id	sid	tid	token	lemma	pos
fcis-6343	1	1	frontiers	frontier	NOUN
fcis-6343	1	2	in	in	ADP
fcis-6343	1	3	computing	computing	NOUN
fcis-6343	1	4	and	and	CCONJ
fcis-6343	1	5	intelligent	intelligent	ADJ
fcis-6343	1	6	systems	system	NOUN
fcis-6343	1	7	issn	issn	VERB
fcis-6343	1	8	:	:	PUNCT
fcis-6343	1	9	2832	2832	NUM
fcis-6343	1	10	-	-	SYM
fcis-6343	1	11	6024	6024	NUM
fcis-6343	1	12	|	|	NOUN
fcis-6343	1	13	vol	vol	NOUN
fcis-6343	1	14	.	.	PROPN
fcis-6343	2	1	3	3	NUM
fcis-6343	2	2	,	,	PUNCT
fcis-6343	2	3	no	no	INTJ
fcis-6343	2	4	.	.	NOUN
fcis-6343	2	5	1	1	NUM
fcis-6343	2	6	,	,	PUNCT
fcis-6343	2	7	2023	2023	NUM
fcis-6343	2	8	110	110	NUM
fcis-6343	2	9	homomorphic	homomorphic	ADJ
fcis-6343	2	10	encryption	encryption	NOUN
fcis-6343	2	11	and	and	CCONJ
fcis-6343	2	12	its	its	PRON
fcis-6343	2	13	application	application	NOUN
fcis-6343	2	14	to	to	PART
fcis-6343	2	15	blockchain	blockchain	PROPN
fcis-6343	2	16	sen	sen	PROPN
fcis-6343	2	17	hu1	hu1	PROPN
fcis-6343	2	18	,	,	PUNCT
fcis-6343	2	19	zhengquan	zhengquan	PROPN
fcis-6343	2	20	zhang1	zhang1	PROPN
fcis-6343	2	21	,	,	PUNCT
fcis-6343	2	22	kevin	kevin	PROPN
fcis-6343	2	23	(	(	PUNCT
fcis-6343	2	24	xiaokang	xiaokang	PROPN
fcis-6343	2	25	)	)	PUNCT
fcis-6343	2	26	mo2,3	mo2,3	NOUN
fcis-6343	2	27	1	1	NUM
fcis-6343	2	28	school	school	NOUN
fcis-6343	2	29	of	of	ADP
fcis-6343	2	30	mathematical	mathematical	ADJ
fcis-6343	2	31	sciences	science	NOUN
fcis-6343	2	32	at	at	ADP
fcis-6343	2	33	ustc	ustc	PROPN
fcis-6343	2	34	and	and	CCONJ
fcis-6343	2	35	wu	wu	PROPN
fcis-6343	2	36	lab	lab	NOUN
fcis-6343	2	37	of	of	ADP
fcis-6343	2	38	mathematics	mathematic	NOUN
fcis-6343	2	39	of	of	ADP
fcis-6343	2	40	chinese	chinese	PROPN
fcis-6343	2	41	academy	academy	PROPN
fcis-6343	2	42	of	of	ADP
fcis-6343	2	43	sciences	sciences	PROPN
fcis-6343	2	44	,	,	PUNCT
fcis-6343	2	45	hefei	hefei	PROPN
fcis-6343	2	46	,	,	PUNCT
fcis-6343	2	47	china	china	PROPN
fcis-6343	2	48	2	2	NUM
fcis-6343	2	49	beijing	beijing	PROPN
fcis-6343	2	50	data	data	PROPN
fcis-6343	2	51	institute	institute	PROPN
fcis-6343	2	52	,	,	PUNCT
fcis-6343	2	53	beijing	beijing	PROPN
fcis-6343	2	54	,	,	PUNCT
fcis-6343	2	55	china	china	PROPN
fcis-6343	2	56	3	3	NUM
fcis-6343	2	57	national	national	PROPN
fcis-6343	2	58	innovation	innovation	PROPN
fcis-6343	2	59	research	research	PROPN
fcis-6343	2	60	institute	institute	PROPN
fcis-6343	2	61	(	(	PUNCT
fcis-6343	2	62	xiamen	xiamen	PROPN
fcis-6343	2	63	)	)	PUNCT
fcis-6343	2	64	,	,	PUNCT
fcis-6343	2	65	inc	inc	PROPN
fcis-6343	2	66	,	,	PUNCT
fcis-6343	2	67	xiamen	xiamen	PROPN
fcis-6343	2	68	,	,	PUNCT
fcis-6343	2	69	china	china	PROPN
fcis-6343	2	70	abstract	abstract	PROPN
fcis-6343	2	71	:	:	PUNCT
fcis-6343	2	72	the	the	DET
fcis-6343	2	73	concept	concept	NOUN
fcis-6343	2	74	,	,	PUNCT
fcis-6343	2	75	method	method	NOUN
fcis-6343	2	76	,	,	PUNCT
fcis-6343	2	77	algorithm	algorithm	NOUN
fcis-6343	2	78	and	and	CCONJ
fcis-6343	2	79	application	application	NOUN
fcis-6343	2	80	of	of	ADP
fcis-6343	2	81	the	the	DET
fcis-6343	2	82	advanced	advanced	ADJ
fcis-6343	2	83	field	field	NOUN
fcis-6343	2	84	of	of	ADP
fcis-6343	2	85	cryptography	cryptography	NOUN
fcis-6343	2	86	,	,	PUNCT
fcis-6343	2	87	homomorphic	homomorphic	ADJ
fcis-6343	2	88	encryption	encryption	NOUN
fcis-6343	2	89	,	,	PUNCT
fcis-6343	2	90	as	as	ADV
fcis-6343	2	91	well	well	ADV
fcis-6343	2	92	as	as	ADP
fcis-6343	2	93	its	its	PRON
fcis-6343	2	94	application	application	NOUN
fcis-6343	2	95	to	to	ADP
fcis-6343	2	96	the	the	DET
fcis-6343	2	97	field	field	NOUN
fcis-6343	2	98	of	of	ADP
fcis-6343	2	99	blockchain	blockchain	PROPN
fcis-6343	2	100	are	be	AUX
fcis-6343	2	101	discussed	discuss	VERB
fcis-6343	2	102	in	in	ADP
fcis-6343	2	103	this	this	DET
fcis-6343	2	104	paper	paper	NOUN
fcis-6343	2	105	.	.	PUNCT
fcis-6343	3	1	there	there	PRON
fcis-6343	3	2	are	be	VERB
fcis-6343	3	3	various	various	ADJ
fcis-6343	3	4	forms	form	NOUN
fcis-6343	3	5	of	of	ADP
fcis-6343	3	6	homomorphic	homomorphic	ADJ
fcis-6343	3	7	encryption	encryption	NOUN
fcis-6343	3	8	and	and	CCONJ
fcis-6343	3	9	they	they	PRON
fcis-6343	3	10	can	can	AUX
fcis-6343	3	11	be	be	AUX
fcis-6343	3	12	classified	classify	VERB
fcis-6343	3	13	into	into	ADP
fcis-6343	3	14	three	three	NUM
fcis-6343	3	15	categories	category	NOUN
fcis-6343	3	16	:	:	PUNCT
fcis-6343	3	17	partially	partially	ADV
fcis-6343	3	18	homomorphic	homomorphic	ADJ
fcis-6343	3	19	encryption	encryption	NOUN
fcis-6343	3	20	,	,	PUNCT
fcis-6343	3	21	hierarchical	hierarchical	ADJ
fcis-6343	3	22	homomorphic	homomorphic	ADJ
fcis-6343	3	23	encryption	encryption	NOUN
fcis-6343	3	24	and	and	CCONJ
fcis-6343	3	25	fully	fully	ADV
fcis-6343	3	26	homomorphic	homomorphic	ADJ
fcis-6343	3	27	encryption	encryption	NOUN
fcis-6343	3	28	.	.	PUNCT
fcis-6343	4	1	we	we	PRON
fcis-6343	4	2	explain	explain	VERB
fcis-6343	4	3	the	the	DET
fcis-6343	4	4	concept	concept	NOUN
fcis-6343	4	5	,	,	PUNCT
fcis-6343	4	6	method	method	NOUN
fcis-6343	4	7	and	and	CCONJ
fcis-6343	4	8	algorithm	algorithm	NOUN
fcis-6343	4	9	for	for	ADP
fcis-6343	4	10	each	each	DET
fcis-6343	4	11	category	category	NOUN
fcis-6343	4	12	with	with	ADP
fcis-6343	4	13	down	down	ADP
fcis-6343	4	14	to	to	ADP
fcis-6343	4	15	earth	earth	NOUN
fcis-6343	4	16	examples	example	NOUN
fcis-6343	4	17	.	.	PUNCT
fcis-6343	5	1	the	the	DET
fcis-6343	5	2	milestone	milestone	NOUN
fcis-6343	5	3	example	example	NOUN
fcis-6343	5	4	of	of	ADP
fcis-6343	5	5	rsa	rsa	PROPN
fcis-6343	5	6	algorithm	algorithm	PROPN
fcis-6343	5	7	is	be	AUX
fcis-6343	5	8	explained	explain	VERB
fcis-6343	5	9	which	which	PRON
fcis-6343	5	10	is	be	AUX
fcis-6343	5	11	still	still	ADV
fcis-6343	5	12	widely	widely	ADV
fcis-6343	5	13	used	use	VERB
fcis-6343	5	14	in	in	ADP
fcis-6343	5	15	the	the	DET
fcis-6343	5	16	internet	internet	NOUN
fcis-6343	5	17	and	and	CCONJ
fcis-6343	5	18	in	in	ADP
fcis-6343	5	19	blockchain	blockchain	PROPN
fcis-6343	5	20	as	as	ADV
fcis-6343	5	21	well	well	ADV
fcis-6343	5	22	.	.	PUNCT
fcis-6343	6	1	applications	application	NOUN
fcis-6343	6	2	of	of	ADP
fcis-6343	6	3	homomorphic	homomorphic	ADJ
fcis-6343	6	4	encryption	encryption	NOUN
fcis-6343	6	5	depends	depend	VERB
fcis-6343	6	6	on	on	ADP
fcis-6343	6	7	efficiency	efficiency	NOUN
fcis-6343	6	8	of	of	ADP
fcis-6343	6	9	implementation	implementation	NOUN
fcis-6343	6	10	which	which	PRON
fcis-6343	6	11	has	have	AUX
fcis-6343	6	12	been	be	AUX
fcis-6343	6	13	in	in	ADP
fcis-6343	6	14	good	good	ADJ
fcis-6343	6	15	progress	progress	NOUN
fcis-6343	6	16	in	in	ADP
fcis-6343	6	17	recent	recent	ADJ
fcis-6343	6	18	years	year	NOUN
fcis-6343	6	19	.	.	PUNCT
fcis-6343	7	1	keywords	keyword	NOUN
fcis-6343	7	2	:	:	PUNCT
fcis-6343	7	3	cryptography	cryptography	NOUN
fcis-6343	7	4	;	;	PUNCT
fcis-6343	7	5	public	public	ADJ
fcis-6343	7	6	key	key	ADJ
fcis-6343	7	7	cryptography	cryptography	NOUN
fcis-6343	7	8	;	;	PUNCT
fcis-6343	7	9	privacy	privacy	NOUN
fcis-6343	7	10	computing	computing	NOUN
fcis-6343	7	11	;	;	PUNCT
fcis-6343	7	12	fully	fully	ADV
fcis-6343	7	13	homomorphic	homomorphic	ADJ
fcis-6343	7	14	encryption	encryption	NOUN
fcis-6343	7	15	;	;	PUNCT
fcis-6343	7	16	blockchain	blockchain	PROPN
fcis-6343	7	17	application	application	NOUN
fcis-6343	7	18	.	.	PUNCT
fcis-6343	8	1	1	1	X
fcis-6343	8	2	.	.	X
fcis-6343	8	3	introduction	introduction	NOUN
fcis-6343	8	4	the	the	DET
fcis-6343	8	5	problem	problem	NOUN
fcis-6343	8	6	of	of	ADP
fcis-6343	8	7	homomorphic	homomorphic	ADJ
fcis-6343	8	8	encryption	encryption	NOUN
fcis-6343	8	9	originates	originate	NOUN
fcis-6343	8	10	from	from	ADP
fcis-6343	8	11	issues	issue	NOUN
fcis-6343	8	12	of	of	ADP
fcis-6343	8	13	data	datum	NOUN
fcis-6343	8	14	confidentiality	confidentiality	NOUN
fcis-6343	8	15	in	in	ADP
fcis-6343	8	16	privacy	privacy	NOUN
fcis-6343	8	17	computing	computing	NOUN
fcis-6343	8	18	,	,	PUNCT
fcis-6343	8	19	such	such	ADJ
fcis-6343	8	20	as	as	ADP
fcis-6343	8	21	cloud	cloud	NOUN
fcis-6343	8	22	computing	computing	NOUN
fcis-6343	8	23	.	.	PUNCT
fcis-6343	9	1	after	after	SCONJ
fcis-6343	9	2	the	the	DET
fcis-6343	9	3	clients	client	NOUN
fcis-6343	9	4	provide	provide	VERB
fcis-6343	9	5	the	the	DET
fcis-6343	9	6	data	datum	NOUN
fcis-6343	9	7	,	,	PUNCT
fcis-6343	9	8	it	it	PRON
fcis-6343	9	9	is	be	AUX
fcis-6343	9	10	required	require	VERB
fcis-6343	9	11	that	that	SCONJ
fcis-6343	9	12	the	the	DET
fcis-6343	9	13	original	original	ADJ
fcis-6343	9	14	data	datum	NOUN
fcis-6343	9	15	shall	shall	AUX
fcis-6343	9	16	not	not	PART
fcis-6343	9	17	be	be	AUX
fcis-6343	9	18	accessed	access	VERB
fcis-6343	9	19	by	by	ADP
fcis-6343	9	20	suppliers	supplier	NOUN
fcis-6343	9	21	of	of	ADP
fcis-6343	9	22	the	the	DET
fcis-6343	9	23	cloud	cloud	NOUN
fcis-6343	9	24	computing	computing	NOUN
fcis-6343	9	25	service	service	NOUN
fcis-6343	9	26	which	which	PRON
fcis-6343	9	27	only	only	ADV
fcis-6343	9	28	access	access	VERB
fcis-6343	9	29	the	the	DET
fcis-6343	9	30	encrypted	encrypt	VERB
fcis-6343	9	31	data	datum	NOUN
fcis-6343	9	32	.	.	PUNCT
fcis-6343	10	1	homomorphic	homomorphic	ADJ
fcis-6343	10	2	encryption	encryption	NOUN
fcis-6343	10	3	refers	refer	VERB
fcis-6343	10	4	to	to	ADP
fcis-6343	10	5	an	an	DET
fcis-6343	10	6	unconventional	unconventional	ADJ
fcis-6343	10	7	encryption	encryption	NOUN
fcis-6343	10	8	mode	mode	NOUN
