpam-3972	287	7	14	14	NUM
ejpam-3972	287	8	(	(	PUNCT
ejpam-3972	287	9	2	2	NUM
ejpam-3972	287	10	)	)	PUNCT
ejpam-3972	287	11	(	(	PUNCT
ejpam-3972	287	12	2021	2021	NUM
ejpam-3972	287	13	)	)	PUNCT
ejpam-3972	287	14	,	,	PUNCT
ejpam-3972	287	15	521	521	NUM
ejpam-3972	287	16	-	-	SYM
ejpam-3972	287	17	536	536	NUM
ejpam-3972	287	18	533	533	NUM
ejpam-3972	287	19	must	must	AUX
ejpam-3972	287	20	be	be	AUX
ejpam-3972	287	21	bcl+	bcl+	PROPN
ejpam-3972	287	22	algebraic	algebraic	ADJ
ejpam-3972	287	23	over	over	ADP
ejpam-3972	287	24	y	y	PROPN
ejpam-3972	288	1	[	[	X
ejpam-3972	288	2	7	7	NUM
ejpam-3972	288	3	,	,	PUNCT
ejpam-3972	288	4	8	8	NUM
ejpam-3972	288	5	]	]	X
ejpam-3972	289	1	[	[	X
ejpam-3972	289	2	13	13	NUM
ejpam-3972	289	3	,	,	PUNCT
ejpam-3972	289	4	14	14	NUM
ejpam-3972	289	5	]	]	PUNCT
ejpam-3972	289	6	[	[	X
ejpam-3972	289	7	15	15	NUM
ejpam-3972	289	8	,	,	PUNCT
ejpam-3972	289	9	16	16	NUM
ejpam-3972	289	10	]	]	PUNCT
ejpam-3972	289	11	.	.	PUNCT
ejpam-3972	290	1	certainly	certainly	ADV
ejpam-3972	290	2	6	6	NUM
ejpam-3972	290	3	∃	∃	PROPN
ejpam-3972	290	4	e−1	e−1	PROPN
ejpam-3972	290	5	implies	imply	VERB
ejpam-3972	290	6	6	6	NUM
ejpam-3972	290	7	∃d	∃d	PROPN
ejpam-3972	290	8	=	=	SYM
ejpam-3972	290	9	λ	λ	PROPN
ejpam-3972	290	10	•	•	NUM
ejpam-3972	290	11	e−1	e−1	PROPN
ejpam-3972	290	12	(	(	PUNCT
ejpam-3972	290	13	bob	bob	PROPN
ejpam-3972	290	14	can	can	AUX
ejpam-3972	290	15	not	not	PART
ejpam-3972	290	16	count	count	VERB
ejpam-3972	290	17	d	d	NOUN
ejpam-3972	290	18	)	)	PUNCT
ejpam-3972	290	19	.	.	PUNCT
ejpam-3972	291	1	(	(	PUNCT
ejpam-3972	291	2	30	30	X
ejpam-3972	291	3	)	)	PUNCT
ejpam-3972	291	4	working	work	VERB
ejpam-3972	291	5	in	in	ADP
ejpam-3972	291	6	algorithm	algorithm	NOUN
ejpam-3972	291	7	(	(	PUNCT
ejpam-3972	291	8	b	b	NOUN
ejpam-3972	291	9	)	)	PUNCT
ejpam-3972	291	10	,	,	PUNCT
ejpam-3972	291	11	we	we	PRON
ejpam-3972	291	12	find	find	VERB
ejpam-3972	291	13	this	this	DET
ejpam-3972	291	14	decryption	decryption	NOUN
ejpam-3972	291	15	key	key	NOUN
ejpam-3972	291	16	d	d	NOUN
ejpam-3972	291	17	is	be	AUX
ejpam-3972	291	18	unsymmetrical	unsymmetrical	ADJ
ejpam-3972	291	19	algebraic	algebraic	ADJ
ejpam-3972	291	20	structure	structure	NOUN
ejpam-3972	291	21	,	,	PUNCT
ejpam-3972	291	22	that	that	PRON
ejpam-3972	291	23	is	be	AUX
ejpam-3972	291	24	d	d	X
ejpam-3972	291	25	•	•	NUM
ejpam-3972	291	26	e	e	X
ejpam-3972	291	27	6=	6=	PROPN
ejpam-3972	291	28	e	e	PROPN
ejpam-3972	291	29	•	•	PROPN
ejpam-3972	291	30	d.	d.	PROPN
ejpam-3972	291	31	(	(	PUNCT
ejpam-3972	291	32	31	31	NUM
ejpam-3972	291	33	)	)	PUNCT
ejpam-3972	291	34	we	we	PRON
ejpam-3972	291	35	have	have	VERB
ejpam-3972	291	36	e	e	NOUN
ejpam-3972	291	37	∈	∈	PROPN
ejpam-3972	291	38	e	e	X
ejpam-3972	291	39	and	and	CCONJ
ejpam-3972	291	40	d	d	PROPN
ejpam-3972	291	41	∈	∈	PROPN
ejpam-3972	292	1	d.	d.	PROPN
ejpam-3972	293	1	so	so	ADV
ejpam-3972	293	2	,	,	PUNCT
ejpam-3972	293	3	we	we	PRON
ejpam-3972	293	4	deduce	deduce	VERB
ejpam-3972	293	5	that	that	PRON
ejpam-3972	293	6	e	e	PROPN
ejpam-3972	294	1	6⇒	6⇒	NOUN
ejpam-3972	294	2	d	d	NOUN
ejpam-3972	294	3	and	and	CCONJ
ejpam-3972	294	4	e	e	X
ejpam-3972	294	5	6	6	NUM
ejpam-3972	294	6	⇐	⇐	PROPN
ejpam-3972	294	7	d.	d.	PROPN
ejpam-3972	294	8	6	6	NUM
ejpam-3972	294	9	.	.	PUNCT
ejpam-3972	295	1	conclusions	conclusion	NOUN
ejpam-3972	295	2	the	the	DET
ejpam-3972	295	3	research	research	NOUN
ejpam-3972	295	4	presented	present	VERB
ejpam-3972	295	5	above	above	ADV
ejpam-3972	295	6	focuses	focus	VERB
ejpam-3972	295	7	on	on	ADP
ejpam-3972	295	8	the	the	DET
ejpam-3972	295	9	creation	creation	NOUN
ejpam-3972	295	10	and	and	CCONJ
ejpam-3972	295	11	implementation	implementation	NOUN
ejpam-3972	295	12	of	of	ADP
ejpam-3972	295	13	the	the	DET
ejpam-3972	295	14	wcs	wcs	NOUN
ejpam-3972	295	15	.	.	PUNCT
ejpam-3972	296	1	we	we	PRON
ejpam-3972	296	2	have	have	AUX
ejpam-3972	296	3	successfully	successfully	ADV
