id	sid	tid	token	lemma	pos
ejpam-5888	1	1	european	european	PROPN
ejpam-5888	1	2	journal	journal	PROPN
ejpam-5888	1	3	of	of	ADP
ejpam-5888	1	4	pure	pure	ADJ
ejpam-5888	1	5	and	and	CCONJ
ejpam-5888	1	6	applied	applied	ADJ
ejpam-5888	1	7	mathematics	mathematic	NOUN
ejpam-5888	1	8	2025	2025	NUM
ejpam-5888	1	9	,	,	PUNCT
ejpam-5888	1	10	vol	vol	NOUN
ejpam-5888	1	11	.	.	PROPN
ejpam-5888	1	12	18	18	NUM
ejpam-5888	1	13	,	,	PUNCT
ejpam-5888	1	14	issue	issue	NOUN
ejpam-5888	1	15	3	3	NUM
ejpam-5888	1	16	,	,	PUNCT
ejpam-5888	1	17	article	article	NOUN
ejpam-5888	1	18	number	number	NOUN
ejpam-5888	1	19	5888	5888	NUM
ejpam-5888	1	20	issn	issn	VERB
ejpam-5888	1	21	1307	1307	NUM
ejpam-5888	1	22	-	-	SYM
ejpam-5888	1	23	5543	5543	NUM
ejpam-5888	1	24	–	–	PUNCT
ejpam-5888	1	25	ejpam.com	ejpam.com	X
ejpam-5888	1	26	published	publish	VERB
ejpam-5888	1	27	by	by	ADP
ejpam-5888	1	28	new	new	PROPN
ejpam-5888	1	29	york	york	PROPN
ejpam-5888	1	30	business	business	PROPN
ejpam-5888	1	31	global	global	PROPN
ejpam-5888	1	32	a	a	DET
ejpam-5888	1	33	key	key	ADJ
ejpam-5888	1	34	exchange	exchange	NOUN
ejpam-5888	1	35	protocol	protocol	NOUN
ejpam-5888	1	36	based	base	VERB
ejpam-5888	1	37	on	on	ADP
ejpam-5888	1	38	the	the	DET
ejpam-5888	1	39	twin	twin	ADJ
ejpam-5888	1	40	conjugacy	conjugacy	ADJ
ejpam-5888	1	41	search	search	NOUN
ejpam-5888	1	42	problem	problem	NOUN
ejpam-5888	1	43	over	over	ADP
ejpam-5888	1	44	tropical	tropical	ADJ
ejpam-5888	1	45	algebra	algebra	NOUN
ejpam-5888	1	46	kashifa	kashifa	PROPN
ejpam-5888	1	47	begum	begum	VERB
ejpam-5888	1	48	a.1	a.1	NOUN
ejpam-5888	1	49	,	,	PUNCT
ejpam-5888	1	50	v.	v.	ADP
ejpam-5888	1	51	muthukumaran1	muthukumaran1	PROPN
ejpam-5888	1	52	,	,	PUNCT
ejpam-5888	1	53	v.	v.	ADP
ejpam-5888	1	54	govindan2	govindan2	NOUN
ejpam-5888	1	55	,	,	PUNCT
ejpam-5888	1	56	haewon	haewon	VERB
ejpam-5888	1	57	byeon3,∗	byeon3,∗	NOUN
ejpam-5888	1	58	1	1	NUM
ejpam-5888	1	59	department	department	NOUN
ejpam-5888	1	60	of	of	ADP
ejpam-5888	1	61	mathematics	mathematic	NOUN
ejpam-5888	1	62	,	,	PUNCT
ejpam-5888	1	63	college	college	NOUN
ejpam-5888	1	64	of	of	ADP
ejpam-5888	1	65	engineering	engineering	NOUN
ejpam-5888	1	66	and	and	CCONJ
ejpam-5888	1	67	technology	technology	NOUN
ejpam-5888	1	68	,	,	PUNCT
ejpam-5888	1	69	faculty	faculty	NOUN
ejpam-5888	1	70	of	of	ADP
ejpam-5888	1	71	engineering	engineering	NOUN
ejpam-5888	1	72	and	and	CCONJ
ejpam-5888	1	73	technology	technology	NOUN
ejpam-5888	1	74	,	,	PUNCT
ejpam-5888	1	75	srm	srm	PROPN
ejpam-5888	1	76	institute	institute	PROPN
ejpam-5888	1	77	of	of	ADP
ejpam-5888	1	78	science	science	NOUN
ejpam-5888	1	79	and	and	CCONJ
ejpam-5888	1	80	technology	technology	NOUN
ejpam-5888	1	81	,	,	PUNCT
ejpam-5888	1	82	kattankulathur	kattankulathur	PROPN
ejpam-5888	1	83	603203	603203	NUM
ejpam-5888	1	84	,	,	PUNCT
ejpam-5888	1	85	chengalpattu	chengalpattu	ADV
ejpam-5888	1	86	,	,	PUNCT
ejpam-5888	1	87	tamil	tamil	PROPN
ejpam-5888	1	88	nadu	nadu	PROPN
ejpam-5888	1	89	,	,	PUNCT
ejpam-5888	1	90	india	india	PROPN
ejpam-5888	1	91	2	2	NUM
ejpam-5888	1	92	department	department	NOUN
ejpam-5888	1	93	of	of	ADP
ejpam-5888	1	94	mathematics	mathematic	NOUN
ejpam-5888	1	95	,	,	PUNCT
ejpam-5888	1	96	hindustan	hindustan	PROPN
ejpam-5888	1	97	institute	institute	PROPN
ejpam-5888	1	98	of	of	ADP
ejpam-5888	1	99	technology	technology	PROPN
ejpam-5888	1	100	and	and	CCONJ
ejpam-5888	1	101	science	science	NOUN
ejpam-5888	1	102	,	,	PUNCT
ejpam-5888	1	103	chennai	chennai	PROPN
ejpam-5888	1	104	603103	603103	NUM
ejpam-5888	1	105	,	,	PUNCT
ejpam-5888	1	106	tamil	tamil	PROPN
ejpam-5888	1	107	nadu	nadu	PROPN
ejpam-5888	1	108	,	,	PUNCT
ejpam-5888	1	109	india	india	PROPN
ejpam-5888	1	110	3	3	NUM
ejpam-5888	1	111	convergence	convergence	PROPN
ejpam-5888	1	112	department	department	PROPN
ejpam-5888	1	113	,	,	PUNCT
ejpam-5888	1	114	korea	korea	PROPN
ejpam-5888	1	115	university	university	PROPN
ejpam-5888	1	116	of	of	ADP
ejpam-5888	1	117	technology	technology	NOUN
ejpam-5888	1	118	and	and	CCONJ
ejpam-5888	1	119	education	education	NOUN
ejpam-5888	1	120	,	,	PUNCT
ejpam-5888	1	121	cheonan	cheonan	PROPN
ejpam-5888	1	122	,	,	PUNCT
ejpam-5888	1	123	south	south	PROPN
ejpam-5888	1	124	korea	korea	PROPN
ejpam-5888	1	125	abstract	abstract	NOUN
ejpam-5888	1	126	.	.	PUNCT
ejpam-5888	2	1	in	in	ADP
ejpam-5888	2	2	public	public	ADJ
ejpam-5888	2	3	key	key	ADJ
ejpam-5888	2	4	cryptography	cryptography	NOUN
ejpam-5888	2	5	,	,	PUNCT
ejpam-5888	2	6	the	the	DET
ejpam-5888	2	7	security	security	NOUN
ejpam-5888	2	8	of	of	ADP
ejpam-5888	2	9	the	the	DET
ejpam-5888	2	10	data	datum	NOUN
ejpam-5888	2	11	leans	lean	VERB
ejpam-5888	2	12	on	on	ADP
ejpam-5888	2	13	the	the	DET
ejpam-5888	2	14	hardness	hardness	NOUN
ejpam-5888	2	15	of	of	ADP
ejpam-5888	2	16	solving	solve	VERB
ejpam-5888	2	17	some	some	DET
ejpam-5888	2	18	mathematical	mathematical	ADJ
ejpam-5888	2	19	problems	problem	NOUN
ejpam-5888	2	20	over	over	ADP
ejpam-5888	2	21	algebraic	algebraic	ADJ
ejpam-5888	2	22	structures	structure	NOUN
ejpam-5888	2	23	,	,	PUNCT
ejpam-5888	2	24	such	such	ADJ
ejpam-5888	2	25	as	as	ADP
ejpam-5888	2	26	groups	group	NOUN
ejpam-5888	2	27	,	,	PUNCT
ejpam-5888	2	28	rings	ring	NOUN
ejpam-5888	2	29	,	,	PUNCT
ejpam-5888	2	30	etc	etc	X
ejpam-5888	2	31	.	.	X
ejpam-5888	3	1	the	the	DET
ejpam-5888	3	2	first	first	ADJ
ejpam-5888	3	3	published	publish	VERB
ejpam-5888	3	4	key	key	ADJ
ejpam-5888	3	5	exchange	exchange	NOUN
ejpam-5888	3	6	protocol	protocol	NOUN
ejpam-5888	3	7	is	be	AUX
ejpam-5888	3	8	by	by	ADP
ejpam-5888	3	9	diffie	diffie	PROPN
ejpam-5888	3	10	and	and	CCONJ
ejpam-5888	3	11	hellman	hellman	NOUN
ejpam-5888	3	12	in	in	ADP
ejpam-5888	3	13	1976	1976	NUM
ejpam-5888	3	14	,	,	PUNCT
ejpam-5888	3	15	whose	whose	DET
ejpam-5888	3	16	security	security	NOUN
ejpam-5888	3	17	hinges	hinge	VERB
ejpam-5888	3	18	on	on	ADP
ejpam-5888	3	19	the	the	DET
ejpam-5888	3	20	challenges	challenge	NOUN
ejpam-5888	3	21	in	in	ADP
ejpam-5888	3	22	solving	solve	VERB
ejpam-5888	3	23	the	the	DET
ejpam-5888	3	24	discrete	discrete	ADJ
ejpam-5888	3	25	logarithm	logarithm	NOUN
ejpam-5888	3	26	problem	problem	NOUN
ejpam-5888	3	27	(	(	PUNCT
ejpam-5888	3	28	dlp	dlp	NOUN
ejpam-5888	3	29	)	)	PUNCT
ejpam-5888	3	30	over	over	ADP
ejpam-5888	3	31	any	any	DET
ejpam-5888	3	32	finite	finite	ADJ
ejpam-5888	3	33	field	field	NOUN
ejpam-5888	3	34	.	.	PUNCT
ejpam-5888	4	1	in	in	ADP
ejpam-5888	4	2	this	this	DET
ejpam-5888	4	3	research	research	NOUN
ejpam-5888	4	4	article	article	NOUN
ejpam-5888	4	5	,	,	PUNCT
ejpam-5888	4	6	we	we	PRON
ejpam-5888	4	7	present	present	VERB
ejpam-5888	4	8	a	a	DET
ejpam-5888	4	9	key	key	ADJ
ejpam-5888	4	10	exchange	exchange	NOUN
ejpam-5888	4	11	protocol	protocol	NOUN
ejpam-5888	4	12	based	base	VERB
ejpam-5888	4	13	on	on	ADP
ejpam-5888	4	14	the	the	DET
ejpam-5888	4	15	twin	twin	ADJ
ejpam-5888	4	16	conjugacy	conjugacy	ADJ
ejpam-5888	4	17	search	search	NOUN
ejpam-5888	4	18	problem	problem	NOUN
ejpam-5888	4	19	(	(	PUNCT
ejpam-5888	4	20	tcsp	tcsp	PROPN
ejpam-5888	4	21	)	)	PUNCT
ejpam-5888	4	22	,	,	PUNCT
ejpam-5888	4	23	a	a	DET
ejpam-5888	4	24	variant	variant	NOUN
ejpam-5888	4	25	of	of	ADP
ejpam-5888	4	26	the	the	DET
ejpam-5888	4	27	well	well	ADV
ejpam-5888	4	28	-	-	PUNCT
ejpam-5888	4	29	known	know	VERB
ejpam-5888	4	30	conjugacy	conjugacy	ADJ
ejpam-5888	4	31	search	search	NOUN
ejpam-5888	4	32	problem	problem	NOUN
ejpam-5888	4	33	(	(	PUNCT
ejpam-5888	4	34	csp	csp	PROPN
ejpam-5888	4	35	)	)	PUNCT
ejpam-5888	4	36	,	,	PUNCT
ejpam-5888	4	37	and	and	CCONJ
ejpam-5888	4	38	tropical	tropical	ADJ
ejpam-5888	4	39	algebra	algebra	NOUN
ejpam-5888	4	40	as	as	ADP
ejpam-5888	4	41	a	a	DET
ejpam-5888	4	42	platform	platform	NOUN
ejpam-5888	4	43	for	for	ADP
ejpam-5888	4	44	the	the	DET
ejpam-5888	4	45	tcsp	tcsp	NOUN
ejpam-5888	4	46	.	.	PUNCT
ejpam-5888	5	1	we	we	PRON
ejpam-5888	5	2	have	have	AUX
ejpam-5888	5	3	provided	provide	VERB
ejpam-5888	5	4	two	two	NUM
ejpam-5888	5	5	variants	variant	NOUN
ejpam-5888	5	6	of	of	ADP
ejpam-5888	5	7	the	the	DET
ejpam-5888	5	8	key	key	ADJ
ejpam-5888	5	9	exchange	exchange	NOUN
ejpam-5888	5	10	protocol	protocol	NOUN
ejpam-5888	5	11	and	and	CCONJ
ejpam-5888	5	12	also	also	ADV
ejpam-5888	5	13	provided	provide	VERB
ejpam-5888	5	14	a	a	DET
ejpam-5888	5	15	toy	toy	NOUN
ejpam-5888	5	16	example	example	NOUN
ejpam-5888	5	17	.	.	PUNCT
ejpam-5888	6	1	the	the	DET
ejpam-5888	6	2	chosen	choose	VERB
ejpam-5888	6	3	platform	platform	NOUN
ejpam-5888	6	4	,	,	PUNCT
ejpam-5888	6	5	tropical	tropical	ADJ
ejpam-5888	6	6	algebra	algebra	NOUN
ejpam-5888	6	7	,	,	PUNCT
ejpam-5888	6	8	is	be	AUX
ejpam-5888	6	9	a	a	DET
ejpam-5888	6	10	new	new	ADJ
ejpam-5888	6	11	approach	approach	NOUN
ejpam-5888	6	12	and	and	CCONJ
ejpam-5888	6	13	is	be	AUX
ejpam-5888	6	14	easy	easy	ADJ
ejpam-5888	6	15	to	to	PART
ejpam-5888	6	16	implement	implement	VERB
ejpam-5888	6	17	and	and	CCONJ
ejpam-5888	6	18	not	not	PART
ejpam-5888	6	19	computationally	computationally	ADV
ejpam-5888	6	20	hard	hard	ADJ
ejpam-5888	6	21	as	as	ADP
ejpam-5888	6	22	with	with	ADP
ejpam-5888	6	23	other	other	ADJ
ejpam-5888	6	24	non	non	ADJ
ejpam-5888	6	25	-	-	ADJ
ejpam-5888	6	26	abelian	abelian	ADJ
ejpam-5888	6	27	groups	group	NOUN
ejpam-5888	6	28	as	as	ADP
ejpam-5888	6	29	a	a	DET
ejpam-5888	6	30	platform	platform	NOUN
ejpam-5888	6	31	,	,	PUNCT
ejpam-5888	6	32	since	since	SCONJ
ejpam-5888	6	33	one	one	NUM
ejpam-5888	6	34	does	do	AUX
ejpam-5888	6	35	n’t	not	PART
ejpam-5888	6	36	have	have	VERB
ejpam-5888	6	37	to	to	PART
ejpam-5888	6	38	perform	perform	VERB
ejpam-5888	6	39	any	any	DET
ejpam-5888	6	40	complex	complex	ADJ
ejpam-5888	6	41	multiplication	multiplication	NOUN
ejpam-5888	6	42	or	or	CCONJ
ejpam-5888	6	43	addition	addition	NOUN
ejpam-5888	6	44	.	.	PUNCT
ejpam-5888	7	1	the	the	DET
ejpam-5888	7	2	security	security	NOUN
ejpam-5888	7	3	and	and	CCONJ
ejpam-5888	7	4	complexity	complexity	NOUN
ejpam-5888	7	5	analysis	analysis	NOUN
ejpam-5888	7	6	of	of	ADP
ejpam-5888	7	7	the	the	DET
ejpam-5888	7	8	protocol	protocol	NOUN
ejpam-5888	7	9	have	have	AUX
ejpam-5888	7	10	also	also	ADV
ejpam-5888	7	11	been	be	AUX
ejpam-5888	7	12	explored	explore	VERB
ejpam-5888	7	13	.	.	PUNCT
ejpam-5888	8	1	2020	2020	NUM
ejpam-5888	8	2	mathematics	mathematics	PROPN
ejpam-5888	8	3	subject	subject	NOUN
ejpam-5888	8	4	classifications	classification	NOUN
ejpam-5888	8	5	:	:	PUNCT
ejpam-5888	8	6	14g50	14g50	NUM
ejpam-5888	8	7	,	,	PUNCT
ejpam-5888	8	8	14t10	14t10	NUM
ejpam-5888	8	9	,	,	PUNCT
ejpam-5888	8	10	15a80	15a80	NUM
ejpam-5888	8	11	,	,	PUNCT
ejpam-5888	8	12	15b33	15b33	NUM
ejpam-5888	8	13	key	key	ADJ
ejpam-5888	8	14	words	word	NOUN
ejpam-5888	8	15	and	and	CCONJ
ejpam-5888	8	16	phrases	phrase	NOUN
ejpam-5888	8	17	:	:	PUNCT
ejpam-5888	8	18	conjugacy	conjugacy	PROPN
ejpam-5888	8	19	search	search	NOUN
ejpam-5888	8	20	problem	problem	NOUN
ejpam-5888	8	21	,	,	PUNCT
ejpam-5888	8	22	twin	twin	ADJ
ejpam-5888	8	23	conjugacy	conjugacy	ADJ
ejpam-5888	8	24	search	search	NOUN
ejpam-5888	8	25	problem	problem	NOUN
ejpam-5888	8	26	,	,	PUNCT
ejpam-5888	8	27	tropical	tropical	ADJ
ejpam-5888	8	28	algebra	algebra	NOUN
ejpam-5888	8	29	,	,	PUNCT
ejpam-5888	8	30	public	public	ADJ
ejpam-5888	8	31	key	key	ADJ
ejpam-5888	8	32	exchange	exchange	NOUN
ejpam-5888	8	33	1	1	NUM
ejpam-5888	8	34	.	.	PUNCT
ejpam-5888	9	1	introduction	introduction	NOUN
ejpam-5888	9	2	in	in	ADP
ejpam-5888	9	3	the	the	DET
ejpam-5888	9	4	zone	zone	NOUN
ejpam-5888	9	5	of	of	ADP
ejpam-5888	9	6	modern	modern	ADJ
ejpam-5888	9	7	cryptography	cryptography	NOUN
ejpam-5888	9	8	,	,	PUNCT
ejpam-5888	9	9	the	the	DET
ejpam-5888	9	10	security	security	NOUN
ejpam-5888	9	11	of	of	ADP
ejpam-5888	9	12	information	information	NOUN
ejpam-5888	9	13	,	,	PUNCT
ejpam-5888	9	14	its	its	PRON
ejpam-5888	9	15	transmission	transmission	NOUN
ejpam-5888	9	16	and	and	CCONJ
ejpam-5888	9	17	storage	storage	NOUN
ejpam-5888	9	18	is	be	AUX
ejpam-5888	9	19	predominant	predominant	ADJ
ejpam-5888	9	20	.	.	PUNCT
ejpam-5888	10	1	the	the	DET
ejpam-5888	10	2	ability	ability	NOUN
ejpam-5888	10	3	to	to	PART
ejpam-5888	10	4	shield	shield	VERB
ejpam-5888	10	5	sensitive	sensitive	ADJ
ejpam-5888	10	6	data	datum	NOUN
ejpam-5888	10	7	in	in	ADP
ejpam-5888	10	8	an	an	DET
ejpam-5888	10	9	age	age	NOUN
ejpam-5888	10	10	of	of	ADP
ejpam-5888	10	11	immanent	immanent	ADJ
ejpam-5888	10	12	digital	digital	ADJ
ejpam-5888	10	13	communication	communication	NOUN
ejpam-5888	10	14	and	and	CCONJ
ejpam-5888	10	15	interconnected	interconnected	ADJ
ejpam-5888	10	16	systems	system	NOUN
ejpam-5888	10	17	is	be	AUX
ejpam-5888	10	18	a	a	DET
ejpam-5888	10	19	primitive	primitive	ADJ
ejpam-5888	10	20	concern	concern	NOUN
ejpam-5888	10	21	.	.	PUNCT
ejpam-5888	11	1	cryptographic	cryptographic	ADJ
ejpam-5888	11	2	algorithms	algorithm	NOUN
ejpam-5888	11	3	serve	serve	VERB
ejpam-5888	11	4	as	as	ADP
ejpam-5888	11	5	the	the	DET
ejpam-5888	11	6	cutting	cutting	NOUN
ejpam-5888	11	7	edge	edge	NOUN
ejpam-5888	11	8	in	in	ADP
ejpam-5888	11	9	this	this	DET
ejpam-5888	11	10	venture	venture	NOUN
ejpam-5888	11	11	,	,	PUNCT
ejpam-5888	11	12	with	with	ADP
ejpam-5888	11	13	one	one	NUM
ejpam-5888	11	14	of	of	ADP
ejpam-5888	11	15	the	the	DET
ejpam-5888	11	16	main	main	ADJ
ejpam-5888	11	17	stay	stay	NOUN
ejpam-5888	11	18	being	be	AUX
ejpam-5888	11	19	the	the	DET
ejpam-5888	11	20	∗corresponding	∗corresponde	VERB
ejpam-5888	11	21	author	author	NOUN
ejpam-5888	11	22	.	.	PUNCT
ejpam-5888	12	1	doi	doi	NOUN
ejpam-5888	12	2	:	:	PUNCT
ejpam-5888	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.5888	https://doi.org/10.29020/nybg.ejpam.v18i3.5888	NOUN
ejpam-5888	12	4	email	email	NOUN
ejpam-5888	12	5	addresses	address	NOUN
ejpam-5888	12	6	:	:	PUNCT
ejpam-5888	12	7	kb5928@srmist.edu.in	kb5928@srmist.edu.in	X
ejpam-5888	12	8	(	(	PUNCT
ejpam-5888	12	9	kashifa	kashifa	PROPN
ejpam-5888	12	10	begum	begum	PROPN
ejpam-5888	12	11	a.	a.	PROPN
ejpam-5888	12	12	)	)	PUNCT
ejpam-5888	12	13	,	,	PUNCT
ejpam-5888	12	14	muthu.v2404@gmail.com	muthu.v2404@gmail.com	X
ejpam-5888	12	15	(	(	PUNCT
ejpam-5888	12	16	v.	v.	ADP
ejpam-5888	12	17	muthukumaran	muthukumaran	ADJ
ejpam-5888	12	18	)	)	PUNCT
ejpam-5888	12	19	,	,	PUNCT
ejpam-5888	12	20	govindoviya@gmail.com	govindoviya@gmail.com	X
ejpam-5888	12	21	(	(	PUNCT
ejpam-5888	12	22	v.	v.	ADP
ejpam-5888	12	23	govindan	govindan	PROPN
ejpam-5888	12	24	)	)	PUNCT
ejpam-5888	12	25	,	,	PUNCT
ejpam-5888	12	26	bhwpuma@naver.com	bhwpuma@naver.com	X
ejpam-5888	12	27	(	(	PUNCT
ejpam-5888	12	28	haewon	haewon	PROPN
ejpam-5888	12	29	byeon	byeon	PROPN
ejpam-5888	12	30	)	)	PUNCT
ejpam-5888	12	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5888	13	1	1	1	NUM
ejpam-5888	13	2	copyright	copyright	NOUN
ejpam-5888	13	3	:	:	PUNCT
ejpam-5888	13	4	©	©	PROPN
ejpam-5888	13	5	2025	2025	NUM
ejpam-5888	13	6	the	the	DET
ejpam-5888	13	7	author(s	author(s	NOUN
ejpam-5888	13	8	)	)	PUNCT
ejpam-5888	13	9	.	.	PUNCT
ejpam-5888	14	1	(	(	PUNCT
ejpam-5888	14	2	cc	cc	NOUN
ejpam-5888	14	3	by	by	ADP
ejpam-5888	14	4	-	-	PUNCT
ejpam-5888	14	5	nc	nc	PROPN
ejpam-5888	14	6	4.0	4.0	NUM
ejpam-5888	14	7	)	)	PUNCT
ejpam-5888	14	8	kashifa	kashifa	PROPN
ejpam-5888	14	9	begum	begum	VERB
ejpam-5888	14	10	a.	a.	NOUN
ejpam-5888	14	11	et	et	PROPN
ejpam-5888	14	12	.	.	PUNCT
ejpam-5888	15	1	al	al	PROPN
ejpam-5888	15	2	/	/	PUNCT
ejpam-5888	15	3	eur	eur	PROPN
ejpam-5888	15	4	.	.	PUNCT
ejpam-5888	16	1	j.	j.	PROPN
ejpam-5888	16	2	pure	pure	PROPN
ejpam-5888	16	3	appl	appl	PROPN
ejpam-5888	16	4	.	.	PROPN
ejpam-5888	16	5	math	math	PROPN
ejpam-5888	16	6	,	,	PUNCT
ejpam-5888	16	7	18	18	NUM
ejpam-5888	16	8	(	(	PUNCT
ejpam-5888	16	9	3	3	NUM
ejpam-5888	16	10	)	)	PUNCT
ejpam-5888	16	11	(	(	PUNCT
ejpam-5888	16	12	2025	2025	NUM
ejpam-5888	16	13	)	)	PUNCT
ejpam-5888	16	14	,	,	PUNCT
ejpam-5888	16	15	5888	5888	NUM
ejpam-5888	16	16	2	2	NUM
ejpam-5888	16	17	of	of	ADP
ejpam-5888	16	18	16	16	NUM
ejpam-5888	16	19	discrete	discrete	ADJ
ejpam-5888	16	20	logarithm	logarithm	NOUN
ejpam-5888	16	21	problem	problem	NOUN
ejpam-5888	16	22	(	(	PUNCT
ejpam-5888	16	23	dlp	dlp	NOUN
ejpam-5888	16	24	)	)	PUNCT
ejpam-5888	16	25	.	.	PUNCT
ejpam-5888	17	1	the	the	DET
ejpam-5888	17	2	dlp	dlp	NOUN
ejpam-5888	17	3	has	have	AUX
ejpam-5888	17	4	portrayed	portray	VERB
ejpam-5888	17	5	a	a	DET
ejpam-5888	17	6	core	core	ADJ
ejpam-5888	17	7	role	role	NOUN
ejpam-5888	17	8	in	in	ADP
ejpam-5888	17	9	the	the	DET
ejpam-5888	17	10	development	development	NOUN
ejpam-5888	17	11	of	of	ADP
ejpam-5888	17	12	secure	secure	ADJ
ejpam-5888	17	13	communication	communication	NOUN
ejpam-5888	17	14	protocol	protocol	NOUN
ejpam-5888	17	15	,	,	PUNCT
ejpam-5888	17	16	digital	digital	ADJ
ejpam-5888	17	17	signatures	signature	NOUN
ejpam-5888	17	18	,	,	PUNCT
ejpam-5888	17	19	and	and	CCONJ
ejpam-5888	17	20	public	public	ADJ
ejpam-5888	17	21	key	key	ADJ
ejpam-5888	17	22	cryptosystems	cryptosystem	NOUN
ejpam-5888	17	23	.	.	PUNCT
ejpam-5888	18	1	its	its	PRON
ejpam-5888	18	2	resilience	resilience	NOUN
ejpam-5888	18	3	to	to	ADP
ejpam-5888	18	4	attacks	attack	NOUN
ejpam-5888	18	5	,	,	PUNCT
ejpam-5888	18	6	at	at	ADP
ejpam-5888	18	7	that	that	DET
ejpam-5888	18	8	time	time	NOUN
ejpam-5888	18	9	,	,	PUNCT
ejpam-5888	18	10	formed	form	VERB
ejpam-5888	18	11	the	the	DET
ejpam-5888	18	12	basis	basis	NOUN
ejpam-5888	18	13	for	for	ADP
ejpam-5888	18	14	the	the	DET
ejpam-5888	18	15	security	security	NOUN
ejpam-5888	18	16	of	of	ADP
ejpam-5888	18	17	widely	widely	ADV
ejpam-5888	18	18	used	use	VERB
ejpam-5888	18	19	schemes	scheme	NOUN
ejpam-5888	18	20	,	,	PUNCT
ejpam-5888	18	21	such	such	ADJ
ejpam-5888	18	22	as	as	ADP
ejpam-5888	18	23	the	the	DET
ejpam-5888	18	24	diffie	diffie	PROPN
ejpam-5888	18	25	–	–	PUNCT
ejpam-5888	18	26	hellman	hellman	PROPN
ejpam-5888	18	27	key	key	PROPN
ejpam-5888	18	28	exchange	exchange	NOUN
ejpam-5888	18	29	,	,	PUNCT
ejpam-5888	18	30	elgamal	elgamal	ADJ
ejpam-5888	18	31	encryption	encryption	NOUN
ejpam-5888	18	32	,	,	PUNCT
ejpam-5888	18	33	and	and	CCONJ
ejpam-5888	18	34	the	the	DET
ejpam-5888	18	35	digital	digital	ADJ
ejpam-5888	18	36	signature	signature	NOUN
ejpam-5888	18	37	algorithm	algorithm	NOUN
ejpam-5888	18	38	(	(	PUNCT
ejpam-5888	18	39	dsa	dsa	X
ejpam-5888	18	40	)	)	PUNCT
ejpam-5888	19	1	[	[	X
ejpam-5888	19	2	1–4	1–4	NOUN
ejpam-5888	19	3	]	]	X
ejpam-5888	19	4	.	.	PUNCT
ejpam-5888	20	1	the	the	DET
ejpam-5888	20	2	discrete	discrete	ADJ
ejpam-5888	20	3	logarithm	logarithm	NOUN
ejpam-5888	20	4	problem	problem	NOUN
ejpam-5888	20	5	(	(	PUNCT
ejpam-5888	20	6	dlp	dlp	NOUN
ejpam-5888	20	7	)	)	PUNCT
ejpam-5888	20	8	for	for	ADP
ejpam-5888	20	9	a	a	DET
ejpam-5888	20	10	group	group	NOUN
ejpam-5888	20	11	g	g	NOUN
ejpam-5888	20	12	is	be	AUX
ejpam-5888	20	13	to	to	PART
ejpam-5888	20	14	find	find	VERB
ejpam-5888	20	15	at	at	ADV
ejpam-5888	20	16	least	least	ADV
ejpam-5888	20	17	one	one	NUM
ejpam-5888	20	18	k	k	NOUN
ejpam-5888	20	19	∈	∈	PROPN
ejpam-5888	20	20	g	g	PROPN
ejpam-5888	20	21	∋	∋	NOUN
ejpam-5888	20	22	,	,	PUNCT
ejpam-5888	20	23	for	for	ADP
ejpam-5888	20	24	given	give	VERB
ejpam-5888	20	25	any	any	DET
ejpam-5888	20	26	two	two	NUM
ejpam-5888	20	27	elements	element	NOUN
ejpam-5888	20	28	a	a	PRON
ejpam-5888	20	29	,	,	PUNCT
ejpam-5888	20	30	b	b	PROPN
ejpam-5888	20	31	∈	∈	PROPN
ejpam-5888	20	32	g	g	PROPN
ejpam-5888	20	33	,	,	PUNCT
ejpam-5888	20	34	b	b	PROPN
ejpam-5888	20	35	=	=	SYM
ejpam-5888	20	36	ak	ak	PROPN
ejpam-5888	20	37	.	.	PROPN
ejpam-5888	20	38	one	one	NUM
ejpam-5888	20	39	of	of	ADP
ejpam-5888	20	40	the	the	DET
ejpam-5888	20	41	popular	popular	ADJ
ejpam-5888	20	42	choices	choice	NOUN
ejpam-5888	20	43	of	of	ADP
ejpam-5888	20	44	g	g	NOUN
ejpam-5888	20	45	for	for	ADP
ejpam-5888	20	46	the	the	DET
ejpam-5888	20	47	dlp	dlp	NOUN
ejpam-5888	20	48	are	be	AUX
ejpam-5888	20	49	cyclic	cyclic	ADJ
ejpam-5888	20	50	groups	group	NOUN
ejpam-5888	20	51	z∗	z∗	PROPN
ejpam-5888	20	52	p	p	NOUN
ejpam-5888	20	53	,	,	PUNCT
ejpam-5888	20	54	where	where	SCONJ
ejpam-5888	20	55	p	p	NOUN
ejpam-5888	20	56	is	be	AUX
ejpam-5888	20	57	any	any	DET
ejpam-5888	20	58	prime	prime	NOUN
ejpam-5888	20	59	.	.	PUNCT
ejpam-5888	21	1	the	the	DET
ejpam-5888	21	2	recent	recent	ADJ
ejpam-5888	21	3	advancements	advancement	NOUN
ejpam-5888	21	4	and	and	CCONJ
ejpam-5888	21	5	evolution	evolution	NOUN
ejpam-5888	21	6	towards	towards	ADP
ejpam-5888	21	7	quantum	quantum	NOUN
ejpam-5888	21	8	computing	computing	NOUN
ejpam-5888	21	9	made	make	VERB
ejpam-5888	21	10	it	it	PRON
ejpam-5888	21	11	easy	easy	ADJ
ejpam-5888	21	12	to	to	PART
ejpam-5888	21	13	solve	solve	VERB
ejpam-5888	21	14	the	the	DET
ejpam-5888	21	15	dlp	dlp	NOUN
ejpam-5888	21	16	.	.	PUNCT
ejpam-5888	22	1	hence	hence	ADV
ejpam-5888	22	2	the	the	DET
ejpam-5888	22	3	search	search	NOUN
ejpam-5888	22	4	for	for	ADP
ejpam-5888	22	5	a	a	DET
ejpam-5888	22	6	new	new	ADJ
ejpam-5888	22	7	hard	hard	ADJ
ejpam-5888	22	8	problem	problem	NOUN
ejpam-5888	22	9	for	for	ADP
ejpam-5888	22	10	key	key	ADJ
ejpam-5888	22	11	exchange	exchange	NOUN
ejpam-5888	22	12	protocols	protocol	NOUN
ejpam-5888	22	13	led	lead	VERB
ejpam-5888	22	14	us	we	PRON
ejpam-5888	22	15	to	to	ADP
ejpam-5888	22	16	the	the	DET
ejpam-5888	22	17	conjugacy	conjugacy	PROPN
ejpam-5888	22	18	search	search	NOUN
ejpam-5888	22	19	problem	problem	NOUN
ejpam-5888	22	20	(	(	PUNCT
ejpam-5888	22	21	csp	csp	PROPN
ejpam-5888	22	22	)	)	PUNCT
ejpam-5888	22	23	,	,	PUNCT
ejpam-5888	22	24	one	one	NUM
ejpam-5888	22	25	of	of	ADP
ejpam-5888	22	26	the	the	DET
ejpam-5888	22	27	flair	flair	ADJ
ejpam-5888	22	28	generalizations	generalization	NOUN
ejpam-5888	22	29	of	of	ADP
ejpam-5888	22	30	the	the	DET
ejpam-5888	22	31	dlp	dlp	NOUN
ejpam-5888	22	32	.	.	PUNCT
ejpam-5888	23	1	the	the	DET
ejpam-5888	23	2	combination	combination	NOUN
ejpam-5888	23	3	of	of	ADP
ejpam-5888	23	4	the	the	DET
ejpam-5888	23	5	dlp	dlp	PROPN
ejpam-5888	23	6	and	and	CCONJ
ejpam-5888	23	7	csp	csp	PROPN
ejpam-5888	23	8	is	be	AUX
ejpam-5888	23	9	given	give	VERB
ejpam-5888	23	10	in	in	ADP
ejpam-5888	23	11	[	[	X
ejpam-5888	23	12	5	5	NUM
ejpam-5888	23	13	]	]	PUNCT
ejpam-5888	23	14	.	.	PUNCT
ejpam-5888	24	1	the	the	DET
ejpam-5888	24	2	conjugacy	conjugacy	ADJ
ejpam-5888	24	3	decision	decision	NOUN
ejpam-5888	24	4	problem	problem	NOUN
ejpam-5888	24	5	(	(	PUNCT
ejpam-5888	24	6	cdp	cdp	X
ejpam-5888	24	7	)	)	PUNCT
ejpam-5888	24	8	for	for	ADP
ejpam-5888	24	9	a	a	DET
ejpam-5888	24	10	group	group	NOUN
ejpam-5888	24	11	g	g	NOUN
ejpam-5888	24	12	is	be	AUX
ejpam-5888	24	13	a	a	DET
ejpam-5888	24	14	decision	decision	NOUN
ejpam-5888	24	15	making	make	VERB
ejpam-5888	24	16	problem	problem	NOUN
ejpam-5888	24	17	of	of	ADP
ejpam-5888	24	18	determining	determine	VERB
ejpam-5888	24	19	,	,	PUNCT
ejpam-5888	24	20	given	give	VERB
ejpam-5888	24	21	any	any	DET
ejpam-5888	24	22	two	two	NUM
ejpam-5888	24	23	elements	element	NOUN
ejpam-5888	24	24	a	a	PRON
ejpam-5888	24	25	,	,	PUNCT
ejpam-5888	24	26	b	b	X
ejpam-5888	24	27	∈	∈	PROPN
ejpam-5888	24	28	g	g	NOUN
ejpam-5888	24	29	,	,	PUNCT
ejpam-5888	24	30	whether	whether	SCONJ
ejpam-5888	24	31	or	or	CCONJ
ejpam-5888	24	32	not	not	PART
ejpam-5888	24	33	they	they	PRON
ejpam-5888	24	34	are	be	AUX
ejpam-5888	24	35	conjugate	conjugate	ADJ
ejpam-5888	24	36	in	in	ADP
ejpam-5888	24	37	g	g	NOUN
ejpam-5888	24	38	,	,	PUNCT
ejpam-5888	24	39	i.e.	i.e.	X
ejpam-5888	24	40	,	,	PUNCT
ejpam-5888	24	41	if	if	SCONJ
ejpam-5888	24	42	∃	∃	PROPN
ejpam-5888	24	43	an	an	DET
ejpam-5888	24	44	element	element	NOUN
ejpam-5888	24	45	g	g	PROPN
ejpam-5888	24	46	∈	∈	PROPN
ejpam-5888	24	47	g	g	PROPN
ejpam-5888	24	48	∋	∋	NOUN
ejpam-5888	24	49	g−1ag	g−1ag	PROPN
ejpam-5888	24	50	=	=	PROPN
ejpam-5888	24	51	b.	b.	PROPN
ejpam-5888	24	52	the	the	DET
ejpam-5888	24	53	conjugacy	conjugacy	PROPN
ejpam-5888	24	54	search	search	NOUN
ejpam-5888	24	55	problem	problem	NOUN
ejpam-5888	24	56	(	(	PUNCT
ejpam-5888	24	57	csp	csp	PROPN
ejpam-5888	24	58	)	)	PUNCT
ejpam-5888	24	59	for	for	ADP
ejpam-5888	24	60	a	a	DET
ejpam-5888	24	61	group	group	NOUN
ejpam-5888	24	62	g	g	PROPN
ejpam-5888	24	63	requires	require	VERB
ejpam-5888	24	64	us	we	PRON
ejpam-5888	24	65	to	to	PART
ejpam-5888	24	66	search	search	VERB
ejpam-5888	24	67	,	,	PUNCT
ejpam-5888	24	68	for	for	ADP
ejpam-5888	24	69	any	any	DET
ejpam-5888	24	70	two	two	NUM
ejpam-5888	24	71	given	give	VERB
ejpam-5888	24	72	conjugate	conjugate	ADJ
ejpam-5888	24	73	elements	element	NOUN
ejpam-5888	24	74	a	a	PRON
ejpam-5888	24	75	,	,	PUNCT
ejpam-5888	24	76	b	b	PROPN
ejpam-5888	24	77	∈	∈	PROPN
ejpam-5888	24	78	g	g	PROPN
ejpam-5888	24	79	,	,	PUNCT
ejpam-5888	24	80	a	a	DET
ejpam-5888	24	81	conjugating	conjugating	ADJ
ejpam-5888	24	82	element	element	NOUN
ejpam-5888	24	83	g	g	PROPN
ejpam-5888	24	84	∈	∈	PROPN
ejpam-5888	24	85	g	g	PROPN
ejpam-5888	24	86	∋	∋	NOUN
ejpam-5888	24	87	g−1ag	g−1ag	NOUN
ejpam-5888	24	88	=	=	PROPN
ejpam-5888	24	89	b.	b.	PROPN
ejpam-5888	25	1	the	the	DET
ejpam-5888	25	2	(	(	PUNCT
ejpam-5888	25	3	presumed	presume	VERB
ejpam-5888	25	4	)	)	PUNCT
ejpam-5888	25	5	computational	computational	ADJ
ejpam-5888	25	6	difficulty	difficulty	NOUN
ejpam-5888	25	7	of	of	ADP
ejpam-5888	25	8	this	this	DET
ejpam-5888	25	9	problem	problem	NOUN
ejpam-5888	25	10	in	in	ADP
ejpam-5888	25	11	some	some	DET
ejpam-5888	25	12	groups	group	NOUN
ejpam-5888	25	13	(	(	PUNCT
ejpam-5888	25	14	namely	namely	ADV
ejpam-5888	25	15	in	in	ADP
ejpam-5888	25	16	braid	braid	ADJ
ejpam-5888	25	17	groups	group	NOUN
ejpam-5888	25	18	,	,	PUNCT
ejpam-5888	25	19	garside	garside	NOUN
ejpam-5888	25	20	groups	group	NOUN
ejpam-5888	25	21	,	,	PUNCT
ejpam-5888	25	22	non	non	ADJ
ejpam-5888	25	23	-	-	ADJ
ejpam-5888	25	24	commutative	commutative	ADJ
ejpam-5888	25	25	semi	semi	ADJ
ejpam-5888	25	26	groups	group	NOUN
ejpam-5888	25	27	)	)	PUNCT
ejpam-5888	25	28	has	have	AUX
ejpam-5888	25	29	been	be	AUX
ejpam-5888	25	30	used	use	VERB
ejpam-5888	25	31	in	in	ADP
ejpam-5888	25	32	several	several	ADJ
ejpam-5888	25	33	group	group	NOUN
ejpam-5888	25	34	based	base	VERB
ejpam-5888	25	35	public	public	ADJ
ejpam-5888	25	36	key	key	ADJ
ejpam-5888	25	37	protocols	protocol	NOUN
ejpam-5888	26	1	[	[	X
ejpam-5888	26	2	6–8	6–8	X
ejpam-5888	26	3	]	]	X
ejpam-5888	26	4	.	.	PUNCT
ejpam-5888	27	1	though	though	SCONJ
ejpam-5888	27	2	csp	csp	PROPN
ejpam-5888	27	3	on	on	ADP
ejpam-5888	27	4	some	some	DET
ejpam-5888	27	5	particular	particular	ADJ
ejpam-5888	27	6	platforms	platform	NOUN
ejpam-5888	27	7	(	(	PUNCT
ejpam-5888	27	8	the	the	DET
ejpam-5888	27	9	solutions	solution	NOUN
ejpam-5888	27	10	to	to	ADP
ejpam-5888	27	11	the	the	DET
ejpam-5888	27	12	csp	csp	PROPN
ejpam-5888	27	13	in	in	ADP
ejpam-5888	27	14	polycyclic	polycyclic	NOUN
ejpam-5888	27	15	groups	group	NOUN
ejpam-5888	27	16	,	,	PUNCT
ejpam-5888	27	17	p	p	NOUN
ejpam-5888	27	18	-	-	PUNCT
ejpam-5888	27	19	groups	group	NOUN
ejpam-5888	27	20	,	,	PUNCT
ejpam-5888	27	21	and	and	CCONJ
ejpam-5888	27	22	matrix	matrix	NOUN
ejpam-5888	27	23	groups	group	NOUN
ejpam-5888	27	24	are	be	AUX
ejpam-5888	27	25	given	give	VERB
ejpam-5888	27	26	in	in	ADP
ejpam-5888	27	27	[	[	PUNCT
ejpam-5888	27	28	9	9	NUM
ejpam-5888	27	29	]	]	PUNCT
ejpam-5888	27	30	)	)	PUNCT
ejpam-5888	27	31	are	be	AUX
ejpam-5888	27	32	vulnerable	vulnerable	ADJ
ejpam-5888	27	33	to	to	ADP
ejpam-5888	27	34	security	security	NOUN
ejpam-5888	27	35	,	,	PUNCT
ejpam-5888	27	36	they	they	PRON
ejpam-5888	27	37	still	still	ADV
ejpam-5888	27	38	have	have	VERB
ejpam-5888	27	39	the	the	DET
ejpam-5888	27	40	value	value	NOUN
ejpam-5888	27	41	of	of	ADP
ejpam-5888	27	42	reference	reference	NOUN
ejpam-5888	27	43	and	and	CCONJ
ejpam-5888	27	44	the	the	DET
ejpam-5888	27	45	search	search	NOUN
ejpam-5888	27	46	for	for	ADP
ejpam-5888	27	47	a	a	DET
ejpam-5888	27	48	suitable	suitable	ADJ
ejpam-5888	27	49	platform	platform	NOUN
ejpam-5888	27	50	is	be	AUX
ejpam-5888	27	51	an	an	DET
ejpam-5888	27	52	active	active	ADJ
ejpam-5888	27	53	area	area	NOUN
ejpam-5888	27	54	of	of	ADP
ejpam-5888	27	55	research	research	NOUN
ejpam-5888	27	56	.	.	PUNCT
ejpam-5888	28	1	despite	despite	SCONJ
ejpam-5888	28	2	that	that	PRON
ejpam-5888	28	3	the	the	DET