fcis-6343	10	9	with	with	ADP
fcis-6343	10	10	special	special	ADJ
fcis-6343	10	11	applications	application	NOUN
fcis-6343	10	12	,	,	PUNCT
fcis-6343	10	13	and	and	CCONJ
fcis-6343	10	14	it	it	PRON
fcis-6343	10	15	can	can	AUX
fcis-6343	10	16	be	be	AUX
fcis-6343	10	17	used	use	VERB
fcis-6343	10	18	to	to	PART
fcis-6343	10	19	realize	realize	VERB
fcis-6343	10	20	encryption	encryption	NOUN
fcis-6343	10	21	operation	operation	NOUN
fcis-6343	10	22	to	to	PART
fcis-6343	10	23	maintain	maintain	VERB
fcis-6343	10	24	some	some	DET
fcis-6343	10	25	algebraic	algebraic	ADJ
fcis-6343	10	26	operations	operation	NOUN
fcis-6343	10	27	,	,	PUNCT
fcis-6343	10	28	that	that	PRON
fcis-6343	10	29	is	be	AUX
fcis-6343	10	30	to	to	PART
fcis-6343	10	31	say	say	VERB
fcis-6343	10	32	,	,	PUNCT
fcis-6343	10	33	the	the	DET
fcis-6343	10	34	homomorphic	homomorphic	ADJ
fcis-6343	10	35	encryption	encryption	NOUN
fcis-6343	10	36	of	of	ADP
fcis-6343	10	37	one	one	NUM
fcis-6343	10	38	of	of	ADP
fcis-6343	10	39	algebraic	algebraic	ADJ
fcis-6343	10	40	operations	operation	NOUN
fcis-6343	10	41	of	of	ADP
fcis-6343	10	42	the	the	DET
fcis-6343	10	43	object	object	NOUN
fcis-6343	10	44	is	be	AUX
fcis-6343	10	45	equal	equal	ADJ
fcis-6343	10	46	to	to	ADP
fcis-6343	10	47	the	the	DET
fcis-6343	10	48	same	same	ADJ
fcis-6343	10	49	algebraic	algebraic	ADJ
fcis-6343	10	50	operation	operation	NOUN
fcis-6343	10	51	of	of	ADP
fcis-6343	10	52	the	the	DET
fcis-6343	10	53	homomorphic	homomorphic	ADJ
fcis-6343	10	54	encryption	encryption	NOUN
fcis-6343	10	55	of	of	ADP
fcis-6343	10	56	the	the	DET
fcis-6343	10	57	object	object	NOUN
fcis-6343	10	58	.	.	PUNCT
fcis-6343	11	1	such	such	ADJ
fcis-6343	11	2	kind	kind	NOUN
fcis-6343	11	3	of	of	ADP
fcis-6343	11	4	encryption	encryption	NOUN
fcis-6343	11	5	mode	mode	NOUN
fcis-6343	11	6	enable	enable	VERB
fcis-6343	11	7	people	people	NOUN
fcis-6343	11	8	to	to	PART
fcis-6343	11	9	operate	operate	VERB
fcis-6343	11	10	the	the	DET
fcis-6343	11	11	ciphertext	ciphertext	NOUN
fcis-6343	11	12	without	without	ADP
fcis-6343	11	13	the	the	DET
fcis-6343	11	14	need	need	NOUN
fcis-6343	11	15	to	to	PART
fcis-6343	11	16	know	know	VERB
fcis-6343	11	17	the	the	DET
fcis-6343	11	18	original	original	ADJ
fcis-6343	11	19	text	text	NOUN
fcis-6343	11	20	,	,	PUNCT
fcis-6343	11	21	thus	thus	ADV
fcis-6343	11	22	to	to	PART
fcis-6343	11	23	conduct	conduct	VERB
fcis-6343	11	24	operations	operation	NOUN
fcis-6343	11	25	and	and	CCONJ
fcis-6343	11	26	manipulations	manipulation	NOUN
fcis-6343	11	27	such	such	ADJ
fcis-6343	11	28	as	as	ADP
fcis-6343	11	29	search	search	NOUN
fcis-6343	11	30	and	and	CCONJ
fcis-6343	11	31	comparison	comparison	NOUN
fcis-6343	11	32	with	with	ADP
fcis-6343	11	33	the	the	DET
fcis-6343	11	34	premise	premise	NOUN
fcis-6343	11	35	of	of	ADP
fcis-6343	11	36	confidentiality	confidentiality	NOUN
fcis-6343	11	37	,	,	PUNCT
fcis-6343	11	38	without	without	ADP
fcis-6343	11	39	the	the	DET
fcis-6343	11	40	need	need	NOUN
fcis-6343	11	41	of	of	ADP
fcis-6343	11	42	decryption	decryption	NOUN
fcis-6343	11	43	before	before	ADP
fcis-6343	11	44	such	such	ADJ
fcis-6343	11	45	kind	kind	NOUN
fcis-6343	11	46	of	of	ADP
fcis-6343	11	47	operations	operation	NOUN
fcis-6343	11	48	and	and	CCONJ
fcis-6343	11	49	manipulations	manipulation	NOUN
fcis-6343	11	50	.	.	PUNCT
fcis-6343	12	1	the	the	DET
fcis-6343	12	2	effect	effect	NOUN
fcis-6343	12	3	of	of	ADP
fcis-6343	12	4	homomorphic	homomorphic	ADJ
fcis-6343	12	5	encryption	encryption	NOUN
fcis-6343	12	6	is	be	AUX
fcis-6343	12	7	to	to	PART
fcis-6343	12	8	improve	improve	VERB
fcis-6343	12	9	the	the	DET
fcis-6343	12	10	confidentiality	confidentiality	NOUN
fcis-6343	12	11	of	of	ADP
fcis-6343	12	12	privacy	privacy	NOUN
fcis-6343	12	13	computing	computing	NOUN
fcis-6343	12	14	.	.	PUNCT
fcis-6343	13	1	that	that	PRON
fcis-6343	13	2	is	be	AUX
fcis-6343	13	3	,	,	PUNCT
fcis-6343	13	4	during	during	ADP
fcis-6343	13	5	the	the	DET
fcis-6343	13	6	process	process	NOUN
fcis-6343	13	7	of	of	ADP
fcis-6343	13	8	data	datum	NOUN
fcis-6343	13	9	encryption	encryption	NOUN
fcis-6343	13	10	,	,	PUNCT
fcis-6343	13	11	the	the	DET
fcis-6343	13	12	calculation	calculation	NOUN
fcis-6343	13	13	can	can	AUX
fcis-6343	13	14	also	also	ADV
fcis-6343	13	15	be	be	AUX
fcis-6343	13	16	entrusted	entrust	VERB
fcis-6343	13	17	to	to	ADP
fcis-6343	13	18	others	other	NOUN
fcis-6343	13	19	,	,	PUNCT
fcis-6343	13	20	so	so	SCONJ
fcis-6343	13	21	that	that	SCONJ
fcis-6343	13	22	people	people	NOUN
fcis-6343	13	23	’s	’s	PART
fcis-6343	13	24	requirement	requirement	NOUN
fcis-6343	13	25	of	of	ADP
fcis-6343	13	26	data	datum	NOUN
fcis-6343	13	27	security	security	NOUN
fcis-6343	13	28	can	can	AUX
fcis-6343	13	29	be	be	AUX
fcis-6343	13	30	better	well	ADV
fcis-6343	13	31	satisfied	satisfied	ADJ
fcis-6343	13	32	.	.	PUNCT
fcis-6343	14	1	compared	compare	VERB
fcis-6343	14	2	with	with	ADP
fcis-6343	14	3	general	general	ADJ
fcis-6343	14	4	forms	form	NOUN
fcis-6343	14	5	of	of	ADP
fcis-6343	14	6	encryption	encryption	NOUN
fcis-6343	14	7	,	,	PUNCT
fcis-6343	14	8	homomorphic	homomorphic	ADJ
fcis-6343	14	9	encryption	encryption	NOUN
fcis-6343	14	10	can	can	AUX
fcis-6343	14	11	avoid	avoid	VERB
fcis-6343	14	12	other	other	ADJ
fcis-6343	14	13	people	people	NOUN
fcis-6343	14	14	’s	’s	PART
fcis-6343	14	15	access	access	NOUN
fcis-6343	14	16	of	of	ADP
fcis-6343	14	17	the	the	DET
fcis-6343	14	18	original	original	ADJ
fcis-6343	14	19	data	datum	NOUN
fcis-6343	14	20	.	.	PUNCT
fcis-6343	15	1	for	for	ADP
fcis-6343	15	2	example	example	NOUN
fcis-6343	15	3	,	,	PUNCT
fcis-6343	15	4	in	in	ADP
fcis-6343	15	5	the	the	DET
fcis-6343	15	6	field	field	NOUN
fcis-6343	15	7	of	of	ADP
fcis-6343	15	8	cloud	cloud	NOUN
fcis-6343	15	9	computing	computing	NOUN
fcis-6343	15	10	,	,	PUNCT
fcis-6343	15	11	the	the	DET
fcis-6343	15	12	provider	provider	NOUN
fcis-6343	15	13	of	of	ADP
fcis-6343	15	14	the	the	DET
fcis-6343	15	15	cloud	cloud	NOUN
fcis-6343	15	16	can	can	AUX
fcis-6343	15	17	compute	compute	VERB
fcis-6343	15	18	on	on	ADP
fcis-6343	15	19	the	the	DET
fcis-6343	15	20	cloud	cloud	NOUN
fcis-6343	15	21	while	while	SCONJ
fcis-6343	15	22	ensuring	ensure	VERB
fcis-6343	15	23	the	the	DET
fcis-6343	15	24	security	security	NOUN
fcis-6343	15	25	and	and	CCONJ
fcis-6343	15	26	confidentiality	confidentiality	NOUN
fcis-6343	15	27	of	of	ADP
fcis-6343	15	28	data	datum	NOUN
fcis-6343	15	29	.	.	PUNCT
fcis-6343	16	1	2	2	X
fcis-6343	16	2	.	.	X
fcis-6343	16	3	various	various	ADJ
fcis-6343	16	4	forms	form	NOUN
fcis-6343	16	5	of	of	ADP
fcis-6343	16	6	homomorphic	homomorphic	ADJ
fcis-6343	16	7	encryption	encryption	NOUN
fcis-6343	16	8	homomorphic	homomorphic	ADJ
fcis-6343	16	9	encryption	encryption	NOUN
fcis-6343	16	10	’s	’s	PART
fcis-6343	16	11	form	form	NOUN
fcis-6343	16	12	is	be	AUX
fcis-6343	16	13	similar	similar	ADJ
fcis-6343	16	14	to	to	ADP
fcis-6343	16	15	the	the	DET
fcis-6343	16	16	concept	concept	NOUN
fcis-6343	16	17	of	of	ADP
fcis-6343	16	18	homomorphism	homomorphism	PROPN
fcis-6343	16	19	in	in	ADP
fcis-6343	16	20	traditional	traditional	ADJ
fcis-6343	16	21	mathematics	mathematic	NOUN
fcis-6343	16	22	.	.	PUNCT
fcis-6343	17	1	definition	definition	NOUN
fcis-6343	17	2	4.1.1	4.1.1	NUM
fcis-6343	17	3	.	.	PUNCT
fcis-6343	18	1	:	:	PUNCT
fcis-6343	18	2	we	we	PRON
fcis-6343	18	3	call	call	VERB
fcis-6343	18	4	e	e	VERB
fcis-6343	18	5	an	an	DET
fcis-6343	18	6	homomorphic	homomorphic	ADJ
fcis-6343	18	7	encryption	encryption	NOUN
fcis-6343	18	8	,	,	PUNCT
fcis-6343	18	9	if	if	SCONJ
fcis-6343	18	10	e	e	PROPN
fcis-6343	18	11	−1(e(m1	−1(e(m1	NOUN
fcis-6343	18	12	)	)	PUNCT
fcis-6343	18	13	∗	∗	NOUN
fcis-6343	18	14	e(m2	e(m2	X
fcis-6343	18	15	)	)	PUNCT
fcis-6343	18	16	)	)	PUNCT
fcis-6343	19	1	=	=	SYM
fcis-6343	19	2	m1	m1	PROPN
fcis-6343	19	3	∗	∗	NOUN
fcis-6343	19	4	m2	m2	PROPN
fcis-6343	19	5	,	,	PUNCT
fcis-6343	19	6	for	for	ADP
fcis-6343	19	7	any	any	DET
fcis-6343	19	8	m1	m1	NOUN
fcis-6343	19	9	,	,	PUNCT
fcis-6343	19	10	m2	m2	PROPN
fcis-6343	19	11	∈	∈	PROPN
fcis-6343	19	12	m.	m.	NOUN
fcis-6343	19	13	in	in	ADP
fcis-6343	19	14	the	the	DET
fcis-6343	19	15	formula	formula	NOUN
fcis-6343	19	16	,	,	PUNCT
fcis-6343	19	17	m	m	VERB
fcis-6343	19	18	is	be	AUX
fcis-6343	19	19	the	the	DET
fcis-6343	19	20	set	set	NOUN
fcis-6343	19	21	of	of	ADP
fcis-6343	19	22	all	all	DET
fcis-6343	19	23	possible	possible	ADJ
fcis-6343	19	24	information	information	NOUN
fcis-6343	19	25	,	,	PUNCT
fcis-6343	19	26	e	e	X
fcis-6343	19	27	is	be	AUX
fcis-6343	19	28	the	the	DET
fcis-6343	19	29	encrypted	encrypt	VERB
fcis-6343	19	30	operator	operator	NOUN
fcis-6343	19	31	,	,	PUNCT
fcis-6343	19	32	∗	∗	NOUN
fcis-6343	19	33	is	be	AUX
fcis-6343	19	34	a	a	DET
fcis-6343	19	35	kind	kind	NOUN
fcis-6343	19	36	of	of	ADP
fcis-6343	19	37	algebraic	algebraic	ADJ
fcis-6343	19	38	operation	operation	NOUN
fcis-6343	19	39	.	.	PUNCT
fcis-6343	20	1	homomorphic	homomorphic	ADJ
fcis-6343	20	2	encryption	encryption	NOUN
fcis-6343	20	3	can	can	AUX
fcis-6343	20	4	be	be	AUX
fcis-6343	20	5	roughly	roughly	ADV
fcis-6343	20	6	divided	divide	VERB
fcis-6343	20	7	into	into	ADP
fcis-6343	20	8	the	the	DET
fcis-6343	20	9	following	follow	VERB
fcis-6343	20	10	categories	category	NOUN
fcis-6343	20	11	:	:	PUNCT