ejpam-3972	296	4	introduced	introduce	VERB
ejpam-3972	296	5	a	a	DET
ejpam-3972	296	6	new	new	ADJ
ejpam-3972	296	7	mathematical	mathematical	ADJ
ejpam-3972	296	8	tool	tool	NOUN
ejpam-3972	296	9	,	,	PUNCT
ejpam-3972	296	10	and	and	CCONJ
ejpam-3972	296	11	named	name	VERB
ejpam-3972	296	12	the	the	DET
ejpam-3972	296	13	groups	group	NOUN
ejpam-3972	296	14	for	for	ADP
ejpam-3972	296	15	proving	prove	VERB
ejpam-3972	296	16	secure	secure	ADJ
ejpam-3972	296	17	wormhole	wormhole	NOUN
ejpam-3972	296	18	public	public	ADJ
ejpam-3972	296	19	-	-	PUNCT
ejpam-3972	296	20	key	key	NOUN
ejpam-3972	296	21	cryptosystems	cryptosystem	NOUN
ejpam-3972	296	22	.	.	PUNCT
ejpam-3972	297	1	unlike	unlike	ADP
ejpam-3972	297	2	other	other	ADJ
ejpam-3972	297	3	encryption	encryption	NOUN
ejpam-3972	297	4	key	key	NOUN
ejpam-3972	297	5	solutions	solution	NOUN
ejpam-3972	297	6	,	,	PUNCT
ejpam-3972	297	7	due	due	ADP
ejpam-3972	297	8	to	to	ADP
ejpam-3972	297	9	this	this	DET
ejpam-3972	297	10	algorithm	algorithm	NOUN
ejpam-3972	297	11	(	(	PUNCT
ejpam-3972	297	12	b	b	NOUN
ejpam-3972	297	13	)	)	PUNCT
ejpam-3972	297	14	that	that	PRON
ejpam-3972	297	15	utilizes	utilize	VERB
ejpam-3972	297	16	an	an	DET
ejpam-3972	297	17	unsymmetrical	unsymmetrical	ADJ
ejpam-3972	297	18	algebraic	algebraic	ADJ
ejpam-3972	297	19	structure	structure	NOUN
ejpam-3972	297	20	will	will	AUX
ejpam-3972	297	21	be	be	AUX
ejpam-3972	297	22	a	a	DET
ejpam-3972	297	23	feature	feature	NOUN
ejpam-3972	297	24	of	of	ADP
ejpam-3972	297	25	cryptography	cryptography	NOUN
ejpam-3972	297	26	.	.	PUNCT
ejpam-3972	298	1	no	no	ADV
ejpam-3972	298	2	doubt	doubt	ADV
ejpam-3972	298	3	,	,	PUNCT
ejpam-3972	298	4	the	the	DET
ejpam-3972	298	5	concept	concept	NOUN
ejpam-3972	298	6	of	of	ADP
ejpam-3972	298	7	wormhole	wormhole	NOUN
ejpam-3972	298	8	come	come	VERB
ejpam-3972	298	9	from	from	ADP
ejpam-3972	298	10	cosmology	cosmology	NOUN
ejpam-3972	298	11	,	,	PUNCT
ejpam-3972	298	12	and	and	CCONJ
ejpam-3972	298	13	is	be	AUX
ejpam-3972	298	14	related	relate	VERB
ejpam-3972	298	15	to	to	ADP
ejpam-3972	298	16	quantum	quantum	ADJ
ejpam-3972	298	17	entanglement	entanglement	NOUN
ejpam-3972	298	18	,	,	PUNCT
ejpam-3972	298	19	which	which	PRON
ejpam-3972	298	20	we	we	PRON
ejpam-3972	298	21	find	find	VERB
ejpam-3972	298	22	to	to	PART
ejpam-3972	298	23	be	be	AUX
ejpam-3972	298	24	an	an	DET
ejpam-3972	298	25	important	important	ADJ
ejpam-3972	298	26	topic	topic	NOUN
ejpam-3972	298	27	.	.	PUNCT
ejpam-3972	299	1	but	but	CCONJ
ejpam-3972	299	2	more	more	ADV
ejpam-3972	299	3	importantly	importantly	ADV
ejpam-3972	299	4	,	,	PUNCT
ejpam-3972	299	5	we	we	PRON
ejpam-3972	299	6	can	can	AUX
ejpam-3972	299	7	use	use	VERB
ejpam-3972	299	8	two	two	NUM
ejpam-3972	299	9	wormholes	wormhole	NOUN
ejpam-3972	299	10	for	for	ADP
ejpam-3972	299	11	physical	physical	ADJ
ejpam-3972	299	12	background	background	NOUN
ejpam-3972	299	13	of	of	ADP
ejpam-3972	299	14	cryptography	cryptography	NOUN
ejpam-3972	299	15	or	or	CCONJ
ejpam-3972	299	16	we	we	PRON
ejpam-3972	299	17	can	can	AUX
ejpam-3972	299	18	also	also	ADV
ejpam-3972	299	19	leave	leave	VERB
ejpam-3972	299	20	it	it	PRON
ejpam-3972	299	21	encryption	encryption	NOUN
ejpam-3972	299	22	.	.	PUNCT
ejpam-3972	300	1	studies	study	NOUN
ejpam-3972	300	2	on	on	ADP
ejpam-3972	300	3	these	these	DET
ejpam-3972	300	4	topics	topic	NOUN
ejpam-3972	300	5	are	be	AUX
ejpam-3972	300	6	not	not	PART
ejpam-3972	300	7	only	only	ADV
ejpam-3972	300	8	providing	provide	VERB
ejpam-3972	300	9	rich	rich	ADJ
ejpam-3972	300	10	scientific	scientific	ADJ
ejpam-3972	300	11	insight	insight	NOUN
ejpam-3972	300	12	in	in	ADP
ejpam-3972	300	13	terms	term	NOUN
ejpam-3972	300	14	of	of	ADP
ejpam-3972	300	15	new	new	ADJ
ejpam-3972	300	16	physics	physics	NOUN
ejpam-3972	300	17	but	but	CCONJ
ejpam-3972	300	18	also	also	ADV
ejpam-3972	300	19	potentially	potentially	ADV
ejpam-3972	300	20	have	have	VERB