ejpam-5888	28	4	csp	csp	PROPN
ejpam-5888	28	5	and	and	CCONJ
ejpam-5888	28	6	its	its	PRON
ejpam-5888	28	7	variant	variant	ADJ
ejpam-5888	28	8	versions	version	NOUN
ejpam-5888	28	9	(	(	PUNCT
ejpam-5888	28	10	namely	namely	ADV
ejpam-5888	28	11	,	,	PUNCT
ejpam-5888	28	12	the	the	DET
ejpam-5888	28	13	twin	twin	ADJ
ejpam-5888	28	14	conjugacy	conjugacy	ADJ
ejpam-5888	28	15	search	search	NOUN
ejpam-5888	28	16	problem	problem	NOUN
ejpam-5888	28	17	(	(	PUNCT
ejpam-5888	28	18	tcsp	tcsp	PROPN
ejpam-5888	28	19	)	)	PUNCT
ejpam-5888	28	20	and	and	CCONJ
ejpam-5888	28	21	the	the	DET
ejpam-5888	28	22	double	double	ADJ
ejpam-5888	28	23	conjugacy	conjugacy	ADJ
ejpam-5888	28	24	search	search	NOUN
ejpam-5888	28	25	problem	problem	NOUN
ejpam-5888	28	26	(	(	PUNCT
ejpam-5888	28	27	dcsp	dcsp	PROPN
ejpam-5888	28	28	)	)	PUNCT
ejpam-5888	29	1	[	[	X
ejpam-5888	29	2	10	10	NUM
ejpam-5888	29	3	,	,	PUNCT
ejpam-5888	29	4	11	11	NUM
ejpam-5888	29	5	]	]	PUNCT
ejpam-5888	29	6	)	)	PUNCT
ejpam-5888	29	7	have	have	VERB
ejpam-5888	29	8	a	a	DET
ejpam-5888	29	9	sufficient	sufficient	ADJ
ejpam-5888	29	10	security	security	NOUN
ejpam-5888	29	11	level	level	NOUN
ejpam-5888	29	12	and	and	CCONJ
ejpam-5888	29	13	play	play	VERB
ejpam-5888	29	14	a	a	DET
ejpam-5888	29	15	significant	significant	ADJ
ejpam-5888	29	16	role	role	NOUN
ejpam-5888	29	17	on	on	ADP
ejpam-5888	29	18	non	non	ADJ
ejpam-5888	29	19	-	-	ADJ
ejpam-5888	29	20	abelian	abelian	ADJ
ejpam-5888	29	21	group	group	NOUN
ejpam-5888	29	22	based	base	VERB
ejpam-5888	29	23	public	public	ADJ
ejpam-5888	29	24	key	key	ADJ
ejpam-5888	29	25	cryptography	cryptography	NOUN
ejpam-5888	29	26	.	.	PUNCT
ejpam-5888	30	1	nevertheless	nevertheless	ADV
ejpam-5888	30	2	,	,	PUNCT
ejpam-5888	30	3	the	the	DET
ejpam-5888	30	4	efficiency	efficiency	NOUN
ejpam-5888	30	5	and	and	CCONJ
ejpam-5888	30	6	security	security	NOUN
ejpam-5888	30	7	of	of	ADP
ejpam-5888	30	8	cryptographic	cryptographic	ADJ
ejpam-5888	30	9	systems	system	NOUN
ejpam-5888	30	10	does	do	AUX
ejpam-5888	30	11	not	not	PART
ejpam-5888	30	12	depend	depend	VERB
ejpam-5888	30	13	only	only	ADV
ejpam-5888	30	14	on	on	ADP
ejpam-5888	30	15	the	the	DET
ejpam-5888	30	16	type	type	NOUN
ejpam-5888	30	17	of	of	ADP
ejpam-5888	30	18	algorithm	algorithm	NOUN
ejpam-5888	30	19	,	,	PUNCT
ejpam-5888	30	20	but	but	CCONJ
ejpam-5888	30	21	also	also	ADV
ejpam-5888	30	22	on	on	ADP
ejpam-5888	30	23	the	the	DET
ejpam-5888	30	24	choice	choice	NOUN
ejpam-5888	30	25	of	of	ADP
ejpam-5888	30	26	the	the	DET
ejpam-5888	30	27	platform	platform	NOUN
ejpam-5888	30	28	.	.	PUNCT
ejpam-5888	31	1	one	one	NUM
ejpam-5888	31	2	such	such	ADJ
ejpam-5888	31	3	unprobed	unprobed	ADJ
ejpam-5888	31	4	platform	platform	NOUN
ejpam-5888	31	5	is	be	AUX
ejpam-5888	31	6	tropical	tropical	ADJ
ejpam-5888	31	7	algebra	algebra	NOUN
ejpam-5888	31	8	,	,	PUNCT
ejpam-5888	31	9	a	a	DET
ejpam-5888	31	10	relatively	relatively	ADV
ejpam-5888	31	11	recent	recent	ADJ
ejpam-5888	31	12	branch	branch	NOUN
ejpam-5888	31	13	of	of	ADP
ejpam-5888	31	14	mathematics	mathematic	NOUN
ejpam-5888	31	15	which	which	PRON
ejpam-5888	31	16	has	have	AUX
ejpam-5888	31	17	emerged	emerge	VERB
ejpam-5888	31	18	as	as	ADP
ejpam-5888	31	19	a	a	DET
ejpam-5888	31	20	cogent	cogent	ADJ
ejpam-5888	31	21	tool	tool	NOUN
ejpam-5888	31	22	with	with	ADP
ejpam-5888	31	23	applications	application	NOUN
ejpam-5888	31	24	extending	extend	VERB
ejpam-5888	31	25	over	over	ADP
ejpam-5888	31	26	diverse	diverse	ADJ
ejpam-5888	31	27	fields	field	NOUN
ejpam-5888	31	28	,	,	PUNCT
ejpam-5888	31	29	from	from	ADP
ejpam-5888	31	30	optimization	optimization	NOUN
ejpam-5888	31	31	,	,	PUNCT
ejpam-5888	31	32	computer	computer	NOUN
ejpam-5888	31	33	science	science	NOUN
ejpam-5888	31	34	to	to	ADP
ejpam-5888	31	35	biology	biology	NOUN
ejpam-5888	31	36	and	and	CCONJ
ejpam-5888	31	37	economics	economic	NOUN
ejpam-5888	31	38	.	.	PUNCT
ejpam-5888	32	1	the	the	DET
ejpam-5888	32	2	phrase	phrase	NOUN
ejpam-5888	32	3	tropical	tropical	NOUN
ejpam-5888	32	4	was	be	AUX
ejpam-5888	32	5	originated	originate	VERB
ejpam-5888	32	6	by	by	ADP
ejpam-5888	32	7	french	french	ADJ
ejpam-5888	32	8	mathematicians	mathematician	NOUN
ejpam-5888	32	9	in	in	ADP
ejpam-5888	32	10	admiration	admiration	NOUN
ejpam-5888	32	11	of	of	ADP
ejpam-5888	32	12	the	the	DET
ejpam-5888	32	13	hungarian	hungarian	ADJ
ejpam-5888	32	14	–	–	PUNCT
ejpam-5888	32	15	born	bear	VERB
ejpam-5888	32	16	brazilian	brazilian	ADJ
ejpam-5888	32	17	computer	computer	NOUN
ejpam-5888	32	18	scientist	scientist	NOUN
ejpam-5888	32	19	imre	imre	PROPN
ejpam-5888	32	20	simon	simon	PROPN
ejpam-5888	32	21	.	.	PUNCT
ejpam-5888	33	1	for	for	ADP
ejpam-5888	33	2	introductory	introductory	ADJ
ejpam-5888	33	3	enlightenment	enlightenment	NOUN
ejpam-5888	33	4	on	on	ADP
ejpam-5888	33	5	tropical	tropical	ADJ
ejpam-5888	33	6	geometry	geometry	NOUN
ejpam-5888	33	7	one	one	PRON
ejpam-5888	33	8	can	can	AUX
ejpam-5888	33	9	refer	refer	VERB
ejpam-5888	33	10	[	[	X
ejpam-5888	33	11	12	12	NUM
ejpam-5888	33	12	,	,	PUNCT
ejpam-5888	33	13	13	13	NUM
ejpam-5888	33	14	]	]	PUNCT
ejpam-5888	33	15	.	.	PUNCT
ejpam-5888	34	1	kashifa	kashifa	PROPN
ejpam-5888	34	2	begum	begum	VERB
ejpam-5888	34	3	a.	a.	NOUN
ejpam-5888	34	4	et	et	PROPN
ejpam-5888	34	5	.	.	PUNCT
ejpam-5888	35	1	al	al	PROPN
ejpam-5888	35	2	/	/	PUNCT
ejpam-5888	35	3	eur	eur	PROPN
ejpam-5888	35	4	.	.	PUNCT
ejpam-5888	36	1	j.	j.	PROPN
ejpam-5888	36	2	pure	pure	PROPN
ejpam-5888	36	3	appl	appl	PROPN
ejpam-5888	36	4	.	.	PROPN
ejpam-5888	36	5	math	math	PROPN
ejpam-5888	36	6	,	,	PUNCT
ejpam-5888	36	7	18	18	NUM
ejpam-5888	36	8	(	(	PUNCT
ejpam-5888	36	9	3	3	NUM
ejpam-5888	36	10	)	)	PUNCT
ejpam-5888	36	11	(	(	PUNCT
ejpam-5888	36	12	2025	2025	NUM
ejpam-5888	36	13	)	)	PUNCT
ejpam-5888	36	14	,	,	PUNCT
ejpam-5888	36	15	5888	5888	NUM
ejpam-5888	36	16	3	3	NUM
ejpam-5888	36	17	of	of	ADP
ejpam-5888	36	18	16	16	NUM
ejpam-5888	36	19	the	the	DET
ejpam-5888	36	20	substance	substance	NOUN
ejpam-5888	36	21	of	of	ADP
ejpam-5888	36	22	tropical	tropical	ADJ
ejpam-5888	36	23	algebra	algebra	NOUN
ejpam-5888	36	24	lies	lie	VERB
ejpam-5888	36	25	in	in	ADP
ejpam-5888	36	26	its	its	PRON
ejpam-5888	36	27	competence	competence	NOUN
ejpam-5888	36	28	to	to	PART
ejpam-5888	36	29	simplify	simplify	VERB
ejpam-5888	36	30	complex	complex	ADJ
ejpam-5888	36	31	problems	problem	NOUN
ejpam-5888	36	32	by	by	ADP
ejpam-5888	36	33	rebuilding	rebuild	VERB
ejpam-5888	36	34	them	they	PRON
ejpam-5888	36	35	into	into	ADP
ejpam-5888	36	36	a	a	DET
ejpam-5888	36	37	more	more	ADV
ejpam-5888	36	38	viable	viable	ADJ
ejpam-5888	36	39	algebraic	algebraic	ADJ
ejpam-5888	36	40	structure	structure	NOUN
ejpam-5888	36	41	,	,	PUNCT
ejpam-5888	36	42	by	by	ADP
ejpam-5888	36	43	replacing	replace	VERB
ejpam-5888	36	44	the	the	DET
ejpam-5888	36	45	traditional	traditional	ADJ
ejpam-5888	36	46	addition	addition	NOUN
ejpam-5888	36	47	with	with	ADP
ejpam-5888	36	48	the	the	DET
ejpam-5888	36	49	maximum	maximum	ADJ
ejpam-5888	36	50	(	(	PUNCT
ejpam-5888	36	51	or	or	CCONJ
ejpam-5888	36	52	minimum	minimum	ADJ
ejpam-5888	36	53	)	)	PUNCT
ejpam-5888	36	54	operation	operation	NOUN
ejpam-5888	36	55	and	and	CCONJ
ejpam-5888	36	56	the	the	DET
ejpam-5888	36	57	traditional	traditional	ADJ
ejpam-5888	36	58	multiplication	multiplication	NOUN
ejpam-5888	36	59	with	with	ADP
ejpam-5888	36	60	the	the	DET
ejpam-5888	36	61	traditional	traditional	ADJ
ejpam-5888	36	62	addition	addition	NOUN
ejpam-5888	36	63	operation	operation	NOUN
ejpam-5888	36	64	.	.	PUNCT
ejpam-5888	37	1	for	for	ADP
ejpam-5888	37	2	contemporary	contemporary	ADJ
ejpam-5888	37	3	evolution	evolution	NOUN
ejpam-5888	37	4	in	in	ADP
ejpam-5888	37	5	tropical	tropical	ADJ
ejpam-5888	37	6	algebra	algebra	NOUN
ejpam-5888	37	7	one	one	PRON
ejpam-5888	37	8	can	can	AUX
ejpam-5888	37	9	refer	refer	VERB
ejpam-5888	37	10	[	[	X
ejpam-5888	37	11	14–18	14–18	NUM
ejpam-5888	37	12	]	]	X
ejpam-5888	37	13	.	.	PUNCT
ejpam-5888	38	1	thus	thus	ADV
ejpam-5888	38	2	we	we	PRON
ejpam-5888	38	3	have	have	AUX
ejpam-5888	38	4	chosen	choose	VERB
ejpam-5888	38	5	tropical	tropical	ADJ
ejpam-5888	38	6	algebra	algebra	NOUN
ejpam-5888	38	7	as	as	ADP
ejpam-5888	38	8	a	a	DET
ejpam-5888	38	9	platform	platform	NOUN
ejpam-5888	38	10	for	for	ADP
ejpam-5888	38	11	the	the	DET
ejpam-5888	38	12	tcsp	tcsp	NOUN
ejpam-5888	38	13	based	base	VERB
ejpam-5888	38	14	key	key	ADJ
ejpam-5888	38	15	exchange	exchange	NOUN
ejpam-5888	38	16	protocol	protocol	NOUN
ejpam-5888	38	17	,	,	PUNCT
ejpam-5888	38	18	and	and	CCONJ
ejpam-5888	38	19	also	also	ADV
ejpam-5888	38	20	elaborated	elaborate	VERB
ejpam-5888	38	21	on	on	ADP
ejpam-5888	38	22	the	the	DET
ejpam-5888	38	23	resilience	resilience	NOUN
ejpam-5888	38	24	of	of	ADP
ejpam-5888	38	25	the	the	DET
ejpam-5888	38	26	protocol	protocol	NOUN
ejpam-5888	38	27	to	to	ADP
ejpam-5888	38	28	various	various	ADJ
ejpam-5888	38	29	attacks	attack	NOUN
ejpam-5888	38	30	including	include	VERB
ejpam-5888	38	31	brute	brute	ADJ
ejpam-5888	38	32	force	force	NOUN
ejpam-5888	38	33	attack	attack	NOUN
ejpam-5888	38	34	and	and	CCONJ
ejpam-5888	38	35	ku	ku	PROPN
ejpam-5888	38	36	attack	attack	NOUN
ejpam-5888	38	37	.	.	PUNCT
ejpam-5888	39	1	the	the	DET
ejpam-5888	39	2	article	article	NOUN
ejpam-5888	39	3	is	be	AUX
ejpam-5888	39	4	arranged	arrange	VERB
ejpam-5888	39	5	as	as	SCONJ
ejpam-5888	39	6	follows	follow	VERB
ejpam-5888	39	7	:	:	PUNCT
ejpam-5888	39	8	in	in	ADP
ejpam-5888	39	9	section	section	NOUN
ejpam-5888	39	10	2	2	NUM
ejpam-5888	39	11	,	,	PUNCT
ejpam-5888	39	12	the	the	DET
ejpam-5888	39	13	preliminaries	preliminary	NOUN
ejpam-5888	39	14	required	require	VERB
ejpam-5888	39	15	are	be	AUX
ejpam-5888	39	16	given	give	VERB
ejpam-5888	39	17	.	.	PUNCT
ejpam-5888	40	1	the	the	DET
ejpam-5888	40	2	tcsp	tcsp	NOUN
ejpam-5888	40	3	over	over	ADP
ejpam-5888	40	4	tropical	tropical	ADJ
ejpam-5888	40	5	algebra	algebra	NOUN
ejpam-5888	40	6	is	be	AUX
ejpam-5888	40	7	given	give	VERB
ejpam-5888	40	8	in	in	ADP
ejpam-5888	40	9	section	section	NOUN
ejpam-5888	40	10	3	3	NUM
ejpam-5888	40	11	.	.	PUNCT
ejpam-5888	41	1	the	the	DET
ejpam-5888	41	2	two	two	NUM
ejpam-5888	41	3	versions	version	NOUN
ejpam-5888	41	4	of	of	ADP
ejpam-5888	41	5	the	the	DET
ejpam-5888	41	6	protocol	protocol	NOUN
ejpam-5888	41	7	proposed	propose	VERB
ejpam-5888	41	8	is	be	AUX
ejpam-5888	41	9	given	give	VERB
ejpam-5888	41	10	in	in	ADP
ejpam-5888	41	11	section	section	NOUN
ejpam-5888	41	12	4	4	NUM
ejpam-5888	41	13	.	.	PUNCT
ejpam-5888	42	1	a	a	DET
ejpam-5888	42	2	toy	toy	NOUN
ejpam-5888	42	3	example	example	NOUN
ejpam-5888	42	4	of	of	ADP
ejpam-5888	42	5	the	the	DET
ejpam-5888	42	6	first	first	ADJ
ejpam-5888	42	7	protocol	protocol	NOUN
ejpam-5888	42	8	is	be	AUX
ejpam-5888	42	9	given	give	VERB
ejpam-5888	42	10	in	in	ADP
ejpam-5888	42	11	section	section	NOUN
ejpam-5888	42	12	5	5	NUM
ejpam-5888	42	13	.	.	PUNCT
ejpam-5888	43	1	in	in	ADP
ejpam-5888	43	2	section	section	NOUN
ejpam-5888	43	3	6	6	NUM
ejpam-5888	43	4	,	,	PUNCT
ejpam-5888	43	5	the	the	DET
ejpam-5888	43	6	security	security	NOUN
ejpam-5888	43	7	and	and	CCONJ
ejpam-5888	43	8	complexity	complexity	NOUN
ejpam-5888	43	9	analysis	analysis	NOUN
ejpam-5888	43	10	of	of	ADP
ejpam-5888	43	11	the	the	DET
ejpam-5888	43	12	protocol	protocol	NOUN
ejpam-5888	43	13	is	be	AUX
ejpam-5888	43	14	given	give	VERB
ejpam-5888	43	15	and	and	CCONJ
ejpam-5888	43	16	the	the	DET
ejpam-5888	43	17	article	article	NOUN
ejpam-5888	43	18	is	be	AUX
ejpam-5888	43	19	concluded	conclude	VERB
ejpam-5888	43	20	in	in	ADP
ejpam-5888	43	21	section	section	NOUN
ejpam-5888	43	22	7	7	NUM
ejpam-5888	43	23	.	.	NOUN
ejpam-5888	43	24	2	2	NUM
ejpam-5888	43	25	.	.	NUM
ejpam-5888	43	26	preliminaries	preliminary	NOUN
ejpam-5888	43	27	2.1	2.1	NUM
ejpam-5888	43	28	.	.	PUNCT
ejpam-5888	44	1	the	the	DET
ejpam-5888	44	2	twin	twin	ADJ
ejpam-5888	44	3	conjugacy	conjugacy	PROPN
ejpam-5888	44	4	search	search	NOUN
ejpam-5888	44	5	problem	problem	NOUN
ejpam-5888	44	6	the	the	DET
ejpam-5888	44	7	tcsp	tcsp	NOUN
ejpam-5888	44	8	is	be	AUX
ejpam-5888	44	9	defined	define	VERB
ejpam-5888	44	10	in	in	ADP
ejpam-5888	44	11	[	[	X
ejpam-5888	44	12	10	10	NUM
ejpam-5888	44	13	]	]	PUNCT
ejpam-5888	44	14	as	as	SCONJ
ejpam-5888	44	15	follows	follow	VERB
ejpam-5888	44	16	:	:	PUNCT
ejpam-5888	44	17	the	the	DET
ejpam-5888	44	18	twin	twin	ADJ
ejpam-5888	44	19	conjugacy	conjugacy	ADJ
ejpam-5888	44	20	search	search	NOUN
ejpam-5888	44	21	problem	problem	NOUN
ejpam-5888	44	22	(	(	PUNCT
ejpam-5888	44	23	tcsp	tcsp	PROPN
ejpam-5888	44	24	)	)	PUNCT
ejpam-5888	44	25	for	for	ADP
ejpam-5888	44	26	a	a	DET
ejpam-5888	44	27	braid	braid	NOUN
ejpam-5888	44	28	group	group	NOUN
ejpam-5888	44	29	bn	bn	PROPN
ejpam-5888	44	30	is	be	AUX
ejpam-5888	44	31	to	to	PART
ejpam-5888	44	32	find	find	VERB
ejpam-5888	44	33	x1	x1	PROPN
ejpam-5888	44	34	,	,	PUNCT
ejpam-5888	44	35	x2	x2	PROPN
ejpam-5888	44	36	∈	∈	PROPN
ejpam-5888	44	37	bn	bn	PROPN
ejpam-5888	44	38	,	,	PUNCT
ejpam-5888	44	39	for	for	ADP
ejpam-5888	44	40	given	give	VERB
ejpam-5888	44	41	g	g	PROPN
ejpam-5888	44	42	,	,	PUNCT
ejpam-5888	44	43	x1	x1	PROPN
ejpam-5888	44	44	,	,	PUNCT
ejpam-5888	44	45	x2	x2	PROPN
ejpam-5888	44	46	∈	∈	PROPN
ejpam-5888	44	47	bn,∋	bn,∋	NOUN
ejpam-5888	44	48	x1	x1	PROPN
ejpam-5888	45	1	=	=	SYM
ejpam-5888	45	2	x1gx	x1gx	PUNCT
ejpam-5888	45	3	−1	−1	NOUN
ejpam-5888	45	4	1	1	NUM
ejpam-5888	45	5	,	,	PUNCT
ejpam-5888	45	6	x2	x2	PROPN
ejpam-5888	45	7	=	=	X
ejpam-5888	45	8	x2gx	x2gx	PUNCT
ejpam-5888	45	9	−1	−1	NOUN
ejpam-5888	45	10	2	2	NUM
ejpam-5888	45	11	.	.	PUNCT
ejpam-5888	46	1	2.2	2.2	NUM
ejpam-5888	46	2	.	.	PUNCT
ejpam-5888	47	1	chen	chen	PROPN
ejpam-5888	47	2	and	and	CCONJ
ejpam-5888	47	3	you	you	PRON
ejpam-5888	47	4	’s	’	VERB
ejpam-5888	47	5	key	key	ADJ
ejpam-5888	47	6	exchange	exchange	NOUN
ejpam-5888	47	7	protocol	protocol	NOUN
ejpam-5888	47	8	there	there	PRON
ejpam-5888	47	9	are	be	VERB
ejpam-5888	47	10	two	two	NUM
ejpam-5888	47	11	versions	version	NOUN
ejpam-5888	47	12	of	of	ADP
ejpam-5888	47	13	the	the	DET
ejpam-5888	47	14	key	key	ADJ
ejpam-5888	47	15	exchange	exchange	NOUN
ejpam-5888	47	16	protocol	protocol	NOUN
ejpam-5888	47	17	based	base	VERB
ejpam-5888	47	18	on	on	ADP
ejpam-5888	47	19	the	the	DET
ejpam-5888	47	20	tcsp	tcsp	NOUN
ejpam-5888	47	21	over	over	ADP
ejpam-5888	47	22	braid	braid	PROPN
ejpam-5888	47	23	group	group	NOUN
ejpam-5888	47	24	in	in	ADP
ejpam-5888	47	25	[	[	X
ejpam-5888	47	26	10	10	NUM
ejpam-5888	47	27	]	]	PUNCT
ejpam-5888	47	28	and	and	CCONJ
ejpam-5888	47	29	we	we	PRON
ejpam-5888	47	30	reiterate	reiterate	VERB
ejpam-5888	47	31	both	both	CCONJ
ejpam-5888	47	32	the	the	DET
ejpam-5888	47	33	versions	version	NOUN
ejpam-5888	47	34	here	here	ADV
ejpam-5888	47	35	.	.	PUNCT
ejpam-5888	48	1	suppose	suppose	VERB
ejpam-5888	48	2	that	that	SCONJ
ejpam-5888	48	3	the	the	DET
ejpam-5888	48	4	two	two	NUM
ejpam-5888	48	5	people	people	NOUN
ejpam-5888	48	6	who	who	PRON
ejpam-5888	48	7	need	need	VERB
ejpam-5888	48	8	to	to	PART
ejpam-5888	48	9	communicate	communicate	VERB
ejpam-5888	48	10	are	be	AUX
ejpam-5888	48	11	alice	alice	PROPN
ejpam-5888	48	12	and	and	CCONJ
ejpam-5888	48	13	bob	bob	PROPN
ejpam-5888	48	14	.	.	PUNCT
ejpam-5888	49	1	consider	consider	VERB
ejpam-5888	49	2	h	h	NOUN
ejpam-5888	49	3	:	:	PUNCT
ejpam-5888	49	4	bl+r	bl+r	PROPN
ejpam-5888	49	5	→	→	SYM
ejpam-5888	49	6	{	{	PUNCT
ejpam-5888	49	7	0	0	NUM
ejpam-5888	49	8	,	,	PUNCT
ejpam-5888	49	9	1}l(k	1}l(k	NUM
ejpam-5888	49	10	)	)	PUNCT
ejpam-5888	49	11	,	,	PUNCT
ejpam-5888	49	12	where	where	SCONJ
ejpam-5888	49	13	h	h	NOUN
ejpam-5888	49	14	is	be	AUX
ejpam-5888	49	15	a	a	DET
ejpam-5888	49	16	hash	hash	NOUN
ejpam-5888	49	17	function	function	NOUN
ejpam-5888	49	18	,	,	PUNCT
ejpam-5888	49	19	bl+r	bl+r	PROPN
ejpam-5888	49	20	is	be	AUX
ejpam-5888	49	21	a	a	DET
ejpam-5888	49	22	braid	braid	NOUN
ejpam-5888	49	23	group	group	NOUN
ejpam-5888	49	24	,	,	PUNCT
ejpam-5888	49	25	and	and	CCONJ
ejpam-5888	49	26	l(k	l(k	PROPN
ejpam-5888	49	27	)	)	PUNCT
ejpam-5888	49	28	is	be	AUX
ejpam-5888	49	29	a	a	DET
ejpam-5888	49	30	security	security	NOUN
ejpam-5888	49	31	parameter	parameter	NOUN
ejpam-5888	49	32	.	.	PUNCT
ejpam-5888	50	1	let	let	VERB
ejpam-5888	50	2	g	g	PROPN
ejpam-5888	50	3	∈	∈	PROPN
ejpam-5888	50	4	bl+r	bl+r	PROPN
ejpam-5888	50	5	be	be	VERB
ejpam-5888	50	6	a	a	DET
ejpam-5888	50	7	public	public	ADJ
ejpam-5888	50	8	element	element	NOUN
ejpam-5888	50	9	.	.	PUNCT
ejpam-5888	51	1	2.2.1	2.2.1	NUM
ejpam-5888	51	2	.	.	PUNCT
ejpam-5888	52	1	protocol	protocol	NOUN
ejpam-5888	52	2	i	i	PRON
ejpam-5888	52	3	(	(	PUNCT
ejpam-5888	52	4	i	i	NOUN
ejpam-5888	52	5	)	)	PUNCT
ejpam-5888	53	1	key	key	ADJ
ejpam-5888	53	2	generation	generation	NOUN
ejpam-5888	53	3	:	:	PUNCT
ejpam-5888	53	4	alice	alice	PROPN
ejpam-5888	53	5	chooses	choose	VERB
ejpam-5888	53	6	two	two	NUM
ejpam-5888	53	7	secret	secret	ADJ
ejpam-5888	53	8	parameters	parameter	NOUN
ejpam-5888	53	9	x1	x1	PROPN
ejpam-5888	53	10	,	,	PUNCT
ejpam-5888	53	11	x2	x2	PROPN
ejpam-5888	53	12	∈	∈	PROPN
ejpam-5888	53	13	lbl	lbl	PROPN
ejpam-5888	53	14	,	,	PUNCT
ejpam-5888	53	15	and	and	CCONJ
ejpam-5888	53	16	computes	compute	VERB
ejpam-5888	53	17	xi	xi	X
ejpam-5888	54	1	=	=	PUNCT
ejpam-5888	54	2	xigx	xigx	PROPN
ejpam-5888	54	3	−1	−1	NOUN
ejpam-5888	55	1	i	i	PRON
ejpam-5888	55	2	,	,	PUNCT
ejpam-5888	55	3	i	i	PRON
ejpam-5888	55	4	=	=	NOUN
ejpam-5888	55	5	1	1	NUM
ejpam-5888	55	6	,	,	PUNCT
ejpam-5888	55	7	2	2	NUM
ejpam-5888	55	8	.	.	PUNCT
ejpam-5888	55	9	(	(	PUNCT
ejpam-5888	55	10	x1	x1	PROPN
ejpam-5888	55	11	,	,	PUNCT
ejpam-5888	55	12	x2	x2	PROPN
ejpam-5888	55	13	,	,	PUNCT
ejpam-5888	55	14	g	g	NOUN
ejpam-5888	55	15	)	)	PUNCT
ejpam-5888	55	16	is	be	AUX
ejpam-5888	55	17	the	the	DET
ejpam-5888	55	18	public	public	ADJ
ejpam-5888	55	19	key	key	NOUN
ejpam-5888	55	20	and	and	CCONJ
ejpam-5888	55	21	the	the	DET
ejpam-5888	55	22	private	private	ADJ
ejpam-5888	55	23	key	key	NOUN
ejpam-5888	55	24	is	be	AUX
ejpam-5888	55	25	(	(	PUNCT
ejpam-5888	55	26	x1	x1	PROPN
ejpam-5888	55	27	,	,	PUNCT
ejpam-5888	55	28	x2	x2	PROPN
ejpam-5888	55	29	)	)	PUNCT
ejpam-5888	55	30	.	.	PUNCT
ejpam-5888	56	1	(	(	PUNCT
ejpam-5888	56	2	ii	ii	NOUN
ejpam-5888	56	3	)	)	PUNCT
ejpam-5888	56	4	encryption	encryption	NOUN
ejpam-5888	56	5	:	:	PUNCT
ejpam-5888	56	6	consider	consider	VERB
ejpam-5888	56	7	the	the	DET
ejpam-5888	56	8	cipher	cipher	ADJ
ejpam-5888	56	9	message	message	NOUN
ejpam-5888	56	10	m	m	PROPN
ejpam-5888	56	11	∈	∈	PROPN
ejpam-5888	56	12	bl+r	bl+r	PROPN
ejpam-5888	56	13	,	,	PUNCT
ejpam-5888	56	14	bob	bob	PROPN
ejpam-5888	56	15	selects	select	VERB
ejpam-5888	56	16	a	a	DET
ejpam-5888	56	17	secret	secret	ADJ
ejpam-5888	56	18	element	element	NOUN
ejpam-5888	56	19	y	y	PROPN
ejpam-5888	56	20	∈	∈	PROPN
ejpam-5888	56	21	rbr	rbr	PROPN
ejpam-5888	56	22	,	,	PUNCT
ejpam-5888	56	23	and	and	CCONJ
ejpam-5888	56	24	calculates	calculate	VERB
ejpam-5888	56	25	y	y	PROPN
ejpam-5888	56	26	=	=	SYM
ejpam-5888	56	27	ygy−1	ygy−1	PROPN
ejpam-5888	56	28	,	,	PUNCT
ejpam-5888	56	29	zi	zi	NOUN
ejpam-5888	56	30	=	=	SYM
ejpam-5888	56	31	yxiy	yxiy	PROPN
ejpam-5888	56	32	−1	−1	NOUN
ejpam-5888	56	33	,	,	PUNCT
ejpam-5888	56	34	i	i	PRON
ejpam-5888	56	35	=	=	NOUN
ejpam-5888	56	36	1	1	NUM
ejpam-5888	56	37	,	,	PUNCT
ejpam-5888	56	38	2	2	NUM
ejpam-5888	56	39	,	,	PUNCT
ejpam-5888	56	40	c	c	NOUN
ejpam-5888	56	41	=	=	SYM
ejpam-5888	56	42	enck(m	enck(m	NOUN
ejpam-5888	56	43	)	)	PUNCT
ejpam-5888	56	44	,	,	PUNCT
ejpam-5888	56	45	k	k	X
ejpam-5888	56	46	=	=	PUNCT
ejpam-5888	56	47	h(y	h(y	ADV
ejpam-5888	56	48	,	,	PUNCT
ejpam-5888	56	49	z	z	NOUN
ejpam-5888	56	50	)	)	PUNCT
ejpam-5888	56	51	.	.	PUNCT
ejpam-5888	57	1	the	the	DET
ejpam-5888	57	2	ciphertext	ciphertext	NOUN
ejpam-5888	57	3	is	be	AUX
ejpam-5888	57	4	(	(	PUNCT
ejpam-5888	57	5	y	y	PROPN
ejpam-5888	57	6	,	,	PUNCT
ejpam-5888	57	7	c	c	NOUN
ejpam-5888	57	8	)	)	PUNCT
ejpam-5888	57	9	.	.	PUNCT
ejpam-5888	58	1	(	(	PUNCT
ejpam-5888	58	2	iii	iii	X
ejpam-5888	58	3	)	)	PUNCT
ejpam-5888	58	4	decryption	decryption	NOUN
ejpam-5888	58	5	:	:	PUNCT
ejpam-5888	58	6	to	to	PART
ejpam-5888	58	7	decrypt	decrypt	VERB
ejpam-5888	58	8	the	the	DET
ejpam-5888	58	9	ciphertext	ciphertext	NOUN
ejpam-5888	58	10	(	(	PUNCT
ejpam-5888	58	11	y	y	PROPN
ejpam-5888	58	12	,	,	PUNCT
ejpam-5888	58	13	c	c	NOUN
ejpam-5888	58	14	)	)	PUNCT
ejpam-5888	58	15	,	,	PUNCT
ejpam-5888	58	16	alice	alice	PROPN
ejpam-5888	58	17	compute	compute	PROPN
ejpam-5888	58	18	zi	zi	PROPN
ejpam-5888	59	1	=	=	PUNCT
ejpam-5888	60	1	xiy	xiy	PROPN
ejpam-5888	61	1	x−1	x−1	PROPN
ejpam-5888	62	1	i	i	PRON
ejpam-5888	62	2	,	,	PUNCT
ejpam-5888	62	3	i	i	PRON
ejpam-5888	62	4	=	=	NOUN
ejpam-5888	62	5	1	1	NUM
ejpam-5888	62	6	,	,	PUNCT
ejpam-5888	62	7	2	2	NUM
ejpam-5888	62	8	,	,	PUNCT
ejpam-5888	62	9	m	m	NOUN
ejpam-5888	62	10	=	=	SYM
ejpam-5888	62	11	deck(c	deck(c	PROPN
ejpam-5888	62	12	)	)	PUNCT
ejpam-5888	62	13	,	,	PUNCT
ejpam-5888	62	14	k	k	X
ejpam-5888	62	15	=	=	PUNCT
ejpam-5888	62	16	h(y	h(y	ADV
ejpam-5888	62	17	,	,	PUNCT
ejpam-5888	62	18	z	z	NOUN
ejpam-5888	62	19	)	)	PUNCT
ejpam-5888	62	20	.	.	PUNCT
ejpam-5888	63	1	kashifa	kashifa	PROPN
ejpam-5888	63	2	begum	begum	VERB
ejpam-5888	63	3	a.	a.	NOUN
ejpam-5888	63	4	et	et	PROPN
ejpam-5888	63	5	.	.	PUNCT
ejpam-5888	64	1	al	al	PROPN
ejpam-5888	64	2	/	/	PUNCT
ejpam-5888	64	3	eur	eur	PROPN
ejpam-5888	64	4	.	.	PUNCT
ejpam-5888	65	1	j.	j.	PROPN
ejpam-5888	65	2	pure	pure	PROPN
ejpam-5888	65	3	appl	appl	PROPN
ejpam-5888	65	4	.	.	PROPN
ejpam-5888	65	5	math	math	PROPN
ejpam-5888	65	6	,	,	PUNCT
ejpam-5888	65	7	18	18	NUM
ejpam-5888	65	8	(	(	PUNCT
ejpam-5888	65	9	3	3	NUM
ejpam-5888	65	10	)	)	PUNCT
ejpam-5888	65	11	(	(	PUNCT
ejpam-5888	65	12	2025	2025	NUM
ejpam-5888	65	13	)	)	PUNCT
ejpam-5888	65	14	,	,	PUNCT
ejpam-5888	65	15	5888	5888	NUM
ejpam-5888	65	16	4	4	NUM
ejpam-5888	65	17	of	of	ADP
ejpam-5888	65	18	16	16	NUM
ejpam-5888	65	19	2.2.2	2.2.2	NUM
ejpam-5888	65	20	.	.	PUNCT
ejpam-5888	66	1	protocol	protocol	PROPN
ejpam-5888	66	2	ii	ii	PROPN
ejpam-5888	66	3	(	(	PUNCT
ejpam-5888	66	4	i	i	NOUN
ejpam-5888	66	5	)	)	PUNCT
ejpam-5888	66	6	key	key	ADJ
ejpam-5888	66	7	generation	generation	NOUN
ejpam-5888	66	8	:	:	PUNCT
ejpam-5888	66	9	alice	alice	PROPN
ejpam-5888	66	10	chooses	choose	VERB
ejpam-5888	66	11	two	two	NUM
ejpam-5888	66	12	secret	secret	ADJ
ejpam-5888	66	13	parameters	parameter	NOUN
ejpam-5888	66	14	x1	x1	PROPN
ejpam-5888	66	15	,	,	PUNCT
ejpam-5888	66	16	x2	x2	PROPN
ejpam-5888	66	17	∈	∈	PROPN
ejpam-5888	66	18	lbl	lbl	PROPN
ejpam-5888	66	19	,	,	PUNCT
ejpam-5888	66	20	and	and	CCONJ
ejpam-5888	66	21	computes	compute	VERB
ejpam-5888	66	22	xi	xi	X
ejpam-5888	67	1	=	=	PUNCT
ejpam-5888	67	2	xigx	xigx	PROPN
ejpam-5888	67	3	−1	−1	NOUN
ejpam-5888	68	1	i	i	PRON
ejpam-5888	68	2	,	,	PUNCT
ejpam-5888	68	3	i	i	PRON
ejpam-5888	68	4	=	=	NOUN
ejpam-5888	68	5	1	1	NUM
ejpam-5888	68	6	,	,	PUNCT
ejpam-5888	68	7	2	2	NUM
ejpam-5888	68	8	.	.	PUNCT
ejpam-5888	69	1	the	the	DET
ejpam-5888	69	2	public	public	ADJ
ejpam-5888	69	3	key	key	NOUN
ejpam-5888	69	4	is	be	AUX
ejpam-5888	69	5	(	(	PUNCT
ejpam-5888	69	6	x1	x1	PROPN
ejpam-5888	69	7	,	,	PUNCT
ejpam-5888	69	8	x2	x2	PROPN
ejpam-5888	69	9	,	,	PUNCT
ejpam-5888	69	10	g	g	NOUN
ejpam-5888	69	11	)	)	PUNCT
ejpam-5888	69	12	and	and	CCONJ
ejpam-5888	69	13	the	the	DET
ejpam-5888	69	14	private	private	ADJ
ejpam-5888	69	15	key	key	NOUN
ejpam-5888	69	16	is	be	AUX
ejpam-5888	69	17	(	(	PUNCT
ejpam-5888	69	18	x1	x1	PROPN
ejpam-5888	69	19	,	,	PUNCT
ejpam-5888	69	20	x2	x2	PROPN
ejpam-5888	69	21	)	)	PUNCT
ejpam-5888	69	22	.	.	PUNCT
ejpam-5888	70	1	(	(	PUNCT
ejpam-5888	70	2	ii	ii	NOUN
ejpam-5888	70	3	)	)	PUNCT
ejpam-5888	70	4	encryption	encryption	NOUN
ejpam-5888	70	5	:	:	PUNCT
ejpam-5888	70	6	bob	bob	PROPN
ejpam-5888	70	7	selects	select	VERB
ejpam-5888	70	8	two	two	NUM
ejpam-5888	70	9	random	random	ADJ
ejpam-5888	70	10	parameters	parameter	NOUN
ejpam-5888	70	11	y1	y1	NOUN
ejpam-5888	70	12	,	,	PUNCT
ejpam-5888	70	13	y2	y2	PROPN
ejpam-5888	70	14	∈	∈	PROPN
ejpam-5888	70	15	rbr	rbr	PROPN
ejpam-5888	70	16	,	,	PUNCT
ejpam-5888	70	17	and	and	CCONJ
ejpam-5888	70	18	calculates	calculate	VERB
ejpam-5888	70	19	yi	yi	NOUN
ejpam-5888	71	1	=	=	SYM
ejpam-5888	71	2	yigy	yigy	NOUN
ejpam-5888	71	3	−1	−1	NOUN
ejpam-5888	72	1	i	i	PRON
ejpam-5888	72	2	,	,	PUNCT
ejpam-5888	72	3	i	i	PRON
ejpam-5888	72	4	=	=	NOUN
ejpam-5888	72	5	1	1	NUM
ejpam-5888	72	6	,	,	PUNCT
ejpam-5888	72	7	2	2	NUM
ejpam-5888	72	8	.	.	PUNCT
ejpam-5888	72	9	bob	bob	PROPN
ejpam-5888	72	10	also	also	ADV
ejpam-5888	72	11	computes	compute	VERB
ejpam-5888	72	12	the	the	DET
ejpam-5888	72	13	secret	secret	NOUN
ejpam-5888	72	14	keys	key	VERB
ejpam-5888	72	15	zij	zij	PROPN
ejpam-5888	72	16	=	=	PROPN
ejpam-5888	72	17	yjxiy	yjxiy	PROPN
ejpam-5888	72	18	−1	−1	NOUN
ejpam-5888	73	1	j	j	PROPN
ejpam-5888	73	2	,	,	PUNCT
ejpam-5888	73	3	i	i	PRON
ejpam-5888	73	4	=	=	NOUN
ejpam-5888	73	5	1	1	NUM
ejpam-5888	73	6	,	,	PUNCT
ejpam-5888	73	7	2	2	NUM
ejpam-5888	73	8	,	,	PUNCT
ejpam-5888	73	9	j	j	NOUN
ejpam-5888	73	10	=	=	SYM
ejpam-5888	73	11	1	1	NUM
ejpam-5888	73	12	,	,	PUNCT
ejpam-5888	73	13	2	2	NUM
ejpam-5888	73	14	.	.	PUNCT
ejpam-5888	74	1	the	the	DET
ejpam-5888	74	2	public	public	ADJ
ejpam-5888	74	3	key	key	NOUN
ejpam-5888	74	4	is	be	AUX
ejpam-5888	74	5	(	(	PUNCT
ejpam-5888	74	6	y1	y1	INTJ
ejpam-5888	74	7	,	,	PUNCT
ejpam-5888	74	8	y2	y2	INTJ
ejpam-5888	74	9	,	,	PUNCT
ejpam-5888	74	10	g	g	NOUN
ejpam-5888	74	11	)	)	PUNCT
ejpam-5888	74	12	and	and	CCONJ
ejpam-5888	74	13	the	the	DET
ejpam-5888	74	14	private	private	ADJ
ejpam-5888	74	15	key	key	NOUN
ejpam-5888	74	16	is	be	AUX
ejpam-5888	74	17	(	(	PUNCT
ejpam-5888	74	18	y1	y1	INTJ
ejpam-5888	74	19	,	,	PUNCT
ejpam-5888	74	20	y2	y2	PROPN
ejpam-5888	74	21	)	)	PUNCT
ejpam-5888	74	22	.	.	PUNCT
ejpam-5888	75	1	(	(	PUNCT
ejpam-5888	75	2	iii	iii	X
ejpam-5888	75	3	)	)	PUNCT
ejpam-5888	75	4	decryption	decryption	NOUN
ejpam-5888	75	5	:	:	PUNCT
ejpam-5888	76	1	alice	alice	PROPN
ejpam-5888	76	2	computes	compute	VERB
ejpam-5888	76	3	the	the	DET
ejpam-5888	76	4	secret	secret	NOUN
ejpam-5888	76	5	keys	key	NOUN
ejpam-5888	76	6	zij	zij	PROPN
ejpam-5888	76	7	=	=	PROPN
ejpam-5888	76	8	xiyjx	xiyjx	PROPN
ejpam-5888	76	9	−1	−1	PROPN
ejpam-5888	77	1	i	i	PRON
ejpam-5888	77	2	,	,	PUNCT
ejpam-5888	77	3	i	i	PRON
ejpam-5888	77	4	=	=	NOUN
ejpam-5888	77	5	1	1	NUM
ejpam-5888	77	6	,	,	PUNCT
ejpam-5888	77	7	2	2	NUM
ejpam-5888	77	8	,	,	PUNCT
ejpam-5888	77	9	j	j	NOUN
ejpam-5888	77	10	=	=	SYM
ejpam-5888	77	11	1	1	NUM
ejpam-5888	77	12	,	,	PUNCT
ejpam-5888	77	13	2	2	NUM
ejpam-5888	77	14	.	.	PUNCT
ejpam-5888	77	15	because	because	SCONJ
ejpam-5888	77	16	of	of	ADP
ejpam-5888	77	17	ccs(xi	ccs(xi	PROPN
ejpam-5888	77	18	,	,	PUNCT
ejpam-5888	77	19	yj	yj	PROPN
ejpam-5888	77	20	)	)	PUNCT
ejpam-5888	77	21	=	=	SYM
ejpam-5888	78	1	zij	zij	PROPN
ejpam-5888	78	2	=	=	PUNCT
ejpam-5888	78	3	xiyjx	xiyjx	PROPN
ejpam-5888	78	4	−1	−1	NOUN
ejpam-5888	79	1	i	i	PRON
ejpam-5888	79	2	=	=	PUNCT
ejpam-5888	79	3	yjxiy	yjxiy	PROPN
ejpam-5888	79	4	−1	−1	NOUN
ejpam-5888	79	5	j	j	PROPN
ejpam-5888	79	6	,	,	PUNCT
ejpam-5888	79	7	i	i	PRON
ejpam-5888	79	8	=	=	NOUN
ejpam-5888	79	9	1	1	NUM
ejpam-5888	79	10	,	,	PUNCT
ejpam-5888	79	11	2	2	NUM
ejpam-5888	79	12	,	,	PUNCT
ejpam-5888	79	13	j	j	NOUN
ejpam-5888	79	14	=	=	SYM
ejpam-5888	79	15	1	1	NUM
ejpam-5888	79	16	,	,	PUNCT
ejpam-5888	79	17	2	2	NUM
ejpam-5888	79	18	,	,	PUNCT
ejpam-5888	79	19	alice	alice	PROPN
ejpam-5888	79	20	and	and	CCONJ
ejpam-5888	79	21	bob	bob	PROPN
ejpam-5888	79	22	can	can	AUX
ejpam-5888	79	23	calculate	calculate	VERB
ejpam-5888	79	24	the	the	DET
ejpam-5888	79	25	same	same	ADJ
ejpam-5888	79	26	value	value	NOUN
ejpam-5888	79	27	through	through	ADP
ejpam-5888	79	28	the	the	DET
ejpam-5888	79	29	hash	hash	NOUN
ejpam-5888	79	30	function	function	NOUN
ejpam-5888	79	31	h	h	NOUN
ejpam-5888	79	32	:	:	PUNCT
ejpam-5888	79	33	k	k	X
ejpam-5888	79	34	=	=	PUNCT
ejpam-5888	79	35	h(ccs(x1	h(ccs(x1	PROPN
ejpam-5888	79	36	,	,	PUNCT
ejpam-5888	79	37	y1	y1	NOUN
ejpam-5888	79	38	)	)	PUNCT
ejpam-5888	79	39	,	,	PUNCT