fcis-6343	20	12	partially	partially	ADV
fcis-6343	20	13	homomorphic	homomorphic	ADJ
fcis-6343	20	14	encryption	encryption	NOUN
fcis-6343	20	15	:	:	PUNCT
fcis-6343	20	16	it	it	PRON
fcis-6343	20	17	refers	refer	VERB
fcis-6343	20	18	to	to	ADP
fcis-6343	20	19	the	the	DET
fcis-6343	20	20	homomorphic	homomorphic	ADJ
fcis-6343	20	21	encryption	encryption	NOUN
fcis-6343	20	22	whose	whose	DET
fcis-6343	20	23	homomorphism	homomorphism	NOUN
fcis-6343	20	24	is	be	AUX
fcis-6343	20	25	only	only	ADV
fcis-6343	20	26	applicable	applicable	ADJ
fcis-6343	20	27	to	to	ADP
fcis-6343	20	28	a	a	DET
fcis-6343	20	29	certain	certain	ADJ
fcis-6343	20	30	kind	kind	NOUN
fcis-6343	20	31	of	of	ADP
fcis-6343	20	32	single	single	ADJ
fcis-6343	20	33	algebraic	algebraic	ADJ
fcis-6343	20	34	operation	operation	NOUN
fcis-6343	20	35	,	,	PUNCT
fcis-6343	20	36	including	include	VERB
fcis-6343	20	37	multiplication	multiplication	NOUN
fcis-6343	20	38	,	,	PUNCT
fcis-6343	20	39	addition	addition	NOUN
fcis-6343	20	40	etc	etc	X
fcis-6343	20	41	.	.	X
fcis-6343	20	42	,	,	PUNCT
fcis-6343	20	43	such	such	ADJ
fcis-6343	20	44	as	as	ADP
fcis-6343	20	45	rsa	rsa	PROPN
fcis-6343	20	46	algorithm	algorithm	NOUN
fcis-6343	20	47	,	,	PUNCT
fcis-6343	20	48	etc	etc	X
fcis-6343	20	49	.	.	X
fcis-6343	21	1	the	the	DET
fcis-6343	21	2	advantage	advantage	NOUN
fcis-6343	21	3	of	of	ADP
fcis-6343	21	4	partially	partially	ADV
fcis-6343	21	5	homomorphic	homomorphic	ADJ
fcis-6343	21	6	encryption	encryption	NOUN
fcis-6343	21	7	lies	lie	VERB
fcis-6343	21	8	in	in	ADP
fcis-6343	21	9	the	the	DET
fcis-6343	21	10	low	low	ADJ
fcis-6343	21	11	degree	degree	NOUN
fcis-6343	21	12	of	of	ADP
fcis-6343	21	13	complexity	complexity	NOUN
fcis-6343	21	14	,	,	PUNCT
fcis-6343	21	15	which	which	PRON
fcis-6343	21	16	means	mean	VERB
fcis-6343	21	17	the	the	DET
fcis-6343	21	18	amount	amount	NOUN
fcis-6343	21	19	of	of	ADP
fcis-6343	21	20	computation	computation	NOUN
fcis-6343	21	21	can	can	AUX
fcis-6343	21	22	be	be	AUX
fcis-6343	21	23	greatly	greatly	ADV
fcis-6343	21	24	reduced	reduce	VERB
fcis-6343	21	25	in	in	ADP
fcis-6343	21	26	most	most	ADJ
fcis-6343	21	27	cases	case	NOUN
fcis-6343	21	28	,	,	PUNCT
fcis-6343	21	29	and	and	CCONJ
fcis-6343	21	30	the	the	DET
fcis-6343	21	31	disadvantage	disadvantage	NOUN
fcis-6343	21	32	of	of	ADP
fcis-6343	21	33	it	it	PRON
fcis-6343	21	34	lies	lie	VERB
fcis-6343	21	35	in	in	ADP
fcis-6343	21	36	that	that	SCONJ
fcis-6343	21	37	it	it	PRON
fcis-6343	21	38	is	be	AUX
fcis-6343	21	39	only	only	ADV
fcis-6343	21	40	applicable	applicable	ADJ
fcis-6343	21	41	to	to	ADP
fcis-6343	21	42	a	a	DET
fcis-6343	21	43	single	single	ADJ
fcis-6343	21	44	kind	kind	NOUN
fcis-6343	21	45	of	of	ADP
fcis-6343	21	46	operation	operation	NOUN
fcis-6343	21	47	.	.	PUNCT
fcis-6343	22	1	hierarchical	hierarchical	ADJ
fcis-6343	22	2	homomorphic	homomorphic	ADJ
fcis-6343	22	3	encryption	encryption	NOUN
fcis-6343	22	4	:	:	PUNCT
fcis-6343	22	5	it	it	PRON
fcis-6343	22	6	refers	refer	VERB
fcis-6343	22	7	to	to	ADP
fcis-6343	22	8	the	the	DET
fcis-6343	22	9	homomorphic	homomorphic	ADJ
fcis-6343	22	10	encryption	encryption	NOUN
fcis-6343	22	11	whose	whose	DET
fcis-6343	22	12	homomorphism	homomorphism	NOUN
fcis-6343	22	13	is	be	AUX
fcis-6343	22	14	only	only	ADV
fcis-6343	22	15	applicable	applicable	ADJ
fcis-6343	22	16	to	to	ADP
fcis-6343	22	17	the	the	DET
fcis-6343	22	18	algebraic	algebraic	ADJ
fcis-6343	22	19	operation	operation	NOUN
fcis-6343	22	20	with	with	ADP
fcis-6343	22	21	limited	limited	ADJ
fcis-6343	22	22	times	time	NOUN
fcis-6343	22	23	.	.	PUNCT
fcis-6343	23	1	its	its	PRON
fcis-6343	23	2	advantage	advantage	NOUN
fcis-6343	23	3	lies	lie	VERB
fcis-6343	23	4	in	in	ADP
fcis-6343	23	5	that	that	SCONJ
fcis-6343	23	6	it	it	PRON
fcis-6343	23	7	can	can	AUX
fcis-6343	23	8	meet	meet	VERB
fcis-6343	23	9	the	the	DET
fcis-6343	23	10	requirement	requirement	NOUN
fcis-6343	23	11	of	of	ADP
fcis-6343	23	12	more	more	ADV
fcis-6343	23	13	complicated	complicated	ADJ
fcis-6343	23	14	operations	operation	NOUN
fcis-6343	23	15	,	,	PUNCT
fcis-6343	23	16	and	and	CCONJ
fcis-6343	23	17	its	its	PRON
fcis-6343	23	18	disadvantage	disadvantage	NOUN
fcis-6343	23	19	is	be	AUX
fcis-6343	23	20	that	that	SCONJ
fcis-6343	23	21	the	the	DET
fcis-6343	23	22	homomorphism	homomorphism	NOUN
fcis-6343	23	23	can	can	AUX
fcis-6343	23	24	no	no	ADV
fcis-6343	23	25	longer	long	ADV
fcis-6343	23	26	be	be	AUX
fcis-6343	23	27	guaranteed	guarantee	VERB
fcis-6343	23	28	in	in	ADP
fcis-6343	23	29	case	case	NOUN
fcis-6343	23	30	of	of	ADP
fcis-6343	23	31	multiple	multiple	ADJ
fcis-6343	23	32	times	time	NOUN
fcis-6343	23	33	of	of	ADP
fcis-6343	23	34	addition	addition	NOUN
fcis-6343	23	35	or	or	CCONJ
fcis-6343	23	36	multiplication	multiplication	NOUN
fcis-6343	23	37	operations	operation	NOUN
fcis-6343	23	38	.	.	PUNCT
fcis-6343	24	1	fully	fully	ADV
fcis-6343	24	2	homomorphic	homomorphic	ADJ
fcis-6343	24	3	encryption	encryption	NOUN
fcis-6343	24	4	:	:	PUNCT
fcis-6343	24	5	such	such	ADJ
fcis-6343	24	6	form	form	NOUN
fcis-6343	24	7	of	of	ADP
fcis-6343	24	8	encryption	encryption	NOUN
fcis-6343	24	9	refers	refer	VERB
fcis-6343	24	10	to	to	ADP
fcis-6343	24	11	the	the	DET
fcis-6343	24	12	homomorphic	homomorphic	ADJ
fcis-6343	24	13	encryption	encryption	NOUN
fcis-6343	24	14	whose	whose	DET
fcis-6343	24	15	homomorphism	homomorphism	NOUN
fcis-6343	24	16	will	will	AUX
fcis-6343	24	17	be	be	AUX
fcis-6343	24	18	remained	remain	VERB
fcis-6343	24	19	no	no	ADV
fcis-6343	24	20	matter	matter	NOUN
fcis-6343	24	21	any	any	DET
fcis-6343	24	22	times	time	NOUN
fcis-6343	24	23	of	of	ADP
fcis-6343	24	24	algebraic	algebraic	ADJ
fcis-6343	24	25	operations	operation	NOUN
fcis-6343	24	26	,	,	PUNCT
fcis-6343	24	27	including	include	VERB
fcis-6343	24	28	addition	addition	NOUN
fcis-6343	24	29	and	and	CCONJ
fcis-6343	24	30	multiplication	multiplication	NOUN
fcis-6343	24	31	are	be	AUX
fcis-6343	24	32	conducted	conduct	VERB
fcis-6343	24	33	.	.	PUNCT
fcis-6343	25	1	its	its	PRON
fcis-6343	25	2	advantage	advantage	NOUN
fcis-6343	25	3	lies	lie	VERB
fcis-6343	25	4	in	in	ADP
fcis-6343	25	5	that	that	SCONJ
fcis-6343	25	6	there	there	PRON
fcis-6343	25	7	is	be	VERB
fcis-6343	25	8	no	no	DET
fcis-6343	25	9	limitation	limitation	NOUN
fcis-6343	25	10	of	of	ADP
fcis-6343	25	11	the	the	DET
fcis-6343	25	12	complexity	complexity	NOUN
fcis-6343	25	13	of	of	ADP
fcis-6343	25	14	the	the	DET
fcis-6343	25	15	operation	operation	NOUN
fcis-6343	25	16	.	.	PUNCT
fcis-6343	26	1	however	however	ADV
fcis-6343	26	2	,	,	PUNCT
fcis-6343	26	3	such	such	ADJ
fcis-6343	26	4	kind	kind	NOUN
fcis-6343	26	5	of	of	ADP
fcis-6343	26	6	homomorphic	homomorphic	ADJ
fcis-6343	26	7	encryption	encryption	NOUN
fcis-6343	26	8	’s	’s	PART
fcis-6343	26	9	calculation	calculation	NOUN
fcis-6343	26	10	is	be	AUX
fcis-6343	26	11	very	very	ADV
fcis-6343	26	12	complicated	complicated	ADJ
fcis-6343	26	13	,	,	PUNCT
fcis-6343	26	14	which	which	PRON
fcis-6343	26	15	will	will	AUX
fcis-6343	26	16	lead	lead	VERB
fcis-6343	26	17	to	to	ADP
fcis-6343	26	18	a	a	DET
fcis-6343	26	19	great	great	ADJ
fcis-6343	26	20	limitation	limitation	NOUN
fcis-6343	26	21	in	in	ADP
fcis-6343	26	22	the	the	DET
fcis-6343	26	23	application	application	NOUN
fcis-6343	26	24	of	of	ADP
fcis-6343	26	25	actual	actual	ADJ
fcis-6343	26	26	projects	project	NOUN
fcis-6343	26	27	.	.	PUNCT
fcis-6343	27	1	classical	classical	ADJ
fcis-6343	27	2	homomorphic	homomorphic	ADJ
fcis-6343	27	3	encryption	encryption	NOUN
fcis-6343	27	4	protocols	protocol	NOUN
fcis-6343	27	5	include	include	VERB
fcis-6343	27	6	rsa	rsa	PROPN
fcis-6343	27	7	protocol	protocol	NOUN
fcis-6343	27	8	,	,	PUNCT
fcis-6343	27	9	elgamal	elgamal	ADJ
fcis-6343	27	10	protocol	protocol	NOUN
fcis-6343	27	11	,	,	PUNCT
fcis-6343	27	12	paillar	paillar	NOUN
fcis-6343	27	13	protocol	protocol	NOUN
fcis-6343	27	14	,	,	PUNCT
fcis-6343	27	15	gm	gm	PROPN
fcis-6343	27	16	protocol	protocol	NOUN
fcis-6343	27	17	and	and	CCONJ
fcis-6343	27	18	bgn	bgn	NOUN
fcis-6343	27	19	protocol	protocol	NOUN
fcis-6343	27	20	.	.	PUNCT
fcis-6343	28	1	in	in	ADP
fcis-6343	28	2	general	general	ADJ
fcis-6343	28	3	,	,	PUNCT
fcis-6343	28	4	homomorphic	homomorphic	ADJ
fcis-6343	28	5	encryption	encryption	NOUN
fcis-6343	28	6	is	be	AUX
fcis-6343	28	7	composed	compose	VERB
fcis-6343	28	8	of	of	ADP
fcis-6343	28	9	four	four	NUM
fcis-6343	28	10	parts	part	NOUN
fcis-6343	28	11	,	,	PUNCT
fcis-6343	28	12	which	which	PRON
fcis-6343	28	13	are	be	AUX
fcis-6343	28	14	secret	secret	ADJ
fcis-6343	28	15	key	key	ADJ
fcis-6343	28	16	generation	generation	NOUN
fcis-6343	28	17	,	,	PUNCT
fcis-6343	28	18	homomorphic	homomorphic	ADJ
fcis-6343	28	19	encryption	encryption	NOUN
fcis-6343	28	20	,	,	PUNCT
fcis-6343	28	21	homomorphic	homomorphic	ADJ
fcis-6343	28	22	decryption	decryption	NOUN
fcis-6343	28	23	and	and	CCONJ
fcis-6343	28	24	homomorphic	homomorphic	ADJ
fcis-6343	28	25	assignment	assignment	NOUN
fcis-6343	28	26	.	.	PUNCT
fcis-6343	29	1	secret	secret	ADJ
fcis-6343	29	2	key	key	ADJ
fcis-6343	29	3	generation	generation	NOUN
fcis-6343	29	4	.	.	PUNCT
fcis-6343	30	1	this	this	DET
fcis-6343	30	2	process	process	NOUN
fcis-6343	30	3	refers	refer	VERB
fcis-6343	30	4	to	to	ADP
fcis-6343	30	5	the	the	DET
fcis-6343	30	6	generation	generation	NOUN