ejpam-3972	300	21	important	important	ADJ
ejpam-3972	300	22	long	long	ADJ
ejpam-3972	300	23	-	-	PUNCT
ejpam-3972	300	24	term	term	NOUN
ejpam-3972	300	25	technological	technological	ADJ
ejpam-3972	300	26	implications	implication	NOUN
ejpam-3972	300	27	,	,	PUNCT
ejpam-3972	300	28	including	include	VERB
ejpam-3972	300	29	the	the	DET
ejpam-3972	300	30	development	development	NOUN
ejpam-3972	300	31	of	of	ADP
ejpam-3972	300	32	cryptosystems	cryptosystem	NOUN
ejpam-3972	300	33	that	that	PRON
ejpam-3972	300	34	support	support	VERB
ejpam-3972	300	35	quantum	quantum	ADJ
ejpam-3972	300	36	communication	communication	NOUN
ejpam-3972	300	37	are	be	AUX
ejpam-3972	300	38	immune	immune	ADJ
ejpam-3972	300	39	to	to	ADP
ejpam-3972	300	40	safety	safety	NOUN
ejpam-3972	300	41	,	,	PUNCT
ejpam-3972	300	42	are	be	AUX
ejpam-3972	300	43	robust	robust	ADJ
ejpam-3972	300	44	against	against	ADP
ejpam-3972	300	45	feature	feature	NOUN
ejpam-3972	300	46	guaranteed	guarantee	VERB
ejpam-3972	300	47	unidirectional	unidirectional	ADJ
ejpam-3972	300	48	transmission	transmission	NOUN
ejpam-3972	300	49	(	(	PUNCT
ejpam-3972	300	50	or	or	CCONJ
ejpam-3972	300	51	a	a	DET
ejpam-3972	300	52	one	one	NUM
ejpam-3972	300	53	-	-	PUNCT
ejpam-3972	300	54	way	way	NOUN
ejpam-3972	300	55	function	function	NOUN
ejpam-3972	300	56	)	)	PUNCT
ejpam-3972	300	57	.	.	PUNCT
ejpam-3972	301	1	to	to	PART
ejpam-3972	301	2	construct	construct	VERB
ejpam-3972	301	3	an	an	DET
ejpam-3972	301	4	encrypted	encrypt	VERB
ejpam-3972	301	5	form	form	NOUN
ejpam-3972	301	6	which	which	PRON
ejpam-3972	301	7	has	have	VERB
ejpam-3972	301	8	the	the	DET
ejpam-3972	301	9	required	require	VERB
ejpam-3972	301	10	properties	property	NOUN
ejpam-3972	301	11	,	,	PUNCT
ejpam-3972	301	12	and	and	CCONJ
ejpam-3972	301	13	to	to	PART
ejpam-3972	301	14	prove	prove	VERB
ejpam-3972	301	15	that	that	SCONJ
ejpam-3972	301	16	it	it	PRON
ejpam-3972	301	17	has	have	VERB
ejpam-3972	301	18	these	these	DET
ejpam-3972	301	19	properties	property	NOUN
ejpam-3972	301	20	,	,	PUNCT
ejpam-3972	301	21	is	be	AUX
ejpam-3972	301	22	a	a	DET
ejpam-3972	301	23	purely	purely	ADV
ejpam-3972	301	24	algebraic	algebraic	ADJ
ejpam-3972	301	25	task	task	NOUN
ejpam-3972	301	26	.	.	PUNCT
ejpam-3972	302	1	it	it	PRON
ejpam-3972	302	2	should	should	AUX
ejpam-3972	302	3	be	be	AUX
ejpam-3972	302	4	interesting	interesting	ADJ
ejpam-3972	302	5	algebraic	algebraic	ADJ
ejpam-3972	302	6	cryptograms	cryptogram	NOUN
ejpam-3972	302	7	and	and	CCONJ
ejpam-3972	302	8	may	may	AUX
ejpam-3972	302	9	represent	represent	VERB
ejpam-3972	302	10	a	a	DET
ejpam-3972	302	11	trend	trend	NOUN
ejpam-3972	302	12	in	in	ADP
ejpam-3972	302	13	the	the	DET
ejpam-3972	302	14	future	future	NOUN
ejpam-3972	302	15	.	.	PUNCT
ejpam-3972	303	1	the	the	DET
ejpam-3972	303	2	reader	reader	NOUN
ejpam-3972	303	3	is	be	AUX
ejpam-3972	303	4	invited	invite	VERB
ejpam-3972	303	5	to	to	PART
ejpam-3972	303	6	consider	consider	VERB
ejpam-3972	303	7	the	the	DET
ejpam-3972	303	8	direction	direction	NOUN
ejpam-3972	303	9	for	for	ADP
ejpam-3972	303	10	wormhole	wormhole	NOUN
ejpam-3972	303	11	cryptography	cryptography	NOUN
ejpam-3972	303	12	.	.	PUNCT
ejpam-3972	304	1	7	7	X
ejpam-3972	304	2	.	.	X
ejpam-3972	304	3	appendix	appendix	VERB
ejpam-3972	304	4	the	the	DET
ejpam-3972	304	5	particles	particle	NOUN
ejpam-3972	304	6	of	of	ADP
ejpam-3972	304	7	entanglement	entanglement	NOUN
ejpam-3972	304	8	in	in	ADP
ejpam-3972	304	9	the	the	DET
ejpam-3972	304	10	two	two	NUM
ejpam-3972	304	11	wormholes	wormhole	NOUN
ejpam-3972	304	12	,	,	PUNCT
ejpam-3972	304	13	as	as	SCONJ
ejpam-3972	304	14	shown	show	VERB
ejpam-3972	304	15	in	in	ADP
ejpam-3972	304	16	the	the	DET
ejpam-3972	304	17	following	follow	VERB
ejpam-3972	304	18	figure	figure	NOUN
ejpam-3972	304	19	a1	a1	NOUN
ejpam-3972	304	20	(	(	PUNCT
ejpam-3972	304	21	see	see	VERB
ejpam-3972	304	22	[	[	X
ejpam-3972	304	23	4	4	NUM
ejpam-3972	304	24	]	]	NUM