ejpam-5888	79	40	ccs(x1	ccs(x1	PROPN
ejpam-5888	79	41	,	,	PUNCT
ejpam-5888	79	42	y2	y2	PROPN
ejpam-5888	79	43	)	)	PUNCT
ejpam-5888	79	44	,	,	PUNCT
ejpam-5888	79	45	ccs(x2	ccs(x2	NOUN
ejpam-5888	79	46	,	,	PUNCT
ejpam-5888	79	47	y1	y1	NOUN
ejpam-5888	79	48	)	)	PUNCT
ejpam-5888	79	49	,	,	PUNCT
ejpam-5888	79	50	ccs(x2	ccs(x2	NOUN
ejpam-5888	79	51	,	,	PUNCT
ejpam-5888	79	52	y2	y2	NOUN
ejpam-5888	79	53	)	)	PUNCT
ejpam-5888	79	54	)	)	PUNCT
ejpam-5888	79	55	.	.	PUNCT
ejpam-5888	80	1	2.3	2.3	NUM
ejpam-5888	80	2	.	.	PUNCT
ejpam-5888	80	3	semiring	semire	VERB
ejpam-5888	80	4	a	a	DET
ejpam-5888	80	5	semiring	semiring	NOUN
ejpam-5888	80	6	is	be	AUX
ejpam-5888	80	7	a	a	DET
ejpam-5888	80	8	set	set	NOUN
ejpam-5888	80	9	r	r	NOUN
ejpam-5888	80	10	together	together	ADV
ejpam-5888	80	11	with	with	ADP
ejpam-5888	80	12	two	two	NUM
ejpam-5888	80	13	binary	binary	ADJ
ejpam-5888	80	14	operations	operation	NOUN
ejpam-5888	80	15	‘	'	PUNCT
ejpam-5888	80	16	+	+	NOUN
ejpam-5888	80	17	’	'	PUNCT
ejpam-5888	80	18	and	and	CCONJ
ejpam-5888	80	19	‘	'	PUNCT
ejpam-5888	80	20	·	·	PUNCT
ejpam-5888	80	21	’	'	PUNCT
ejpam-5888	80	22	∋	∋	NOUN
ejpam-5888	80	23	•	•	ADV
ejpam-5888	80	24	(	(	PUNCT
ejpam-5888	80	25	r,+	r,+	NUM
ejpam-5888	80	26	)	)	PUNCT
ejpam-5888	80	27	is	be	AUX
ejpam-5888	80	28	a	a	DET
ejpam-5888	80	29	commutative	commutative	ADJ
ejpam-5888	80	30	monoid	monoid	NOUN
ejpam-5888	80	31	,	,	PUNCT
ejpam-5888	80	32	•	•	X
ejpam-5888	80	33	(	(	PUNCT
ejpam-5888	80	34	r	r	NOUN
ejpam-5888	80	35	,	,	PUNCT
ejpam-5888	80	36	·	·	PUNCT
ejpam-5888	80	37	)	)	PUNCT
ejpam-5888	80	38	is	be	AUX
ejpam-5888	80	39	a	a	DET
ejpam-5888	80	40	monoid	monoid	NOUN
ejpam-5888	80	41	,	,	PUNCT
ejpam-5888	80	42	•	•	ADJ
ejpam-5888	80	43	multiplication	multiplication	NOUN
ejpam-5888	80	44	by	by	ADP
ejpam-5888	80	45	0	0	NUM
ejpam-5888	80	46	annihilates	annihilate	VERB
ejpam-5888	80	47	r	r	NOUN
ejpam-5888	80	48	,	,	PUNCT
ejpam-5888	80	49	i.e.	i.e.	X
ejpam-5888	80	50	,	,	PUNCT
ejpam-5888	80	51	r	r	NOUN
ejpam-5888	80	52	·	·	PUNCT
ejpam-5888	80	53	0	0	PUNCT
ejpam-5888	81	1	=	=	SYM
ejpam-5888	81	2	0	0	PUNCT
ejpam-5888	81	3	·	·	PUNCT
ejpam-5888	81	4	r	r	NOUN
ejpam-5888	81	5	=	=	SYM
ejpam-5888	81	6	0	0	NUM
ejpam-5888	81	7	,	,	PUNCT
ejpam-5888	81	8	∀	∀	X
ejpam-5888	81	9	r	r	NOUN
ejpam-5888	81	10	∈	∈	NOUN
ejpam-5888	81	11	r	r	NOUN
ejpam-5888	81	12	,	,	PUNCT
ejpam-5888	81	13	and	and	CCONJ
ejpam-5888	81	14	•	•	NUM
ejpam-5888	81	15	multiplication	multiplication	NOUN
ejpam-5888	81	16	is	be	AUX
ejpam-5888	81	17	both	both	PRON
ejpam-5888	81	18	left	leave	VERB
ejpam-5888	81	19	and	and	CCONJ
ejpam-5888	81	20	right	right	ADV
ejpam-5888	81	21	distributive	distributive	ADJ
ejpam-5888	81	22	over	over	ADP
ejpam-5888	81	23	addition	addition	NOUN
ejpam-5888	81	24	,	,	PUNCT
ejpam-5888	81	25	i.e.	i.e.	X
ejpam-5888	81	26	,	,	PUNCT
ejpam-5888	81	27	r	r	NOUN
ejpam-5888	81	28	·	·	PUNCT
ejpam-5888	81	29	(	(	PUNCT
ejpam-5888	81	30	s+	s+	X
ejpam-5888	81	31	t	t	PROPN
ejpam-5888	81	32	)	)	PUNCT
ejpam-5888	81	33	=	=	PUNCT
ejpam-5888	81	34	(	(	PUNCT
ejpam-5888	81	35	r	r	NOUN
ejpam-5888	81	36	·	·	PUNCT
ejpam-5888	81	37	s	s	X
ejpam-5888	81	38	)	)	PUNCT
ejpam-5888	81	39	+	+	CCONJ
ejpam-5888	81	40	(	(	PUNCT
ejpam-5888	81	41	r	r	NOUN
ejpam-5888	81	42	·	·	SYM
ejpam-5888	81	43	t	t	NOUN
ejpam-5888	81	44	)	)	PUNCT
ejpam-5888	81	45	(	(	PUNCT
ejpam-5888	81	46	s+	s+	X
ejpam-5888	81	47	t	t	PROPN
ejpam-5888	81	48	)	)	PUNCT
ejpam-5888	81	49	·	·	PUNCT
ejpam-5888	82	1	r	r	X
ejpam-5888	82	2	=	=	PUNCT
ejpam-5888	82	3	(	(	PUNCT
ejpam-5888	82	4	s	s	X
ejpam-5888	82	5	·	·	PUNCT
ejpam-5888	82	6	r	r	X
ejpam-5888	82	7	)	)	PUNCT
ejpam-5888	82	8	+	+	CCONJ
ejpam-5888	82	9	(	(	PUNCT
ejpam-5888	82	10	t	t	NOUN
ejpam-5888	82	11	·	·	PUNCT
ejpam-5888	82	12	r	r	X
ejpam-5888	82	13	)	)	PUNCT
ejpam-5888	82	14	,	,	PUNCT
ejpam-5888	82	15	∀	∀	X
ejpam-5888	82	16	r	r	NOUN
ejpam-5888	82	17	,	,	PUNCT
ejpam-5888	82	18	s	s	PROPN
ejpam-5888	82	19	,	,	PUNCT
ejpam-5888	82	20	t	t	PROPN
ejpam-5888	82	21	∈	∈	PROPN
ejpam-5888	82	22	r.	r.	PROPN
ejpam-5888	82	23	2.4	2.4	NUM
ejpam-5888	82	24	.	.	PUNCT
ejpam-5888	83	1	tropical	tropical	ADJ
ejpam-5888	83	2	algebra	algebra	PROPN
ejpam-5888	83	3	a	a	DET
ejpam-5888	83	4	tropical	tropical	ADJ
ejpam-5888	83	5	algebra	algebra	NOUN
ejpam-5888	83	6	is	be	AUX
ejpam-5888	83	7	the	the	DET
ejpam-5888	83	8	semiring	semire	VERB
ejpam-5888	83	9	rmin	rmin	NOUN
ejpam-5888	83	10	=	=	PUNCT
ejpam-5888	84	1	(	(	PUNCT
ejpam-5888	84	2	r	r	NOUN
ejpam-5888	84	3	∪	∪	X
ejpam-5888	84	4	{	{	PUNCT
ejpam-5888	84	5	+	+	NOUN
ejpam-5888	84	6	∞},⊕,⊗	∞},⊕,⊗	NOUN
ejpam-5888	84	7	)	)	PUNCT
ejpam-5888	84	8	,	,	PUNCT
ejpam-5888	84	9	where	where	SCONJ
ejpam-5888	84	10	the	the	DET
ejpam-5888	84	11	operations	operation	NOUN
ejpam-5888	84	12	⊕	⊕	PROPN
ejpam-5888	84	13	and	and	CCONJ
ejpam-5888	84	14	⊗	⊗	PROPN
ejpam-5888	84	15	,	,	PUNCT
ejpam-5888	84	16	referred	refer	VERB
ejpam-5888	84	17	to	to	ADP
ejpam-5888	84	18	as	as	ADP
ejpam-5888	84	19	tropical	tropical	ADJ
ejpam-5888	84	20	addition	addition	NOUN
ejpam-5888	84	21	and	and	CCONJ
ejpam-5888	84	22	tropical	tropical	ADJ
ejpam-5888	84	23	multiplication	multiplication	NOUN
ejpam-5888	84	24	,	,	PUNCT
ejpam-5888	84	25	respectively	respectively	ADV
ejpam-5888	84	26	,	,	PUNCT
ejpam-5888	84	27	are	be	AUX
ejpam-5888	84	28	defined	define	VERB
ejpam-5888	84	29	as	as	ADP
ejpam-5888	84	30	(	(	PUNCT
ejpam-5888	84	31	∀	∀	X
ejpam-5888	84	32	s	s	PART
ejpam-5888	84	33	,	,	PUNCT
ejpam-5888	84	34	t	t	PROPN
ejpam-5888	84	35	∈	∈	PROPN
ejpam-5888	84	36	r	r	NOUN
ejpam-5888	84	37	∪	∪	X
ejpam-5888	84	38	{	{	PUNCT
ejpam-5888	84	39	+	+	NOUN
ejpam-5888	84	40	∞	∞	NOUN
ejpam-5888	84	41	}	}	PUNCT
ejpam-5888	84	42	)	)	PUNCT
ejpam-5888	84	43	s⊕	s⊕	PROPN
ejpam-5888	84	44	t	t	NOUN
ejpam-5888	84	45	=	=	SYM
ejpam-5888	84	46	min{s	min{s	PROPN
ejpam-5888	84	47	,	,	PUNCT
ejpam-5888	84	48	t	t	PROPN
ejpam-5888	84	49	}	}	PUNCT
ejpam-5888	84	50	,	,	PUNCT
ejpam-5888	84	51	s⊗	s⊗	NOUN
ejpam-5888	84	52	t	t	PROPN
ejpam-5888	84	53	=	=	PUNCT
ejpam-5888	84	54	s+	s+	NUM
ejpam-5888	84	55	t.	t.	PROPN
ejpam-5888	84	56	2.5	2.5	NUM
ejpam-5888	84	57	.	.	PUNCT
ejpam-5888	85	1	tropical	tropical	ADJ
ejpam-5888	85	2	monomial	monomial	PROPN
ejpam-5888	85	3	let	let	VERB
ejpam-5888	85	4	x	x	SYM
ejpam-5888	85	5	=	=	PRON
ejpam-5888	85	6	(	(	PUNCT
ejpam-5888	85	7	x1	x1	PROPN
ejpam-5888	85	8	,	,	PUNCT
ejpam-5888	85	9	x2	x2	PROPN
ejpam-5888	85	10	,	,	PUNCT
ejpam-5888	85	11	.	.	PUNCT
ejpam-5888	85	12	.	.	PUNCT
ejpam-5888	85	13	.	.	PUNCT
ejpam-5888	86	1	,	,	PUNCT
ejpam-5888	86	2	xn	xn	X
ejpam-5888	86	3	)	)	PUNCT
ejpam-5888	86	4	∈	∈	PROPN
ejpam-5888	86	5	rn	rn	PROPN
ejpam-5888	86	6	min	min	PROPN
ejpam-5888	86	7	,	,	PUNCT
ejpam-5888	86	8	a	a	DET
ejpam-5888	86	9	∈	∈	PROPN
ejpam-5888	86	10	r	r	NOUN
ejpam-5888	86	11	,	,	PUNCT
ejpam-5888	86	12	and	and	CCONJ
ejpam-5888	86	13	α	α	NOUN
ejpam-5888	86	14	=	=	SYM
ejpam-5888	86	15	(	(	PUNCT
ejpam-5888	86	16	α1	α1	PROPN
ejpam-5888	86	17	,	,	PUNCT
ejpam-5888	86	18	α2	α2	ADJ
ejpam-5888	86	19	,	,	PUNCT
ejpam-5888	86	20	.	.	PUNCT
ejpam-5888	86	21	.	.	PUNCT
ejpam-5888	87	1	.	.	PUNCT
ejpam-5888	88	1	,	,	PUNCT
ejpam-5888	88	2	αn	αn	X
ejpam-5888	88	3	)	)	PUNCT
ejpam-5888	88	4	∈	∈	PROPN
ejpam-5888	89	1	zn	zn	X
ejpam-5888	89	2	.	.	PUNCT
ejpam-5888	90	1	then	then	ADV
ejpam-5888	90	2	a	a	DET
ejpam-5888	90	3	tropical	tropical	ADJ
ejpam-5888	90	4	monomial	monomial	NOUN
ejpam-5888	90	5	is	be	AUX
ejpam-5888	90	6	the	the	DET
ejpam-5888	90	7	function	function	NOUN
ejpam-5888	90	8	p(x	p(x	NOUN
ejpam-5888	90	9	)	)	PUNCT
ejpam-5888	90	10	=	=	PUNCT
ejpam-5888	91	1	a⊗	a⊗	NOUN
ejpam-5888	91	2	x⊗α1	x⊗α1	PROPN
ejpam-5888	91	3	1	1	NUM
ejpam-5888	92	1	⊗	⊗	PROPN
ejpam-5888	92	2	x⊗α2	x⊗α2	PROPN
ejpam-5888	92	3	2	2	NUM
ejpam-5888	92	4	⊗	⊗	PROPN
ejpam-5888	92	5	·	·	PUNCT
ejpam-5888	92	6	·	·	PUNCT
ejpam-5888	92	7	·	·	PUNCT
ejpam-5888	93	1	⊗	⊗	NUM
ejpam-5888	93	2	x⊗αn	x⊗αn	PROPN
ejpam-5888	93	3	n	n	CCONJ
ejpam-5888	93	4	,	,	PUNCT
ejpam-5888	93	5	where	where	SCONJ
ejpam-5888	93	6	exponentiation	exponentiation	NOUN
ejpam-5888	93	7	is	be	AUX
ejpam-5888	93	8	defined	define	VERB
ejpam-5888	93	9	tropically	tropically	ADV
ejpam-5888	93	10	as	as	ADP
ejpam-5888	93	11	repeated	repeat	VERB
ejpam-5888	93	12	tropical	tropical	ADJ
ejpam-5888	93	13	multiplication	multiplication	NOUN
ejpam-5888	93	14	,	,	PUNCT
ejpam-5888	93	15	i.e.	i.e.	X
ejpam-5888	93	16	,	,	PUNCT
ejpam-5888	93	17	x⊗αi	x⊗αi	PROPN
ejpam-5888	93	18	i	i	NOUN
ejpam-5888	93	19	=	=	SYM
ejpam-5888	93	20	αixi	αixi	NOUN
ejpam-5888	93	21	.	.	PUNCT
ejpam-5888	94	1	ex	ex	X
ejpam-5888	94	2	.	.	PUNCT
ejpam-5888	95	1	x1	x1	PROPN
ejpam-5888	95	2	⊗	⊗	PROPN
ejpam-5888	96	1	x2	x2	PROPN
ejpam-5888	97	1	⊗	⊗	NUM
ejpam-5888	97	2	x2	x2	PROPN
ejpam-5888	98	1	=	=	PUNCT
ejpam-5888	98	2	x1	x1	PROPN
ejpam-5888	98	3	⊗	⊗	PROPN
ejpam-5888	98	4	x⊗2	x⊗2	ADJ
ejpam-5888	98	5	2	2	NUM
ejpam-5888	98	6	=	=	SYM
ejpam-5888	98	7	x1	x1	PROPN
ejpam-5888	98	8	+	+	NUM
ejpam-5888	98	9	2x2	2x2	NUM
ejpam-5888	98	10	.	.	PUNCT
ejpam-5888	99	1	kashifa	kashifa	PROPN
ejpam-5888	99	2	begum	begum	VERB
ejpam-5888	99	3	a.	a.	NOUN
ejpam-5888	99	4	et	et	PROPN
ejpam-5888	99	5	.	.	PUNCT
ejpam-5888	100	1	al	al	PROPN
ejpam-5888	100	2	/	/	PUNCT
ejpam-5888	100	3	eur	eur	PROPN
ejpam-5888	100	4	.	.	PUNCT
ejpam-5888	101	1	j.	j.	PROPN
ejpam-5888	101	2	pure	pure	PROPN
ejpam-5888	101	3	appl	appl	PROPN
ejpam-5888	101	4	.	.	PROPN
ejpam-5888	101	5	math	math	PROPN
ejpam-5888	101	6	,	,	PUNCT
ejpam-5888	101	7	18	18	NUM
ejpam-5888	101	8	(	(	PUNCT
ejpam-5888	101	9	3	3	NUM
ejpam-5888	101	10	)	)	PUNCT
ejpam-5888	101	11	(	(	PUNCT
ejpam-5888	101	12	2025	2025	NUM
ejpam-5888	101	13	)	)	PUNCT
ejpam-5888	101	14	,	,	PUNCT
ejpam-5888	101	15	5888	5888	NUM
ejpam-5888	101	16	5	5	NUM
ejpam-5888	101	17	of	of	ADP
ejpam-5888	101	18	16	16	NUM
ejpam-5888	101	19	2.6	2.6	NUM
ejpam-5888	101	20	.	.	PUNCT
ejpam-5888	102	1	inverse	inverse	NOUN
ejpam-5888	102	2	of	of	ADP
ejpam-5888	102	3	a	a	DET
ejpam-5888	102	4	tropical	tropical	ADJ
ejpam-5888	102	5	monomial	monomial	NOUN
ejpam-5888	102	6	let	let	VERB
ejpam-5888	102	7	p(x	p(x	PROPN
ejpam-5888	102	8	)	)	PUNCT
ejpam-5888	102	9	be	be	AUX
ejpam-5888	102	10	a	a	DET
ejpam-5888	102	11	tropical	tropical	ADJ
ejpam-5888	102	12	monomial	monomial	NOUN
ejpam-5888	102	13	over	over	ADP
ejpam-5888	102	14	rmin	rmin	NOUN
ejpam-5888	102	15	.	.	PUNCT
ejpam-5888	103	1	we	we	PRON
ejpam-5888	103	2	define	define	VERB
ejpam-5888	103	3	the	the	DET
ejpam-5888	103	4	inverse	inverse	NOUN
ejpam-5888	103	5	of	of	ADP
ejpam-5888	103	6	p(x	p(x	PROPN
ejpam-5888	103	7	)	)	PUNCT
ejpam-5888	103	8	to	to	PART
ejpam-5888	103	9	be	be	AUX
ejpam-5888	103	10	a	a	DET
ejpam-5888	103	11	monomial	monomial	ADJ
ejpam-5888	103	12	p′(x	p′(x	NOUN
ejpam-5888	103	13	)	)	PUNCT
ejpam-5888	103	14	over	over	ADP
ejpam-5888	103	15	rmin	rmin	ADJ
ejpam-5888	103	16	∋	∋	NOUN
ejpam-5888	103	17	p(x)⊗	p(x)⊗	NOUN
ejpam-5888	103	18	p′(x	p′(x	NOUN
ejpam-5888	103	19	)	)	PUNCT
ejpam-5888	103	20	=	=	SYM
ejpam-5888	103	21	0	0	X
ejpam-5888	103	22	.	.	PUNCT
ejpam-5888	104	1	ex	ex	X
ejpam-5888	104	2	.	.	PUNCT
ejpam-5888	105	1	if	if	SCONJ
ejpam-5888	105	2	p(x	p(x	NOUN
ejpam-5888	105	3	)	)	PUNCT
ejpam-5888	105	4	=	=	PUNCT
ejpam-5888	105	5	a⊗	a⊗	NOUN
ejpam-5888	105	6	x⊗n	x⊗n	NOUN
ejpam-5888	105	7	,	,	PUNCT
ejpam-5888	105	8	then	then	ADV
ejpam-5888	105	9	p′(x	p′(x	NOUN
ejpam-5888	105	10	)	)	PUNCT
ejpam-5888	105	11	=	=	SYM
ejpam-5888	105	12	−a⊗	−a⊗	NOUN
ejpam-5888	105	13	(	(	PUNCT
ejpam-5888	105	14	−x)⊗n	−x)⊗n	PROPN
ejpam-5888	105	15	,	,	PUNCT
ejpam-5888	105	16	where	where	SCONJ
ejpam-5888	105	17	a	a	X
ejpam-5888	105	18	,	,	PUNCT
ejpam-5888	105	19	x	x	SYM
ejpam-5888	105	20	∈	∈	NOUN
ejpam-5888	105	21	r	r	NOUN
ejpam-5888	105	22	and	and	CCONJ
ejpam-5888	105	23	n	n	CCONJ
ejpam-5888	105	24	∈	∈	PROPN
ejpam-5888	105	25	n.	n.	NOUN
ejpam-5888	105	26	2.7	2.7	NUM
ejpam-5888	105	27	.	.	PUNCT
ejpam-5888	105	28	tropical	tropical	ADJ
ejpam-5888	105	29	matrix	matrix	NOUN
ejpam-5888	105	30	algebra	algebra	NOUN
ejpam-5888	105	31	2.7.1	2.7.1	NUM
ejpam-5888	105	32	.	.	PUNCT
ejpam-5888	106	1	tropical	tropical	ADJ
ejpam-5888	106	2	matrix	matrix	NOUN
ejpam-5888	106	3	a	a	DET
ejpam-5888	106	4	matrix	matrix	NOUN
ejpam-5888	106	5	of	of	ADP
ejpam-5888	106	6	order	order	NOUN
ejpam-5888	106	7	n	n	CCONJ
ejpam-5888	106	8	×	×	VERB
ejpam-5888	106	9	n	n	NOUN
ejpam-5888	106	10	with	with	ADP
ejpam-5888	106	11	entries	entry	NOUN
ejpam-5888	106	12	from	from	ADP
ejpam-5888	106	13	tropical	tropical	ADJ
ejpam-5888	106	14	algebra	algebra	NOUN
ejpam-5888	106	15	rmin	rmin	NOUN
ejpam-5888	106	16	equipped	equip	VERB
ejpam-5888	106	17	with	with	ADP
ejpam-5888	106	18	tropical	tropical	ADJ
ejpam-5888	106	19	addition	addition	NOUN
ejpam-5888	106	20	⊕	⊕	PROPN
ejpam-5888	106	21	and	and	CCONJ
ejpam-5888	106	22	multiplication	multiplication	NOUN
ejpam-5888	106	23	⊗	⊗	PROPN
ejpam-5888	106	24	is	be	AUX
ejpam-5888	106	25	called	call	VERB
ejpam-5888	106	26	a	a	DET
ejpam-5888	106	27	tropical	tropical	ADJ
ejpam-5888	106	28	matrix	matrix	NOUN
ejpam-5888	106	29	.	.	PUNCT
ejpam-5888	107	1	the	the	DET
ejpam-5888	107	2	set	set	NOUN
ejpam-5888	107	3	of	of	ADP
ejpam-5888	107	4	all	all	DET
ejpam-5888	107	5	n×	n×	PROPN
ejpam-5888	107	6	n	n	PRON
ejpam-5888	107	7	tropical	tropical	ADJ
ejpam-5888	107	8	matrices	matrix	NOUN
ejpam-5888	107	9	over	over	ADP
ejpam-5888	107	10	rmin	rmin	NOUN
ejpam-5888	107	11	is	be	AUX
ejpam-5888	107	12	denoted	denote	VERB
ejpam-5888	107	13	by	by	ADP
ejpam-5888	107	14	mn(rmin	mn(rmin	PROPN
ejpam-5888	107	15	)	)	PUNCT
ejpam-5888	107	16	.	.	PUNCT
ejpam-5888	108	1	2.7.2	2.7.2	NUM
ejpam-5888	108	2	.	.	PUNCT
ejpam-5888	108	3	tropical	tropical	ADJ
ejpam-5888	108	4	diagonal	diagonal	ADJ
ejpam-5888	108	5	matrix	matrix	NOUN
ejpam-5888	108	6	a	a	DET
ejpam-5888	108	7	tropical	tropical	ADJ
ejpam-5888	108	8	diagonal	diagonal	ADJ
ejpam-5888	108	9	matrix	matrix	NOUN
ejpam-5888	108	10	is	be	AUX
ejpam-5888	108	11	an	an	DET
ejpam-5888	108	12	n×n	n×n	PROPN
ejpam-5888	108	13	tropical	tropical	ADJ
ejpam-5888	108	14	matrix	matrix	NOUN
ejpam-5888	108	15	with	with	ADP
ejpam-5888	108	16	entries	entry	NOUN
ejpam-5888	108	17	ai	ai	VERB
ejpam-5888	108	18	∈	∈	PROPN
ejpam-5888	108	19	r	r	NOUN
ejpam-5888	108	20	,	,	PUNCT
ejpam-5888	108	21	i	i	NOUN
ejpam-5888	108	22	=	=	NOUN
ejpam-5888	108	23	1	1	NUM
ejpam-5888	108	24	,	,	PUNCT
ejpam-5888	108	25	...	...	PUNCT
ejpam-5888	108	26	,	,	PUNCT
ejpam-5888	108	27	n	n	CCONJ
ejpam-5888	108	28	,	,	PUNCT
ejpam-5888	108	29	on	on	ADP
ejpam-5888	108	30	the	the	DET
ejpam-5888	108	31	diagonal	diagonal	ADJ
ejpam-5888	108	32	and	and	CCONJ
ejpam-5888	108	33	∞	∞	NUM
ejpam-5888	108	34	elsewhere	elsewhere	ADV
ejpam-5888	108	35	,	,	PUNCT
ejpam-5888	108	36	that	that	ADV
ejpam-5888	108	37	is	is	ADV
ejpam-5888	108	38	,	,	PUNCT
ejpam-5888	108	39	d	d	PROPN
ejpam-5888	108	40	=	=	PUNCT
ejpam-5888	108	41			NOUN
ejpam-5888	108	42	a1	a1	NOUN
ejpam-5888	108	43	∞	∞	PROPN
ejpam-5888	108	44	.	.	PUNCT
ejpam-5888	108	45	.	.	PUNCT
ejpam-5888	108	46	.	.	PUNCT
ejpam-5888	109	1	∞	∞	NUM
ejpam-5888	109	2	∞	∞	NUM
ejpam-5888	109	3	a2	a2	PROPN
ejpam-5888	109	4	.	.	PUNCT
ejpam-5888	109	5	.	.	PUNCT
ejpam-5888	109	6	.	.	PUNCT
ejpam-5888	110	1	∞	∞	NUM
ejpam-5888	110	2	...	...	PUNCT
ejpam-5888	110	3	...	...	PUNCT
ejpam-5888	110	4	.	.	PUNCT
ejpam-5888	110	5	.	.	PUNCT
ejpam-5888	110	6	.	.	PUNCT
ejpam-5888	111	1	...	...	PUNCT
ejpam-5888	112	1	∞	∞	NUM
ejpam-5888	112	2	∞	∞	NUM
ejpam-5888	112	3	.	.	PUNCT
ejpam-5888	112	4	.	.	PUNCT
ejpam-5888	112	5	.	.	PUNCT
ejpam-5888	113	1	an	an	DET
ejpam-5888	113	2	.	.	PROPN
ejpam-5888	113	3	2.7.3	2.7.3	PROPN
ejpam-5888	113	4	.	.	PUNCT
ejpam-5888	114	1	tropical	tropical	ADJ
ejpam-5888	114	2	matrix	matrix	NOUN
ejpam-5888	114	3	multiplication	multiplication	NOUN
ejpam-5888	114	4	let	let	VERB
ejpam-5888	114	5	p	p	NOUN
ejpam-5888	114	6	,	,	PUNCT
ejpam-5888	114	7	q	q	PROPN
ejpam-5888	114	8	∈mn(rmin	∈mn(rmin	PROPN
ejpam-5888	114	9	)	)	PUNCT
ejpam-5888	114	10	.	.	PUNCT
ejpam-5888	115	1	then	then	ADV
ejpam-5888	115	2	t	t	X
ejpam-5888	116	1	=	=	PUNCT
ejpam-5888	116	2	p	p	NOUN
ejpam-5888	116	3	⊗q	⊗q	NOUN
ejpam-5888	116	4	is	be	AUX
ejpam-5888	116	5	given	give	VERB
ejpam-5888	116	6	by	by	ADP
ejpam-5888	116	7	tij	tij	PROPN
ejpam-5888	116	8	=	=	PUNCT
ejpam-5888	116	9	⊕n	⊕n	NOUN
ejpam-5888	116	10	k=1(pik	k=1(pik	NOUN
ejpam-5888	116	11	⊗	⊗	NUM
ejpam-5888	116	12	qkj	qkj	PROPN
ejpam-5888	116	13	)	)	PUNCT
ejpam-5888	116	14	.	.	PUNCT
ejpam-5888	117	1	ex	ex	X
ejpam-5888	117	2	.	.	PROPN
ejpam-5888	117	3	1	1	PROPN
ejpam-5888	117	4	2	2	NUM
ejpam-5888	117	5	−1	−1	NOUN
ejpam-5888	117	6	3	3	NUM
ejpam-5888	117	7	1	1	NUM
ejpam-5888	117	8	3	3	NUM
ejpam-5888	117	9	2	2	NUM
ejpam-5888	117	10	−2	−2	NOUN
ejpam-5888	117	11	3	3	NUM
ejpam-5888	117	12	⊗	⊗	ADJ
ejpam-5888	117	13	3	3	VERB
ejpam-5888	117	14	1	1	NUM
ejpam-5888	117	15	2	2	NUM
ejpam-5888	117	16	4	4	NUM
ejpam-5888	117	17	−1	−1	NOUN
ejpam-5888	117	18	3	3	NUM
ejpam-5888	117	19	2	2	NUM
ejpam-5888	117	20	1	1	NUM
ejpam-5888	117	21	−2	−2	NOUN
ejpam-5888	117	22			PROPN
ejpam-5888	117	23	=	=	SYM
ejpam-5888	117	24	1	1	PROPN
ejpam-5888	117	25	0	0	PUNCT
ejpam-5888	118	1	−3	−3	PROPN
ejpam-5888	118	2	5	5	NUM
ejpam-5888	118	3	0	0	NUM
ejpam-5888	118	4	1	1	NUM
ejpam-5888	118	5	2	2	NUM
ejpam-5888	118	6	−3	−3	NOUN
ejpam-5888	118	7	1	1	NUM
ejpam-5888	118	8	.	.	PROPN
ejpam-5888	118	9	2.7.4	2.7.4	NUM
ejpam-5888	118	10	.	.	PUNCT
ejpam-5888	119	1	tropical	tropical	ADJ
ejpam-5888	119	2	matrix	matrix	NOUN
ejpam-5888	119	3	scalar	scalar	ADJ
ejpam-5888	119	4	multiplication	multiplication	NOUN
ejpam-5888	119	5	let	let	VERB
ejpam-5888	119	6	p	p	PROPN
ejpam-5888	119	7	∈mn(rmin	∈mn(rmin	PROPN
ejpam-5888	119	8	)	)	PUNCT
ejpam-5888	119	9	and	and	CCONJ
ejpam-5888	119	10	s	s	PROPN
ejpam-5888	119	11	∈	∈	PROPN
ejpam-5888	119	12	rmin	rmin	NOUN
ejpam-5888	119	13	.	.	PUNCT
ejpam-5888	120	1	then	then	ADV
ejpam-5888	120	2	the	the	DET
ejpam-5888	120	3	tropical	tropical	ADJ
ejpam-5888	120	4	matrix	matrix	NOUN
ejpam-5888	120	5	scalar	scalar	ADJ
ejpam-5888	120	6	multiplication	multiplication	NOUN
ejpam-5888	120	7	s⊗	s⊗	NOUN
ejpam-5888	120	8	p	p	PROPN
ejpam-5888	120	9	is	be	AUX
ejpam-5888	120	10	given	give	VERB
ejpam-5888	120	11	by	by	ADP
ejpam-5888	120	12	s⊗	s⊗	NOUN
ejpam-5888	120	13	p	p	NOUN
ejpam-5888	120	14	=	=	PUNCT
ejpam-5888	120	15	(	(	PUNCT
ejpam-5888	120	16	s⊗	s⊗	NOUN
ejpam-5888	121	1	e)⊗	e)⊗	PROPN
ejpam-5888	121	2	p	p	NOUN
ejpam-5888	121	3	=	=	PUNCT
ejpam-5888	121	4	s⊗	s⊗	NOUN
ejpam-5888	121	5	pij	pij	NOUN
ejpam-5888	121	6	=	=	PUNCT
ejpam-5888	121	7	s+	s+	ADV
ejpam-5888	121	8	pij	pij	NOUN
ejpam-5888	121	9	,	,	PUNCT
ejpam-5888	121	10	where	where	SCONJ
ejpam-5888	121	11	e	e	NOUN
ejpam-5888	121	12	is	be	AUX
ejpam-5888	121	13	the	the	DET
ejpam-5888	121	14	multiplicative	multiplicative	ADJ
ejpam-5888	121	15	identity	identity	NOUN
ejpam-5888	121	16	matrix	matrix	NOUN
ejpam-5888	121	17	.	.	PUNCT
ejpam-5888	122	1	ex	ex	X
ejpam-5888	122	2	.	.	PROPN
ejpam-5888	122	3	5	5	NUM
ejpam-5888	122	4	⊗	⊗	PROPN
ejpam-5888	122	5	1	1	PROPN
ejpam-5888	122	6	2	2	NUM
ejpam-5888	122	7	−1	−1	NOUN
ejpam-5888	122	8	3	3	NUM
ejpam-5888	122	9	1	1	NUM
ejpam-5888	122	10	3	3	NUM
ejpam-5888	122	11	2	2	NUM
ejpam-5888	122	12	−2	−2	NOUN
ejpam-5888	122	13	3	3	NUM
ejpam-5888	122	14			PROPN
ejpam-5888	122	15	=	=	SYM
ejpam-5888	122	16			PROPN
ejpam-5888	122	17	5	5	NUM
ejpam-5888	122	18	∞	∞	NUM
ejpam-5888	122	19	∞	∞	NUM
ejpam-5888	122	20	∞	∞	NUM
ejpam-5888	122	21	5	5	NUM
ejpam-5888	122	22	∞	∞	NUM
ejpam-5888	122	23	∞	∞	NUM
ejpam-5888	122	24	∞	∞	NUM
ejpam-5888	122	25	5	5	NUM
ejpam-5888	122	26	⊗	⊗	NOUN
ejpam-5888	122	27	1	1	PROPN
ejpam-5888	122	28	2	2	NUM
ejpam-5888	122	29	−1	−1	NOUN
ejpam-5888	122	30	3	3	NUM
ejpam-5888	122	31	1	1	NUM
ejpam-5888	122	32	3	3	NUM
ejpam-5888	122	33	2	2	NUM
ejpam-5888	122	34	−2	−2	NOUN
ejpam-5888	122	35	3	3	NUM
ejpam-5888	122	36			PROPN
ejpam-5888	122	37	=	=	SYM
ejpam-5888	122	38	6	6	NOUN
ejpam-5888	122	39	7	7	NUM
ejpam-5888	122	40	4	4	NUM
ejpam-5888	122	41	8	8	NUM
ejpam-5888	122	42	6	6	NUM
ejpam-5888	122	43	8	8	NUM
ejpam-5888	122	44	7	7	NUM
ejpam-5888	122	45	3	3	NUM
ejpam-5888	122	46	8	8	NUM
ejpam-5888	122	47	.	.	PROPN
ejpam-5888	122	48	kashifa	kashifa	NOUN
ejpam-5888	122	49	begum	begum	VERB
ejpam-5888	122	50	a.	a.	NOUN
ejpam-5888	122	51	et	et	PROPN
ejpam-5888	122	52	.	.	PUNCT
ejpam-5888	123	1	al	al	PROPN
ejpam-5888	123	2	/	/	PUNCT
ejpam-5888	123	3	eur	eur	PROPN
ejpam-5888	123	4	.	.	PUNCT
ejpam-5888	124	1	j.	j.	PROPN
ejpam-5888	124	2	pure	pure	PROPN
ejpam-5888	124	3	appl	appl	PROPN
ejpam-5888	124	4	.	.	PROPN
ejpam-5888	124	5	math	math	PROPN
ejpam-5888	124	6	,	,	PUNCT
ejpam-5888	124	7	18	18	NUM
ejpam-5888	124	8	(	(	PUNCT
ejpam-5888	124	9	3	3	NUM
ejpam-5888	124	10	)	)	PUNCT
ejpam-5888	124	11	(	(	PUNCT
ejpam-5888	124	12	2025	2025	NUM
ejpam-5888	124	13	)	)	PUNCT
ejpam-5888	124	14	,	,	PUNCT
ejpam-5888	124	15	5888	5888	NUM
ejpam-5888	124	16	6	6	NUM
ejpam-5888	124	17	of	of	ADP
ejpam-5888	124	18	16	16	NUM
ejpam-5888	124	19	2.7.5	2.7.5	NUM
ejpam-5888	124	20	.	.	PUNCT
ejpam-5888	125	1	properties	property	NOUN
ejpam-5888	125	2	the	the	DET
ejpam-5888	125	3	following	follow	VERB
ejpam-5888	125	4	are	be	AUX
ejpam-5888	125	5	properties	property	NOUN
ejpam-5888	125	6	with	with	ADP
ejpam-5888	125	7	respect	respect	NOUN
ejpam-5888	125	8	to	to	ADP
ejpam-5888	125	9	tropical	tropical	ADJ
ejpam-5888	125	10	matrix	matrix	NOUN
ejpam-5888	125	11	multiplication	multiplication	NOUN
ejpam-5888	125	12	and	and	CCONJ
ejpam-5888	125	13	scalar	scalar	ADJ
ejpam-5888	125	14	multiplication	multiplication	NOUN
ejpam-5888	125	15	.	.	PUNCT
ejpam-5888	126	1	for	for	ADP
ejpam-5888	126	2	all	all	DET
ejpam-5888	126	3	p	p	NOUN
ejpam-5888	126	4	,	,	PUNCT
ejpam-5888	126	5	q	q	NOUN
ejpam-5888	126	6	,	,	PUNCT
ejpam-5888	126	7	s	s	PROPN
ejpam-5888	126	8	∈mn(rmin	∈mn(rmin	PROPN
ejpam-5888	126	9	)	)	PUNCT
ejpam-5888	126	10	,	,	PUNCT
ejpam-5888	126	11	m	m	PROPN
ejpam-5888	126	12	,	,	PUNCT
ejpam-5888	126	13	n	n	PROPN
ejpam-5888	126	14	∈	∈	PROPN
ejpam-5888	126	15	z	z	PROPN
ejpam-5888	126	16	and	and	CCONJ
ejpam-5888	126	17	s	s	PROPN
ejpam-5888	126	18	,	,	PUNCT
ejpam-5888	126	19	t	t	PROPN
ejpam-5888	126	20	∈	∈	PROPN
ejpam-5888	126	21	rmin	rmin	NOUN
ejpam-5888	126	22	,	,	PUNCT
ejpam-5888	126	23	•	•	ADP
ejpam-5888	126	24	p	p	PROPN
ejpam-5888	126	25	⊗	⊗	PROPN
ejpam-5888	126	26	(	(	PUNCT
ejpam-5888	126	27	q⊗	q⊗	NOUN
ejpam-5888	126	28	s	s	PART
ejpam-5888	126	29	)	)	PUNCT
ejpam-5888	126	30	=	=	SYM
ejpam-5888	126	31	(	(	PUNCT
ejpam-5888	126	32	p	p	X
ejpam-5888	126	33	⊗q)⊗	⊗q)⊗	NUM
ejpam-5888	126	34	s	s	X
ejpam-5888	126	35	(	(	PUNCT
ejpam-5888	126	36	associativity	associativity	NOUN
ejpam-5888	126	37	)	)	PUNCT
ejpam-5888	126	38	•	•	ADP
ejpam-5888	126	39	p⊗m	p⊗m	PROPN
ejpam-5888	126	40	⊗	⊗	PROPN
ejpam-5888	126	41	p⊗n	p⊗n	PROPN
ejpam-5888	126	42	=	=	SYM
ejpam-5888	126	43	p⊗n	p⊗n	VERB
ejpam-5888	126	44	⊗	⊗	PROPN
ejpam-5888	126	45	p⊗m	p⊗m	PROPN
ejpam-5888	126	46	=	=	SYM
ejpam-5888	126	47	p⊗(m+n	p⊗(m+n	NOUN
ejpam-5888	126	48	)	)	PUNCT
ejpam-5888	126	49	(	(	PUNCT
ejpam-5888	126	50	commutativity	commutativity	NOUN
ejpam-5888	126	51	)	)	PUNCT
ejpam-5888	126	52	•	•	NOUN
ejpam-5888	126	53	multiplicative	multiplicative	ADJ
ejpam-5888	126	54	identity	identity	NOUN
ejpam-5888	126	55	matrix	matrix	NOUN
ejpam-5888	126	56	:	:	PUNCT
ejpam-5888	126	57	∃	∃	PROPN
ejpam-5888	126	58	an	an	DET
ejpam-5888	126	59	unique	unique	ADJ
ejpam-5888	126	60	n	n	NUM
ejpam-5888	126	61	×	×	NOUN
ejpam-5888	126	62	n	n	NOUN
ejpam-5888	126	63	matrix	matrix	NOUN
ejpam-5888	126	64	e	e	X
ejpam-5888	126	65	∈	∈	PROPN
ejpam-5888	126	66	mn(rmin),∋	mn(rmin),∋	PUNCT
ejpam-5888	126	67	p	p	PROPN
ejpam-5888	126	68	⊗	⊗	PROPN
ejpam-5888	126	69	e	e	X
ejpam-5888	126	70	=	=	SYM
ejpam-5888	126	71	e	e	X
ejpam-5888	126	72	⊗	⊗	NOUN
ejpam-5888	126	73	p	p	X
ejpam-5888	126	74	=	=	X
ejpam-5888	126	75	p	p	X
ejpam-5888	126	76	,	,	PUNCT
ejpam-5888	126	77	where	where	SCONJ
ejpam-5888	126	78	e	e	NOUN
ejpam-5888	126	79	=	=	PUNCT
ejpam-5888	126	80			PROPN
ejpam-5888	126	81	0	0	NUM
ejpam-5888	126	82	∞	∞	NUM
ejpam-5888	126	83	.	.	PUNCT
ejpam-5888	126	84	.	.	PUNCT
ejpam-5888	126	85	.	.	PUNCT
ejpam-5888	127	1	∞	∞	NUM
ejpam-5888	127	2	∞	∞	NUM
ejpam-5888	127	3	0	0	NUM
ejpam-5888	127	4	.	.	PUNCT
ejpam-5888	127	5	.	.	PUNCT
ejpam-5888	128	1	.	.	PUNCT
ejpam-5888	129	1	∞	∞	NUM
ejpam-5888	129	2	...	...	PUNCT
ejpam-5888	129	3	...	...	PUNCT
ejpam-5888	129	4	.	.	PUNCT
ejpam-5888	129	5	.	.	PUNCT
ejpam-5888	129	6	.	.	PUNCT
ejpam-5888	130	1	...	...	PUNCT
ejpam-5888	131	1	∞	∞	NUM
ejpam-5888	131	2	∞	∞	NUM
ejpam-5888	131	3	.	.	PUNCT
ejpam-5888	131	4	.	.	PUNCT
ejpam-5888	132	1	.	.	PUNCT
ejpam-5888	133	1	0	0	NUM
ejpam-5888	134	1	.	.	PROPN
ejpam-5888	134	2	•	•	NUM
ejpam-5888	134	3	multiplicative	multiplicative	ADJ
ejpam-5888	134	4	inverse	inverse	NOUN
ejpam-5888	134	5	matrix	matrix	NOUN
ejpam-5888	134	6	:	:	PUNCT
ejpam-5888	134	7	multiplicative	multiplicative	ADJ
ejpam-5888	134	8	inverse	inverse	NOUN
ejpam-5888	134	9	of	of	ADP
ejpam-5888	134	10	a	a	DET
ejpam-5888	134	11	matrix	matrix	NOUN
ejpam-5888	134	12	p	p	NOUN
ejpam-5888	134	13	is	be	AUX
ejpam-5888	134	14	a	a	DET
ejpam-5888	134	15	matrix	matrix	NOUN
ejpam-5888	134	16	p	p	NOUN
ejpam-5888	134	17	′	′	NUM
ejpam-5888	134	18	∈mn(rmin	∈mn(rmin	PROPN
ejpam-5888	134	19	)	)	PUNCT
ejpam-5888	134	20	∋	∋	NOUN
ejpam-5888	134	21	p	p	NOUN
ejpam-5888	134	22	⊗	⊗	PROPN
ejpam-5888	134	23	p	p	NOUN
ejpam-5888	134	24	′	′	NUM
ejpam-5888	134	25	=	=	PUNCT
ejpam-5888	134	26	e.	e.	PROPN
ejpam-5888	134	27	in	in	ADP
ejpam-5888	134	28	general	general	ADJ
ejpam-5888	134	29	,	,	PUNCT
ejpam-5888	134	30	tropical	tropical	ADJ
ejpam-5888	134	31	matrices	matrix	NOUN
ejpam-5888	134	32	are	be	AUX
ejpam-5888	134	33	non	non	ADJ
ejpam-5888	134	34	-	-	ADJ
ejpam-5888	134	35	invertible	invertible	ADJ
ejpam-5888	134	36	.	.	PUNCT
ejpam-5888	135	1	•	•	NUM
ejpam-5888	135	2	miscellaneous	miscellaneous	ADJ
ejpam-5888	135	3	:	:	PUNCT
ejpam-5888	135	4	s⊗	s⊗	NOUN
ejpam-5888	135	5	p	p	NOUN
ejpam-5888	136	1	=	=	PUNCT
ejpam-5888	136	2	p	p	PROPN
ejpam-5888	136	3	⊗	⊗	PROPN
ejpam-5888	136	4	s	s	X
ejpam-5888	136	5	(	(	PUNCT
ejpam-5888	136	6	s⊗	s⊗	NOUN
ejpam-5888	136	7	p	p	NOUN
ejpam-5888	136	8	)	)	PUNCT
ejpam-5888	136	9	⊗	⊗	PROPN
ejpam-5888	136	10	(	(	PUNCT
ejpam-5888	136	11	t⊗	t⊗	NOUN
ejpam-5888	136	12	p	p	NOUN
ejpam-5888	136	13	)	)	PUNCT
ejpam-5888	136	14	=	=	SYM
ejpam-5888	136	15	(	(	PUNCT
ejpam-5888	136	16	s⊗	s⊗	NOUN
ejpam-5888	136	17	t)⊕	t)⊕	PROPN
ejpam-5888	136	18	(	(	PUNCT
ejpam-5888	136	19	p	p	PROPN
ejpam-5888	136	20	⊗	⊗	PROPN
ejpam-5888	136	21	p	p	NOUN
ejpam-5888	136	22	)	)	PUNCT
ejpam-5888	136	23	=	=	PUNCT
ejpam-5888	136	24	(	(	PUNCT
ejpam-5888	136	25	s+	s+	ADP
ejpam-5888	136	26	t)⊗	t)⊗	VERB
ejpam-5888	136	27	p⊗2	p⊗2	NOUN
ejpam-5888	136	28	3	3	NUM
ejpam-5888	136	29	.	.	PUNCT
ejpam-5888	137	1	the	the	DET
ejpam-5888	137	2	twin	twin	ADJ
ejpam-5888	137	3	conjugacy	conjugacy	PROPN
ejpam-5888	137	4	search	search	NOUN
ejpam-5888	137	5	problem	problem	NOUN
ejpam-5888	137	6	over	over	ADP
ejpam-5888	137	7	tropical	tropical	ADJ
ejpam-5888	137	8	algebra	algebra	NOUN
ejpam-5888	137	9	in	in	ADP
ejpam-5888	137	10	this	this	DET
ejpam-5888	137	11	section	section	NOUN
ejpam-5888	137	12	,	,	PUNCT
ejpam-5888	137	13	the	the	DET
ejpam-5888	137	14	tcsp	tcsp	NOUN
ejpam-5888	137	15	over	over	ADP
ejpam-5888	137	16	tropical	tropical	ADJ
ejpam-5888	137	17	algebra	algebra	NOUN
ejpam-5888	137	18	is	be	AUX
ejpam-5888	137	19	defined	define	VERB
ejpam-5888	137	20	.	.	PUNCT
ejpam-5888	138	1	the	the	DET
ejpam-5888	138	2	security	security	NOUN
ejpam-5888	138	3	and	and	CCONJ
ejpam-5888	138	4	complexity	complexity	NOUN
ejpam-5888	138	5	of	of	ADP
ejpam-5888	138	6	the	the	DET
ejpam-5888	138	7	problem	problem	NOUN
ejpam-5888	138	8	is	be	AUX
ejpam-5888	138	9	also	also	ADV
ejpam-5888	138	10	explored	explore	VERB
ejpam-5888	138	11	.	.	PUNCT
ejpam-5888	139	1	3.1	3.1	NUM
ejpam-5888	139	2	.	.	PUNCT
ejpam-5888	140	1	the	the	DET
ejpam-5888	140	2	twin	twin	ADJ
ejpam-5888	140	3	conjugacy	conjugacy	PROPN
