id	sid	tid	token	lemma	pos
ejpam-3226	1	1	european	european	PROPN
ejpam-3226	1	2	journal	journal	PROPN
ejpam-3226	1	3	of	of	ADP
ejpam-3226	1	4	pure	pure	ADJ
ejpam-3226	1	5	and	and	CCONJ
ejpam-3226	1	6	applied	apply	VERB
ejpam-3226	1	7	mathematics	mathematic	NOUN
ejpam-3226	1	8	vol	vol	NOUN
ejpam-3226	1	9	.	.	PUNCT
ejpam-3226	2	1	11	11	NUM
ejpam-3226	2	2	,	,	PUNCT
ejpam-3226	2	3	no	no	INTJ
ejpam-3226	2	4	.	.	NOUN
ejpam-3226	2	5	2	2	NUM
ejpam-3226	2	6	,	,	PUNCT
ejpam-3226	2	7	2018	2018	NUM
ejpam-3226	2	8	,	,	PUNCT
ejpam-3226	2	9	410	410	NUM
ejpam-3226	2	10	-	-	SYM
ejpam-3226	2	11	416	416	NUM
ejpam-3226	2	12	issn	issn	PROPN
ejpam-3226	2	13	1307	1307	NUM
ejpam-3226	2	14	-	-	SYM
ejpam-3226	2	15	5543	5543	NUM
ejpam-3226	2	16	–	–	PUNCT
ejpam-3226	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3226	2	18	published	publish	VERB
ejpam-3226	2	19	by	by	ADP
ejpam-3226	2	20	new	new	PROPN
ejpam-3226	2	21	york	york	PROPN
ejpam-3226	2	22	business	business	PROPN
ejpam-3226	2	23	global	global	ADJ
ejpam-3226	2	24	secret	secret	ADJ
ejpam-3226	2	25	sharing	sharing	NOUN
ejpam-3226	2	26	schemes	scheme	NOUN
ejpam-3226	2	27	based	base	VERB
ejpam-3226	2	28	on	on	ADP
ejpam-3226	2	29	extension	extension	NOUN
ejpam-3226	2	30	fields	field	NOUN
ejpam-3226	2	31	selda	selda	PROPN
ejpam-3226	2	32	çalkavur	çalkavur	PROPN
ejpam-3226	2	33	department	department	PROPN
ejpam-3226	2	34	of	of	ADP
ejpam-3226	2	35	mathematics	mathematics	PROPN
ejpam-3226	2	36	,	,	PUNCT
ejpam-3226	2	37	kocaeli	kocaeli	PROPN
ejpam-3226	2	38	university	university	PROPN
ejpam-3226	2	39	,	,	PUNCT
ejpam-3226	2	40	kocaeli	kocaeli	VERB
ejpam-3226	2	41	,	,	PUNCT
ejpam-3226	2	42	turkey	turkey	PROPN
ejpam-3226	2	43	abstract	abstract	NOUN
ejpam-3226	2	44	.	.	PUNCT
ejpam-3226	3	1	a	a	DET
ejpam-3226	3	2	(	(	PUNCT
ejpam-3226	3	3	t	t	PROPN
ejpam-3226	3	4	,	,	PUNCT
ejpam-3226	3	5	n)−secret	n)−secret	ADJ
ejpam-3226	3	6	sharing	sharing	NOUN
ejpam-3226	3	7	scheme	scheme	NOUN
ejpam-3226	3	8	is	be	AUX
ejpam-3226	3	9	a	a	DET
ejpam-3226	3	10	method	method	NOUN
ejpam-3226	3	11	of	of	ADP
ejpam-3226	3	12	distribution	distribution	NOUN
ejpam-3226	3	13	of	of	ADP
ejpam-3226	3	14	information	information	NOUN
ejpam-3226	3	15	among	among	ADP
ejpam-3226	3	16	n	n	NUM
ejpam-3226	3	17	participants	participant	NOUN
ejpam-3226	3	18	such	such	ADJ
ejpam-3226	3	19	that	that	SCONJ
ejpam-3226	3	20	t	t	PROPN
ejpam-3226	3	21	>	>	X
ejpam-3226	3	22	1	1	NUM
ejpam-3226	3	23	can	can	AUX
ejpam-3226	3	24	reconstruct	reconstruct	VERB
ejpam-3226	3	25	the	the	DET
ejpam-3226	3	26	secret	secret	NOUN
ejpam-3226	3	27	but	but	CCONJ
ejpam-3226	3	28	t	t	PROPN
ejpam-3226	3	29	−	−	PROPN
ejpam-3226	3	30	1	1	NUM
ejpam-3226	3	31	can	can	AUX
ejpam-3226	3	32	not	not	PART
ejpam-3226	3	33	.	.	PUNCT
ejpam-3226	4	1	there	there	PRON
ejpam-3226	4	2	is	be	VERB
ejpam-3226	4	3	numerous	numerous	ADJ
ejpam-3226	4	4	research	research	NOUN
ejpam-3226	4	5	about	about	ADP
ejpam-3226	4	6	secret	secret	ADJ
ejpam-3226	4	7	sharing	sharing	NOUN
ejpam-3226	4	8	schemes	scheme	NOUN
ejpam-3226	4	9	.	.	PUNCT
ejpam-3226	5	1	however	however	ADV
ejpam-3226	5	2	there	there	PRON
ejpam-3226	5	3	is	be	VERB
ejpam-3226	5	4	little	little	ADJ
ejpam-3226	5	5	research	research	NOUN
ejpam-3226	5	6	on	on	ADP
ejpam-3226	5	7	secret	secret	ADJ
ejpam-3226	5	8	sharing	sharing	NOUN
ejpam-3226	5	9	schemes	scheme	NOUN
ejpam-3226	5	10	based	base	VERB
ejpam-3226	5	11	on	on	ADP
ejpam-3226	5	12	extension	extension	NOUN
ejpam-3226	5	13	fields	field	NOUN
ejpam-3226	5	14	.	.	PUNCT
ejpam-3226	6	1	in	in	ADP
ejpam-3226	6	2	this	this	DET
ejpam-3226	6	3	paper	paper	NOUN
ejpam-3226	6	4	,	,	PUNCT
ejpam-3226	6	5	we	we	PRON
ejpam-3226	6	6	study	study	VERB
ejpam-3226	6	7	secret	secret	ADJ
ejpam-3226	6	8	sharing	sharing	NOUN
ejpam-3226	6	9	schemes	scheme	NOUN
ejpam-3226	6	10	based	base	VERB
ejpam-3226	6	11	on	on	ADP
ejpam-3226	6	12	extension	extension	NOUN
ejpam-3226	6	13	fields	field	NOUN
ejpam-3226	6	14	over	over	ADP
ejpam-3226	6	15	finite	finite	ADJ
ejpam-3226	6	16	fields	field	NOUN
ejpam-3226	6	17	.	.	PUNCT
ejpam-3226	7	1	we	we	PRON
ejpam-3226	7	2	use	use	VERB
ejpam-3226	7	3	two	two	NUM
ejpam-3226	7	4	methods	method	NOUN
ejpam-3226	7	5	to	to	PART
ejpam-3226	7	6	recover	recover	VERB
ejpam-3226	7	7	the	the	DET
ejpam-3226	7	8	secret	secret	NOUN
ejpam-3226	7	9	.	.	PUNCT
ejpam-3226	8	1	we	we	PRON
ejpam-3226	8	2	define	define	VERB
ejpam-3226	8	3	the	the	DET
ejpam-3226	8	4	access	access	NOUN
ejpam-3226	8	5	structure	structure	NOUN
ejpam-3226	8	6	and	and	CCONJ
ejpam-3226	8	7	the	the	DET
ejpam-3226	8	8	accessibility	accessibility	NOUN
ejpam-3226	8	9	degree	degree	NOUN
ejpam-3226	8	10	for	for	ADP
ejpam-3226	8	11	these	these	DET
ejpam-3226	8	12	secret	secret	ADJ
ejpam-3226	8	13	sharing	sharing	NOUN
ejpam-3226	8	14	schemes	scheme	NOUN
ejpam-3226	8	15	.	.	PUNCT
ejpam-3226	9	1	we	we	PRON
ejpam-3226	9	2	also	also	ADV
ejpam-3226	9	3	describe	describe	VERB
ejpam-3226	9	4	our	our	PRON
ejpam-3226	9	5	theorems	theorem	NOUN
ejpam-3226	9	6	,	,	PUNCT
ejpam-3226	9	7	definitions	definition	NOUN
ejpam-3226	9	8	and	and	CCONJ
ejpam-3226	9	9	a	a	DET
ejpam-3226	9	10	corollary	corollary	NOUN
ejpam-3226	9	11	.	.	PUNCT
ejpam-3226	10	1	2010	2010	NUM
ejpam-3226	10	2	mathematics	mathematic	NOUN
ejpam-3226	10	3	subject	subject	NOUN
ejpam-3226	10	4	classifications	classification	NOUN
ejpam-3226	10	5	:	:	PUNCT
ejpam-3226	10	6	12f05	12f05	NUM
ejpam-3226	10	7	,	,	PUNCT
ejpam-3226	10	8	94a62	94a62	PRON
ejpam-3226	10	9	key	key	ADJ
ejpam-3226	10	10	words	word	NOUN
ejpam-3226	10	11	and	and	CCONJ
ejpam-3226	10	12	phrases	phrase	NOUN
ejpam-3226	10	13	:	:	PUNCT
ejpam-3226	10	14	extension	extension	NOUN
ejpam-3226	10	15	fields	field	NOUN
ejpam-3226	10	16	,	,	PUNCT
ejpam-3226	10	17	secret	secret	ADJ
ejpam-3226	10	18	sharing	sharing	NOUN
ejpam-3226	10	19	,	,	PUNCT
ejpam-3226	10	20	secret	secret	ADJ
ejpam-3226	10	21	sharing	sharing	NOUN
ejpam-3226	10	22	schemes	scheme	NOUN
ejpam-3226	10	23	1	1	NUM
ejpam-3226	10	24	.	.	PUNCT
ejpam-3226	11	1	introduction	introduction	NOUN
ejpam-3226	11	2	secret	secret	ADJ
ejpam-3226	11	3	sharing	sharing	NOUN
ejpam-3226	11	4	has	have	AUX
ejpam-3226	11	5	been	be	AUX
ejpam-3226	11	6	a	a	DET
ejpam-3226	11	7	subject	subject	NOUN
ejpam-3226	11	8	of	of	ADP
ejpam-3226	11	9	study	study	NOUN
ejpam-3226	11	10	for	for	ADP
ejpam-3226	11	11	over	over	ADP
ejpam-3226	11	12	30	30	NUM
ejpam-3226	11	13	years	year	NOUN
ejpam-3226	11	14	.	.	PUNCT
ejpam-3226	12	1	a	a	DET
ejpam-3226	12	2	secret	secret	ADJ
ejpam-3226	12	3	sharing	sharing	NOUN
ejpam-3226	12	4	scheme	scheme	NOUN
ejpam-3226	12	5	is	be	AUX
ejpam-3226	12	6	a	a	DET
ejpam-3226	12	7	way	way	NOUN
ejpam-3226	12	8	of	of	ADP
ejpam-3226	12	9	distributing	distribute	VERB
ejpam-3226	12	10	a	a	DET
ejpam-3226	12	11	secret	secret	NOUN
ejpam-3226	12	12	among	among	ADP
ejpam-3226	12	13	a	a	DET
ejpam-3226	12	14	finite	finite	ADJ
ejpam-3226	12	15	set	set	NOUN
ejpam-3226	12	16	of	of	ADP
ejpam-3226	12	17	people	people	NOUN
ejpam-3226	12	18	such	such	ADJ
ejpam-3226	12	19	that	that	SCONJ
ejpam-3226	12	20	only	only	ADV
ejpam-3226	12	21	some	some	DET
ejpam-3226	12	22	distinguished	distinguished	ADJ
ejpam-3226	12	23	subsets	subset	NOUN
ejpam-3226	12	24	of	of	ADP
ejpam-3226	12	25	these	these	DET
ejpam-3226	12	26	subsets	subset	NOUN
ejpam-3226	12	27	can	can	AUX
ejpam-3226	12	28	recover	recover	VERB
ejpam-3226	12	29	the	the	DET
ejpam-3226	12	30	secret	secret	NOUN
ejpam-3226	12	31	.	.	PUNCT
ejpam-3226	13	1	the	the	DET
ejpam-3226	13	2	collection	collection	NOUN
ejpam-3226	13	3	of	of	ADP
ejpam-3226	13	4	these	these	DET
ejpam-3226	13	5	special	special	ADJ
ejpam-3226	13	6	subsets	subset	NOUN
ejpam-3226	13	7	is	be	AUX
ejpam-3226	13	8	called	call	VERB
ejpam-3226	13	9	the	the	DET
ejpam-3226	13	10	access	access	NOUN
ejpam-3226	13	11	structure	structure	NOUN
ejpam-3226	13	12	of	of	ADP
ejpam-3226	13	13	the	the	DET
ejpam-3226	13	14	scheme	scheme	NOUN
ejpam-3226	13	15	.	.	PUNCT
ejpam-3226	14	1	secret	secret	ADJ
ejpam-3226	14	2	sharing	sharing	NOUN
ejpam-3226	14	3	schemes	scheme	NOUN
ejpam-3226	14	4	were	be	AUX
ejpam-3226	14	5	constructed	construct	VERB
ejpam-3226	14	6	by	by	ADP
ejpam-3226	14	7	shamir	shamir	PROPN
ejpam-3226	14	8	[	[	X
ejpam-3226	14	9	11	11	NUM
ejpam-3226	14	10	]	]	PUNCT
ejpam-3226	14	11	and	and	CCONJ
ejpam-3226	14	12	blakley	blakley	ADJ
ejpam-3226	14	13	[	[	X
ejpam-3226	14	14	1	1	X
ejpam-3226	14	15	]	]	PUNCT
ejpam-3226	14	16	in	in	ADP
ejpam-3226	14	17	1979	1979	NUM
ejpam-3226	14	18	.	.	PUNCT
ejpam-3226	15	1	shamir	shamir	PROPN
ejpam-3226	15	2	scheme	scheme	PROPN
ejpam-3226	15	3	was	be	AUX
ejpam-3226	15	4	based	base	VERB
ejpam-3226	15	5	on	on	ADP
ejpam-3226	15	6	polynomial	polynomial	ADJ
ejpam-3226	15	7	interpolation	interpolation	NOUN
ejpam-3226	15	8	but	but	CCONJ
ejpam-3226	15	9	was	be	AUX
ejpam-3226	15	10	later	later	ADV
ejpam-3226	15	11	shown	show	VERB
ejpam-3226	15	12	by	by	ADP
ejpam-3226	15	13	mc	mc	PROPN
ejpam-3226	15	14	eliece	eliece	PROPN
ejpam-3226	15	15	and	and	CCONJ
ejpam-3226	15	16	sarwate	sarwate	VERB
ejpam-3226	15	17	to	to	PART
ejpam-3226	15	18	be	be	AUX
ejpam-3226	15	19	an	an	DET
ejpam-3226	15	20	application	application	NOUN
ejpam-3226	15	21	of	of	ADP
ejpam-3226	15	22	massey	massey	PROPN
ejpam-3226	15	23	scheme	scheme	NOUN
ejpam-3226	16	1	[	[	X
ejpam-3226	16	2	8	8	NUM
ejpam-3226	16	3	]	]	PUNCT
ejpam-3226	16	4	,	,	PUNCT
ejpam-3226	16	5	a	a	DET
ejpam-3226	16	6	scheme	scheme	NOUN
ejpam-3226	16	7	based	base	VERB
ejpam-3226	16	8	on	on	ADP
ejpam-3226	16	9	codes	code	NOUN
ejpam-3226	16	10	,	,	PUNCT
ejpam-3226	16	11	to	to	PART
ejpam-3226	16	12	reed	reed	VERB
ejpam-3226	16	13	solomon	solomon	PROPN
ejpam-3226	16	14	codes	code	VERB
ejpam-3226	16	15	[	[	X
ejpam-3226	16	16	9	9	NUM
ejpam-3226	16	17	]	]	PUNCT
ejpam-3226	16	18	.	.	PUNCT
ejpam-3226	17	1	massey	massey	PROPN
ejpam-3226	18	1	[	[	X
ejpam-3226	18	2	8	8	X
ejpam-3226	18	3	]	]	PUNCT
ejpam-3226	18	4	used	use	VERB
ejpam-3226	18	5	linear	linear	PROPN
ejpam-3226	18	6	codes	code	NOUN
ejpam-3226	18	7	for	for	ADP
ejpam-3226	18	8	secret	secret	ADJ
ejpam-3226	18	9	sharing	sharing	NOUN
ejpam-3226	18	10	and	and	CCONJ
ejpam-3226	18	11	explored	explore	VERB
ejpam-3226	18	12	the	the	DET
ejpam-3226	18	13	relationship	relationship	NOUN
ejpam-3226	18	14	between	between	ADP
ejpam-3226	18	15	the	the	DET
ejpam-3226	18	16	access	access	NOUN
ejpam-3226	18	17	structure	structure	NOUN
ejpam-3226	18	18	and	and	CCONJ
ejpam-3226	18	19	the	the	DET
ejpam-3226	18	20	minimal	minimal	ADJ
ejpam-3226	18	21	codewords	codeword	NOUN
ejpam-3226	18	22	of	of	ADP
ejpam-3226	18	23	the	the	DET
ejpam-3226	18	24	dual	dual	ADJ
ejpam-3226	18	25	code	code	NOUN
ejpam-3226	18	26	of	of	ADP
ejpam-3226	18	27	the	the	DET
ejpam-3226	18	28	underlying	underlie	VERB
ejpam-3226	18	29	code	code	NOUN
ejpam-3226	18	30	in	in	ADP
ejpam-3226	18	31	1993	1993	NUM
ejpam-3226	18	32	.	.	PUNCT
ejpam-3226	19	1	several	several	ADJ
ejpam-3226	19	2	authors	author	NOUN
ejpam-3226	19	3	has	have	AUX
ejpam-3226	19	4	been	be	AUX
ejpam-3226	19	5	studied	study	VERB
ejpam-3226	19	6	on	on	ADP
ejpam-3226	19	7	secret	secret	ADJ
ejpam-3226	19	8	sharing	sharing	NOUN
ejpam-3226	19	9	schemes	scheme	NOUN
ejpam-3226	19	10	[	[	X
ejpam-3226	19	11	3	3	NUM
ejpam-3226	19	12	]	]	PUNCT
ejpam-3226	19	13	,	,	PUNCT
ejpam-3226	19	14	[	[	X
ejpam-3226	19	15	4	4	NUM
ejpam-3226	19	16	]	]	PUNCT
ejpam-3226	19	17	,	,	PUNCT
ejpam-3226	19	18	[	[	X
ejpam-3226	19	19	7	7	NUM
ejpam-3226	19	20	]	]	PUNCT
ejpam-3226	19	21	,	,	PUNCT
ejpam-3226	19	22	[	[	X
ejpam-3226	19	23	8	8	NUM
ejpam-3226	19	24	]	]	PUNCT
ejpam-3226	19	25	.	.	PUNCT
ejpam-3226	20	1	secret	secret	ADJ
ejpam-3226	20	2	sharing	sharing	NOUN
ejpam-3226	20	3	schemes	scheme	NOUN
ejpam-3226	20	4	were	be	AUX
ejpam-3226	20	5	applied	apply	VERB
ejpam-3226	20	6	to	to	ADP
ejpam-3226	20	7	various	various	ADJ
ejpam-3226	20	8	fields	field	NOUN
ejpam-3226	20	9	such	such	ADJ
ejpam-3226	20	10	as	as	ADP
ejpam-3226	20	11	cloud	cloud	NOUN
ejpam-3226	20	12	computing	computing	NOUN
ejpam-3226	20	13	,	,	PUNCT
ejpam-3226	20	14	controlling	control	VERB
ejpam-3226	20	15	,	,	PUNCT
ejpam-3226	20	16	nuclear	nuclear	ADJ
ejpam-3226	20	17	weapons	weapon	NOUN
ejpam-3226	20	18	in	in	ADP
ejpam-3226	20	19	military	military	NOUN
ejpam-3226	20	20	,	,	PUNCT
ejpam-3226	20	21	recovering	recover	VERB
ejpam-3226	20	22	information	information	NOUN
ejpam-3226	20	23	from	from	ADP
ejpam-3226	20	24	multiple	multiple	ADJ
ejpam-3226	20	25	servers	server	NOUN
ejpam-3226	20	26	,	,	PUNCT
ejpam-3226	20	27	and	and	CCONJ
ejpam-3226	20	28	controlling	control	VERB
ejpam-3226	20	29	access	access	NOUN
ejpam-3226	20	30	in	in	ADP
ejpam-3226	20	31	banking	banking	NOUN
ejpam-3226	20	32	system	system	NOUN
ejpam-3226	20	33	[	[	X
ejpam-3226	20	34	5	5	NUM
ejpam-3226	20	35	]	]	PUNCT
ejpam-3226	20	36	.	.	PUNCT
ejpam-3226	21	1	another	another	DET
ejpam-3226	21	2	secret	secret	ADJ
ejpam-3226	21	3	sharing	sharing	NOUN
ejpam-3226	21	4	system	system	NOUN
ejpam-3226	21	5	is	be	AUX
ejpam-3226	21	6	the	the	DET
ejpam-3226	21	7	(	(	PUNCT
ejpam-3226	21	8	t	t	PROPN
ejpam-3226	21	9	,	,	PUNCT
ejpam-3226	21	10	n)-threshold	n)-threshold	ADJ
ejpam-3226	21	11	system	system	NOUN
ejpam-3226	21	12	[	[	X
ejpam-3226	21	13	10	10	NUM
ejpam-3226	21	14	]	]	PUNCT
ejpam-3226	21	15	.	.	PUNCT
ejpam-3226	22	1	a	a	DET
ejpam-3226	22	2	(	(	PUNCT
ejpam-3226	22	3	t	t	PROPN
ejpam-3226	22	4	,	,	PUNCT
ejpam-3226	22	5	n)-threshold	n)-threshold	ADJ
ejpam-3226	22	6	scheme	scheme	NOUN
ejpam-3226	22	7	is	be	AUX
ejpam-3226	22	8	a	a	DET
ejpam-3226	22	9	method	method	NOUN
ejpam-3226	22	10	of	of	ADP
ejpam-3226	22	11	distribution	distribution	NOUN
ejpam-3226	22	12	of	of	ADP
ejpam-3226	22	13	information	information	NOUN
ejpam-3226	22	14	among	among	ADP
ejpam-3226	22	15	n	n	NUM
ejpam-3226	22	16	participants	participant	NOUN
ejpam-3226	22	17	such	such	ADJ