ejpam-3972	304	25	)	)	PUNCT
ejpam-3972	304	26	.	.	PUNCT
ejpam-3972	305	1	acknowledgements	acknowledgement	VERB
ejpam-3972	305	2	the	the	DET
ejpam-3972	305	3	author	author	NOUN
ejpam-3972	305	4	is	be	AUX
ejpam-3972	305	5	grateful	grateful	ADJ
ejpam-3972	305	6	to	to	ADP
ejpam-3972	305	7	the	the	DET
ejpam-3972	305	8	anonymous	anonymous	ADJ
ejpam-3972	305	9	referees	referee	NOUN
ejpam-3972	305	10	for	for	ADP
ejpam-3972	305	11	useful	useful	ADJ
ejpam-3972	305	12	comments	comment	NOUN
ejpam-3972	305	13	and	and	CCONJ
ejpam-3972	305	14	suggestions	suggestion	NOUN
ejpam-3972	305	15	.	.	PUNCT
ejpam-3972	306	1	y.	y.	PROPN
ejpam-3972	306	2	liu	liu	PROPN
ejpam-3972	306	3	/	/	SYM
ejpam-3972	306	4	eur	eur	PROPN
ejpam-3972	306	5	.	.	PUNCT
ejpam-3972	307	1	j.	j.	PROPN
ejpam-3972	307	2	pure	pure	PROPN
ejpam-3972	307	3	appl	appl	PROPN
ejpam-3972	307	4	.	.	PROPN
ejpam-3972	307	5	math	math	PROPN
ejpam-3972	307	6	,	,	PUNCT
ejpam-3972	307	7	14	14	NUM
ejpam-3972	307	8	(	(	PUNCT
ejpam-3972	307	9	2	2	NUM
ejpam-3972	307	10	)	)	PUNCT
ejpam-3972	307	11	(	(	PUNCT
ejpam-3972	307	12	2021	2021	NUM
ejpam-3972	307	13	)	)	PUNCT
ejpam-3972	307	14	,	,	PUNCT
ejpam-3972	307	15	521	521	NUM
ejpam-3972	307	16	-	-	SYM
ejpam-3972	307	17	536	536	NUM
ejpam-3972	307	18	534	534	NUM
ejpam-3972	307	19	figure	figure	NOUN
ejpam-3972	307	20	a1	a1	NOUN
ejpam-3972	307	21	.	.	PUNCT
ejpam-3972	308	1	two	two	NUM
ejpam-3972	308	2	wormholes	wormhole	NOUN
ejpam-3972	308	3	of	of	ADP
ejpam-3972	308	4	wcs	wcs	PROPN
ejpam-3972	308	5	.	.	PUNCT
ejpam-3972	309	1	figure	figure	NOUN
ejpam-3972	309	2	credit	credit	NOUN
ejpam-3972	309	3	:	:	PUNCT
ejpam-3972	309	4	y.	y.	PROPN
ejpam-3972	309	5	liu	liu	PROPN
ejpam-3972	309	6	,	,	PUNCT
ejpam-3972	309	7	2019	2019	NUM
ejpam-3972	309	8	,	,	PUNCT
ejpam-3972	309	9	ijcaa	ijcaa	NOUN
ejpam-3972	309	10	,	,	PUNCT
ejpam-3972	309	11	1	1	NUM
ejpam-3972	309	12	,	,	PUNCT
ejpam-3972	309	13	33	33	NUM
ejpam-3972	309	14	.	.	PUNCT
ejpam-3972	310	1	references	reference	NOUN
ejpam-3972	310	2	535	535	NUM
ejpam-3972	310	3	references	reference	NOUN
ejpam-3972	310	4	[	[	X
ejpam-3972	310	5	1	1	NUM
ejpam-3972	310	6	]	]	PUNCT
ejpam-3972	310	7	van	van	PROPN
ejpam-3972	310	8	raamsdonk	raamsdonk	NOUN
ejpam-3972	310	9	,	,	PUNCT
ejpam-3972	310	10	m.	m.	NOUN
ejpam-3972	310	11	:	:	PUNCT
ejpam-3972	310	12	building	build	VERB
ejpam-3972	310	13	up	up	ADP
ejpam-3972	310	14	spacetime	spacetime	NOUN
ejpam-3972	310	15	with	with	ADP
ejpam-3972	310	16	quantum	quantum	ADJ
ejpam-3972	310	17	entanglement	entanglement	NOUN
ejpam-3972	310	18	.	.	PUNCT
ejpam-3972	311	1	gen	gen	PROPN
ejpam-3972	311	2	.	.	PROPN
ejpam-3972	311	3	rel	rel	PROPN
ejpam-3972	311	4	.	.	PUNCT
ejpam-3972	312	1	grav	grav	PROPN
ejpam-3972	312	2	.	.	PUNCT
ejpam-3972	313	1	42	42	NUM
ejpam-3972	313	2	,	,	PUNCT
ejpam-3972	313	3	2323	2323	NUM
ejpam-3972	313	4	-	-	SYM
ejpam-3972	313	5	2329	2329	NUM
ejpam-3972	313	6	,	,	PUNCT
ejpam-3972	313	7	(	(	PUNCT
ejpam-3972	313	8	2010	2010	NUM
ejpam-3972	313	9	)	)	PUNCT
ejpam-3972	313	10	.	.	PUNCT
ejpam-3972	314	1	https://doi.org/10.1142/s0218271810018529	https://doi.org/10.1142/s0218271810018529	NUM
ejpam-3972	314	2	[	[	SYM
ejpam-3972	314	3	2	2	NUM
ejpam-3972	314	4	]	]	PUNCT
ejpam-3972	314	5	maldacena	maldacena	NOUN
ejpam-3972	314	6	,	,	PUNCT
ejpam-3972	314	7	j.	j.	PROPN
ejpam-3972	314	8	,	,	PUNCT
ejpam-3972	314	9	susskind	susskind	PROPN
ejpam-3972	314	10	,	,	PUNCT
ejpam-3972	314	11	l.	l.	PROPN
ejpam-3972	314	12	:	:	PUNCT
ejpam-3972	314	13	cool	cool	ADJ
ejpam-3972	314	14	horizons	horizon	NOUN
ejpam-3972	314	15	for	for	ADP
ejpam-3972	314	16	entangled	entangle	VERB
ejpam-3972	314	17	black	black	ADJ
ejpam-3972	314	18	holes	hole	NOUN
ejpam-3972	314	19	.	.	PUNCT
ejpam-3972	315	1	fortsch	fortsch	PROPN
ejpam-3972	315	2	.	.	PUNCT
ejpam-3972	316	1	phys	phy	NOUN
ejpam-3972	316	2	.	.	PUNCT
ejpam-3972	317	1	61	61	NUM
ejpam-3972	317	2	,	,	PUNCT