ejpam-5888	140	4	search	search	NOUN
ejpam-5888	140	5	problem	problem	NOUN
ejpam-5888	140	6	over	over	ADP
ejpam-5888	140	7	tropical	tropical	ADJ
ejpam-5888	140	8	algebra	algebra	NOUN
ejpam-5888	140	9	the	the	DET
ejpam-5888	140	10	twin	twin	ADJ
ejpam-5888	140	11	conjugacy	conjugacy	ADJ
ejpam-5888	140	12	search	search	NOUN
ejpam-5888	140	13	problem	problem	NOUN
ejpam-5888	140	14	(	(	PUNCT
ejpam-5888	140	15	tcsp	tcsp	PROPN
ejpam-5888	140	16	)	)	PUNCT
ejpam-5888	140	17	for	for	ADP
ejpam-5888	140	18	the	the	DET
ejpam-5888	140	19	tropical	tropical	ADJ
ejpam-5888	140	20	algebra	algebra	NOUN
ejpam-5888	140	21	r	r	NOUN
ejpam-5888	140	22	=	=	SYM
ejpam-5888	140	23	mn(rmin	mn(rmin	PROPN
ejpam-5888	140	24	)	)	PUNCT
ejpam-5888	140	25	is	be	AUX
ejpam-5888	140	26	to	to	PART
ejpam-5888	140	27	find	find	VERB
ejpam-5888	140	28	two	two	NUM
ejpam-5888	140	29	matrices	matrix	NOUN
ejpam-5888	140	30	a1	a1	NOUN
ejpam-5888	140	31	,	,	PUNCT
ejpam-5888	140	32	a2	a2	PROPN
ejpam-5888	140	33	∈	∈	PROPN
ejpam-5888	140	34	r	r	NOUN
ejpam-5888	140	35	and	and	CCONJ
ejpam-5888	140	36	two	two	NUM
ejpam-5888	140	37	tropical	tropical	ADJ
ejpam-5888	140	38	monomials	monomial	NOUN
ejpam-5888	140	39	p1(x	p1(x	NOUN
ejpam-5888	140	40	)	)	PUNCT
ejpam-5888	140	41	,	,	PUNCT
ejpam-5888	140	42	p2(x	p2(x	X
ejpam-5888	140	43	)	)	PUNCT
ejpam-5888	140	44	over	over	ADP
ejpam-5888	140	45	rmin	rmin	NOUN
ejpam-5888	140	46	,	,	PUNCT
ejpam-5888	140	47	for	for	ADP
ejpam-5888	140	48	given	give	VERB
ejpam-5888	140	49	(	(	PUNCT
ejpam-5888	140	50	g(a	g(a	PROPN
ejpam-5888	140	51	)	)	PUNCT
ejpam-5888	140	52	,	,	PUNCT
ejpam-5888	140	53	x1	x1	PROPN
ejpam-5888	140	54	,	,	PUNCT
ejpam-5888	140	55	x2	x2	ADJ
ejpam-5888	140	56	)	)	PUNCT
ejpam-5888	140	57	∈	∈	PROPN
ejpam-5888	141	1	r	r	NOUN
ejpam-5888	141	2	×	×	NOUN
ejpam-5888	141	3	r	r	NOUN
ejpam-5888	141	4	×	×	NOUN
ejpam-5888	141	5	r	r	NOUN
ejpam-5888	141	6	,	,	PUNCT
ejpam-5888	141	7	where	where	SCONJ
ejpam-5888	141	8	g(x	g(x	NOUN
ejpam-5888	141	9	)	)	PUNCT
ejpam-5888	141	10	is	be	AUX
ejpam-5888	141	11	a	a	DET
ejpam-5888	141	12	tropical	tropical	ADJ
ejpam-5888	141	13	monomial	monomial	NOUN
ejpam-5888	141	14	and	and	CCONJ
ejpam-5888	141	15	a	a	DET
ejpam-5888	141	16	∈	∈	PROPN
ejpam-5888	141	17	r,∋	r,∋	NOUN
ejpam-5888	141	18	x1	x1	PROPN
ejpam-5888	141	19	=	=	PUNCT
ejpam-5888	141	20	p1(a1)⊗	p1(a1)⊗	PROPN
ejpam-5888	141	21	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	141	22	p	p	NOUN
ejpam-5888	141	23	′	′	NUM
ejpam-5888	141	24	1(a1	1(a1	NUM
ejpam-5888	141	25	)	)	PUNCT
ejpam-5888	141	26	,	,	PUNCT
ejpam-5888	141	27	x2	x2	NOUN
ejpam-5888	141	28	=	=	PUNCT
ejpam-5888	142	1	p2(a2)⊗	p2(a2)⊗	PRON
ejpam-5888	142	2	g(a)⊗	g(a)⊗	VERB
ejpam-5888	142	3	p	p	NOUN
ejpam-5888	142	4	′	′	NOUN
ejpam-5888	142	5	2(a2	2(a2	NUM
ejpam-5888	142	6	)	)	PUNCT
ejpam-5888	142	7	.	.	PUNCT
ejpam-5888	143	1	3.2	3.2	NUM
ejpam-5888	143	2	.	.	PUNCT
ejpam-5888	144	1	security	security	NOUN
ejpam-5888	144	2	of	of	ADP
ejpam-5888	144	3	the	the	DET
ejpam-5888	144	4	twin	twin	ADJ
ejpam-5888	144	5	conjugacy	conjugacy	ADJ
ejpam-5888	144	6	search	search	NOUN
ejpam-5888	144	7	problem	problem	NOUN
ejpam-5888	144	8	(	(	PUNCT
ejpam-5888	144	9	i	i	NOUN
ejpam-5888	144	10	)	)	PUNCT
ejpam-5888	144	11	determinant	determinant	ADJ
ejpam-5888	144	12	attack	attack	NOUN
ejpam-5888	144	13	:	:	PUNCT
ejpam-5888	144	14	the	the	DET
ejpam-5888	144	15	determinant	determinant	ADJ
ejpam-5888	144	16	attack	attack	NOUN
ejpam-5888	144	17	is	be	AUX
ejpam-5888	144	18	not	not	PART
ejpam-5888	144	19	valid	valid	ADJ
ejpam-5888	144	20	because	because	SCONJ
ejpam-5888	144	21	of	of	ADP
ejpam-5888	144	22	the	the	DET
ejpam-5888	144	23	non	non	ADJ
ejpam-5888	144	24	commutative	commutative	ADJ
ejpam-5888	144	25	property	property	NOUN
ejpam-5888	144	26	of	of	ADP
ejpam-5888	144	27	determinants	determinant	NOUN
ejpam-5888	144	28	in	in	ADP
ejpam-5888	144	29	tropical	tropical	ADJ
ejpam-5888	144	30	algebra	algebra	NOUN
ejpam-5888	144	31	.	.	PUNCT
ejpam-5888	145	1	even	even	ADV
ejpam-5888	145	2	if	if	SCONJ
ejpam-5888	145	3	an	an	DET
ejpam-5888	145	4	adversary	adversary	NOUN
ejpam-5888	145	5	knows	know	VERB
ejpam-5888	145	6	det(xi	det(xi	PROPN
ejpam-5888	145	7	)	)	PUNCT
ejpam-5888	145	8	and	and	CCONJ
ejpam-5888	145	9	det(g(a	det(g(a	PROPN
ejpam-5888	145	10	)	)	PUNCT
ejpam-5888	145	11	)	)	PUNCT
ejpam-5888	145	12	,	,	PUNCT
ejpam-5888	145	13	since	since	SCONJ
ejpam-5888	145	14	pi(ai	pi(ai	PROPN
ejpam-5888	145	15	)	)	PUNCT
ejpam-5888	145	16	,	,	PUNCT
ejpam-5888	145	17	i	i	PRON
ejpam-5888	145	18	=	=	NOUN
ejpam-5888	145	19	1	1	NUM
ejpam-5888	145	20	,	,	PUNCT
ejpam-5888	145	21	2	2	NUM
ejpam-5888	145	22	are	be	AUX
ejpam-5888	145	23	unknowns	unknown	NOUN
ejpam-5888	145	24	,	,	PUNCT
ejpam-5888	145	25	this	this	DET
ejpam-5888	145	26	attack	attack	NOUN
ejpam-5888	145	27	is	be	AUX
ejpam-5888	145	28	invalid	invalid	ADJ
ejpam-5888	145	29	.	.	PUNCT
ejpam-5888	146	1	kashifa	kashifa	PROPN
ejpam-5888	146	2	begum	begum	PROPN
ejpam-5888	146	3	a.	a.	NOUN
ejpam-5888	146	4	et	et	PROPN
ejpam-5888	146	5	.	.	PUNCT
ejpam-5888	147	1	al	al	PROPN
ejpam-5888	147	2	/	/	PUNCT
ejpam-5888	147	3	eur	eur	PROPN
ejpam-5888	147	4	.	.	PUNCT
ejpam-5888	148	1	j.	j.	PROPN
ejpam-5888	148	2	pure	pure	PROPN
ejpam-5888	148	3	appl	appl	PROPN
ejpam-5888	148	4	.	.	PROPN
ejpam-5888	148	5	math	math	PROPN
ejpam-5888	148	6	,	,	PUNCT
ejpam-5888	148	7	18	18	NUM
ejpam-5888	148	8	(	(	PUNCT
ejpam-5888	148	9	3	3	NUM
ejpam-5888	148	10	)	)	PUNCT
ejpam-5888	148	11	(	(	PUNCT
ejpam-5888	148	12	2025	2025	NUM
ejpam-5888	148	13	)	)	PUNCT
ejpam-5888	148	14	,	,	PUNCT
ejpam-5888	148	15	5888	5888	NUM
ejpam-5888	148	16	7	7	NUM
ejpam-5888	148	17	of	of	ADP
ejpam-5888	148	18	16	16	NUM
ejpam-5888	148	19	(	(	PUNCT
ejpam-5888	148	20	ii	ii	NOUN
ejpam-5888	148	21	)	)	PUNCT
ejpam-5888	148	22	eigenvalue	eigenvalue	NOUN
ejpam-5888	148	23	attack	attack	NOUN
ejpam-5888	148	24	:	:	PUNCT
ejpam-5888	148	25	this	this	DET
ejpam-5888	148	26	attack	attack	NOUN
ejpam-5888	148	27	may	may	AUX
ejpam-5888	148	28	work	work	VERB
ejpam-5888	148	29	in	in	ADP
ejpam-5888	148	30	some	some	DET
ejpam-5888	148	31	classical	classical	ADJ
ejpam-5888	148	32	group	group	NOUN
ejpam-5888	148	33	or	or	CCONJ
ejpam-5888	148	34	ring	ring	NOUN
ejpam-5888	148	35	,	,	PUNCT
ejpam-5888	148	36	but	but	CCONJ
ejpam-5888	148	37	we	we	PRON
ejpam-5888	148	38	have	have	AUX
ejpam-5888	148	39	considered	consider	VERB
ejpam-5888	148	40	tropical	tropical	ADJ
ejpam-5888	148	41	algebra	algebra	NOUN
ejpam-5888	148	42	where	where	SCONJ
ejpam-5888	148	43	finding	find	VERB
ejpam-5888	148	44	the	the	DET
ejpam-5888	148	45	eigenvalues	eigenvalue	NOUN
ejpam-5888	148	46	of	of	ADP
ejpam-5888	148	47	a	a	DET
ejpam-5888	148	48	matrix	matrix	NOUN
ejpam-5888	148	49	is	be	AUX
ejpam-5888	148	50	feeble	feeble	ADJ
ejpam-5888	148	51	.	.	PUNCT
ejpam-5888	149	1	even	even	ADV
ejpam-5888	149	2	if	if	SCONJ
ejpam-5888	149	3	an	an	DET
ejpam-5888	149	4	adversary	adversary	NOUN
ejpam-5888	149	5	finds	find	VERB
ejpam-5888	149	6	the	the	DET
ejpam-5888	149	7	eigenvalues	eigenvalue	NOUN
ejpam-5888	149	8	of	of	ADP
ejpam-5888	149	9	xi	xi	PROPN
ejpam-5888	149	10	and	and	CCONJ
ejpam-5888	149	11	g(a	g(a	PROPN
ejpam-5888	149	12	)	)	PUNCT
ejpam-5888	149	13	,	,	PUNCT
ejpam-5888	149	14	using	use	VERB
ejpam-5888	149	15	it	it	PRON
ejpam-5888	149	16	to	to	PART
ejpam-5888	149	17	find	find	VERB
ejpam-5888	149	18	the	the	DET
ejpam-5888	149	19	secret	secret	ADJ
ejpam-5888	149	20	elements	element	NOUN
ejpam-5888	149	21	pi(ai	pi(ai	PROPN
ejpam-5888	149	22	)	)	PUNCT
ejpam-5888	149	23	is	be	AUX
ejpam-5888	149	24	not	not	PART
ejpam-5888	149	25	effectual	effectual	ADJ
ejpam-5888	149	26	.	.	PUNCT
ejpam-5888	150	1	(	(	PUNCT
ejpam-5888	150	2	iii	iii	NOUN
ejpam-5888	150	3	)	)	PUNCT
ejpam-5888	150	4	cayley	cayley	ADJ
ejpam-5888	150	5	-	-	PUNCT
ejpam-5888	150	6	hamilton	hamilton	NOUN
ejpam-5888	150	7	attack	attack	NOUN
ejpam-5888	150	8	:	:	PUNCT
ejpam-5888	150	9	in	in	ADP
ejpam-5888	150	10	[	[	X
ejpam-5888	150	11	19	19	NUM
ejpam-5888	150	12	]	]	PUNCT
ejpam-5888	150	13	,	,	PUNCT
ejpam-5888	150	14	it	it	PRON
ejpam-5888	150	15	is	be	AUX
ejpam-5888	150	16	said	say	VERB
ejpam-5888	150	17	that	that	SCONJ
ejpam-5888	150	18	finding	find	VERB
ejpam-5888	150	19	the	the	DET
ejpam-5888	150	20	value	value	NOUN
ejpam-5888	150	21	of	of	ADP
ejpam-5888	150	22	a	a	DET
ejpam-5888	150	23	matrix	matrix	NOUN
ejpam-5888	150	24	substituted	substitute	VERB
ejpam-5888	150	25	in	in	ADP
ejpam-5888	150	26	a	a	DET
ejpam-5888	150	27	polynomial	polynomial	NOUN
ejpam-5888	150	28	is	be	AUX
ejpam-5888	150	29	manageable	manageable	ADJ
ejpam-5888	150	30	if	if	SCONJ
ejpam-5888	150	31	the	the	DET
ejpam-5888	150	32	matrix	matrix	NOUN
ejpam-5888	150	33	is	be	AUX
ejpam-5888	150	34	known	know	VERB
ejpam-5888	150	35	.	.	PUNCT
ejpam-5888	151	1	along	along	ADP
ejpam-5888	151	2	with	with	ADP
ejpam-5888	151	3	that	that	PRON
ejpam-5888	151	4	to	to	PART
ejpam-5888	151	5	use	use	VERB
ejpam-5888	151	6	the	the	DET
ejpam-5888	151	7	cayley	cayley	ADJ
ejpam-5888	151	8	-	-	PUNCT
ejpam-5888	151	9	hamilton	hamilton	NOUN
ejpam-5888	151	10	attack	attack	NOUN
ejpam-5888	151	11	,	,	PUNCT
ejpam-5888	151	12	an	an	DET
ejpam-5888	151	13	adversary	adversary	NOUN
ejpam-5888	151	14	must	must	AUX
ejpam-5888	151	15	know	know	VERB
ejpam-5888	151	16	two	two	NUM
ejpam-5888	151	17	polynomials	polynomial	NOUN
ejpam-5888	151	18	ri	ri	NOUN
ejpam-5888	151	19	over	over	ADP
ejpam-5888	151	20	rmin	rmin	ADJ
ejpam-5888	151	21	∋	∋	NOUN
ejpam-5888	151	22	ri(ai	ri(ai	PROPN
ejpam-5888	151	23	)	)	PUNCT
ejpam-5888	151	24	=	=	SYM
ejpam-5888	151	25	⊕n−1	⊕n−1	PROPN
ejpam-5888	151	26	k=1(ak	k=1(ak	VERB
ejpam-5888	151	27	⊗ak	⊗ak	NUM
ejpam-5888	151	28	i	i	PROPN
ejpam-5888	151	29	)	)	PUNCT
ejpam-5888	151	30	,	,	PUNCT
ejpam-5888	151	31	since	since	SCONJ
ejpam-5888	151	32	ai	ai	INTJ
ejpam-5888	151	33	are	be	AUX
ejpam-5888	151	34	unknown	unknown	ADJ
ejpam-5888	151	35	this	this	DET
ejpam-5888	151	36	attack	attack	NOUN
ejpam-5888	151	37	is	be	AUX
ejpam-5888	151	38	invalid	invalid	ADJ
ejpam-5888	151	39	.	.	PUNCT
ejpam-5888	152	1	3.3	3.3	NUM
ejpam-5888	152	2	.	.	PUNCT
ejpam-5888	153	1	brute	brute	ADJ
ejpam-5888	153	2	force	force	PROPN
ejpam-5888	153	3	complexity	complexity	NOUN
ejpam-5888	153	4	to	to	PART
ejpam-5888	153	5	find	find	VERB
ejpam-5888	153	6	the	the	DET
ejpam-5888	153	7	secret	secret	ADJ
ejpam-5888	153	8	keys	key	NOUN
ejpam-5888	153	9	pi(ai	pi(ai	PROPN
ejpam-5888	153	10	)	)	PUNCT
ejpam-5888	153	11	,	,	PUNCT
ejpam-5888	153	12	i	i	PRON
ejpam-5888	153	13	=	=	NOUN
ejpam-5888	153	14	1	1	NUM
ejpam-5888	153	15	,	,	PUNCT
ejpam-5888	153	16	2	2	NUM
ejpam-5888	153	17	,	,	PUNCT
ejpam-5888	153	18	by	by	ADP
ejpam-5888	153	19	brute	brute	ADJ
ejpam-5888	153	20	force	force	NOUN
ejpam-5888	153	21	attack	attack	NOUN
ejpam-5888	153	22	,	,	PUNCT
ejpam-5888	153	23	is	be	AUX
ejpam-5888	153	24	to	to	PART
ejpam-5888	153	25	find	find	VERB
ejpam-5888	153	26	both	both	DET
ejpam-5888	153	27	pi	pi	NOUN
ejpam-5888	153	28	and	and	CCONJ
ejpam-5888	153	29	ai	ai	VERB
ejpam-5888	153	30	,	,	PUNCT
ejpam-5888	153	31	i	i	PRON
ejpam-5888	153	32	=	=	NOUN
ejpam-5888	153	33	1	1	NUM
ejpam-5888	153	34	,	,	PUNCT
ejpam-5888	153	35	2	2	NUM
ejpam-5888	153	36	or	or	CCONJ
ejpam-5888	153	37	two	two	NUM
ejpam-5888	153	38	n×	n×	CCONJ
ejpam-5888	153	39	n	n	NOUN
ejpam-5888	153	40	matrices	matrix	NOUN
ejpam-5888	153	41	pi	pi	NOUN
ejpam-5888	153	42	∈	∈	PROPN
ejpam-5888	153	43	r	r	NOUN
ejpam-5888	153	44	∋	∋	NOUN
ejpam-5888	153	45	pi	pi	NOUN
ejpam-5888	153	46	=	=	SYM
ejpam-5888	153	47	pi(ai	pi(ai	PROPN
ejpam-5888	153	48	)	)	PUNCT
ejpam-5888	153	49	,	,	PUNCT
ejpam-5888	153	50	i	i	PRON
ejpam-5888	153	51	=	=	NOUN
ejpam-5888	153	52	1	1	NUM
ejpam-5888	153	53	,	,	PUNCT
ejpam-5888	153	54	2	2	NUM
ejpam-5888	153	55	.	.	PUNCT
ejpam-5888	153	56	the	the	DET
ejpam-5888	153	57	time	time	NOUN
ejpam-5888	153	58	complexity	complexity	NOUN
ejpam-5888	153	59	of	of	ADP
ejpam-5888	153	60	finding	find	VERB
ejpam-5888	153	61	an	an	DET
ejpam-5888	153	62	n×	n×	PRON
ejpam-5888	153	63	n	n	NOUN
ejpam-5888	153	64	matrix	matrix	NOUN
ejpam-5888	153	65	is	be	AUX
ejpam-5888	153	66	o(n2	o(n2	ADJ
ejpam-5888	153	67	)	)	PUNCT
ejpam-5888	153	68	.	.	PUNCT
ejpam-5888	154	1	suppose	suppose	VERB
ejpam-5888	154	2	that	that	SCONJ
ejpam-5888	154	3	r	r	NOUN
ejpam-5888	154	4	is	be	AUX
ejpam-5888	154	5	finite	finite	ADJ
ejpam-5888	154	6	,	,	PUNCT
ejpam-5888	154	7	i.e.	i.e.	X
ejpam-5888	154	8	,	,	PUNCT
ejpam-5888	154	9	we	we	PRON
ejpam-5888	154	10	take	take	VERB
ejpam-5888	154	11	r	r	NOUN
ejpam-5888	154	12	=	=	PUNCT
ejpam-5888	154	13	mn(zηmin	mn(zηmin	NOUN
ejpam-5888	154	14	)	)	PUNCT
ejpam-5888	154	15	,	,	PUNCT
ejpam-5888	154	16	then	then	ADV
ejpam-5888	154	17	the	the	DET
ejpam-5888	154	18	exhaustive	exhaustive	ADJ
ejpam-5888	154	19	search	search	NOUN
ejpam-5888	154	20	algorithm	algorithm	NOUN
ejpam-5888	154	21	is	be	AUX
ejpam-5888	154	22	given	give	VERB
ejpam-5888	154	23	in	in	ADP
ejpam-5888	154	24	algorithm	algorithm	NOUN
ejpam-5888	154	25	1	1	NUM
ejpam-5888	154	26	.	.	PUNCT
ejpam-5888	154	27	algorithm	algorithm	NOUN
ejpam-5888	154	28	1	1	NUM
ejpam-5888	154	29	exhaustive	exhaustive	ADJ
ejpam-5888	154	30	search	search	NOUN
ejpam-5888	154	31	algorithm	algorithm	NOUN
ejpam-5888	154	32	input	input	NOUN
ejpam-5888	154	33	:	:	PUNCT
ejpam-5888	154	34	x	x	X
ejpam-5888	154	35	,	,	PUNCT
ejpam-5888	154	36	g(a	g(a	PROPN
ejpam-5888	154	37	)	)	PUNCT
ejpam-5888	154	38	∈	∈	PROPN
ejpam-5888	154	39	r	r	NOUN
ejpam-5888	154	40	∋	∋	NOUN
ejpam-5888	154	41	x	x	SYM
ejpam-5888	154	42	=	=	SYM
ejpam-5888	154	43	p(a1)⊗	p(a1)⊗	PROPN
ejpam-5888	154	44	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	154	45	p′(a1	p′(a1	VERB
ejpam-5888	154	46	)	)	PUNCT
ejpam-5888	154	47	output	output	NOUN
ejpam-5888	154	48	:	:	PUNCT
ejpam-5888	154	49	secret	secret	ADJ
ejpam-5888	154	50	parameter	parameter	NOUN
ejpam-5888	154	51	p(a1	p(a1	NOUN
ejpam-5888	154	52	)	)	PUNCT
ejpam-5888	154	53	∈	∈	PROPN
ejpam-5888	154	54	r	r	NOUN
ejpam-5888	154	55	for	for	ADP
ejpam-5888	154	56	i←	i←	X
ejpam-5888	154	57	1	1	NUM
ejpam-5888	154	58	to	to	ADP
ejpam-5888	154	59	η	η	PROPN
ejpam-5888	154	60	−	−	PROPN
ejpam-5888	154	61	1	1	NUM
ejpam-5888	154	62	do	do	VERB
ejpam-5888	154	63	p̃(ai)←	p̃(ai)←	PROPN
ejpam-5888	154	64	pi(ai	pi(ai	PROPN
ejpam-5888	154	65	)	)	PUNCT
ejpam-5888	154	66	for	for	ADP
ejpam-5888	154	67	j	j	PROPN
ejpam-5888	154	68	←	←	PROPN
ejpam-5888	154	69	1	1	NUM
ejpam-5888	154	70	to	to	ADP
ejpam-5888	154	71	η	η	PROPN
ejpam-5888	154	72	−	−	PROPN
ejpam-5888	154	73	1	1	NUM
ejpam-5888	154	74	do	do	NOUN
ejpam-5888	154	75	xj	xj	PROPN
ejpam-5888	154	76	=	=	PROPN
ejpam-5888	154	77	p̃(ai)⊗	p̃(ai)⊗	PROPN
ejpam-5888	154	78	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	154	79	p̃′(ai	p̃′(ai	PROPN
ejpam-5888	154	80	)	)	PUNCT
ejpam-5888	154	81	if	if	SCONJ
ejpam-5888	154	82	x	x	PROPN
ejpam-5888	154	83	=	=	SYM
ejpam-5888	154	84	xj	xj	PROPN
ejpam-5888	154	85	then	then	ADV
ejpam-5888	154	86	return	return	VERB
ejpam-5888	154	87	xj	xj	PROPN
ejpam-5888	154	88	and	and	CCONJ
ejpam-5888	154	89	pi(ai	pi(ai	PROPN
ejpam-5888	154	90	)	)	PUNCT
ejpam-5888	154	91	end	end	VERB
ejpam-5888	154	92	if	if	SCONJ
ejpam-5888	154	93	end	end	NOUN
ejpam-5888	154	94	for	for	ADP
ejpam-5888	154	95	end	end	NOUN
ejpam-5888	154	96	for	for	ADP
ejpam-5888	154	97	4	4	NUM
ejpam-5888	154	98	.	.	PUNCT
ejpam-5888	155	1	the	the	DET
ejpam-5888	155	2	key	key	ADJ
ejpam-5888	155	3	exchange	exchange	NOUN
ejpam-5888	155	4	protocol	protocol	NOUN
ejpam-5888	155	5	based	base	VERB
ejpam-5888	155	6	on	on	ADP
ejpam-5888	155	7	the	the	DET
ejpam-5888	155	8	twin	twin	ADJ
ejpam-5888	155	9	conjugacy	conjugacy	ADJ
ejpam-5888	155	10	search	search	NOUN
ejpam-5888	155	11	problem	problem	NOUN
ejpam-5888	155	12	over	over	ADP
ejpam-5888	155	13	tropical	tropical	ADJ
ejpam-5888	155	14	algebra	algebra	NOUN
ejpam-5888	155	15	we	we	PRON
ejpam-5888	155	16	propose	propose	VERB
ejpam-5888	155	17	two	two	NUM
ejpam-5888	155	18	key	key	ADJ
ejpam-5888	155	19	exchange	exchange	NOUN
ejpam-5888	155	20	protocols	protocol	NOUN
ejpam-5888	155	21	based	base	VERB
ejpam-5888	155	22	on	on	ADP
ejpam-5888	155	23	the	the	DET
ejpam-5888	155	24	tcsp	tcsp	NOUN
ejpam-5888	155	25	over	over	ADP
ejpam-5888	155	26	tropical	tropical	ADJ
ejpam-5888	155	27	algebra	algebra	NOUN
ejpam-5888	155	28	.	.	PUNCT
ejpam-5888	156	1	assume	assume	VERB
ejpam-5888	156	2	alice	alice	PROPN
ejpam-5888	156	3	and	and	CCONJ
ejpam-5888	156	4	bob	bob	PROPN
ejpam-5888	156	5	are	be	AUX
ejpam-5888	156	6	the	the	DET
ejpam-5888	156	7	two	two	NUM
ejpam-5888	156	8	parties	party	NOUN
ejpam-5888	156	9	who	who	PRON
ejpam-5888	156	10	need	need	VERB
ejpam-5888	156	11	to	to	PART
ejpam-5888	156	12	exchange	exchange	VERB
ejpam-5888	156	13	information	information	NOUN
ejpam-5888	156	14	.	.	PUNCT
ejpam-5888	157	1	consider	consider	VERB
ejpam-5888	157	2	the	the	DET
ejpam-5888	157	3	tropical	tropical	ADJ
ejpam-5888	157	4	algebra	algebra	NOUN
ejpam-5888	157	5	r	r	NOUN
ejpam-5888	157	6	=	=	SYM
ejpam-5888	157	7	mn(rmin	mn(rmin	PROPN
ejpam-5888	157	8	)	)	PUNCT
ejpam-5888	157	9	.	.	PUNCT
ejpam-5888	158	1	let	let	VERB
ejpam-5888	158	2	h	h	PRON
ejpam-5888	158	3	⊂	⊂	PROPN
ejpam-5888	158	4	r	r	PRON
ejpam-5888	158	5	be	be	AUX
ejpam-5888	158	6	the	the	DET
ejpam-5888	158	7	subset	subset	NOUN
ejpam-5888	158	8	containing	contain	VERB
ejpam-5888	158	9	all	all	DET
ejpam-5888	158	10	the	the	DET
ejpam-5888	158	11	tropical	tropical	ADJ
ejpam-5888	158	12	diagonal	diagonal	ADJ
ejpam-5888	158	13	matrices	matrix	NOUN
ejpam-5888	158	14	.	.	PUNCT
ejpam-5888	159	1	let	let	VERB
ejpam-5888	159	2	g(x	g(x	NOUN
ejpam-5888	159	3	)	)	PUNCT
ejpam-5888	159	4	be	be	AUX
ejpam-5888	159	5	a	a	DET
ejpam-5888	159	6	public	public	ADJ
ejpam-5888	159	7	tropical	tropical	ADJ
ejpam-5888	159	8	monomial	monomial	NOUN
ejpam-5888	159	9	over	over	ADP
ejpam-5888	159	10	rmin	rmin	NOUN
ejpam-5888	159	11	and	and	CCONJ
ejpam-5888	159	12	a	a	DET
ejpam-5888	159	13	∈	∈	NOUN
ejpam-5888	159	14	r	r	NOUN
ejpam-5888	159	15	\h	\h	X
ejpam-5888	159	16	be	be	AUX
ejpam-5888	159	17	public	public	ADJ
ejpam-5888	159	18	tropical	tropical	ADJ
ejpam-5888	159	19	matrix	matrix	NOUN
ejpam-5888	159	20	.	.	PUNCT
ejpam-5888	160	1	kashifa	kashifa	PROPN
ejpam-5888	160	2	begum	begum	VERB
ejpam-5888	160	3	a.	a.	NOUN
ejpam-5888	160	4	et	et	PROPN
ejpam-5888	160	5	.	.	PUNCT
ejpam-5888	161	1	al	al	PROPN
ejpam-5888	161	2	/	/	PUNCT
ejpam-5888	161	3	eur	eur	PROPN
ejpam-5888	161	4	.	.	PUNCT
ejpam-5888	162	1	j.	j.	PROPN
ejpam-5888	162	2	pure	pure	PROPN
ejpam-5888	162	3	appl	appl	PROPN
ejpam-5888	162	4	.	.	PROPN
ejpam-5888	162	5	math	math	PROPN
ejpam-5888	162	6	,	,	PUNCT
ejpam-5888	162	7	18	18	NUM
ejpam-5888	162	8	(	(	PUNCT
ejpam-5888	162	9	3	3	NUM
ejpam-5888	162	10	)	)	PUNCT
ejpam-5888	162	11	(	(	PUNCT
ejpam-5888	162	12	2025	2025	NUM
ejpam-5888	162	13	)	)	PUNCT
ejpam-5888	162	14	,	,	PUNCT
ejpam-5888	162	15	5888	5888	NUM
ejpam-5888	162	16	8	8	NUM
ejpam-5888	162	17	of	of	ADP
ejpam-5888	162	18	16	16	NUM
ejpam-5888	162	19	4.1	4.1	NUM
ejpam-5888	162	20	.	.	PUNCT
ejpam-5888	163	1	the	the	DET
ejpam-5888	163	2	key	key	ADJ
ejpam-5888	163	3	exchange	exchange	NOUN
ejpam-5888	163	4	protocol	protocol	NOUN
ejpam-5888	163	5	i	i	PRON
ejpam-5888	163	6	(	(	PUNCT
ejpam-5888	163	7	i	i	NOUN
ejpam-5888	163	8	)	)	PUNCT
ejpam-5888	163	9	key	key	ADJ
ejpam-5888	163	10	generation	generation	NOUN
ejpam-5888	163	11	:	:	PUNCT
ejpam-5888	163	12	alice	alice	PROPN
ejpam-5888	163	13	chooses	choose	VERB
ejpam-5888	163	14	two	two	NUM
ejpam-5888	163	15	random	random	ADJ
ejpam-5888	163	16	secret	secret	ADJ
ejpam-5888	163	17	tropical	tropical	ADJ
ejpam-5888	163	18	monomials	monomial	NOUN
ejpam-5888	163	19	p1(x	p1(x	NOUN
ejpam-5888	163	20	)	)	PUNCT
ejpam-5888	163	21	,	,	PUNCT
ejpam-5888	163	22	p2(x	p2(x	X
ejpam-5888	163	23	)	)	PUNCT
ejpam-5888	163	24	over	over	ADP
ejpam-5888	163	25	rmin	rmin	NOUN
ejpam-5888	163	26	,	,	PUNCT
ejpam-5888	163	27	two	two	NUM
ejpam-5888	163	28	secret	secret	ADJ
ejpam-5888	163	29	matrices	matrix	NOUN
ejpam-5888	163	30	di	di	X
ejpam-5888	163	31	∈	∈	PROPN
ejpam-5888	163	32	h	h	NOUN
ejpam-5888	163	33	,	,	PUNCT
ejpam-5888	163	34	i	i	PRON
ejpam-5888	163	35	=	=	NOUN
ejpam-5888	163	36	1	1	NUM
ejpam-5888	163	37	,	,	PUNCT
ejpam-5888	163	38	2	2	NUM
ejpam-5888	163	39	and	and	CCONJ
ejpam-5888	163	40	sends	send	VERB
ejpam-5888	163	41	(	(	PUNCT
ejpam-5888	163	42	x1	x1	PROPN
ejpam-5888	163	43	,	,	PUNCT
ejpam-5888	163	44	x2	x2	PROPN
ejpam-5888	163	45	)	)	PUNCT
ejpam-5888	163	46	to	to	ADP
ejpam-5888	163	47	bob	bob	PROPN
ejpam-5888	163	48	,	,	PUNCT
ejpam-5888	163	49	where	where	SCONJ
ejpam-5888	163	50	x1	x1	PROPN
ejpam-5888	163	51	=	=	SYM
ejpam-5888	163	52	p1(d1	p1(d1	PROPN
ejpam-5888	163	53	)	)	PUNCT
ejpam-5888	163	54	⊗	⊗	PROPN
ejpam-5888	163	55	g(a	g(a	PROPN
ejpam-5888	163	56	)	)	PUNCT
ejpam-5888	163	57	⊗	⊗	PROPN
ejpam-5888	163	58	p′1(d1	p′1(d1	NOUN
ejpam-5888	163	59	)	)	PUNCT
ejpam-5888	163	60	and	and	CCONJ
ejpam-5888	163	61	x2	x2	NOUN
ejpam-5888	163	62	=	=	PUNCT
ejpam-5888	163	63	p2(d2	p2(d2	PROPN
ejpam-5888	163	64	)	)	PUNCT
ejpam-5888	163	65	⊗	⊗	PROPN
ejpam-5888	163	66	g(a	g(a	PROPN
ejpam-5888	163	67	)	)	PUNCT
ejpam-5888	163	68	⊗	⊗	PROPN
ejpam-5888	163	69	p′2(d2	p′2(d2	PROPN
ejpam-5888	163	70	)	)	PUNCT
ejpam-5888	163	71	.	.	PUNCT
ejpam-5888	164	1	thus	thus	ADV
ejpam-5888	164	2	the	the	DET
ejpam-5888	164	3	public	public	ADJ
ejpam-5888	164	4	key	key	NOUN
ejpam-5888	164	5	is	be	AUX
ejpam-5888	164	6	(	(	PUNCT
ejpam-5888	164	7	x1	x1	PROPN
ejpam-5888	164	8	,	,	PUNCT
ejpam-5888	164	9	x2	x2	PROPN
ejpam-5888	164	10	,	,	PUNCT
ejpam-5888	164	11	g	g	PROPN
ejpam-5888	164	12	,	,	PUNCT
ejpam-5888	164	13	a	a	PRON
ejpam-5888	164	14	)	)	PUNCT
ejpam-5888	164	15	,	,	PUNCT
ejpam-5888	164	16	and	and	CCONJ
ejpam-5888	164	17	the	the	DET
ejpam-5888	164	18	private	private	ADJ
ejpam-5888	164	19	key	key	NOUN
ejpam-5888	164	20	is	be	AUX
ejpam-5888	164	21	(	(	PUNCT
ejpam-5888	164	22	p1	p1	NOUN
ejpam-5888	164	23	,	,	PUNCT
ejpam-5888	164	24	p2	p2	NOUN
ejpam-5888	164	25	,	,	PUNCT
ejpam-5888	164	26	d1	d1	NOUN
ejpam-5888	164	27	,	,	PUNCT
ejpam-5888	164	28	d2	d2	PROPN
ejpam-5888	164	29	)	)	PUNCT
ejpam-5888	164	30	.	.	PUNCT
ejpam-5888	165	1	(	(	PUNCT
ejpam-5888	165	2	ii	ii	NOUN
ejpam-5888	165	3	)	)	PUNCT
ejpam-5888	165	4	encryption	encryption	NOUN
ejpam-5888	165	5	:	:	PUNCT
ejpam-5888	165	6	bob	bob	PROPN
ejpam-5888	165	7	chooses	choose	VERB
ejpam-5888	165	8	a	a	DET
ejpam-5888	165	9	random	random	ADJ
ejpam-5888	165	10	secret	secret	ADJ
ejpam-5888	165	11	tropical	tropical	ADJ
ejpam-5888	165	12	monomial	monomial	PROPN
ejpam-5888	165	13	q(x	q(x	PROPN
ejpam-5888	165	14	)	)	PUNCT
ejpam-5888	165	15	over	over	ADP
ejpam-5888	165	16	rmin	rmin	NOUN
ejpam-5888	165	17	,	,	PUNCT
ejpam-5888	165	18	a	a	DET
ejpam-5888	165	19	secret	secret	ADJ
ejpam-5888	165	20	matrix	matrix	NOUN
ejpam-5888	165	21	b	b	NOUN
ejpam-5888	165	22	∈	∈	NOUN
ejpam-5888	165	23	h	h	NOUN
ejpam-5888	165	24	and	and	CCONJ
ejpam-5888	165	25	sends	send	VERB
ejpam-5888	165	26	y	y	PROPN
ejpam-5888	165	27	to	to	ADP
ejpam-5888	165	28	alice	alice	PROPN
ejpam-5888	165	29	,	,	PUNCT
ejpam-5888	165	30	where	where	SCONJ
ejpam-5888	165	31	y	y	NOUN
ejpam-5888	165	32	=	=	SYM
ejpam-5888	165	33	q(b	q(b	ADJ
ejpam-5888	165	34	)	)	PUNCT
ejpam-5888	166	1	⊗	⊗	PROPN
ejpam-5888	166	2	g(a	g(a	PROPN
ejpam-5888	166	3	)	)	PUNCT
ejpam-5888	166	4	⊗	⊗	PROPN
ejpam-5888	166	5	q′(b	q′(b	PROPN
ejpam-5888	166	6	)	)	PUNCT
ejpam-5888	166	7	.	.	PUNCT
ejpam-5888	167	1	thus	thus	ADV
ejpam-5888	167	2	the	the	DET
ejpam-5888	167	3	public	public	ADJ
ejpam-5888	167	4	key	key	NOUN
ejpam-5888	167	5	is	be	AUX
ejpam-5888	167	6	(	(	PUNCT
ejpam-5888	167	7	y	y	NOUN
ejpam-5888	167	8	,	,	PUNCT
ejpam-5888	167	9	g	g	PROPN
ejpam-5888	167	10	,	,	PUNCT
ejpam-5888	167	11	a	a	PRON
ejpam-5888	167	12	)	)	PUNCT
ejpam-5888	167	13	,	,	PUNCT
ejpam-5888	167	14	and	and	CCONJ
ejpam-5888	167	15	the	the	DET
ejpam-5888	167	16	private	private	ADJ
ejpam-5888	167	17	key	key	NOUN
ejpam-5888	167	18	is	be	AUX
ejpam-5888	167	19	(	(	PUNCT
ejpam-5888	167	20	q	q	ADJ
ejpam-5888	167	21	,	,	PUNCT
ejpam-5888	167	22	b	b	NOUN
ejpam-5888	167	23	)	)	PUNCT
ejpam-5888	167	24	.	.	PUNCT
ejpam-5888	168	1	(	(	PUNCT
ejpam-5888	168	2	iii	iii	X
ejpam-5888	168	3	)	)	PUNCT
ejpam-5888	168	4	decryption	decryption	NOUN
ejpam-5888	168	5	:	:	PUNCT
ejpam-5888	169	1	alice	alice	PROPN
ejpam-5888	169	2	receives	receive	VERB
ejpam-5888	169	3	y	y	PROPN
ejpam-5888	169	4	and	and	CCONJ
ejpam-5888	169	5	computes	compute	VERB
ejpam-5888	169	6	z1	z1	PROPN
ejpam-5888	169	7	=	=	SYM
ejpam-5888	169	8	p1(d1	p1(d1	NOUN
ejpam-5888	169	9	)	)	PUNCT
ejpam-5888	169	10	⊗	⊗	PROPN
ejpam-5888	169	11	y	y	PROPN
ejpam-5888	169	12	⊗	⊗	PROPN
ejpam-5888	169	13	p′1(d1	p′1(d1	PROPN
ejpam-5888	169	14	)	)	PUNCT
ejpam-5888	169	15	,	,	PUNCT
ejpam-5888	169	16	z2	z2	NOUN
ejpam-5888	169	17	=	=	SYM
ejpam-5888	169	18	p2(d2	p2(d2	PROPN
ejpam-5888	169	19	)	)	PUNCT
ejpam-5888	169	20	⊗	⊗	PROPN
ejpam-5888	169	21	y	y	PROPN
ejpam-5888	169	22	⊗	⊗	PROPN
ejpam-5888	169	23	p′2(d2	p′2(d2	PROPN
ejpam-5888	169	24	)	)	PUNCT
ejpam-5888	169	25	.	.	PUNCT
ejpam-5888	170	1	bob	bob	PROPN
ejpam-5888	170	2	receives	receive	VERB
ejpam-5888	170	3	(	(	PUNCT
ejpam-5888	170	4	x1	x1	PROPN
ejpam-5888	170	5	,	,	PUNCT
ejpam-5888	170	6	x2	x2	PROPN
ejpam-5888	170	7	)	)	PUNCT
ejpam-5888	170	8	and	and	CCONJ
ejpam-5888	170	9	computes	compute	VERB
ejpam-5888	170	10	z̃1	z̃1	X
ejpam-5888	170	11	=	=	SYM
ejpam-5888	170	12	q(b	q(b	ADV
ejpam-5888	170	13	)	)	PUNCT
ejpam-5888	171	1	⊗	⊗	PROPN
ejpam-5888	171	2	x1	x1	PROPN
ejpam-5888	172	1	⊗	⊗	NUM
ejpam-5888	172	2	q′(b	q′(b	PROPN
ejpam-5888	172	3	)	)	PUNCT
ejpam-5888	172	4	,	,	PUNCT
ejpam-5888	172	5	z̃2	z̃2	PROPN
ejpam-5888	172	6	=	=	PUNCT
ejpam-5888	172	7	q(b)⊗x2	q(b)⊗x2	VERB
ejpam-5888	172	8	⊗	⊗	PROPN
ejpam-5888	172	9	q′(b	q′(b	PROPN
ejpam-5888	172	10	)	)	PUNCT
ejpam-5888	172	11	.	.	PUNCT
ejpam-5888	173	1	(	(	PUNCT
ejpam-5888	173	2	iv	iv	X
ejpam-5888	173	3	)	)	PUNCT
ejpam-5888	173	4	correctness	correctness	NOUN
ejpam-5888	173	5	:	:	PUNCT
ejpam-5888	173	6	since	since	SCONJ
ejpam-5888	173	7	pi(di	pi(di	PROPN
ejpam-5888	173	8	)	)	PUNCT
ejpam-5888	173	9	⊗	⊗	PROPN
ejpam-5888	173	10	q(b	q(b	ADJ
ejpam-5888	173	11	)	)	PUNCT
ejpam-5888	174	1	=	=	SYM
ejpam-5888	174	2	q(b	q(b	ADJ
ejpam-5888	174	3	)	)	PUNCT
ejpam-5888	174	4	⊗	⊗	PROPN
ejpam-5888	174	5	pi(di	pi(di	NOUN
ejpam-5888	174	6	)	)	PUNCT
ejpam-5888	174	7	,	,	PUNCT
ejpam-5888	174	8	and	and	CCONJ
ejpam-5888	174	9	p′i(di	p′i(di	NUM
ejpam-5888	174	10	)	)	PUNCT
ejpam-5888	174	11	⊗	⊗	PROPN
ejpam-5888	174	12	q(b	q(b	ADJ
ejpam-5888	174	13	)	)	PUNCT
ejpam-5888	174	14	=	=	SYM
ejpam-5888	175	1	q(b	q(b	ADJ
ejpam-5888	175	2	)	)	PUNCT
ejpam-5888	175	3	⊗	⊗	PROPN
ejpam-5888	175	4	p′i(di	p′i(di	NOUN
ejpam-5888	175	5	)	)	PUNCT
ejpam-5888	175	6	,	,	PUNCT
ejpam-5888	176	1	i	i	PRON
ejpam-5888	176	2	=	=	NOUN
ejpam-5888	176	3	1	1	NUM
ejpam-5888	176	4	,	,	PUNCT
ejpam-5888	176	5	2	2	NUM
ejpam-5888	176	6	,	,	PUNCT
ejpam-5888	176	7	alice	alice	PROPN
ejpam-5888	176	8	and	and	CCONJ
ejpam-5888	176	9	bob	bob	PROPN
ejpam-5888	176	10	have	have	VERB
ejpam-5888	176	11	same	same	ADJ
ejpam-5888	176	12	secret	secret	ADJ
ejpam-5888	176	13	key	key	NOUN
ejpam-5888	176	14	,	,	PUNCT
ejpam-5888	176	15	that	that	ADV
ejpam-5888	176	16	is	be	AUX
ejpam-5888	176	17	,	,	PUNCT
ejpam-5888	177	1	zi	zi	PROPN
ejpam-5888	177	2	=	=	SYM
ejpam-5888	177	3	z̃i	z̃i	PROPN
ejpam-5888	177	4	,	,	PUNCT
ejpam-5888	177	5	i	i	PRON
ejpam-5888	177	6	=	=	NOUN
ejpam-5888	177	7	1	1	NUM
ejpam-5888	177	8	,	,	PUNCT
ejpam-5888	177	9	2	2	NUM
ejpam-5888	177	10	.	.	PUNCT
ejpam-5888	177	11	table	table	NOUN
ejpam-5888	177	12	1	1	NUM
ejpam-5888	177	13	:	:	PUNCT
ejpam-5888	177	14	the	the	DET
ejpam-5888	177	15	key	key	ADJ
ejpam-5888	177	16	exchange	exchange	NOUN
ejpam-5888	177	17	protocol	protocol	NOUN
ejpam-5888	178	1	i	i	PRON
ejpam-5888	178	2	alice	alice	PROPN
ejpam-5888	178	3	bob	bob	PROPN
ejpam-5888	178	4	p1(x	p1(x	PROPN
ejpam-5888	178	5	)	)	PUNCT