ejpam-3226	22	18	that	that	SCONJ
ejpam-3226	22	19	t	t	PROPN
ejpam-3226	22	20	>	>	X
ejpam-3226	22	21	1	1	NUM
ejpam-3226	22	22	participants	participant	NOUN
ejpam-3226	22	23	can	can	AUX
ejpam-3226	22	24	reconstruct	reconstruct	VERB
ejpam-3226	22	25	the	the	DET
ejpam-3226	22	26	secret	secret	NOUN
ejpam-3226	22	27	but	but	CCONJ
ejpam-3226	22	28	t−	t−	PROPN
ejpam-3226	22	29	1	1	NUM
ejpam-3226	22	30	can	can	AUX
ejpam-3226	22	31	not	not	PART
ejpam-3226	22	32	.	.	PUNCT
ejpam-3226	23	1	email	email	NOUN
ejpam-3226	23	2	address	address	NOUN
ejpam-3226	23	3	:	:	PUNCT
ejpam-3226	23	4	selda.calkavur@kocaeli.edu.tr	selda.calkavur@kocaeli.edu.tr	X
ejpam-3226	23	5	(	(	PUNCT
ejpam-3226	23	6	s.	s.	PROPN
ejpam-3226	23	7	çalkavur	çalkavur	PROPN
ejpam-3226	23	8	)	)	PUNCT
ejpam-3226	23	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3226	24	1	410	410	NUM
ejpam-3226	24	2	c	c	NOUN
ejpam-3226	24	3	©	©	PROPN
ejpam-3226	24	4	2018	2018	NUM
ejpam-3226	24	5	ejpam	ejpam	VERB
ejpam-3226	24	6	all	all	DET
ejpam-3226	24	7	rights	right	NOUN
ejpam-3226	24	8	reserved	reserve	VERB
ejpam-3226	24	9	.	.	PUNCT
ejpam-3226	25	1	s.	s.	PROPN
ejpam-3226	25	2	çalkavur	çalkavur	PROPN
ejpam-3226	25	3	/	/	SYM
ejpam-3226	25	4	eur	eur	PROPN
ejpam-3226	25	5	.	.	PUNCT
ejpam-3226	26	1	j.	j.	PROPN
ejpam-3226	26	2	pure	pure	PROPN
ejpam-3226	26	3	appl	appl	PROPN
ejpam-3226	26	4	.	.	PROPN
ejpam-3226	26	5	math	math	PROPN
ejpam-3226	26	6	,	,	PUNCT
ejpam-3226	26	7	11	11	NUM
ejpam-3226	26	8	(	(	PUNCT
ejpam-3226	26	9	2	2	NUM
ejpam-3226	26	10	)	)	PUNCT
ejpam-3226	26	11	(	(	PUNCT
ejpam-3226	26	12	2018	2018	NUM
ejpam-3226	26	13	)	)	PUNCT
ejpam-3226	26	14	,	,	PUNCT
ejpam-3226	26	15	410	410	NUM
ejpam-3226	26	16	-	-	SYM
ejpam-3226	26	17	416	416	NUM
ejpam-3226	26	18	411	411	NUM
ejpam-3226	26	19	in	in	ADP
ejpam-3226	26	20	this	this	DET
ejpam-3226	26	21	work	work	NOUN
ejpam-3226	27	1	,	,	PUNCT
ejpam-3226	27	2	we	we	PRON
ejpam-3226	27	3	present	present	VERB
ejpam-3226	27	4	a	a	DET
ejpam-3226	27	5	(	(	PUNCT
ejpam-3226	27	6	t	t	PROPN
ejpam-3226	27	7	,	,	PUNCT
ejpam-3226	27	8	n)-threshold	n)-threshold	ADJ
ejpam-3226	27	9	scheme	scheme	NOUN
ejpam-3226	27	10	based	base	VERB
ejpam-3226	27	11	on	on	ADP
ejpam-3226	27	12	extension	extension	NOUN
ejpam-3226	27	13	fields	field	NOUN
ejpam-3226	27	14	over	over	ADP
ejpam-3226	27	15	finite	finite	ADJ
ejpam-3226	27	16	fields	field	NOUN
ejpam-3226	27	17	.	.	PUNCT
ejpam-3226	28	1	the	the	DET
ejpam-3226	28	2	material	material	NOUN
ejpam-3226	28	3	is	be	AUX
ejpam-3226	28	4	organized	organize	VERB
ejpam-3226	28	5	as	as	SCONJ
ejpam-3226	28	6	follows	follow	VERB
ejpam-3226	28	7	.	.	PUNCT
ejpam-3226	29	1	section	section	PROPN
ejpam-3226	29	2	ii	ii	PROPN
ejpam-3226	29	3	contains	contain	VERB
ejpam-3226	29	4	some	some	DET
ejpam-3226	29	5	algebraic	algebraic	ADJ
ejpam-3226	29	6	background	background	NOUN
ejpam-3226	29	7	.	.	PUNCT
ejpam-3226	30	1	section	section	NOUN
ejpam-3226	30	2	iii	iii	PROPN
ejpam-3226	30	3	describes	describe	VERB
ejpam-3226	30	4	the	the	DET
ejpam-3226	30	5	schemes	scheme	NOUN
ejpam-3226	30	6	and	and	CCONJ
ejpam-3226	30	7	analyses	analyse	VERB
ejpam-3226	30	8	their	their	PRON
ejpam-3226	30	9	security	security	NOUN
ejpam-3226	30	10	.	.	PUNCT
ejpam-3226	31	1	we	we	PRON
ejpam-3226	31	2	also	also	ADV
ejpam-3226	31	3	determine	determine	VERB
ejpam-3226	31	4	the	the	DET
ejpam-3226	31	5	access	access	NOUN
ejpam-3226	31	6	structure	structure	NOUN
ejpam-3226	31	7	of	of	ADP
ejpam-3226	31	8	these	these	DET
ejpam-3226	31	9	secret	secret	ADJ
ejpam-3226	31	10	sharing	sharing	NOUN
ejpam-3226	31	11	schemes	scheme	NOUN
ejpam-3226	31	12	and	and	CCONJ
ejpam-3226	31	13	prove	prove	VERB
ejpam-3226	31	14	its	its	PRON
ejpam-3226	31	15	properties	property	NOUN
ejpam-3226	31	16	.	.	PUNCT
ejpam-3226	32	1	section	section	NOUN
ejpam-3226	32	2	iv	iv	NUM
ejpam-3226	32	3	collects	collect	VERB
ejpam-3226	32	4	concluding	conclude	VERB
ejpam-3226	32	5	remarks	remark	NOUN
ejpam-3226	32	6	.	.	PUNCT
ejpam-3226	33	1	2	2	X
ejpam-3226	33	2	.	.	X
ejpam-3226	33	3	algebraic	algebraic	ADJ
ejpam-3226	33	4	preliminaries	preliminary	NOUN
ejpam-3226	33	5	2.1	2.1	NUM
ejpam-3226	33	6	.	.	PUNCT
ejpam-3226	34	1	roots	root	NOUN
ejpam-3226	34	2	of	of	ADP
ejpam-3226	34	3	irreducible	irreducible	ADJ
ejpam-3226	34	4	polynomials	polynomial	NOUN
ejpam-3226	34	5	in	in	ADP
ejpam-3226	34	6	this	this	DET
ejpam-3226	34	7	section	section	NOUN
ejpam-3226	34	8	,	,	PUNCT
ejpam-3226	34	9	we	we	PRON
ejpam-3226	34	10	remind	remind	VERB
ejpam-3226	34	11	some	some	DET
ejpam-3226	34	12	information	information	NOUN
ejpam-3226	34	13	about	about	ADP
ejpam-3226	34	14	the	the	DET
ejpam-3226	34	15	set	set	NOUN
ejpam-3226	34	16	of	of	ADP
ejpam-3226	34	17	roots	root	NOUN
ejpam-3226	34	18	of	of	ADP
ejpam-3226	34	19	an	an	DET
ejpam-3226	34	20	irreducible	irreducible	ADJ
ejpam-3226	34	21	polynomial	polynomial	NOUN
ejpam-3226	34	22	over	over	ADP
ejpam-3226	34	23	a	a	DET
ejpam-3226	34	24	finite	finite	ADJ
ejpam-3226	34	25	field	field	NOUN
ejpam-3226	34	26	.	.	PUNCT
ejpam-3226	35	1	lemma	lemma	PROPN
ejpam-3226	35	2	1	1	X
ejpam-3226	35	3	.	.	PUNCT
ejpam-3226	36	1	let	let	VERB
ejpam-3226	36	2	f	f	PRON
ejpam-3226	36	3	∈	∈	PROPN
ejpam-3226	36	4	fq[x	fq[x	PROPN
ejpam-3226	36	5	]	]	PUNCT
ejpam-3226	36	6	be	be	AUX
ejpam-3226	36	7	an	an	DET
ejpam-3226	36	8	irreducible	irreducible	ADJ
ejpam-3226	36	9	polynomial	polynomial	NOUN
ejpam-3226	36	10	over	over	ADP
ejpam-3226	36	11	a	a	DET
ejpam-3226	36	12	finite	finite	ADJ
ejpam-3226	36	13	field	field	NOUN
ejpam-3226	36	14	fq	fq	PROPN
ejpam-3226	36	15	and	and	CCONJ
ejpam-3226	36	16	α	α	PRON
ejpam-3226	36	17	be	be	VERB
ejpam-3226	36	18	a	a	DET
ejpam-3226	36	19	root	root	NOUN
ejpam-3226	36	20	of	of	ADP
ejpam-3226	36	21	f	f	PROPN
ejpam-3226	36	22	in	in	ADP
ejpam-3226	36	23	extension	extension	NOUN
ejpam-3226	36	24	field	field	NOUN
ejpam-3226	36	25	of	of	ADP
ejpam-3226	36	26	fq	fq	PROPN
ejpam-3226	36	27	.	.	PROPN
ejpam-3226	37	1	then	then	ADV
ejpam-3226	37	2	for	for	ADP
ejpam-3226	37	3	a	a	DET
ejpam-3226	37	4	polynomial	polynomial	ADJ
ejpam-3226	37	5	h	h	NOUN
ejpam-3226	37	6	∈	∈	NOUN
ejpam-3226	37	7	fq[x	fq[x	PROPN
ejpam-3226	37	8	]	]	PUNCT
ejpam-3226	37	9	we	we	PRON
ejpam-3226	37	10	have	have	VERB
ejpam-3226	37	11	h(α)=0	h(α)=0	VERB
ejpam-3226	37	12	if	if	SCONJ
ejpam-3226	38	1	and	and	CCONJ
ejpam-3226	38	2	only	only	ADV
ejpam-3226	38	3	if	if	SCONJ
ejpam-3226	38	4	f	f	PROPN
ejpam-3226	38	5	divides	divide	VERB
ejpam-3226	38	6	h	h	NOUN
ejpam-3226	39	1	[	[	X
ejpam-3226	39	2	6	6	NUM
ejpam-3226	39	3	]	]	PUNCT
ejpam-3226	39	4	.	.	PUNCT
ejpam-3226	40	1	lemma	lemma	PROPN
ejpam-3226	40	2	2	2	X
ejpam-3226	40	3	.	.	PUNCT
ejpam-3226	41	1	let	let	VERB
ejpam-3226	41	2	f	f	PRON
ejpam-3226	41	3	∈	∈	PROPN
ejpam-3226	41	4	fq[x	fq[x	PROPN
ejpam-3226	41	5	]	]	PUNCT
ejpam-3226	41	6	be	be	AUX
ejpam-3226	41	7	an	an	DET
ejpam-3226	41	8	irreducible	irreducible	ADJ
ejpam-3226	41	9	polynomial	polynomial	NOUN
ejpam-3226	41	10	over	over	ADP
ejpam-3226	41	11	fq	fq	PROPN
ejpam-3226	41	12	of	of	ADP
ejpam-3226	41	13	degree	degree	NOUN
ejpam-3226	41	14	m.	m.	NOUN
ejpam-3226	41	15	then	then	ADV
ejpam-3226	41	16	f(x	f(x	PROPN
ejpam-3226	41	17	)	)	PUNCT
ejpam-3226	41	18	divides	divide	VERB
ejpam-3226	41	19	xq	xq	PROPN
ejpam-3226	41	20	n	n	CCONJ
ejpam-3226	41	21	−	−	PROPN
ejpam-3226	41	22	x	x	NOUN
ejpam-3226	42	1	if	if	SCONJ
ejpam-3226	42	2	and	and	CCONJ
ejpam-3226	42	3	only	only	ADV
ejpam-3226	42	4	if	if	SCONJ
ejpam-3226	42	5	f	f	PROPN
ejpam-3226	42	6	divides	divide	VERB
ejpam-3226	42	7	h	h	NOUN
ejpam-3226	43	1	[	[	X
ejpam-3226	43	2	6	6	NUM
ejpam-3226	43	3	]	]	PUNCT
ejpam-3226	43	4	.	.	PUNCT
ejpam-3226	44	1	theorem	theorem	NOUN
ejpam-3226	44	2	1	1	NUM
ejpam-3226	44	3	.	.	PUNCT
ejpam-3226	45	1	if	if	SCONJ
ejpam-3226	45	2	f	f	PROPN
ejpam-3226	45	3	is	be	AUX
ejpam-3226	45	4	an	an	DET
ejpam-3226	45	5	irreducible	irreducible	ADJ
ejpam-3226	45	6	polynomial	polynomial	NOUN
ejpam-3226	45	7	in	in	ADP
ejpam-3226	45	8	fq[x	fq[x	PROPN
ejpam-3226	45	9	]	]	PUNCT
ejpam-3226	45	10	of	of	ADP
ejpam-3226	45	11	degree	degree	NOUN
ejpam-3226	45	12	m	m	PROPN
ejpam-3226	45	13	,	,	PUNCT
ejpam-3226	45	14	then	then	ADV
ejpam-3226	45	15	f	f	PROPN
ejpam-3226	45	16	has	have	VERB
ejpam-3226	45	17	a	a	DET
ejpam-3226	45	18	root	root	NOUN
ejpam-3226	45	19	α	α	NOUN
ejpam-3226	45	20	in	in	ADP
ejpam-3226	45	21	fqm	fqm	NOUN
ejpam-3226	45	22	.	.	PUNCT
ejpam-3226	46	1	furthermore	furthermore	ADV
ejpam-3226	46	2	,	,	PUNCT
ejpam-3226	46	3	all	all	DET
ejpam-3226	46	4	the	the	DET
ejpam-3226	46	5	roots	root	NOUN
ejpam-3226	46	6	of	of	ADP
ejpam-3226	46	7	f	f	PROPN
ejpam-3226	46	8	are	be	AUX
ejpam-3226	46	9	simple	simple	ADJ
ejpam-3226	46	10	and	and	CCONJ
ejpam-3226	46	11	are	be	AUX
ejpam-3226	46	12	given	give	VERB
ejpam-3226	46	13	by	by	ADP
ejpam-3226	46	14	the	the	DET
ejpam-3226	46	15	m	m	NOUN
ejpam-3226	46	16	distinct	distinct	ADJ
ejpam-3226	46	17	elements	element	NOUN
ejpam-3226	46	18	α	α	NOUN
ejpam-3226	46	19	,	,	PUNCT
ejpam-3226	46	20	αq	αq	ADP
ejpam-3226	46	21	,	,	PUNCT
ejpam-3226	46	22	αq2	αq2	NOUN
ejpam-3226	46	23	,	,	PUNCT
ejpam-3226	46	24	...	...	PUNCT
ejpam-3226	46	25	,	,	PUNCT
ejpam-3226	46	26	αqm−1	αqm−1	PROPN
ejpam-3226	46	27	of	of	ADP
ejpam-3226	46	28	fqm	fqm	NOUN
ejpam-3226	46	29	[	[	X
ejpam-3226	46	30	6	6	NUM
ejpam-3226	46	31	]	]	PUNCT
ejpam-3226	46	32	.	.	PUNCT
ejpam-3226	47	1	corollary	corollary	ADJ
ejpam-3226	47	2	1	1	NUM
ejpam-3226	47	3	.	.	PUNCT
ejpam-3226	48	1	let	let	VERB
ejpam-3226	48	2	f	f	PRON
ejpam-3226	48	3	be	be	AUX
ejpam-3226	48	4	an	an	DET
ejpam-3226	48	5	irreducible	irreducible	ADJ
ejpam-3226	48	6	polynomial	polynomial	NOUN
ejpam-3226	48	7	in	in	ADP
ejpam-3226	48	8	fq[x	fq[x	PROPN
ejpam-3226	48	9	]	]	PUNCT
ejpam-3226	48	10	of	of	ADP
ejpam-3226	48	11	degree	degree	NOUN
ejpam-3226	48	12	m.	m.	NOUN
ejpam-3226	48	13	then	then	ADV
ejpam-3226	48	14	the	the	DET
ejpam-3226	48	15	splitting	splitting	NOUN
ejpam-3226	48	16	field	field	NOUN
ejpam-3226	48	17	of	of	ADP
ejpam-3226	48	18	f	f	PROPN
ejpam-3226	48	19	over	over	ADP
ejpam-3226	48	20	fq	fq	PROPN
ejpam-3226	48	21	is	be	AUX
ejpam-3226	48	22	given	give	VERB
ejpam-3226	48	23	by	by	ADP
ejpam-3226	48	24	fqm	fqm	NOUN
ejpam-3226	48	25	[	[	X
ejpam-3226	48	26	6	6	NUM
ejpam-3226	48	27	]	]	PUNCT
ejpam-3226	48	28	.	.	PUNCT
ejpam-3226	49	1	definition	definition	NOUN
ejpam-3226	49	2	1	1	NUM
ejpam-3226	49	3	.	.	PUNCT
ejpam-3226	50	1	let	let	VERB
ejpam-3226	50	2	fqm	fqm	NOUN
ejpam-3226	50	3	be	be	AUX
ejpam-3226	50	4	an	an	DET
ejpam-3226	50	5	extension	extension	NOUN
ejpam-3226	50	6	of	of	ADP
ejpam-3226	50	7	fq	fq	PROPN
ejpam-3226	50	8	and	and	CCONJ
ejpam-3226	50	9	let	let	VERB
ejpam-3226	50	10	α	α	PRON
ejpam-3226	50	11	∈	∈	PROPN
ejpam-3226	50	12	fqm	fqm	NOUN
ejpam-3226	50	13	.	.	PUNCT
ejpam-3226	51	1	then	then	ADV
ejpam-3226	51	2	the	the	DET
ejpam-3226	51	3	elements	element	NOUN
ejpam-3226	51	4	α	α	NOUN
ejpam-3226	51	5	,	,	PUNCT
ejpam-3226	51	6	αq	αq	ADP
ejpam-3226	51	7	,	,	PUNCT
ejpam-3226	51	8	αq2	αq2	NOUN
ejpam-3226	51	9	,	,	PUNCT
ejpam-3226	51	10	...	...	PUNCT
ejpam-3226	51	11	,	,	PUNCT
ejpam-3226	51	12	αqm−1	αqm−1	PROPN
ejpam-3226	51	13	are	be	AUX
ejpam-3226	51	14	called	call	VERB
ejpam-3226	51	15	the	the	DET
ejpam-3226	51	16	conjugates	conjugate	NOUN
ejpam-3226	51	17	of	of	ADP
ejpam-3226	51	18	α	α	NOUN
ejpam-3226	51	19	with	with	ADP
ejpam-3226	51	20	respect	respect	NOUN
ejpam-3226	51	21	to	to	ADP
ejpam-3226	51	22	fq	fq	PROPN
ejpam-3226	51	23	[	[	X
ejpam-3226	51	24	6	6	NUM
ejpam-3226	51	25	]	]	PUNCT
ejpam-3226	51	26	.	.	PUNCT
ejpam-3226	52	1	the	the	DET
ejpam-3226	52	2	conjugates	conjugate	NOUN
ejpam-3226	52	3	of	of	ADP
ejpam-3226	52	4	α	α	PROPN
ejpam-3226	52	5	∈	∈	PROPN
ejpam-3226	52	6	fqm	fqm	NOUN
ejpam-3226	52	7	with	with	ADP
ejpam-3226	52	8	respect	respect	NOUN
ejpam-3226	52	9	to	to	ADP
ejpam-3226	52	10	fq	fq	PROPN
ejpam-3226	52	11	are	be	AUX
ejpam-3226	52	12	distinct	distinct	ADJ
ejpam-3226	52	13	if	if	SCONJ
ejpam-3226	52	14	and	and	CCONJ
ejpam-3226	52	15	only	only	ADV
ejpam-3226	52	16	if	if	SCONJ
ejpam-3226	52	17	minimal	minimal	ADJ
ejpam-3226	52	18	polynomial	polynomial	NOUN
ejpam-3226	52	19	of	of	ADP
ejpam-3226	52	20	α	α	PROPN
ejpam-3226	52	21	over	over	ADP
ejpam-3226	52	22	fq	fq	PROPN
ejpam-3226	52	23	has	have	VERB
ejpam-3226	52	24	degree	degree	NOUN
ejpam-3226	52	25	m.	m.	NOUN
ejpam-3226	52	26	otherwise	otherwise	ADV
ejpam-3226	52	27	,	,	PUNCT
ejpam-3226	52	28	the	the	DET
ejpam-3226	52	29	degree	degree	NOUN
ejpam-3226	52	30	d	d	NOUN
ejpam-3226	52	31	of	of	ADP
ejpam-3226	52	32	this	this	DET
ejpam-3226	52	33	polynomial	polynomial	NOUN
ejpam-3226	52	34	is	be	AUX
ejpam-3226	52	35	a	a	DET
ejpam-3226	52	36	proper	proper	ADJ
ejpam-3226	52	37	divisor	divisor	NOUN
ejpam-3226	52	38	of	of	ADP
ejpam-3226	52	39	m	m	PROPN
ejpam-3226	53	1	and	and	CCONJ
ejpam-3226	53	2	then	then	ADV
ejpam-3226	53	3	the	the	DET
ejpam-3226	53	4	conjugates	conjugate	NOUN
ejpam-3226	53	5	of	of	ADP
ejpam-3226	53	6	α	α	NOUN
ejpam-3226	53	7	with	with	ADP
ejpam-3226	53	8	respect	respect	NOUN
ejpam-3226	53	9	to	to	ADP
ejpam-3226	53	10	fq	fq	PROPN
ejpam-3226	53	11	are	be	AUX
ejpam-3226	53	12	the	the	DET
ejpam-3226	53	13	distinct	distinct	ADJ
ejpam-3226	53	14	elements	element	NOUN
ejpam-3226	53	15	α	α	NOUN
ejpam-3226	53	16	,	,	PUNCT
ejpam-3226	53	17	αq	αq	ADP
ejpam-3226	53	18	,	,	PUNCT
ejpam-3226	53	19	αq2	αq2	NOUN
ejpam-3226	53	20	,	,	PUNCT
ejpam-3226	53	21	...	...	PUNCT
ejpam-3226	53	22	,	,	PUNCT
ejpam-3226	53	23	αqd−1	αqd−1	PRON
ejpam-3226	53	24	each	each	DET
ejpam-3226	53	25	repeated	repeat	VERB
ejpam-3226	53	26	m	m	PROPN
ejpam-3226	53	27	/	/	SYM
ejpam-3226	53	28	d	d	PROPN
ejpam-3226	53	29	times	time	NOUN
ejpam-3226	53	30	.	.	PUNCT
ejpam-3226	54	1	theorem	theorem	NOUN
ejpam-3226	54	2	2	2	NUM
ejpam-3226	54	3	.	.	PUNCT
ejpam-3226	55	1	the	the	DET
ejpam-3226	55	2	conjugates	conjugate	NOUN