ejpam-3972	317	3	781	781	NUM
ejpam-3972	317	4	-	-	SYM
ejpam-3972	317	5	811	811	NUM
ejpam-3972	317	6	,	,	PUNCT
ejpam-3972	317	7	(	(	PUNCT
ejpam-3972	317	8	2013	2013	NUM
ejpam-3972	317	9	)	)	PUNCT
ejpam-3972	317	10	.	.	PUNCT
ejpam-3972	318	1	https://doi.org/10.1002/prop.201300020	https://doi.org/10.1002/prop.201300020	NOUN
ejpam-3972	319	1	[	[	X
ejpam-3972	319	2	3	3	NUM
ejpam-3972	319	3	]	]	X
ejpam-3972	319	4	ron	ron	PROPN
ejpam-3972	319	5	,	,	PUNCT
ejpam-3972	319	6	c.	c.	PROPN
ejpam-3972	319	7	:	:	PUNCT
ejpam-3972	319	8	the	the	DET
ejpam-3972	319	9	quantum	quantum	ADJ
ejpam-3972	319	10	source	source	NOUN
ejpam-3972	319	11	of	of	ADP
ejpam-3972	319	12	space	space	NOUN
ejpam-3972	319	13	-	-	PUNCT
ejpam-3972	319	14	time	time	NOUN
ejpam-3972	319	15	.	.	PUNCT
ejpam-3972	320	1	nature	nature	NOUN
ejpam-3972	320	2	.	.	PUNCT
ejpam-3972	321	1	527(16	527(16	NUM
ejpam-3972	321	2	)	)	PUNCT
ejpam-3972	321	3	,	,	PUNCT
ejpam-3972	321	4	290	290	NUM
ejpam-3972	321	5	-	-	SYM
ejpam-3972	321	6	293	293	NUM
ejpam-3972	321	7	,	,	PUNCT
ejpam-3972	321	8	(	(	PUNCT
ejpam-3972	321	9	2015	2015	NUM
ejpam-3972	321	10	)	)	PUNCT
ejpam-3972	321	11	.	.	PUNCT
ejpam-3972	322	1	https://doi.org/10.1038/527290a	https://doi.org/10.1038/527290a	NOUN
ejpam-3972	323	1	[	[	X
ejpam-3972	323	2	4	4	NUM
ejpam-3972	323	3	]	]	SYM
ejpam-3972	323	4	yonghong	yonghong	NOUN
ejpam-3972	323	5	,	,	PUNCT
ejpam-3972	323	6	l.	l.	PROPN
ejpam-3972	323	7	:	:	PUNCT
ejpam-3972	323	8	new	new	ADJ
ejpam-3972	323	9	groups	group	NOUN
ejpam-3972	323	10	to	to	ADP
ejpam-3972	323	11	er	er	INTJ
ejpam-3972	323	12	=	=	PUNCT
ejpam-3972	323	13	epr	epr	PROPN
ejpam-3972	323	14	conjecture	conjecture	NOUN
ejpam-3972	323	15	.	.	PUNCT
ejpam-3972	324	1	international	international	ADJ
ejpam-3972	324	2	journal	journal	PROPN
ejpam-3972	324	3	of	of	ADP
ejpam-3972	324	4	cosmology	cosmology	NOUN
ejpam-3972	324	5	,	,	PUNCT
ejpam-3972	324	6	astronomy	astronomy	NOUN
ejpam-3972	324	7	and	and	CCONJ
ejpam-3972	324	8	astrophysics	astrophysic	NOUN
ejpam-3972	324	9	.	.	PUNCT
ejpam-3972	325	1	1(1	1(1	NUM
ejpam-3972	325	2	)	)	PUNCT
ejpam-3972	325	3	,	,	PUNCT
ejpam-3972	325	4	33	33	NUM
ejpam-3972	325	5	-	-	SYM
ejpam-3972	325	6	37	37	NUM
ejpam-3972	325	7	,	,	PUNCT
ejpam-3972	325	8	(	(	PUNCT
ejpam-3972	325	9	2019	2019	NUM
ejpam-3972	325	10	)	)	PUNCT
ejpam-3972	325	11	.	.	PUNCT
ejpam-3972	326	1	[	[	X
ejpam-3972	326	2	5	5	NUM
ejpam-3972	326	3	]	]	PUNCT
ejpam-3972	326	4	shor	shor	NOUN
ejpam-3972	326	5	,	,	PUNCT
ejpam-3972	326	6	p.w	p.w	PROPN
ejpam-3972	326	7	.	.	PUNCT
ejpam-3972	326	8	:	:	PUNCT
ejpam-3972	326	9	algorithms	algorithm	NOUN
ejpam-3972	326	10	for	for	ADP
ejpam-3972	326	11	quantum	quantum	ADJ
ejpam-3972	326	12	computation	computation	NOUN
ejpam-3972	326	13	:	:	PUNCT
ejpam-3972	326	14	discrete	discrete	ADJ
ejpam-3972	326	15	logarithms	logarithm	NOUN
ejpam-3972	326	16	and	and	CCONJ
ejpam-3972	326	17	factoring	factoring	NOUN
ejpam-3972	326	18	.	.	PUNCT
ejpam-3972	327	1	in	in	ADP
ejpam-3972	327	2	proc	proc	NOUN
ejpam-3972	327	3	.	.	PUNCT
ejpam-3972	328	1	35th	35th	ADJ
ejpam-3972	328	2	ann	ann	PROPN
ejpam-3972	328	3	.	.	PUNCT
ejpam-3972	328	4	symp	symp	PROPN
ejpam-3972	328	5	.	.	PUNCT
ejpam-3972	329	1	foundations	foundation	NOUN
ejpam-3972	329	2	of	of	ADP
ejpam-3972	329	3	computer	computer	NOUN
ejpam-3972	329	4	science	science	NOUN
ejpam-3972	329	5	.	.	PUNCT
ejpam-3972	330	1	ieee	ieee	PROPN
ejpam-3972	330	2	press	press	PROPN
ejpam-3972	330	3	,	,	PUNCT
ejpam-3972	330	4	pp	pp	ADV
ejpam-3972	330	5	124	124	NUM
ejpam-3972	330	6	-	-	SYM
ejpam-3972	330	7	134	134	NUM
ejpam-3972	330	8	,	,	PUNCT
ejpam-3972	330	9	(	(	PUNCT
ejpam-3972	330	10	1994	1994	NUM
ejpam-3972	330	11	)	)	PUNCT
ejpam-3972	330	12	.	.	PUNCT
ejpam-3972	331	1	[	[	X
ejpam-3972	331	2	6	6	NUM
ejpam-3972	331	3	]	]	X
ejpam-3972	331	4	diffie	diffie	PROPN
ejpam-3972	331	5	,	,	PUNCT
ejpam-3972	331	6	w.	w.	PROPN
ejpam-3972	331	7	,	,	PUNCT