fcis-6343	30	7	of	of	ADP
fcis-6343	30	8	secret	secret	ADJ
fcis-6343	30	9	keys	key	NOUN
fcis-6343	30	10	,	,	PUNCT
fcis-6343	30	11	including	include	VERB
fcis-6343	30	12	the	the	DET
fcis-6343	30	13	public	public	ADJ
fcis-6343	30	14	key	key	ADJ
fcis-6343	30	15	pk	pk	NOUN
fcis-6343	30	16	and	and	CCONJ
fcis-6343	30	17	the	the	DET
fcis-6343	30	18	private	private	ADJ
fcis-6343	30	19	key	key	NOUN
fcis-6343	30	20	sk	sk	NOUN
fcis-6343	30	21	,	,	PUNCT
fcis-6343	30	22	with	with	ADP
fcis-6343	30	23	the	the	DET
fcis-6343	30	24	parameter	parameter	NOUN
fcis-6343	30	25	λ	λ	PROPN
fcis-6343	30	26	.	.	PUNCT
fcis-6343	31	1	homomorphic	homomorphic	ADJ
fcis-6343	31	2	encryption	encryption	NOUN
fcis-6343	31	3	.	.	PUNCT
fcis-6343	32	1	this	this	DET
fcis-6343	32	2	process	process	NOUN
fcis-6343	32	3	refers	refer	VERB
fcis-6343	32	4	to	to	ADP
fcis-6343	32	5	the	the	DET
fcis-6343	32	6	process	process	NOUN
fcis-6343	32	7	of	of	ADP
fcis-6343	32	8	using	use	VERB
fcis-6343	32	9	the	the	DET
fcis-6343	32	10	open	open	ADJ
fcis-6343	32	11	public	public	ADJ
fcis-6343	32	12	key	key	ADJ
fcis-6343	32	13	pk	pk	NOUN
fcis-6343	32	14	to	to	PART
fcis-6343	32	15	conduct	conduct	VERB
fcis-6343	32	16	the	the	DET
fcis-6343	32	17	encryption	encryption	NOUN
fcis-6343	32	18	for	for	ADP
fcis-6343	32	19	the	the	DET
fcis-6343	32	20	provided	provide	VERB
fcis-6343	32	21	original	original	ADJ
fcis-6343	32	22	text	text	NOUN
fcis-6343	32	23	m	m	VERB
fcis-6343	32	24	∈	∈	PROPN
fcis-6343	32	25	{	{	PUNCT
fcis-6343	32	26	0	0	NUM
fcis-6343	32	27	,	,	PUNCT
fcis-6343	32	28	1	1	NUM
fcis-6343	32	29	}	}	PUNCT
fcis-6343	32	30	to	to	ADP
fcis-6343	32	31	111	111	NUM
fcis-6343	32	32	obtain	obtain	VERB
fcis-6343	32	33	the	the	DET
fcis-6343	32	34	ciphertext	ciphertext	NOUN
fcis-6343	32	35	c.	c.	PROPN
fcis-6343	32	36	homomorphic	homomorphic	ADJ
fcis-6343	32	37	decryption	decryption	NOUN
fcis-6343	32	38	.	.	PUNCT
fcis-6343	33	1	this	this	DET
fcis-6343	33	2	process	process	NOUN
fcis-6343	33	3	refers	refer	VERB
fcis-6343	33	4	to	to	ADP
fcis-6343	33	5	the	the	DET
fcis-6343	33	6	process	process	NOUN
fcis-6343	33	7	of	of	ADP
fcis-6343	33	8	using	use	VERB
fcis-6343	33	9	the	the	DET
fcis-6343	33	10	private	private	ADJ
fcis-6343	33	11	key	key	NOUN
fcis-6343	33	12	secretly	secretly	ADV
fcis-6343	33	13	kept	keep	VERB
fcis-6343	33	14	by	by	ADP
fcis-6343	33	15	the	the	DET
fcis-6343	33	16	individual	individual	NOUN
fcis-6343	33	17	to	to	PART
fcis-6343	33	18	conduct	conduct	VERB
fcis-6343	33	19	the	the	DET
fcis-6343	33	20	decryption	decryption	NOUN
fcis-6343	33	21	for	for	ADP
fcis-6343	33	22	the	the	DET
fcis-6343	33	23	ciphertext	ciphertext	NOUN
fcis-6343	33	24	to	to	PART
fcis-6343	33	25	obtain	obtain	VERB
fcis-6343	33	26	the	the	DET
fcis-6343	33	27	new	new	ADJ
fcis-6343	33	28	original	original	ADJ
fcis-6343	33	29	text	text	NOUN
fcis-6343	33	30	.	.	PUNCT
fcis-6343	34	1	homomorphic	homomorphic	ADJ
fcis-6343	34	2	assignment	assignment	NOUN
fcis-6343	34	3	.	.	PUNCT
fcis-6343	35	1	this	this	DET
fcis-6343	35	2	process	process	NOUN
fcis-6343	35	3	refers	refer	VERB
fcis-6343	35	4	to	to	ADP
fcis-6343	35	5	the	the	DET
fcis-6343	35	6	process	process	NOUN
fcis-6343	35	7	of	of	ADP
fcis-6343	35	8	calculation	calculation	NOUN
fcis-6343	35	9	based	base	VERB
fcis-6343	35	10	on	on	ADP
fcis-6343	35	11	the	the	DET
fcis-6343	35	12	public	public	ADJ
fcis-6343	35	13	key	key	ADJ
fcis-6343	35	14	pk	pk	NOUN
fcis-6343	35	15	and	and	CCONJ
fcis-6343	35	16	t	t	PROPN
fcis-6343	35	17	circuits	circuit	NOUN
fcis-6343	35	18	c	c	NOUN
fcis-6343	35	19	,	,	PUNCT
fcis-6343	35	20	and	and	CCONJ
fcis-6343	35	21	the	the	DET
fcis-6343	35	22	ciphertext	ciphertext	NOUN
fcis-6343	35	23	c	c	NOUN
fcis-6343	35	24	=	=	SYM
fcis-6343	35	25	(	(	PUNCT
fcis-6343	35	26	c1	c1	PROPN
fcis-6343	35	27	,	,	PUNCT
fcis-6343	35	28	...	...	PUNCT
fcis-6343	35	29	,	,	PUNCT
fcis-6343	35	30	ct	ct	PROPN
fcis-6343	35	31	)	)	PUNCT
fcis-6343	35	32	to	to	PART
fcis-6343	35	33	obtain	obtain	VERB
fcis-6343	35	34	c∗	c∗	NOUN
fcis-6343	35	35	=	=	SYM
fcis-6343	35	36	evaluate(pk	evaluate(pk	PROPN
fcis-6343	35	37	,	,	PUNCT
fcis-6343	35	38	c	c	X
fcis-6343	35	39	,	,	PUNCT
fcis-6343	35	40	c	c	NOUN
fcis-6343	35	41	)	)	PUNCT
fcis-6343	35	42	,	,	PUNCT
fcis-6343	35	43	and	and	CCONJ
fcis-6343	35	44	it	it	PRON
fcis-6343	35	45	is	be	AUX
fcis-6343	35	46	required	require	VERB
fcis-6343	35	47	that	that	SCONJ
fcis-6343	35	48	the	the	DET
fcis-6343	35	49	equation	equation	NOUN
fcis-6343	35	50	dec(sk	dec(sk	NOUN
fcis-6343	35	51	,	,	PUNCT
fcis-6343	35	52	c∗	c∗	NOUN
fcis-6343	35	53	)	)	PUNCT
fcis-6343	35	54	=	=	SYM
fcis-6343	35	55	c(m1	c(m1	NOUN
fcis-6343	35	56	,	,	PUNCT
fcis-6343	35	57	...	...	PUNCT
fcis-6343	35	58	,	,	PUNCT
fcis-6343	35	59	mn	mn	PROPN
fcis-6343	35	60	)	)	PUNCT
fcis-6343	35	61	be	be	AUX
fcis-6343	35	62	valid	valid	ADJ
fcis-6343	35	63	.	.	PUNCT
fcis-6343	36	1	remark	remark	PROPN
fcis-6343	36	2	:	:	PUNCT
fcis-6343	36	3	during	during	ADP
fcis-6343	36	4	the	the	DET
fcis-6343	36	5	whole	whole	ADJ
fcis-6343	36	6	process	process	NOUN
fcis-6343	36	7	of	of	ADP
fcis-6343	36	8	secret	secret	ADJ
fcis-6343	36	9	key	key	ADJ
fcis-6343	36	10	generation	generation	NOUN
fcis-6343	36	11	,	,	PUNCT
fcis-6343	36	12	encryption	encryption	NOUN
fcis-6343	36	13	,	,	PUNCT
fcis-6343	36	14	decryption	decryption	NOUN
fcis-6343	36	15	and	and	CCONJ
fcis-6343	36	16	assignment	assignment	NOUN
fcis-6343	36	17	,	,	PUNCT
fcis-6343	36	18	homomorphic	homomorphic	ADJ
fcis-6343	36	19	assignment	assignment	NOUN
fcis-6343	36	20	is	be	AUX
fcis-6343	36	21	the	the	DET
fcis-6343	36	22	most	most	ADV
fcis-6343	36	23	crucial	crucial	ADJ
fcis-6343	36	24	step	step	NOUN
fcis-6343	36	25	.	.	PUNCT
fcis-6343	37	1	the	the	DET
fcis-6343	37	2	homomorphic	homomorphic	ADJ
fcis-6343	37	3	assignment	assignment	NOUN
fcis-6343	37	4	can	can	AUX
fcis-6343	37	5	be	be	AUX
fcis-6343	37	6	conducted	conduct	VERB
fcis-6343	37	7	for	for	ADP
fcis-6343	37	8	any	any	DET
fcis-6343	37	9	function	function	NOUN
fcis-6343	37	10	through	through	ADP
fcis-6343	37	11	assignment	assignment	NOUN
fcis-6343	37	12	,	,	PUNCT
fcis-6343	37	13	which	which	PRON
fcis-6343	37	14	is	be	AUX
fcis-6343	37	15	conducted	conduct	VERB
fcis-6343	37	16	for	for	ADP
fcis-6343	37	17	the	the	DET
fcis-6343	37	18	ciphertext	ciphertext	NOUN
fcis-6343	37	19	.	.	PUNCT
fcis-6343	38	1	the	the	DET
fcis-6343	38	2	most	most	ADV
fcis-6343	38	3	important	important	ADJ
fcis-6343	38	4	is	be	AUX
fcis-6343	38	5	that	that	SCONJ
fcis-6343	38	6	the	the	DET
fcis-6343	38	7	decryption	decryption	NOUN
fcis-6343	38	8	function	function	NOUN
fcis-6343	38	9	can	can	AUX
fcis-6343	38	10	be	be	AUX
fcis-6343	38	11	obtained	obtain	VERB
fcis-6343	38	12	in	in	ADP
fcis-6343	38	13	this	this	DET
fcis-6343	38	14	way	way	NOUN
fcis-6343	38	15	.	.	PUNCT
fcis-6343	39	1	the	the	DET
fcis-6343	39	2	secret	secret	ADJ
fcis-6343	39	3	key	key	NOUN
fcis-6343	39	4	generated	generate	VERB
fcis-6343	39	5	in	in	ADP
fcis-6343	39	6	the	the	DET
fcis-6343	39	7	homomorphic	homomorphic	ADJ
fcis-6343	39	8	encryption	encryption	NOUN
fcis-6343	39	9	protocol	protocol	NOUN
fcis-6343	39	10	can	can	AUX
fcis-6343	39	11	be	be	AUX
fcis-6343	39	12	used	use	VERB
fcis-6343	39	13	for	for	ADP
fcis-6343	39	14	not	not	PART
fcis-6343	39	15	only	only	ADV
fcis-6343	39	16	the	the	DET
fcis-6343	39	17	scheme	scheme	NOUN
fcis-6343	39	18	applying	apply	VERB
fcis-6343	39	19	the	the	DET
fcis-6343	39	20	same	same	ADJ
fcis-6343	39	21	secret	secret	ADJ
fcis-6343	39	22	key	key	NOUN
fcis-6343	39	23	for	for	ADP
fcis-6343	39	24	encryption	encryption	NOUN
fcis-6343	39	25	and	and	CCONJ
fcis-6343	39	26	decryption	decryption	NOUN
fcis-6343	39	27	,	,	PUNCT
fcis-6343	39	28	but	but	CCONJ
fcis-6343	39	29	also	also	ADV
fcis-6343	39	30	the	the	DET
fcis-6343	39	31	scheme	scheme	NOUN
fcis-6343	39	32	applying	apply	VERB
fcis-6343	39	33	different	different	ADJ
fcis-6343	39	34	secret	secret	ADJ
fcis-6343	39	35	keys	key	NOUN
fcis-6343	39	36	for	for	ADP
fcis-6343	39	37	encryption	encryption	NOUN
fcis-6343	39	38	and	and	CCONJ
fcis-6343	39	39	decryption	decryption	NOUN
fcis-6343	39	40	.	.	PUNCT
fcis-6343	40	1	such	such	ADJ
fcis-6343	40	2	two	two	NUM
fcis-6343	40	3	kinds	kind	NOUN
fcis-6343	40	4	of	of	ADP
fcis-6343	40	5	schemes	scheme	NOUN
fcis-6343	40	6	are	be	AUX
fcis-6343	40	7	named	name	VERB
fcis-6343	40	8	as	as	ADP
fcis-6343	40	9	symmetric	symmetric	ADJ
fcis-6343	40	10	homomorphic	homomorphic	ADJ
fcis-6343	40	11	encryption	encryption	NOUN
fcis-6343	40	12	and	and	CCONJ
fcis-6343	40	13	asymmetric	asymmetric	ADJ
fcis-6343	40	14	homomorphic	homomorphic	ADJ
fcis-6343	40	15	encryption	encryption	NOUN
fcis-6343	40	16	,	,	PUNCT
fcis-6343	40	17	and	and	CCONJ
fcis-6343	40	18	the	the	DET
fcis-6343	40	19	latter	latter	ADJ
fcis-6343	40	20	is	be	AUX
fcis-6343	40	21	generally	generally	ADV
fcis-6343	40	22	more	more	ADV
fcis-6343	40	23	popular	popular	ADJ
fcis-6343	40	24	scheme	scheme	NOUN
fcis-6343	40	25	.	.	PUNCT
fcis-6343	41	1	3	3	X
fcis-6343	41	2	.	.	X
fcis-6343	41	3	examples	example	NOUN
fcis-6343	41	4	of	of	ADP
fcis-6343	41	5	partially	partially	ADV
fcis-6343	41	6	homomorphic	homomorphic	ADJ
fcis-6343	41	7	encryption	encryption	NOUN
fcis-6343	41	8	the	the	DET