ejpam-3226	55	3	of	of	ADP
ejpam-3226	55	4	α	α	PROPN
ejpam-3226	55	5	∈	∈	PROPN
ejpam-3226	55	6	fq∗	fq∗	NOUN
ejpam-3226	55	7	with	with	ADP
ejpam-3226	55	8	respect	respect	NOUN
ejpam-3226	55	9	to	to	ADP
ejpam-3226	55	10	any	any	DET
ejpam-3226	55	11	subfield	subfield	NOUN
ejpam-3226	55	12	of	of	ADP
ejpam-3226	55	13	fq	fq	PROPN
ejpam-3226	55	14	have	have	VERB
ejpam-3226	55	15	the	the	DET
ejpam-3226	55	16	same	same	ADJ
ejpam-3226	55	17	order	order	NOUN
ejpam-3226	55	18	in	in	ADP
ejpam-3226	55	19	the	the	DET
ejpam-3226	55	20	group	group	NOUN
ejpam-3226	55	21	fq∗	fq∗	NOUN
ejpam-3226	55	22	,	,	PUNCT
ejpam-3226	55	23	where	where	SCONJ
ejpam-3226	55	24	fq∗	fq∗	NOUN
ejpam-3226	55	25	is	be	AUX
ejpam-3226	55	26	a	a	DET
ejpam-3226	55	27	cyclic	cyclic	ADJ
ejpam-3226	55	28	group	group	NOUN
ejpam-3226	55	29	of	of	ADP
ejpam-3226	55	30	nonzero	nonzero	PROPN
ejpam-3226	55	31	elements	element	NOUN
ejpam-3226	55	32	of	of	ADP
ejpam-3226	55	33	which	which	PRON
ejpam-3226	55	34	consists	consist	VERB
ejpam-3226	55	35	of	of	ADP
ejpam-3226	55	36	nonzero	nonzero	ADJ
ejpam-3226	55	37	elements	element	NOUN
ejpam-3226	55	38	of	of	ADP
ejpam-3226	55	39	fq	fq	PROPN
ejpam-3226	55	40	[	[	X
ejpam-3226	55	41	6	6	NUM
ejpam-3226	55	42	]	]	PUNCT
ejpam-3226	55	43	.	.	PUNCT
ejpam-3226	56	1	corollary	corollary	ADJ
ejpam-3226	56	2	2	2	NUM
ejpam-3226	56	3	.	.	PUNCT
ejpam-3226	57	1	if	if	SCONJ
ejpam-3226	57	2	α	α	PRON
ejpam-3226	57	3	is	be	AUX
ejpam-3226	57	4	a	a	DET
ejpam-3226	57	5	primitive	primitive	ADJ
ejpam-3226	57	6	element	element	NOUN
ejpam-3226	57	7	of	of	ADP
ejpam-3226	57	8	fq	fq	PROPN
ejpam-3226	57	9	,	,	PUNCT
ejpam-3226	57	10	then	then	ADV
ejpam-3226	57	11	so	so	ADV
ejpam-3226	57	12	are	be	AUX
ejpam-3226	57	13	all	all	PRON
ejpam-3226	57	14	its	its	PRON
ejpam-3226	57	15	conjugates	conjugate	NOUN
ejpam-3226	57	16	with	with	ADP
ejpam-3226	57	17	respect	respect	NOUN
ejpam-3226	57	18	to	to	ADP
ejpam-3226	57	19	any	any	DET
ejpam-3226	57	20	subfield	subfield	NOUN
ejpam-3226	57	21	of	of	ADP
ejpam-3226	57	22	fq	fq	PROPN
ejpam-3226	57	23	[	[	X
ejpam-3226	57	24	6	6	NUM
ejpam-3226	57	25	]	]	PUNCT
ejpam-3226	57	26	.	.	PUNCT
ejpam-3226	58	1	2.2	2.2	NUM
ejpam-3226	58	2	.	.	PUNCT
ejpam-3226	58	3	traces	trace	NOUN
ejpam-3226	58	4	and	and	CCONJ
ejpam-3226	58	5	norms	norm	NOUN
ejpam-3226	58	6	in	in	ADP
ejpam-3226	58	7	this	this	DET
ejpam-3226	58	8	part	part	NOUN
ejpam-3226	58	9	,	,	PUNCT
ejpam-3226	58	10	we	we	PRON
ejpam-3226	58	11	consider	consider	VERB
ejpam-3226	58	12	the	the	DET
ejpam-3226	58	13	viewpoint	viewpoint	NOUN
ejpam-3226	58	14	of	of	ADP
ejpam-3226	58	15	regarding	regard	VERB
ejpam-3226	58	16	a	a	DET
ejpam-3226	58	17	finite	finite	ADJ
ejpam-3226	58	18	extension	extension	NOUN
ejpam-3226	58	19	f	f	NOUN
ejpam-3226	58	20	=	=	PUNCT
ejpam-3226	58	21	fqm	fqm	NOUN
ejpam-3226	58	22	of	of	ADP
ejpam-3226	58	23	the	the	DET
ejpam-3226	58	24	finite	finite	ADJ
ejpam-3226	58	25	field	field	NOUN
ejpam-3226	58	26	k	k	PROPN
ejpam-3226	59	1	=	=	SYM
ejpam-3226	59	2	fq	fq	PROPN
ejpam-3226	59	3	as	as	ADP
ejpam-3226	59	4	a	a	DET
ejpam-3226	59	5	vector	vector	NOUN
ejpam-3226	59	6	space	space	NOUN
ejpam-3226	59	7	over	over	ADP
ejpam-3226	59	8	k.	k.	PROPN
ejpam-3226	59	9	s.	s.	PROPN
ejpam-3226	59	10	çalkavur	çalkavur	PROPN
ejpam-3226	59	11	/	/	SYM
ejpam-3226	59	12	eur	eur	PROPN
ejpam-3226	59	13	.	.	PUNCT
ejpam-3226	60	1	j.	j.	PROPN
ejpam-3226	60	2	pure	pure	PROPN
ejpam-3226	60	3	appl	appl	PROPN
ejpam-3226	60	4	.	.	PROPN
ejpam-3226	60	5	math	math	PROPN
ejpam-3226	60	6	,	,	PUNCT
ejpam-3226	60	7	11	11	NUM
ejpam-3226	60	8	(	(	PUNCT
ejpam-3226	60	9	2	2	NUM
ejpam-3226	60	10	)	)	PUNCT
ejpam-3226	60	11	(	(	PUNCT
ejpam-3226	60	12	2018	2018	NUM
ejpam-3226	60	13	)	)	PUNCT
ejpam-3226	60	14	,	,	PUNCT
ejpam-3226	60	15	410	410	NUM
ejpam-3226	60	16	-	-	SYM
ejpam-3226	60	17	416	416	NUM
ejpam-3226	60	18	412	412	NUM
ejpam-3226	60	19	definition	definition	NOUN
ejpam-3226	60	20	2	2	NUM
ejpam-3226	60	21	.	.	PUNCT
ejpam-3226	61	1	for	for	ADP
ejpam-3226	61	2	α	α	DET
ejpam-3226	61	3	∈	∈	PROPN
ejpam-3226	61	4	f	f	PROPN
ejpam-3226	61	5	=	=	PUNCT
ejpam-3226	61	6	fqm	fqm	NOUN
ejpam-3226	61	7	and	and	CCONJ
ejpam-3226	61	8	k	k	NOUN
ejpam-3226	61	9	=	=	SYM
ejpam-3226	61	10	fq	fq	PROPN
ejpam-3226	61	11	,	,	PUNCT
ejpam-3226	61	12	the	the	DET
ejpam-3226	61	13	trace	trace	NOUN
ejpam-3226	61	14	trf	trf	PROPN
ejpam-3226	61	15	/	/	SYM
ejpam-3226	61	16	k	k	PROPN
ejpam-3226	61	17	(	(	PUNCT
ejpam-3226	61	18	α	α	NOUN
ejpam-3226	61	19	)	)	PUNCT
ejpam-3226	61	20	of	of	ADP
ejpam-3226	61	21	α	α	PROPN
ejpam-3226	61	22	over	over	ADP
ejpam-3226	61	23	k	k	PROPN
ejpam-3226	61	24	is	be	AUX
ejpam-3226	61	25	defined	define	VERB
ejpam-3226	61	26	by	by	ADP
ejpam-3226	61	27	trf	trf	PROPN
ejpam-3226	61	28	/	/	SYM
ejpam-3226	61	29	k	k	PROPN
ejpam-3226	61	30	(	(	PUNCT
ejpam-3226	61	31	α	α	NOUN
ejpam-3226	61	32	)	)	PUNCT
ejpam-3226	62	1	=	=	NOUN
ejpam-3226	62	2	α+	α+	PUNCT
ejpam-3226	63	1	αq	αq	X
ejpam-3226	63	2	+	+	CCONJ
ejpam-3226	63	3	αq2	αq2	NOUN
ejpam-3226	63	4	+	+	CCONJ
ejpam-3226	63	5	...	...	PUNCT
ejpam-3226	64	1	+	+	CCONJ
ejpam-3226	64	2	αqm−1	αqm−1	PROPN
ejpam-3226	64	3	.	.	PUNCT
ejpam-3226	65	1	if	if	SCONJ
ejpam-3226	65	2	k	k	PROPN
ejpam-3226	65	3	is	be	AUX
ejpam-3226	65	4	the	the	DET
ejpam-3226	65	5	prime	prime	ADJ
ejpam-3226	65	6	subfield	subfield	NOUN
ejpam-3226	65	7	of	of	ADP
ejpam-3226	65	8	f	f	PROPN
ejpam-3226	65	9	,	,	PUNCT
ejpam-3226	65	10	then	then	ADV
ejpam-3226	65	11	trf	trf	PROPN
ejpam-3226	65	12	/	/	SYM
ejpam-3226	65	13	k	k	PROPN
ejpam-3226	65	14	(	(	PUNCT
ejpam-3226	65	15	α	α	NOUN
ejpam-3226	65	16	)	)	PUNCT
ejpam-3226	65	17	is	be	AUX
ejpam-3226	65	18	called	call	VERB
ejpam-3226	65	19	the	the	DET
ejpam-3226	65	20	absolute	absolute	ADJ
ejpam-3226	65	21	trace	trace	NOUN
ejpam-3226	65	22	of	of	ADP
ejpam-3226	65	23	α	α	NOUN
ejpam-3226	65	24	and	and	CCONJ
ejpam-3226	65	25	simply	simply	ADV
ejpam-3226	65	26	denoted	denote	VERB
ejpam-3226	65	27	by	by	ADP
ejpam-3226	65	28	trf	trf	PROPN
ejpam-3226	65	29	(	(	PUNCT
ejpam-3226	65	30	α	α	X
ejpam-3226	65	31	)	)	PUNCT
ejpam-3226	66	1	[	[	X
ejpam-3226	66	2	6	6	NUM
ejpam-3226	66	3	]	]	PUNCT
ejpam-3226	66	4	.	.	PUNCT
ejpam-3226	67	1	definition	definition	NOUN
ejpam-3226	67	2	of	of	ADP
ejpam-3226	67	3	the	the	DET
ejpam-3226	67	4	trace	trace	NOUN
ejpam-3226	67	5	may	may	AUX
ejpam-3226	67	6	be	be	AUX
ejpam-3226	67	7	obtained	obtain	VERB
ejpam-3226	67	8	as	as	ADP
ejpam-3226	67	9	follows	follow	VERB
ejpam-3226	67	10	.	.	PUNCT
ejpam-3226	68	1	let	let	VERB
ejpam-3226	68	2	f	f	PROPN
ejpam-3226	68	3	∈	∈	PROPN
ejpam-3226	68	4	k[x	k[x	PROPN
ejpam-3226	68	5	]	]	PUNCT
ejpam-3226	68	6	be	be	VERB
ejpam-3226	68	7	the	the	DET
ejpam-3226	68	8	minimal	minimal	ADJ
ejpam-3226	68	9	polynomial	polynomial	NOUN
ejpam-3226	68	10	of	of	ADP
ejpam-3226	68	11	α	α	PROPN
ejpam-3226	68	12	over	over	ADP
ejpam-3226	68	13	k	k	PROPN
ejpam-3226	68	14	and	and	CCONJ
ejpam-3226	68	15	its	its	PRON
ejpam-3226	68	16	degree	degree	NOUN
ejpam-3226	69	1	d	d	NOUN
ejpam-3226	69	2	is	be	AUX
ejpam-3226	69	3	a	a	DET
ejpam-3226	69	4	divisor	divisor	NOUN
ejpam-3226	69	5	of	of	ADP
ejpam-3226	69	6	m.	m.	NOUN
ejpam-3226	69	7	then	then	ADV
ejpam-3226	69	8	g(x	g(x	NOUN
ejpam-3226	69	9	)	)	PUNCT
ejpam-3226	69	10	=	=	PUNCT
ejpam-3226	69	11	f(x)m	f(x)m	PROPN
ejpam-3226	69	12	/	/	SYM
ejpam-3226	69	13	d	d	PROPN
ejpam-3226	69	14	∈	∈	PROPN
ejpam-3226	69	15	k[x	k[x	PROPN
ejpam-3226	69	16	]	]	PUNCT
ejpam-3226	69	17	is	be	AUX
ejpam-3226	69	18	called	call	VERB
ejpam-3226	69	19	the	the	DET
ejpam-3226	69	20	characteristic	characteristic	ADJ
ejpam-3226	69	21	polynomial	polynomial	NOUN
ejpam-3226	69	22	of	of	ADP
ejpam-3226	69	23	α	α	PROPN
ejpam-3226	69	24	over	over	ADP
ejpam-3226	69	25	k.	k.	PROPN
ejpam-3226	69	26	by	by	ADP
ejpam-3226	69	27	theorem	theorem	NOUN
ejpam-3226	69	28	1	1	NUM
ejpam-3226	69	29	,	,	PUNCT
ejpam-3226	69	30	the	the	DET
ejpam-3226	69	31	roots	root	NOUN
ejpam-3226	69	32	of	of	ADP
ejpam-3226	69	33	f	f	PROPN
ejpam-3226	69	34	in	in	ADP
ejpam-3226	69	35	f	f	PROPN
ejpam-3226	69	36	are	be	AUX
ejpam-3226	69	37	given	give	VERB
ejpam-3226	69	38	by	by	ADP
ejpam-3226	69	39	α	α	NOUN
ejpam-3226	69	40	,	,	PUNCT
ejpam-3226	69	41	αq	αq	ADJ
ejpam-3226	69	42	,	,	PUNCT
ejpam-3226	69	43	αq2	αq2	NOUN
ejpam-3226	69	44	,	,	PUNCT
ejpam-3226	69	45	...	...	PUNCT
ejpam-3226	69	46	,	,	PUNCT
ejpam-3226	69	47	αqd−1	αqd−1	NOUN
ejpam-3226	69	48	and	and	CCONJ
ejpam-3226	69	49	by	by	ADP
ejpam-3226	69	50	definition	definition	NOUN
ejpam-3226	69	51	1	1	NUM
ejpam-3226	69	52	,	,	PUNCT
ejpam-3226	69	53	the	the	DET
ejpam-3226	69	54	roots	root	NOUN
ejpam-3226	69	55	of	of	ADP
ejpam-3226	69	56	g	g	NOUN
ejpam-3226	69	57	in	in	ADP
ejpam-3226	69	58	f	f	PROPN
ejpam-3226	69	59	are	be	AUX
ejpam-3226	69	60	precisely	precisely	ADV
ejpam-3226	69	61	the	the	DET
ejpam-3226	69	62	conjugates	conjugate	NOUN
ejpam-3226	69	63	of	of	ADP
ejpam-3226	69	64	α	α	NOUN
ejpam-3226	69	65	with	with	ADP
ejpam-3226	69	66	respect	respect	NOUN
ejpam-3226	69	67	to	to	ADP
ejpam-3226	69	68	k.	k.	PROPN
ejpam-3226	69	69	hence	hence	ADV
ejpam-3226	69	70	g(x	g(x	NOUN
ejpam-3226	69	71	)	)	PUNCT
ejpam-3226	70	1	=	=	SYM
ejpam-3226	70	2	xm	xm	PROPN
ejpam-3226	71	1	+	+	PUNCT
ejpam-3226	71	2	am−1x	am−1x	ADP
ejpam-3226	71	3	m−1	m−1	PROPN
ejpam-3226	71	4	+	+	CCONJ
ejpam-3226	71	5	...	...	PUNCT
ejpam-3226	72	1	+	+	CCONJ
ejpam-3226	72	2	a0	a0	NOUN
ejpam-3226	72	3	=	=	SYM
ejpam-3226	72	4	(	(	PUNCT
ejpam-3226	72	5	x−	x−	PROPN
ejpam-3226	72	6	α).(x−	α).(x−	PROPN
ejpam-3226	72	7	αq)	αq)	NUM
ejpam-3226	72	8	...	...	PUNCT
ejpam-3226	72	9	(x−	(x−	PUNCT
ejpam-3226	72	10	αqm−1	αqm−1	PROPN
ejpam-3226	72	11	)	)	PUNCT
ejpam-3226	72	12	(	(	PUNCT
ejpam-3226	72	13	1	1	X
ejpam-3226	72	14	)	)	PUNCT
ejpam-3226	72	15	and	and	CCONJ
ejpam-3226	72	16	a	a	DET
ejpam-3226	72	17	comparison	comparison	NOUN
ejpam-3226	72	18	of	of	ADP
ejpam-3226	72	19	coefficients	coefficient	NOUN
ejpam-3226	72	20	shows	show	VERB
ejpam-3226	72	21	that	that	SCONJ
ejpam-3226	72	22	trf	trf	PROPN
ejpam-3226	72	23	/	/	SYM
ejpam-3226	72	24	k	k	PROPN
ejpam-3226	72	25	(	(	PUNCT
ejpam-3226	72	26	α	α	NOUN
ejpam-3226	72	27	)	)	PUNCT
ejpam-3226	72	28	=	=	PUNCT
ejpam-3226	73	1	−am−1	−am−1	X
ejpam-3226	73	2	.	.	PUNCT
ejpam-3226	74	1	(	(	PUNCT
ejpam-3226	74	2	2	2	NUM
ejpam-3226	74	3	)	)	PUNCT
ejpam-3226	74	4	trf	trf	PROPN
ejpam-3226	74	5	/	/	SYM
ejpam-3226	74	6	k	k	PROPN
ejpam-3226	74	7	(	(	PUNCT
ejpam-3226	74	8	α	α	NOUN
ejpam-3226	74	9	)	)	PUNCT
ejpam-3226	74	10	is	be	AUX
ejpam-3226	74	11	always	always	ADV
ejpam-3226	74	12	an	an	DET
ejpam-3226	74	13	element	element	NOUN
ejpam-3226	74	14	of	of	ADP
ejpam-3226	74	15	k	k	PROPN
ejpam-3226	75	1	[	[	X
ejpam-3226	75	2	6	6	NUM
ejpam-3226	75	3	]	]	PUNCT
ejpam-3226	75	4	.	.	PUNCT
ejpam-3226	76	1	definition	definition	NOUN
ejpam-3226	76	2	3	3	NUM
ejpam-3226	76	3	.	.	PUNCT
ejpam-3226	76	4	for	for	ADP
ejpam-3226	76	5	α	α	DET
ejpam-3226	76	6	∈	∈	PROPN
ejpam-3226	76	7	f	f	PROPN
ejpam-3226	76	8	=	=	PUNCT
ejpam-3226	76	9	fqm	fqm	NOUN
ejpam-3226	76	10	and	and	CCONJ
ejpam-3226	76	11	k	k	NOUN
ejpam-3226	76	12	=	=	SYM
ejpam-3226	76	13	fq	fq	PROPN
ejpam-3226	76	14	,	,	PUNCT
ejpam-3226	76	15	the	the	DET
ejpam-3226	76	16	norm	norm	NOUN
ejpam-3226	76	17	nf	nf	PROPN
ejpam-3226	76	18	/	/	SYM
ejpam-3226	76	19	k(α	k(α	PROPN
ejpam-3226	76	20	)	)	PUNCT
ejpam-3226	76	21	of	of	ADP
ejpam-3226	76	22	α	α	PROPN
ejpam-3226	76	23	over	over	ADP
ejpam-3226	76	24	k	k	PROPN
ejpam-3226	76	25	is	be	AUX
ejpam-3226	76	26	defined	define	VERB
ejpam-3226	76	27	by	by	ADP
ejpam-3226	76	28	nf	nf	PROPN
ejpam-3226	76	29	/	/	SYM
ejpam-3226	76	30	k(α	k(α	PROPN
ejpam-3226	76	31	)	)	PUNCT
ejpam-3226	76	32	=	=	PUNCT
ejpam-3226	77	1	α.αq.αq2	α.αq.αq2	PUNCT
ejpam-3226	77	2	.....	.....	PUNCT
ejpam-3226	78	1	αqm−1	αqm−1	PROPN
ejpam-3226	78	2	=	=	SYM
ejpam-3226	78	3	αqm−1/(q	αqm−1/(q	PROPN
ejpam-3226	78	4	−	−	PROPN
ejpam-3226	78	5	1	1	NUM
ejpam-3226	78	6	)	)	PUNCT
ejpam-3226	78	7	.	.	PUNCT
ejpam-3226	79	1	moreover	moreover	ADV
ejpam-3226	79	2	,	,	PUNCT
ejpam-3226	79	3	by	by	ADP
ejpam-3226	79	4	comparing	compare	VERB
ejpam-3226	79	5	the	the	DET
ejpam-3226	79	6	constant	constant	ADJ
ejpam-3226	79	7	terms	term	NOUN
ejpam-3226	79	8	in	in	ADP
ejpam-3226	79	9	(	(	PUNCT
ejpam-3226	79	10	1	1	NUM
ejpam-3226	79	11	)	)	PUNCT
ejpam-3226	79	12	,	,	PUNCT
ejpam-3226	79	13	it	it	PRON
ejpam-3226	79	14	can	can	AUX
ejpam-3226	79	15	be	be	AUX
ejpam-3226	79	16	written	write	VERB
ejpam-3226	79	17	the	the	DET
ejpam-3226	79	18	following	follow	VERB
ejpam-3226	79	19	equation	equation	NOUN
ejpam-3226	79	20	:	:	PUNCT
ejpam-3226	79	21	nf	nf	X
ejpam-3226	79	22	/	/	SYM
ejpam-3226	79	23	k(α	k(α	PROPN
ejpam-3226	79	24	)	)	PUNCT
ejpam-3226	79	25	=	=	SYM
ejpam-3226	79	26	(	(	PUNCT
ejpam-3226	79	27	−1)m.a0	−1)m.a0	PROPN
ejpam-3226	79	28	.	.	PUNCT
ejpam-3226	80	1	nf	nf	PROPN
ejpam-3226	80	2	/	/	SYM
ejpam-3226	80	3	k(α	k(α	PROPN
ejpam-3226	80	4	)	)	PUNCT
ejpam-3226	80	5	is	be	AUX
ejpam-3226	80	6	also	also	ADV
ejpam-3226	80	7	an	an	DET
ejpam-3226	80	8	element	element	NOUN
ejpam-3226	80	9	of	of	ADP
ejpam-3226	80	10	k	k	PROPN
ejpam-3226	81	1	[	[	X
ejpam-3226	81	2	6	6	NUM
ejpam-3226	81	3	]	]	PUNCT
ejpam-3226	81	4	.	.	PUNCT
ejpam-3226	82	1	the	the	DET
ejpam-3226	82	2	number	number	NOUN
ejpam-3226	82	3	of	of	ADP
ejpam-3226	82	4	distinct	distinct	ADJ
ejpam-3226	82	5	bases	basis	NOUN
ejpam-3226	82	6	of	of	ADP
ejpam-3226	82	7	f	f	PROPN
ejpam-3226	82	8	over	over	ADP
ejpam-3226	82	9	k	k	PROPN
ejpam-3226	82	10	is	be	AUX
ejpam-3226	82	11	too	too	ADV
ejpam-3226	82	12	large	large	ADJ
ejpam-3226	82	13	,	,	PUNCT
ejpam-3226	82	14	but	but	CCONJ
ejpam-3226	82	15	there	there	PRON
ejpam-3226	82	16	are	be	VERB
ejpam-3226	82	17	two	two	NUM
ejpam-3226	82	18	special	special	ADJ
ejpam-3226	82	19	types	type	NOUN
ejpam-3226	82	20	of	of	ADP
ejpam-3226	82	21	bases	basis	NOUN
ejpam-3226	82	22	.	.	PUNCT