ejpam-3972	331	8	hellman	hellman	PROPN
ejpam-3972	331	9	,	,	PUNCT
ejpam-3972	331	10	m.e	m.e	PROPN
ejpam-3972	331	11	.	.	PROPN
ejpam-3972	331	12	:	:	PUNCT
ejpam-3972	331	13	multiuser	multiuser	PROPN
ejpam-3972	331	14	cryptographic	cryptographic	ADJ
ejpam-3972	331	15	techniques	technique	NOUN
ejpam-3972	331	16	.	.	PUNCT
ejpam-3972	332	1	in	in	ADP
ejpam-3972	332	2	proc	proc	PROPN
ejpam-3972	332	3	.	.	PUNCT
ejpam-3972	333	1	afips	afips	PROPN
ejpam-3972	333	2	national	national	PROPN
ejpam-3972	333	3	computer	computer	PROPN
ejpam-3972	333	4	conference	conference	NOUN
ejpam-3972	333	5	,	,	PUNCT
ejpam-3972	333	6	pp	pp	ADV
ejpam-3972	333	7	109	109	NUM
ejpam-3972	333	8	-	-	SYM
ejpam-3972	333	9	112	112	NUM
ejpam-3972	333	10	,	,	PUNCT
ejpam-3972	333	11	(	(	PUNCT
ejpam-3972	333	12	1976	1976	NUM
ejpam-3972	333	13	)	)	PUNCT
ejpam-3972	333	14	.	.	PUNCT
ejpam-3972	334	1	[	[	X
ejpam-3972	334	2	7	7	X
ejpam-3972	334	3	]	]	SYM
ejpam-3972	334	4	yonghong	yonghong	NOUN
ejpam-3972	334	5	,	,	PUNCT
ejpam-3972	334	6	l.	l.	PROPN
ejpam-3972	334	7	:	:	PUNCT
ejpam-3972	334	8	on	on	ADP
ejpam-3972	334	9	bcl+-algebras	bcl+-algebra	NOUN
ejpam-3972	334	10	.	.	PROPN
ejpam-3972	334	11	advances	advance	NOUN
ejpam-3972	334	12	in	in	ADP
ejpam-3972	334	13	pure	pure	ADJ
ejpam-3972	334	14	mathematics	mathematic	NOUN
ejpam-3972	334	15	.	.	PUNCT
ejpam-3972	335	1	2(1	2(1	NUM
ejpam-3972	335	2	)	)	PUNCT
ejpam-3972	335	3	,	,	PUNCT
ejpam-3972	335	4	59	59	NUM
ejpam-3972	335	5	-	-	SYM
ejpam-3972	335	6	61	61	NUM
ejpam-3972	335	7	,	,	PUNCT
ejpam-3972	335	8	(	(	PUNCT
ejpam-3972	335	9	2012	2012	NUM
ejpam-3972	335	10	)	)	PUNCT
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ejpam-3972	337	2	8	8	NUM
ejpam-3972	337	3	]	]	SYM
ejpam-3972	337	4	yonghong	yonghong	NOUN
ejpam-3972	337	5	,	,	PUNCT
ejpam-3972	337	6	l.	l.	PROPN
ejpam-3972	337	7	:	:	PUNCT
ejpam-3972	337	8	topological	topological	PROPN
ejpam-3972	337	9	bcl+-algebras	bcl+-algebra	NOUN
ejpam-3972	337	10	.	.	PUNCT
ejpam-3972	338	1	pure	pure	ADJ
ejpam-3972	338	2	and	and	CCONJ
ejpam-3972	338	3	applied	applied	ADJ
ejpam-3972	338	4	mathematics	mathematic	NOUN
ejpam-3972	338	5	journal	journal	NOUN
ejpam-3972	338	6	.	.	PUNCT
ejpam-3972	339	1	3(1	3(1	NUM
ejpam-3972	339	2	)	)	PUNCT
ejpam-3972	339	3	,	,	PUNCT
ejpam-3972	339	4	11	11	NUM
ejpam-3972	339	5	-	-	SYM
ejpam-3972	339	6	13	13	NUM
ejpam-3972	339	7	,	,	PUNCT
ejpam-3972	339	8	(	(	PUNCT
ejpam-3972	339	9	2014	2014	NUM
ejpam-3972	339	10	)	)	PUNCT
ejpam-3972	339	11	.	.	PUNCT
ejpam-3972	340	1	https://doi.org/10.11648/j.pamj.20140301.13	https://doi.org/10.11648/j.pamj.20140301.13	X
ejpam-3972	341	1	[	[	X
ejpam-3972	341	2	9	9	NUM
ejpam-3972	341	3	]	]	SYM
ejpam-3972	341	4	goldwasser	goldwasser	NOUN
ejpam-3972	341	5	,	,	PUNCT
ejpam-3972	341	6	s.	s.	PROPN
ejpam-3972	341	7	,	,	PUNCT
ejpam-3972	341	8	micali	micali	PROPN
ejpam-3972	341	9	,	,	PUNCT
ejpam-3972	341	10	s.	s.	PROPN
ejpam-3972	341	11	,	,	PUNCT
ejpam-3972	341	12	rackoff	rackoff	NOUN
ejpam-3972	341	13	,	,	PUNCT
ejpam-3972	341	14	c.	c.	PROPN
ejpam-3972	341	15	:	:	PUNCT
ejpam-3972	341	16	the	the	DET
ejpam-3972	341	17	knowledge	knowledge	NOUN
ejpam-3972	341	18	complexity	complexity	NOUN
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ejpam-3972	341	20	interactive	interactive	ADJ
ejpam-3972	341	21	proof	proof	NOUN
ejpam-3972	341	22	systems	system	NOUN
ejpam-3972	341	23	.	.	PUNCT
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ejpam-3972	342	2	proc	proc	NOUN
ejpam-3972	342	3	.	.	PUNCT
ejpam-3972	343	1	17th	17th	ADJ
ejpam-3972	343	2	acm	acm	PROPN
ejpam-3972	343	3	symposium	symposium	NOUN
ejpam-3972	343	4	on	on	ADP
ejpam-3972	343	5	theory	theory	NOUN
ejpam-3972	343	6	of	of	ADP
ejpam-3972	343	7	computing	computing	NOUN
ejpam-3972	343	8	,	,	PUNCT
ejpam-3972	343	9	pp	pp	PROPN
ejpam-3972	343	10	291	291	NUM
ejpam-3972	343	11	-	-	SYM
ejpam-3972	343	12	304	304	NUM