ejpam-5888	178	6	,	,	PUNCT
ejpam-5888	178	7	p2(x)←	p2(x)←	PROPN
ejpam-5888	178	8	rmin	rmin	NOUN
ejpam-5888	178	9	,	,	PUNCT
ejpam-5888	178	10	d1	d1	PROPN
ejpam-5888	178	11	,	,	PUNCT
ejpam-5888	178	12	d2	d2	PROPN
ejpam-5888	178	13	←	←	PROPN
ejpam-5888	178	14	h	h	PROPN
ejpam-5888	178	15	x1	x1	PROPN
ejpam-5888	179	1	=	=	PUNCT
ejpam-5888	179	2	p1(d1)⊗	p1(d1)⊗	PROPN
ejpam-5888	179	3	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	179	4	p′1(d1	p′1(d1	NOUN
ejpam-5888	179	5	)	)	PUNCT
ejpam-5888	179	6	x2	x2	NOUN
ejpam-5888	180	1	=	=	PUNCT
ejpam-5888	180	2	p2(d2)⊗	p2(d2)⊗	NOUN
ejpam-5888	180	3	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	180	4	p′2(d2	p′2(d2	NOUN
ejpam-5888	180	5	)	)	PUNCT
ejpam-5888	180	6	x1,x2−→	x1,x2−→	PROPN
ejpam-5888	180	7	q(x)←	q(x)←	PROPN
ejpam-5888	180	8	rmin	rmin	NOUN
ejpam-5888	180	9	,	,	PUNCT
ejpam-5888	180	10	b	b	PROPN
ejpam-5888	180	11	←	←	PROPN
ejpam-5888	180	12	h	h	PROPN
ejpam-5888	180	13	y	y	PROPN
ejpam-5888	180	14	=	=	PUNCT
ejpam-5888	180	15	q(b)⊗	q(b)⊗	PROPN
ejpam-5888	180	16	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	180	17	q′(b	q′(b	ADV
ejpam-5888	180	18	)	)	PUNCT
ejpam-5888	181	1	y←−	y←−	PROPN
ejpam-5888	181	2	z1	z1	NOUN
ejpam-5888	181	3	=	=	PUNCT
ejpam-5888	181	4	p1(d1)⊗	p1(d1)⊗	NOUN
ejpam-5888	181	5	y	y	PROPN
ejpam-5888	181	6	⊗	⊗	PROPN
ejpam-5888	181	7	p′1(d1	p′1(d1	PROPN
ejpam-5888	181	8	)	)	PUNCT
ejpam-5888	181	9	z̃1	z̃1	PROPN
ejpam-5888	181	10	=	=	PUNCT
ejpam-5888	181	11	q(b)⊗x1	q(b)⊗x1	PROPN
ejpam-5888	181	12	⊗	⊗	PROPN
ejpam-5888	181	13	q′(b	q′(b	PROPN
ejpam-5888	181	14	)	)	PUNCT
ejpam-5888	181	15	z2	z2	NOUN
ejpam-5888	181	16	=	=	PUNCT
ejpam-5888	181	17	p2(d2)⊗	p2(d2)⊗	VERB
ejpam-5888	181	18	y	y	PROPN
ejpam-5888	181	19	⊗	⊗	PROPN
ejpam-5888	181	20	p′2(d2	p′2(d2	PROPN
ejpam-5888	181	21	)	)	PUNCT
ejpam-5888	181	22	z̃2	z̃2	PROPN
ejpam-5888	181	23	=	=	PUNCT
ejpam-5888	181	24	q(b)⊗x2	q(b)⊗x2	VERB
ejpam-5888	181	25	⊗	⊗	PROPN
ejpam-5888	181	26	q′(b	q′(b	PROPN
ejpam-5888	181	27	)	)	PUNCT
ejpam-5888	181	28	z1	z1	PROPN
ejpam-5888	181	29	=	=	SYM
ejpam-5888	181	30	z̃1	z̃1	PROPN
ejpam-5888	181	31	z2	z2	NOUN
ejpam-5888	181	32	=	=	PUNCT
ejpam-5888	182	1	z̃2	z̃2	PROPN
ejpam-5888	182	2	4.2	4.2	NUM
ejpam-5888	182	3	.	.	PUNCT
ejpam-5888	183	1	the	the	DET
ejpam-5888	183	2	key	key	ADJ
ejpam-5888	183	3	exchange	exchange	NOUN
ejpam-5888	183	4	protocol	protocol	NOUN
ejpam-5888	183	5	ii	ii	PROPN
ejpam-5888	183	6	(	(	PUNCT
ejpam-5888	183	7	i	i	NOUN
ejpam-5888	183	8	)	)	PUNCT
ejpam-5888	183	9	key	key	ADJ
ejpam-5888	183	10	generation	generation	NOUN
ejpam-5888	183	11	:	:	PUNCT
ejpam-5888	183	12	alice	alice	PROPN
ejpam-5888	183	13	chooses	choose	VERB
ejpam-5888	183	14	two	two	NUM
ejpam-5888	183	15	random	random	ADJ
ejpam-5888	183	16	secret	secret	ADJ
ejpam-5888	183	17	tropical	tropical	ADJ
ejpam-5888	183	18	monomials	monomial	NOUN
ejpam-5888	183	19	p1(x	p1(x	NOUN
ejpam-5888	183	20	)	)	PUNCT
ejpam-5888	183	21	,	,	PUNCT
ejpam-5888	183	22	p2(x	p2(x	X
ejpam-5888	183	23	)	)	PUNCT
ejpam-5888	183	24	over	over	ADP
ejpam-5888	183	25	rmin	rmin	NOUN
ejpam-5888	183	26	,	,	PUNCT
ejpam-5888	183	27	two	two	NUM
ejpam-5888	183	28	secret	secret	ADJ
ejpam-5888	183	29	matrices	matrix	NOUN
ejpam-5888	183	30	d1	d1	PROPN
ejpam-5888	183	31	,	,	PUNCT
ejpam-5888	183	32	d2	d2	PROPN
ejpam-5888	183	33	∈	∈	PROPN
ejpam-5888	183	34	h	h	NOUN
ejpam-5888	183	35	and	and	CCONJ
ejpam-5888	183	36	sends	send	VERB
ejpam-5888	183	37	(	(	PUNCT
ejpam-5888	183	38	x1	x1	PROPN
ejpam-5888	183	39	,	,	PUNCT
ejpam-5888	183	40	x2	x2	PROPN
ejpam-5888	183	41	)	)	PUNCT
ejpam-5888	183	42	to	to	ADP
ejpam-5888	183	43	bob	bob	PROPN
ejpam-5888	183	44	,	,	PUNCT
ejpam-5888	183	45	where	where	SCONJ
ejpam-5888	183	46	x1	x1	PROPN
ejpam-5888	183	47	=	=	SYM
ejpam-5888	183	48	p1(d1	p1(d1	PROPN
ejpam-5888	183	49	)	)	PUNCT
ejpam-5888	183	50	⊗	⊗	PROPN
ejpam-5888	183	51	g(a	g(a	PROPN
ejpam-5888	183	52	)	)	PUNCT
ejpam-5888	183	53	⊗	⊗	PROPN
ejpam-5888	183	54	p′1(d1	p′1(d1	NOUN
ejpam-5888	183	55	)	)	PUNCT
ejpam-5888	183	56	and	and	CCONJ
ejpam-5888	183	57	x2	x2	NOUN
ejpam-5888	183	58	=	=	PUNCT
ejpam-5888	183	59	p2(d2	p2(d2	PROPN
ejpam-5888	183	60	)	)	PUNCT
ejpam-5888	183	61	⊗	⊗	PROPN
ejpam-5888	183	62	g(a	g(a	PROPN
ejpam-5888	183	63	)	)	PUNCT
ejpam-5888	183	64	⊗	⊗	PROPN
ejpam-5888	183	65	p′2(d2	p′2(d2	PROPN
ejpam-5888	183	66	)	)	PUNCT
ejpam-5888	183	67	.	.	PUNCT
ejpam-5888	184	1	then	then	ADV
ejpam-5888	184	2	the	the	DET
ejpam-5888	184	3	public	public	ADJ
ejpam-5888	184	4	key	key	NOUN
ejpam-5888	184	5	is	be	AUX
ejpam-5888	184	6	(	(	PUNCT
ejpam-5888	184	7	x1	x1	PROPN
ejpam-5888	184	8	,	,	PUNCT
ejpam-5888	184	9	x2	x2	PROPN
ejpam-5888	184	10	,	,	PUNCT
ejpam-5888	184	11	g	g	PROPN
ejpam-5888	184	12	,	,	PUNCT
ejpam-5888	184	13	a	a	PRON
ejpam-5888	184	14	)	)	PUNCT
ejpam-5888	184	15	,	,	PUNCT
ejpam-5888	184	16	while	while	SCONJ
ejpam-5888	184	17	the	the	DET
ejpam-5888	184	18	private	private	ADJ
ejpam-5888	184	19	key	key	NOUN
ejpam-5888	184	20	is	be	AUX
ejpam-5888	184	21	(	(	PUNCT
ejpam-5888	184	22	p1	p1	NOUN
ejpam-5888	184	23	,	,	PUNCT
ejpam-5888	184	24	p2	p2	NOUN
ejpam-5888	184	25	,	,	PUNCT
ejpam-5888	184	26	d1	d1	NOUN
ejpam-5888	184	27	,	,	PUNCT
ejpam-5888	184	28	d2	d2	PROPN
ejpam-5888	184	29	)	)	PUNCT
ejpam-5888	184	30	.	.	PUNCT
ejpam-5888	185	1	(	(	PUNCT
ejpam-5888	185	2	ii	ii	NOUN
ejpam-5888	185	3	)	)	PUNCT
ejpam-5888	185	4	encryption	encryption	NOUN
ejpam-5888	185	5	:	:	PUNCT
ejpam-5888	185	6	bob	bob	PROPN
ejpam-5888	185	7	chooses	choose	VERB
ejpam-5888	185	8	two	two	NUM
ejpam-5888	185	9	random	random	ADJ
ejpam-5888	185	10	secret	secret	ADJ
ejpam-5888	185	11	tropical	tropical	ADJ
ejpam-5888	185	12	monomials	monomial	NOUN
ejpam-5888	185	13	q1(x	q1(x	NOUN
ejpam-5888	185	14	)	)	PUNCT
ejpam-5888	185	15	,	,	PUNCT
ejpam-5888	185	16	q2(x	q2(x	X
ejpam-5888	185	17	)	)	PUNCT
ejpam-5888	185	18	over	over	ADP
ejpam-5888	185	19	rmin	rmin	NOUN
ejpam-5888	185	20	,	,	PUNCT
ejpam-5888	185	21	two	two	NUM
ejpam-5888	185	22	secret	secret	ADJ
ejpam-5888	185	23	matrices	matrix	NOUN
ejpam-5888	185	24	b1	b1	NOUN
ejpam-5888	185	25	,	,	PUNCT
ejpam-5888	185	26	b2	b2	NOUN
ejpam-5888	185	27	∈	∈	PROPN
ejpam-5888	185	28	h	h	NOUN
ejpam-5888	185	29	and	and	CCONJ
ejpam-5888	185	30	sends	send	VERB
ejpam-5888	185	31	(	(	PUNCT
ejpam-5888	185	32	y1	y1	INTJ
ejpam-5888	185	33	,	,	PUNCT
ejpam-5888	185	34	y2	y2	PROPN
ejpam-5888	185	35	)	)	PUNCT
ejpam-5888	185	36	to	to	ADP
ejpam-5888	185	37	alice	alice	PROPN
ejpam-5888	185	38	,	,	PUNCT
ejpam-5888	185	39	where	where	SCONJ
ejpam-5888	185	40	y1	y1	PROPN
ejpam-5888	185	41	=	=	NOUN
ejpam-5888	185	42	q1(b1	q1(b1	X
ejpam-5888	185	43	)	)	PUNCT
ejpam-5888	185	44	⊗	⊗	PROPN
ejpam-5888	185	45	g(a	g(a	PROPN
ejpam-5888	185	46	)	)	PUNCT
ejpam-5888	185	47	⊗	⊗	PROPN
ejpam-5888	185	48	q′1(b1	q′1(b1	PROPN
ejpam-5888	185	49	)	)	PUNCT
ejpam-5888	185	50	and	and	CCONJ
ejpam-5888	186	1	y2	y2	NOUN
ejpam-5888	186	2	=	=	SYM
ejpam-5888	186	3	q2(b2	q2(b2	NOUN
ejpam-5888	186	4	)	)	PUNCT
ejpam-5888	186	5	⊗	⊗	PROPN
ejpam-5888	186	6	g(a	g(a	PROPN
ejpam-5888	186	7	)	)	PUNCT
ejpam-5888	186	8	⊗	⊗	PROPN
ejpam-5888	186	9	q′2(b2	q′2(b2	PROPN
ejpam-5888	186	10	)	)	PUNCT
ejpam-5888	186	11	.	.	PUNCT
ejpam-5888	187	1	then	then	ADV
ejpam-5888	187	2	the	the	DET
ejpam-5888	187	3	public	public	ADJ
ejpam-5888	187	4	key	key	NOUN
ejpam-5888	187	5	is	be	AUX
ejpam-5888	187	6	(	(	PUNCT
ejpam-5888	187	7	y1	y1	INTJ
ejpam-5888	187	8	,	,	PUNCT
ejpam-5888	187	9	y2	y2	INTJ
ejpam-5888	187	10	,	,	PUNCT
ejpam-5888	187	11	g	g	PROPN
ejpam-5888	187	12	,	,	PUNCT
ejpam-5888	187	13	a	a	PRON
ejpam-5888	187	14	)	)	PUNCT
ejpam-5888	187	15	,	,	PUNCT
ejpam-5888	187	16	while	while	SCONJ
ejpam-5888	187	17	the	the	DET
ejpam-5888	187	18	private	private	ADJ
ejpam-5888	187	19	key	key	NOUN
ejpam-5888	187	20	is	be	AUX
ejpam-5888	187	21	(	(	PUNCT
ejpam-5888	187	22	q1	q1	PROPN
ejpam-5888	187	23	,	,	PUNCT
ejpam-5888	187	24	q2	q2	NOUN
ejpam-5888	187	25	,	,	PUNCT
ejpam-5888	187	26	b1	b1	NOUN
ejpam-5888	187	27	,	,	PUNCT
ejpam-5888	187	28	b2	b2	NOUN
ejpam-5888	187	29	)	)	PUNCT
ejpam-5888	187	30	.	.	PUNCT
ejpam-5888	188	1	kashifa	kashifa	PROPN
ejpam-5888	188	2	begum	begum	VERB
ejpam-5888	188	3	a.	a.	NOUN
ejpam-5888	188	4	et	et	PROPN
ejpam-5888	188	5	.	.	PUNCT
ejpam-5888	189	1	al	al	PROPN
ejpam-5888	189	2	/	/	PUNCT
ejpam-5888	189	3	eur	eur	PROPN
ejpam-5888	189	4	.	.	PUNCT
ejpam-5888	190	1	j.	j.	PROPN
ejpam-5888	190	2	pure	pure	PROPN
ejpam-5888	190	3	appl	appl	PROPN
ejpam-5888	190	4	.	.	PROPN
ejpam-5888	190	5	math	math	PROPN
ejpam-5888	190	6	,	,	PUNCT
ejpam-5888	190	7	18	18	NUM
ejpam-5888	190	8	(	(	PUNCT
ejpam-5888	190	9	3	3	NUM
ejpam-5888	190	10	)	)	PUNCT
ejpam-5888	190	11	(	(	PUNCT
ejpam-5888	190	12	2025	2025	NUM
ejpam-5888	190	13	)	)	PUNCT
ejpam-5888	190	14	,	,	PUNCT
ejpam-5888	190	15	5888	5888	NUM
ejpam-5888	190	16	9	9	NUM
ejpam-5888	190	17	of	of	ADP
ejpam-5888	190	18	16	16	NUM
ejpam-5888	190	19	(	(	PUNCT
ejpam-5888	190	20	iii	iii	NOUN
ejpam-5888	190	21	)	)	PUNCT
ejpam-5888	190	22	decryption	decryption	NOUN
ejpam-5888	190	23	:	:	PUNCT
ejpam-5888	190	24	alice	alice	PROPN
ejpam-5888	190	25	receives	receive	VERB
ejpam-5888	190	26	(	(	PUNCT
ejpam-5888	190	27	y1	y1	INTJ
ejpam-5888	190	28	,	,	PUNCT
ejpam-5888	190	29	y2	y2	PROPN
ejpam-5888	190	30	)	)	PUNCT
ejpam-5888	190	31	and	and	CCONJ
ejpam-5888	190	32	computes	compute	VERB
ejpam-5888	190	33	zij	zij	PROPN
ejpam-5888	190	34	=	=	SYM
ejpam-5888	190	35	pi(di)⊗yj⊗	pi(di)⊗yj⊗	PROPN
ejpam-5888	190	36	p′i(di	p′i(di	NOUN
ejpam-5888	190	37	)	)	PUNCT
ejpam-5888	190	38	,	,	PUNCT
ejpam-5888	190	39	i	i	PRON
ejpam-5888	190	40	,	,	PUNCT
ejpam-5888	190	41	j	j	PROPN
ejpam-5888	190	42	=	=	SYM
ejpam-5888	190	43	1	1	NUM
ejpam-5888	190	44	,	,	PUNCT
ejpam-5888	190	45	2	2	NUM
ejpam-5888	190	46	.	.	PUNCT
ejpam-5888	190	47	bob	bob	PROPN
ejpam-5888	190	48	receives	receive	VERB
ejpam-5888	190	49	(	(	PUNCT
ejpam-5888	190	50	x1	x1	PROPN
ejpam-5888	190	51	,	,	PUNCT
ejpam-5888	190	52	x2	x2	PROPN
ejpam-5888	190	53	)	)	PUNCT
ejpam-5888	190	54	and	and	CCONJ
ejpam-5888	190	55	computes	compute	VERB
ejpam-5888	191	1	z̃ij	z̃ij	PROPN
ejpam-5888	191	2	=	=	PUNCT
ejpam-5888	191	3	qj(bj)⊗xi⊗	qj(bj)⊗xi⊗	PROPN
ejpam-5888	191	4	q′j(bj	q′j(bj	NOUN
ejpam-5888	191	5	)	)	PUNCT
ejpam-5888	191	6	,	,	PUNCT
ejpam-5888	191	7	i	i	PRON
ejpam-5888	191	8	=	=	NOUN
ejpam-5888	191	9	1	1	NUM
ejpam-5888	191	10	,	,	PUNCT
ejpam-5888	191	11	2	2	NUM
ejpam-5888	191	12	,	,	PUNCT
ejpam-5888	191	13	j	j	NOUN
ejpam-5888	191	14	=	=	SYM
ejpam-5888	191	15	1	1	NUM
ejpam-5888	191	16	,	,	PUNCT
ejpam-5888	191	17	2	2	NUM
ejpam-5888	191	18	.	.	PUNCT
ejpam-5888	191	19	(	(	PUNCT
ejpam-5888	191	20	iv	iv	X
ejpam-5888	191	21	)	)	PUNCT
ejpam-5888	191	22	correctness	correctness	NOUN
ejpam-5888	191	23	:	:	PUNCT
ejpam-5888	191	24	since	since	SCONJ
ejpam-5888	191	25	pi(di	pi(di	PROPN
ejpam-5888	191	26	)	)	PUNCT
ejpam-5888	191	27	⊗	⊗	PROPN
ejpam-5888	191	28	qj(bj	qj(bj	PROPN
ejpam-5888	191	29	)	)	PUNCT
ejpam-5888	191	30	=	=	SYM
ejpam-5888	191	31	qj(bj	qj(bj	PROPN
ejpam-5888	191	32	)	)	PUNCT
ejpam-5888	191	33	⊗	⊗	PROPN
ejpam-5888	191	34	pi(di	pi(di	PROPN
ejpam-5888	191	35	)	)	PUNCT
ejpam-5888	191	36	,	,	PUNCT
ejpam-5888	191	37	and	and	CCONJ
ejpam-5888	191	38	p′i(di	p′i(di	NUM
ejpam-5888	191	39	)	)	PUNCT
ejpam-5888	191	40	⊗	⊗	PROPN
ejpam-5888	191	41	qj(bj	qj(bj	PROPN
ejpam-5888	191	42	)	)	PUNCT
ejpam-5888	191	43	=	=	SYM
ejpam-5888	191	44	qj(bj	qj(bj	PROPN
ejpam-5888	191	45	)	)	PUNCT
ejpam-5888	191	46	⊗	⊗	PROPN
ejpam-5888	191	47	p′i(ai	p′i(ai	PROPN
ejpam-5888	191	48	)	)	PUNCT
ejpam-5888	191	49	,	,	PUNCT
ejpam-5888	191	50	i	i	PRON
ejpam-5888	191	51	,	,	PUNCT
ejpam-5888	191	52	j	j	PROPN
ejpam-5888	191	53	=	=	SYM
ejpam-5888	191	54	1	1	NUM
ejpam-5888	191	55	,	,	PUNCT
ejpam-5888	191	56	2	2	NUM
ejpam-5888	191	57	,	,	PUNCT
ejpam-5888	191	58	alice	alice	PROPN
ejpam-5888	191	59	and	and	CCONJ
ejpam-5888	191	60	bob	bob	PROPN
ejpam-5888	191	61	have	have	VERB
ejpam-5888	191	62	same	same	ADJ
ejpam-5888	191	63	secret	secret	ADJ
ejpam-5888	191	64	key	key	NOUN
ejpam-5888	191	65	,	,	PUNCT
ejpam-5888	191	66	that	that	ADV
ejpam-5888	191	67	is	is	ADV
ejpam-5888	191	68	,	,	PUNCT
ejpam-5888	191	69	zij	zij	PROPN
ejpam-5888	191	70	=	=	PROPN
ejpam-5888	191	71	z̃ij	z̃ij	PROPN
ejpam-5888	191	72	,	,	PUNCT
ejpam-5888	191	73	i	i	PRON
ejpam-5888	191	74	=	=	NOUN
ejpam-5888	191	75	1	1	NUM
ejpam-5888	191	76	,	,	PUNCT
ejpam-5888	191	77	2	2	NUM
ejpam-5888	191	78	,	,	PUNCT
ejpam-5888	191	79	j	j	NOUN
ejpam-5888	191	80	=	=	SYM
ejpam-5888	191	81	1	1	NUM
ejpam-5888	191	82	,	,	PUNCT
ejpam-5888	191	83	2	2	NUM
ejpam-5888	191	84	.	.	PUNCT
ejpam-5888	191	85	table	table	NOUN
ejpam-5888	191	86	2	2	NUM
ejpam-5888	191	87	:	:	PUNCT
ejpam-5888	191	88	the	the	DET
ejpam-5888	191	89	key	key	ADJ
ejpam-5888	191	90	exchange	exchange	NOUN
ejpam-5888	191	91	protocol	protocol	PROPN
ejpam-5888	191	92	ii	ii	PROPN
ejpam-5888	191	93	alice	alice	PROPN
ejpam-5888	191	94	bob	bob	PROPN
ejpam-5888	191	95	p1(x	p1(x	PROPN
ejpam-5888	191	96	)	)	PUNCT
ejpam-5888	191	97	,	,	PUNCT
ejpam-5888	191	98	p2(x)←	p2(x)←	PROPN
ejpam-5888	191	99	rmin	rmin	NOUN
ejpam-5888	191	100	,	,	PUNCT
ejpam-5888	191	101	d1	d1	PROPN
ejpam-5888	191	102	,	,	PUNCT
ejpam-5888	191	103	d2	d2	PROPN
ejpam-5888	191	104	←	←	PROPN
ejpam-5888	191	105	h	h	PROPN
ejpam-5888	191	106	x1	x1	PROPN
ejpam-5888	192	1	=	=	PUNCT
ejpam-5888	192	2	p1(d1)⊗	p1(d1)⊗	PROPN
ejpam-5888	192	3	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	192	4	p′1(d1	p′1(d1	NOUN
ejpam-5888	192	5	)	)	PUNCT
ejpam-5888	192	6	x2	x2	NOUN
ejpam-5888	193	1	=	=	PUNCT
ejpam-5888	193	2	p2(d2)⊗	p2(d2)⊗	NOUN
ejpam-5888	193	3	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	193	4	p′2(d2	p′2(d2	NOUN
ejpam-5888	193	5	)	)	PUNCT
ejpam-5888	193	6	x1,x2−→	x1,x2−→	PROPN
ejpam-5888	193	7	q1(x	q1(x	NOUN
ejpam-5888	193	8	)	)	PUNCT
ejpam-5888	193	9	,	,	PUNCT
ejpam-5888	193	10	q2(x)←	q2(x)←	PUNCT
ejpam-5888	193	11	rmin	rmin	NOUN
ejpam-5888	193	12	,	,	PUNCT
ejpam-5888	193	13	b1	b1	NOUN
ejpam-5888	193	14	,	,	PUNCT
ejpam-5888	193	15	b2	b2	NOUN
ejpam-5888	193	16	←	←	PROPN
ejpam-5888	193	17	h	h	NOUN
ejpam-5888	193	18	y1	y1	PROPN
ejpam-5888	193	19	=	=	PUNCT
ejpam-5888	194	1	q1(b1)⊗	q1(b1)⊗	PROPN
ejpam-5888	194	2	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	194	3	q′1(b1	q′1(b1	AUX
ejpam-5888	194	4	)	)	PUNCT
ejpam-5888	194	5	y2	y2	NOUN
ejpam-5888	194	6	=	=	NOUN
ejpam-5888	194	7	q2(b2)⊗	q2(b2)⊗	PROPN
ejpam-5888	194	8	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	194	9	q′2(b2	q′2(b2	NOUN
ejpam-5888	194	10	)	)	PUNCT
ejpam-5888	195	1	y1,y2←−	y1,y2←−	PROPN
ejpam-5888	195	2	zij	zij	PROPN
ejpam-5888	195	3	=	=	PUNCT
ejpam-5888	195	4	pi(di)⊗	pi(di)⊗	PROPN
ejpam-5888	195	5	yj	yj	PROPN
ejpam-5888	195	6	⊗	⊗	PROPN
ejpam-5888	195	7	p′i(di	p′i(di	PROPN
ejpam-5888	195	8	)	)	PUNCT
ejpam-5888	196	1	z̃ij	z̃ij	PROPN
ejpam-5888	196	2	=	=	PUNCT
ejpam-5888	197	1	qj(bj)⊗xi	qj(bj)⊗xi	PROPN
ejpam-5888	197	2	⊗	⊗	NUM
ejpam-5888	197	3	q′j(bj	q′j(bj	NOUN
ejpam-5888	197	4	)	)	PUNCT
ejpam-5888	198	1	zij	zij	PROPN
ejpam-5888	198	2	=	=	PROPN
ejpam-5888	198	3	z̃ij	z̃ij	PROPN
ejpam-5888	198	4	,	,	PUNCT
ejpam-5888	198	5	i	i	PRON
ejpam-5888	198	6	=	=	NOUN
ejpam-5888	198	7	1	1	NUM
ejpam-5888	198	8	,	,	PUNCT
ejpam-5888	198	9	2	2	NUM
ejpam-5888	198	10	,	,	PUNCT
ejpam-5888	198	11	j	j	NOUN
ejpam-5888	198	12	=	=	SYM
ejpam-5888	198	13	1	1	NUM
ejpam-5888	198	14	,	,	PUNCT
ejpam-5888	198	15	2	2	NUM
ejpam-5888	198	16	5	5	NUM
ejpam-5888	198	17	.	.	PUNCT
ejpam-5888	199	1	a	a	DET
ejpam-5888	199	2	toy	toy	NOUN
ejpam-5888	199	3	example	example	NOUN
ejpam-5888	199	4	of	of	ADP
ejpam-5888	199	5	the	the	DET
ejpam-5888	199	6	protocol	protocol	NOUN
ejpam-5888	199	7	in	in	ADP
ejpam-5888	199	8	this	this	DET
ejpam-5888	199	9	section	section	NOUN
ejpam-5888	199	10	,	,	PUNCT
ejpam-5888	199	11	a	a	DET
ejpam-5888	199	12	toy	toy	NOUN
ejpam-5888	199	13	example	example	NOUN
ejpam-5888	199	14	of	of	ADP
ejpam-5888	199	15	the	the	DET
ejpam-5888	199	16	first	first	ADJ
ejpam-5888	199	17	protocol	protocol	NOUN
ejpam-5888	199	18	is	be	AUX
ejpam-5888	199	19	given	give	VERB
ejpam-5888	199	20	.	.	PUNCT
ejpam-5888	200	1	let	let	VERB
ejpam-5888	200	2	p1(x	p1(x	NOUN
ejpam-5888	200	3	)	)	PUNCT
ejpam-5888	200	4	=	=	SYM
ejpam-5888	200	5	2	2	NUM
ejpam-5888	200	6	⊗	⊗	NOUN
ejpam-5888	200	7	x⊗2	x⊗2	NOUN
ejpam-5888	200	8	,	,	PUNCT
ejpam-5888	200	9	p2(x	p2(x	X
ejpam-5888	200	10	)	)	PUNCT
ejpam-5888	200	11	=	=	SYM
ejpam-5888	200	12	5	5	NUM
ejpam-5888	200	13	⊗	⊗	PROPN
ejpam-5888	200	14	x⊗3	x⊗3	PROPN
ejpam-5888	200	15	,	,	PUNCT
ejpam-5888	200	16	q(x	q(x	PROPN
ejpam-5888	200	17	)	)	PUNCT
ejpam-5888	200	18	=	=	PUNCT
ejpam-5888	200	19	2	2	NUM
ejpam-5888	200	20	⊗	⊗	NUM
ejpam-5888	200	21	x	x	NOUN
ejpam-5888	200	22	,	,	PUNCT
ejpam-5888	200	23	d1	d1	PROPN
ejpam-5888	200	24	=	=	PUNCT
ejpam-5888	201	1			PROPN
ejpam-5888	201	2	2	2	NUM
ejpam-5888	201	3	∞	∞	NUM
ejpam-5888	201	4	∞	∞	NUM
ejpam-5888	201	5	∞	∞	NUM
ejpam-5888	201	6	3	3	NUM
ejpam-5888	201	7	∞	∞	NUM
ejpam-5888	201	8	∞	∞	NUM
ejpam-5888	201	9	∞	∞	NUM
ejpam-5888	201	10	6	6	NUM
ejpam-5888	201	11			PROPN
ejpam-5888	201	12	,	,	PUNCT
ejpam-5888	201	13	d2	d2	PROPN
ejpam-5888	201	14	=	=	SYM
ejpam-5888	201	15			PROPN
ejpam-5888	201	16	1	1	NUM
ejpam-5888	201	17	∞	∞	NUM
ejpam-5888	201	18	∞	∞	NUM
ejpam-5888	201	19	∞	∞	NUM
ejpam-5888	201	20	−5	−5	NOUN
ejpam-5888	201	21	∞	∞	NUM
ejpam-5888	201	22	∞	∞	NUM
ejpam-5888	201	23	∞	∞	NUM
ejpam-5888	201	24	4	4	NUM
ejpam-5888	201	25			PROPN
ejpam-5888	201	26	,	,	PUNCT
ejpam-5888	201	27	b	b	X
ejpam-5888	201	28	=	=	SYM
ejpam-5888	201	29			PROPN
ejpam-5888	201	30	6	6	NUM
ejpam-5888	201	31	∞	∞	NUM
ejpam-5888	201	32	∞	∞	NUM
ejpam-5888	201	33	∞	∞	NUM
ejpam-5888	201	34	5	5	NUM
ejpam-5888	201	35	∞	∞	NUM
ejpam-5888	201	36	∞	∞	NUM
ejpam-5888	201	37	∞	∞	NUM
ejpam-5888	201	38	−3	−3	PROPN
ejpam-5888	202	1			PROPN
ejpam-5888	202	2	be	be	AUX
ejpam-5888	202	3	private	private	ADJ
ejpam-5888	202	4	.	.	PUNCT
ejpam-5888	203	1	let	let	VERB
ejpam-5888	203	2	g(x	g(x	NOUN
ejpam-5888	203	3	)	)	PUNCT
ejpam-5888	204	1	=	=	SYM
ejpam-5888	204	2	3⊗	3⊗	NUM
ejpam-5888	204	3	x⊗2	x⊗2	NOUN
ejpam-5888	204	4	and	and	CCONJ
ejpam-5888	204	5	a	a	DET
ejpam-5888	204	6	=	=	X
ejpam-5888	204	7			PROPN
ejpam-5888	204	8	1	1	NUM
ejpam-5888	204	9	2	2	NUM
ejpam-5888	204	10	−1	−1	NOUN
ejpam-5888	204	11	3	3	NUM
ejpam-5888	204	12	5	5	NUM
ejpam-5888	204	13	−2	−2	NOUN
ejpam-5888	204	14	−1	−1	NOUN
ejpam-5888	204	15	2	2	NUM
ejpam-5888	204	16	3	3	NUM
ejpam-5888	204	17			PROPN
ejpam-5888	204	18	be	be	AUX
ejpam-5888	204	19	public	public	ADJ
ejpam-5888	204	20	.	.	PUNCT
ejpam-5888	205	1	then	then	ADV
ejpam-5888	205	2	p′1(x	p′1(x	PROPN
ejpam-5888	205	3	)	)	PUNCT
ejpam-5888	206	1	=	=	SYM
ejpam-5888	206	2	−2⊗	−2⊗	NOUN
ejpam-5888	206	3	(	(	PUNCT
ejpam-5888	206	4	−x)⊗2	−x)⊗2	NOUN
ejpam-5888	206	5	,	,	PUNCT
ejpam-5888	206	6	p2(x	p2(x	NOUN
ejpam-5888	206	7	)	)	PUNCT
ejpam-5888	206	8	=	=	SYM
ejpam-5888	206	9	−5⊗	−5⊗	ADJ
ejpam-5888	206	10	(	(	PUNCT
ejpam-5888	206	11	−x)⊗3	−x)⊗3	PROPN
ejpam-5888	206	12	,	,	PUNCT
ejpam-5888	206	13	q(x	q(x	PROPN
ejpam-5888	206	14	)	)	PUNCT
ejpam-5888	206	15	=	=	SYM
ejpam-5888	206	16	−2⊗	−2⊗	NOUN
ejpam-5888	206	17	(	(	PUNCT
ejpam-5888	206	18	−x	−x	NOUN
ejpam-5888	206	19	)	)	PUNCT
ejpam-5888	206	20	.	.	PUNCT
ejpam-5888	207	1	alice	alice	PROPN
ejpam-5888	207	2	calculates	calculate	VERB
ejpam-5888	207	3	kashifa	kashifa	PROPN
ejpam-5888	207	4	begum	begum	PROPN
ejpam-5888	207	5	a.	a.	NOUN
ejpam-5888	207	6	et	et	PROPN
ejpam-5888	207	7	.	.	PUNCT
ejpam-5888	208	1	al	al	PROPN
ejpam-5888	208	2	/	/	PUNCT
ejpam-5888	208	3	eur	eur	PROPN
ejpam-5888	208	4	.	.	PUNCT
ejpam-5888	209	1	j.	j.	PROPN
ejpam-5888	209	2	pure	pure	PROPN
ejpam-5888	209	3	appl	appl	PROPN
ejpam-5888	209	4	.	.	PROPN
ejpam-5888	209	5	math	math	PROPN
ejpam-5888	209	6	,	,	PUNCT
ejpam-5888	209	7	18	18	NUM
ejpam-5888	209	8	(	(	PUNCT
ejpam-5888	209	9	3	3	NUM
ejpam-5888	209	10	)	)	PUNCT
ejpam-5888	209	11	(	(	PUNCT
ejpam-5888	209	12	2025	2025	NUM
ejpam-5888	209	13	)	)	PUNCT
ejpam-5888	209	14	,	,	PUNCT
ejpam-5888	209	15	5888	5888	NUM
ejpam-5888	209	16	10	10	NUM
ejpam-5888	209	17	of	of	ADP
ejpam-5888	209	18	16	16	NUM
ejpam-5888	209	19	p1(d1	p1(d1	NOUN
ejpam-5888	209	20	)	)	PUNCT
ejpam-5888	209	21	=	=	SYM
ejpam-5888	209	22	2	2	NUM
ejpam-5888	209	23	⊗	⊗	NOUN
ejpam-5888	209	24			PROPN
ejpam-5888	209	25	2	2	NUM
ejpam-5888	209	26	∞	∞	NUM
ejpam-5888	209	27	∞	∞	NUM
ejpam-5888	209	28	∞	∞	NUM
ejpam-5888	209	29	3	3	NUM
ejpam-5888	209	30	∞	∞	NUM
ejpam-5888	209	31	∞	∞	NUM
ejpam-5888	209	32	∞	∞	NUM
ejpam-5888	209	33	6	6	NUM
ejpam-5888	209	34	⊗2	⊗2	PUNCT
ejpam-5888	209	35	=	=	SYM
ejpam-5888	210	1	2	2	NUM
ejpam-5888	210	2	⊗	⊗	PROPN
ejpam-5888	210	3			PROPN
ejpam-5888	210	4	4	4	NUM
ejpam-5888	210	5	∞	∞	NUM
ejpam-5888	210	6	∞	∞	NUM
ejpam-5888	210	7	∞	∞	NUM
ejpam-5888	210	8	6	6	NUM
ejpam-5888	210	9	∞	∞	NUM
ejpam-5888	210	10	∞	∞	NUM
ejpam-5888	210	11	∞	∞	NUM
ejpam-5888	210	12	12	12	NUM
ejpam-5888	210	13			PROPN
ejpam-5888	210	14	=	=	SYM
ejpam-5888	210	15			PROPN
ejpam-5888	210	16	6	6	NUM
ejpam-5888	210	17	∞	∞	NUM
ejpam-5888	210	18	∞	∞	NUM
ejpam-5888	210	19	∞	∞	NUM
ejpam-5888	210	20	8	8	NUM
ejpam-5888	210	21	∞	∞	NUM
ejpam-5888	210	22	∞	∞	NUM
ejpam-5888	210	23	∞	∞	NUM
ejpam-5888	210	24	14	14	NUM
ejpam-5888	210	25			PROPN
ejpam-5888	210	26	,	,	PUNCT
ejpam-5888	210	27	p′1(d1	p′1(d1	NOUN
ejpam-5888	210	28	)	)	PUNCT
ejpam-5888	210	29	=	=	SYM
ejpam-5888	211	1	−2	−2	PROPN
ejpam-5888	211	2	⊗	⊗	NOUN
ejpam-5888	211	3	−2	−2	PROPN
ejpam-5888	212	1	∞	∞	NUM
ejpam-5888	212	2	∞	∞	NUM
ejpam-5888	212	3	∞	∞	NUM
ejpam-5888	212	4	−3	−3	PROPN
ejpam-5888	213	1	∞	∞	NUM
ejpam-5888	213	2	∞	∞	NUM
ejpam-5888	213	3	∞	∞	NUM
ejpam-5888	213	4	−6	−6	NOUN
ejpam-5888	213	5	⊗2	⊗2	PUNCT
ejpam-5888	214	1	=	=	PUNCT
ejpam-5888	215	1	−2	−2	PROPN
ejpam-5888	215	2	⊗	⊗	NOUN
ejpam-5888	215	3	−4	−4	NUM
ejpam-5888	215	4	∞	∞	NUM
ejpam-5888	215	5	∞	∞	NUM
ejpam-5888	216	1	∞	∞	NUM
ejpam-5888	216	2	−6	−6	NOUN
ejpam-5888	217	1	∞	∞	NUM
ejpam-5888	217	2	∞	∞	NUM
ejpam-5888	217	3	∞	∞	PROPN
ejpam-5888	217	4	−12	−12	NOUN
ejpam-5888	218	1			PROPN
ejpam-5888	218	2	=	=	SYM
ejpam-5888	218	3	−6	−6	NUM
ejpam-5888	218	4	∞	∞	NUM
ejpam-5888	219	1	∞	∞	NUM
ejpam-5888	219	2	∞	∞	NUM
ejpam-5888	219	3	−8	−8	X
ejpam-5888	220	1	∞	∞	NUM
ejpam-5888	220	2	∞	∞	NUM
ejpam-5888	220	3	∞	∞	NUM
ejpam-5888	220	4	−14	−14	NUM
ejpam-5888	220	5			PROPN
ejpam-5888	220	6	,	,	PUNCT
ejpam-5888	220	7	p2(d2	p2(d2	NUM
ejpam-5888	220	8	)	)	PUNCT
ejpam-5888	220	9	=	=	SYM
ejpam-5888	220	10	5	5	NUM
ejpam-5888	220	11	⊗	⊗	PROPN
ejpam-5888	220	12			PROPN
ejpam-5888	220	13	1	1	NUM
ejpam-5888	220	14	∞	∞	NUM
ejpam-5888	220	15	∞	∞	NUM
ejpam-5888	220	16	∞	∞	NUM
ejpam-5888	220	17	−5	−5	NOUN
ejpam-5888	220	18	∞	∞	NUM
ejpam-5888	220	19	∞	∞	NUM
ejpam-5888	220	20	∞	∞	NUM
ejpam-5888	220	21	4	4	NUM
ejpam-5888	220	22	⊗3	⊗3	NOUN
ejpam-5888	220	23	=	=	SYM
ejpam-5888	220	24	5	5	NUM
ejpam-5888	220	25	⊗	⊗	PROPN
ejpam-5888	220	26			PROPN
ejpam-5888	220	27	3	3	NUM
ejpam-5888	220	28	∞	∞	NUM
ejpam-5888	220	29	∞	∞	NUM
ejpam-5888	220	30	∞	∞	NUM
ejpam-5888	220	31	−15	−15	NOUN
ejpam-5888	220	32	∞	∞	NUM
ejpam-5888	220	33	∞	∞	NUM
ejpam-5888	220	34	∞	∞	NUM
ejpam-5888	220	35	12	12	NUM
ejpam-5888	220	36			PROPN
ejpam-5888	220	37	=	=	SYM
ejpam-5888	220	38			PROPN
ejpam-5888	220	39	8	8	NUM
ejpam-5888	220	40	∞	∞	NUM
ejpam-5888	220	41	∞	∞	NUM
ejpam-5888	220	42	∞	∞	NUM
ejpam-5888	220	43	−10	−10	PROPN
ejpam-5888	221	1	∞	∞	NUM
ejpam-5888	221	2	∞	∞	NUM
ejpam-5888	221	3	∞	∞	NUM
ejpam-5888	221	4	17	17	NUM
ejpam-5888	221	5			PROPN
ejpam-5888	221	6	,	,	PUNCT
ejpam-5888	221	7	p′2(d2	p′2(d2	NOUN
ejpam-5888	221	8	)	)	PUNCT
ejpam-5888	221	9	=	=	SYM
ejpam-5888	222	1	−5	−5	PROPN
ejpam-5888	222	2	⊗	⊗	PROPN
ejpam-5888	222	3	−1	−1	NUM
ejpam-5888	223	1	∞	∞	NUM
ejpam-5888	223	2	∞	∞	NUM
ejpam-5888	223	3	∞	∞	NUM
ejpam-5888	223	4	5	5	NUM
ejpam-5888	223	5	∞	∞	NUM
ejpam-5888	223	6	∞	∞	NUM
ejpam-5888	223	7	∞	∞	NUM
ejpam-5888	223	8	−4	−4	X
ejpam-5888	223	9	⊗3	⊗3	X
ejpam-5888	224	1	=	=	PUNCT
ejpam-5888	224	2	−5	−5	PROPN
ejpam-5888	224	3	⊗	⊗	PROPN
ejpam-5888	224	4	−3	−3	NUM
ejpam-5888	224	5	∞	∞	NUM
ejpam-5888	224	6	∞	∞	NUM
ejpam-5888	224	7	∞	∞	NUM
ejpam-5888	224	8	15	15	NUM
ejpam-5888	224	9	∞	∞	NUM
ejpam-5888	224	10	∞	∞	NUM
ejpam-5888	224	11	∞	∞	PROPN
ejpam-5888	224	12	−12	−12	NUM
ejpam-5888	225	1			PROPN
ejpam-5888	225	2	=	=	SYM
ejpam-5888	225	3	−8	−8	NUM
ejpam-5888	225	4	∞	∞	NUM
ejpam-5888	225	5	∞	∞	NUM
ejpam-5888	225	6	∞	∞	NUM
ejpam-5888	225	7	10	10	NUM
ejpam-5888	225	8	∞	∞	NUM
ejpam-5888	225	9	∞	∞	NUM
ejpam-5888	225	10	∞	∞	NUM
ejpam-5888	225	11	−17	−17	X
ejpam-5888	226	1			PROPN
ejpam-5888	226	2	,	,	PUNCT
ejpam-5888	226	3	g(a	g(a	PROPN
ejpam-5888	226	4	)	)	PUNCT
ejpam-5888	226	5	=	=	PUNCT
ejpam-5888	227	1	3	3	NUM
ejpam-5888	227	2	⊗	⊗	PROPN
ejpam-5888	227	3			PROPN
ejpam-5888	227	4	1	1	NUM
ejpam-5888	227	5	2	2	NUM
ejpam-5888	227	6	−1	−1	NOUN
ejpam-5888	227	7	3	3	NUM
ejpam-5888	227	8	5	5	NUM
ejpam-5888	227	9	−2	−2	NOUN
ejpam-5888	227	10	−1	−1	NOUN
ejpam-5888	227	11	2	2	NUM
ejpam-5888	227	12	3	3	NUM
ejpam-5888	227	13	⊗2	⊗2	PUNCT
ejpam-5888	227	14	=	=	PUNCT
ejpam-5888	227	15	3	3	NUM
ejpam-5888	227	16	⊗	⊗	PROPN
ejpam-5888	227	17	−2	−2	PROPN
ejpam-5888	227	18	1	1	NUM
ejpam-5888	227	19	0	0	NUM
ejpam-5888	227	20	−3	−3	NOUN
ejpam-5888	227	21	0	0	NUM
ejpam-5888	227	22	1	1	NUM
ejpam-5888	227	23	0	0	NUM
ejpam-5888	227	24	1	1	NUM
ejpam-5888	227	25	−2	−2	NOUN
ejpam-5888	227	26			PROPN
ejpam-5888	227	27	=	=	SYM
ejpam-5888	227	28	1	1	PROPN
ejpam-5888	227	29	4	4	NUM
ejpam-5888	227	30	3	3	NUM
ejpam-5888	227	31	0	0	NUM
ejpam-5888	227	32	3	3	NUM
ejpam-5888	227	33	4	4	NUM
ejpam-5888	227	34	3	3	NUM
ejpam-5888	227	35	4	4	NUM
ejpam-5888	227	36	1	1	NUM
ejpam-5888	227	37	.	.	ADV
ejpam-5888	227	38	also	also	ADV
ejpam-5888	227	39	x1	x1	PROPN
ejpam-5888	228	1	=	=	SYM
ejpam-5888	229	1			PROPN
ejpam-5888	229	2	6	6	NUM
ejpam-5888	229	3	∞	∞	NUM
ejpam-5888	229	4	∞	∞	NUM
ejpam-5888	229	5	∞	∞	NUM
ejpam-5888	229	6	8	8	NUM
ejpam-5888	229	7	∞	∞	NUM
ejpam-5888	229	8	∞	∞	NUM
ejpam-5888	229	9	∞	∞	NUM
ejpam-5888	229	10	14	14	NUM
ejpam-5888	229	11	⊗	⊗	NOUN
ejpam-5888	229	12	1	1	PROPN
ejpam-5888	229	13	4	4	NUM
ejpam-5888	229	14	3	3	NUM
ejpam-5888	229	15	0	0	NUM
ejpam-5888	229	16	3	3	NUM
ejpam-5888	229	17	4	4	NUM
ejpam-5888	229	18	3	3	NUM
ejpam-5888	229	19	4	4	NUM
ejpam-5888	229	20	1	1	NUM
ejpam-5888	229	21	⊗	⊗	VERB
ejpam-5888	229	22	−6	−6	NUM
ejpam-5888	229	23	∞	∞	NUM
ejpam-5888	230	1	∞	∞	NUM
ejpam-5888	230	2	∞	∞	NUM
ejpam-5888	230	3	−8	−8	X
ejpam-5888	231	1	∞	∞	NUM
ejpam-5888	231	2	∞	∞	NUM
ejpam-5888	231	3	∞	∞	NUM
ejpam-5888	231	4	−14	−14	NUM
ejpam-5888	231	5			PROPN
ejpam-5888	231	6	=	=	SYM
ejpam-5888	231	7			PROPN
ejpam-5888	231	8	1	1	NUM
ejpam-5888	231	9	2	2	NUM
ejpam-5888	231	10	−5	−5	NOUN
ejpam-5888	231	11	2	2	NUM
ejpam-5888	231	12	3	3	NUM
ejpam-5888	231	13	−2	−2	NOUN
ejpam-5888	231	14	11	11	NUM
ejpam-5888	231	15	10	10	NUM
ejpam-5888	231	16	1	1	NUM
ejpam-5888	231	17			PROPN
ejpam-5888	231	18	,	,	PUNCT
ejpam-5888	231	19	x2	x2	NOUN
ejpam-5888	232	1	=	=	PUNCT
ejpam-5888	232	2			PROPN
ejpam-5888	232	3	8	8	NUM
ejpam-5888	232	4	∞	∞	NUM
ejpam-5888	232	5	∞	∞	NUM
ejpam-5888	232	6	∞	∞	NUM
ejpam-5888	232	7	−10	−10	PROPN
ejpam-5888	232	8	∞	∞	NUM
ejpam-5888	232	9	∞	∞	NUM
ejpam-5888	232	10	∞	∞	NUM
ejpam-5888	232	11	17	17	NUM
ejpam-5888	232	12	⊗	⊗	NOUN
ejpam-5888	232	13	1	1	PROPN
ejpam-5888	232	14	4	4	NUM
ejpam-5888	232	15	3	3	NUM
ejpam-5888	232	16	0	0	NUM
ejpam-5888	232	17	3	3	NUM
ejpam-5888	232	18	4	4	NUM
ejpam-5888	232	19	3	3	NUM
ejpam-5888	232	20	4	4	NUM
ejpam-5888	232	21	1	1	NUM
ejpam-5888	232	22	⊗	⊗	NOUN
ejpam-5888	232	23	−8	−8	NUM
ejpam-5888	233	1	∞	∞	NUM
ejpam-5888	233	2	∞	∞	NUM
ejpam-5888	233	3	∞	∞	NUM
ejpam-5888	233	4	10	10	NUM
ejpam-5888	233	5	∞	∞	NUM
ejpam-5888	233	6	∞	∞	NUM
ejpam-5888	233	7	∞	∞	NOUN
ejpam-5888	233	8	−17	−17	NOUN
ejpam-5888	234	1			PROPN
ejpam-5888	234	2	=	=	SYM
ejpam-5888	234	3			PROPN
ejpam-5888	234	4	1	1	NUM
ejpam-5888	234	5	22	22	NUM
ejpam-5888	234	6	−6	−6	NOUN
ejpam-5888	234	7	−18	−18	NUM
ejpam-5888	234	8	3	3	NUM