ejpam-3226	83	1	the	the	DET
ejpam-3226	83	2	first	first	ADJ
ejpam-3226	83	3	base	base	NOUN
ejpam-3226	83	4	is	be	AUX
ejpam-3226	83	5	a	a	DET
ejpam-3226	83	6	polynomial	polynomial	ADJ
ejpam-3226	83	7	basis	basis	NOUN
ejpam-3226	83	8	{	{	PUNCT
ejpam-3226	83	9	1	1	NUM
ejpam-3226	83	10	,	,	PUNCT
ejpam-3226	83	11	α	α	NOUN
ejpam-3226	83	12	,	,	PUNCT
ejpam-3226	83	13	α2	α2	ADJ
ejpam-3226	83	14	,	,	PUNCT
ejpam-3226	83	15	...	...	PUNCT
ejpam-3226	83	16	,	,	PUNCT
ejpam-3226	83	17	αm−1	αm−1	PROPN
ejpam-3226	83	18	}	}	PUNCT
ejpam-3226	83	19	,	,	PUNCT
ejpam-3226	83	20	made	make	VERB
ejpam-3226	83	21	up	up	ADP
ejpam-3226	83	22	of	of	ADP
ejpam-3226	83	23	the	the	DET
ejpam-3226	83	24	powers	power	NOUN
ejpam-3226	83	25	of	of	ADP
ejpam-3226	83	26	a	a	DET
ejpam-3226	83	27	defining	define	VERB
ejpam-3226	83	28	element	element	NOUN
ejpam-3226	83	29	α	α	NOUN
ejpam-3226	83	30	of	of	ADP
ejpam-3226	83	31	f	f	PROPN
ejpam-3226	83	32	over	over	ADP
ejpam-3226	83	33	k	k	PROPN
ejpam-3226	83	34	,	,	PUNCT
ejpam-3226	83	35	where	where	SCONJ
ejpam-3226	83	36	α	α	NOUN
ejpam-3226	83	37	is	be	AUX
ejpam-3226	83	38	taken	take	VERB
ejpam-3226	83	39	to	to	PART
ejpam-3226	83	40	be	be	AUX
ejpam-3226	83	41	a	a	DET
ejpam-3226	83	42	primitive	primitive	ADJ
ejpam-3226	83	43	element	element	NOUN
ejpam-3226	83	44	of	of	ADP
ejpam-3226	83	45	f	f	PROPN
ejpam-3226	83	46	.	.	PUNCT
ejpam-3226	84	1	another	another	DET
ejpam-3226	84	2	type	type	NOUN
ejpam-3226	84	3	of	of	ADP
ejpam-3226	84	4	basis	basis	NOUN
ejpam-3226	84	5	is	be	AUX
ejpam-3226	84	6	a	a	DET
ejpam-3226	84	7	normal	normal	ADJ
ejpam-3226	84	8	basis	basis	NOUN
ejpam-3226	84	9	.	.	PUNCT
ejpam-3226	85	1	definition	definition	NOUN
ejpam-3226	85	2	4	4	NUM
ejpam-3226	85	3	.	.	PUNCT
ejpam-3226	86	1	let	let	VERB
ejpam-3226	86	2	k	k	PROPN
ejpam-3226	86	3	=	=	SYM
ejpam-3226	86	4	fq	fq	PROPN
ejpam-3226	86	5	and	and	CCONJ
ejpam-3226	86	6	f	f	NOUN
ejpam-3226	86	7	=	=	PUNCT
ejpam-3226	86	8	fqm	fqm	NOUN
ejpam-3226	86	9	.	.	PUNCT
ejpam-3226	87	1	then	then	ADV
ejpam-3226	87	2	a	a	DET
ejpam-3226	87	3	basis	basis	NOUN
ejpam-3226	87	4	of	of	ADP
ejpam-3226	87	5	f	f	PROPN
ejpam-3226	87	6	over	over	ADP
ejpam-3226	87	7	k	k	PROPN
ejpam-3226	87	8	of	of	ADP
ejpam-3226	87	9	the	the	DET
ejpam-3226	87	10	form	form	NOUN
ejpam-3226	87	11	{	{	PUNCT
ejpam-3226	87	12	α	α	NOUN
ejpam-3226	87	13	,	,	PUNCT
ejpam-3226	87	14	αq	αq	ADJ
ejpam-3226	87	15	,	,	PUNCT
ejpam-3226	87	16	αq2	αq2	NOUN
ejpam-3226	87	17	,	,	PUNCT
ejpam-3226	87	18	...	...	PUNCT
ejpam-3226	87	19	,	,	PUNCT
ejpam-3226	87	20	αqm−1	αqm−1	PROPN
ejpam-3226	87	21	}	}	PUNCT
ejpam-3226	87	22	,	,	PUNCT
ejpam-3226	87	23	consisting	consist	VERB
ejpam-3226	87	24	of	of	ADP
ejpam-3226	87	25	a	a	DET
ejpam-3226	87	26	suitable	suitable	ADJ
ejpam-3226	87	27	element	element	NOUN
ejpam-3226	87	28	α	α	PROPN
ejpam-3226	87	29	∈	∈	PROPN
ejpam-3226	87	30	f	f	PROPN
ejpam-3226	87	31	and	and	CCONJ
ejpam-3226	87	32	its	its	PRON
ejpam-3226	87	33	conjugates	conjugate	NOUN
ejpam-3226	87	34	with	with	ADP
ejpam-3226	87	35	respect	respect	NOUN
ejpam-3226	87	36	to	to	ADP
ejpam-3226	87	37	k	k	NOUN
ejpam-3226	87	38	,	,	PUNCT
ejpam-3226	87	39	is	be	AUX
ejpam-3226	87	40	called	call	VERB
ejpam-3226	87	41	a	a	DET
ejpam-3226	87	42	normal	normal	ADJ
ejpam-3226	87	43	basis	basis	NOUN
ejpam-3226	87	44	of	of	ADP
ejpam-3226	87	45	f	f	PROPN
ejpam-3226	87	46	over	over	ADP
ejpam-3226	87	47	k	k	PROPN
ejpam-3226	88	1	[	[	X
ejpam-3226	88	2	6	6	NUM
ejpam-3226	88	3	]	]	PUNCT
ejpam-3226	88	4	.	.	PUNCT
ejpam-3226	89	1	2.3	2.3	NUM
ejpam-3226	89	2	.	.	PUNCT
ejpam-3226	90	1	secret	secret	ADJ
ejpam-3226	90	2	sharing	sharing	NOUN
ejpam-3226	90	3	schemes	scheme	NOUN
ejpam-3226	90	4	in	in	ADP
ejpam-3226	90	5	this	this	DET
ejpam-3226	90	6	section	section	NOUN
ejpam-3226	90	7	we	we	PRON
ejpam-3226	90	8	should	should	AUX
ejpam-3226	90	9	think	think	VERB
ejpam-3226	90	10	about	about	ADP
ejpam-3226	90	11	a	a	DET
ejpam-3226	90	12	case	case	NOUN
ejpam-3226	90	13	of	of	ADP
ejpam-3226	90	14	some	some	DET
ejpam-3226	90	15	malicious	malicious	ADJ
ejpam-3226	90	16	behaviors	behavior	NOUN
ejpam-3226	90	17	lying	lie	VERB
ejpam-3226	90	18	among	among	ADP
ejpam-3226	90	19	participants	participant	NOUN
ejpam-3226	90	20	which	which	PRON
ejpam-3226	90	21	are	be	AUX
ejpam-3226	90	22	called	call	VERB
ejpam-3226	90	23	cheaters	cheater	NOUN
ejpam-3226	90	24	.	.	PUNCT
ejpam-3226	91	1	they	they	PRON
ejpam-3226	91	2	modify	modify	VERB
ejpam-3226	91	3	their	their	PRON
ejpam-3226	91	4	shares	share	NOUN
ejpam-3226	91	5	in	in	ADP
ejpam-3226	91	6	order	order	NOUN
ejpam-3226	91	7	to	to	PART
ejpam-3226	91	8	cheat	cheat	VERB
ejpam-3226	91	9	.	.	PUNCT
ejpam-3226	92	1	if	if	SCONJ
ejpam-3226	92	2	a	a	DET
ejpam-3226	92	3	group	group	NOUN
ejpam-3226	92	4	of	of	ADP
ejpam-3226	92	5	participants	participant	NOUN
ejpam-3226	92	6	can	can	AUX
ejpam-3226	92	7	recover	recover	VERB
ejpam-3226	92	8	the	the	DET
ejpam-3226	92	9	secret	secret	NOUN
ejpam-3226	92	10	by	by	ADP
ejpam-3226	92	11	combining	combine	VERB
ejpam-3226	92	12	their	their	PRON
ejpam-3226	92	13	shares	share	NOUN
ejpam-3226	92	14	,	,	PUNCT
ejpam-3226	92	15	then	then	ADV
ejpam-3226	92	16	any	any	DET
ejpam-3226	92	17	group	group	NOUN
ejpam-3226	92	18	of	of	ADP
ejpam-3226	92	19	participants	participant	NOUN
ejpam-3226	92	20	containing	contain	VERB
ejpam-3226	92	21	this	this	DET
ejpam-3226	92	22	group	group	NOUN
ejpam-3226	92	23	can	can	AUX
ejpam-3226	92	24	also	also	ADV
ejpam-3226	92	25	recover	recover	VERB
ejpam-3226	92	26	the	the	DET
ejpam-3226	92	27	secret	secret	NOUN
ejpam-3226	92	28	.	.	PUNCT
ejpam-3226	93	1	definition	definition	NOUN
ejpam-3226	93	2	5	5	NUM
ejpam-3226	93	3	.	.	PUNCT
ejpam-3226	94	1	an	an	DET
ejpam-3226	94	2	access	access	NOUN
ejpam-3226	94	3	group	group	NOUN
ejpam-3226	94	4	is	be	AUX
ejpam-3226	94	5	a	a	DET
ejpam-3226	94	6	subset	subset	NOUN
ejpam-3226	94	7	of	of	ADP
ejpam-3226	94	8	a	a	DET
ejpam-3226	94	9	set	set	NOUN
ejpam-3226	94	10	of	of	ADP
ejpam-3226	94	11	participants	participant	NOUN
ejpam-3226	94	12	that	that	PRON
ejpam-3226	94	13	can	can	AUX
ejpam-3226	94	14	recover	recover	VERB
ejpam-3226	94	15	the	the	DET
ejpam-3226	94	16	secret	secret	NOUN
ejpam-3226	94	17	from	from	ADP
ejpam-3226	94	18	its	its	PRON
ejpam-3226	94	19	shares	share	NOUN
ejpam-3226	94	20	.	.	PUNCT
ejpam-3226	95	1	a	a	DET
ejpam-3226	95	2	collection	collection	NOUN
ejpam-3226	95	3	γ	γ	NOUN
ejpam-3226	95	4	of	of	ADP
ejpam-3226	95	5	access	access	NOUN
ejpam-3226	95	6	groups	group	NOUN
ejpam-3226	95	7	of	of	ADP
ejpam-3226	95	8	participants	participant	NOUN
ejpam-3226	95	9	is	be	AUX
ejpam-3226	95	10	called	call	VERB
ejpam-3226	95	11	an	an	DET
ejpam-3226	95	12	access	access	NOUN
ejpam-3226	95	13	s.	s.	PROPN
ejpam-3226	95	14	çalkavur	çalkavur	PROPN
ejpam-3226	95	15	/	/	SYM
ejpam-3226	95	16	eur	eur	PROPN
ejpam-3226	95	17	.	.	PUNCT
ejpam-3226	96	1	j.	j.	PROPN
ejpam-3226	96	2	pure	pure	PROPN
ejpam-3226	96	3	appl	appl	PROPN
ejpam-3226	96	4	.	.	PROPN
ejpam-3226	96	5	math	math	PROPN
ejpam-3226	96	6	,	,	PUNCT
ejpam-3226	96	7	11	11	NUM
ejpam-3226	96	8	(	(	PUNCT
ejpam-3226	96	9	2	2	NUM
ejpam-3226	96	10	)	)	PUNCT
ejpam-3226	96	11	(	(	PUNCT
ejpam-3226	96	12	2018	2018	NUM
ejpam-3226	96	13	)	)	PUNCT
ejpam-3226	96	14	,	,	PUNCT
ejpam-3226	96	15	410	410	NUM
ejpam-3226	96	16	-	-	SYM
ejpam-3226	96	17	416	416	NUM
ejpam-3226	96	18	413	413	NUM
ejpam-3226	96	19	structure	structure	NOUN
ejpam-3226	96	20	of	of	ADP
ejpam-3226	96	21	the	the	DET
ejpam-3226	96	22	scheme	scheme	NOUN
ejpam-3226	96	23	.	.	PUNCT
ejpam-3226	97	1	an	an	DET
ejpam-3226	97	2	element	element	NOUN
ejpam-3226	97	3	a	a	DET
ejpam-3226	97	4	∈	∈	NOUN
ejpam-3226	97	5	γ	γ	NOUN
ejpam-3226	97	6	is	be	AUX
ejpam-3226	97	7	called	call	VERB
ejpam-3226	97	8	a	a	DET
ejpam-3226	97	9	minimal	minimal	ADJ
ejpam-3226	97	10	access	access	NOUN
ejpam-3226	97	11	element	element	NOUN
ejpam-3226	97	12	.	.	PUNCT
ejpam-3226	98	1	hence	hence	ADV
ejpam-3226	98	2	a	a	DET
ejpam-3226	98	3	set	set	NOUN
ejpam-3226	98	4	is	be	AUX
ejpam-3226	98	5	a	a	DET
ejpam-3226	98	6	minimal	minimal	ADJ
ejpam-3226	98	7	access	access	NOUN
ejpam-3226	98	8	group	group	NOUN
ejpam-3226	98	9	if	if	SCONJ
ejpam-3226	98	10	it	it	PRON
ejpam-3226	98	11	can	can	AUX
ejpam-3226	98	12	recover	recover	VERB
ejpam-3226	98	13	the	the	DET
ejpam-3226	98	14	secret	secret	NOUN
ejpam-3226	98	15	but	but	CCONJ
ejpam-3226	98	16	no	no	DET
ejpam-3226	98	17	proper	proper	ADJ
ejpam-3226	98	18	subset	subset	NOUN
ejpam-3226	98	19	can	can	AUX
ejpam-3226	98	20	recover	recover	VERB
ejpam-3226	98	21	the	the	DET
ejpam-3226	98	22	secret	secret	NOUN
ejpam-3226	98	23	.	.	PUNCT
ejpam-3226	99	1	let	let	VERB
ejpam-3226	99	2	γ̄	γ̄	PROPN
ejpam-3226	99	3	be	be	AUX
ejpam-3226	99	4	the	the	DET
ejpam-3226	99	5	set	set	NOUN
ejpam-3226	99	6	of	of	ADP
ejpam-3226	99	7	all	all	DET
ejpam-3226	99	8	minimal	minimal	ADJ
ejpam-3226	99	9	access	access	NOUN
ejpam-3226	99	10	elements	element	NOUN
ejpam-3226	99	11	.	.	PUNCT
ejpam-3226	100	1	we	we	PRON
ejpam-3226	100	2	call	call	VERB
ejpam-3226	100	3	γ̄	γ̄	PROPN
ejpam-3226	100	4	the	the	DET
ejpam-3226	100	5	minimal	minimal	ADJ
ejpam-3226	100	6	access	access	NOUN
ejpam-3226	100	7	structure	structure	NOUN
ejpam-3226	100	8	[	[	X
ejpam-3226	100	9	5	5	NUM
ejpam-3226	100	10	]	]	PUNCT
ejpam-3226	100	11	.	.	PUNCT
ejpam-3226	101	1	determining	determine	VERB
ejpam-3226	101	2	the	the	DET
ejpam-3226	101	3	minimal	minimal	ADJ
ejpam-3226	101	4	access	access	NOUN
ejpam-3226	101	5	structure	structure	NOUN
ejpam-3226	101	6	is	be	AUX
ejpam-3226	101	7	a	a	DET
ejpam-3226	101	8	hard	hard	ADJ
ejpam-3226	101	9	problem	problem	NOUN
ejpam-3226	101	10	[	[	X
ejpam-3226	101	11	3	3	NUM
ejpam-3226	101	12	]	]	PUNCT
ejpam-3226	101	13	.	.	PUNCT
ejpam-3226	102	1	now	now	ADV
ejpam-3226	102	2	let	let	VERB
ejpam-3226	102	3	us	we	PRON
ejpam-3226	102	4	consider	consider	VERB
ejpam-3226	102	5	the	the	DET
ejpam-3226	102	6	accessibility	accessibility	NOUN
ejpam-3226	102	7	of	of	ADP
ejpam-3226	102	8	an	an	DET
ejpam-3226	102	9	access	access	NOUN
ejpam-3226	102	10	structure	structure	NOUN
ejpam-3226	102	11	of	of	ADP
ejpam-3226	102	12	secret	secret	ADJ
ejpam-3226	102	13	sharing	sharing	NOUN
ejpam-3226	102	14	scheme	scheme	NOUN
ejpam-3226	102	15	based	base	VERB
ejpam-3226	102	16	on	on	ADP
ejpam-3226	102	17	binary	binary	PROPN
ejpam-3226	102	18	linear	linear	PROPN
ejpam-3226	102	19	code	code	PROPN
ejpam-3226	102	20	.	.	PUNCT
ejpam-3226	103	1	let	let	VERB
ejpam-3226	103	2	p	p	NOUN
ejpam-3226	103	3	=	=	X
ejpam-3226	103	4	{	{	PUNCT
ejpam-3226	103	5	p1	p1	PROPN
ejpam-3226	103	6	,	,	PUNCT
ejpam-3226	103	7	p2	p2	NOUN
ejpam-3226	103	8	,	,	PUNCT
ejpam-3226	103	9	...	...	PUNCT
ejpam-3226	103	10	,	,	PUNCT
ejpam-3226	103	11	pm	pm	AUX
ejpam-3226	103	12	}	}	PUNCT
ejpam-3226	103	13	be	be	AUX
ejpam-3226	103	14	a	a	DET
ejpam-3226	103	15	set	set	NOUN
ejpam-3226	103	16	of	of	ADP
ejpam-3226	103	17	m	m	PROPN
ejpam-3226	103	18	participants	participant	NOUN
ejpam-3226	103	19	and	and	CCONJ
ejpam-3226	103	20	let	let	VERB
ejpam-3226	103	21	ap	ap	PROPN
ejpam-3226	103	22	be	be	AUX
ejpam-3226	103	23	the	the	DET
ejpam-3226	103	24	set	set	NOUN
ejpam-3226	103	25	of	of	ADP
ejpam-3226	103	26	all	all	DET
ejpam-3226	103	27	access	access	NOUN
ejpam-3226	103	28	elements	element	NOUN
ejpam-3226	103	29	on	on	ADP
ejpam-3226	103	30	p	p	PROPN
ejpam-3226	103	31	.	.	PUNCT
ejpam-3226	104	1	definition	definition	NOUN
ejpam-3226	104	2	6	6	NUM
ejpam-3226	104	3	.	.	PUNCT
ejpam-3226	105	1	the	the	DET
ejpam-3226	105	2	accessibility	accessibility	NOUN
ejpam-3226	105	3	index	index	NOUN
ejpam-3226	105	4	on	on	ADP
ejpam-3226	105	5	p	p	PROPN
ejpam-3226	105	6	is	be	AUX
ejpam-3226	105	7	the	the	DET
ejpam-3226	105	8	map	map	NOUN
ejpam-3226	105	9	δp(γ	δp(γ	NOUN
ejpam-3226	105	10	):	):	PUNCT
ejpam-3226	105	11	ap	ap	PROPN
ejpam-3226	105	12	→	→	SYM
ejpam-3226	105	13	r	r	NOUN
ejpam-3226	105	14	given	give	VERB
ejpam-3226	105	15	by	by	ADP
ejpam-3226	105	16	δp(γ	δp(γ	NOUN
ejpam-3226	105	17	)	)	PUNCT
ejpam-3226	105	18	=	=	SYM
ejpam-3226	106	1	|γ|	|γ|	PROPN
ejpam-3226	106	2	2	2	NUM
ejpam-3226	106	3	m	m	NOUN
ejpam-3226	106	4	for	for	ADP
ejpam-3226	106	5	γ	γ	PROPN
ejpam-3226	106	6	∈	∈	PROPN
ejpam-3226	106	7	ap	ap	PROPN
ejpam-3226	106	8	,	,	PUNCT
ejpam-3226	106	9	where	where	SCONJ
ejpam-3226	106	10	m	m	VERB
ejpam-3226	106	11	=	=	SYM
ejpam-3226	106	12	|p	|p	NOUN
ejpam-3226	106	13	|	|	ADV
ejpam-3226	106	14	.	.	PUNCT
ejpam-3226	107	1	the	the	DET
ejpam-3226	107	2	number	number	NOUN
ejpam-3226	107	3	δp(γ	δp(γ	NOUN
ejpam-3226	107	4	)	)	PUNCT
ejpam-3226	107	5	will	will	AUX
ejpam-3226	107	6	be	be	AUX
ejpam-3226	107	7	called	call	VERB
ejpam-3226	107	8	the	the	DET
ejpam-3226	107	9	accessibility	accessibility	NOUN
ejpam-3226	107	10	degree	degree	NOUN
ejpam-3226	107	11	of	of	ADP
ejpam-3226	107	12	structure	structure	NOUN
ejpam-3226	107	13	γ	γ	NOUN
ejpam-3226	107	14	[	[	X
ejpam-3226	107	15	2	2	NUM
ejpam-3226	107	16	]	]	PUNCT
ejpam-3226	107	17	.	.	PUNCT
ejpam-3226	108	1	3	3	X
ejpam-3226	108	2	.	.	PUNCT
ejpam-3226	109	1	the	the	DET
ejpam-3226	109	2	schemes	scheme	NOUN
ejpam-3226	109	3	in	in	ADP
ejpam-3226	109	4	this	this	DET
ejpam-3226	109	5	section	section	NOUN
ejpam-3226	109	6	,	,	PUNCT
ejpam-3226	109	7	we	we	PRON
ejpam-3226	109	8	present	present	VERB
ejpam-3226	109	9	the	the	DET
ejpam-3226	109	10	new	new	ADJ
ejpam-3226	109	11	(	(	PUNCT
ejpam-3226	109	12	t	t	PROPN
ejpam-3226	109	13	,	,	PUNCT
ejpam-3226	109	14	n)−	n)−	PROPN
ejpam-3226	109	15	threshold	threshold	VERB
ejpam-3226	109	16	schemes	scheme	NOUN
ejpam-3226	109	17	that	that	PRON
ejpam-3226	109	18	combine	combine	VERB
ejpam-3226	109	19	of	of	ADP
ejpam-3226	109	20	shamir	shamir	PROPN
ejpam-3226	109	21	scheme	scheme	NOUN
ejpam-3226	109	22	with	with	ADP
ejpam-3226	109	23	our	our	PRON
ejpam-3226	109	24	schemes	scheme	NOUN
ejpam-3226	109	25	.	.	PUNCT
ejpam-3226	110	1	3.1	3.1	NUM