ejpam-3972	343	13	,	,	PUNCT
ejpam-3972	343	14	(	(	PUNCT
ejpam-3972	343	15	1985	1985	NUM
ejpam-3972	343	16	)	)	PUNCT
ejpam-3972	343	17	.	.	PUNCT
ejpam-3972	344	1	[	[	X
ejpam-3972	344	2	10	10	NUM
ejpam-3972	344	3	]	]	X
ejpam-3972	344	4	diffie	diffie	PROPN
ejpam-3972	344	5	,	,	PUNCT
ejpam-3972	344	6	w.	w.	PROPN
ejpam-3972	344	7	,	,	PUNCT
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ejpam-3972	344	9	,	,	PUNCT
ejpam-3972	344	10	m.e	m.e	PROPN
ejpam-3972	344	11	.	.	PROPN
ejpam-3972	344	12	:	:	PUNCT
ejpam-3972	345	1	new	new	ADJ
ejpam-3972	345	2	directions	direction	NOUN
ejpam-3972	345	3	in	in	ADP
ejpam-3972	345	4	cryptography	cryptography	NOUN
ejpam-3972	345	5	.	.	PUNCT
ejpam-3972	346	1	ieee	ieee	PROPN
ejpam-3972	346	2	trans	trans	PROPN
ejpam-3972	346	3	.	.	PROPN
ejpam-3972	346	4	info	info	PROPN
ejpam-3972	346	5	.	.	PUNCT
ejpam-3972	347	1	theory	theory	NOUN
ejpam-3972	347	2	.	.	PUNCT
ejpam-3972	348	1	it-22(6	it-22(6	NUM
ejpam-3972	348	2	)	)	PUNCT
ejpam-3972	348	3	,	,	PUNCT
ejpam-3972	348	4	644	644	NUM
ejpam-3972	348	5	-	-	SYM
ejpam-3972	348	6	654	654	NUM
ejpam-3972	348	7	,	,	PUNCT
ejpam-3972	348	8	(	(	PUNCT
ejpam-3972	348	9	1976	1976	NUM
ejpam-3972	348	10	)	)	PUNCT
ejpam-3972	348	11	.	.	PUNCT
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ejpam-3972	349	2	11	11	NUM
ejpam-3972	349	3	]	]	SYM
ejpam-3972	349	4	merkle	merkle	NOUN
ejpam-3972	349	5	,	,	PUNCT
ejpam-3972	349	6	r.c	r.c	PROPN
ejpam-3972	349	7	.	.	PROPN
ejpam-3972	349	8	:	:	PUNCT
ejpam-3972	349	9	secure	secure	VERB
ejpam-3972	349	10	communication	communication	NOUN
ejpam-3972	349	11	over	over	ADP
ejpam-3972	349	12	insecure	insecure	ADJ
ejpam-3972	349	13	channels	channel	NOUN
ejpam-3972	349	14	.	.	PUNCT
ejpam-3972	350	1	communications	communication	NOUN
ejpam-3972	350	2	of	of	ADP
ejpam-3972	350	3	the	the	DET
ejpam-3972	350	4	acm	acm	PROPN
ejpam-3972	350	5	.	.	PUNCT
ejpam-3972	351	1	21(4	21(4	NUM
ejpam-3972	351	2	)	)	PUNCT
ejpam-3972	351	3	,	,	PUNCT
ejpam-3972	351	4	294	294	NUM
ejpam-3972	351	5	-	-	SYM
ejpam-3972	351	6	299	299	NUM
ejpam-3972	351	7	,	,	PUNCT
ejpam-3972	351	8	(	(	PUNCT
ejpam-3972	351	9	1978	1978	NUM
ejpam-3972	351	10	)	)	PUNCT
ejpam-3972	351	11	.	.	PUNCT
ejpam-3972	352	1	[	[	X
ejpam-3972	352	2	12	12	NUM
ejpam-3972	352	3	]	]	X
ejpam-3972	352	4	coppersmith	coppersmith	PROPN
ejpam-3972	352	5	,	,	PUNCT
ejpam-3972	352	6	d.	d.	PROPN
ejpam-3972	352	7	:	:	PUNCT
ejpam-3972	352	8	the	the	DET
ejpam-3972	352	9	data	data	NOUN
ejpam-3972	352	10	encryption	encryption	NOUN
ejpam-3972	352	11	standard	standard	NOUN
ejpam-3972	352	12	(	(	PUNCT
ejpam-3972	352	13	des	des	PROPN
ejpam-3972	352	14	)	)	PUNCT
ejpam-3972	352	15	and	and	CCONJ
ejpam-3972	352	16	its	its	PRON
ejpam-3972	352	17	strength	strength	NOUN
ejpam-3972	352	18	against	against	ADP
ejpam-3972	352	19	attacks	attack	NOUN
ejpam-3972	352	20	.	.	PUNCT
ejpam-3972	353	1	ibm	ibm	PROPN
ejpam-3972	353	2	journal	journal	PROPN
ejpam-3972	353	3	of	of	ADP
ejpam-3972	353	4	research	research	NOUN
ejpam-3972	353	5	and	and	CCONJ
ejpam-3972	353	6	development	development	NOUN
ejpam-3972	353	7	.	.	PUNCT
ejpam-3972	354	1	38	38	NUM
ejpam-3972	354	2	,	,	PUNCT
ejpam-3972	354	3	243	243	NUM
ejpam-3972	354	4	-	-	SYM
ejpam-3972	354	5	250	250	NUM
ejpam-3972	354	6	,	,	PUNCT
ejpam-3972	354	7	(	(	PUNCT
ejpam-3972	354	8	1994	1994	NUM
ejpam-3972	354	9	)	)	PUNCT
ejpam-3972	354	10	.	.	PUNCT
ejpam-3972	355	1	[	[	X
ejpam-3972	355	2	13	13	NUM
ejpam-3972	355	3	]	]	SYM
ejpam-3972	355	4	yonghong	yonghong	NOUN
ejpam-3972	355	5	,	,	PUNCT
ejpam-3972	355	6	l.	l.	PROPN
ejpam-3972	355	7	:	:	PUNCT
ejpam-3972	355	8	filtrations	filtration	NOUN
ejpam-3972	355	9	and	and	CCONJ
ejpam-3972	355	10	deductive	deductive	ADJ
ejpam-3972	355	11	systems	system	NOUN
ejpam-3972	355	12	in	in	ADP
ejpam-3972	355	13	bcl+	bcl+	PROPN
ejpam-3972	355	14	algebras	algebras	PROPN
ejpam-3972	355	15	.	.	PUNCT
ejpam-3972	356	1	british	british	PROPN