ejpam-5888	234	9	−23	−23	NUM
ejpam-5888	234	10	12	12	NUM
ejpam-5888	234	11	31	31	NUM
ejpam-5888	234	12	1	1	NUM
ejpam-5888	234	13	.	.	PROPN
ejpam-5888	234	14	bob	bob	NOUN
ejpam-5888	234	15	calculates	calculate	NOUN
ejpam-5888	234	16	q(b	q(b	ADV
ejpam-5888	234	17	)	)	PUNCT
ejpam-5888	234	18	=	=	SYM
ejpam-5888	235	1	2	2	NUM
ejpam-5888	235	2	⊗	⊗	PROPN
ejpam-5888	235	3			PROPN
ejpam-5888	235	4	6	6	NUM
ejpam-5888	235	5	∞	∞	NUM
ejpam-5888	235	6	∞	∞	NUM
ejpam-5888	235	7	∞	∞	NUM
ejpam-5888	235	8	5	5	NUM
ejpam-5888	235	9	∞	∞	NUM
ejpam-5888	235	10	∞	∞	NUM
ejpam-5888	235	11	∞	∞	NUM
ejpam-5888	235	12	−3	−3	PROPN
ejpam-5888	236	1			PROPN
ejpam-5888	236	2	=	=	SYM
ejpam-5888	236	3			PROPN
ejpam-5888	236	4	8	8	NUM
ejpam-5888	236	5	∞	∞	NUM
ejpam-5888	236	6	∞	∞	NUM
ejpam-5888	236	7	∞	∞	NUM
ejpam-5888	236	8	7	7	NUM
ejpam-5888	236	9	∞	∞	NUM
ejpam-5888	236	10	∞	∞	NUM
ejpam-5888	236	11	∞	∞	NUM
ejpam-5888	236	12	−1	−1	NOUN
ejpam-5888	236	13			PROPN
ejpam-5888	236	14	,	,	PUNCT
ejpam-5888	236	15	q′(b	q′(b	PROPN
ejpam-5888	236	16	)	)	PUNCT
ejpam-5888	237	1	=	=	SYM
ejpam-5888	237	2	−2	−2	PROPN
ejpam-5888	238	1	⊗	⊗	NOUN
ejpam-5888	238	2	−6	−6	PROPN
ejpam-5888	238	3	∞	∞	NUM
ejpam-5888	239	1	∞	∞	NUM
ejpam-5888	239	2	∞	∞	NUM
ejpam-5888	239	3	−5	−5	NOUN
ejpam-5888	239	4	∞	∞	NUM
ejpam-5888	239	5	∞	∞	NUM
ejpam-5888	240	1	∞	∞	NUM
ejpam-5888	240	2	3	3	NUM
ejpam-5888	240	3			PROPN
ejpam-5888	240	4	=	=	SYM
ejpam-5888	240	5	−8	−8	NUM
ejpam-5888	240	6	∞	∞	NUM
ejpam-5888	240	7	∞	∞	NUM
ejpam-5888	240	8	∞	∞	PROPN
ejpam-5888	240	9	−7	−7	NOUN
ejpam-5888	240	10	∞	∞	NUM
ejpam-5888	240	11	∞	∞	NUM
ejpam-5888	240	12	∞	∞	NUM
ejpam-5888	240	13	1	1	NUM
ejpam-5888	240	14			PROPN
ejpam-5888	240	15	,	,	PUNCT
ejpam-5888	240	16	g(a	g(a	PROPN
ejpam-5888	240	17	)	)	PUNCT
ejpam-5888	240	18	=	=	PUNCT
ejpam-5888	241	1	3	3	NUM
ejpam-5888	241	2	⊗	⊗	PROPN
ejpam-5888	241	3			PROPN
ejpam-5888	241	4	1	1	NUM
ejpam-5888	241	5	2	2	NUM
ejpam-5888	241	6	−1	−1	NOUN
ejpam-5888	241	7	3	3	NUM
ejpam-5888	241	8	5	5	NUM
ejpam-5888	241	9	−2	−2	NOUN
ejpam-5888	241	10	−1	−1	NOUN
ejpam-5888	241	11	2	2	NUM
ejpam-5888	241	12	3	3	NUM
ejpam-5888	241	13	⊗2	⊗2	PUNCT
ejpam-5888	241	14	=	=	PUNCT
ejpam-5888	241	15	3	3	NUM
ejpam-5888	241	16	⊗	⊗	PROPN
ejpam-5888	241	17	−2	−2	PROPN
ejpam-5888	241	18	1	1	NUM
ejpam-5888	241	19	0	0	NUM
ejpam-5888	241	20	−3	−3	NOUN
ejpam-5888	241	21	0	0	NUM
ejpam-5888	241	22	1	1	NUM
ejpam-5888	241	23	0	0	NUM
ejpam-5888	241	24	1	1	NUM
ejpam-5888	241	25	−2	−2	NOUN
ejpam-5888	241	26			PROPN
ejpam-5888	241	27	=	=	SYM
ejpam-5888	241	28	1	1	PROPN
ejpam-5888	241	29	4	4	NUM
ejpam-5888	241	30	3	3	NUM
ejpam-5888	241	31	0	0	NUM
ejpam-5888	241	32	3	3	NUM
ejpam-5888	241	33	4	4	NUM
ejpam-5888	241	34	3	3	NUM
ejpam-5888	241	35	4	4	NUM
ejpam-5888	241	36	1	1	NUM
ejpam-5888	241	37	.	.	ADV
ejpam-5888	241	38	also	also	ADV
ejpam-5888	241	39	y	y	PROPN
ejpam-5888	241	40	=	=	SYM
ejpam-5888	241	41			PROPN
ejpam-5888	241	42	8	8	NUM
ejpam-5888	241	43	∞	∞	NUM
ejpam-5888	241	44	∞	∞	NUM
ejpam-5888	241	45	∞	∞	NUM
ejpam-5888	241	46	7	7	NUM
ejpam-5888	241	47	∞	∞	NUM
ejpam-5888	241	48	∞	∞	NUM
ejpam-5888	241	49	∞	∞	NUM
ejpam-5888	241	50	−1	−1	NOUN
ejpam-5888	241	51	⊗	⊗	NOUN
ejpam-5888	242	1	1	1	PROPN
ejpam-5888	242	2	4	4	NUM
ejpam-5888	242	3	3	3	NUM
ejpam-5888	242	4	0	0	NUM
ejpam-5888	242	5	3	3	NUM
ejpam-5888	242	6	4	4	NUM
ejpam-5888	242	7	3	3	NUM
ejpam-5888	242	8	4	4	NUM
ejpam-5888	242	9	1	1	NUM
ejpam-5888	242	10	⊗	⊗	NOUN
ejpam-5888	243	1	−8	−8	NUM
ejpam-5888	244	1	∞	∞	NUM
ejpam-5888	244	2	∞	∞	NUM
ejpam-5888	244	3	∞	∞	PROPN
ejpam-5888	244	4	−7	−7	NOUN
ejpam-5888	244	5	∞	∞	NUM
ejpam-5888	244	6	∞	∞	NUM
ejpam-5888	244	7	∞	∞	NUM
ejpam-5888	245	1	1	1	NUM
ejpam-5888	245	2			PROPN
ejpam-5888	245	3	=	=	SYM
ejpam-5888	245	4			PROPN
ejpam-5888	245	5	1	1	NUM
ejpam-5888	245	6	5	5	NUM
ejpam-5888	245	7	12	12	NUM
ejpam-5888	245	8	−1	−1	NOUN
ejpam-5888	245	9	3	3	NUM
ejpam-5888	245	10	12	12	NUM
ejpam-5888	245	11	−6	−6	NOUN
ejpam-5888	245	12	−4	−4	PROPN
ejpam-5888	245	13	1	1	NUM
ejpam-5888	245	14	.	.	PROPN
ejpam-5888	245	15	alice	alice	PROPN
ejpam-5888	245	16	’s	’s	PART
ejpam-5888	245	17	shared	share	VERB
ejpam-5888	245	18	secret	secret	ADJ
ejpam-5888	245	19	key	key	ADJ
ejpam-5888	245	20	z1	z1	NOUN
ejpam-5888	245	21	=	=	SYM
ejpam-5888	245	22			PROPN
ejpam-5888	245	23	6	6	NUM
ejpam-5888	245	24	∞	∞	NUM
ejpam-5888	245	25	∞	∞	NUM
ejpam-5888	245	26	∞	∞	NUM
ejpam-5888	245	27	8	8	NUM
ejpam-5888	245	28	∞	∞	NUM
ejpam-5888	245	29	∞	∞	NUM
ejpam-5888	245	30	∞	∞	NUM
ejpam-5888	245	31	14	14	NUM
ejpam-5888	245	32	⊗	⊗	NOUN
ejpam-5888	245	33			PROPN
ejpam-5888	245	34	1	1	NUM
ejpam-5888	245	35	5	5	NUM
ejpam-5888	245	36	12	12	NUM
ejpam-5888	245	37	−1	−1	NOUN
ejpam-5888	245	38	3	3	NUM
ejpam-5888	245	39	12	12	NUM
ejpam-5888	245	40	−6	−6	NOUN
ejpam-5888	245	41	−4	−4	PROPN
ejpam-5888	245	42	1	1	NUM
ejpam-5888	245	43	⊗	⊗	VERB
ejpam-5888	245	44	−6	−6	NUM
ejpam-5888	245	45	∞	∞	NUM
ejpam-5888	246	1	∞	∞	NUM
ejpam-5888	246	2	∞	∞	NUM
ejpam-5888	246	3	−8	−8	X
ejpam-5888	247	1	∞	∞	NUM
ejpam-5888	247	2	∞	∞	NUM
ejpam-5888	247	3	∞	∞	NUM
ejpam-5888	247	4	−14	−14	NUM
ejpam-5888	247	5			PROPN
ejpam-5888	247	6	=	=	SYM
ejpam-5888	247	7	1	1	PROPN
ejpam-5888	247	8	3	3	NUM
ejpam-5888	247	9	4	4	NUM
ejpam-5888	247	10	1	1	NUM
ejpam-5888	247	11	3	3	NUM
ejpam-5888	247	12	6	6	NUM
ejpam-5888	247	13	2	2	NUM
ejpam-5888	247	14	2	2	NUM
ejpam-5888	247	15	1	1	NUM
ejpam-5888	247	16			PROPN
ejpam-5888	247	17	,	,	PUNCT
ejpam-5888	247	18	kashifa	kashifa	PROPN
ejpam-5888	247	19	begum	begum	PROPN
ejpam-5888	247	20	a.	a.	NOUN
ejpam-5888	247	21	et	et	PROPN
ejpam-5888	247	22	.	.	PUNCT
ejpam-5888	248	1	al	al	PROPN
ejpam-5888	248	2	/	/	PUNCT
ejpam-5888	248	3	eur	eur	PROPN
ejpam-5888	248	4	.	.	PUNCT
ejpam-5888	249	1	j.	j.	PROPN
ejpam-5888	249	2	pure	pure	PROPN
ejpam-5888	249	3	appl	appl	PROPN
ejpam-5888	249	4	.	.	PROPN
ejpam-5888	249	5	math	math	PROPN
ejpam-5888	249	6	,	,	PUNCT
ejpam-5888	249	7	18	18	NUM
ejpam-5888	249	8	(	(	PUNCT
ejpam-5888	249	9	3	3	NUM
ejpam-5888	249	10	)	)	PUNCT
ejpam-5888	249	11	(	(	PUNCT
ejpam-5888	249	12	2025	2025	NUM
ejpam-5888	249	13	)	)	PUNCT
ejpam-5888	249	14	,	,	PUNCT
ejpam-5888	249	15	5888	5888	NUM
ejpam-5888	249	16	11	11	NUM
ejpam-5888	249	17	of	of	ADP
ejpam-5888	249	18	16	16	NUM
ejpam-5888	249	19	z2	z2	NOUN
ejpam-5888	249	20	=	=	SYM
ejpam-5888	250	1			PROPN
ejpam-5888	250	2	8	8	NUM
ejpam-5888	250	3	∞	∞	NUM
ejpam-5888	250	4	∞	∞	NUM
ejpam-5888	250	5	∞	∞	NUM
ejpam-5888	250	6	−10	−10	PROPN
ejpam-5888	250	7	∞	∞	NUM
ejpam-5888	250	8	∞	∞	NUM
ejpam-5888	250	9	∞	∞	NUM
ejpam-5888	250	10	17	17	NUM
ejpam-5888	250	11	⊗	⊗	VERB
ejpam-5888	250	12			PROPN
ejpam-5888	250	13	1	1	NUM
ejpam-5888	250	14	5	5	NUM
ejpam-5888	250	15	12	12	NUM
ejpam-5888	250	16	−1	−1	NOUN
ejpam-5888	250	17	3	3	NUM
ejpam-5888	250	18	12	12	NUM
ejpam-5888	250	19	−6	−6	NOUN
ejpam-5888	250	20	−4	−4	PROPN
ejpam-5888	250	21	1	1	NUM
ejpam-5888	250	22	⊗	⊗	NOUN
ejpam-5888	250	23	−8	−8	NUM
ejpam-5888	250	24	∞	∞	NUM
ejpam-5888	250	25	∞	∞	NUM
ejpam-5888	250	26	∞	∞	NUM
ejpam-5888	250	27	10	10	NUM
ejpam-5888	250	28	∞	∞	NUM
ejpam-5888	250	29	∞	∞	NUM
ejpam-5888	250	30	∞	∞	NOUN
ejpam-5888	250	31	−17	−17	NOUN
ejpam-5888	251	1			PROPN
ejpam-5888	251	2	=	=	SYM
ejpam-5888	251	3			PROPN
ejpam-5888	251	4	1	1	NUM
ejpam-5888	251	5	23	23	NUM
ejpam-5888	251	6	3	3	NUM
ejpam-5888	251	7	−19	−19	NOUN
ejpam-5888	251	8	3	3	NUM
ejpam-5888	251	9	−15	−15	NOUN
ejpam-5888	251	10	3	3	NUM
ejpam-5888	251	11	23	23	NUM
ejpam-5888	251	12	1	1	NUM
ejpam-5888	251	13	.	.	PROPN
ejpam-5888	251	14	bob	bob	PROPN
ejpam-5888	251	15	’s	’s	PART
ejpam-5888	251	16	shared	share	VERB
ejpam-5888	251	17	secret	secret	ADJ
ejpam-5888	251	18	key	key	ADJ
ejpam-5888	251	19	z̃1	z̃1	NOUN
ejpam-5888	251	20	=	=	SYM
ejpam-5888	251	21			PROPN
ejpam-5888	251	22	8	8	NUM
ejpam-5888	251	23	∞	∞	NUM
ejpam-5888	251	24	∞	∞	NUM
ejpam-5888	251	25	∞	∞	NUM
ejpam-5888	251	26	7	7	NUM
ejpam-5888	251	27	∞	∞	NUM
ejpam-5888	251	28	∞	∞	NUM
ejpam-5888	251	29	∞	∞	NUM
ejpam-5888	251	30	−1	−1	NOUN
ejpam-5888	251	31	⊗	⊗	VERB
ejpam-5888	252	1			PROPN
ejpam-5888	252	2	1	1	NUM
ejpam-5888	252	3	2	2	NUM
ejpam-5888	252	4	−5	−5	NOUN
ejpam-5888	252	5	2	2	NUM
ejpam-5888	252	6	3	3	NUM
ejpam-5888	252	7	−2	−2	NOUN
ejpam-5888	252	8	11	11	NUM
ejpam-5888	252	9	10	10	NUM
ejpam-5888	252	10	1	1	NUM
ejpam-5888	252	11	⊗	⊗	NOUN
ejpam-5888	252	12	−8	−8	NUM
ejpam-5888	252	13	∞	∞	NUM
ejpam-5888	252	14	∞	∞	NUM
ejpam-5888	252	15	∞	∞	PROPN
ejpam-5888	252	16	−7	−7	NOUN
ejpam-5888	252	17	∞	∞	NUM
ejpam-5888	252	18	∞	∞	NUM
ejpam-5888	252	19	∞	∞	NUM
ejpam-5888	252	20	1	1	NUM
ejpam-5888	252	21			PROPN
ejpam-5888	252	22	=	=	SYM
ejpam-5888	252	23	1	1	PROPN
ejpam-5888	252	24	3	3	NUM
ejpam-5888	252	25	4	4	NUM
ejpam-5888	252	26	1	1	NUM
ejpam-5888	252	27	3	3	NUM
ejpam-5888	252	28	6	6	NUM
ejpam-5888	252	29	2	2	NUM
ejpam-5888	252	30	2	2	NUM
ejpam-5888	252	31	1	1	NUM
ejpam-5888	252	32			PROPN
ejpam-5888	252	33	,	,	PUNCT
ejpam-5888	252	34	z̃2	z̃2	PROPN
ejpam-5888	252	35	=	=	SYM
ejpam-5888	253	1			PROPN
ejpam-5888	253	2	8	8	NUM
ejpam-5888	253	3	∞	∞	NUM
ejpam-5888	253	4	∞	∞	NUM
ejpam-5888	253	5	∞	∞	NUM
ejpam-5888	253	6	7	7	NUM
ejpam-5888	253	7	∞	∞	NUM
ejpam-5888	253	8	∞	∞	NUM
ejpam-5888	253	9	∞	∞	NUM
ejpam-5888	253	10	−1	−1	NOUN
ejpam-5888	253	11	⊗	⊗	VERB
ejpam-5888	253	12			PROPN
ejpam-5888	253	13	1	1	NUM
ejpam-5888	253	14	22	22	NUM
ejpam-5888	253	15	−6	−6	NOUN
ejpam-5888	253	16	−18	−18	NUM
ejpam-5888	253	17	3	3	NUM
ejpam-5888	253	18	−23	−23	NUM
ejpam-5888	253	19	12	12	NUM
ejpam-5888	253	20	31	31	NUM
ejpam-5888	253	21	1	1	NUM
ejpam-5888	253	22	⊗	⊗	NOUN
ejpam-5888	254	1	−8	−8	NUM
ejpam-5888	255	1	∞	∞	NUM
ejpam-5888	255	2	∞	∞	NUM
ejpam-5888	255	3	∞	∞	PROPN
ejpam-5888	255	4	−7	−7	NOUN
ejpam-5888	255	5	∞	∞	NUM
ejpam-5888	255	6	∞	∞	NUM
ejpam-5888	255	7	∞	∞	NUM
ejpam-5888	255	8	1	1	NUM
ejpam-5888	255	9			PROPN
ejpam-5888	255	10	=	=	SYM
ejpam-5888	255	11			PROPN
ejpam-5888	255	12	1	1	NUM
ejpam-5888	255	13	23	23	NUM
ejpam-5888	255	14	3	3	NUM
ejpam-5888	255	15	−19	−19	NOUN
ejpam-5888	255	16	3	3	NUM
ejpam-5888	255	17	−15	−15	NOUN
ejpam-5888	255	18	3	3	NUM
ejpam-5888	255	19	23	23	NUM
ejpam-5888	255	20	1	1	NUM
ejpam-5888	255	21	.	.	ADV
ejpam-5888	255	22	thus	thus	ADV
ejpam-5888	255	23	z1	z1	VERB
ejpam-5888	255	24	=	=	SYM
ejpam-5888	255	25	z̃1	z̃1	PROPN
ejpam-5888	255	26	=	=	SYM
ejpam-5888	255	27	1	1	PROPN
ejpam-5888	255	28	3	3	NUM
ejpam-5888	255	29	4	4	NUM
ejpam-5888	255	30	1	1	NUM
ejpam-5888	255	31	3	3	NUM
ejpam-5888	255	32	6	6	NUM
ejpam-5888	255	33	2	2	NUM
ejpam-5888	255	34	2	2	NUM
ejpam-5888	255	35	1	1	NUM
ejpam-5888	255	36			PROPN
ejpam-5888	255	37	and	and	CCONJ
ejpam-5888	255	38	z2	z2	PROPN
ejpam-5888	255	39	=	=	SYM
ejpam-5888	256	1	z̃2	z̃2	NUM
ejpam-5888	257	1	=	=	SYM
ejpam-5888	257	2			PROPN
ejpam-5888	257	3	1	1	NUM
ejpam-5888	257	4	23	23	NUM
ejpam-5888	257	5	3	3	NUM
ejpam-5888	257	6	−19	−19	NOUN
ejpam-5888	257	7	3	3	NUM
ejpam-5888	257	8	−15	−15	NOUN
ejpam-5888	257	9	3	3	NUM
ejpam-5888	257	10	23	23	NUM
ejpam-5888	257	11	1	1	NUM
ejpam-5888	257	12			PROPN
ejpam-5888	257	13	.	.	PUNCT
ejpam-5888	258	1	6	6	X
ejpam-5888	258	2	.	.	X
ejpam-5888	258	3	security	security	NOUN
ejpam-5888	258	4	and	and	CCONJ
ejpam-5888	258	5	complexity	complexity	NOUN
ejpam-5888	258	6	analysis	analysis	NOUN
ejpam-5888	258	7	of	of	ADP
ejpam-5888	258	8	the	the	DET
ejpam-5888	258	9	protocol	protocol	NOUN
ejpam-5888	258	10	6.1	6.1	NUM
ejpam-5888	258	11	.	.	PUNCT
ejpam-5888	259	1	completeness	completeness	NOUN
ejpam-5888	259	2	of	of	ADP
ejpam-5888	259	3	the	the	DET
ejpam-5888	259	4	protocol	protocol	NOUN
ejpam-5888	259	5	in	in	ADP
ejpam-5888	259	6	this	this	DET
ejpam-5888	259	7	subsection	subsection	NOUN
ejpam-5888	259	8	,	,	PUNCT
ejpam-5888	259	9	we	we	PRON
ejpam-5888	259	10	prove	prove	VERB
ejpam-5888	259	11	the	the	DET
ejpam-5888	259	12	completeness	completeness	NOUN
ejpam-5888	259	13	of	of	ADP
ejpam-5888	259	14	the	the	DET
ejpam-5888	259	15	proposed	propose	VERB
ejpam-5888	259	16	key	key	ADJ
ejpam-5888	259	17	exchange	exchange	NOUN
ejpam-5888	259	18	protocols	protocol	NOUN
ejpam-5888	259	19	.	.	PUNCT
ejpam-5888	260	1	lemma	lemma	PROPN
ejpam-5888	260	2	1	1	NUM
ejpam-5888	260	3	.	.	PUNCT
ejpam-5888	260	4	tropical	tropical	ADJ
ejpam-5888	260	5	diagonal	diagonal	ADJ
ejpam-5888	260	6	matrix	matrix	NOUN
ejpam-5888	260	7	multiplication	multiplication	NOUN
ejpam-5888	260	8	is	be	AUX
ejpam-5888	260	9	commutative	commutative	ADJ
ejpam-5888	260	10	.	.	PUNCT
ejpam-5888	261	1	proof	proof	NOUN
ejpam-5888	261	2	.	.	PUNCT
ejpam-5888	262	1	let	let	VERB
ejpam-5888	262	2	d	d	NOUN
ejpam-5888	262	3	and	and	CCONJ
ejpam-5888	262	4	e	e	AUX
ejpam-5888	262	5	be	be	AUX
ejpam-5888	262	6	two	two	NUM
ejpam-5888	262	7	n	n	NUM
ejpam-5888	262	8	×	×	NOUN
ejpam-5888	262	9	n	n	CCONJ
ejpam-5888	262	10	tropical	tropical	ADJ
ejpam-5888	262	11	diagonal	diagonal	ADJ
ejpam-5888	262	12	matrices	matrix	NOUN
ejpam-5888	262	13	∈	∈	PROPN
ejpam-5888	262	14	h.	h.	NOUN
ejpam-5888	262	15	we	we	PRON
ejpam-5888	262	16	wish	wish	VERB
ejpam-5888	262	17	to	to	PART
ejpam-5888	262	18	prove	prove	VERB
ejpam-5888	262	19	that	that	SCONJ
ejpam-5888	263	1	d	d	PROPN
ejpam-5888	263	2	⊗	⊗	PROPN
ejpam-5888	263	3	e	e	PROPN
ejpam-5888	263	4	=	=	SYM
ejpam-5888	263	5	e	e	PROPN
ejpam-5888	263	6	⊗d	⊗d	NOUN
ejpam-5888	263	7	.	.	PUNCT
ejpam-5888	264	1	(	(	PUNCT
ejpam-5888	264	2	d	d	X
ejpam-5888	264	3	⊗	⊗	PROPN
ejpam-5888	264	4	e)ij	e)ij	PROPN
ejpam-5888	264	5	=	=	SYM
ejpam-5888	264	6	n⊕	n⊕	PROPN
ejpam-5888	264	7	j=1	j=1	PROPN
ejpam-5888	264	8	(	(	PUNCT
ejpam-5888	264	9	dij	dij	PROPN
ejpam-5888	264	10	⊗	⊗	PROPN
ejpam-5888	264	11	eji	eji	PROPN
ejpam-5888	264	12	)	)	PUNCT
ejpam-5888	264	13	=	=	SYM
ejpam-5888	264	14	min	min	PROPN
ejpam-5888	264	15	j	j	PROPN
ejpam-5888	264	16	(	(	PUNCT
ejpam-5888	264	17	dij	dij	PROPN
ejpam-5888	264	18	+	+	NUM
ejpam-5888	264	19	eji	eji	NOUN
ejpam-5888	264	20	)	)	PUNCT
ejpam-5888	264	21	since	since	SCONJ
ejpam-5888	264	22	d	d	PROPN
ejpam-5888	264	23	and	and	CCONJ
ejpam-5888	264	24	e	e	NOUN
ejpam-5888	264	25	are	be	AUX
ejpam-5888	264	26	diagonal	diagonal	ADJ
ejpam-5888	264	27	matrices	matrix	NOUN
ejpam-5888	264	28	,	,	PUNCT
ejpam-5888	264	29	dij	dij	PROPN
ejpam-5888	264	30	=	=	SYM
ejpam-5888	264	31	∞	∞	NOUN
ejpam-5888	264	32	for	for	ADP
ejpam-5888	264	33	i	i	PRON
ejpam-5888	264	34	̸=	̸=	PROPN
ejpam-5888	264	35	j	j	PROPN
ejpam-5888	264	36	and	and	CCONJ
ejpam-5888	264	37	eji	eji	VERB
ejpam-5888	264	38	=	=	NOUN
ejpam-5888	264	39	∞	∞	PROPN
ejpam-5888	264	40	for	for	ADP
ejpam-5888	264	41	i	i	PRON
ejpam-5888	264	42	̸=	̸=	PROPN
ejpam-5888	264	43	j.	j.	PROPN
ejpam-5888	264	44	therefore	therefore	ADV
ejpam-5888	264	45	,	,	PUNCT
ejpam-5888	264	46	(	(	PUNCT
ejpam-5888	264	47	d⊗e)ij	d⊗e)ij	NOUN
ejpam-5888	264	48	=	=	SYM
ejpam-5888	264	49	∞	∞	PROPN
ejpam-5888	264	50	for	for	ADP
ejpam-5888	264	51	i	i	PRON
ejpam-5888	264	52	̸=	̸=	PROPN
ejpam-5888	264	53	j	j	PROPN
ejpam-5888	264	54	and	and	CCONJ
ejpam-5888	264	55	the	the	DET
ejpam-5888	264	56	only	only	ADJ
ejpam-5888	264	57	non	non	ADJ
ejpam-5888	264	58	-	-	ADJ
ejpam-5888	264	59	infinite	infinite	ADJ
ejpam-5888	264	60	term	term	NOUN
ejpam-5888	264	61	in	in	ADP
ejpam-5888	264	62	the	the	DET
ejpam-5888	264	63	product	product	NOUN
ejpam-5888	264	64	occurs	occur	VERB
ejpam-5888	264	65	when	when	SCONJ
ejpam-5888	264	66	i	i	PRON
ejpam-5888	264	67	=	=	PROPN
ejpam-5888	264	68	j.	j.	PROPN
ejpam-5888	264	69	therefore	therefore	ADV
ejpam-5888	264	70	,	,	PUNCT
ejpam-5888	264	71	(	(	PUNCT
ejpam-5888	265	1	d	d	PROPN
ejpam-5888	265	2	⊗	⊗	PROPN
ejpam-5888	265	3	e)ii	e)ii	PROPN
ejpam-5888	265	4	=	=	SYM
ejpam-5888	265	5	min	min	NOUN
ejpam-5888	266	1	i	i	PRON
ejpam-5888	266	2	(	(	PUNCT
ejpam-5888	266	3	dii	dii	PROPN
ejpam-5888	266	4	+	+	CCONJ
ejpam-5888	266	5	eii	eii	PROPN
ejpam-5888	266	6	)	)	PUNCT
ejpam-5888	266	7	similarly	similarly	ADV
ejpam-5888	266	8	,	,	PUNCT
ejpam-5888	266	9	for	for	ADP
ejpam-5888	266	10	the	the	DET
ejpam-5888	266	11	product	product	NOUN
ejpam-5888	266	12	matrix	matrix	NOUN
ejpam-5888	266	13	e	e	NOUN
ejpam-5888	266	14	⊗d	⊗d	PROPN
ejpam-5888	266	15	,	,	PUNCT
ejpam-5888	266	16	we	we	PRON
ejpam-5888	266	17	have	have	VERB
ejpam-5888	266	18	(	(	PUNCT
ejpam-5888	266	19	e	e	NOUN
ejpam-5888	266	20	⊗d)ij	⊗d)ij	NUM
ejpam-5888	266	21	=	=	SYM
ejpam-5888	266	22	n⊕	n⊕	PROPN
ejpam-5888	266	23	j=1	j=1	PROPN
ejpam-5888	266	24	(	(	PUNCT
ejpam-5888	266	25	eij	eij	PROPN
ejpam-5888	266	26	⊗dji	⊗dji	PROPN
ejpam-5888	266	27	)	)	PUNCT
ejpam-5888	267	1	=	=	SYM
ejpam-5888	267	2	min	min	PROPN
ejpam-5888	267	3	j	j	PROPN
ejpam-5888	267	4	(	(	PUNCT
ejpam-5888	267	5	eij	eij	PROPN
ejpam-5888	267	6	+	+	NOUN
ejpam-5888	267	7	dji	dji	NOUN
ejpam-5888	267	8	)	)	PUNCT
ejpam-5888	267	9	(	(	PUNCT
ejpam-5888	267	10	e	e	X
ejpam-5888	267	11	⊗d)ii	⊗d)ii	PROPN
ejpam-5888	267	12	=	=	SYM
ejpam-5888	267	13	min	min	PROPN
ejpam-5888	268	1	i	i	PRON
ejpam-5888	268	2	(	(	PUNCT
ejpam-5888	268	3	eii	eii	PROPN
ejpam-5888	268	4	+	+	NOUN
ejpam-5888	268	5	dii	dii	NOUN
ejpam-5888	268	6	)	)	PUNCT
ejpam-5888	268	7	thus	thus	ADV
ejpam-5888	268	8	,	,	PUNCT
ejpam-5888	268	9	d	d	PROPN
ejpam-5888	268	10	⊗	⊗	PROPN
ejpam-5888	268	11	e	e	X
ejpam-5888	268	12	=	=	SYM
ejpam-5888	268	13	e	e	PROPN
ejpam-5888	268	14	⊗d	⊗d	NOUN
ejpam-5888	268	15	.	.	PUNCT
ejpam-5888	269	1	□	□	PUNCT
ejpam-5888	269	2	kashifa	kashifa	PROPN
ejpam-5888	269	3	begum	begum	VERB
ejpam-5888	269	4	a.	a.	NOUN
ejpam-5888	269	5	et	et	PROPN
ejpam-5888	269	6	.	.	PUNCT
ejpam-5888	270	1	al	al	PROPN
ejpam-5888	270	2	/	/	PUNCT
ejpam-5888	270	3	eur	eur	PROPN
ejpam-5888	270	4	.	.	PUNCT
ejpam-5888	271	1	j.	j.	PROPN
ejpam-5888	271	2	pure	pure	PROPN
ejpam-5888	271	3	appl	appl	PROPN
ejpam-5888	271	4	.	.	PROPN
ejpam-5888	271	5	math	math	PROPN
ejpam-5888	271	6	,	,	PUNCT
ejpam-5888	271	7	18	18	NUM
ejpam-5888	271	8	(	(	PUNCT
ejpam-5888	271	9	3	3	NUM
ejpam-5888	271	10	)	)	PUNCT
ejpam-5888	271	11	(	(	PUNCT
ejpam-5888	271	12	2025	2025	NUM
ejpam-5888	271	13	)	)	PUNCT
ejpam-5888	271	14	,	,	PUNCT
ejpam-5888	271	15	5888	5888	NUM
ejpam-5888	271	16	12	12	NUM
ejpam-5888	271	17	of	of	ADP
ejpam-5888	271	18	16	16	NUM
ejpam-5888	271	19	theorem	theorem	NOUN
ejpam-5888	271	20	1	1	NUM
ejpam-5888	271	21	.	.	PUNCT
ejpam-5888	272	1	the	the	DET
ejpam-5888	272	2	protocols	protocol	NOUN
ejpam-5888	272	3	are	be	AUX
ejpam-5888	272	4	complete	complete	ADJ
ejpam-5888	272	5	,	,	PUNCT
ejpam-5888	272	6	i.e.	i.e.	X
ejpam-5888	272	7	,	,	PUNCT
ejpam-5888	272	8	zi	zi	PROPN
ejpam-5888	272	9	=	=	SYM
ejpam-5888	272	10	z̃i	z̃i	PROPN
ejpam-5888	272	11	,	,	PUNCT
ejpam-5888	272	12	i	i	PRON
ejpam-5888	272	13	=	=	NOUN
ejpam-5888	272	14	1	1	NUM
ejpam-5888	272	15	,	,	PUNCT
ejpam-5888	272	16	2	2	NUM
ejpam-5888	272	17	and	and	CCONJ
ejpam-5888	272	18	zij	zij	PROPN
ejpam-5888	272	19	=	=	PROPN
ejpam-5888	272	20	z̃ij	z̃ij	PROPN
ejpam-5888	272	21	,	,	PUNCT
ejpam-5888	272	22	i	i	PRON
ejpam-5888	272	23	=	=	NOUN
ejpam-5888	272	24	1	1	NUM
ejpam-5888	272	25	,	,	PUNCT
ejpam-5888	272	26	2	2	NUM
ejpam-5888	272	27	,	,	PUNCT
ejpam-5888	272	28	j	j	NOUN
ejpam-5888	272	29	=	=	SYM
ejpam-5888	272	30	1	1	NUM
ejpam-5888	272	31	,	,	PUNCT
ejpam-5888	272	32	2	2	NUM
ejpam-5888	272	33	.	.	PUNCT
ejpam-5888	272	34	proof	proof	NOUN
ejpam-5888	272	35	.	.	PUNCT
ejpam-5888	273	1	to	to	PART
ejpam-5888	273	2	prove	prove	VERB
ejpam-5888	273	3	that	that	SCONJ
ejpam-5888	273	4	protocol	protocol	NOUN
ejpam-5888	273	5	i	i	PRON
ejpam-5888	273	6	is	be	AUX
ejpam-5888	273	7	complete	complete	ADJ
ejpam-5888	273	8	,	,	PUNCT
ejpam-5888	273	9	we	we	PRON
ejpam-5888	273	10	need	need	VERB
ejpam-5888	273	11	to	to	PART
ejpam-5888	273	12	prove	prove	VERB
ejpam-5888	273	13	that	that	DET
ejpam-5888	273	14	zi	zi	NOUN
ejpam-5888	273	15	=	=	SYM
ejpam-5888	273	16	z̃i	z̃i	PROPN
ejpam-5888	273	17	,	,	PUNCT
ejpam-5888	273	18	i	i	PRON
ejpam-5888	273	19	=	=	NOUN
ejpam-5888	273	20	1	1	NUM
ejpam-5888	273	21	,	,	PUNCT
ejpam-5888	273	22	2	2	NUM
ejpam-5888	273	23	.	.	X
ejpam-5888	273	24	zi	zi	NOUN
ejpam-5888	274	1	=	=	PUNCT
ejpam-5888	275	1	pi(di)⊗	pi(di)⊗	VERB
ejpam-5888	275	2	y	y	PROPN
ejpam-5888	275	3	⊗	⊗	PROPN
ejpam-5888	275	4	p′i(di	p′i(di	PROPN
ejpam-5888	275	5	)	)	PUNCT
ejpam-5888	275	6	,	,	PUNCT
ejpam-5888	275	7	i	i	PRON
ejpam-5888	275	8	=	=	NOUN
ejpam-5888	275	9	1	1	NUM
ejpam-5888	275	10	,	,	PUNCT
ejpam-5888	275	11	2	2	NUM
ejpam-5888	275	12	=	=	SYM
ejpam-5888	275	13	pi(di)⊗	pi(di)⊗	NOUN
ejpam-5888	275	14	(	(	PUNCT
ejpam-5888	275	15	q(b)⊗	q(b)⊗	NOUN
ejpam-5888	275	16	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	275	17	q′(b))⊗	q′(b))⊗	VERB
ejpam-5888	275	18	p′i(di	p′i(di	NOUN
ejpam-5888	275	19	)	)	PUNCT
ejpam-5888	276	1	=	=	PUNCT
ejpam-5888	276	2	(	(	PUNCT
ejpam-5888	276	3	pi(di)⊗	pi(di)⊗	VERB
ejpam-5888	276	4	q(b))⊗	q(b))⊗	ADJ
ejpam-5888	276	5	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	276	6	(	(	PUNCT
ejpam-5888	276	7	q′(b)⊗	q′(b)⊗	NOUN
ejpam-5888	276	8	p′i(di	p′i(di	PROPN
ejpam-5888	276	9	)	)	PUNCT
ejpam-5888	276	10	)	)	PUNCT
ejpam-5888	277	1	=	=	PRON
ejpam-5888	277	2	(	(	PUNCT
ejpam-5888	277	3	q(b)⊗	q(b)⊗	NOUN
ejpam-5888	277	4	pi(di))⊗	pi(di))⊗	NOUN
ejpam-5888	277	5	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	277	6	(	(	PUNCT
ejpam-5888	277	7	p′i(di)⊗	p′i(di)⊗	NOUN
ejpam-5888	277	8	q′(b	q′(b	PROPN
ejpam-5888	277	9	)	)	PUNCT
ejpam-5888	277	10	)	)	PUNCT
ejpam-5888	278	1	=	=	PUNCT
ejpam-5888	278	2	q(b)⊗	q(b)⊗	NOUN
ejpam-5888	278	3	(	(	PUNCT
ejpam-5888	278	4	pi(di)⊗	pi(di)⊗	VERB
ejpam-5888	278	5	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	278	6	p′i(di))⊗	p′i(di))⊗	PRON
ejpam-5888	278	7	q′(b	q′(b	PRON
ejpam-5888	278	8	)	)	PUNCT
ejpam-5888	278	9	=	=	PUNCT
ejpam-5888	278	10	q(b)⊗xi	q(b)⊗xi	PROPN
ejpam-5888	278	11	⊗	⊗	PROPN
ejpam-5888	278	12	q′(b	q′(b	PROPN
ejpam-5888	278	13	)	)	PUNCT
ejpam-5888	279	1	=	=	SYM
ejpam-5888	279	2	z̃i	z̃i	PROPN
ejpam-5888	279	3	,	,	PUNCT
ejpam-5888	279	4	i	i	PRON
ejpam-5888	279	5	=	=	NOUN
ejpam-5888	279	6	1	1	NUM
ejpam-5888	279	7	,	,	PUNCT
ejpam-5888	279	8	2	2	NUM
ejpam-5888	279	9	.	.	PUNCT
ejpam-5888	279	10	to	to	PART
ejpam-5888	279	11	prove	prove	VERB
ejpam-5888	279	12	that	that	SCONJ
ejpam-5888	279	13	protocol	protocol	PROPN
ejpam-5888	279	14	ii	ii	PROPN
ejpam-5888	279	15	is	be	AUX
ejpam-5888	279	16	complete	complete	ADJ
ejpam-5888	279	17	,	,	PUNCT
ejpam-5888	279	18	we	we	PRON
ejpam-5888	279	19	need	need	VERB
ejpam-5888	279	20	to	to	PART
ejpam-5888	279	21	prove	prove	VERB
ejpam-5888	279	22	that	that	SCONJ
ejpam-5888	279	23	zij	zij	PROPN
ejpam-5888	279	24	=	=	PROPN
ejpam-5888	279	25	z̃ij	z̃ij	PROPN
ejpam-5888	279	26	,	,	PUNCT
ejpam-5888	279	27	i	i	PRON
ejpam-5888	279	28	=	=	NOUN
ejpam-5888	279	29	1	1	NUM
ejpam-5888	279	30	,	,	PUNCT
ejpam-5888	279	31	2	2	NUM
ejpam-5888	279	32	,	,	PUNCT
ejpam-5888	279	33	j	j	NOUN
ejpam-5888	280	1	=	=	SYM
ejpam-5888	280	2	1	1	NUM
ejpam-5888	280	3	,	,	PUNCT
ejpam-5888	280	4	2	2	NUM
ejpam-5888	280	5	.	.	PUNCT
ejpam-5888	281	1	zij	zij	PROPN
ejpam-5888	281	2	=	=	PROPN
ejpam-5888	281	3	pi(di)⊗	pi(di)⊗	PROPN
ejpam-5888	281	4	yj	yj	PROPN
ejpam-5888	281	5	⊗	⊗	PROPN
ejpam-5888	281	6	p′i(di	p′i(di	PROPN
ejpam-5888	281	7	)	)	PUNCT
ejpam-5888	281	8	,	,	PUNCT
ejpam-5888	282	1	i	i	PRON
ejpam-5888	282	2	=	=	NOUN
ejpam-5888	282	3	1	1	NUM
ejpam-5888	282	4	,	,	PUNCT
ejpam-5888	282	5	2	2	NUM
ejpam-5888	282	6	,	,	PUNCT
ejpam-5888	282	7	j	j	NOUN
ejpam-5888	282	8	=	=	SYM
ejpam-5888	282	9	1	1	NUM
ejpam-5888	282	10	,	,	PUNCT
ejpam-5888	282	11	2	2	NUM
ejpam-5888	282	12	=	=	SYM
ejpam-5888	282	13	pi(di)⊗	pi(di)⊗	NOUN
ejpam-5888	282	14	(	(	PUNCT
ejpam-5888	282	15	qj(bj)⊗	qj(bj)⊗	NOUN
ejpam-5888	282	16	g(a)⊗	g(a)⊗	VERB
ejpam-5888	282	17	q′j(bj))⊗	q′j(bj))⊗	PROPN
ejpam-5888	282	18	p′i(di	p′i(di	NUM
ejpam-5888	282	19	)	)	PUNCT
ejpam-5888	283	1	=	=	PUNCT
ejpam-5888	283	2	(	(	PUNCT
ejpam-5888	283	3	pi(di)⊗	pi(di)⊗	VERB
ejpam-5888	283	4	qj(bj))⊗	qj(bj))⊗	ADJ
ejpam-5888	283	5	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	283	6	(	(	PUNCT
ejpam-5888	283	7	q′j(bj)⊗	q′j(bj)⊗	NOUN
ejpam-5888	283	8	p′i(di	p′i(di	NUM
ejpam-5888	283	9	)	)	PUNCT
ejpam-5888	283	10	)	)	PUNCT
ejpam-5888	284	1	=	=	PUNCT
ejpam-5888	284	2	qj(bj)⊗	qj(bj)⊗	NOUN
ejpam-5888	284	3	pi(di)⊗	pi(di)⊗	VERB
ejpam-5888	284	4	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	284	5	p′i(di)⊗	p′i(di)⊗	ADJ
ejpam-5888	284	6	q′j(bj	q′j(bj	NOUN
ejpam-5888	284	7	)	)	PUNCT
ejpam-5888	284	8	=	=	SYM
ejpam-5888	284	9	qj(bj)⊗	qj(bj)⊗	NOUN
ejpam-5888	284	10	(	(	PUNCT
ejpam-5888	284	11	pi(di)⊗	pi(di)⊗	NOUN
ejpam-5888	284	12	g(a)⊗	g(a)⊗	NOUN
ejpam-5888	284	13	p′i(di))⊗	p′i(di))⊗	PART
ejpam-5888	284	14	q′j(bj	q′j(bj	NOUN
ejpam-5888	284	15	)	)	PUNCT
ejpam-5888	284	16	=	=	VERB
ejpam-5888	285	1	qj(bj)⊗xi	qj(bj)⊗xi	PROPN
ejpam-5888	285	2	⊗	⊗	NUM
ejpam-5888	285	3	q′j(bj	q′j(bj	NOUN
ejpam-5888	285	4	)	)	PUNCT
ejpam-5888	286	1	=	=	SYM
ejpam-5888	286	2	z̃ij	z̃ij	PROPN
ejpam-5888	286	3	,	,	PUNCT
ejpam-5888	286	4	i	i	PRON
ejpam-5888	286	5	=	=	NOUN
ejpam-5888	286	6	1	1	NUM
ejpam-5888	286	7	,	,	PUNCT
ejpam-5888	286	8	2	2	NUM
ejpam-5888	286	9	,	,	PUNCT
ejpam-5888	286	10	j	j	NOUN
ejpam-5888	286	11	=	=	SYM
ejpam-5888	286	12	1	1	NUM
ejpam-5888	286	13	,	,	PUNCT
ejpam-5888	286	14	2	2	NUM
ejpam-5888	286	15	.	.	PUNCT
ejpam-5888	286	16	□	□	SYM
ejpam-5888	286	17	6.2	6.2	NUM
ejpam-5888	286	18	.	.	PUNCT
ejpam-5888	287	1	security	security	NOUN
ejpam-5888	287	2	analysis	analysis	NOUN
ejpam-5888	287	3	6.2.1	6.2.1	NOUN
ejpam-5888	287	4	.	.	PUNCT
ejpam-5888	288	1	linear	linear	ADJ
ejpam-5888	288	2	algebra	algebra	NOUN
ejpam-5888	288	3	attack	attack	NOUN
ejpam-5888	288	4	in	in	ADP
ejpam-5888	288	5	linear	linear	ADJ
ejpam-5888	288	6	algebra	algebra	NOUN
ejpam-5888	288	7	attack	attack	NOUN
ejpam-5888	288	8	,	,	PUNCT
ejpam-5888	288	9	an	an	DET
ejpam-5888	288	10	adversary	adversary	NOUN
ejpam-5888	288	11	uses	use	VERB
ejpam-5888	288	12	the	the	DET
ejpam-5888	288	13	algebraic	algebraic	ADJ
ejpam-5888	288	14	properties	property	NOUN
ejpam-5888	288	15	to	to	PART
ejpam-5888	288	16	discover	discover	VERB
ejpam-5888	288	17	the	the	DET
ejpam-5888	288	18	secret	secret	ADJ
ejpam-5888	288	19	key	key	NOUN
ejpam-5888	288	20	.	.	PUNCT
ejpam-5888	289	1	since	since	SCONJ
ejpam-5888	289	2	we	we	PRON
ejpam-5888	289	3	have	have	AUX
ejpam-5888	289	4	considered	consider	VERB
ejpam-5888	289	5	tropical	tropical	ADJ
ejpam-5888	289	6	algebra	algebra	NOUN
ejpam-5888	289	7	as	as	ADP
ejpam-5888	289	8	a	a	DET
ejpam-5888	289	9	platform	platform	NOUN
ejpam-5888	289	10	for	for	ADP
ejpam-5888	289	11	our	our	PRON
ejpam-5888	289	12	protocol	protocol	NOUN
ejpam-5888	289	13	,	,	PUNCT
ejpam-5888	289	14	to	to	PART
ejpam-5888	289	15	find	find	VERB
ejpam-5888	289	16	exactly	exactly	ADV
ejpam-5888	289	17	the	the	DET
ejpam-5888	289	18	secret	secret	ADJ
ejpam-5888	289	19	matrices	matrix	NOUN
ejpam-5888	289	20	by	by	ADP
ejpam-5888	289	21	this	this	DET
ejpam-5888	289	22	attack	attack	NOUN
ejpam-5888	289	23	is	be	AUX
ejpam-5888	289	24	not	not	PART
ejpam-5888	289	25	likely	likely	ADJ
ejpam-5888	289	26	.	.	PUNCT
ejpam-5888	290	1	for	for	ADP
ejpam-5888	290	2	the	the	DET
ejpam-5888	290	3	first	first	ADJ
ejpam-5888	290	4	protocol	protocol	NOUN
ejpam-5888	290	5	,	,	PUNCT
ejpam-5888	290	6	to	to	PART
ejpam-5888	290	7	find	find	VERB
ejpam-5888	290	8	the	the	DET
ejpam-5888	290	9	key	key	ADJ
ejpam-5888	290	10	zi	zi	NOUN
ejpam-5888	290	11	from	from	ADP
ejpam-5888	290	12	xi	xi	PROPN
ejpam-5888	290	13	,	,	PUNCT
ejpam-5888	290	14	one	one	PRON
ejpam-5888	290	15	needs	need	VERB
ejpam-5888	290	16	to	to	PART
ejpam-5888	290	17	know	know	VERB
ejpam-5888	290	18	pi(di	pi(di	PROPN
ejpam-5888	290	19	)	)	PUNCT
ejpam-5888	290	20	,	,	PUNCT
ejpam-5888	290	21	i	i	PRON
ejpam-5888	290	22	=	=	NOUN
ejpam-5888	290	23	1	1	NUM
ejpam-5888	290	24	,	,	PUNCT
ejpam-5888	290	25	2	2	NUM
ejpam-5888	290	26	,	,	PUNCT
ejpam-5888	290	27	or	or	CCONJ
ejpam-5888	290	28	to	to	PART
ejpam-5888	290	29	find	find	VERB
ejpam-5888	290	30	the	the	DET
ejpam-5888	290	31	key	key	NOUN
ejpam-5888	290	32	from	from	ADP
ejpam-5888	290	33	y	y	PROPN
ejpam-5888	290	34	,	,	PUNCT