ejpam-3226	110	2	.	.	PUNCT
ejpam-3226	110	3	first	first	ADJ
ejpam-3226	110	4	scheme	scheme	NOUN
ejpam-3226	110	5	let	let	VERB
ejpam-3226	110	6	fq	fq	PRON
ejpam-3226	110	7	be	be	AUX
ejpam-3226	110	8	the	the	DET
ejpam-3226	110	9	secret	secret	ADJ
ejpam-3226	110	10	space	space	NOUN
ejpam-3226	110	11	and	and	CCONJ
ejpam-3226	110	12	fqm	fqm	NOUN
ejpam-3226	110	13	be	be	AUX
ejpam-3226	110	14	the	the	DET
ejpam-3226	110	15	sharing	sharing	NOUN
ejpam-3226	110	16	space	space	NOUN
ejpam-3226	110	17	.	.	PUNCT
ejpam-3226	111	1	we	we	PRON
ejpam-3226	111	2	consider	consider	VERB
ejpam-3226	111	3	a	a	DET
ejpam-3226	111	4	finite	finite	ADJ
ejpam-3226	111	5	extension	extension	NOUN
ejpam-3226	111	6	of	of	ADP
ejpam-3226	111	7	fqm	fqm	NOUN
ejpam-3226	111	8	of	of	ADP
ejpam-3226	111	9	the	the	DET
ejpam-3226	111	10	finite	finite	ADJ
ejpam-3226	111	11	field	field	NOUN
ejpam-3226	111	12	fq	fq	PROPN
ejpam-3226	111	13	as	as	ADP
ejpam-3226	111	14	a	a	DET
ejpam-3226	111	15	vector	vector	NOUN
ejpam-3226	111	16	space	space	NOUN
ejpam-3226	111	17	over	over	ADP
ejpam-3226	111	18	fq	fq	PROPN
ejpam-3226	111	19	,	,	PUNCT
ejpam-3226	111	20	where	where	SCONJ
ejpam-3226	111	21	m	m	PROPN
ejpam-3226	111	22	is	be	AUX
ejpam-3226	111	23	the	the	DET
ejpam-3226	111	24	dimensional	dimensional	ADJ
ejpam-3226	111	25	of	of	ADP
ejpam-3226	111	26	fqm	fqm	NOUN
ejpam-3226	111	27	over	over	ADP
ejpam-3226	111	28	fq	fq	PROPN
ejpam-3226	111	29	.	.	PROPN
ejpam-3226	111	30	assume	assume	VERB
ejpam-3226	111	31	a	a	DET
ejpam-3226	111	32	characteristic	characteristic	ADJ
ejpam-3226	111	33	polynomial	polynomial	ADJ
ejpam-3226	111	34	g(x	g(x	NOUN
ejpam-3226	111	35	)	)	PUNCT
ejpam-3226	111	36	of	of	ADP
ejpam-3226	111	37	α	α	NOUN
ejpam-3226	111	38	,	,	PUNCT
ejpam-3226	111	39	where	where	SCONJ
ejpam-3226	111	40	α	α	PROPN
ejpam-3226	111	41	∈	∈	PROPN
ejpam-3226	111	42	fqm	fqm	NOUN
ejpam-3226	111	43	and	and	CCONJ
ejpam-3226	111	44	the	the	DET
ejpam-3226	111	45	degree	degree	NOUN
ejpam-3226	111	46	of	of	ADP
ejpam-3226	111	47	g(x	g(x	NOUN
ejpam-3226	111	48	)	)	PUNCT
ejpam-3226	111	49	is	be	AUX
ejpam-3226	111	50	m	m	VERB
ejpam-3226	111	51	such	such	ADJ
ejpam-3226	111	52	that	that	SCONJ
ejpam-3226	111	53	g(x	g(x	NOUN
ejpam-3226	111	54	)	)	PUNCT
ejpam-3226	112	1	=	=	SYM
ejpam-3226	112	2	xm	xm	PROPN
ejpam-3226	113	1	+	+	PUNCT
ejpam-3226	113	2	am−1x	am−1x	ADP
ejpam-3226	113	3	m−1	m−1	PROPN
ejpam-3226	113	4	+	+	CCONJ
ejpam-3226	113	5	...	...	PUNCT
ejpam-3226	114	1	+	+	CCONJ
ejpam-3226	114	2	a0	a0	PROPN
ejpam-3226	114	3	.	.	PROPN
ejpam-3226	114	4	•	•	NUM
ejpam-3226	114	5	let	let	VERB
ejpam-3226	114	6	all	all	PRON
ejpam-3226	114	7	of	of	ADP
ejpam-3226	114	8	elements	element	NOUN
ejpam-3226	114	9	of	of	ADP
ejpam-3226	114	10	fqm	fqm	NOUN
ejpam-3226	114	11	,	,	PUNCT
ejpam-3226	114	12	except	except	SCONJ
ejpam-3226	114	13	0	0	NUM
ejpam-3226	114	14	,	,	PUNCT
ejpam-3226	114	15	be	be	AUX
ejpam-3226	114	16	the	the	DET
ejpam-3226	114	17	participants	participant	NOUN
ejpam-3226	114	18	.	.	PUNCT
ejpam-3226	115	1	•	•	NUM
ejpam-3226	115	2	the	the	DET
ejpam-3226	115	3	dealer	dealer	NOUN
ejpam-3226	115	4	pics	pic	VERB
ejpam-3226	115	5	the	the	DET
ejpam-3226	115	6	element	element	NOUN
ejpam-3226	115	7	−am−1	−am−1	X
ejpam-3226	115	8	∈	∈	PROPN
ejpam-3226	115	9	fq	fq	PROPN
ejpam-3226	115	10	as	as	ADP
ejpam-3226	115	11	the	the	DET
ejpam-3226	115	12	secret	secret	NOUN
ejpam-3226	115	13	and	and	CCONJ
ejpam-3226	115	14	distributes	distribute	VERB
ejpam-3226	115	15	to	to	ADP
ejpam-3226	115	16	m	m	PROPN
ejpam-3226	115	17	elements	element	NOUN
ejpam-3226	115	18	of	of	ADP
ejpam-3226	115	19	fqm	fqm	NOUN
ejpam-3226	115	20	which	which	PRON
ejpam-3226	115	21	are	be	AUX
ejpam-3226	115	22	α	α	PRON
ejpam-3226	115	23	,	,	PUNCT
ejpam-3226	115	24	αq	αq	ADJ
ejpam-3226	115	25	,	,	PUNCT
ejpam-3226	115	26	αq2	αq2	NOUN
ejpam-3226	115	27	,	,	PUNCT
ejpam-3226	115	28	...	...	PUNCT
ejpam-3226	115	29	,	,	PUNCT
ejpam-3226	115	30	αqm−1	αqm−1	PROPN
ejpam-3226	115	31	.	.	PUNCT
ejpam-3226	116	1	we	we	PRON
ejpam-3226	116	2	know	know	VERB
ejpam-3226	116	3	that	that	SCONJ
ejpam-3226	116	4	these	these	DET
ejpam-3226	116	5	elements	element	NOUN
ejpam-3226	116	6	are	be	AUX
ejpam-3226	116	7	also	also	ADV
ejpam-3226	116	8	the	the	DET
ejpam-3226	116	9	normal	normal	ADJ
ejpam-3226	116	10	basis	basis	NOUN
ejpam-3226	116	11	elements	element	NOUN
ejpam-3226	116	12	of	of	ADP
ejpam-3226	116	13	fqm	fqm	NOUN
ejpam-3226	116	14	and	and	CCONJ
ejpam-3226	116	15	uniquely	uniquely	ADV
ejpam-3226	116	16	determined	determined	ADJ
ejpam-3226	116	17	and	and	CCONJ
ejpam-3226	116	18	each	each	DET
ejpam-3226	116	19	element	element	NOUN
ejpam-3226	116	20	of	of	ADP
ejpam-3226	116	21	fqm	fqm	NOUN
ejpam-3226	116	22	can	can	AUX
ejpam-3226	116	23	be	be	AUX
ejpam-3226	116	24	written	write	VERB
ejpam-3226	116	25	as	as	ADP
ejpam-3226	116	26	the	the	DET
ejpam-3226	116	27	linear	linear	ADJ
ejpam-3226	116	28	combination	combination	NOUN
ejpam-3226	116	29	of	of	ADP
ejpam-3226	116	30	basis	basis	NOUN
ejpam-3226	116	31	elements	element	NOUN
ejpam-3226	116	32	.	.	PUNCT
ejpam-3226	117	1	these	these	DET
ejpam-3226	117	2	m	m	VERB
ejpam-3226	117	3	participants	participant	NOUN
ejpam-3226	117	4	recover	recover	VERB
ejpam-3226	117	5	the	the	DET
ejpam-3226	117	6	secret	secret	NOUN
ejpam-3226	117	7	while	while	SCONJ
ejpam-3226	117	8	pooling	pool	VERB
ejpam-3226	117	9	their	their	PRON
ejpam-3226	117	10	shares	share	NOUN
ejpam-3226	117	11	.	.	PUNCT
ejpam-3226	118	1	in	in	ADP
ejpam-3226	118	2	the	the	DET
ejpam-3226	118	3	first	first	ADJ
ejpam-3226	118	4	scheme	scheme	NOUN
ejpam-3226	118	5	,	,	PUNCT
ejpam-3226	118	6	we	we	PRON
ejpam-3226	118	7	need	need	VERB
ejpam-3226	118	8	the	the	DET
ejpam-3226	118	9	trace	trace	NOUN
ejpam-3226	118	10	function	function	NOUN
ejpam-3226	118	11	of	of	ADP
ejpam-3226	118	12	α	α	PRON
ejpam-3226	118	13	to	to	PART
ejpam-3226	118	14	recover	recover	VERB
ejpam-3226	118	15	the	the	DET
ejpam-3226	118	16	secret	secret	NOUN
ejpam-3226	118	17	.	.	PUNCT
ejpam-3226	119	1	trf	trf	PROPN
ejpam-3226	119	2	/	/	SYM
ejpam-3226	119	3	k	k	PROPN
ejpam-3226	119	4	(	(	PUNCT
ejpam-3226	119	5	α	α	NOUN
ejpam-3226	119	6	)	)	PUNCT
ejpam-3226	119	7	=	=	NOUN
ejpam-3226	120	1	α+	α+	PUNCT
ejpam-3226	120	2	αq	αq	X
ejpam-3226	120	3	+	+	CCONJ
ejpam-3226	120	4	αq2	αq2	NOUN
ejpam-3226	120	5	+	+	CCONJ
ejpam-3226	120	6	...	...	PUNCT
ejpam-3226	121	1	+	+	CCONJ
ejpam-3226	121	2	αqm−1	αqm−1	PROPN
ejpam-3226	121	3	.	.	PUNCT
ejpam-3226	122	1	we	we	PRON
ejpam-3226	122	2	also	also	ADV
ejpam-3226	122	3	know	know	VERB
ejpam-3226	122	4	that	that	SCONJ
ejpam-3226	122	5	trf	trf	PROPN
ejpam-3226	122	6	/	/	SYM
ejpam-3226	122	7	k	k	PROPN
ejpam-3226	122	8	(	(	PUNCT
ejpam-3226	122	9	α	α	NOUN
ejpam-3226	122	10	)	)	PUNCT
ejpam-3226	122	11	is	be	AUX
ejpam-3226	122	12	also	also	ADV
ejpam-3226	122	13	equal	equal	ADJ
ejpam-3226	122	14	to	to	ADP
ejpam-3226	122	15	−am−1	−am−1	PROPN
ejpam-3226	122	16	,	,	PUNCT
ejpam-3226	122	17	where	where	SCONJ
ejpam-3226	122	18	−am−1	−am−1	PRON
ejpam-3226	122	19	is	be	AUX
ejpam-3226	122	20	the	the	DET
ejpam-3226	122	21	coefficient	coefficient	NOUN
ejpam-3226	122	22	of	of	ADP
ejpam-3226	122	23	xm−1	xm−1	PROPN
ejpam-3226	122	24	for	for	ADP
ejpam-3226	122	25	the	the	DET
ejpam-3226	122	26	characteristic	characteristic	ADJ
ejpam-3226	122	27	polynomial	polynomial	ADJ
ejpam-3226	122	28	g(x	g(x	NOUN
ejpam-3226	122	29	)	)	PUNCT
ejpam-3226	122	30	.	.	PUNCT
ejpam-3226	123	1	so	so	ADV
ejpam-3226	123	2	α	α	X
ejpam-3226	123	3	,	,	PUNCT
ejpam-3226	123	4	αq	αq	ADJ
ejpam-3226	123	5	,	,	PUNCT
ejpam-3226	123	6	αq2	αq2	NOUN
ejpam-3226	123	7	,	,	PUNCT
ejpam-3226	123	8	...	...	PUNCT
ejpam-3226	123	9	,	,	PUNCT
ejpam-3226	123	10	αqm−1	αqm−1	PROPN
ejpam-3226	123	11	elements	element	NOUN
ejpam-3226	123	12	can	can	AUX
ejpam-3226	123	13	reach	reach	VERB
ejpam-3226	123	14	the	the	DET
ejpam-3226	123	15	secret	secret	NOUN
ejpam-3226	123	16	together	together	ADV
ejpam-3226	123	17	.	.	PUNCT
ejpam-3226	124	1	s.	s.	PROPN
ejpam-3226	124	2	çalkavur	çalkavur	PROPN
ejpam-3226	124	3	/	/	SYM
ejpam-3226	124	4	eur	eur	PROPN
ejpam-3226	124	5	.	.	PUNCT
ejpam-3226	125	1	j.	j.	PROPN
ejpam-3226	125	2	pure	pure	PROPN
ejpam-3226	125	3	appl	appl	PROPN
ejpam-3226	125	4	.	.	PROPN
ejpam-3226	125	5	math	math	PROPN
ejpam-3226	125	6	,	,	PUNCT
ejpam-3226	125	7	11	11	NUM
ejpam-3226	125	8	(	(	PUNCT
ejpam-3226	125	9	2	2	NUM
ejpam-3226	125	10	)	)	PUNCT
ejpam-3226	125	11	(	(	PUNCT
ejpam-3226	125	12	2018	2018	NUM
ejpam-3226	125	13	)	)	PUNCT
ejpam-3226	125	14	,	,	PUNCT
ejpam-3226	125	15	410	410	NUM
ejpam-3226	125	16	-	-	SYM
ejpam-3226	125	17	416	416	NUM
ejpam-3226	125	18	414	414	NUM
ejpam-3226	125	19	3.2	3.2	NUM
ejpam-3226	125	20	.	.	PUNCT
ejpam-3226	126	1	second	second	ADJ
ejpam-3226	126	2	scheme	scheme	NOUN
ejpam-3226	126	3	now	now	ADV
ejpam-3226	126	4	we	we	PRON
ejpam-3226	126	5	construct	construct	VERB
ejpam-3226	126	6	another	another	DET
ejpam-3226	126	7	scheme	scheme	NOUN
ejpam-3226	126	8	using	use	VERB
ejpam-3226	126	9	the	the	DET
ejpam-3226	126	10	norm	norm	NOUN
ejpam-3226	126	11	function	function	NOUN
ejpam-3226	126	12	.	.	PUNCT
ejpam-3226	127	1	in	in	ADP
ejpam-3226	127	2	this	this	DET
ejpam-3226	127	3	scheme	scheme	NOUN
ejpam-3226	127	4	the	the	DET
ejpam-3226	127	5	dealer	dealer	NOUN
ejpam-3226	127	6	pics	pic	NOUN
ejpam-3226	127	7	the	the	DET
ejpam-3226	127	8	element	element	NOUN
ejpam-3226	127	9	(	(	PUNCT
ejpam-3226	127	10	−1)m.a0	−1)m.a0	PROPN
ejpam-3226	127	11	∈	∈	PROPN
ejpam-3226	127	12	fq	fq	PROPN
ejpam-3226	127	13	as	as	ADP
ejpam-3226	127	14	the	the	DET
ejpam-3226	127	15	secret	secret	NOUN
ejpam-3226	127	16	and	and	CCONJ
ejpam-3226	127	17	distributes	distribute	VERB
ejpam-3226	127	18	to	to	ADP
ejpam-3226	127	19	the	the	DET
ejpam-3226	127	20	m	m	ADJ
ejpam-3226	127	21	elements	element	NOUN
ejpam-3226	127	22	of	of	ADP
ejpam-3226	127	23	fqm	fqm	NOUN
ejpam-3226	127	24	which	which	PRON
ejpam-3226	127	25	are	be	AUX
ejpam-3226	127	26	α	α	PRON
ejpam-3226	127	27	,	,	PUNCT
ejpam-3226	127	28	αq	αq	ADJ
ejpam-3226	127	29	,	,	PUNCT
ejpam-3226	127	30	αq2	αq2	NOUN
ejpam-3226	127	31	,	,	PUNCT
ejpam-3226	127	32	...	...	PUNCT
ejpam-3226	127	33	,	,	PUNCT
ejpam-3226	127	34	αqm−1	αqm−1	PROPN
ejpam-3226	127	35	.	.	PUNCT
ejpam-3226	128	1	these	these	PRON
ejpam-3226	128	2	m	m	VERB
ejpam-3226	128	3	participants	participant	NOUN
ejpam-3226	128	4	recover	recover	VERB
ejpam-3226	128	5	the	the	DET
ejpam-3226	128	6	secret	secret	NOUN
ejpam-3226	128	7	while	while	SCONJ
ejpam-3226	128	8	combining	combine	VERB
ejpam-3226	128	9	their	their	PRON
ejpam-3226	128	10	shares	share	NOUN
ejpam-3226	128	11	as	as	SCONJ
ejpam-3226	128	12	follows	follow	VERB
ejpam-3226	128	13	.	.	PUNCT
ejpam-3226	129	1	nf	nf	X
ejpam-3226	129	2	/	/	SYM
ejpam-3226	129	3	k(α	k(α	PROPN
ejpam-3226	129	4	)	)	PUNCT
ejpam-3226	129	5	=	=	PUNCT
ejpam-3226	130	1	α.αq.αq2	α.αq.αq2	PUNCT
ejpam-3226	130	2	.....	.....	PUNCT
ejpam-3226	130	3	αqm−1	αqm−1	PROPN
ejpam-3226	130	4	.	.	PUNCT
ejpam-3226	131	1	we	we	PRON
ejpam-3226	131	2	know	know	VERB
ejpam-3226	131	3	that	that	SCONJ
ejpam-3226	131	4	nf	nf	PROPN
ejpam-3226	131	5	/	/	SYM
ejpam-3226	131	6	k(α	k(α	PROPN
ejpam-3226	131	7	)	)	PUNCT
ejpam-3226	131	8	is	be	AUX
ejpam-3226	131	9	also	also	ADV
ejpam-3226	131	10	equal	equal	ADJ
ejpam-3226	131	11	to	to	ADP
ejpam-3226	131	12	(	(	PUNCT
ejpam-3226	131	13	−1)ma0	−1)ma0	NOUN
ejpam-3226	131	14	.	.	PUNCT
ejpam-3226	132	1	so	so	ADV
ejpam-3226	132	2	α	α	X
ejpam-3226	132	3	,	,	PUNCT
ejpam-3226	132	4	αq	αq	ADJ
ejpam-3226	132	5	,	,	PUNCT
ejpam-3226	132	6	αq2	αq2	NOUN
ejpam-3226	132	7	,	,	PUNCT
ejpam-3226	132	8	...	...	PUNCT
ejpam-3226	132	9	,	,	PUNCT
ejpam-3226	132	10	αqm−1	αqm−1	PROPN
ejpam-3226	132	11	elements	element	NOUN
ejpam-3226	132	12	can	can	AUX
ejpam-3226	132	13	reach	reach	VERB
ejpam-3226	132	14	the	the	DET
ejpam-3226	132	15	secret	secret	NOUN
ejpam-3226	132	16	together	together	ADV
ejpam-3226	132	17	.	.	PUNCT
ejpam-3226	133	1	if	if	SCONJ
ejpam-3226	133	2	m	m	VERB
ejpam-3226	133	3	−	−	PROPN
ejpam-3226	133	4	h	h	NOUN
ejpam-3226	133	5	say	say	VERB
ejpam-3226	133	6	,	,	PUNCT
ejpam-3226	133	7	with	with	ADP
ejpam-3226	133	8	1	1	NUM
ejpam-3226	133	9	≤	≤	NUM
ejpam-3226	133	10	h	h	NOUN
ejpam-3226	133	11	<	<	X
ejpam-3226	133	12	m	m	PROPN
ejpam-3226	133	13	,	,	PUNCT
ejpam-3226	133	14	participants	participant	NOUN
ejpam-3226	133	15	group	group	NOUN
ejpam-3226	133	16	together	together	ADV
ejpam-3226	133	17	they	they	PRON
ejpam-3226	133	18	can	can	AUX
ejpam-3226	133	19	guess	guess	VERB
ejpam-3226	133	20	the	the	DET
ejpam-3226	133	21	secret	secret	NOUN
ejpam-3226	133	22	with	with	ADP
ejpam-3226	133	23	probability	probability	NOUN
ejpam-3226	133	24	1	1	NUM
ejpam-3226	133	25	h+1	h+1	NOUN
ejpam-3226	133	26	≤	≤	NUM
ejpam-3226	133	27	1	1	NUM
ejpam-3226	133	28	2	2	NUM
ejpam-3226	133	29	.	.	PUNCT
ejpam-3226	134	1	another	another	DET
ejpam-3226	134	2	possible	possible	ADJ
ejpam-3226	134	3	attack	attack	NOUN
ejpam-3226	134	4	would	would	AUX
ejpam-3226	134	5	be	be	AUX
ejpam-3226	134	6	to	to	PART
ejpam-3226	134	7	isolate	isolate	VERB
ejpam-3226	134	8	elements	element	NOUN
ejpam-3226	134	9	of	of	ADP
ejpam-3226	134	10	fqm	fqm	NOUN
ejpam-3226	134	11	which	which	PRON
ejpam-3226	134	12	are	be	AUX
ejpam-3226	134	13	reached	reach	VERB
ejpam-3226	134	14	the	the	DET
ejpam-3226	134	15	secret	secret	NOUN
ejpam-3226	134	16	.	.	PUNCT
ejpam-3226	135	1	in	in	ADP
ejpam-3226	135	2	our	our	PRON
ejpam-3226	135	3	secret	secret	ADJ
ejpam-3226	135	4	sharing	sharing	NOUN
ejpam-3226	135	5	schemes	scheme	NOUN
ejpam-3226	135	6	,	,	PUNCT
ejpam-3226	135	7	only	only	ADV
ejpam-3226	135	8	the	the	DET
ejpam-3226	135	9	conjugates	conjugate	NOUN
ejpam-3226	135	10	of	of	ADP
ejpam-3226	135	11	α	α	NOUN
ejpam-3226	135	12	with	with	ADP
ejpam-3226	135	13	respect	respect	NOUN
ejpam-3226	135	14	to	to	ADP
ejpam-3226	135	15	fq	fq	PROPN