fcis-6343	41	9	homomorphism	homomorphism	NOUN
fcis-6343	41	10	of	of	ADP
fcis-6343	41	11	partial	partial	ADJ
fcis-6343	41	12	homomorphic	homomorphic	ADJ
fcis-6343	41	13	encryption	encryption	NOUN
fcis-6343	41	14	is	be	AUX
fcis-6343	41	15	only	only	ADV
fcis-6343	41	16	applicable	applicable	ADJ
fcis-6343	41	17	to	to	ADP
fcis-6343	41	18	single	single	ADJ
fcis-6343	41	19	algebraic	algebraic	ADJ
fcis-6343	41	20	operations	operation	NOUN
fcis-6343	41	21	,	,	PUNCT
fcis-6343	41	22	such	such	ADJ
fcis-6343	41	23	as	as	ADP
fcis-6343	41	24	addition	addition	NOUN
fcis-6343	41	25	,	,	PUNCT
fcis-6343	41	26	multiplication	multiplication	NOUN
fcis-6343	41	27	,	,	PUNCT
fcis-6343	41	28	etc	etc	X
fcis-6343	41	29	.	.	X
fcis-6343	42	1	its	its	PRON
fcis-6343	42	2	calculation	calculation	NOUN
fcis-6343	42	3	is	be	AUX
fcis-6343	42	4	relatively	relatively	ADV
fcis-6343	42	5	simple	simple	ADJ
fcis-6343	42	6	,	,	PUNCT
fcis-6343	42	7	but	but	CCONJ
fcis-6343	42	8	the	the	DET
fcis-6343	42	9	range	range	NOUN
fcis-6343	42	10	of	of	ADP
fcis-6343	42	11	application	application	NOUN
fcis-6343	42	12	is	be	AUX
fcis-6343	42	13	also	also	ADV
fcis-6343	42	14	narrow	narrow	ADJ
fcis-6343	42	15	.	.	PUNCT
fcis-6343	43	1	example	example	NOUN
fcis-6343	44	1	4.2.1	4.2.1	NUM
fcis-6343	44	2	(	(	PUNCT
fcis-6343	44	3	rsa	rsa	NOUN
fcis-6343	44	4	scheme	scheme	NOUN
fcis-6343	44	5	):	):	PUNCT
fcis-6343	44	6	the	the	DET
fcis-6343	44	7	rsa	rsa	PROPN
fcis-6343	44	8	encryption	encryption	NOUN
fcis-6343	44	9	scheme	scheme	NOUN
fcis-6343	44	10	refers	refer	VERB
fcis-6343	44	11	to	to	ADP
fcis-6343	44	12	the	the	DET
fcis-6343	44	13	protocol	protocol	NOUN
fcis-6343	44	14	that	that	PRON
fcis-6343	44	15	is	be	AUX
fcis-6343	44	16	applicable	applicable	ADJ
fcis-6343	44	17	to	to	ADP
fcis-6343	44	18	the	the	DET
fcis-6343	44	19	homomorphism	homomorphism	NOUN
fcis-6343	44	20	of	of	ADP
fcis-6343	44	21	multiplication	multiplication	NOUN
fcis-6343	44	22	,	,	PUNCT
fcis-6343	44	23	and	and	CCONJ
fcis-6343	44	24	its	its	PRON
fcis-6343	44	25	brief	brief	ADJ
fcis-6343	44	26	structure	structure	NOUN
fcis-6343	44	27	and	and	CCONJ
fcis-6343	44	28	the	the	DET
fcis-6343	44	29	form	form	NOUN
fcis-6343	44	30	of	of	ADP
fcis-6343	44	31	presentation	presentation	NOUN
fcis-6343	44	32	are	be	AUX
fcis-6343	44	33	as	as	SCONJ
fcis-6343	44	34	follows	follow	VERB
fcis-6343	44	35	:	:	PUNCT
fcis-6343	44	36	key	key	ADJ
fcis-6343	44	37	generation	generation	NOUN
fcis-6343	44	38	:	:	PUNCT
fcis-6343	44	39	1	1	NUM
fcis-6343	44	40	.	.	X
fcis-6343	44	41	two	two	NUM
fcis-6343	44	42	prime	prime	ADJ
fcis-6343	44	43	numbers	number	NOUN
fcis-6343	44	44	that	that	PRON
fcis-6343	44	45	are	be	AUX
fcis-6343	44	46	large	large	ADJ
fcis-6343	44	47	enough	enough	ADV
fcis-6343	44	48	and	and	CCONJ
fcis-6343	44	49	not	not	PART
fcis-6343	44	50	close	close	ADJ
fcis-6343	44	51	to	to	ADP
fcis-6343	44	52	each	each	DET
fcis-6343	44	53	other	other	ADJ
fcis-6343	44	54	,	,	PUNCT
fcis-6343	44	55	p	p	NOUN
fcis-6343	44	56	and	and	CCONJ
fcis-6343	44	57	q	q	NOUN
fcis-6343	44	58	,	,	PUNCT
fcis-6343	44	59	are	be	AUX
fcis-6343	44	60	arbitrarily	arbitrarily	ADV
fcis-6343	44	61	chosen	choose	VERB
fcis-6343	44	62	and	and	CCONJ
fcis-6343	44	63	let	let	VERB
fcis-6343	44	64	n	n	PROPN
fcis-6343	44	65	=	=	PROPN
fcis-6343	44	66	pq	pq	PROPN
fcis-6343	44	67	,	,	PUNCT
fcis-6343	44	68	ϕ(n	ϕ(n	X
fcis-6343	44	69	)	)	PUNCT
fcis-6343	45	1	=	=	SYM
fcis-6343	46	1	(	(	PUNCT
fcis-6343	46	2	p	p	X
fcis-6343	46	3	−	−	PROPN
fcis-6343	46	4	1)(q	1)(q	NUM
fcis-6343	46	5	−	−	NOUN
fcis-6343	46	6	1	1	NUM
fcis-6343	46	7	)	)	PUNCT
fcis-6343	46	8	.	.	PUNCT
fcis-6343	47	1	2	2	X
fcis-6343	47	2	.	.	X
fcis-6343	47	3	the	the	DET
fcis-6343	47	4	integer	integer	NOUN
fcis-6343	47	5	e	e	NOUN
fcis-6343	47	6	is	be	AUX
fcis-6343	47	7	chosen	choose	VERB
fcis-6343	47	8	at	at	ADP
fcis-6343	47	9	random	random	ADJ
fcis-6343	47	10	,	,	PUNCT
fcis-6343	47	11	and	and	CCONJ
fcis-6343	47	12	e	e	NOUN
fcis-6343	47	13	and	and	CCONJ
fcis-6343	47	14	ϕ(n	ϕ(n	NUM
fcis-6343	47	15	)	)	PUNCT
fcis-6343	47	16	are	be	AUX
fcis-6343	47	17	relative	relative	ADJ
fcis-6343	47	18	prime	prime	NOUN
fcis-6343	47	19	of	of	ADP
fcis-6343	47	20	each	each	DET
fcis-6343	47	21	other	other	ADJ
fcis-6343	47	22	and	and	CCONJ
fcis-6343	47	23	1	1	NUM
fcis-6343	47	24	<	<	X
fcis-6343	47	25	e	e	X
fcis-6343	47	26	<	<	X
fcis-6343	47	27	ϕ(n	ϕ(n	PROPN
fcis-6343	47	28	)	)	PUNCT
fcis-6343	47	29	.	.	PUNCT
fcis-6343	48	1	d	d	NOUN
fcis-6343	48	2	is	be	AUX
fcis-6343	48	3	found	find	VERB
fcis-6343	48	4	such	such	ADJ
fcis-6343	48	5	that	that	SCONJ
fcis-6343	48	6	de	de	X
fcis-6343	48	7	=	=	SYM
fcis-6343	48	8	1	1	NUM
fcis-6343	48	9	mod	mod	PROPN
fcis-6343	48	10	ϕ(n	ϕ(n	PROPN
fcis-6343	48	11	)	)	PUNCT
fcis-6343	48	12	.	.	PUNCT
fcis-6343	49	1	3	3	X
fcis-6343	49	2	.	.	X
fcis-6343	50	1	the	the	DET
fcis-6343	50	2	public	public	ADJ
fcis-6343	50	3	key	key	NOUN
fcis-6343	50	4	is	be	AUX
fcis-6343	50	5	(	(	PUNCT
fcis-6343	50	6	n	n	X
fcis-6343	50	7	,	,	PUNCT
fcis-6343	50	8	e	e	NOUN
fcis-6343	50	9	)	)	PUNCT
fcis-6343	50	10	,	,	PUNCT
fcis-6343	50	11	and	and	CCONJ
fcis-6343	50	12	the	the	DET
fcis-6343	50	13	private	private	ADJ
fcis-6343	50	14	key	key	NOUN
fcis-6343	50	15	is	be	AUX
fcis-6343	50	16	(	(	PUNCT
fcis-6343	50	17	n	n	X
fcis-6343	50	18	,	,	PUNCT
fcis-6343	50	19	d	d	NOUN
fcis-6343	50	20	)	)	PUNCT
fcis-6343	50	21	.	.	PUNCT
fcis-6343	51	1	encryption	encryption	NOUN
fcis-6343	51	2	:	:	PUNCT
fcis-6343	51	3	for	for	ADP
fcis-6343	51	4	the	the	DET
fcis-6343	51	5	random	random	ADJ
fcis-6343	51	6	number	number	NOUN
fcis-6343	51	7	r	r	NOUN
fcis-6343	51	8	∈	∈	PROPN
fcis-6343	51	9	zp	zp	NOUN
fcis-6343	51	10	,	,	PUNCT
fcis-6343	51	11	calculate	calculate	NOUN
fcis-6343	51	12	c	c	NOUN
fcis-6343	51	13	=	=	SYM
fcis-6343	51	14	e(r	e(r	X
fcis-6343	51	15	)	)	PUNCT
fcis-6343	51	16	=	=	SYM
fcis-6343	51	17	re	re	X
fcis-6343	51	18	(	(	PUNCT
fcis-6343	51	19	mod	mod	PROPN
fcis-6343	51	20	n	n	CCONJ
fcis-6343	51	21	)	)	PUNCT
fcis-6343	51	22	.	.	PUNCT
fcis-6343	52	1	decryption	decryption	NOUN
fcis-6343	52	2	:	:	PUNCT
fcis-6343	52	3	m	m	PROPN
fcis-6343	52	4	=	=	PROPN
fcis-6343	52	5	d(c	d(c	PROPN
fcis-6343	52	6	)	)	PUNCT
fcis-6343	53	1	=	=	SYM
fcis-6343	53	2	cd	cd	PROPN
fcis-6343	53	3	(	(	PUNCT
fcis-6343	53	4	mod	mod	PROPN
fcis-6343	53	5	n	n	CCONJ
fcis-6343	53	6	)	)	PUNCT
fcis-6343	53	7	.	.	PUNCT
fcis-6343	54	1	here	here	ADV
fcis-6343	54	2	is	be	AUX
fcis-6343	54	3	another	another	DET
fcis-6343	54	4	partial	partial	ADJ
fcis-6343	54	5	homomorphic	homomorphic	ADJ
fcis-6343	54	6	encryption	encryption	NOUN
fcis-6343	54	7	scheme	scheme	NOUN
fcis-6343	54	8	.	.	PUNCT
fcis-6343	55	1	example	example	NOUN
fcis-6343	56	1	4.2.2	4.2.2	NUM
fcis-6343	56	2	(	(	PUNCT
fcis-6343	56	3	paillier	paillier	ADJ
fcis-6343	56	4	scheme	scheme	NOUN
fcis-6343	56	5	):	):	PUNCT
fcis-6343	56	6	paillier	paillier	ADJ
fcis-6343	56	7	scheme	scheme	NOUN
fcis-6343	56	8	refers	refer	VERB
fcis-6343	56	9	to	to	ADP
fcis-6343	56	10	the	the	DET
fcis-6343	56	11	scheme	scheme	NOUN
fcis-6343	56	12	that	that	PRON
fcis-6343	56	13	carries	carry	VERB
fcis-6343	56	14	out	out	ADP
fcis-6343	56	15	homomorphic	homomorphic	ADJ
fcis-6343	56	16	encryption	encryption	NOUN
fcis-6343	56	17	for	for	ADP
fcis-6343	56	18	the	the	DET
fcis-6343	56	19	part	part	NOUN
fcis-6343	56	20	of	of	ADP
fcis-6343	56	21	the	the	DET
fcis-6343	56	22	addition	addition	NOUN
fcis-6343	56	23	that	that	PRON
fcis-6343	56	24	conforms	conform	VERB
fcis-6343	56	25	to	to	ADP
fcis-6343	56	26	homomorphism	homomorphism	NOUN
fcis-6343	56	27	,	,	PUNCT
fcis-6343	56	28	and	and	CCONJ
fcis-6343	56	29	its	its	PRON
fcis-6343	56	30	brief	brief	ADJ
fcis-6343	56	31	structure	structure	NOUN
fcis-6343	56	32	and	and	CCONJ
fcis-6343	56	33	the	the	DET
fcis-6343	56	34	form	form	NOUN
fcis-6343	56	35	of	of	ADP
fcis-6343	56	36	presentation	presentation	NOUN
fcis-6343	56	37	are	be	AUX
fcis-6343	56	38	as	as	SCONJ
fcis-6343	56	39	follows	follow	VERB
fcis-6343	56	40	:	:	PUNCT
fcis-6343	56	41	key	key	ADJ
fcis-6343	56	42	generation	generation	NOUN
fcis-6343	56	43	:	:	PUNCT
fcis-6343	56	44	1	1	NUM
fcis-6343	56	45	.	.	X
fcis-6343	56	46	two	two	NUM
fcis-6343	56	47	prime	prime	ADJ
fcis-6343	56	48	numbers	number	NOUN
fcis-6343	56	49	that	that	PRON
fcis-6343	56	50	are	be	AUX
fcis-6343	56	51	large	large	ADJ
fcis-6343	56	52	enough	enough	ADV
fcis-6343	56	53	and	and	CCONJ
fcis-6343	56	54	not	not	PART
fcis-6343	56	55	close	close	ADJ
fcis-6343	56	56	to	to	ADP
fcis-6343	56	57	each	each	DET
fcis-6343	56	58	other	other	ADJ
fcis-6343	56	59	,	,	PUNCT
fcis-6343	56	60	p	p	NOUN
fcis-6343	56	61	and	and	CCONJ
fcis-6343	56	62	q	q	NOUN
fcis-6343	56	63	,	,	PUNCT
fcis-6343	56	64	are	be	AUX
fcis-6343	56	65	arbitrarily	arbitrarily	ADV
fcis-6343	56	66	chosen	choose	VERB
fcis-6343	56	67	.	.	PUNCT
fcis-6343	57	1	pq	pq	INTJ
fcis-6343	57	2	and	and	CCONJ
fcis-6343	57	3	(	(	PUNCT
fcis-6343	57	4	p−1)(q	p−1)(q	INTJ
fcis-6343	57	5	−	−	NOUN
fcis-6343	57	6	1	1	NUM
fcis-6343	57	7	)	)	PUNCT
fcis-6343	57	8	are	be	AUX
fcis-6343	57	9	relative	relative	ADJ
fcis-6343	57	10	prime	prime	NOUN
fcis-6343	57	11	of	of	ADP
fcis-6343	57	12	each	each	DET
fcis-6343	57	13	other	other	ADJ
fcis-6343	57	14	.	.	PUNCT
fcis-6343	58	1	let	let	VERB
fcis-6343	58	2	n	n	PRON
fcis-6343	58	3	=	=	SYM