ejpam-5888	290	35	one	one	PRON
ejpam-5888	290	36	needs	need	VERB
ejpam-5888	290	37	to	to	PART
ejpam-5888	290	38	know	know	VERB
ejpam-5888	290	39	q(b	q(b	ADV
ejpam-5888	290	40	)	)	PUNCT
ejpam-5888	290	41	.	.	PUNCT
ejpam-5888	291	1	similarly	similarly	ADV
ejpam-5888	291	2	,	,	PUNCT
ejpam-5888	291	3	for	for	ADP
ejpam-5888	291	4	the	the	DET
ejpam-5888	291	5	protocol	protocol	PROPN
ejpam-5888	291	6	ii	ii	PROPN
ejpam-5888	291	7	,	,	PUNCT
ejpam-5888	291	8	to	to	PART
ejpam-5888	291	9	find	find	VERB
ejpam-5888	291	10	the	the	DET
ejpam-5888	291	11	key	key	ADJ
ejpam-5888	291	12	zij	zij	PROPN
ejpam-5888	291	13	from	from	ADP
ejpam-5888	291	14	xi	xi	PROPN
ejpam-5888	291	15	,	,	PUNCT
ejpam-5888	291	16	one	one	PRON
ejpam-5888	291	17	needs	need	VERB
ejpam-5888	291	18	to	to	PART
ejpam-5888	291	19	know	know	VERB
ejpam-5888	291	20	pi(di	pi(di	PROPN
ejpam-5888	291	21	)	)	PUNCT
ejpam-5888	291	22	,	,	PUNCT
ejpam-5888	291	23	i	i	PRON
ejpam-5888	291	24	=	=	NOUN
ejpam-5888	291	25	1	1	NUM
ejpam-5888	291	26	,	,	PUNCT
ejpam-5888	291	27	2	2	NUM
ejpam-5888	291	28	or	or	CCONJ
ejpam-5888	291	29	to	to	PART
ejpam-5888	291	30	find	find	VERB
ejpam-5888	291	31	the	the	DET
ejpam-5888	291	32	key	key	NOUN
ejpam-5888	291	33	from	from	ADP
ejpam-5888	291	34	yj	yj	PROPN
ejpam-5888	291	35	,	,	PUNCT
ejpam-5888	291	36	one	one	NUM
ejpam-5888	291	37	needs	need	VERB
ejpam-5888	291	38	to	to	PART
ejpam-5888	291	39	know	know	VERB
ejpam-5888	291	40	qj(bj	qj(bj	PROPN
ejpam-5888	291	41	)	)	PUNCT
ejpam-5888	291	42	,	,	PUNCT
ejpam-5888	291	43	j	j	PROPN
ejpam-5888	291	44	=	=	SYM
ejpam-5888	291	45	1	1	NUM
ejpam-5888	291	46	,	,	PUNCT
ejpam-5888	291	47	2	2	NUM
ejpam-5888	291	48	.	.	PUNCT
ejpam-5888	292	1	since	since	SCONJ
ejpam-5888	292	2	tropical	tropical	ADJ
ejpam-5888	292	3	addition	addition	NOUN
ejpam-5888	292	4	and	and	CCONJ
ejpam-5888	292	5	multiplication	multiplication	NOUN
ejpam-5888	292	6	of	of	ADP
ejpam-5888	292	7	matrices	matrix	NOUN
ejpam-5888	292	8	are	be	AUX
ejpam-5888	292	9	not	not	PART
ejpam-5888	292	10	invertible	invertible	ADJ
ejpam-5888	292	11	,	,	PUNCT
ejpam-5888	292	12	this	this	DET
ejpam-5888	292	13	attack	attack	NOUN
ejpam-5888	292	14	is	be	AUX
ejpam-5888	292	15	not	not	PART
ejpam-5888	292	16	possible	possible	ADJ
ejpam-5888	292	17	.	.	PUNCT
ejpam-5888	293	1	kashifa	kashifa	PROPN
ejpam-5888	293	2	begum	begum	VERB
ejpam-5888	293	3	a.	a.	NOUN
ejpam-5888	293	4	et	et	PROPN
ejpam-5888	293	5	.	.	PUNCT
ejpam-5888	294	1	al	al	PROPN
ejpam-5888	294	2	/	/	PUNCT
ejpam-5888	294	3	eur	eur	PROPN
ejpam-5888	294	4	.	.	PUNCT
ejpam-5888	295	1	j.	j.	PROPN
ejpam-5888	295	2	pure	pure	PROPN
ejpam-5888	295	3	appl	appl	PROPN
ejpam-5888	295	4	.	.	PROPN
ejpam-5888	295	5	math	math	PROPN
ejpam-5888	295	6	,	,	PUNCT
ejpam-5888	295	7	18	18	NUM
ejpam-5888	295	8	(	(	PUNCT
ejpam-5888	295	9	3	3	NUM
ejpam-5888	295	10	)	)	PUNCT
ejpam-5888	295	11	(	(	PUNCT
ejpam-5888	295	12	2025	2025	NUM
ejpam-5888	295	13	)	)	PUNCT
ejpam-5888	295	14	,	,	PUNCT
ejpam-5888	295	15	5888	5888	NUM
ejpam-5888	295	16	13	13	NUM
ejpam-5888	295	17	of	of	ADP
ejpam-5888	295	18	16	16	NUM
ejpam-5888	295	19	6.2.2	6.2.2	NUM
ejpam-5888	295	20	.	.	PUNCT
ejpam-5888	295	21	brute	brute	ADJ
ejpam-5888	295	22	-	-	PUNCT
ejpam-5888	295	23	force	force	NOUN
ejpam-5888	295	24	attack	attack	NOUN
ejpam-5888	295	25	in	in	ADP
ejpam-5888	295	26	this	this	DET
ejpam-5888	295	27	attack	attack	NOUN
ejpam-5888	295	28	,	,	PUNCT
ejpam-5888	295	29	an	an	DET
ejpam-5888	295	30	adversary	adversary	NOUN
ejpam-5888	295	31	uses	use	VERB
ejpam-5888	295	32	every	every	DET
ejpam-5888	295	33	possible	possible	ADJ
ejpam-5888	295	34	matrix	matrix	NOUN
ejpam-5888	295	35	to	to	PART
ejpam-5888	295	36	obtain	obtain	VERB
ejpam-5888	295	37	the	the	DET
ejpam-5888	295	38	secret	secret	ADJ
ejpam-5888	295	39	matrices	matrix	NOUN
ejpam-5888	295	40	from	from	ADP
ejpam-5888	295	41	xi	xi	PROPN
ejpam-5888	295	42	,	,	PUNCT
ejpam-5888	295	43	i	i	NOUN
ejpam-5888	295	44	=	=	NOUN
ejpam-5888	295	45	1	1	NUM
ejpam-5888	295	46	,	,	PUNCT
ejpam-5888	295	47	2	2	NUM
ejpam-5888	295	48	and	and	CCONJ
ejpam-5888	295	49	g(a	g(a	PROPN
ejpam-5888	295	50	)	)	PUNCT
ejpam-5888	295	51	.	.	PUNCT
ejpam-5888	296	1	as	as	SCONJ
ejpam-5888	296	2	we	we	PRON
ejpam-5888	296	3	have	have	AUX
ejpam-5888	296	4	considered	consider	VERB
ejpam-5888	296	5	r	r	NOUN
ejpam-5888	296	6	=	=	SYM
ejpam-5888	296	7	mn(rmin	mn(rmin	PROPN
ejpam-5888	296	8	)	)	PUNCT
ejpam-5888	296	9	,	,	PUNCT
ejpam-5888	296	10	an	an	DET
ejpam-5888	296	11	infinite	infinite	ADJ
ejpam-5888	296	12	number	number	NOUN
ejpam-5888	296	13	of	of	ADP
ejpam-5888	296	14	possible	possible	ADJ
ejpam-5888	296	15	matrices	matrix	NOUN
ejpam-5888	296	16	are	be	AUX
ejpam-5888	296	17	at	at	ADP
ejpam-5888	296	18	hand	hand	NOUN
ejpam-5888	296	19	,	,	PUNCT
ejpam-5888	296	20	it	it	PRON
ejpam-5888	296	21	becomes	become	VERB
ejpam-5888	296	22	hard	hard	ADJ
ejpam-5888	296	23	to	to	PART
ejpam-5888	296	24	get	get	VERB
ejpam-5888	296	25	the	the	DET
ejpam-5888	296	26	desired	desire	VERB
ejpam-5888	296	27	matrix	matrix	NOUN
ejpam-5888	296	28	by	by	ADP
ejpam-5888	296	29	this	this	DET
ejpam-5888	296	30	attack	attack	NOUN
ejpam-5888	296	31	for	for	ADP
ejpam-5888	296	32	adequate	adequate	ADJ
ejpam-5888	296	33	size	size	NOUN
ejpam-5888	296	34	of	of	ADP
ejpam-5888	296	35	the	the	DET
ejpam-5888	296	36	matrix	matrix	NOUN
ejpam-5888	296	37	.	.	PUNCT
ejpam-5888	297	1	also	also	ADV
ejpam-5888	297	2	,	,	PUNCT
ejpam-5888	297	3	the	the	DET
ejpam-5888	297	4	brute	brute	ADJ
ejpam-5888	297	5	force	force	NOUN
ejpam-5888	297	6	complexity	complexity	NOUN
ejpam-5888	297	7	for	for	ADP
ejpam-5888	297	8	finite	finite	ADJ
ejpam-5888	297	9	r	r	NOUN
ejpam-5888	297	10	is	be	AUX
ejpam-5888	297	11	discussed	discuss	VERB
ejpam-5888	297	12	in	in	ADP
ejpam-5888	297	13	section	section	NOUN
ejpam-5888	297	14	3.3	3.3	NUM
ejpam-5888	297	15	.	.	PUNCT
ejpam-5888	298	1	thus	thus	ADV
ejpam-5888	298	2	this	this	DET
ejpam-5888	298	3	attack	attack	NOUN
ejpam-5888	298	4	is	be	AUX
ejpam-5888	298	5	not	not	PART
ejpam-5888	298	6	feasible	feasible	ADJ
ejpam-5888	298	7	.	.	PUNCT
ejpam-5888	299	1	6.2.3	6.2.3	NUM
ejpam-5888	299	2	.	.	PUNCT
ejpam-5888	299	3	kotov	kotov	ADJ
ejpam-5888	299	4	-	-	PUNCT
ejpam-5888	299	5	ushakov	ushakov	NOUN
ejpam-5888	299	6	attack	attack	NOUN
ejpam-5888	299	7	in	in	ADP
ejpam-5888	299	8	[	[	X
ejpam-5888	299	9	19	19	NUM
ejpam-5888	299	10	]	]	PUNCT
ejpam-5888	299	11	,	,	PUNCT
ejpam-5888	299	12	the	the	DET
ejpam-5888	299	13	authors	author	NOUN
ejpam-5888	299	14	expressed	express	VERB
ejpam-5888	299	15	that	that	SCONJ
ejpam-5888	299	16	tropical	tropical	ADJ
ejpam-5888	299	17	power	power	NOUN
ejpam-5888	299	18	of	of	ADP
ejpam-5888	299	19	matrices	matrix	NOUN
ejpam-5888	299	20	exhibit	exhibit	VERB
ejpam-5888	299	21	a	a	DET
ejpam-5888	299	22	specific	specific	ADJ
ejpam-5888	299	23	pattern	pattern	NOUN
ejpam-5888	299	24	.	.	PUNCT
ejpam-5888	300	1	this	this	DET
ejpam-5888	300	2	attack	attack	NOUN
ejpam-5888	300	3	is	be	AUX
ejpam-5888	300	4	not	not	PART
ejpam-5888	300	5	possible	possible	ADJ
ejpam-5888	300	6	,	,	PUNCT
ejpam-5888	300	7	since	since	SCONJ
ejpam-5888	300	8	in	in	ADP
ejpam-5888	300	9	both	both	CCONJ
ejpam-5888	300	10	the	the	DET
ejpam-5888	300	11	protocols	protocol	NOUN
ejpam-5888	300	12	powers	power	NOUN
ejpam-5888	300	13	of	of	ADP
ejpam-5888	300	14	unknown	unknown	ADJ
ejpam-5888	300	15	matrices	matrix	NOUN
ejpam-5888	300	16	di	di	NOUN
ejpam-5888	300	17	,	,	PUNCT
ejpam-5888	300	18	i	i	NOUN
ejpam-5888	300	19	=	=	NOUN
ejpam-5888	300	20	1	1	NUM
ejpam-5888	300	21	,	,	PUNCT
ejpam-5888	300	22	2	2	NUM
ejpam-5888	300	23	and	and	CCONJ
ejpam-5888	300	24	b	b	NOUN
ejpam-5888	300	25	,	,	PUNCT
ejpam-5888	300	26	bj	bj	NOUN
ejpam-5888	300	27	,	,	PUNCT
ejpam-5888	300	28	j	j	PROPN
ejpam-5888	300	29	=	=	SYM
ejpam-5888	300	30	1	1	NUM
ejpam-5888	300	31	,	,	PUNCT
ejpam-5888	300	32	2	2	NUM
ejpam-5888	300	33	are	be	AUX
ejpam-5888	300	34	used	use	VERB
ejpam-5888	300	35	to	to	PART
ejpam-5888	300	36	generate	generate	VERB
ejpam-5888	300	37	the	the	DET
ejpam-5888	300	38	keys	key	NOUN
ejpam-5888	300	39	zi	zi	PROPN
ejpam-5888	300	40	and	and	CCONJ
ejpam-5888	300	41	zij	zij	PROPN
ejpam-5888	300	42	,	,	PUNCT
ejpam-5888	300	43	i	i	PRON
ejpam-5888	300	44	=	=	NOUN
ejpam-5888	300	45	1	1	NUM
ejpam-5888	300	46	,	,	PUNCT
ejpam-5888	300	47	2	2	NUM
ejpam-5888	300	48	,	,	PUNCT
ejpam-5888	301	1	j	j	NOUN
ejpam-5888	301	2	=	=	SYM
ejpam-5888	301	3	1	1	NUM
ejpam-5888	301	4	,	,	PUNCT
ejpam-5888	301	5	2	2	NUM
ejpam-5888	301	6	.	.	X
ejpam-5888	302	1	6.2.4	6.2.4	NUM
ejpam-5888	302	2	.	.	PUNCT
ejpam-5888	303	1	rudy	rudy	NOUN
ejpam-5888	303	2	-	-	PUNCT
ejpam-5888	303	3	monico	monico	PROPN
ejpam-5888	303	4	attack	attack	NOUN
ejpam-5888	303	5	this	this	DET
ejpam-5888	303	6	attack	attack	NOUN
ejpam-5888	303	7	lies	lie	VERB
ejpam-5888	303	8	on	on	ADP
ejpam-5888	303	9	the	the	DET
ejpam-5888	303	10	strength	strength	NOUN
ejpam-5888	303	11	of	of	ADP
ejpam-5888	303	12	finding	find	VERB
ejpam-5888	303	13	the	the	DET
ejpam-5888	303	14	power	power	NOUN
ejpam-5888	303	15	of	of	ADP
ejpam-5888	303	16	a	a	DET
ejpam-5888	303	17	known	know	VERB
ejpam-5888	303	18	tropical	tropical	ADJ
ejpam-5888	303	19	matrix	matrix	NOUN
ejpam-5888	303	20	[	[	X
ejpam-5888	303	21	20	20	NUM
ejpam-5888	303	22	]	]	PUNCT
ejpam-5888	303	23	.	.	PUNCT
ejpam-5888	304	1	since	since	SCONJ
ejpam-5888	304	2	we	we	PRON
ejpam-5888	304	3	have	have	AUX
ejpam-5888	304	4	used	use	VERB
ejpam-5888	304	5	powers	power	NOUN
ejpam-5888	304	6	of	of	ADP
ejpam-5888	304	7	unknown	unknown	ADJ
ejpam-5888	304	8	matrices	matrix	NOUN
ejpam-5888	304	9	di	di	NOUN
ejpam-5888	304	10	,	,	PUNCT
ejpam-5888	304	11	i	i	NOUN
ejpam-5888	304	12	=	=	NOUN
ejpam-5888	304	13	1	1	NUM
ejpam-5888	304	14	,	,	PUNCT
ejpam-5888	304	15	2	2	NUM
ejpam-5888	304	16	and	and	CCONJ
ejpam-5888	304	17	b	b	NOUN
ejpam-5888	304	18	,	,	PUNCT
ejpam-5888	304	19	bj	bj	NOUN
ejpam-5888	304	20	,	,	PUNCT
ejpam-5888	304	21	j	j	PROPN
ejpam-5888	304	22	=	=	SYM
ejpam-5888	304	23	1	1	NUM
ejpam-5888	304	24	,	,	PUNCT
ejpam-5888	304	25	2	2	NUM
ejpam-5888	304	26	in	in	ADP
ejpam-5888	304	27	our	our	PRON
ejpam-5888	304	28	protocols	protocol	NOUN
ejpam-5888	304	29	,	,	PUNCT
ejpam-5888	304	30	this	this	DET
ejpam-5888	304	31	attack	attack	NOUN
ejpam-5888	304	32	is	be	AUX
ejpam-5888	304	33	not	not	PART
ejpam-5888	304	34	achievable	achievable	ADJ
ejpam-5888	304	35	.	.	PUNCT
ejpam-5888	305	1	6.3	6.3	NUM
ejpam-5888	305	2	.	.	PUNCT
ejpam-5888	306	1	complexity	complexity	NOUN
ejpam-5888	306	2	analysis	analysis	NOUN
ejpam-5888	306	3	we	we	PRON
ejpam-5888	306	4	bestow	bestow	VERB
ejpam-5888	306	5	the	the	DET
ejpam-5888	306	6	number	number	NOUN
ejpam-5888	306	7	of	of	ADP
ejpam-5888	306	8	bit	bit	NOUN
ejpam-5888	306	9	operations	operation	NOUN
ejpam-5888	306	10	required	require	VERB
ejpam-5888	306	11	for	for	ADP
ejpam-5888	306	12	the	the	DET
ejpam-5888	306	13	generation	generation	NOUN
ejpam-5888	306	14	of	of	ADP
ejpam-5888	306	15	the	the	DET
ejpam-5888	306	16	secret	secret	ADJ
ejpam-5888	306	17	keys	key	NOUN
ejpam-5888	306	18	:	:	PUNCT
ejpam-5888	306	19	for	for	ADP
ejpam-5888	306	20	the	the	DET
ejpam-5888	306	21	first	first	ADJ
ejpam-5888	306	22	protocol	protocol	NOUN
ejpam-5888	306	23	,	,	PUNCT
ejpam-5888	306	24	•	•	ADP
ejpam-5888	306	25	the	the	DET
ejpam-5888	306	26	number	number	NOUN
ejpam-5888	306	27	of	of	ADP
ejpam-5888	306	28	bit	bit	NOUN
ejpam-5888	306	29	operations	operation	NOUN
ejpam-5888	306	30	required	require	VERB
ejpam-5888	306	31	to	to	ADP
ejpam-5888	306	32	tropical	tropical	ADJ
ejpam-5888	306	33	multiply	multiply	VERB
ejpam-5888	306	34	two	two	NUM
ejpam-5888	306	35	n	n	NUM
ejpam-5888	306	36	×	×	NOUN
ejpam-5888	306	37	n	n	PRON
ejpam-5888	306	38	matrices	matrix	NOUN
ejpam-5888	306	39	is	be	AUX
ejpam-5888	306	40	o(n3	o(n3	NOUN
ejpam-5888	306	41	)	)	PUNCT
ejpam-5888	306	42	.	.	PUNCT
ejpam-5888	307	1	•	•	NOUN
ejpam-5888	307	2	the	the	DET
ejpam-5888	307	3	number	number	NOUN
ejpam-5888	307	4	of	of	ADP
ejpam-5888	307	5	bit	bit	NOUN
ejpam-5888	307	6	operations	operation	NOUN
ejpam-5888	307	7	required	require	VERB
ejpam-5888	307	8	to	to	ADP
ejpam-5888	307	9	tropical	tropical	ADJ
ejpam-5888	307	10	multiply	multiply	VERB
ejpam-5888	307	11	a	a	DET
ejpam-5888	307	12	diagonal	diagonal	ADJ
ejpam-5888	307	13	matrix	matrix	NOUN
ejpam-5888	307	14	and	and	CCONJ
ejpam-5888	307	15	usual	usual	ADJ
ejpam-5888	307	16	non	non	ADJ
ejpam-5888	307	17	-	-	ADJ
ejpam-5888	307	18	diagonal	diagonal	ADJ
ejpam-5888	307	19	matrix	matrix	NOUN
ejpam-5888	307	20	is	be	AUX
ejpam-5888	307	21	o(n2	o(n2	ADJ
ejpam-5888	307	22	)	)	PUNCT
ejpam-5888	307	23	.	.	PUNCT
ejpam-5888	308	1	•	•	ADP
ejpam-5888	308	2	to	to	PART
ejpam-5888	308	3	find	find	VERB
ejpam-5888	308	4	xi	xi	ADP
ejpam-5888	308	5	,	,	PUNCT
ejpam-5888	308	6	i	i	PRON
ejpam-5888	308	7	=	=	NOUN
ejpam-5888	308	8	1	1	NUM
ejpam-5888	308	9	,	,	PUNCT
ejpam-5888	308	10	2	2	NUM
ejpam-5888	308	11	the	the	DET
ejpam-5888	308	12	number	number	NOUN
ejpam-5888	308	13	of	of	ADP
ejpam-5888	308	14	bit	bit	NOUN
ejpam-5888	308	15	operations	operation	NOUN
ejpam-5888	308	16	required	require	VERB
ejpam-5888	308	17	is	be	AUX
ejpam-5888	308	18	n2	n2	ADJ
ejpam-5888	308	19	+	+	CCONJ
ejpam-5888	308	20	n2	n2	ADJ
ejpam-5888	308	21	,	,	PUNCT
ejpam-5888	308	22	which	which	PRON
ejpam-5888	308	23	is	be	AUX
ejpam-5888	308	24	proportional	proportional	ADJ
ejpam-5888	308	25	to	to	ADP
ejpam-5888	308	26	o(n2	o(n2	NUM
ejpam-5888	308	27	)	)	PUNCT
ejpam-5888	308	28	.	.	PUNCT
ejpam-5888	309	1	•	•	ADP
ejpam-5888	309	2	to	to	PART
ejpam-5888	309	3	find	find	VERB
ejpam-5888	309	4	y	y	PRON
ejpam-5888	309	5	,	,	PUNCT
ejpam-5888	309	6	the	the	DET
ejpam-5888	309	7	number	number	NOUN
ejpam-5888	309	8	of	of	ADP
ejpam-5888	309	9	bit	bit	NOUN
ejpam-5888	309	10	operations	operation	NOUN
ejpam-5888	309	11	required	require	VERB
ejpam-5888	309	12	is	be	AUX
ejpam-5888	309	13	n2	n2	ADJ
ejpam-5888	309	14	+	+	CCONJ
ejpam-5888	309	15	n2	n2	ADJ
ejpam-5888	309	16	,	,	PUNCT
ejpam-5888	309	17	which	which	PRON
ejpam-5888	309	18	is	be	AUX
ejpam-5888	309	19	proportional	proportional	ADJ
ejpam-5888	309	20	to	to	ADP
ejpam-5888	309	21	o(n2	o(n2	NUM
ejpam-5888	309	22	)	)	PUNCT
ejpam-5888	309	23	.	.	PUNCT
ejpam-5888	310	1	hence	hence	ADV
ejpam-5888	310	2	to	to	PART
ejpam-5888	310	3	find	find	VERB
ejpam-5888	310	4	the	the	DET
ejpam-5888	310	5	secret	secret	ADJ
ejpam-5888	310	6	keys	key	NOUN
ejpam-5888	310	7	zi	zi	VERB
ejpam-5888	310	8	,	,	PUNCT
ejpam-5888	310	9	i	i	PRON
ejpam-5888	310	10	=	=	NOUN
ejpam-5888	310	11	1	1	NUM
ejpam-5888	310	12	,	,	PUNCT
ejpam-5888	310	13	2	2	NUM
ejpam-5888	310	14	,	,	PUNCT
ejpam-5888	310	15	the	the	DET
ejpam-5888	310	16	number	number	NOUN
ejpam-5888	310	17	of	of	ADP
ejpam-5888	310	18	bit	bit	NOUN
ejpam-5888	310	19	operations	operation	NOUN
ejpam-5888	310	20	required	require	VERB
ejpam-5888	310	21	is	be	AUX
ejpam-5888	310	22	o(n2	o(n2	ADJ
ejpam-5888	310	23	)	)	PUNCT
ejpam-5888	310	24	.	.	PUNCT
ejpam-5888	311	1	similarly	similarly	ADV
ejpam-5888	311	2	,	,	PUNCT
ejpam-5888	311	3	for	for	ADP
ejpam-5888	311	4	the	the	DET
ejpam-5888	311	5	protocol	protocol	PROPN
ejpam-5888	311	6	ii	ii	PROPN
ejpam-5888	311	7	,	,	PUNCT
ejpam-5888	311	8	the	the	DET
ejpam-5888	311	9	number	number	NOUN
ejpam-5888	311	10	of	of	ADP
ejpam-5888	311	11	bit	bit	NOUN
ejpam-5888	311	12	operations	operation	NOUN
ejpam-5888	311	13	required	require	VERB
ejpam-5888	311	14	to	to	PART
ejpam-5888	311	15	find	find	VERB
ejpam-5888	311	16	the	the	DET
ejpam-5888	311	17	secret	secret	ADJ
ejpam-5888	311	18	keys	key	NOUN
ejpam-5888	311	19	zij	zij	PROPN
ejpam-5888	311	20	,	,	PUNCT
ejpam-5888	311	21	i	i	PRON
ejpam-5888	311	22	=	=	NOUN
ejpam-5888	311	23	1	1	NUM
ejpam-5888	311	24	,	,	PUNCT
ejpam-5888	311	25	2	2	NUM
ejpam-5888	311	26	,	,	PUNCT
ejpam-5888	311	27	j	j	NOUN
ejpam-5888	311	28	=	=	SYM
ejpam-5888	311	29	1	1	NUM
ejpam-5888	311	30	,	,	PUNCT
ejpam-5888	311	31	2	2	NUM
ejpam-5888	311	32	is	be	AUX
ejpam-5888	311	33	o(n2	o(n2	ADJ
ejpam-5888	311	34	)	)	PUNCT
ejpam-5888	311	35	.	.	PUNCT
ejpam-5888	312	1	kashifa	kashifa	PROPN
ejpam-5888	312	2	begum	begum	VERB
ejpam-5888	312	3	a.	a.	NOUN
ejpam-5888	312	4	et	et	PROPN
ejpam-5888	312	5	.	.	PUNCT
ejpam-5888	313	1	al	al	PROPN
ejpam-5888	313	2	/	/	PUNCT
ejpam-5888	313	3	eur	eur	PROPN
ejpam-5888	313	4	.	.	PUNCT
ejpam-5888	314	1	j.	j.	PROPN
ejpam-5888	314	2	pure	pure	PROPN
ejpam-5888	314	3	appl	appl	PROPN
ejpam-5888	314	4	.	.	PROPN
ejpam-5888	314	5	math	math	PROPN
ejpam-5888	314	6	,	,	PUNCT
ejpam-5888	314	7	18	18	NUM
ejpam-5888	314	8	(	(	PUNCT
ejpam-5888	314	9	3	3	NUM
ejpam-5888	314	10	)	)	PUNCT
ejpam-5888	314	11	(	(	PUNCT
ejpam-5888	314	12	2025	2025	NUM
ejpam-5888	314	13	)	)	PUNCT
ejpam-5888	314	14	,	,	PUNCT
ejpam-5888	314	15	5888	5888	NUM
ejpam-5888	314	16	14	14	NUM
ejpam-5888	314	17	of	of	ADP
ejpam-5888	314	18	16	16	NUM
ejpam-5888	314	19	table	table	NOUN
ejpam-5888	314	20	3	3	NUM
ejpam-5888	314	21	:	:	PUNCT
ejpam-5888	314	22	comparative	comparative	ADJ
ejpam-5888	314	23	analysis	analysis	NOUN
ejpam-5888	315	1	i	i	PRON
ejpam-5888	315	2	aspect	aspect	VERB
ejpam-5888	315	3	braid	braid	NOUN
ejpam-5888	315	4	group	group	NOUN
ejpam-5888	315	5	,	,	PUNCT
ejpam-5888	315	6	bn	bn	ADP
ejpam-5888	315	7	tropical	tropical	ADJ
ejpam-5888	315	8	matrix	matrix	NOUN
ejpam-5888	315	9	algebra	algebra	NOUN
ejpam-5888	315	10	algebraic	algebraic	ADJ
ejpam-5888	315	11	structure	structure	NOUN
ejpam-5888	315	12	group	group	NOUN
ejpam-5888	315	13	semiring	semire	VERB
ejpam-5888	315	14	commutativity	commutativity	NOUN
ejpam-5888	315	15	non	non	ADJ
ejpam-5888	315	16	-	-	ADJ
ejpam-5888	315	17	commutative	commutative	ADJ
ejpam-5888	315	18	non	non	ADJ
ejpam-5888	315	19	-	-	ADJ
ejpam-5888	315	20	commutative	commutative	ADJ
ejpam-5888	315	21	generators	generator	NOUN
ejpam-5888	315	22	σ1	σ1	PROPN
ejpam-5888	315	23	,	,	PUNCT
ejpam-5888	315	24	σ2	σ2	PROPN
ejpam-5888	315	25	,	,	PUNCT
ejpam-5888	315	26	.	.	PUNCT
ejpam-5888	315	27	.	.	PUNCT
ejpam-5888	316	1	.	.	PUNCT
ejpam-5888	317	1	,	,	PUNCT
ejpam-5888	317	2	σn−1	σn−1	PROPN
ejpam-5888	317	3	mn(rmin	mn(rmin	PROPN
ejpam-5888	317	4	)	)	PUNCT
ejpam-5888	317	5	is	be	AUX
ejpam-5888	317	6	not	not	PART
ejpam-5888	317	7	finitely	finitely	ADV
ejpam-5888	317	8	generated	generate	VERB
ejpam-5888	317	9	operations	operation	NOUN
ejpam-5888	317	10	composition	composition	NOUN
ejpam-5888	317	11	of	of	ADP
ejpam-5888	317	12	braids	braid	NOUN
ejpam-5888	317	13	tropical	tropical	ADJ
ejpam-5888	317	14	addition	addition	NOUN
ejpam-5888	317	15	(	(	PUNCT
ejpam-5888	317	16	min	min	NOUN
ejpam-5888	317	17	/	/	SYM
ejpam-5888	317	18	max	max	PROPN
ejpam-5888	317	19	)	)	PUNCT
ejpam-5888	317	20	,	,	PUNCT
ejpam-5888	317	21	tropical	tropical	ADJ
ejpam-5888	317	22	multiplication	multiplication	NOUN
ejpam-5888	317	23	(	(	PUNCT
ejpam-5888	317	24	addition	addition	NOUN
ejpam-5888	317	25	)	)	PUNCT
ejpam-5888	317	26	accessibility	accessibility	NOUN
ejpam-5888	317	27	it	it	PRON
ejpam-5888	317	28	is	be	AUX
ejpam-5888	317	29	n’t	not	PART
ejpam-5888	317	30	widely	widely	ADV
ejpam-5888	317	31	accessible	accessible	ADJ
ejpam-5888	317	32	since	since	SCONJ
ejpam-5888	317	33	braid	braid	ADJ
ejpam-5888	317	34	groups	group	NOUN
ejpam-5888	317	35	require	require	VERB
ejpam-5888	317	36	deeper	deep	ADJ
ejpam-5888	317	37	understanding	understanding	NOUN
ejpam-5888	317	38	of	of	ADP
ejpam-5888	317	39	group	group	NOUN
ejpam-5888	317	40	theory	theory	NOUN
ejpam-5888	317	41	it	it	PRON
ejpam-5888	317	42	is	be	AUX
ejpam-5888	317	43	widely	widely	ADV
ejpam-5888	317	44	accessible	accessible	ADJ
ejpam-5888	317	45	since	since	SCONJ
ejpam-5888	317	46	tropical	tropical	ADJ
ejpam-5888	317	47	algebra	algebra	NOUN
ejpam-5888	317	48	relies	rely	VERB
ejpam-5888	317	49	on	on	ADP
ejpam-5888	317	50	basic	basic	ADJ
ejpam-5888	317	51	arithmetic	arithmetic	ADJ
ejpam-5888	317	52	.	.	PUNCT
ejpam-5888	317	53	table	table	NOUN
ejpam-5888	318	1	4	4	NUM
ejpam-5888	318	2	:	:	PUNCT
ejpam-5888	318	3	comparative	comparative	ADJ
ejpam-5888	318	4	analysis	analysis	NOUN
ejpam-5888	318	5	ii	ii	PROPN
ejpam-5888	318	6	aspect	aspect	PROPN
ejpam-5888	318	7	chen	chen	PROPN
ejpam-5888	318	8	et	et	PROPN
ejpam-5888	318	9	al	al	PROPN
ejpam-5888	318	10	.	.	PUNCT
ejpam-5888	319	1	[	[	X
ejpam-5888	319	2	10	10	NUM
ejpam-5888	319	3	]	]	X
ejpam-5888	319	4	our	our	PRON
ejpam-5888	319	5	protocol	protocol	NOUN
ejpam-5888	319	6	algebraic	algebraic	ADJ
ejpam-5888	319	7	structure	structure	NOUN
ejpam-5888	319	8	braid	braid	PROPN
ejpam-5888	319	9	group	group	NOUN
ejpam-5888	319	10	tropical	tropical	ADJ
ejpam-5888	319	11	matrix	matrix	NOUN
ejpam-5888	319	12	algebra	algebra	NOUN
ejpam-5888	319	13	base	base	NOUN
ejpam-5888	319	14	problem	problem	NOUN
ejpam-5888	319	15	tcsp	tcsp	NOUN
ejpam-5888	319	16	tcsp	tcsp	VERB
ejpam-5888	319	17	time	time	NOUN
ejpam-5888	319	18	complexity	complexity	NOUN
ejpam-5888	319	19	for	for	ADP
ejpam-5888	319	20	braid	braid	PROPN
ejpam-5888	319	21	concatenation	concatenation	NOUN
ejpam-5888	319	22	,	,	PUNCT
ejpam-5888	319	23	o(n	o(n	PROPN
ejpam-5888	319	24	)	)	PUNCT
ejpam-5888	319	25	,	,	PUNCT
ejpam-5888	319	26	and	and	CCONJ
ejpam-5888	319	27	for	for	ADP
ejpam-5888	319	28	braid	braid	ADJ
ejpam-5888	319	29	simplification	simplification	NOUN
ejpam-5888	319	30	,	,	PUNCT
ejpam-5888	319	31	o(n2	o(n2	ADV
ejpam-5888	319	32	)	)	PUNCT
ejpam-5888	319	33	o(n2	o(n2	ADV
ejpam-5888	319	34	)	)	PUNCT
ejpam-5888	319	35	6.4	6.4	NUM
ejpam-5888	319	36	.	.	PUNCT
ejpam-5888	320	1	comparative	comparative	ADJ
ejpam-5888	320	2	analysis	analysis	NOUN
ejpam-5888	320	3	in	in	ADP
ejpam-5888	320	4	this	this	DET
ejpam-5888	320	5	section	section	NOUN
ejpam-5888	320	6	,	,	PUNCT
ejpam-5888	320	7	we	we	PRON
ejpam-5888	320	8	have	have	AUX
ejpam-5888	320	9	compared	compare	VERB
ejpam-5888	320	10	our	our	PRON
ejpam-5888	320	11	chosen	choose	VERB
ejpam-5888	320	12	platform	platform	NOUN
ejpam-5888	320	13	,	,	PUNCT
ejpam-5888	320	14	tropical	tropical	ADJ
ejpam-5888	320	15	algebra	algebra	NOUN
ejpam-5888	320	16	,	,	PUNCT
ejpam-5888	320	17	with	with	ADP
ejpam-5888	320	18	another	another	DET
ejpam-5888	320	19	algebraic	algebraic	ADJ
ejpam-5888	320	20	structure	structure	NOUN
ejpam-5888	320	21	,	,	PUNCT
ejpam-5888	320	22	i.e.	i.e.	X
ejpam-5888	320	23	,	,	PUNCT
ejpam-5888	320	24	a	a	DET
ejpam-5888	320	25	braid	braid	NOUN
ejpam-5888	320	26	group	group	NOUN
ejpam-5888	320	27	.	.	PUNCT
ejpam-5888	321	1	while	while	SCONJ
ejpam-5888	321	2	the	the	DET
ejpam-5888	321	3	braid	braid	PROPN
ejpam-5888	321	4	group	group	NOUN
ejpam-5888	321	5	holds	hold	VERB
ejpam-5888	321	6	significant	significant	ADJ
ejpam-5888	321	7	theoretical	theoretical	ADJ
ejpam-5888	321	8	value	value	NOUN
ejpam-5888	321	9	and	and	CCONJ
ejpam-5888	321	10	serves	serve	VERB
ejpam-5888	321	11	specialized	specialized	ADJ
ejpam-5888	321	12	applications	application	NOUN
ejpam-5888	321	13	,	,	PUNCT
ejpam-5888	321	14	it	it	PRON
ejpam-5888	321	15	remains	remain	VERB
ejpam-5888	321	16	conceptually	conceptually	ADV
ejpam-5888	321	17	and	and	CCONJ
ejpam-5888	321	18	computationally	computationally	ADV
ejpam-5888	321	19	complex	complex	ADJ
ejpam-5888	321	20	,	,	PUNCT
ejpam-5888	321	21	with	with	ADP
ejpam-5888	321	22	relatively	relatively	ADV
ejpam-5888	321	23	limited	limited	ADJ
ejpam-5888	321	24	practical	practical	ADJ
ejpam-5888	321	25	accessibility	accessibility	NOUN
ejpam-5888	321	26	.	.	PUNCT
ejpam-5888	322	1	tropical	tropical	ADJ
ejpam-5888	322	2	algebra	algebra	PROPN
ejpam-5888	322	3	,	,	PUNCT
ejpam-5888	322	4	on	on	ADP
ejpam-5888	322	5	the	the	DET
ejpam-5888	322	6	other	other	ADJ
ejpam-5888	322	7	hand	hand	NOUN
ejpam-5888	322	8	,	,	PUNCT
ejpam-5888	322	9	are	be	AUX
ejpam-5888	322	10	quite	quite	ADV
ejpam-5888	322	11	computationally	computationally	ADV
ejpam-5888	322	12	and	and	CCONJ
ejpam-5888	322	13	conceptually	conceptually	ADV
ejpam-5888	322	14	approachable	approachable	ADJ
ejpam-5888	322	15	,	,	PUNCT
ejpam-5888	322	16	making	make	VERB
ejpam-5888	322	17	them	they	PRON
ejpam-5888	322	18	easily	easily	ADV
ejpam-5888	322	19	implementable	implementable	ADJ
ejpam-5888	322	20	and	and	CCONJ
ejpam-5888	322	21	widely	widely	ADV
ejpam-5888	322	22	usable	usable	ADJ
ejpam-5888	322	23	in	in	ADP
ejpam-5888	322	24	everyday	everyday	ADJ
ejpam-5888	322	25	applications	application	NOUN
ejpam-5888	322	26	.	.	PUNCT
ejpam-5888	323	1	therefore	therefore	ADV
ejpam-5888	323	2	,	,	PUNCT
ejpam-5888	323	3	in	in	ADP
ejpam-5888	323	4	terms	term	NOUN
ejpam-5888	323	5	of	of	ADP
ejpam-5888	323	6	practical	practical	ADJ
ejpam-5888	323	7	utility	utility	NOUN
ejpam-5888	323	8	and	and	CCONJ
ejpam-5888	323	9	accessibility	accessibility	NOUN
ejpam-5888	323	10	,	,	PUNCT
ejpam-5888	323	11	tropical	tropical	ADJ
ejpam-5888	323	12	algebra	algebra	NOUN
ejpam-5888	323	13	offer	offer	VERB
ejpam-5888	323	14	a	a	DET
ejpam-5888	323	15	clear	clear	ADJ
ejpam-5888	323	16	advantage	advantage	NOUN
ejpam-5888	323	17	,	,	PUNCT
ejpam-5888	323	18	whereas	whereas	SCONJ
ejpam-5888	323	19	braid	braid	ADJ
ejpam-5888	323	20	groups	group	NOUN
ejpam-5888	323	21	are	be	AUX
ejpam-5888	323	22	better	well	ADV
ejpam-5888	323	23	suited	suited	ADJ
ejpam-5888	323	24	to	to	ADP
ejpam-5888	323	25	specialized	specialize	VERB
ejpam-5888	323	26	,	,	PUNCT
ejpam-5888	323	27	niche	niche	NOUN
ejpam-5888	323	28	domains	domain	NOUN
ejpam-5888	323	29	.	.	PUNCT
ejpam-5888	324	1	kashifa	kashifa	PROPN
ejpam-5888	324	2	begum	begum	VERB
ejpam-5888	324	3	a.	a.	NOUN
ejpam-5888	324	4	et	et	PROPN
ejpam-5888	324	5	.	.	PUNCT
ejpam-5888	325	1	al	al	PROPN
ejpam-5888	325	2	/	/	PUNCT
ejpam-5888	325	3	eur	eur	PROPN
ejpam-5888	325	4	.	.	PUNCT
ejpam-5888	326	1	j.	j.	PROPN
ejpam-5888	326	2	pure	pure	PROPN
ejpam-5888	326	3	appl	appl	PROPN
ejpam-5888	326	4	.	.	PROPN
ejpam-5888	326	5	math	math	PROPN
ejpam-5888	326	6	,	,	PUNCT
ejpam-5888	326	7	18	18	NUM
ejpam-5888	326	8	(	(	PUNCT
ejpam-5888	326	9	3	3	NUM
ejpam-5888	326	10	)	)	PUNCT
ejpam-5888	326	11	(	(	PUNCT
ejpam-5888	326	12	2025	2025	NUM
ejpam-5888	326	13	)	)	PUNCT
ejpam-5888	326	14	,	,	PUNCT
ejpam-5888	326	15	5888	5888	NUM
ejpam-5888	326	16	15	15	NUM
ejpam-5888	326	17	of	of	ADP
ejpam-5888	326	18	16	16	NUM
ejpam-5888	326	19	7	7	NUM
ejpam-5888	326	20	.	.	PUNCT
ejpam-5888	326	21	conclusion	conclusion	NOUN
ejpam-5888	326	22	the	the	DET
ejpam-5888	326	23	permanent	permanent	ADJ
ejpam-5888	326	24	increase	increase	NOUN
ejpam-5888	326	25	in	in	ADP
ejpam-5888	326	26	computational	computational	ADJ
ejpam-5888	326	27	power	power	NOUN
ejpam-5888	326	28	requires	require	VERB
ejpam-5888	326	29	us	we	PRON
ejpam-5888	326	30	to	to	PART
ejpam-5888	326	31	search	search	VERB
ejpam-5888	326	32	for	for	ADP
ejpam-5888	326	33	new	new	ADJ
ejpam-5888	326	34	platforms	platform	NOUN
ejpam-5888	326	35	for	for	ADP
ejpam-5888	326	36	existing	exist	VERB
ejpam-5888	326	37	protocols	protocol	NOUN
ejpam-5888	326	38	.	.	PUNCT
ejpam-5888	327	1	tropical	tropical	ADJ
ejpam-5888	327	2	algebra	algebra	PROPN
ejpam-5888	327	3	seems	seem	VERB
ejpam-5888	327	4	to	to	PART
ejpam-5888	327	5	be	be	AUX
ejpam-5888	327	6	an	an	DET
ejpam-5888	327	7	ideal	ideal	ADJ
ejpam-5888	327	8	candidate	candidate	NOUN
ejpam-5888	327	9	.	.	PUNCT
ejpam-5888	328	1	in	in	ADP
ejpam-5888	328	2	this	this	DET
ejpam-5888	328	3	article	article	NOUN
ejpam-5888	328	4	,	,	PUNCT
ejpam-5888	328	5	we	we	PRON
ejpam-5888	328	6	have	have	AUX
ejpam-5888	328	7	delved	delve	VERB
ejpam-5888	328	8	into	into	ADP
ejpam-5888	328	9	the	the	DET
ejpam-5888	328	10	intriguing	intriguing	ADJ
ejpam-5888	328	11	realm	realm	NOUN
ejpam-5888	328	12	of	of	ADP
ejpam-5888	328	13	the	the	DET
ejpam-5888	328	14	twin	twin	ADJ
ejpam-5888	328	15	conjugacy	conjugacy	ADJ
ejpam-5888	328	16	search	search	NOUN
ejpam-5888	328	17	problem	problem	NOUN
ejpam-5888	328	18	by	by	ADP
ejpam-5888	328	19	employing	employ	VERB
ejpam-5888	328	20	the	the	DET
ejpam-5888	328	21	innovative	innovative	ADJ
ejpam-5888	328	22	framework	framework	NOUN
ejpam-5888	328	23	of	of	ADP
ejpam-5888	328	24	tropical	tropical	ADJ