ejpam-3226	135	16	can	can	AUX
ejpam-3226	135	17	recover	recover	VERB
ejpam-3226	135	18	the	the	DET
ejpam-3226	135	19	secret	secret	NOUN
ejpam-3226	135	20	.	.	PUNCT
ejpam-3226	136	1	these	these	DET
ejpam-3226	136	2	elements	element	NOUN
ejpam-3226	136	3	are	be	AUX
ejpam-3226	136	4	also	also	ADV
ejpam-3226	136	5	the	the	DET
ejpam-3226	136	6	normal	normal	ADJ
ejpam-3226	136	7	basis	basis	NOUN
ejpam-3226	136	8	elements	element	NOUN
ejpam-3226	136	9	which	which	PRON
ejpam-3226	136	10	are	be	AUX
ejpam-3226	136	11	uniquely	uniquely	ADV
ejpam-3226	136	12	determined	determine	VERB
ejpam-3226	136	13	.	.	PUNCT
ejpam-3226	137	1	theorem	theorem	NOUN
ejpam-3226	137	2	3	3	NUM
ejpam-3226	137	3	.	.	PUNCT
ejpam-3226	138	1	in	in	ADP
ejpam-3226	138	2	these	these	DET
ejpam-3226	138	3	secret	secret	ADJ
ejpam-3226	138	4	sharing	sharing	NOUN
ejpam-3226	138	5	schemes	scheme	NOUN
ejpam-3226	138	6	based	base	VERB
ejpam-3226	138	7	on	on	ADP
ejpam-3226	138	8	extension	extension	NOUN
ejpam-3226	138	9	fields	field	NOUN
ejpam-3226	138	10	we	we	PRON
ejpam-3226	138	11	have	have	VERB
ejpam-3226	138	12	the	the	DET
ejpam-3226	138	13	following	following	NOUN
ejpam-3226	138	14	.	.	PUNCT
ejpam-3226	139	1	i	i	PRON
ejpam-3226	139	2	)	)	PUNCT
ejpam-3226	139	3	the	the	DET
ejpam-3226	139	4	access	access	NOUN
ejpam-3226	139	5	structure	structure	NOUN
ejpam-3226	139	6	consists	consist	VERB
ejpam-3226	139	7	of	of	ADP
ejpam-3226	139	8	the	the	DET
ejpam-3226	139	9	m	m	PROPN
ejpam-3226	139	10	elements	element	NOUN
ejpam-3226	139	11	.	.	PUNCT
ejpam-3226	140	1	ii	ii	X
ejpam-3226	140	2	)	)	PUNCT
ejpam-3226	140	3	no	no	DET
ejpam-3226	140	4	element	element	NOUN
ejpam-3226	140	5	of	of	ADP
ejpam-3226	140	6	number	number	NOUN
ejpam-3226	140	7	less	less	ADJ
ejpam-3226	140	8	than	than	SCONJ
ejpam-3226	140	9	m	m	PROPN
ejpam-3226	140	10	can	can	AUX
ejpam-3226	140	11	be	be	AUX
ejpam-3226	140	12	used	use	VERB
ejpam-3226	140	13	in	in	ADP
ejpam-3226	140	14	recovering	recover	VERB
ejpam-3226	140	15	the	the	DET
ejpam-3226	140	16	secret	secret	NOUN
ejpam-3226	140	17	.	.	PUNCT
ejpam-3226	141	1	proof	proof	NOUN
ejpam-3226	141	2	.	.	PUNCT
ejpam-3226	142	1	i	i	PRON
ejpam-3226	142	2	)	)	PUNCT
ejpam-3226	142	3	the	the	DET
ejpam-3226	142	4	secret	secret	NOUN
ejpam-3226	142	5	is	be	AUX
ejpam-3226	142	6	recovered	recover	VERB
ejpam-3226	142	7	thanks	thank	NOUN
ejpam-3226	142	8	to	to	ADP
ejpam-3226	142	9	the	the	DET
ejpam-3226	142	10	normal	normal	ADJ
ejpam-3226	142	11	basis	basis	NOUN
ejpam-3226	142	12	elements	element	NOUN
ejpam-3226	142	13	and	and	CCONJ
ejpam-3226	142	14	their	their	PRON
ejpam-3226	142	15	number	number	NOUN
ejpam-3226	142	16	is	be	AUX
ejpam-3226	142	17	m.	m.	PROPN
ejpam-3226	142	18	ii	ii	PROPN
ejpam-3226	142	19	)	)	PUNCT
ejpam-3226	142	20	these	these	DET
ejpam-3226	142	21	m	m	VERB
ejpam-3226	142	22	elements	element	NOUN
ejpam-3226	142	23	are	be	AUX
ejpam-3226	142	24	uniquely	uniquely	ADV
ejpam-3226	142	25	determined	determine	VERB
ejpam-3226	142	26	.	.	PUNCT
ejpam-3226	143	1	so	so	ADV
ejpam-3226	143	2	there	there	PRON
ejpam-3226	143	3	is	be	VERB
ejpam-3226	143	4	no	no	DET
ejpam-3226	143	5	element	element	NOUN
ejpam-3226	143	6	which	which	PRON
ejpam-3226	143	7	has	have	VERB
ejpam-3226	143	8	this	this	DET
ejpam-3226	143	9	property	property	NOUN
ejpam-3226	143	10	.	.	PUNCT
ejpam-3226	144	1	the	the	DET
ejpam-3226	144	2	proof	proof	NOUN
ejpam-3226	144	3	is	be	AUX
ejpam-3226	144	4	clear	clear	ADJ
ejpam-3226	144	5	.	.	PUNCT
ejpam-3226	145	1	corollary	corollary	ADJ
ejpam-3226	145	2	3	3	NUM
ejpam-3226	145	3	.	.	PUNCT
ejpam-3226	146	1	with	with	ADP
ejpam-3226	146	2	the	the	DET
ejpam-3226	146	3	above	above	ADJ
ejpam-3226	146	4	condition	condition	NOUN
ejpam-3226	146	5	the	the	DET
ejpam-3226	146	6	extension	extension	NOUN
ejpam-3226	146	7	field	field	NOUN
ejpam-3226	146	8	fqm	fqm	VERB
ejpam-3226	146	9	determines	determine	NOUN
ejpam-3226	146	10	(	(	PUNCT
ejpam-3226	146	11	m	m	PROPN
ejpam-3226	146	12	,	,	PUNCT
ejpam-3226	146	13	qm	qm	PROPN
ejpam-3226	146	14	−	−	NOUN
ejpam-3226	146	15	1)−threshold	1)−threshold	ADJ
ejpam-3226	146	16	scheme	scheme	NOUN
ejpam-3226	146	17	.	.	PUNCT
ejpam-3226	147	1	proof	proof	NOUN
ejpam-3226	147	2	.	.	PUNCT
ejpam-3226	148	1	it	it	PRON
ejpam-3226	148	2	is	be	AUX
ejpam-3226	148	3	clear	clear	ADJ
ejpam-3226	148	4	that	that	SCONJ
ejpam-3226	148	5	the	the	DET
ejpam-3226	148	6	number	number	NOUN
ejpam-3226	148	7	of	of	ADP
ejpam-3226	148	8	non	non	ADJ
ejpam-3226	148	9	-	-	ADJ
ejpam-3226	148	10	zero	zero	NUM
ejpam-3226	148	11	elements	element	NOUN
ejpam-3226	148	12	of	of	ADP
ejpam-3226	148	13	fqm	fqm	NOUN
ejpam-3226	148	14	is	be	AUX
ejpam-3226	148	15	qm	qm	PROPN
ejpam-3226	148	16	−	−	PROPN
ejpam-3226	148	17	1	1	NUM
ejpam-3226	148	18	and	and	CCONJ
ejpam-3226	148	19	the	the	DET
ejpam-3226	148	20	number	number	NOUN
ejpam-3226	148	21	of	of	ADP
ejpam-3226	148	22	normal	normal	ADJ
ejpam-3226	148	23	basis	basis	NOUN
ejpam-3226	148	24	elements	element	NOUN
ejpam-3226	148	25	is	be	AUX
ejpam-3226	148	26	m.	m.	NOUN
ejpam-3226	148	27	these	these	DET
ejpam-3226	148	28	m	m	NOUN
ejpam-3226	148	29	elements	element	NOUN
ejpam-3226	148	30	out	out	ADP
ejpam-3226	148	31	of	of	ADP
ejpam-3226	148	32	qm	qm	PROPN
ejpam-3226	148	33	−	−	PROPN
ejpam-3226	148	34	1	1	NUM
ejpam-3226	148	35	can	can	AUX
ejpam-3226	148	36	reach	reach	VERB
ejpam-3226	148	37	the	the	DET
ejpam-3226	148	38	secret	secret	NOUN
ejpam-3226	148	39	together	together	ADV
ejpam-3226	148	40	.	.	PUNCT
ejpam-3226	149	1	definition	definition	NOUN
ejpam-3226	149	2	7	7	NUM
ejpam-3226	149	3	.	.	PUNCT
ejpam-3226	150	1	the	the	DET
ejpam-3226	150	2	access	access	NOUN
ejpam-3226	150	3	structure	structure	NOUN
ejpam-3226	150	4	of	of	ADP
ejpam-3226	150	5	these	these	DET
ejpam-3226	150	6	secret	secret	ADJ
ejpam-3226	150	7	sharing	sharing	NOUN
ejpam-3226	150	8	schemes	scheme	NOUN
ejpam-3226	150	9	is	be	AUX
ejpam-3226	150	10	given	give	VERB
ejpam-3226	150	11	by	by	ADP
ejpam-3226	150	12	γ	γ	X
ejpam-3226	150	13	=	=	SYM
ejpam-3226	150	14	{	{	PUNCT
ejpam-3226	150	15	(	(	PUNCT
ejpam-3226	150	16	αk	αk	NOUN
ejpam-3226	150	17	,	,	PUNCT
ejpam-3226	150	18	β)|k	β)|k	NOUN
ejpam-3226	150	19	=	=	NOUN
ejpam-3226	150	20	1	1	NUM
ejpam-3226	150	21	,	,	PUNCT
ejpam-3226	150	22	q	q	NOUN
ejpam-3226	150	23	,	,	PUNCT
ejpam-3226	150	24	q2	q2	NOUN
ejpam-3226	150	25	,	,	PUNCT
ejpam-3226	150	26	...	...	PUNCT
ejpam-3226	150	27	,	,	PUNCT
ejpam-3226	150	28	qm−1	qm−1	NOUN
ejpam-3226	150	29	,	,	PUNCT
ejpam-3226	150	30	β	β	X
ejpam-3226	150	31	∈	∈	PROPN
ejpam-3226	150	32	fqm	fqm	NOUN
ejpam-3226	150	33	}	}	PUNCT
ejpam-3226	150	34	.	.	PUNCT
ejpam-3226	151	1	theorem	theorem	VERB
ejpam-3226	151	2	4	4	NUM
ejpam-3226	151	3	.	.	PUNCT
ejpam-3226	152	1	the	the	DET
ejpam-3226	152	2	number	number	NOUN
ejpam-3226	152	3	of	of	ADP
ejpam-3226	152	4	parties	party	NOUN
ejpam-3226	152	5	in	in	ADP
ejpam-3226	152	6	these	these	DET
ejpam-3226	152	7	secret	secret	ADJ
ejpam-3226	152	8	sharing	sharing	NOUN
ejpam-3226	152	9	schemes	scheme	NOUN
ejpam-3226	152	10	is	be	AUX
ejpam-3226	152	11	qm	qm	PROPN
ejpam-3226	152	12	−	−	PROPN
ejpam-3226	152	13	1	1	NUM
ejpam-3226	152	14	and	and	CCONJ
ejpam-3226	152	15	the	the	DET
ejpam-3226	152	16	access	access	NOUN
ejpam-3226	152	17	structure	structure	NOUN
ejpam-3226	152	18	has	have	VERB
ejpam-3226	152	19	the	the	DET
ejpam-3226	152	20	following	follow	VERB
ejpam-3226	152	21	properties	property	NOUN
ejpam-3226	152	22	:	:	PUNCT
ejpam-3226	152	23	i	i	NOUN
ejpam-3226	152	24	)	)	PUNCT
ejpam-3226	152	25	only	only	ADV
ejpam-3226	152	26	m	m	VERB
ejpam-3226	152	27	elements	element	NOUN
ejpam-3226	152	28	can	can	AUX
ejpam-3226	152	29	be	be	AUX
ejpam-3226	152	30	used	use	VERB
ejpam-3226	152	31	to	to	PART
ejpam-3226	152	32	recover	recover	VERB
ejpam-3226	152	33	the	the	DET
ejpam-3226	152	34	secret	secret	NOUN
ejpam-3226	152	35	but	but	CCONJ
ejpam-3226	152	36	(	(	PUNCT
ejpam-3226	152	37	m−	m−	PROPN
ejpam-3226	152	38	1	1	NUM
ejpam-3226	152	39	)	)	PUNCT
ejpam-3226	152	40	can	can	AUX
ejpam-3226	152	41	not	not	PART
ejpam-3226	152	42	.	.	PUNCT
ejpam-3226	153	1	ii	ii	X
ejpam-3226	153	2	)	)	PUNCT
ejpam-3226	153	3	when	when	SCONJ
ejpam-3226	153	4	the	the	DET
ejpam-3226	153	5	parties	party	NOUN
ejpam-3226	153	6	come	come	VERB
ejpam-3226	153	7	together	together	ADV
ejpam-3226	153	8	,	,	PUNCT
ejpam-3226	153	9	up	up	ADP
ejpam-3226	153	10	to	to	ADP
ejpam-3226	153	11	[	[	X
ejpam-3226	153	12	m2	m2	X
ejpam-3226	153	13	]	]	X
ejpam-3226	153	14	cheaters	cheater	NOUN
ejpam-3226	153	15	can	can	AUX
ejpam-3226	153	16	be	be	AUX
ejpam-3226	153	17	found	find	VERB
ejpam-3226	153	18	in	in	ADP
ejpam-3226	153	19	each	each	DET
ejpam-3226	153	20	group	group	NOUN
ejpam-3226	153	21	.	.	PUNCT
ejpam-3226	154	1	(	(	PUNCT
ejpam-3226	154	2	”	"	PUNCT
ejpam-3226	154	3	[	[	X
ejpam-3226	154	4	x	x	X
ejpam-3226	154	5	]	]	X
ejpam-3226	154	6	”	"	PUNCT
ejpam-3226	154	7	denotes	denote	VERB
ejpam-3226	154	8	the	the	DET
ejpam-3226	154	9	greatest	great	ADJ
ejpam-3226	154	10	integer	integer	NOUN
ejpam-3226	154	11	less	less	ADJ
ejpam-3226	154	12	than	than	ADP
ejpam-3226	154	13	or	or	CCONJ
ejpam-3226	154	14	equal	equal	ADJ
ejpam-3226	154	15	to	to	ADP
ejpam-3226	154	16	x.	x.	NOUN
ejpam-3226	154	17	)	)	PUNCT
ejpam-3226	154	18	proof	proof	NOUN
ejpam-3226	154	19	.	.	PUNCT
ejpam-3226	155	1	i	i	PRON
ejpam-3226	155	2	)	)	PUNCT
ejpam-3226	156	1	it	it	PRON
ejpam-3226	156	2	is	be	AUX
ejpam-3226	156	3	seen	see	VERB
ejpam-3226	156	4	that	that	SCONJ
ejpam-3226	156	5	by	by	ADP
ejpam-3226	156	6	definition	definition	NOUN
ejpam-3226	156	7	7	7	NUM
ejpam-3226	156	8	.	.	SYM
ejpam-3226	156	9	ii	ii	PROPN
ejpam-3226	156	10	)	)	PUNCT
ejpam-3226	156	11	by	by	ADP
ejpam-3226	156	12	definition	definition	NOUN
ejpam-3226	156	13	of	of	ADP
ejpam-3226	156	14	our	our	PRON
ejpam-3226	156	15	scheme	scheme	NOUN
ejpam-3226	156	16	is	be	AUX
ejpam-3226	156	17	2	2	NUM
ejpam-3226	156	18	≤	≤	NUM
ejpam-3226	156	19	m	m	VERB
ejpam-3226	156	20	iff	iff	PROPN
ejpam-3226	156	21	1	1	NUM
ejpam-3226	156	22	≤	≤	NUM
ejpam-3226	156	23	m	m	VERB
ejpam-3226	156	24	2	2	NUM
ejpam-3226	156	25	.	.	PUNCT
ejpam-3226	157	1	s.	s.	PROPN
ejpam-3226	157	2	çalkavur	çalkavur	PROPN
ejpam-3226	157	3	/	/	SYM
ejpam-3226	157	4	eur	eur	PROPN
ejpam-3226	157	5	.	.	PUNCT
ejpam-3226	158	1	j.	j.	PROPN
ejpam-3226	158	2	pure	pure	PROPN
ejpam-3226	158	3	appl	appl	PROPN
ejpam-3226	158	4	.	.	PROPN
ejpam-3226	158	5	math	math	PROPN
ejpam-3226	158	6	,	,	PUNCT
ejpam-3226	158	7	11	11	NUM
ejpam-3226	158	8	(	(	PUNCT
ejpam-3226	158	9	2	2	NUM
ejpam-3226	158	10	)	)	PUNCT
ejpam-3226	158	11	(	(	PUNCT
ejpam-3226	158	12	2018	2018	NUM
ejpam-3226	158	13	)	)	PUNCT
ejpam-3226	158	14	,	,	PUNCT
ejpam-3226	158	15	410	410	NUM
ejpam-3226	158	16	-	-	SYM
ejpam-3226	158	17	416	416	NUM
ejpam-3226	158	18	415	415	NUM
ejpam-3226	158	19	the	the	DET
ejpam-3226	158	20	accessibility	accessibility	NOUN
ejpam-3226	158	21	degree	degree	NOUN
ejpam-3226	158	22	of	of	ADP
ejpam-3226	158	23	the	the	DET
ejpam-3226	158	24	access	access	NOUN
ejpam-3226	158	25	structure	structure	NOUN
ejpam-3226	158	26	for	for	ADP
ejpam-3226	158	27	these	these	DET
ejpam-3226	158	28	secret	secret	ADJ
ejpam-3226	158	29	sharing	sharing	NOUN
ejpam-3226	158	30	schemes	scheme	NOUN
ejpam-3226	158	31	based	base	VERB
ejpam-3226	158	32	on	on	ADP
ejpam-3226	158	33	extension	extension	NOUN
ejpam-3226	158	34	fields	field	NOUN
ejpam-3226	158	35	over	over	ADP
ejpam-3226	158	36	finite	finite	ADJ
ejpam-3226	158	37	fields	field	NOUN
ejpam-3226	158	38	can	can	AUX
ejpam-3226	158	39	be	be	AUX
ejpam-3226	158	40	defined	define	VERB
ejpam-3226	158	41	as	as	ADP
ejpam-3226	158	42	follows	follow	VERB
ejpam-3226	158	43	.	.	PUNCT
ejpam-3226	159	1	definition	definition	NOUN
ejpam-3226	159	2	8	8	NUM
ejpam-3226	159	3	.	.	PUNCT
ejpam-3226	160	1	the	the	DET
ejpam-3226	160	2	accessibility	accessibility	NOUN
ejpam-3226	160	3	index	index	NOUN
ejpam-3226	160	4	on	on	ADP
ejpam-3226	160	5	p	p	PROPN
ejpam-3226	160	6	is	be	AUX
ejpam-3226	160	7	the	the	DET
ejpam-3226	160	8	map	map	NOUN
ejpam-3226	160	9	δp(γ):ap	δp(γ):ap	NOUN
ejpam-3226	160	10	→	→	PUNCT
ejpam-3226	160	11	r	r	NOUN
ejpam-3226	160	12	given	give	VERB
ejpam-3226	160	13	by	by	ADP
ejpam-3226	160	14	δp(γ	δp(γ	NOUN
ejpam-3226	160	15	)	)	PUNCT
ejpam-3226	160	16	=	=	PUNCT
ejpam-3226	161	1	|γ|	|γ|	VERB
ejpam-3226	161	2	qm	qm	NOUN
ejpam-3226	161	3	−	−	NOUN
ejpam-3226	161	4	1	1	NUM
ejpam-3226	161	5	,	,	PUNCT
ejpam-3226	161	6	for	for	ADP
ejpam-3226	161	7	γ	γ	PROPN
ejpam-3226	161	8	∈	∈	PROPN
ejpam-3226	161	9	ap	ap	PROPN
ejpam-3226	161	10	,	,	PUNCT
ejpam-3226	161	11	where	where	SCONJ
ejpam-3226	161	12	m	m	VERB
ejpam-3226	161	13	=	=	VERB
ejpam-3226	161	14	|p	|p	PUNCT
ejpam-3226	161	15	|	|	ADV
ejpam-3226	161	16	is	be	AUX
ejpam-3226	161	17	the	the	DET
ejpam-3226	161	18	number	number	NOUN
ejpam-3226	161	19	of	of	ADP
ejpam-3226	161	20	participants	participant	NOUN
ejpam-3226	161	21	in	in	ADP
ejpam-3226	161	22	the	the	DET
ejpam-3226	161	23	access	access	NOUN
ejpam-3226	161	24	structure	structure	NOUN
ejpam-3226	161	25	.	.	PUNCT
ejpam-3226	162	1	the	the	DET
ejpam-3226	162	2	number	number	NOUN
ejpam-3226	162	3	δp(γ	δp(γ	NOUN
ejpam-3226	162	4	)	)	PUNCT
ejpam-3226	162	5	will	will	AUX
ejpam-3226	162	6	be	be	AUX
ejpam-3226	162	7	called	call	VERB
ejpam-3226	162	8	the	the	DET
ejpam-3226	162	9	accessibility	accessibility	NOUN
ejpam-3226	162	10	degree	degree	NOUN
ejpam-3226	162	11	of	of	ADP
ejpam-3226	162	12	structure	structure	NOUN
ejpam-3226	162	13	γ	γ	PROPN
ejpam-3226	162	14	.	.	PROPN
ejpam-3226	162	15	example	example	NOUN
ejpam-3226	163	1	1	1	NUM
ejpam-3226	163	2	.	.	PUNCT
ejpam-3226	164	1	let	let	VERB
ejpam-3226	164	2	f23	f23	PROPN
ejpam-3226	164	3	be	be	AUX
ejpam-3226	164	4	the	the	DET
ejpam-3226	164	5	secret	secret	ADJ
ejpam-3226	164	6	sharing	sharing	NOUN
ejpam-3226	164	7	space	space	NOUN
ejpam-3226	164	8	.	.	PUNCT