fcis-6343	58	4	pq	pq	PROPN
fcis-6343	58	5	and	and	CCONJ
fcis-6343	58	6	λ	λ	PROPN
fcis-6343	58	7	is	be	AUX
fcis-6343	58	8	equal	equal	ADJ
fcis-6343	58	9	to	to	ADP
fcis-6343	58	10	the	the	DET
fcis-6343	58	11	least	least	ADJ
fcis-6343	58	12	common	common	ADJ
fcis-6343	58	13	multiple	multiple	NOUN
fcis-6343	58	14	of	of	ADP
fcis-6343	58	15	p	p	NOUN
fcis-6343	58	16	−	−	PROPN
fcis-6343	58	17	1	1	NUM
fcis-6343	58	18	and	and	CCONJ
fcis-6343	58	19	q	q	ADJ
fcis-6343	58	20	−	−	PROPN
fcis-6343	58	21	1	1	NUM
fcis-6343	58	22	.	.	NOUN
fcis-6343	58	23	2	2	NUM
fcis-6343	58	24	.	.	X
fcis-6343	58	25	a	a	DET
fcis-6343	58	26	random	random	ADJ
fcis-6343	58	27	integer	integer	NOUN
fcis-6343	58	28	g	g	PROPN
fcis-6343	58	29	∈	∈	PROPN
fcis-6343	58	30	zn∗2	zn∗2	NOUN
fcis-6343	58	31	is	be	AUX
fcis-6343	58	32	chosen	choose	VERB
fcis-6343	58	33	,	,	PUNCT
fcis-6343	58	34	and	and	CCONJ
fcis-6343	58	35	there	there	PRON
fcis-6343	58	36	is	be	VERB
fcis-6343	58	37	an	an	DET
fcis-6343	58	38	µ	µ	NOUN
fcis-6343	58	39	=	=	PUNCT
fcis-6343	58	40	(	(	PUNCT
fcis-6343	58	41	l(gλ	l(gλ	X
fcis-6343	58	42	mod	mod	PROPN
fcis-6343	58	43	n2	n2	PROPN
fcis-6343	58	44	)	)	PUNCT
fcis-6343	58	45	)	)	PUNCT
fcis-6343	58	46	−1	−1	NOUN
fcis-6343	58	47	mod	mod	PROPN
fcis-6343	58	48	n.	n.	PROPN
fcis-6343	58	49	3	3	NUM
fcis-6343	58	50	.	.	PUNCT
fcis-6343	59	1	the	the	DET
fcis-6343	59	2	public	public	ADJ
fcis-6343	59	3	key	key	NOUN
fcis-6343	59	4	is	be	AUX
fcis-6343	59	5	(	(	PUNCT
fcis-6343	59	6	n	n	X
fcis-6343	59	7	,	,	PUNCT
fcis-6343	59	8	g	g	NOUN
fcis-6343	59	9	)	)	PUNCT
fcis-6343	59	10	,	,	PUNCT
fcis-6343	59	11	and	and	CCONJ
fcis-6343	59	12	the	the	DET
fcis-6343	59	13	private	private	ADJ
fcis-6343	59	14	key	key	NOUN
fcis-6343	59	15	is	be	AUX
fcis-6343	59	16	(	(	PUNCT
fcis-6343	59	17	λ,µ	λ,µ	NOUN
fcis-6343	59	18	)	)	PUNCT
fcis-6343	59	19	.	.	PUNCT
fcis-6343	60	1	encryption	encryption	NOUN
fcis-6343	60	2	:	:	PUNCT
fcis-6343	61	1	c	c	NOUN
fcis-6343	61	2	=	=	SYM
fcis-6343	61	3	e(m	e(m	PROPN
fcis-6343	61	4	,	,	PUNCT
fcis-6343	61	5	r	r	NOUN
fcis-6343	61	6	)	)	PUNCT
fcis-6343	61	7	=	=	NOUN
fcis-6343	61	8	gmrn(mod	gmrn(mod	PROPN
fcis-6343	61	9	n	n	PROPN
fcis-6343	61	10	)	)	PUNCT
fcis-6343	61	11	,	,	PUNCT
fcis-6343	61	12	r2	r2	PROPN
fcis-6343	61	13	∈	∈	PROPN
fcis-6343	61	14	zn	zn	PROPN
fcis-6343	61	15	is	be	AUX
fcis-6343	61	16	calculated	calculate	VERB
fcis-6343	61	17	for	for	ADP
fcis-6343	61	18	the	the	DET
fcis-6343	61	19	random	random	ADJ
fcis-6343	61	20	number	number	NOUN
fcis-6343	61	21	r	r	NOUN
fcis-6343	61	22	∈	∈	PROPN
fcis-6343	61	23	zp	zp	PROPN
fcis-6343	61	24	with	with	ADP
fcis-6343	61	25	m	m	PROPN
fcis-6343	61	26	the	the	DET
fcis-6343	61	27	encrypted	encrypt	VERB
fcis-6343	61	28	text	text	NOUN
fcis-6343	61	29	.	.	PUNCT
fcis-6343	62	1	decryption	decryption	NOUN
fcis-6343	62	2	:	:	PUNCT
fcis-6343	63	1	m	m	PROPN
fcis-6343	63	2	=	=	PROPN
fcis-6343	63	3	d(c	d(c	PROPN
fcis-6343	63	4	,	,	PUNCT
fcis-6343	63	5	r	r	NOUN
fcis-6343	63	6	)	)	PUNCT
fcis-6343	63	7	=	=	SYM
fcis-6343	63	8	mod	mod	PROPN
fcis-6343	63	9	n.	n.	NOUN
fcis-6343	63	10	in	in	ADP
fcis-6343	63	11	the	the	DET
fcis-6343	63	12	above	above	ADJ
fcis-6343	63	13	,	,	PUNCT
fcis-6343	63	14	l(x	l(x	PROPN
fcis-6343	63	15	)	)	PUNCT
fcis-6343	63	16	=	=	PUNCT
fcis-6343	63	17	.	.	PUNCT
fcis-6343	64	1	partially	partially	ADV
fcis-6343	64	2	homomorphic	homomorphic	ADJ
fcis-6343	64	3	encryption	encryption	NOUN
fcis-6343	64	4	is	be	AUX
fcis-6343	64	5	still	still	ADV
fcis-6343	64	6	applied	apply	VERB
fcis-6343	64	7	in	in	ADP
fcis-6343	64	8	some	some	DET
fcis-6343	64	9	relatively	relatively	ADV
fcis-6343	64	10	simple	simple	ADJ
fcis-6343	64	11	systems	system	NOUN
fcis-6343	64	12	of	of	ADP
fcis-6343	64	13	encryption	encryption	NOUN
fcis-6343	64	14	.	.	PUNCT
fcis-6343	65	1	4	4	X
fcis-6343	65	2	.	.	X
fcis-6343	65	3	an	an	DET
fcis-6343	65	4	implementation	implementation	NOUN
fcis-6343	65	5	of	of	ADP
fcis-6343	65	6	hierarchical	hierarchical	ADJ
fcis-6343	65	7	homomorphic	homomorphic	ADJ
fcis-6343	65	8	encryption	encryption	NOUN
fcis-6343	65	9	compared	compare	VERB
fcis-6343	65	10	with	with	ADP
fcis-6343	65	11	partially	partially	ADV
fcis-6343	65	12	homomorphic	homomorphic	ADJ
fcis-6343	65	13	encryption	encryption	NOUN
fcis-6343	65	14	,	,	PUNCT
fcis-6343	65	15	hierarchical	hierarchical	ADJ
fcis-6343	65	16	homomorphic	homomorphic	ADJ
fcis-6343	65	17	encryption	encryption	NOUN
fcis-6343	65	18	could	could	AUX
fcis-6343	65	19	apply	apply	VERB
fcis-6343	65	20	to	to	ADP
fcis-6343	65	21	more	more	ADV
fcis-6343	65	22	complicated	complicated	ADJ
fcis-6343	65	23	operations	operation	NOUN
fcis-6343	65	24	.	.	PUNCT
fcis-6343	66	1	however	however	ADV
fcis-6343	66	2	,	,	PUNCT
fcis-6343	66	3	the	the	DET
fcis-6343	66	4	homomorphism	homomorphism	NOUN
fcis-6343	66	5	ca	can	AUX
fcis-6343	66	6	n’t	not	PART
fcis-6343	66	7	be	be	AUX
fcis-6343	66	8	ensured	ensure	VERB
fcis-6343	66	9	if	if	SCONJ
fcis-6343	66	10	the	the	DET
fcis-6343	66	11	time	time	NOUN
fcis-6343	66	12	of	of	ADP
fcis-6343	66	13	operation	operation	NOUN
fcis-6343	66	14	of	of	ADP
fcis-6343	66	15	addition	addition	NOUN
fcis-6343	66	16	and	and	CCONJ
fcis-6343	66	17	multiplication	multiplication	NOUN
fcis-6343	66	18	exceeds	exceed	VERB
fcis-6343	66	19	a	a	DET
fcis-6343	66	20	limit	limit	NOUN
fcis-6343	66	21	.	.	PUNCT
fcis-6343	67	1	a	a	DET
fcis-6343	67	2	simple	simple	ADJ
fcis-6343	67	3	example	example	NOUN
fcis-6343	67	4	of	of	ADP
fcis-6343	67	5	hierarchical	hierarchical	ADJ
fcis-6343	67	6	homomorphic	homomorphic	ADJ
fcis-6343	67	7	encryption	encryption	NOUN
fcis-6343	67	8	is	be	AUX
fcis-6343	67	9	given	give	VERB
fcis-6343	67	10	here	here	ADV
fcis-6343	67	11	.	.	PUNCT
fcis-6343	68	1	example	example	NOUN
fcis-6343	69	1	4.3.1	4.3.1	NUM
fcis-6343	69	2	:	:	PUNCT
fcis-6343	69	3	b	b	NOUN
fcis-6343	69	4	is	be	AUX
fcis-6343	69	5	a	a	DET
fcis-6343	69	6	binary	binary	ADJ
fcis-6343	69	7	number	number	NOUN
fcis-6343	69	8	,	,	PUNCT
fcis-6343	69	9	and	and	CCONJ
fcis-6343	69	10	the	the	DET
fcis-6343	69	11	encryption	encryption	NOUN
fcis-6343	69	12	scheme	scheme	NOUN
fcis-6343	69	13	meet	meet	NOUN
fcis-6343	69	14	c	c	NOUN
fcis-6343	69	15	=	=	SYM
fcis-6343	69	16	e(b	e(b	X
fcis-6343	69	17	)	)	PUNCT
fcis-6343	69	18	=	=	SYM
fcis-6343	69	19	b	b	PROPN
fcis-6343	69	20	+	+	NUM
fcis-6343	69	21	2x	2x	NUM
fcis-6343	69	22	+	+	CCONJ
fcis-6343	69	23	kp	kp	NOUN
fcis-6343	69	24	.	.	PUNCT
fcis-6343	70	1	in	in	ADP
fcis-6343	70	2	this	this	DET
fcis-6343	70	3	formula	formula	NOUN
fcis-6343	70	4	,	,	PUNCT
fcis-6343	70	5	p	p	NOUN
fcis-6343	70	6	is	be	AUX
fcis-6343	70	7	an	an	DET
fcis-6343	70	8	odd	odd	ADJ
fcis-6343	70	9	number	number	NOUN
fcis-6343	70	10	and	and	CCONJ
fcis-6343	70	11	the	the	DET
fcis-6343	70	12	secret	secret	ADJ
fcis-6343	70	13	key	key	NOUN
fcis-6343	70	14	of	of	ADP
fcis-6343	70	15	the	the	DET
fcis-6343	70	16	encryption	encryption	NOUN
fcis-6343	70	17	b	b	NOUN
fcis-6343	70	18	,	,	PUNCT
fcis-6343	70	19	and	and	CCONJ
fcis-6343	70	20	x	x	X
fcis-6343	70	21	is	be	AUX
fcis-6343	70	22	a	a	DET
fcis-6343	70	23	random	random	ADJ
fcis-6343	70	24	number	number	NOUN
fcis-6343	70	25	.	.	PUNCT
fcis-6343	71	1	since	since	SCONJ
fcis-6343	71	2	x	x	PRON
fcis-6343	71	3	is	be	AUX
fcis-6343	71	4	random	random	ADJ
fcis-6343	71	5	,	,	PUNCT
fcis-6343	71	6	the	the	DET
fcis-6343	71	7	parity	parity	NOUN
fcis-6343	71	8	of	of	ADP
fcis-6343	71	9	c	c	PROPN
fcis-6343	71	10	is	be	AUX
fcis-6343	71	11	also	also	ADV
fcis-6343	71	12	random	random	ADJ
fcis-6343	71	13	.	.	PUNCT
fcis-6343	72	1	however	however	ADV
fcis-6343	72	2	,	,	PUNCT
fcis-6343	72	3	the	the	DET
fcis-6343	72	4	parity	parity	NOUN
fcis-6343	72	5	of	of	ADP
fcis-6343	72	6	b	b	NOUN
fcis-6343	72	7	can	can	AUX
fcis-6343	72	8	be	be	AUX
fcis-6343	72	9	known	know	VERB
fcis-6343	72	10	after	after	ADP
fcis-6343	72	11	mod	mod	PROPN
fcis-6343	72	12	p	p	PROPN
fcis-6343	72	13	for	for	ADP
fcis-6343	72	14	c	c	PROPN
fcis-6343	72	15	,	,	PUNCT
fcis-6343	72	16	that	that	ADV
fcis-6343	72	17	is	is	ADV
fcis-6343	72	18	,	,	PUNCT
fcis-6343	72	19	decryption	decryption	NOUN
fcis-6343	72	20	is	be	AUX
fcis-6343	72	21	conducted	conduct	VERB
fcis-6343	72	22	for	for	ADP
fcis-6343	72	23	c.	c.	PROPN
fcis-6343	72	24	the	the	DET
fcis-6343	72	25	homomorphism	homomorphism	NOUN
fcis-6343	72	26	of	of	ADP
fcis-6343	72	27	the	the	DET
fcis-6343	72	28	encryption	encryption	NOUN
fcis-6343	72	29	is	be	AUX
fcis-6343	72	30	not	not	PART
fcis-6343	72	31	hard	hard	ADJ
fcis-6343	72	32	to	to	PART
fcis-6343	72	33	be	be	AUX
fcis-6343	72	34	verified	verify	VERB
fcis-6343	72	35	.	.	PUNCT
fcis-6343	73	1	assuming	assume	VERB
fcis-6343	73	2	that	that	SCONJ
fcis-6343	73	3	:	:	PUNCT
fcis-6343	73	4	c1	c1	NOUN
fcis-6343	73	5	=	=	PUNCT
fcis-6343	73	6	e(b1	e(b1	VERB
fcis-6343	73	7	)	)	PUNCT
fcis-6343	74	1	=	=	SYM
fcis-6343	74	2	b1	b1	NOUN
fcis-6343	74	3	+	+	CCONJ
fcis-6343	74	4	2x1	2x1	NUM
fcis-6343	75	1	+	+	CCONJ
fcis-6343	75	2	k1p	k1p	PROPN
fcis-6343	75	3	,	,	PUNCT
fcis-6343	75	4	c2	c2	PROPN
fcis-6343	75	5	=	=	PUNCT
fcis-6343	75	6	e(b2	e(b2	NOUN
fcis-6343	75	7	)	)	PUNCT
fcis-6343	76	1	=	=	SYM
fcis-6343	76	2	b2	b2	NOUN
fcis-6343	76	3	+	+	CCONJ
fcis-6343	76	4	2x2	2x2	NUM
fcis-6343	76	5	+	+	CCONJ
fcis-6343	76	6	k2p	k2p	PROPN
fcis-6343	76	7	.	.	PUNCT