ejpam-3972	356	2	journal	journal	PROPN
ejpam-3972	356	3	of	of	ADP
ejpam-3972	356	4	mathematics	mathematics	PROPN
ejpam-3972	356	5	&	&	CCONJ
ejpam-3972	356	6	computer	computer	NOUN
ejpam-3972	356	7	science	science	NOUN
ejpam-3972	356	8	.	.	PUNCT
ejpam-3972	357	1	8(4	8(4	NUM
ejpam-3972	357	2	)	)	PUNCT
ejpam-3972	357	3	,	,	PUNCT
ejpam-3972	357	4	274	274	NUM
ejpam-3972	357	5	-	-	SYM
ejpam-3972	357	6	285	285	NUM
ejpam-3972	357	7	,	,	PUNCT
ejpam-3972	357	8	(	(	PUNCT
ejpam-3972	357	9	2015	2015	NUM
ejpam-3972	357	10	)	)	PUNCT
ejpam-3972	357	11	.	.	PUNCT
ejpam-3972	358	1	https://doi.org/10.9734/bjmcs/2015/15901	https://doi.org/10.9734/bjmcs/2015/15901	PRON
ejpam-3972	359	1	[	[	X
ejpam-3972	359	2	14	14	NUM
ejpam-3972	359	3	]	]	SYM
ejpam-3972	359	4	yonghong	yonghong	PROPN
ejpam-3972	359	5	,	,	PUNCT
ejpam-3972	359	6	l.	l.	PROPN
ejpam-3972	359	7	:	:	PUNCT
ejpam-3972	359	8	liu	liu	PROPN
ejpam-3972	359	9	’s	’s	PART
ejpam-3972	359	10	laws	law	NOUN
ejpam-3972	359	11	and	and	CCONJ
ejpam-3972	359	12	p	p	PROPN
ejpam-3972	359	13	-	-	PUNCT
ejpam-3972	359	14	bcl+	bcl+	PROPN
ejpam-3972	359	15	algebras	algebra	NOUN
ejpam-3972	359	16	.	.	PUNCT
ejpam-3972	360	1	international	international	ADJ
ejpam-3972	360	2	j.	j.	PROPN
ejpam-3972	360	3	of	of	ADP
ejpam-3972	360	4	pure	pure	PROPN
ejpam-3972	360	5	&	&	CCONJ
ejpam-3972	360	6	engg	engg	PROPN
ejpam-3972	360	7	.	.	PUNCT
ejpam-3972	361	1	mathematics	mathematic	NOUN
ejpam-3972	361	2	.	.	PUNCT
ejpam-3972	362	1	3(ii	3(ii	NUM
ejpam-3972	362	2	)	)	PUNCT
ejpam-3972	362	3	,	,	PUNCT
ejpam-3972	362	4	51	51	NUM
ejpam-3972	362	5	-	-	SYM
ejpam-3972	362	6	58	58	NUM
ejpam-3972	362	7	,	,	PUNCT
ejpam-3972	362	8	(	(	PUNCT
ejpam-3972	362	9	2015	2015	NUM
ejpam-3972	362	10	)	)	PUNCT
ejpam-3972	362	11	.	.	PUNCT
ejpam-3972	363	1	[	[	X
ejpam-3972	363	2	15	15	NUM
ejpam-3972	363	3	]	]	X
ejpam-3972	363	4	yonghong	yonghong	NOUN
ejpam-3972	363	5	,	,	PUNCT
ejpam-3972	363	6	l.	l.	PROPN
ejpam-3972	363	7	:	:	PUNCT
ejpam-3972	363	8	standard	standard	ADJ
ejpam-3972	363	9	ideals	ideal	NOUN
ejpam-3972	363	10	in	in	ADP
ejpam-3972	363	11	bcl+	bcl+	PROPN
ejpam-3972	363	12	algebras	algebras	PROPN
ejpam-3972	363	13	.	.	PUNCT
ejpam-3972	363	14	journal	journal	PROPN
ejpam-3972	363	15	of	of	ADP
ejpam-3972	363	16	mathematics	mathematics	PROPN
ejpam-3972	363	17	research	research	NOUN
ejpam-3972	363	18	.	.	PUNCT
ejpam-3972	364	1	8(2	8(2	NUM
ejpam-3972	364	2	)	)	PUNCT
ejpam-3972	364	3	,	,	PUNCT
ejpam-3972	364	4	37	37	NUM
ejpam-3972	364	5	-	-	SYM
ejpam-3972	364	6	44	44	NUM
ejpam-3972	364	7	,	,	PUNCT
ejpam-3972	364	8	(	(	PUNCT
ejpam-3972	364	9	2016	2016	NUM
ejpam-3972	364	10	)	)	PUNCT
ejpam-3972	364	11	.	.	PUNCT
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ejpam-3972	365	2	references	reference	NOUN
ejpam-3972	365	3	536	536	NUM
ejpam-3972	365	4	[	[	SYM
ejpam-3972	365	5	16	16	NUM
ejpam-3972	365	6	]	]	SYM
ejpam-3972	365	7	yonghong	yonghong	PROPN
ejpam-3972	365	8	,	,	PUNCT
ejpam-3972	365	9	l.	l.	PROPN
ejpam-3972	365	10	:	:	PUNCT
ejpam-3972	365	11	pa	pa	PROPN
ejpam-3972	365	12	-	-	PUNCT
ejpam-3972	365	13	bcl+	bcl+	PROPN
ejpam-3972	365	14	algebras	algebra	NOUN
ejpam-3972	365	15	and	and	CCONJ
ejpam-3972	365	16	groups	group	NOUN
ejpam-3972	365	17	,	,	PUNCT
ejpam-3972	365	18	applied	apply	VERB
ejpam-3972	365	19	mathematics	mathematics	PROPN
ejpam-3972	365	20	&	&	CCONJ
ejpam-3972	365	21	information	information	NOUN
ejpam-3972	365	22	sciences	sciences	PROPN
ejpam-3972	365	23	.	.	PUNCT
ejpam-3972	366	1	3(11	3(11	NUM
ejpam-3972	366	2	)	)	PUNCT
ejpam-3972	367	1	,	,	PUNCT
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ejpam-3972	367	3	-	-	SYM
ejpam-3972	367	4	897	897	NUM
ejpam-3972	367	5	,	,	PUNCT
ejpam-3972	367	6	(	(	PUNCT
ejpam-3972	367	7	2017	2017	NUM
ejpam-3972	367	8	)	)	PUNCT
ejpam-3972	367	9	.	.	PUNCT
ejpam-3972	368	1	https://doi.org/10.18576/amis/110329	https://doi.org/10.18576/amis/110329	PROPN