ejpam-3226	165	1	this	this	DET
ejpam-3226	165	2	space	space	NOUN
ejpam-3226	165	3	is	be	AUX
ejpam-3226	165	4	also	also	ADV
ejpam-3226	165	5	m−dimensional	m−dimensional	ADJ
ejpam-3226	165	6	vector	vector	NOUN
ejpam-3226	165	7	space	space	NOUN
ejpam-3226	165	8	over	over	ADP
ejpam-3226	165	9	f2	f2	PROPN
ejpam-3226	165	10	.	.	PUNCT
ejpam-3226	166	1	consider	consider	VERB
ejpam-3226	166	2	the	the	DET
ejpam-3226	166	3	polynomial	polynomial	ADJ
ejpam-3226	166	4	f(x	f(x	PROPN
ejpam-3226	166	5	)	)	PUNCT
ejpam-3226	167	1	=	=	PUNCT
ejpam-3226	168	1	x3	x3	VERB
ejpam-3226	169	1	+	+	NOUN
ejpam-3226	169	2	x2	x2	PROPN
ejpam-3226	169	3	+1	+1	PROPN
ejpam-3226	169	4	∈	∈	PROPN
ejpam-3226	169	5	f2[x	f2[x	NOUN
ejpam-3226	169	6	]	]	PUNCT
ejpam-3226	169	7	.	.	PUNCT
ejpam-3226	170	1	the	the	DET
ejpam-3226	170	2	coefficients	coefficient	NOUN
ejpam-3226	170	3	of	of	ADP
ejpam-3226	170	4	polynomial	polynomial	ADJ
ejpam-3226	170	5	are	be	AUX
ejpam-3226	170	6	a0	a0	NOUN
ejpam-3226	170	7	=	=	SYM
ejpam-3226	170	8	1	1	NUM
ejpam-3226	170	9	,	,	PUNCT
ejpam-3226	170	10	a1	a1	NOUN
ejpam-3226	170	11	=	=	SYM
ejpam-3226	170	12	1	1	NUM
ejpam-3226	170	13	,	,	PUNCT
ejpam-3226	170	14	a2	a2	NOUN
ejpam-3226	170	15	=	=	NOUN
ejpam-3226	170	16	1	1	X
ejpam-3226	170	17	.	.	PUNCT
ejpam-3226	171	1	so	so	ADV
ejpam-3226	171	2	the	the	DET
ejpam-3226	171	3	secret	secret	NOUN
ejpam-3226	171	4	is	be	AUX
ejpam-3226	171	5	−a2	−a2	NOUN
ejpam-3226	171	6	=	=	PUNCT
ejpam-3226	171	7	−1	−1	NOUN
ejpam-3226	171	8	=	=	SYM
ejpam-3226	171	9	1	1	NUM
ejpam-3226	171	10	and	and	CCONJ
ejpam-3226	171	11	m	m	PROPN
ejpam-3226	171	12	=	=	SYM
ejpam-3226	171	13	3	3	NUM
ejpam-3226	171	14	,	,	PUNCT
ejpam-3226	171	15	q	q	NOUN
ejpam-3226	171	16	=	=	NOUN
ejpam-3226	171	17	2	2	X
ejpam-3226	171	18	.	.	PUNCT
ejpam-3226	172	1	the	the	DET
ejpam-3226	172	2	normal	normal	ADJ
ejpam-3226	172	3	basis	basis	NOUN
ejpam-3226	172	4	elements	element	NOUN
ejpam-3226	172	5	of	of	ADP
ejpam-3226	172	6	fqm	fqm	NOUN
ejpam-3226	172	7	are	be	AUX
ejpam-3226	172	8	α	α	PRON
ejpam-3226	172	9	,	,	PUNCT
ejpam-3226	172	10	α2	α2	ADJ
ejpam-3226	172	11	,	,	PUNCT
ejpam-3226	172	12	α23−1	α23−1	NOUN
ejpam-3226	173	1	=	=	SYM
ejpam-3226	173	2	α4	α4	NOUN
ejpam-3226	173	3	.	.	PUNCT
ejpam-3226	174	1	it	it	PRON
ejpam-3226	174	2	is	be	AUX
ejpam-3226	174	3	clear	clear	ADJ
ejpam-3226	174	4	that	that	SCONJ
ejpam-3226	174	5	α0	α0	ADJ
ejpam-3226	174	6	=	=	SYM
ejpam-3226	174	7	1	1	NUM
ejpam-3226	174	8	,	,	PUNCT
ejpam-3226	174	9	α1	α1	PROPN
ejpam-3226	174	10	=	=	SYM
ejpam-3226	174	11	α	α	PROPN
ejpam-3226	174	12	,	,	PUNCT
ejpam-3226	174	13	α2	α2	NOUN
ejpam-3226	174	14	=	=	SYM
ejpam-3226	174	15	α2	α2	PROPN
ejpam-3226	174	16	,	,	PUNCT
ejpam-3226	174	17	α3	α3	NOUN
ejpam-3226	174	18	=	=	SYM
ejpam-3226	174	19	α2	α2	PROPN
ejpam-3226	174	20	+	+	CCONJ
ejpam-3226	174	21	1	1	NUM
ejpam-3226	174	22	,	,	PUNCT
ejpam-3226	174	23	α4	α4	NOUN
ejpam-3226	174	24	=	=	SYM
ejpam-3226	174	25	α3	α3	PROPN
ejpam-3226	174	26	+	+	CCONJ
ejpam-3226	174	27	α	α	NOUN
ejpam-3226	174	28	=	=	SYM
ejpam-3226	174	29	α2	α2	PROPN
ejpam-3226	175	1	+	+	CCONJ
ejpam-3226	175	2	α+	α+	PUNCT
ejpam-3226	175	3	1	1	NUM
ejpam-3226	175	4	,	,	PUNCT
ejpam-3226	175	5	α5	α5	NOUN
ejpam-3226	175	6	=	=	SYM
ejpam-3226	175	7	α3	α3	PROPN
ejpam-3226	175	8	+	+	CCONJ
ejpam-3226	175	9	α2	α2	ADJ
ejpam-3226	175	10	+	+	CCONJ
ejpam-3226	175	11	α	α	NOUN
ejpam-3226	175	12	=	=	SYM
ejpam-3226	175	13	α+	α+	PUNCT
ejpam-3226	175	14	1	1	NUM
ejpam-3226	175	15	,	,	PUNCT
ejpam-3226	175	16	α6	α6	NOUN
ejpam-3226	175	17	=	=	SYM
ejpam-3226	175	18	α2	α2	PROPN
ejpam-3226	175	19	+	+	CCONJ
ejpam-3226	175	20	α	α	NOUN
ejpam-3226	175	21	,	,	PUNCT
ejpam-3226	175	22	α7	α7	NOUN
ejpam-3226	175	23	=	=	SYM
ejpam-3226	175	24	α3	α3	PROPN
ejpam-3226	175	25	+	+	CCONJ
ejpam-3226	175	26	α2	α2	ADJ
ejpam-3226	175	27	=	=	SYM
ejpam-3226	175	28	1	1	X
ejpam-3226	175	29	.	.	PUNCT
ejpam-3226	176	1	all	all	DET
ejpam-3226	176	2	the	the	DET
ejpam-3226	176	3	sharings	sharing	NOUN
ejpam-3226	176	4	are	be	AUX
ejpam-3226	176	5	k1	k1	NOUN
ejpam-3226	176	6	=	=	SYM
ejpam-3226	176	7	(	(	PUNCT
ejpam-3226	176	8	α0	α0	ADJ
ejpam-3226	176	9	,	,	PUNCT
ejpam-3226	176	10	1	1	NUM
ejpam-3226	176	11	)	)	PUNCT
ejpam-3226	176	12	,	,	PUNCT
ejpam-3226	176	13	k2	k2	NOUN
ejpam-3226	176	14	=	=	SYM
ejpam-3226	176	15	(	(	PUNCT
ejpam-3226	176	16	α1	α1	PROPN
ejpam-3226	176	17	,	,	PUNCT
ejpam-3226	176	18	α	α	NOUN
ejpam-3226	176	19	)	)	PUNCT
ejpam-3226	176	20	,	,	PUNCT
ejpam-3226	176	21	k3	k3	PROPN
ejpam-3226	176	22	=	=	SYM
ejpam-3226	176	23	(	(	PUNCT
ejpam-3226	176	24	α2	α2	ADJ
ejpam-3226	176	25	,	,	PUNCT
ejpam-3226	176	26	α2	α2	PROPN
ejpam-3226	176	27	)	)	PUNCT
ejpam-3226	176	28	,	,	PUNCT
ejpam-3226	176	29	k4	k4	NOUN
ejpam-3226	176	30	=	=	SYM
ejpam-3226	176	31	(	(	PUNCT
ejpam-3226	176	32	α3	α3	NOUN
ejpam-3226	176	33	,	,	PUNCT
ejpam-3226	176	34	α2	α2	PROPN
ejpam-3226	176	35	+	+	CCONJ
ejpam-3226	176	36	1	1	NUM
ejpam-3226	176	37	)	)	PUNCT
ejpam-3226	176	38	,	,	PUNCT
ejpam-3226	176	39	k5	k5	PROPN
ejpam-3226	176	40	=	=	PUNCT
ejpam-3226	176	41	(	(	PUNCT
ejpam-3226	176	42	α4	α4	PROPN
ejpam-3226	176	43	,	,	PUNCT
ejpam-3226	176	44	α2	α2	PROPN
ejpam-3226	176	45	+	+	CCONJ
ejpam-3226	176	46	α+	α+	PUNCT
ejpam-3226	176	47	1	1	NUM
ejpam-3226	176	48	)	)	PUNCT
ejpam-3226	176	49	,	,	PUNCT
ejpam-3226	176	50	k6	k6	NOUN
ejpam-3226	176	51	=	=	SYM
ejpam-3226	176	52	(	(	PUNCT
ejpam-3226	176	53	α6	α6	NOUN
ejpam-3226	176	54	,	,	PUNCT
ejpam-3226	176	55	α2	α2	PROPN
ejpam-3226	176	56	+	+	CCONJ
ejpam-3226	176	57	α	α	X
ejpam-3226	176	58	)	)	PUNCT
ejpam-3226	176	59	,	,	PUNCT
ejpam-3226	176	60	k7	k7	PROPN
ejpam-3226	176	61	=	=	PUNCT
ejpam-3226	176	62	(	(	PUNCT
ejpam-3226	176	63	α7	α7	NOUN
ejpam-3226	176	64	,	,	PUNCT
ejpam-3226	176	65	1	1	NUM
ejpam-3226	176	66	)	)	PUNCT
ejpam-3226	176	67	.	.	PUNCT
ejpam-3226	177	1	k2,k3	k2,k3	PROPN
ejpam-3226	177	2	and	and	CCONJ
ejpam-3226	177	3	k5	k5	PROPN
ejpam-3226	177	4	participants	participant	NOUN
ejpam-3226	177	5	recover	recover	VERB
ejpam-3226	177	6	the	the	DET
ejpam-3226	177	7	secret	secret	NOUN
ejpam-3226	177	8	while	while	SCONJ
ejpam-3226	177	9	combining	combine	VERB
ejpam-3226	177	10	their	their	PRON
ejpam-3226	177	11	shares	share	NOUN
ejpam-3226	177	12	by	by	ADP
ejpam-3226	177	13	using	use	VERB
ejpam-3226	177	14	the	the	DET
ejpam-3226	177	15	trace	trace	NOUN
ejpam-3226	177	16	function	function	NOUN
ejpam-3226	177	17	of	of	ADP
ejpam-3226	177	18	α	α	PROPN
ejpam-3226	177	19	as	as	SCONJ
ejpam-3226	177	20	follows	follow	VERB
ejpam-3226	177	21	.	.	PUNCT
ejpam-3226	178	1	trf	trf	PROPN
ejpam-3226	178	2	/	/	SYM
ejpam-3226	178	3	k	k	PROPN
ejpam-3226	178	4	(	(	PUNCT
ejpam-3226	178	5	α	α	NOUN
ejpam-3226	178	6	)	)	PUNCT
ejpam-3226	178	7	=	=	SYM
ejpam-3226	178	8	α+	α+	PUNCT
ejpam-3226	178	9	α2	α2	ADJ
ejpam-3226	178	10	+	+	CCONJ
ejpam-3226	178	11	α4	α4	NOUN
ejpam-3226	178	12	=	=	SYM
ejpam-3226	178	13	α+	α+	PUNCT
ejpam-3226	178	14	α2	α2	PROPN
ejpam-3226	178	15	+	+	CCONJ
ejpam-3226	178	16	(	(	PUNCT
ejpam-3226	178	17	α2	α2	ADJ
ejpam-3226	178	18	+	+	CCONJ
ejpam-3226	178	19	α+	α+	PUNCT
ejpam-3226	178	20	1	1	X
ejpam-3226	178	21	)	)	PUNCT
ejpam-3226	178	22	=	=	SYM
ejpam-3226	179	1	1	1	X
ejpam-3226	179	2	.	.	PUNCT
ejpam-3226	180	1	now	now	ADV
ejpam-3226	180	2	we	we	PRON
ejpam-3226	180	3	assume	assume	VERB
ejpam-3226	180	4	that	that	SCONJ
ejpam-3226	180	5	the	the	DET
ejpam-3226	180	6	secret	secret	NOUN
ejpam-3226	180	7	is	be	AUX
ejpam-3226	180	8	(	(	PUNCT
ejpam-3226	180	9	−1)3.a0	−1)3.a0	PROPN
ejpam-3226	180	10	=	=	PUNCT
ejpam-3226	180	11	(	(	PUNCT
ejpam-3226	180	12	−1).1	−1).1	PRON
ejpam-3226	180	13	=	=	SYM
ejpam-3226	180	14	−1	−1	NOUN
ejpam-3226	180	15	=	=	SYM
ejpam-3226	180	16	1	1	NUM
ejpam-3226	180	17	and	and	CCONJ
ejpam-3226	180	18	the	the	DET
ejpam-3226	180	19	same	same	ADJ
ejpam-3226	180	20	participants	participant	NOUN
ejpam-3226	180	21	recover	recover	VERB
ejpam-3226	180	22	the	the	DET
ejpam-3226	180	23	secret	secret	NOUN
ejpam-3226	180	24	calculating	calculate	VERB
ejpam-3226	180	25	the	the	DET
ejpam-3226	180	26	norm	norm	NOUN
ejpam-3226	180	27	of	of	ADP
ejpam-3226	180	28	α	α	NOUN
ejpam-3226	180	29	as	as	SCONJ
ejpam-3226	180	30	follows	follow	VERB
ejpam-3226	180	31	.	.	PUNCT
ejpam-3226	181	1	nf	nf	X
ejpam-3226	181	2	/	/	SYM
ejpam-3226	181	3	k(α	k(α	PROPN
ejpam-3226	181	4	)	)	PUNCT
ejpam-3226	181	5	=	=	SYM
ejpam-3226	181	6	α.α2.α2	α.α2.α2	NOUN
ejpam-3226	181	7	=	=	SYM
ejpam-3226	181	8	α3.α4	α3.α4	NOUN
ejpam-3226	181	9	=	=	SYM
ejpam-3226	181	10	(	(	PUNCT
ejpam-3226	181	11	α2	α2	ADJ
ejpam-3226	181	12	+	+	CCONJ
ejpam-3226	181	13	1).(α2	1).(α2	NUM
ejpam-3226	181	14	+	+	CCONJ
ejpam-3226	181	15	α+	α+	PUNCT
ejpam-3226	181	16	1	1	X
ejpam-3226	181	17	)	)	PUNCT
ejpam-3226	181	18	=	=	SYM
ejpam-3226	182	1	1	1	X
ejpam-3226	182	2	.	.	PUNCT
ejpam-3226	182	3	as	as	SCONJ
ejpam-3226	182	4	it	it	PRON
ejpam-3226	182	5	is	be	AUX
ejpam-3226	182	6	seen	see	VERB
ejpam-3226	182	7	that	that	SCONJ
ejpam-3226	182	8	both	both	PRON
ejpam-3226	182	9	of	of	ADP
ejpam-3226	182	10	these	these	DET
ejpam-3226	182	11	schemes	scheme	NOUN
ejpam-3226	182	12	are	be	AUX
ejpam-3226	182	13	the	the	DET
ejpam-3226	182	14	(	(	PUNCT
ejpam-3226	182	15	3	3	NUM
ejpam-3226	182	16	,	,	PUNCT
ejpam-3226	182	17	7)−threshold	7)−threshold	PROPN
ejpam-3226	182	18	schemes	scheme	NOUN
ejpam-3226	182	19	.	.	PUNCT
ejpam-3226	183	1	the	the	DET
ejpam-3226	183	2	accessibility	accessibility	NOUN
ejpam-3226	183	3	degree	degree	NOUN
ejpam-3226	183	4	of	of	ADP
ejpam-3226	183	5	the	the	DET
ejpam-3226	183	6	access	access	NOUN
ejpam-3226	183	7	structure	structure	NOUN
ejpam-3226	183	8	is	be	AUX
ejpam-3226	183	9	3	3	NUM
ejpam-3226	183	10	23−1	23−1	NUM
ejpam-3226	183	11	=	=	NOUN
ejpam-3226	183	12	3	3	NUM
ejpam-3226	183	13	7	7	NUM
ejpam-3226	183	14	=	=	SYM
ejpam-3226	183	15	0	0	NUM
ejpam-3226	183	16	,	,	PUNCT
ejpam-3226	183	17	42	42	NUM
ejpam-3226	183	18	.	.	NOUN
ejpam-3226	184	1	4	4	NUM
ejpam-3226	184	2	.	.	X
ejpam-3226	184	3	conclusion	conclusion	NOUN
ejpam-3226	184	4	in	in	ADP
ejpam-3226	184	5	the	the	DET
ejpam-3226	184	6	present	present	ADJ
ejpam-3226	184	7	article	article	NOUN
ejpam-3226	184	8	we	we	PRON
ejpam-3226	184	9	constructed	construct	VERB
ejpam-3226	184	10	some	some	PRON
ejpam-3226	184	11	(	(	PUNCT
ejpam-3226	184	12	t	t	PROPN
ejpam-3226	184	13	,	,	PUNCT
ejpam-3226	184	14	n)−threshold	n)−threshold	ADJ
ejpam-3226	184	15	schemes	scheme	NOUN
ejpam-3226	184	16	using	use	VERB
ejpam-3226	184	17	the	the	DET
ejpam-3226	184	18	trace	trace	NOUN
ejpam-3226	184	19	and	and	CCONJ
ejpam-3226	184	20	norm	norm	NOUN
ejpam-3226	184	21	functions	function	NOUN
ejpam-3226	184	22	.	.	PUNCT
ejpam-3226	185	1	these	these	DET
ejpam-3226	185	2	schemes	scheme	NOUN
ejpam-3226	185	3	are	be	AUX
ejpam-3226	185	4	mainly	mainly	ADV
ejpam-3226	185	5	based	base	VERB
ejpam-3226	185	6	on	on	ADP
ejpam-3226	185	7	finite	finite	ADJ
ejpam-3226	185	8	extensions	extension	NOUN
ejpam-3226	185	9	over	over	ADP
ejpam-3226	185	10	finite	finite	ADJ
ejpam-3226	185	11	fields	field	NOUN
ejpam-3226	185	12	.	.	PUNCT
ejpam-3226	186	1	references	reference	NOUN
ejpam-3226	186	2	416	416	NUM
ejpam-3226	186	3	we	we	PRON
ejpam-3226	186	4	introduced	introduce	VERB
ejpam-3226	186	5	the	the	DET
ejpam-3226	186	6	access	access	NOUN
ejpam-3226	186	7	structure	structure	NOUN
ejpam-3226	186	8	of	of	ADP
ejpam-3226	186	9	these	these	DET
ejpam-3226	186	10	schemes	scheme	NOUN
ejpam-3226	186	11	.	.	PUNCT
ejpam-3226	187	1	we	we	PRON
ejpam-3226	187	2	defined	define	VERB
ejpam-3226	187	3	the	the	DET
ejpam-3226	187	4	accessibility	accessibility	NOUN
ejpam-3226	187	5	degree	degree	NOUN
ejpam-3226	187	6	of	of	ADP
ejpam-3226	187	7	the	the	DET
ejpam-3226	187	8	access	access	NOUN
ejpam-3226	187	9	structure	structure	NOUN
ejpam-3226	187	10	.	.	PUNCT
ejpam-3226	188	1	we	we	PRON
ejpam-3226	188	2	obtained	obtain	VERB
ejpam-3226	188	3	the	the	DET
ejpam-3226	188	4	new	new	ADJ
ejpam-3226	188	5	results	result	NOUN
ejpam-3226	188	6	.	.	PUNCT
ejpam-3226	189	1	possible	possible	ADJ
ejpam-3226	189	2	attacks	attack	NOUN
ejpam-3226	189	3	have	have	AUX
ejpam-3226	189	4	been	be	AUX
ejpam-3226	189	5	considered	consider	VERB
ejpam-3226	189	6	.	.	PUNCT
ejpam-3226	190	1	our	our	PRON
ejpam-3226	190	2	scheme	scheme	NOUN
ejpam-3226	190	3	has	have	VERB
ejpam-3226	190	4	the	the	DET
ejpam-3226	190	5	same	same	ADJ
ejpam-3226	190	6	distributed	distribute	VERB
ejpam-3226	190	7	as	as	ADP
ejpam-3226	190	8	shamir	shamir	NOUN
ejpam-3226	190	9	’s	’s	PART
ejpam-3226	190	10	scheme	scheme	NOUN
ejpam-3226	190	11	does	do	AUX
ejpam-3226	190	12	.	.	PUNCT
ejpam-3226	191	1	we	we	PRON
ejpam-3226	191	2	send	send	VERB
ejpam-3226	191	3	an	an	DET
ejpam-3226	191	4	element	element	NOUN
ejpam-3226	191	5	of	of	ADP
ejpam-3226	191	6	fq	fq	PROPN
ejpam-3226	191	7	and	and	CCONJ
ejpam-3226	191	8	the	the	DET
ejpam-3226	191	9	normal	normal	ADJ
ejpam-3226	191	10	basis	basis	NOUN
ejpam-3226	191	11	elements	element	NOUN
ejpam-3226	191	12	of	of	ADP
ejpam-3226	191	13	fqm	fqm	NOUN
ejpam-3226	191	14	use	use	VERB
ejpam-3226	191	15	the	the	DET
ejpam-3226	191	16	trace	trace	NOUN
ejpam-3226	191	17	and	and	CCONJ
ejpam-3226	191	18	norm	norm	NOUN
ejpam-3226	191	19	functions	function	NOUN
ejpam-3226	191	20	to	to	PART
ejpam-3226	191	21	recover	recover	VERB
ejpam-3226	191	22	the	the	DET
ejpam-3226	191	23	secret	secret	NOUN
ejpam-3226	191	24	.	.	PUNCT
ejpam-3226	192	1	the	the	DET
ejpam-3226	192	2	secret	secret	NOUN
ejpam-3226	192	3	can	can	AUX
ejpam-3226	192	4	be	be	AUX
ejpam-3226	192	5	recovered	recover	VERB
ejpam-3226	192	6	only	only	ADV
ejpam-3226	192	7	by	by	ADP
ejpam-3226	192	8	the	the	DET
ejpam-3226	192	9	special	special	ADJ
ejpam-3226	192	10	participants	participant	NOUN
ejpam-3226	192	11	which	which	PRON
ejpam-3226	192	12	are	be	AUX
ejpam-3226	192	13	uniquely	uniquely	ADV
ejpam-3226	192	14	determined	determined	ADJ
ejpam-3226	192	15	.	.	PUNCT