fcis-6343	77	1	then	then	ADV
fcis-6343	77	2	the	the	DET
fcis-6343	77	3	homomorphism	homomorphism	NOUN
fcis-6343	77	4	of	of	ADP
fcis-6343	77	5	the	the	DET
fcis-6343	77	6	addition	addition	NOUN
fcis-6343	77	7	is	be	AUX
fcis-6343	77	8	:	:	PUNCT
fcis-6343	77	9	e(b1	e(b1	VERB
fcis-6343	77	10	)	)	PUNCT
fcis-6343	78	1	+	+	CCONJ
fcis-6343	78	2	e(b2	e(b2	NOUN
fcis-6343	78	3	)	)	PUNCT
fcis-6343	79	1	=	=	PROPN
fcis-6343	79	2	c1	c1	PROPN
fcis-6343	79	3	+	+	CCONJ
fcis-6343	79	4	c2	c2	PROPN
fcis-6343	79	5	=	=	SYM
fcis-6343	79	6	(	(	PUNCT
fcis-6343	79	7	b1	b1	NOUN
fcis-6343	79	8	+	+	CCONJ
fcis-6343	79	9	b2	b2	NOUN
fcis-6343	79	10	)	)	PUNCT
fcis-6343	79	11	+	+	CCONJ
fcis-6343	79	12	2(x1	2(x1	NUM
fcis-6343	79	13	+	+	CCONJ
fcis-6343	79	14	x2	x2	NOUN
fcis-6343	79	15	)	)	PUNCT
fcis-6343	80	1	+	+	CCONJ
fcis-6343	80	2	(	(	PUNCT
fcis-6343	80	3	k1	k1	X
fcis-6343	80	4	+	+	CCONJ
fcis-6343	80	5	k2	k2	ADJ
fcis-6343	80	6	)	)	PUNCT
fcis-6343	80	7	p	p	NOUN
fcis-6343	80	8	=	=	NOUN
fcis-6343	80	9	e(b1	e(b1	VERB
fcis-6343	80	10	+	+	X
fcis-6343	80	11	b2	b2	NOUN
fcis-6343	80	12	)	)	PUNCT
fcis-6343	80	13	.	.	PUNCT
fcis-6343	81	1	the	the	DET
fcis-6343	81	2	homomorphism	homomorphism	NOUN
fcis-6343	81	3	of	of	ADP
fcis-6343	81	4	the	the	DET
fcis-6343	81	5	multiplication	multiplication	NOUN
fcis-6343	81	6	:	:	PUNCT
fcis-6343	81	7	e(b1	e(b1	NOUN
fcis-6343	81	8	)	)	PUNCT
fcis-6343	81	9	e(b2	e(b2	NOUN
fcis-6343	81	10	)	)	PUNCT
fcis-6343	82	1	=	=	PROPN
fcis-6343	82	2	c1	c1	PROPN
fcis-6343	82	3	c2	c2	PROPN
fcis-6343	82	4	=	=	PROPN
fcis-6343	82	5	b1	b1	PROPN
fcis-6343	82	6	b2	b2	NOUN
fcis-6343	82	7	+	+	CCONJ
fcis-6343	82	8	2(b1x2	2(b1x2	NUM
fcis-6343	83	1	+	+	CCONJ
fcis-6343	83	2	b2x1	b2x1	X
fcis-6343	83	3	+	+	NOUN
fcis-6343	83	4	2x1x2	2x1x2	NUM
fcis-6343	83	5	)	)	PUNCT
fcis-6343	84	1	+	+	CCONJ
fcis-6343	84	2	kp	kp	X
fcis-6343	84	3	=	=	NOUN
fcis-6343	84	4	e(b1	e(b1	NOUN
fcis-6343	84	5	b2	b2	NOUN
fcis-6343	84	6	)	)	PUNCT
fcis-6343	84	7	.	.	PUNCT
fcis-6343	85	1	x	x	X
fcis-6343	85	2	will	will	AUX
fcis-6343	85	3	gradually	gradually	ADV
fcis-6343	85	4	increase	increase	VERB
fcis-6343	85	5	during	during	ADP
fcis-6343	85	6	the	the	DET
fcis-6343	85	7	accumulation	accumulation	NOUN
fcis-6343	85	8	of	of	ADP
fcis-6343	85	9	the	the	DET
fcis-6343	85	10	time	time	NOUN
fcis-6343	85	11	of	of	ADP
fcis-6343	85	12	calculations	calculation	NOUN
fcis-6343	85	13	until	until	SCONJ
fcis-6343	85	14	it	it	PRON
fcis-6343	85	15	affects	affect	VERB
fcis-6343	85	16	the	the	DET
fcis-6343	85	17	parity	parity	NOUN
fcis-6343	85	18	of	of	ADP
fcis-6343	85	19	the	the	DET
fcis-6343	85	20	ciphertext	ciphertext	PROPN
fcis-6343	85	21	c	c	PROPN
fcis-6343	85	22	(	(	PUNCT
fcis-6343	85	23	mod	mod	PROPN
fcis-6343	85	24	p	p	X
fcis-6343	85	25	)	)	PUNCT
fcis-6343	85	26	.	.	PUNCT
fcis-6343	86	1	therefore	therefore	ADV
fcis-6343	86	2	,	,	PUNCT
fcis-6343	86	3	this	this	DET
fcis-6343	86	4	scheme	scheme	NOUN
fcis-6343	86	5	is	be	AUX
fcis-6343	86	6	hierarchical	hierarchical	ADJ
fcis-6343	86	7	homo	homo	NOUN
fcis-6343	86	8	morphic	morphic	ADJ
fcis-6343	86	9	encryption	encryption	NOUN
fcis-6343	86	10	rather	rather	ADV
fcis-6343	86	11	than	than	ADP
fcis-6343	86	12	fully	fully	ADV
fcis-6343	86	13	homomorphic	homomorphic	ADJ
fcis-6343	86	14	encryption	encryption	NOUN
fcis-6343	86	15	.	.	PUNCT
fcis-6343	87	1	5	5	X
fcis-6343	87	2	.	.	X
fcis-6343	87	3	fully	fully	ADV
fcis-6343	87	4	homomorphic	homomorphic	ADJ
fcis-6343	87	5	encryption	encryption	NOUN
fcis-6343	87	6	the	the	DET
fcis-6343	87	7	requirement	requirement	NOUN
fcis-6343	87	8	of	of	ADP
fcis-6343	87	9	fully	fully	ADV
fcis-6343	87	10	homomorphic	homomorphic	ADJ
fcis-6343	87	11	encryption	encryption	NOUN
fcis-6343	87	12	should	should	AUX
fcis-6343	87	13	be	be	AUX
fcis-6343	87	14	met	meet	VERB
fcis-6343	87	15	for	for	ADP
fcis-6343	87	16	the	the	DET
fcis-6343	87	17	practical	practical	ADJ
fcis-6343	87	18	application	application	NOUN
fcis-6343	87	19	of	of	ADP
fcis-6343	87	20	homomorphic	homomorphic	ADJ
fcis-6343	87	21	encryption	encryption	NOUN
fcis-6343	87	22	.	.	PUNCT
fcis-6343	88	1	in	in	ADP
fcis-6343	88	2	1978	1978	NUM
fcis-6343	88	3	,	,	PUNCT
fcis-6343	88	4	a	a	DET
fcis-6343	88	5	protocol	protocol	NOUN
fcis-6343	88	6	of	of	ADP
fcis-6343	88	7	homomorphic	homomorphic	ADJ
fcis-6343	88	8	encryption	encryption	NOUN
fcis-6343	88	9	[	[	X
fcis-6343	88	10	1	1	NUM
fcis-6343	88	11	]	]	PUNCT
fcis-6343	88	12	was	be	AUX
fcis-6343	88	13	put	put	VERB
fcis-6343	88	14	forward	forward	ADV
fcis-6343	88	15	,	,	PUNCT
fcis-6343	88	16	which	which	PRON
fcis-6343	88	17	was	be	AUX
fcis-6343	88	18	attributed	attribute	VERB
fcis-6343	88	19	to	to	ADP
fcis-6343	88	20	rivest	riv	ADJ
fcis-6343	88	21	et	et	PROPN
fcis-6343	88	22	al	al	PROPN
fcis-6343	88	23	.	.	PUNCT
fcis-6343	89	1	in	in	ADP
fcis-6343	89	2	comparison	comparison	NOUN
fcis-6343	89	3	with	with	ADP
fcis-6343	89	4	the	the	DET
fcis-6343	89	5	ordinary	ordinary	ADJ
fcis-6343	89	6	definition	definition	NOUN
fcis-6343	89	7	of	of	ADP
fcis-6343	89	8	homomorphic	homomorphic	ADJ
fcis-6343	89	9	encryption	encryption	NOUN
fcis-6343	89	10	,	,	PUNCT
fcis-6343	89	11	the	the	DET
fcis-6343	89	12	homomorphism	homomorphism	NOUN
fcis-6343	89	13	of	of	ADP
fcis-6343	89	14	fully	fully	ADV
fcis-6343	89	15	homomorphic	homomorphic	ADJ
fcis-6343	89	16	encryption	encryption	NOUN
fcis-6343	89	17	for	for	ADP
fcis-6343	89	18	the	the	DET
fcis-6343	89	19	two	two	NUM
fcis-6343	89	20	algebraic	algebraic	ADJ
fcis-6343	89	21	operations	operation	NOUN
fcis-6343	89	22	of	of	ADP
fcis-6343	89	23	addition	addition	NOUN
fcis-6343	89	24	and	and	CCONJ
fcis-6343	89	25	multiplication	multiplication	NOUN
fcis-6343	89	26	should	should	AUX
fcis-6343	89	27	be	be	AUX
fcis-6343	89	28	met	meet	VERB
fcis-6343	89	29	,	,	PUNCT
fcis-6343	89	30	and	and	CCONJ
fcis-6343	89	31	the	the	DET
fcis-6343	89	32	degree	degree	NOUN
fcis-6343	89	33	of	of	ADP
fcis-6343	89	34	complexity	complexity	NOUN
fcis-6343	89	35	of	of	ADP
fcis-6343	89	36	the	the	DET
fcis-6343	89	37	calculation	calculation	NOUN
fcis-6343	89	38	is	be	AUX
fcis-6343	89	39	very	very	ADV
fcis-6343	89	40	high	high	ADJ
fcis-6343	89	41	.	.	PUNCT
fcis-6343	90	1	the	the	DET
fcis-6343	90	2	first	first	ADJ
fcis-6343	90	3	fully	fully	ADV
fcis-6343	90	4	homomorphic	homomorphic	ADJ
fcis-6343	90	5	encryption	encryption	NOUN
fcis-6343	90	6	algorithm	algorithm	NOUN
fcis-6343	90	7	was	be	AUX
fcis-6343	90	8	put	put	VERB
fcis-6343	90	9	forward	forward	ADV
fcis-6343	90	10	by	by	ADP
fcis-6343	90	11	gentry	gentry	NOUN
fcis-6343	90	12	in	in	ADP
fcis-6343	90	13	2009	2009	NUM
fcis-6343	90	14	[	[	X
fcis-6343	90	15	2	2	NUM
fcis-6343	90	16	]	]	PUNCT
fcis-6343	90	17	.	.	PUNCT
fcis-6343	91	1	after	after	ADP
fcis-6343	91	2	continuous	continuous	ADJ
fcis-6343	91	3	research	research	NOUN
fcis-6343	91	4	and	and	CCONJ
fcis-6343	91	5	improvement	improvement	NOUN
fcis-6343	91	6	,	,	PUNCT
fcis-6343	91	7	the	the	DET
fcis-6343	91	8	efficiency	efficiency	NOUN
fcis-6343	91	9	of	of	ADP
fcis-6343	91	10	the	the	DET
fcis-6343	91	11	latest	late	ADJ
fcis-6343	91	12	protocol	protocol	NOUN
fcis-6343	91	13	is	be	AUX
fcis-6343	91	14	close	close	ADJ
fcis-6343	91	15	to	to	ADP
fcis-6343	91	16	the	the	DET
fcis-6343	91	17	degree	degree	NOUN
fcis-6343	91	18	accepted	accept	VERB
fcis-6343	91	19	by	by	ADP
fcis-6343	91	20	people	people	NOUN
fcis-6343	91	21	.	.	PUNCT
fcis-6343	92	1	in	in	ADP
fcis-6343	92	2	2017	2017	NUM
fcis-6343	92	3	,	,	PUNCT
fcis-6343	92	4	the	the	DET
fcis-6343	92	5	academic	academic	ADJ
fcis-6343	92	6	circle	circle	NOUN
fcis-6343	92	7	and	and	CCONJ
fcis-6343	92	8	the	the	DET
fcis-6343	92	9	industrial	industrial	ADJ
fcis-6343	92	10	circle	circle	NOUN
fcis-6343	92	11	jointly	jointly	ADV
fcis-6343	92	12	founded	found	VERB
fcis-6343	92	13	the	the	DET
fcis-6343	92	14	organization	organization	NOUN
fcis-6343	92	15	of	of	ADP
fcis-6343	92	16	fully	fully	ADV
fcis-6343	92	17	homomorphic	homomorphic	ADJ
fcis-6343	92	18	encryption	encryption	NOUN
fcis-6343	92	19	standardization	standardization	NOUN
fcis-6343	92	20	,	,	PUNCT
fcis-6343	92	21	indicating	indicate	VERB
fcis-6343	92	22	that	that	SCONJ
fcis-6343	92	23	homomorphic	homomorphic	ADJ
fcis-6343	92	24	encryption	encryption	NOUN
fcis-6343	92	25	fully	fully	ADV
fcis-6343	92	26	entered	enter	VERB
fcis-6343	92	27	the	the	DET
fcis-6343	92	28	stage	stage	NOUN
fcis-6343	92	29	of	of	ADP
fcis-6343	92	30	application	application	NOUN
fcis-6343	92	31	or	or	CCONJ
fcis-6343	92	32	even	even	ADV
fcis-6343	92	33	standardization	standardization	NOUN
fcis-6343	92	34	[	[	X
fcis-6343	92	35	3	3	NUM
fcis-6343	92	36	,	,	PUNCT
fcis-6343	92	37	4	4	NUM
fcis-6343	92	38	]	]	PUNCT
fcis-6343	92	39	.	.	PUNCT
fcis-6343	93	1	on	on	ADP
fcis-6343	93	2	may	may	PROPN
fcis-6343	93	3	22	22	NUM
fcis-6343	93	4	,	,	PUNCT
fcis-6343	93	5	2022	2022	NUM
fcis-6343	93	6	,	,	PUNCT
fcis-6343	93	7	the	the	DET
fcis-6343	93	8	special	special	ADJ
fcis-6343	93	9	interest	interest	NOUN
fcis-6343	93	10	group	group	NOUN
fcis-6343	93	11	on	on	ADP
fcis-6343	93	12	automata	automata	NOUN
fcis-6343	93	13	and	and	CCONJ
fcis-6343	93	14	computability	computability	NOUN
fcis-6343	93	15	theory	theory	NOUN
fcis-6343	93	16	of	of	ADP
fcis-6343	93	17	acm	acm	PROPN