ejpam-5888	328	25	algebra	algebra	NOUN
ejpam-5888	328	26	.	.	PUNCT
ejpam-5888	329	1	the	the	DET
ejpam-5888	329	2	security	security	NOUN
ejpam-5888	329	3	and	and	CCONJ
ejpam-5888	329	4	complexity	complexity	NOUN
ejpam-5888	329	5	of	of	ADP
ejpam-5888	329	6	the	the	DET
ejpam-5888	329	7	tcsp	tcsp	NOUN
ejpam-5888	329	8	over	over	ADP
ejpam-5888	329	9	tropical	tropical	ADJ
ejpam-5888	329	10	algebra	algebra	NOUN
ejpam-5888	329	11	have	have	AUX
ejpam-5888	329	12	been	be	AUX
ejpam-5888	329	13	explored	explore	VERB
ejpam-5888	329	14	.	.	PUNCT
ejpam-5888	330	1	we	we	PRON
ejpam-5888	330	2	showed	show	VERB
ejpam-5888	330	3	that	that	SCONJ
ejpam-5888	330	4	our	our	PRON
ejpam-5888	330	5	our	our	PRON
ejpam-5888	330	6	key	key	ADJ
ejpam-5888	330	7	exchange	exchange	NOUN
ejpam-5888	330	8	protocols	protocol	NOUN
ejpam-5888	330	9	based	base	VERB
ejpam-5888	330	10	on	on	ADP
ejpam-5888	330	11	the	the	DET
ejpam-5888	330	12	tcsp	tcsp	NOUN
ejpam-5888	330	13	over	over	ADP
ejpam-5888	330	14	tropical	tropical	ADJ
ejpam-5888	330	15	algebra	algebra	NOUN
ejpam-5888	330	16	are	be	AUX
ejpam-5888	330	17	secure	secure	ADJ
ejpam-5888	330	18	against	against	ADP
ejpam-5888	330	19	linear	linear	PROPN
ejpam-5888	330	20	algebra	algebra	NOUN
ejpam-5888	330	21	,	,	PUNCT
ejpam-5888	330	22	kotov	kotov	NOUN
ejpam-5888	330	23	-	-	PUNCT
ejpam-5888	330	24	ushakov	ushakov	NOUN
ejpam-5888	330	25	,	,	PUNCT
ejpam-5888	330	26	rudy	rudy	NOUN
ejpam-5888	330	27	-	-	PUNCT
ejpam-5888	330	28	monico	monico	PROPN
ejpam-5888	330	29	and	and	CCONJ
ejpam-5888	330	30	brute	brute	ADJ
ejpam-5888	330	31	force	force	NOUN
ejpam-5888	330	32	attack	attack	NOUN
ejpam-5888	330	33	.	.	PUNCT
ejpam-5888	331	1	the	the	DET
ejpam-5888	331	2	complexity	complexity	NOUN
ejpam-5888	331	3	of	of	ADP
ejpam-5888	331	4	the	the	DET
ejpam-5888	331	5	protocols	protocol	NOUN
ejpam-5888	331	6	along	along	ADP
ejpam-5888	331	7	with	with	ADP
ejpam-5888	331	8	a	a	DET
ejpam-5888	331	9	comparative	comparative	ADJ
ejpam-5888	331	10	analysis	analysis	NOUN
ejpam-5888	331	11	have	have	AUX
ejpam-5888	331	12	also	also	ADV
ejpam-5888	331	13	been	be	AUX
ejpam-5888	331	14	described	describe	VERB
ejpam-5888	331	15	.	.	PUNCT
ejpam-5888	332	1	acknowledgements	acknowledgement	NOUN
ejpam-5888	332	2	we	we	PRON
ejpam-5888	332	3	sincerely	sincerely	ADV
ejpam-5888	332	4	appreciate	appreciate	VERB
ejpam-5888	332	5	the	the	DET
ejpam-5888	332	6	editors	editor	NOUN
ejpam-5888	332	7	and	and	CCONJ
ejpam-5888	332	8	anonymous	anonymous	ADJ
ejpam-5888	332	9	reviewers	reviewer	NOUN
ejpam-5888	332	10	for	for	ADP
ejpam-5888	332	11	their	their	PRON
ejpam-5888	332	12	insightful	insightful	ADJ
ejpam-5888	332	13	suggestions	suggestion	NOUN
ejpam-5888	332	14	,	,	PUNCT
ejpam-5888	332	15	which	which	PRON
ejpam-5888	332	16	greatly	greatly	ADV
ejpam-5888	332	17	enhanced	enhance	VERB
ejpam-5888	332	18	the	the	DET
ejpam-5888	332	19	quality	quality	NOUN
ejpam-5888	332	20	of	of	ADP
ejpam-5888	332	21	this	this	DET
ejpam-5888	332	22	paper	paper	NOUN
ejpam-5888	332	23	.	.	PUNCT
ejpam-5888	333	1	funding	fund	VERB
ejpam-5888	333	2	this	this	DET
ejpam-5888	333	3	research	research	NOUN
ejpam-5888	333	4	supported	support	VERB
ejpam-5888	333	5	by	by	ADP
ejpam-5888	333	6	basic	basic	ADJ
ejpam-5888	333	7	science	science	NOUN
ejpam-5888	333	8	research	research	NOUN
ejpam-5888	333	9	program	program	NOUN
ejpam-5888	333	10	through	through	ADP
ejpam-5888	333	11	the	the	DET
ejpam-5888	333	12	national	national	PROPN
ejpam-5888	333	13	research	research	PROPN
ejpam-5888	333	14	foundation	foundation	PROPN
ejpam-5888	333	15	of	of	ADP
ejpam-5888	333	16	korea	korea	PROPN
ejpam-5888	333	17	(	(	PUNCT
ejpam-5888	333	18	nrf	nrf	NOUN
ejpam-5888	333	19	)	)	PUNCT
ejpam-5888	333	20	funded	fund	VERB
ejpam-5888	333	21	by	by	ADP
ejpam-5888	333	22	the	the	DET
ejpam-5888	333	23	ministry	ministry	PROPN
ejpam-5888	333	24	of	of	ADP
ejpam-5888	333	25	education	education	PROPN
ejpam-5888	333	26	(	(	PUNCT
ejpam-5888	333	27	nrfrs-202300237287	nrfrs-202300237287	ADJ
ejpam-5888	333	28	,	,	PUNCT
ejpam-5888	333	29	nrf-2021s1a5a8062526	nrf-2021s1a5a8062526	PROPN
ejpam-5888	333	30	)	)	PUNCT
ejpam-5888	333	31	and	and	CCONJ
ejpam-5888	333	32	local	local	ADJ
ejpam-5888	333	33	government	government	NOUN
ejpam-5888	333	34	-	-	PUNCT
ejpam-5888	333	35	university	university	NOUN
ejpam-5888	333	36	cooperation	cooperation	NOUN
ejpam-5888	333	37	-	-	PUNCT
ejpam-5888	333	38	based	base	VERB
ejpam-5888	333	39	regional	regional	ADJ
ejpam-5888	333	40	innovation	innovation	NOUN
ejpam-5888	333	41	projects	project	NOUN
ejpam-5888	333	42	(	(	PUNCT
ejpam-5888	333	43	2021ris-003	2021ris-003	NOUN
ejpam-5888	333	44	)	)	PUNCT
ejpam-5888	333	45	.	.	PUNCT
ejpam-5888	334	1	declaration	declaration	NOUN
ejpam-5888	334	2	of	of	ADP
ejpam-5888	334	3	competing	compete	VERB
ejpam-5888	334	4	interest	interest	NOUN
ejpam-5888	334	5	:	:	PUNCT
ejpam-5888	334	6	the	the	DET
ejpam-5888	334	7	author	author	NOUN
ejpam-5888	334	8	confirms	confirm	VERB
ejpam-5888	334	9	the	the	DET
ejpam-5888	334	10	absence	absence	NOUN
ejpam-5888	334	11	of	of	ADP
ejpam-5888	334	12	any	any	DET
ejpam-5888	334	13	known	know	VERB
ejpam-5888	334	14	financial	financial	ADJ
ejpam-5888	334	15	conflicts	conflict	NOUN
ejpam-5888	334	16	of	of	ADP
ejpam-5888	334	17	interest	interest	NOUN
ejpam-5888	334	18	or	or	CCONJ
ejpam-5888	334	19	personal	personal	ADJ
ejpam-5888	334	20	relationships	relationship	NOUN
ejpam-5888	334	21	that	that	PRON
ejpam-5888	334	22	might	might	AUX
ejpam-5888	334	23	have	have	AUX
ejpam-5888	334	24	influenced	influence	VERB
ejpam-5888	334	25	the	the	DET
ejpam-5888	334	26	work	work	NOUN
ejpam-5888	334	27	presented	present	VERB
ejpam-5888	334	28	in	in	ADP
ejpam-5888	334	29	this	this	DET
ejpam-5888	334	30	paper	paper	NOUN
ejpam-5888	334	31	.	.	PUNCT
ejpam-5888	335	1	author	author	NOUN
ejpam-5888	335	2	’s	’s	PART
ejpam-5888	335	3	contribution	contribution	NOUN
ejpam-5888	335	4	:	:	PUNCT
ejpam-5888	335	5	all	all	DET
ejpam-5888	335	6	authors	author	NOUN
ejpam-5888	335	7	made	make	VERB
ejpam-5888	335	8	equal	equal	ADJ
ejpam-5888	335	9	contributions	contribution	NOUN
ejpam-5888	335	10	to	to	ADP
ejpam-5888	335	11	the	the	DET
ejpam-5888	335	12	manuscript	manuscript	NOUN
ejpam-5888	335	13	,	,	PUNCT
ejpam-5888	335	14	participated	participate	VERB
ejpam-5888	335	15	in	in	ADP
ejpam-5888	335	16	its	its	PRON
ejpam-5888	335	17	drafting	drafting	NOUN
ejpam-5888	335	18	and	and	CCONJ
ejpam-5888	335	19	revision	revision	NOUN
ejpam-5888	335	20	,	,	PUNCT
ejpam-5888	335	21	and	and	CCONJ
ejpam-5888	335	22	approved	approve	VERB
ejpam-5888	335	23	the	the	DET
ejpam-5888	335	24	final	final	ADJ
ejpam-5888	335	25	version	version	NOUN
ejpam-5888	335	26	.	.	PUNCT
ejpam-5888	336	1	references	reference	NOUN
ejpam-5888	336	2	[	[	X
ejpam-5888	336	3	1	1	NUM
ejpam-5888	336	4	]	]	X
ejpam-5888	336	5	w	w	PROPN
ejpam-5888	336	6	diffie	diffie	PROPN
ejpam-5888	336	7	and	and	CCONJ
ejpam-5888	336	8	m	m	PROPN
ejpam-5888	336	9	hellman	hellman	NOUN
ejpam-5888	336	10	.	.	PUNCT
ejpam-5888	337	1	new	new	ADJ
ejpam-5888	337	2	directions	direction	NOUN
ejpam-5888	337	3	in	in	ADP
ejpam-5888	337	4	cryptography	cryptography	NOUN
ejpam-5888	337	5	.	.	PUNCT
ejpam-5888	338	1	ieee	ieee	NOUN
ejpam-5888	338	2	transactions	transaction	NOUN
ejpam-5888	338	3	on	on	ADP
ejpam-5888	338	4	information	information	NOUN
ejpam-5888	338	5	theory	theory	NOUN
ejpam-5888	338	6	,	,	PUNCT
ejpam-5888	338	7	22(6):644–654	22(6):644–654	PROPN
ejpam-5888	338	8	,	,	PUNCT
ejpam-5888	338	9	nov	nov	PROPN
ejpam-5888	338	10	1976	1976	NUM
ejpam-5888	338	11	.	.	PUNCT
ejpam-5888	339	1	[	[	X
ejpam-5888	339	2	2	2	NUM
ejpam-5888	339	3	]	]	PUNCT
ejpam-5888	339	4	t	t	X
ejpam-5888	339	5	elgamal	elgamal	ADJ
ejpam-5888	339	6	.	.	PUNCT
ejpam-5888	340	1	a	a	DET
ejpam-5888	340	2	public	public	ADJ
ejpam-5888	340	3	key	key	ADJ
ejpam-5888	340	4	cryptosystem	cryptosystem	NOUN
ejpam-5888	340	5	and	and	CCONJ
ejpam-5888	340	6	a	a	DET
ejpam-5888	340	7	signature	signature	NOUN
ejpam-5888	340	8	scheme	scheme	NOUN
ejpam-5888	340	9	based	base	VERB
ejpam-5888	340	10	on	on	ADP
ejpam-5888	340	11	discrete	discrete	ADJ
ejpam-5888	340	12	logarithms	logarithm	NOUN
ejpam-5888	340	13	.	.	PUNCT
ejpam-5888	341	1	ieee	ieee	NOUN
ejpam-5888	341	2	transactions	transaction	NOUN
ejpam-5888	341	3	on	on	ADP
ejpam-5888	341	4	information	information	NOUN
ejpam-5888	341	5	theory	theory	NOUN
ejpam-5888	341	6	,	,	PUNCT
ejpam-5888	341	7	31(4):469–472	31(4):469–472	NUM
ejpam-5888	341	8	,	,	PUNCT
ejpam-5888	341	9	jul	jul	PROPN
ejpam-5888	341	10	1985	1985	NUM
ejpam-5888	341	11	.	.	PUNCT
ejpam-5888	342	1	[	[	X
ejpam-5888	342	2	3	3	X
ejpam-5888	342	3	]	]	X
ejpam-5888	342	4	digital	digital	ADJ
ejpam-5888	342	5	signature	signature	NOUN
ejpam-5888	342	6	standard	standard	NOUN
ejpam-5888	342	7	(	(	PUNCT
ejpam-5888	342	8	dss	dss	NOUN
ejpam-5888	342	9	)	)	PUNCT
ejpam-5888	342	10	.	.	PUNCT
ejpam-5888	343	1	national	national	PROPN
ejpam-5888	343	2	institute	institute	PROPN
ejpam-5888	343	3	of	of	ADP
ejpam-5888	343	4	standards	standard	NOUN
ejpam-5888	343	5	and	and	CCONJ
ejpam-5888	343	6	technology	technology	NOUN
ejpam-5888	343	7	(	(	PUNCT
ejpam-5888	343	8	u.s	u.s	PROPN
ejpam-5888	343	9	.	.	PROPN
ejpam-5888	343	10	)	)	PUNCT
ejpam-5888	343	11	,	,	PUNCT
ejpam-5888	343	12	1994	1994	NUM
ejpam-5888	343	13	.	.	PUNCT
ejpam-5888	344	1	[	[	X
ejpam-5888	344	2	4	4	X
ejpam-5888	344	3	]	]	PUNCT
ejpam-5888	344	4	any	any	DET
ejpam-5888	344	5	muanalifah	muanalifah	ADJ
ejpam-5888	344	6	and	and	CCONJ
ejpam-5888	344	7	sergĕı	sergĕı	ADJ
ejpam-5888	344	8	sergeev	sergeev	PROPN
ejpam-5888	344	9	.	.	PUNCT
ejpam-5888	345	1	on	on	ADP
ejpam-5888	345	2	the	the	DET
ejpam-5888	345	3	tropical	tropical	ADJ
ejpam-5888	345	4	discrete	discrete	ADJ
ejpam-5888	345	5	logarithm	logarithm	NOUN
ejpam-5888	345	6	problem	problem	NOUN
ejpam-5888	345	7	and	and	CCONJ
ejpam-5888	345	8	security	security	NOUN
ejpam-5888	345	9	of	of	ADP
ejpam-5888	345	10	a	a	DET
ejpam-5888	345	11	protocol	protocol	NOUN
ejpam-5888	345	12	based	base	VERB
ejpam-5888	345	13	on	on	ADP
ejpam-5888	345	14	tropical	tropical	ADJ
ejpam-5888	345	15	semidirect	semidirect	NOUN
ejpam-5888	345	16	product	product	NOUN
ejpam-5888	345	17	.	.	PUNCT
ejpam-5888	346	1	communications	communication	NOUN
ejpam-5888	346	2	in	in	ADP
ejpam-5888	346	3	algebra	algebra	NOUN
ejpam-5888	346	4	,	,	PUNCT
ejpam-5888	346	5	50(2):861–879	50(2):861–879	NUM
ejpam-5888	346	6	,	,	PUNCT
ejpam-5888	346	7	2022	2022	NUM
ejpam-5888	346	8	.	.	PUNCT
ejpam-5888	347	1	kashifa	kashifa	PROPN
ejpam-5888	347	2	begum	begum	VERB
ejpam-5888	347	3	a.	a.	NOUN
ejpam-5888	347	4	et	et	PROPN
ejpam-5888	347	5	.	.	PUNCT
ejpam-5888	348	1	al	al	PROPN
ejpam-5888	348	2	/	/	PUNCT
ejpam-5888	348	3	eur	eur	PROPN
ejpam-5888	348	4	.	.	PUNCT
ejpam-5888	349	1	j.	j.	PROPN
ejpam-5888	349	2	pure	pure	PROPN
ejpam-5888	349	3	appl	appl	PROPN
ejpam-5888	349	4	.	.	PROPN
ejpam-5888	349	5	math	math	PROPN
ejpam-5888	349	6	,	,	PUNCT
ejpam-5888	349	7	18	18	NUM
ejpam-5888	349	8	(	(	PUNCT
ejpam-5888	349	9	3	3	NUM
ejpam-5888	349	10	)	)	PUNCT
ejpam-5888	349	11	(	(	PUNCT
ejpam-5888	349	12	2025	2025	NUM
ejpam-5888	349	13	)	)	PUNCT
ejpam-5888	349	14	,	,	PUNCT
ejpam-5888	349	15	5888	5888	NUM
ejpam-5888	349	16	16	16	NUM
ejpam-5888	349	17	of	of	ADP
ejpam-5888	349	18	16	16	NUM
ejpam-5888	350	1	[	[	X
ejpam-5888	350	2	5	5	NUM
ejpam-5888	350	3	]	]	PUNCT
ejpam-5888	350	4	neha	neha	NOUN
ejpam-5888	350	5	goel	goel	PROPN
ejpam-5888	350	6	,	,	PUNCT
ejpam-5888	350	7	indivar	indivar	PROPN
ejpam-5888	350	8	gupta	gupta	PROPN
ejpam-5888	350	9	,	,	PUNCT
ejpam-5888	350	10	m.	m.	PROPN
ejpam-5888	350	11	k.	k.	PROPN
ejpam-5888	350	12	dubey	dubey	PROPN
ejpam-5888	350	13	,	,	PUNCT
ejpam-5888	350	14	and	and	CCONJ
ejpam-5888	350	15	b.	b.	PROPN
ejpam-5888	350	16	k.	k.	PROPN
ejpam-5888	350	17	dass	dass	PROPN
ejpam-5888	350	18	.	.	PUNCT
ejpam-5888	351	1	undeniable	undeniable	ADJ
ejpam-5888	351	2	signature	signature	NOUN
ejpam-5888	351	3	scheme	scheme	NOUN
ejpam-5888	351	4	based	base	VERB
ejpam-5888	351	5	over	over	ADP
ejpam-5888	351	6	group	group	NOUN
ejpam-5888	351	7	ring	ring	NOUN
ejpam-5888	351	8	.	.	PUNCT
ejpam-5888	352	1	applicable	applicable	ADJ
ejpam-5888	352	2	algebra	algebra	PROPN
ejpam-5888	352	3	in	in	ADP
ejpam-5888	352	4	engineering	engineering	NOUN
ejpam-5888	352	5	,	,	PUNCT
ejpam-5888	352	6	communication	communication	NOUN
ejpam-5888	352	7	and	and	CCONJ
ejpam-5888	352	8	computing	computing	NOUN
ejpam-5888	352	9	,	,	PUNCT
ejpam-5888	352	10	27(6):523–535	27(6):523–535	NUM
ejpam-5888	352	11	,	,	PUNCT
ejpam-5888	352	12	dec	dec	PROPN
ejpam-5888	352	13	2016	2016	NUM
ejpam-5888	352	14	.	.	PUNCT
ejpam-5888	353	1	[	[	X
ejpam-5888	353	2	6	6	NUM
ejpam-5888	353	3	]	]	PUNCT
ejpam-5888	353	4	ki	ki	PROPN
ejpam-5888	353	5	hyoung	hyoung	PROPN
ejpam-5888	353	6	ko	ko	PROPN
ejpam-5888	353	7	,	,	PUNCT
ejpam-5888	353	8	sang	sing	VERB
ejpam-5888	353	9	jin	jin	PROPN
ejpam-5888	353	10	lee	lee	PROPN
ejpam-5888	353	11	,	,	PUNCT
ejpam-5888	353	12	jung	jung	PROPN
ejpam-5888	353	13	hee	hee	PROPN
ejpam-5888	353	14	cheon	cheon	PROPN
ejpam-5888	353	15	,	,	PUNCT
ejpam-5888	353	16	jae	jae	PROPN
ejpam-5888	353	17	woo	woo	PROPN
ejpam-5888	353	18	han	han	PROPN
ejpam-5888	353	19	,	,	PUNCT
ejpam-5888	353	20	ju	ju	PROPN
ejpam-5888	353	21	sung	sung	PROPN
ejpam-5888	353	22	kang	kang	PROPN
ejpam-5888	353	23	,	,	PUNCT
ejpam-5888	353	24	and	and	CCONJ
ejpam-5888	353	25	choonsik	choonsik	NOUN
ejpam-5888	353	26	park	park	NOUN
ejpam-5888	353	27	.	.	PUNCT
ejpam-5888	354	1	new	new	ADJ
ejpam-5888	354	2	public	public	ADJ
ejpam-5888	354	3	-	-	PUNCT
ejpam-5888	354	4	key	key	NOUN
ejpam-5888	354	5	cryptosystem	cryptosystem	NOUN
ejpam-5888	354	6	using	use	VERB
ejpam-5888	354	7	braid	braid	ADJ
ejpam-5888	354	8	groups	group	NOUN
ejpam-5888	354	9	.	.	PUNCT
ejpam-5888	355	1	lecture	lecture	NOUN
ejpam-5888	355	2	notes	note	NOUN
ejpam-5888	355	3	in	in	ADP
ejpam-5888	355	4	computer	computer	NOUN
ejpam-5888	355	5	science	science	NOUN
ejpam-5888	355	6	,	,	PUNCT
ejpam-5888	355	7	pages	page	NOUN
ejpam-5888	355	8	166–183	166–183	NUM
ejpam-5888	355	9	,	,	PUNCT
ejpam-5888	355	10	2000	2000	NUM
ejpam-5888	355	11	.	.	PUNCT
ejpam-5888	356	1	[	[	X
ejpam-5888	356	2	7	7	X
ejpam-5888	356	3	]	]	PUNCT
ejpam-5888	356	4	volker	volker	NOUN
ejpam-5888	356	5	gebhardt	gebhardt	PROPN
ejpam-5888	356	6	and	and	CCONJ
ejpam-5888	356	7	juan	juan	PROPN
ejpam-5888	356	8	gonzález	gonzález	PROPN
ejpam-5888	356	9	-	-	PUNCT
ejpam-5888	356	10	meneses	menese	NOUN
ejpam-5888	356	11	.	.	PUNCT
ejpam-5888	357	1	solving	solve	VERB
ejpam-5888	357	2	the	the	DET
ejpam-5888	357	3	conjugacy	conjugacy	PROPN
ejpam-5888	357	4	problem	problem	NOUN
ejpam-5888	357	5	in	in	ADP
ejpam-5888	357	6	garside	garside	NOUN
ejpam-5888	357	7	groups	group	NOUN
ejpam-5888	357	8	by	by	ADP
ejpam-5888	357	9	cyclic	cyclic	PROPN
ejpam-5888	357	10	sliding	sliding	NOUN
ejpam-5888	357	11	.	.	PUNCT
ejpam-5888	358	1	journal	journal	PROPN
ejpam-5888	358	2	of	of	ADP
ejpam-5888	358	3	symbolic	symbolic	ADJ
ejpam-5888	358	4	computation	computation	NOUN
ejpam-5888	358	5	,	,	PUNCT
ejpam-5888	358	6	45(6):629–656	45(6):629–656	PROPN
ejpam-5888	358	7	,	,	PUNCT
ejpam-5888	358	8	jun	jun	PROPN
ejpam-5888	358	9	2010	2010	NUM
ejpam-5888	358	10	.	.	PUNCT
ejpam-5888	359	1	[	[	X
ejpam-5888	359	2	8	8	NUM
ejpam-5888	359	3	]	]	X
ejpam-5888	359	4	dima	dima	PROPN
ejpam-5888	359	5	grigoriev	grigoriev	PROPN
ejpam-5888	359	6	and	and	CCONJ
ejpam-5888	359	7	vladimir	vladimir	PROPN
ejpam-5888	359	8	shpilrain	shpilrain	PROPN
ejpam-5888	359	9	.	.	PUNCT
ejpam-5888	360	1	authentication	authentication	NOUN
ejpam-5888	360	2	from	from	ADP
ejpam-5888	360	3	matrix	matrix	NOUN
ejpam-5888	360	4	conjugation	conjugation	NOUN
ejpam-5888	360	5	.	.	PUNCT
ejpam-5888	361	1	groups	group	NOUN
ejpam-5888	361	2	–	–	PUNCT
ejpam-5888	361	3	complexity	complexity	NOUN
ejpam-5888	361	4	–	–	PUNCT
ejpam-5888	361	5	cryptology	cryptology	NOUN
ejpam-5888	361	6	,	,	PUNCT
ejpam-5888	361	7	1(2	1(2	NUM
ejpam-5888	361	8	)	)	PUNCT
ejpam-5888	361	9	,	,	PUNCT
ejpam-5888	361	10	jan	jan	PROPN
ejpam-5888	361	11	2009	2009	NUM
ejpam-5888	361	12	.	.	PUNCT
ejpam-5888	362	1	[	[	X
ejpam-5888	362	2	9	9	NUM
ejpam-5888	362	3	]	]	X
ejpam-5888	362	4	simran	simran	ADJ
ejpam-5888	362	5	tinani	tinani	PROPN
ejpam-5888	362	6	,	,	PUNCT
ejpam-5888	362	7	carlo	carlo	PROPN
ejpam-5888	362	8	matteotti	matteotti	PROPN
ejpam-5888	362	9	,	,	PUNCT
ejpam-5888	362	10	and	and	CCONJ
ejpam-5888	362	11	joachim	joachim	PROPN
ejpam-5888	362	12	rosenthal	rosenthal	PROPN
ejpam-5888	362	13	.	.	PUNCT
ejpam-5888	363	1	solutions	solution	NOUN
ejpam-5888	363	2	to	to	ADP
ejpam-5888	363	3	the	the	DET
ejpam-5888	363	4	conjugacy	conjugacy	PROPN
ejpam-5888	363	5	search	search	NOUN
ejpam-5888	363	6	problem	problem	NOUN
ejpam-5888	363	7	in	in	ADP
ejpam-5888	363	8	various	various	ADJ
ejpam-5888	363	9	platform	platform	NOUN
ejpam-5888	363	10	groups	group	NOUN
ejpam-5888	363	11	.	.	PUNCT
ejpam-5888	364	1	awm	awm	PROPN
ejpam-5888	364	2	research	research	PROPN
ejpam-5888	364	3	symposium	symposium	NOUN
ejpam-5888	364	4	,	,	PUNCT
ejpam-5888	364	5	2022	2022	NUM
ejpam-5888	364	6	.	.	PUNCT
ejpam-5888	365	1	[	[	X
ejpam-5888	365	2	10	10	NUM
ejpam-5888	365	3	]	]	PUNCT
ejpam-5888	365	4	xiaoming	xiaoming	PROPN
ejpam-5888	365	5	chen	chen	PROPN
ejpam-5888	365	6	,	,	PUNCT
ejpam-5888	365	7	weiqing	weiqe	VERB
ejpam-5888	365	8	you	you	PRON
ejpam-5888	365	9	,	,	PUNCT
ejpam-5888	365	10	and	and	CCONJ
ejpam-5888	365	11	li	li	PROPN
ejpam-5888	365	12	wenxi	wenxi	PROPN
ejpam-5888	365	13	.	.	PUNCT
ejpam-5888	366	1	the	the	DET
ejpam-5888	366	2	twin	twin	ADJ
ejpam-5888	366	3	conjugacy	conjugacy	PROPN
ejpam-5888	366	4	search	search	NOUN
ejpam-5888	366	5	problem	problem	NOUN
ejpam-5888	366	6	and	and	CCONJ
ejpam-5888	366	7	applications	application	NOUN
ejpam-5888	366	8	,	,	PUNCT
ejpam-5888	366	9	jun	jun	PROPN
ejpam-5888	366	10	2018	2018	NUM
ejpam-5888	366	11	.	.	PUNCT
ejpam-5888	367	1	[	[	X
ejpam-5888	367	2	11	11	NUM
ejpam-5888	367	3	]	]	PUNCT
ejpam-5888	367	4	v.	v.	CCONJ
ejpam-5888	367	5	muthukumaran	muthukumaran	NOUN
ejpam-5888	367	6	,	,	PUNCT
ejpam-5888	367	7	m.	m.	NOUN
ejpam-5888	367	8	adhiyaman	adhiyaman	NOUN
ejpam-5888	367	9	,	,	PUNCT
ejpam-5888	367	10	and	and	CCONJ
ejpam-5888	367	11	d.	d.	PROPN
ejpam-5888	367	12	ezhilmaran	ezhilmaran	ADJ
ejpam-5888	367	13	.	.	PUNCT
ejpam-5888	368	1	a	a	DET
ejpam-5888	368	2	secure	secure	ADJ
ejpam-5888	368	3	and	and	CCONJ
ejpam-5888	368	4	enhanced	enhance	VERB
ejpam-5888	368	5	public	public	ADJ
ejpam-5888	368	6	key	key	ADJ
ejpam-5888	368	7	cryptosystem	cryptosystem	NOUN
ejpam-5888	368	8	using	use	VERB
ejpam-5888	368	9	double	double	ADJ
ejpam-5888	368	10	conjugacy	conjugacy	ADJ
ejpam-5888	368	11	search	search	NOUN
ejpam-5888	368	12	problem	problem	NOUN
ejpam-5888	368	13	near	near	ADP
ejpam-5888	368	14	-	-	PUNCT
ejpam-5888	368	15	ring	ring	NOUN
ejpam-5888	368	16	.	.	PUNCT
ejpam-5888	369	1	advances	advance	NOUN
ejpam-5888	369	2	in	in	ADP
ejpam-5888	369	3	mathematics	mathematic	NOUN
ejpam-5888	369	4	:	:	PUNCT
ejpam-5888	369	5	scientific	scientific	ADJ
ejpam-5888	369	6	journal	journal	NOUN
ejpam-5888	369	7	,	,	PUNCT
ejpam-5888	369	8	9(3):1389–1395	9(3):1389–1395	PROPN
ejpam-5888	369	9	,	,	PUNCT
ejpam-5888	369	10	jul	jul	PROPN
ejpam-5888	369	11	2020	2020	NUM
ejpam-5888	369	12	.	.	PUNCT
ejpam-5888	370	1	[	[	X
ejpam-5888	370	2	12	12	NUM
ejpam-5888	370	3	]	]	X
ejpam-5888	370	4	illia	illia	PROPN
ejpam-5888	370	5	itenberg	itenberg	PROPN
ejpam-5888	370	6	,	,	PUNCT
ejpam-5888	370	7	grigory	grigory	NOUN
ejpam-5888	370	8	mikhalkin	mikhalkin	NOUN
ejpam-5888	370	9	,	,	PUNCT
ejpam-5888	370	10	and	and	CCONJ
ejpam-5888	370	11	eugenii	eugenii	PROPN
ejpam-5888	370	12	shustin	shustin	NOUN
ejpam-5888	370	13	.	.	PUNCT
ejpam-5888	371	1	tropical	tropical	ADJ
ejpam-5888	371	2	algebraic	algebraic	ADJ
ejpam-5888	371	3	geometry	geometry	NOUN
ejpam-5888	371	4	.	.	PUNCT
ejpam-5888	372	1	birkhäuser	birkhäuser	X
ejpam-5888	372	2	basel	basel	PROPN
ejpam-5888	372	3	,	,	PUNCT
ejpam-5888	372	4	2009	2009	NUM
ejpam-5888	372	5	.	.	PUNCT
ejpam-5888	373	1	[	[	X
ejpam-5888	373	2	13	13	NUM
ejpam-5888	373	3	]	]	X
ejpam-5888	373	4	diane	diane	NOUN
ejpam-5888	373	5	maclagan	maclagan	VERB
ejpam-5888	373	6	and	and	CCONJ
ejpam-5888	373	7	bernd	bernd	PROPN
ejpam-5888	373	8	sturmfels	sturmfel	NOUN
ejpam-5888	373	9	.	.	PUNCT
ejpam-5888	374	1	introduction	introduction	NOUN
ejpam-5888	374	2	to	to	ADP
ejpam-5888	374	3	tropical	tropical	ADJ
ejpam-5888	374	4	geometry	geometry	NOUN
ejpam-5888	374	5	.	.	PUNCT
ejpam-5888	375	1	graduate	graduate	NOUN
ejpam-5888	375	2	studies	study	NOUN
ejpam-5888	375	3	in	in	ADP
ejpam-5888	375	4	mathematics	mathematic	NOUN
ejpam-5888	375	5	,	,	PUNCT
ejpam-5888	375	6	apr	apr	NOUN
ejpam-5888	375	7	2015	2015	NUM
ejpam-5888	375	8	.	.	PUNCT
ejpam-5888	376	1	[	[	X
ejpam-5888	376	2	14	14	NUM
ejpam-5888	376	3	]	]	X
ejpam-5888	376	4	sara	sara	PROPN
ejpam-5888	376	5	kalǐsnik	kalǐsnik	PROPN
ejpam-5888	376	6	and	and	CCONJ
ejpam-5888	376	7	davorin	davorin	PROPN
ejpam-5888	376	8	lešnik	lešnik	PUNCT
ejpam-5888	376	9	.	.	PUNCT
ejpam-5888	377	1	symmetric	symmetric	ADJ
ejpam-5888	377	2	polynomials	polynomial	NOUN
ejpam-5888	377	3	in	in	ADP
ejpam-5888	377	4	tropical	tropical	ADJ
ejpam-5888	377	5	algebra	algebra	NOUN
ejpam-5888	377	6	semirings	semiring	NOUN
ejpam-5888	377	7	.	.	PUNCT
ejpam-5888	378	1	journal	journal	PROPN
ejpam-5888	378	2	of	of	ADP
ejpam-5888	378	3	symbolic	symbolic	ADJ
ejpam-5888	378	4	computation	computation	NOUN
ejpam-5888	378	5	,	,	PUNCT
ejpam-5888	378	6	93:100–119	93:100–119	PROPN
ejpam-5888	378	7	,	,	PUNCT
ejpam-5888	378	8	jul	jul	PROPN
ejpam-5888	378	9	2019	2019	NUM
ejpam-5888	378	10	.	.	PUNCT
ejpam-5888	379	1	[	[	X
ejpam-5888	379	2	15	15	NUM
ejpam-5888	379	3	]	]	X
ejpam-5888	379	4	dima	dima	PROPN
ejpam-5888	379	5	grigoriev	grigoriev	PROPN
ejpam-5888	379	6	and	and	CCONJ
ejpam-5888	379	7	vladimir	vladimir	PROPN
ejpam-5888	379	8	shpilrain	shpilrain	PROPN
ejpam-5888	379	9	.	.	PUNCT
ejpam-5888	380	1	tropical	tropical	ADJ
ejpam-5888	380	2	cryptography	cryptography	NOUN
ejpam-5888	380	3	.	.	PUNCT
ejpam-5888	381	1	communications	communication	NOUN
ejpam-5888	381	2	in	in	ADP
ejpam-5888	381	3	algebra	algebra	NOUN
ejpam-5888	381	4	,	,	PUNCT
ejpam-5888	381	5	42(6):2624–2632	42(6):2624–2632	NUM
ejpam-5888	381	6	,	,	PUNCT
ejpam-5888	381	7	jun	jun	PROPN
ejpam-5888	381	8	2014	2014	NUM
ejpam-5888	381	9	.	.	PUNCT
ejpam-5888	382	1	[	[	X
ejpam-5888	382	2	16	16	NUM
ejpam-5888	382	3	]	]	X
ejpam-5888	382	4	huawei	huawei	PROPN
ejpam-5888	382	5	huang	huang	PROPN
ejpam-5888	382	6	and	and	CCONJ
ejpam-5888	382	7	chunhua	chunhua	PROPN
ejpam-5888	382	8	li	li	PROPN
ejpam-5888	382	9	.	.	PROPN
ejpam-5888	382	10	tropical	tropical	ADJ
ejpam-5888	382	11	cryptography	cryptography	NOUN
ejpam-5888	382	12	based	base	VERB
ejpam-5888	382	13	on	on	ADP
ejpam-5888	382	14	multiple	multiple	ADJ
ejpam-5888	382	15	exponentiation	exponentiation	NOUN
ejpam-5888	382	16	problem	problem	NOUN
ejpam-5888	382	17	of	of	ADP
ejpam-5888	382	18	matrices	matrix	NOUN
ejpam-5888	382	19	.	.	PUNCT
ejpam-5888	383	1	security	security	NOUN
ejpam-5888	383	2	and	and	CCONJ
ejpam-5888	383	3	communication	communication	NOUN
ejpam-5888	383	4	networks	network	NOUN
ejpam-5888	383	5	,	,	PUNCT
ejpam-5888	383	6	2022:1–9	2022:1–9	NUM
ejpam-5888	383	7	,	,	PUNCT
ejpam-5888	383	8	sep	sep	PROPN
ejpam-5888	383	9	2022	2022	NUM
ejpam-5888	383	10	.	.	PUNCT
ejpam-5888	384	1	[	[	X
ejpam-5888	384	2	17	17	NUM
ejpam-5888	384	3	]	]	X
ejpam-5888	384	4	mariana	mariana	PROPN
ejpam-5888	384	5	ivanova	ivanova	PROPN
ejpam-5888	384	6	durcheva	durcheva	PROPN
ejpam-5888	384	7	.	.	PROPN
ejpam-5888	384	8	tres	tre	NOUN
ejpam-5888	384	9	:	:	PUNCT
ejpam-5888	384	10	tropical	tropical	ADJ
ejpam-5888	384	11	encryption	encryption	NOUN
ejpam-5888	384	12	scheme	scheme	NOUN
ejpam-5888	384	13	based	base	VERB
ejpam-5888	384	14	on	on	ADP
ejpam-5888	384	15	double	double	ADJ
ejpam-5888	384	16	key	key	ADJ
ejpam-5888	384	17	exchange	exchange	NOUN
ejpam-5888	384	18	.	.	PUNCT
ejpam-5888	385	1	european	european	ADJ
ejpam-5888	385	2	journal	journal	PROPN
ejpam-5888	385	3	of	of	ADP
ejpam-5888	385	4	information	information	NOUN
ejpam-5888	385	5	technologies	technology	NOUN
ejpam-5888	385	6	and	and	CCONJ
ejpam-5888	385	7	computer	computer	NOUN
ejpam-5888	385	8	science	science	NOUN
ejpam-5888	385	9	,	,	PUNCT
ejpam-5888	385	10	2(4):11–17	2(4):11–17	NUM
ejpam-5888	385	11	,	,	PUNCT
ejpam-5888	385	12	aug	aug	PROPN
ejpam-5888	385	13	2022	2022	NUM
ejpam-5888	385	14	.	.	PUNCT
ejpam-5888	386	1	[	[	X
ejpam-5888	386	2	18	18	NUM
ejpam-5888	386	3	]	]	X
ejpam-5888	386	4	sulaiman	sulaiman	PROPN
ejpam-5888	386	5	alhussaini	alhussaini	PROPN
ejpam-5888	386	6	,	,	PUNCT
ejpam-5888	386	7	craig	craig	PROPN
ejpam-5888	386	8	collett	collett	PROPN
ejpam-5888	386	9	,	,	PUNCT
ejpam-5888	386	10	and	and	CCONJ
ejpam-5888	386	11	sergĕı	sergĕı	PROPN
ejpam-5888	386	12	sergeev	sergeev	PROPN
ejpam-5888	386	13	.	.	PUNCT
ejpam-5888	387	1	on	on	ADP
ejpam-5888	387	2	the	the	DET
ejpam-5888	387	3	tropical	tropical	ADJ
ejpam-5888	387	4	two	two	NUM
ejpam-5888	387	5	-	-	PUNCT
ejpam-5888	387	6	sided	sided	ADJ
ejpam-5888	387	7	discrete	discrete	ADJ
ejpam-5888	387	8	logarithm	logarithm	NOUN
ejpam-5888	387	9	and	and	CCONJ
ejpam-5888	387	10	a	a	DET
ejpam-5888	387	11	key	key	ADJ
ejpam-5888	387	12	exchange	exchange	NOUN
ejpam-5888	387	13	protocol	protocol	NOUN
ejpam-5888	387	14	based	base	VERB
ejpam-5888	387	15	on	on	ADP
ejpam-5888	387	16	the	the	DET
ejpam-5888	387	17	tropical	tropical	ADJ
ejpam-5888	387	18	algebra	algebra	NOUN
ejpam-5888	387	19	of	of	ADP
ejpam-5888	387	20	pairs	pair	NOUN
ejpam-5888	387	21	.	.	PUNCT
ejpam-5888	388	1	communications	communication	NOUN
ejpam-5888	388	2	in	in	ADP
ejpam-5888	388	3	algebra	algebra	NOUN
ejpam-5888	388	4	,	,	PUNCT
ejpam-5888	388	5	52(10):4115–4134	52(10):4115–4134	NUM
ejpam-5888	388	6	,	,	PUNCT
ejpam-5888	388	7	2024	2024	NUM
ejpam-5888	388	8	.	.	PUNCT
ejpam-5888	389	1	[	[	X
ejpam-5888	389	2	19	19	NUM
ejpam-5888	389	3	]	]	X
ejpam-5888	389	4	matvei	matvei	NOUN
ejpam-5888	389	5	kotov	kotov	NOUN
ejpam-5888	389	6	and	and	CCONJ
ejpam-5888	389	7	alexander	alexander	PROPN
ejpam-5888	389	8	ushakov	ushakov	PROPN
ejpam-5888	389	9	.	.	PUNCT
ejpam-5888	390	1	analysis	analysis	NOUN
ejpam-5888	390	2	of	of	ADP
ejpam-5888	390	3	a	a	DET
ejpam-5888	390	4	key	key	ADJ
ejpam-5888	390	5	exchange	exchange	NOUN
ejpam-5888	390	6	protocol	protocol	NOUN
ejpam-5888	390	7	based	base	VERB
ejpam-5888	390	8	on	on	ADP
ejpam-5888	390	9	tropical	tropical	ADJ
ejpam-5888	390	10	matrix	matrix	NOUN
ejpam-5888	390	11	algebra	algebra	NOUN
ejpam-5888	390	12	.	.	PUNCT
ejpam-5888	391	1	journal	journal	PROPN
ejpam-5888	391	2	of	of	ADP
ejpam-5888	391	3	mathematical	mathematical	ADJ
ejpam-5888	391	4	cryptology	cryptology	NOUN
ejpam-5888	391	5	,	,	PUNCT
ejpam-5888	391	6	12(3):137–141	12(3):137–141	PROPN
ejpam-5888	391	7	,	,	PUNCT
ejpam-5888	391	8	sep	sep	PROPN
ejpam-5888	391	9	2018	2018	NUM
ejpam-5888	391	10	.	.	PUNCT
ejpam-5888	392	1	[	[	X
ejpam-5888	392	2	20	20	NUM
ejpam-5888	392	3	]	]	X
ejpam-5888	392	4	dylan	dylan	PROPN
ejpam-5888	392	5	rudy	rudy	PROPN
ejpam-5888	392	6	and	and	CCONJ
ejpam-5888	392	7	chris	chris	PROPN
ejpam-5888	392	8	monico	monico	PROPN
ejpam-5888	392	9	.	.	PUNCT
ejpam-5888	392	10	remarks	remark	NOUN
ejpam-5888	392	11	on	on	ADP
ejpam-5888	392	12	a	a	DET
ejpam-5888	392	13	tropical	tropical	ADJ
ejpam-5888	392	14	key	key	ADJ
ejpam-5888	392	15	exchange	exchange	NOUN
ejpam-5888	392	16	system	system	NOUN
ejpam-5888	392	17	.	.	PUNCT
ejpam-5888	393	1	journal	journal	PROPN
ejpam-5888	393	2	of	of	ADP
ejpam-5888	393	3	mathematical	mathematical	ADJ
ejpam-5888	393	4	cryptology	cryptology	NOUN
ejpam-5888	393	5	,	,	PUNCT
ejpam-5888	393	6	15(1):280–283	15(1):280–283	NUM
ejpam-5888	393	7	,	,	PUNCT
ejpam-5888	393	8	dec	dec	PROPN
ejpam-5888	393	9	2020	2020	NUM
ejpam-5888	393	10	.	.	PUNCT