ejpam-3226	193	1	this	this	PRON
ejpam-3226	193	2	means	mean	VERB
ejpam-3226	193	3	the	the	DET
ejpam-3226	193	4	access	access	NOUN
ejpam-3226	193	5	structure	structure	NOUN
ejpam-3226	193	6	of	of	ADP
ejpam-3226	193	7	these	these	DET
ejpam-3226	193	8	schemes	scheme	NOUN
ejpam-3226	193	9	is	be	AUX
ejpam-3226	193	10	very	very	ADV
ejpam-3226	193	11	strong	strong	ADJ
ejpam-3226	193	12	and	and	CCONJ
ejpam-3226	193	13	reliable	reliable	ADJ
ejpam-3226	193	14	.	.	PUNCT
ejpam-3226	194	1	references	reference	NOUN
ejpam-3226	194	2	[	[	X
ejpam-3226	194	3	1	1	NUM
ejpam-3226	194	4	]	]	X
ejpam-3226	194	5	blakley	blakley	PROPN
ejpam-3226	194	6	,	,	PUNCT
ejpam-3226	194	7	g.r	g.r	PROPN
ejpam-3226	194	8	.	.	PROPN
ejpam-3226	194	9	,	,	PUNCT
ejpam-3226	194	10	”	"	PUNCT
ejpam-3226	194	11	safeguarding	safeguard	VERB
ejpam-3226	194	12	cryptographic	cryptographic	ADJ
ejpam-3226	194	13	keys	key	NOUN
ejpam-3226	194	14	”	"	PUNCT
ejpam-3226	194	15	,	,	PUNCT
ejpam-3226	194	16	american	american	PROPN
ejpam-3226	194	17	federation	federation	PROPN
ejpam-3226	194	18	of	of	ADP
ejpam-3226	194	19	information	information	NOUN
ejpam-3226	194	20	processing	processing	NOUN
ejpam-3226	194	21	societies	society	NOUN
ejpam-3226	194	22	,	,	PUNCT
ejpam-3226	194	23	national	national	ADJ
ejpam-3226	194	24	computer	computer	NOUN
ejpam-3226	194	25	conference	conference	NOUN
ejpam-3226	194	26	,	,	PUNCT
ejpam-3226	194	27	pp	pp	PROPN
ejpam-3226	194	28	.	.	PUNCT
ejpam-3226	195	1	313	313	NUM
ejpam-3226	195	2	-	-	SYM
ejpam-3226	195	3	317	317	NUM
ejpam-3226	195	4	,	,	PUNCT
ejpam-3226	195	5	(	(	PUNCT
ejpam-3226	195	6	1979	1979	NUM
ejpam-3226	195	7	)	)	PUNCT
ejpam-3226	195	8	.	.	PUNCT
ejpam-3226	196	1	[	[	X
ejpam-3226	196	2	2	2	NUM
ejpam-3226	196	3	]	]	X
ejpam-3226	196	4	carreras	carreras	X
ejpam-3226	196	5	,	,	PUNCT
ejpam-3226	196	6	f.	f.	PROPN
ejpam-3226	196	7	,	,	PUNCT
ejpam-3226	196	8	magana	magana	PROPN
ejpam-3226	196	9	,	,	PUNCT
ejpam-3226	196	10	a.	a.	PROPN
ejpam-3226	196	11	,	,	PUNCT
ejpam-3226	196	12	munuera	munuera	PROPN
ejpam-3226	196	13	,	,	PUNCT
ejpam-3226	196	14	c.	c.	PROPN
ejpam-3226	196	15	,	,	PUNCT
ejpam-3226	196	16	the	the	DET
ejpam-3226	196	17	accessibility	accessibility	NOUN
ejpam-3226	196	18	of	of	ADP
ejpam-3226	196	19	an	an	DET
ejpam-3226	196	20	access	access	NOUN
ejpam-3226	196	21	structure	structure	NOUN
ejpam-3226	196	22	,	,	PUNCT
ejpam-3226	196	23	rairo	rairo	NOUN
ejpam-3226	196	24	-	-	PUNCT
ejpam-3226	196	25	theoretical	theoretical	ADJ
ejpam-3226	196	26	informatics	informatic	NOUN
ejpam-3226	196	27	and	and	CCONJ
ejpam-3226	196	28	applications	application	NOUN
ejpam-3226	196	29	,	,	PUNCT
ejpam-3226	196	30	40.04	40.04	NUM
ejpam-3226	196	31	,	,	PUNCT
ejpam-3226	196	32	pp	pp	ADJ
ejpam-3226	196	33	.	.	PUNCT
ejpam-3226	197	1	559	559	NUM
ejpam-3226	197	2	-	-	SYM
ejpam-3226	197	3	567	567	NUM
ejpam-3226	197	4	.	.	PUNCT
ejpam-3226	197	5	(	(	PUNCT
ejpam-3226	197	6	2006	2006	NUM
ejpam-3226	197	7	)	)	PUNCT
ejpam-3226	197	8	.	.	PUNCT
ejpam-3226	198	1	[	[	X
ejpam-3226	198	2	3	3	X
ejpam-3226	198	3	]	]	X
ejpam-3226	198	4	ding	ding	NOUN
ejpam-3226	198	5	,	,	PUNCT
ejpam-3226	198	6	c.	c.	PROPN
ejpam-3226	198	7	,	,	PUNCT
ejpam-3226	198	8	kohel	kohel	PROPN
ejpam-3226	198	9	,	,	PUNCT
ejpam-3226	198	10	d.	d.	PROPN
ejpam-3226	198	11	r.	r.	PROPN
ejpam-3226	198	12	,	,	PUNCT
ejpam-3226	198	13	ling	ling	PROPN
ejpam-3226	198	14	,	,	PUNCT
ejpam-3226	198	15	s.	s.	PROPN
ejpam-3226	198	16	,	,	PUNCT
ejpam-3226	198	17	secret	secret	ADJ
ejpam-3226	198	18	-	-	PUNCT
ejpam-3226	198	19	sharing	sharing	NOUN
ejpam-3226	198	20	with	with	ADP
ejpam-3226	198	21	a	a	DET
ejpam-3226	198	22	class	class	NOUN
ejpam-3226	198	23	of	of	ADP
ejpam-3226	198	24	ternary	ternary	ADJ
ejpam-3226	198	25	codes	code	NOUN
ejpam-3226	198	26	,	,	PUNCT
ejpam-3226	198	27	theoretical	theoretical	ADJ
ejpam-3226	198	28	computer	computer	NOUN
ejpam-3226	198	29	science	science	NOUN
ejpam-3226	198	30	,	,	PUNCT
ejpam-3226	198	31	246(1	246(1	NUM
ejpam-3226	198	32	)	)	PUNCT
ejpam-3226	198	33	,	,	PUNCT
ejpam-3226	198	34	pp.285	pp.285	PROPN
ejpam-3226	198	35	-	-	PUNCT
ejpam-3226	198	36	298	298	NUM
ejpam-3226	198	37	,	,	PUNCT
ejpam-3226	198	38	(	(	PUNCT
ejpam-3226	198	39	2000	2000	NUM
ejpam-3226	198	40	)	)	PUNCT
ejpam-3226	198	41	.	.	PUNCT
ejpam-3226	199	1	[	[	X
ejpam-3226	199	2	4	4	NUM
ejpam-3226	199	3	]	]	X
ejpam-3226	199	4	dougherty	dougherty	PROPN
ejpam-3226	199	5	,	,	PUNCT
ejpam-3226	199	6	s.	s.	PROPN
ejpam-3226	199	7	t.	t.	PROPN
ejpam-3226	199	8	,	,	PUNCT
ejpam-3226	199	9	mesnager	mesnager	NOUN
ejpam-3226	199	10	,	,	PUNCT
ejpam-3226	199	11	s.	s.	PROPN
ejpam-3226	199	12	,	,	PUNCT
ejpam-3226	199	13	solé	solé	NOUN
ejpam-3226	199	14	,	,	PUNCT
ejpam-3226	199	15	p.	p.	NOUN
ejpam-3226	199	16	,	,	PUNCT
ejpam-3226	199	17	secret	secret	ADJ
ejpam-3226	199	18	sharing	sharing	NOUN
ejpam-3226	199	19	schemes	scheme	NOUN
ejpam-3226	199	20	based	base	VERB
ejpam-3226	199	21	on	on	ADP
ejpam-3226	199	22	self	self	NOUN
ejpam-3226	199	23	-	-	PUNCT
ejpam-3226	199	24	dual	dual	ADJ
ejpam-3226	199	25	codes	code	NOUN
ejpam-3226	199	26	,	,	PUNCT
ejpam-3226	199	27	information	information	NOUN
ejpam-3226	199	28	theory	theory	NOUN
ejpam-3226	199	29	workshop	workshop	NOUN
ejpam-3226	199	30	(	(	PUNCT
ejpam-3226	199	31	2008	2008	NUM
ejpam-3226	199	32	)	)	PUNCT
ejpam-3226	199	33	,	,	PUNCT
ejpam-3226	199	34	itw’08	itw’08	NOUN
ejpam-3226	199	35	,	,	PUNCT
ejpam-3226	199	36	ieee	ieee	NOUN
ejpam-3226	199	37	(	(	PUNCT
ejpam-3226	199	38	2008	2008	NUM
ejpam-3226	199	39	)	)	PUNCT
ejpam-3226	199	40	.	.	PUNCT
ejpam-3226	200	1	[	[	X
ejpam-3226	200	2	5	5	X
ejpam-3226	200	3	]	]	X
ejpam-3226	200	4	kim	kim	PROPN
ejpam-3226	200	5	.	.	PUNCT
ejpam-3226	201	1	j.l	j.l	PROPN
ejpam-3226	201	2	.	.	PROPN
ejpam-3226	201	3	,	,	PUNCT
ejpam-3226	201	4	lee	lee	PROPN
ejpam-3226	201	5	,	,	PUNCT
ejpam-3226	201	6	n.	n.	NOUN
ejpam-3226	201	7	,	,	PUNCT
ejpam-3226	201	8	secret	secret	ADJ
ejpam-3226	201	9	sharing	sharing	NOUN
ejpam-3226	201	10	schemes	scheme	NOUN
ejpam-3226	201	11	based	base	VERB
ejpam-3226	201	12	on	on	ADP
ejpam-3226	201	13	additive	additive	ADJ
ejpam-3226	201	14	codes	code	NOUN
ejpam-3226	201	15	over	over	ADP
ejpam-3226	201	16	gf	gf	PROPN
ejpam-3226	201	17	(	(	PUNCT
ejpam-3226	201	18	4	4	NUM
ejpam-3226	201	19	)	)	PUNCT
ejpam-3226	201	20	,	,	PUNCT
ejpam-3226	201	21	applicable	applicable	ADJ
ejpam-3226	201	22	algebra	algebra	NOUN
ejpam-3226	201	23	in	in	ADP
ejpam-3226	201	24	engineering	engineering	NOUN
ejpam-3226	201	25	,	,	PUNCT
ejpam-3226	201	26	communication	communication	NOUN
ejpam-3226	201	27	and	and	CCONJ
ejpam-3226	201	28	computing	computing	NOUN
ejpam-3226	201	29	,	,	PUNCT
ejpam-3226	201	30	pp	pp	ADJ
ejpam-3226	201	31	.	.	PUNCT
ejpam-3226	202	1	1	1	NUM
ejpam-3226	202	2	-	-	SYM
ejpam-3226	202	3	19	19	NUM
ejpam-3226	202	4	,	,	PUNCT
ejpam-3226	202	5	(	(	PUNCT
ejpam-3226	202	6	2016	2016	NUM
ejpam-3226	202	7	)	)	PUNCT
ejpam-3226	202	8	.	.	PUNCT
ejpam-3226	203	1	[	[	X
ejpam-3226	203	2	6	6	NUM
ejpam-3226	203	3	]	]	PUNCT
ejpam-3226	203	4	r.	r.	PROPN
ejpam-3226	203	5	lidl	lidl	PROPN
ejpam-3226	203	6	,	,	PUNCT
ejpam-3226	203	7	h.	h.	PROPN
ejpam-3226	203	8	niederreiter	niederreiter	PROPN
ejpam-3226	203	9	,	,	PUNCT
ejpam-3226	203	10	finite	finite	ADJ
ejpam-3226	203	11	fields	field	NOUN
ejpam-3226	203	12	,	,	PUNCT
ejpam-3226	203	13	vol	vol	NOUN
ejpam-3226	203	14	.	.	PROPN
ejpam-3226	203	15	20	20	NUM
ejpam-3226	203	16	,	,	PUNCT
ejpam-3226	203	17	cambridge	cambridge	NOUN
ejpam-3226	203	18	.	.	PUNCT
ejpam-3226	204	1	[	[	X
ejpam-3226	204	2	7	7	X
ejpam-3226	204	3	]	]	SYM
ejpam-3226	204	4	li	li	PROPN
ejpam-3226	204	5	,	,	PUNCT
ejpam-3226	204	6	zhihui	zhihui	PROPN
ejpam-3226	204	7	,	,	PUNCT
ejpam-3226	204	8	xue	xue	PROPN
ejpam-3226	204	9	,	,	PUNCT
ejpam-3226	204	10	ting	ting	PROPN
ejpam-3226	204	11	xue	xue	PROPN
ejpam-3226	204	12	,	,	PUNCT
ejpam-3226	204	13	lai	lai	PROPN
ejpam-3226	204	14	,	,	PUNCT
ejpam-3226	204	15	hong	hong	PROPN
ejpam-3226	204	16	,	,	PUNCT
ejpam-3226	204	17	secret	secret	ADJ
ejpam-3226	204	18	sharing	sharing	NOUN
ejpam-3226	204	19	schemes	scheme	NOUN
ejpam-3226	204	20	from	from	ADP
ejpam-3226	204	21	binary	binary	ADJ
ejpam-3226	204	22	linear	linear	PROPN
ejpam-3226	204	23	codes	code	NOUN
ejpam-3226	204	24	,	,	PUNCT
ejpam-3226	204	25	information	information	NOUN
ejpam-3226	204	26	sciences	science	NOUN
ejpam-3226	204	27	180(22	180(22	NUM
ejpam-3226	204	28	)	)	PUNCT
ejpam-3226	204	29	,	,	PUNCT
ejpam-3226	204	30	pp	pp	PROPN
ejpam-3226	204	31	.	.	PUNCT
ejpam-3226	205	1	4412	4412	NUM
ejpam-3226	205	2	-	-	SYM
ejpam-3226	205	3	4419	4419	NUM
ejpam-3226	205	4	,	,	PUNCT
ejpam-3226	205	5	(	(	PUNCT
ejpam-3226	205	6	2010	2010	NUM
ejpam-3226	205	7	)	)	PUNCT
ejpam-3226	205	8	.	.	PUNCT
ejpam-3226	206	1	[	[	X
ejpam-3226	206	2	8	8	NUM
ejpam-3226	206	3	]	]	X
ejpam-3226	206	4	massey	massey	PROPN
ejpam-3226	206	5	,	,	PUNCT
ejpam-3226	206	6	j.	j.	PROPN
ejpam-3226	206	7	l.	l.	PROPN
ejpam-3226	206	8	,	,	PUNCT
ejpam-3226	206	9	minimal	minimal	ADJ
ejpam-3226	206	10	codewords	codeword	NOUN
ejpam-3226	206	11	and	and	CCONJ
ejpam-3226	206	12	secret	secret	ADJ
ejpam-3226	206	13	sharing,“in	sharing,“in	PROPN
ejpam-3226	206	14	proc	proc	NOUN
ejpam-3226	206	15	.	.	PUNCT
ejpam-3226	207	1	6th	6th	ADJ
ejpam-3226	207	2	joint	joint	ADJ
ejpam-3226	207	3	swedishrussian	swedishrussian	ADJ
ejpam-3226	207	4	workshop	workshop	NOUN
ejpam-3226	207	5	on	on	ADP
ejpam-3226	207	6	information	information	NOUN
ejpam-3226	207	7	theory	theory	NOUN
ejpam-3226	207	8	,	,	PUNCT
ejpam-3226	207	9	mölle	mölle	PROPN
ejpam-3226	207	10	,	,	PUNCT
ejpam-3226	207	11	sweden	sweden	ADJ
ejpam-3226	207	12	,	,	PUNCT
ejpam-3226	207	13	pp	pp	ADJ
ejpam-3226	207	14	.	.	PUNCT
ejpam-3226	208	1	276	276	NUM
ejpam-3226	208	2	-	-	SYM
ejpam-3226	208	3	279	279	NUM
ejpam-3226	208	4	,	,	PUNCT
ejpam-3226	208	5	(	(	PUNCT
ejpam-3226	208	6	1993	1993	NUM
ejpam-3226	208	7	)	)	PUNCT
ejpam-3226	208	8	.	.	PUNCT
ejpam-3226	209	1	[	[	X
ejpam-3226	209	2	9	9	X
ejpam-3226	209	3	]	]	X
ejpam-3226	209	4	mceliece	mceliece	PROPN
ejpam-3226	209	5	r	r	PROPN
ejpam-3226	209	6	,	,	PUNCT
ejpam-3226	209	7	j.	j.	PROPN
ejpam-3226	209	8	and	and	CCONJ
ejpam-3226	209	9	sarwate	sarwate	VERB
ejpam-3226	209	10	d.	d.	PROPN
ejpam-3226	209	11	v.	v.	PROPN
ejpam-3226	209	12	,	,	PUNCT
ejpam-3226	209	13	on	on	ADP
ejpam-3226	209	14	sharing	share	VERB
ejpam-3226	209	15	secrets	secret	NOUN
ejpam-3226	209	16	and	and	CCONJ
ejpam-3226	209	17	reed	reed	PROPN
ejpam-3226	209	18	-	-	PUNCT
ejpam-3226	209	19	solomon	solomon	PROPN
ejpam-3226	209	20	codes	code	NOUN
ejpam-3226	209	21	,	,	PUNCT
ejpam-3226	209	22	common	common	ADJ
ejpam-3226	209	23	.	.	PUNCT
ejpam-3226	210	1	assoc	assoc	PROPN
ejpam-3226	210	2	.	.	PUNCT
ejpam-3226	211	1	comp	comp	PROPN
ejpam-3226	211	2	.	.	PUNCT
ejpam-3226	212	1	mach	mach	PROPN
ejpam-3226	212	2	.	.	PUNCT
ejpam-3226	212	3	,	,	PUNCT
ejpam-3226	212	4	vol	vol	NOUN
ejpam-3226	212	5	.	.	PROPN
ejpam-3226	213	1	24	24	NUM
ejpam-3226	213	2	,	,	PUNCT
ejpam-3226	213	3	pp	pp	ADJ
ejpam-3226	213	4	.	.	PUNCT
ejpam-3226	214	1	583	583	NUM
ejpam-3226	214	2	-	-	SYM
ejpam-3226	214	3	584	584	NUM
ejpam-3226	214	4	,	,	PUNCT
ejpam-3226	214	5	(	(	PUNCT
ejpam-3226	214	6	1981	1981	NUM
ejpam-3226	214	7	)	)	PUNCT
ejpam-3226	214	8	.	.	PUNCT
ejpam-3226	215	1	[	[	X
ejpam-3226	215	2	10	10	NUM
ejpam-3226	215	3	]	]	X
ejpam-3226	215	4	piepryzk	piepryzk	NOUN
ejpam-3226	215	5	,	,	PUNCT
ejpam-3226	215	6	j.	j.	PROPN
ejpam-3226	215	7	and	and	CCONJ
ejpam-3226	215	8	zhang	zhang	PROPN
ejpam-3226	215	9	,	,	PUNCT
ejpam-3226	215	10	x.	x.	PROPN
ejpam-3226	215	11	m.	m.	NOUN
ejpam-3226	215	12	,	,	PUNCT
ejpam-3226	215	13	ideal	ideal	ADJ
ejpam-3226	215	14	threshold	threshold	NOUN
ejpam-3226	215	15	schemes	scheme	NOUN
ejpam-3226	215	16	from	from	ADP
ejpam-3226	215	17	mds	mds	NOUN
ejpam-3226	215	18	codes	code	NOUN
ejpam-3226	215	19	,	,	PUNCT
ejpam-3226	215	20	proceedings	proceeding	NOUN
ejpam-3226	215	21	of	of	ADP
ejpam-3226	215	22	information	information	NOUN
ejpam-3226	215	23	security	security	NOUN
ejpam-3226	215	24	and	and	CCONJ
ejpam-3226	215	25	cryptology	cryptology	NOUN
ejpam-3226	215	26	icisc	icisc	NOUN
ejpam-3226	215	27	2002	2002	NUM
ejpam-3226	215	28	,	,	PUNCT
ejpam-3226	215	29	lecture	lecture	NOUN
ejpam-3226	215	30	notes	note	NOUN
ejpam-3226	215	31	in	in	ADP
ejpam-3226	215	32	computer	computer	NOUN
ejpam-3226	215	33	science	science	NOUN
ejpam-3226	215	34	,	,	PUNCT
ejpam-3226	215	35	vol	vol	NOUN
ejpam-3226	215	36	.	.	NOUN
ejpam-3226	215	37	2587	2587	NUM
ejpam-3226	215	38	,	,	PUNCT
ejpam-3226	215	39	springer	springer	NOUN
ejpam-3226	215	40	-	-	PUNCT
ejpam-3226	215	41	verlag	verlag	PROPN
ejpam-3226	215	42	,	,	PUNCT
ejpam-3226	215	43	berlin	berlin	PROPN
ejpam-3226	215	44	,	,	PUNCT
ejpam-3226	215	45	pp	pp	PROPN
ejpam-3226	215	46	.	.	PUNCT
ejpam-3226	215	47	269	269	NUM
ejpam-3226	215	48	-	-	SYM
ejpam-3226	215	49	279	279	NUM
ejpam-3226	215	50	,	,	PUNCT
ejpam-3226	215	51	(	(	PUNCT
ejpam-3226	215	52	2003	2003	NUM
ejpam-3226	215	53	)	)	PUNCT
ejpam-3226	215	54	.	.	PUNCT
ejpam-3226	216	1	[	[	X
ejpam-3226	216	2	11	11	NUM
ejpam-3226	216	3	]	]	SYM
ejpam-3226	216	4	shamir	shamir	PROPN
ejpam-3226	216	5	,	,	PUNCT
ejpam-3226	216	6	a.	a.	NOUN
ejpam-3226	216	7	,	,	PUNCT
ejpam-3226	216	8	how	how	SCONJ
ejpam-3226	216	9	to	to	PART
ejpam-3226	216	10	share	share	VERB
ejpam-3226	216	11	a	a	DET
ejpam-3226	216	12	secret	secret	ADJ
ejpam-3226	216	13	,	,	PUNCT
ejpam-3226	216	14	comm	comm	NOUN
ejpam-3226	216	15	.	.	PUNCT
ejpam-3226	217	1	of	of	ADP
ejpam-3226	217	2	the	the	DET
ejpam-3226	217	3	acm	acm	PROPN
ejpam-3226	217	4	22	22	NUM
ejpam-3226	217	5	pp	pp	NOUN
ejpam-3226	217	6	.	.	PUNCT
ejpam-3226	218	1	612	612	NUM
ejpam-3226	218	2	-	-	SYM
ejpam-3226	218	3	613	613	NUM
ejpam-3226	218	4	,	,	PUNCT
ejpam-3226	218	5	(	(	PUNCT
ejpam-3226	218	6	1979	1979	NUM
ejpam-3226	218	7	)	)	PUNCT
ejpam-3226	218	8	.	.	PUNCT