fcis-6343	93	18	announced	announce	VERB
fcis-6343	93	19	that	that	SCONJ
fcis-6343	93	20	the	the	DET
fcis-6343	93	21	go¨del	go¨del	PROPN
fcis-6343	93	22	prize	prize	NOUN
fcis-6343	93	23	of	of	ADP
fcis-6343	93	24	2022	2022	NUM
fcis-6343	93	25	was	be	AUX
fcis-6343	93	26	awarded	award	VERB
fcis-6343	93	27	to	to	ADP
fcis-6343	93	28	craig	craig	PROPN
fcis-6343	93	29	gentry	gentry	PROPN
fcis-6343	93	30	,	,	PUNCT
fcis-6343	93	31	zvika	zvika	X
fcis-6343	93	32	112	112	NUM
fcis-6343	93	33	brakerski	brakerski	NOUN
fcis-6343	93	34	and	and	CCONJ
fcis-6343	93	35	vinod	vinod	PROPN
fcis-6343	93	36	vaikuntanathan	vaikuntanathan	ADV
fcis-6343	94	1	[	[	X
fcis-6343	94	2	5	5	NUM
fcis-6343	94	3	]	]	PUNCT
fcis-6343	94	4	to	to	PART
fcis-6343	94	5	commend	commend	VERB
fcis-6343	94	6	their	their	PRON
fcis-6343	94	7	revolutionary	revolutionary	ADJ
fcis-6343	94	8	contributions	contribution	NOUN
fcis-6343	94	9	to	to	ADP
fcis-6343	94	10	the	the	DET
fcis-6343	94	11	homomorphic	homomorphic	ADJ
fcis-6343	94	12	encryption	encryption	NOUN
fcis-6343	94	13	system	system	NOUN
fcis-6343	94	14	.	.	PUNCT
fcis-6343	95	1	5.1	5.1	NUM
fcis-6343	95	2	.	.	PUNCT
fcis-6343	95	3	realization	realization	NOUN
fcis-6343	95	4	of	of	ADP
fcis-6343	95	5	fully	fully	ADV
fcis-6343	95	6	homomorphic	homomorphic	ADJ
fcis-6343	95	7	encryption	encryption	NOUN
fcis-6343	95	8	the	the	DET
fcis-6343	95	9	algorithm	algorithm	NOUN
fcis-6343	95	10	scheme	scheme	NOUN
fcis-6343	95	11	of	of	ADP
fcis-6343	95	12	this	this	DET
fcis-6343	95	13	protocol	protocol	NOUN
fcis-6343	95	14	shall	shall	AUX
fcis-6343	95	15	be	be	AUX
fcis-6343	95	16	attributed	attribute	VERB
fcis-6343	95	17	to	to	ADP
fcis-6343	95	18	the	the	DET
fcis-6343	95	19	talented	talented	ADJ
fcis-6343	95	20	cryptologist	cryptologist	NOUN
fcis-6343	95	21	,	,	PUNCT
fcis-6343	95	22	zvika	zvika	X
fcis-6343	95	23	brakerski	brakerski	NOUN
fcis-6343	95	24	,	,	PUNCT
fcis-6343	95	25	whose	whose	DET
fcis-6343	95	26	research	research	NOUN
fcis-6343	95	27	was	be	AUX
fcis-6343	95	28	based	base	VERB
fcis-6343	95	29	on	on	ADP
fcis-6343	95	30	the	the	DET
fcis-6343	95	31	learning	learning	NOUN
fcis-6343	95	32	with	with	ADP
fcis-6343	95	33	errors	error	NOUN
fcis-6343	95	34	(	(	PUNCT
fcis-6343	95	35	lwe	lwe	PROPN
fcis-6343	95	36	)	)	PUNCT
fcis-6343	95	37	.	.	PUNCT
fcis-6343	96	1	the	the	DET
fcis-6343	96	2	confidentiality	confidentiality	NOUN
fcis-6343	96	3	of	of	ADP
fcis-6343	96	4	the	the	DET
fcis-6343	96	5	algorithm	algorithm	NOUN
fcis-6343	96	6	is	be	AUX
fcis-6343	96	7	ensured	ensure	VERB
fcis-6343	96	8	by	by	ADP
fcis-6343	96	9	the	the	DET
fcis-6343	96	10	difficulty	difficulty	NOUN
fcis-6343	96	11	of	of	ADP
fcis-6343	96	12	the	the	DET
fcis-6343	96	13	worst	bad	ADJ
fcis-6343	96	14	case	case	NOUN
fcis-6343	96	15	in	in	ADP
fcis-6343	96	16	any	any	DET
fcis-6343	96	17	problems	problem	NOUN
fcis-6343	96	18	of	of	ADP
fcis-6343	96	19	short	short	ADJ
fcis-6343	96	20	vectors	vector	NOUN
fcis-6343	96	21	,	,	PUNCT
fcis-6343	96	22	that	that	ADV
fcis-6343	96	23	is	is	ADV
fcis-6343	96	24	,	,	PUNCT
fcis-6343	96	25	the	the	DET
fcis-6343	96	26	resolution	resolution	NOUN
fcis-6343	96	27	of	of	ADP
fcis-6343	96	28	such	such	ADJ
fcis-6343	96	29	kind	kind	NOUN
fcis-6343	96	30	of	of	ADP
fcis-6343	96	31	problem	problem	NOUN
fcis-6343	96	32	shall	shall	AUX
fcis-6343	96	33	not	not	PART
fcis-6343	96	34	be	be	AUX
fcis-6343	96	35	used	use	VERB
fcis-6343	96	36	as	as	ADP
fcis-6343	96	37	the	the	DET
fcis-6343	96	38	guarantee	guarantee	NOUN
fcis-6343	96	39	of	of	ADP
fcis-6343	96	40	finishing	finish	VERB
fcis-6343	96	41	in	in	ADP
fcis-6343	96	42	the	the	DET
fcis-6343	96	43	time	time	NOUN
fcis-6343	96	44	of	of	ADP
fcis-6343	96	45	multiple	multiple	ADJ
fcis-6343	96	46	-	-	PUNCT
fcis-6343	96	47	term	term	NOUN
fcis-6343	96	48	formulae	formulae	NOUN
fcis-6343	96	49	.	.	PUNCT
fcis-6343	97	1	the	the	DET
fcis-6343	97	2	famous	famous	ADJ
fcis-6343	97	3	cryptologist	cryptologist	NOUN
fcis-6343	97	4	regev	regev	PROPN
fcis-6343	97	5	creatively	creatively	ADV
fcis-6343	97	6	proposed	propose	VERB
fcis-6343	97	7	the	the	DET
fcis-6343	97	8	difficulty	difficulty	NOUN
fcis-6343	97	9	of	of	ADP
fcis-6343	97	10	learning	learn	VERB
fcis-6343	97	11	with	with	ADP
fcis-6343	97	12	errors	error	NOUN
fcis-6343	97	13	.	.	PUNCT
fcis-6343	98	1	definition	definition	NOUN
fcis-6343	98	2	4.5.1	4.5.1	NUM
fcis-6343	98	3	:	:	PUNCT
fcis-6343	98	4	let	let	VERB
fcis-6343	98	5	s	s	PRON
fcis-6343	98	6	∈	∈	PROPN
fcis-6343	98	7	zqn	zqn	PROPN
fcis-6343	98	8	.	.	PUNCT
fcis-6343	99	1	linear	linear	ADJ
fcis-6343	99	2	combination	combination	NOUN
fcis-6343	99	3	of	of	ADP
fcis-6343	99	4	scoefficient	scoefficient	ADJ
fcis-6343	99	5	random	random	ADJ
fcis-6343	99	6	polynomials	polynomial	NOUN
fcis-6343	99	7	is	be	AUX
fcis-6343	99	8	not	not	PART
fcis-6343	99	9	distinguishable	distinguishable	ADJ
fcis-6343	99	10	with	with	ADP
fcis-6343	99	11	elements	element	NOUN
fcis-6343	99	12	in	in	ADP
fcis-6343	99	13	zq	zq	PROPN
fcis-6343	99	14	of	of	ADP
fcis-6343	99	15	uniform	uniform	ADJ
fcis-6343	99	16	distribution	distribution	NOUN
fcis-6343	99	17	.	.	PUNCT
fcis-6343	100	1	we	we	PRON
fcis-6343	100	2	use	use	VERB
fcis-6343	100	3	the	the	DET
fcis-6343	100	4	secret	secret	ADJ
fcis-6343	100	5	key	key	NOUN
fcis-6343	100	6	s	s	NOUN
fcis-6343	100	7	to	to	PART
fcis-6343	100	8	encrypt	encrypt	VERB
fcis-6343	100	9	the	the	DET
fcis-6343	100	10	text	text	NOUN
fcis-6343	100	11	m	m	NOUN
fcis-6343	100	12	∈	∈	PROPN
fcis-6343	100	13	{	{	PUNCT
fcis-6343	100	14	0	0	NUM
fcis-6343	100	15	,	,	PUNCT
fcis-6343	100	16	1	1	NUM
fcis-6343	100	17	}	}	PUNCT
fcis-6343	100	18	.	.	PUNCT
fcis-6343	101	1	randomly	randomly	ADV
fcis-6343	101	2	choose	choose	VERB
fcis-6343	101	3	a	a	DET
fcis-6343	101	4	vector	vector	NOUN
fcis-6343	101	5	a	a	DET
fcis-6343	101	6	∈	∈	PROPN
fcis-6343	101	7	zqn	zqn	NOUN
fcis-6343	101	8	,	,	PUNCT
fcis-6343	101	9	adding	add	VERB
fcis-6343	101	10	a	a	DET
fcis-6343	101	11	noise	noise	NOUN
fcis-6343	101	12	e	e	NOUN
fcis-6343	101	13	,	,	PUNCT
fcis-6343	101	14	we	we	PRON
fcis-6343	101	15	have	have	AUX
fcis-6343	101	16	encrypted	encrypt	VERB
fcis-6343	101	17	cipertext	cipertext	NOUN
fcis-6343	101	18	:	:	PUNCT
fcis-6343	101	19	c	c	X
fcis-6343	101	20	=	=	SYM
fcis-6343	101	21	(	(	PUNCT
fcis-6343	101	22	a	a	PRON
fcis-6343	101	23	,	,	PUNCT
fcis-6343	101	24	b	b	NOUN
fcis-6343	101	25	=	=	NOUN
fcis-6343	101	26	<	<	X
fcis-6343	101	27	a	a	PRON
fcis-6343	101	28	,	,	PUNCT
fcis-6343	101	29	s	s	PART
fcis-6343	101	30	>	>	X
fcis-6343	101	31	+2e	+2e	PROPN
fcis-6343	101	32	+	+	NUM
fcis-6343	101	33	m	m	NOUN
fcis-6343	101	34	)	)	PUNCT
fcis-6343	101	35	∈	∈	PROPN
fcis-6343	101	36	zqn	zqn	PROPN
fcis-6343	101	37	×	×	PROPN
fcis-6343	101	38	zq	zq	PROPN
fcis-6343	101	39	.	.	PUNCT
fcis-6343	102	1	the	the	DET
fcis-6343	102	2	key	key	ADJ
fcis-6343	102	3	point	point	NOUN
fcis-6343	102	4	of	of	ADP
fcis-6343	102	5	decryption	decryption	NOUN
fcis-6343	102	6	is	be	AUX
fcis-6343	102	7	the	the	DET
fcis-6343	102	8	elimination	elimination	NOUN
fcis-6343	102	9	of	of	ADP
fcis-6343	102	10	two	two	NUM
fcis-6343	102	11	interference	interference	NOUN
fcis-6343	102	12	:	:	PUNCT
fcis-6343	102	13	<	<	X
fcis-6343	102	14	a	a	X
fcis-6343	102	15	,	,	PUNCT
fcis-6343	102	16	s	s	X
fcis-6343	102	17	>	>	X
fcis-6343	102	18	and	and	CCONJ
fcis-6343	102	19	2e	2e	NUM
fcis-6343	102	20	,	,	PUNCT
fcis-6343	102	21	which	which	PRON
fcis-6343	102	22	can	can	AUX
fcis-6343	102	23	be	be	AUX
fcis-6343	102	24	respectively	respectively	ADV
fcis-6343	102	25	eliminated	eliminate	VERB
fcis-6343	102	26	by	by	ADP
fcis-6343	102	27	the	the	DET
fcis-6343	102	28	calculation	calculation	NOUN
fcis-6343	102	29	of	of	ADP
fcis-6343	102	30	<	<	X
fcis-6343	102	31	a	a	PRON
fcis-6343	102	32	,	,	PUNCT
fcis-6343	102	33	s	s	X
fcis-6343	102	34	>	>	X
fcis-6343	102	35	and	and	CCONJ
fcis-6343	102	36	the	the	DET
fcis-6343	102	37	verification	verification	NOUN
fcis-6343	102	38	of	of	ADP
fcis-6343	102	39	parity	parity	NOUN
fcis-6343	102	40	.	.	PUNCT
fcis-6343	103	1	proof	proof	NOUN
fcis-6343	103	2	:	:	PUNCT
fcis-6343	103	3	the	the	DET
fcis-6343	103	4	homomorphism	homomorphism	NOUN
fcis-6343	103	5	of	of	ADP
fcis-6343	103	6	addition	addition	NOUN
fcis-6343	103	7	is	be	AUX
fcis-6343	103	8	easy	easy	ADJ
fcis-6343	103	9	to	to	PART
fcis-6343	103	10	be	be	AUX
fcis-6343	103	11	verified	verify	VERB
fcis-6343	103	12	.	.	PUNCT
fcis-6343	104	1	the	the	DET
fcis-6343	104	2	decryption	decryption	NOUN
fcis-6343	104	3	algorithm	algorithm	NOUN
fcis-6343	104	4	is	be	AUX
fcis-6343	104	5	taken	take	VERB
fcis-6343	104	6	into	into	ADP
fcis-6343	104	7	account	account	NOUN
fcis-6343	104	8	to	to	PART
fcis-6343	104	9	verify	verify	VERB
fcis-6343	104	10	the	the	DET
fcis-6343	104	11	homomorphism	homomorphism	NOUN
fcis-6343	104	12	of	of	ADP
fcis-6343	104	13	multiplication	multiplication	NOUN
fcis-6343	104	14	.	.	PUNCT
fcis-6343	105	1	the	the	DET
fcis-6343	105	2	ciphertext	ciphertext	NOUN
fcis-6343	105	3	(	(	PUNCT
fcis-6343	105	4	a	a	DET
fcis-6343	105	5	,	,	PUNCT
fcis-6343	105	6	b	b	NOUN
fcis-6343	105	7	)	)	PUNCT
fcis-6343	105	8	and	and	CCONJ
fcis-6343	105	9	the	the	DET
fcis-6343	105	10	linear	linear	ADJ
fcis-6343	105	11	function	function	NOUN
fcis-6343	105	12	f(a	f(a	PROPN
fcis-6343	105	13	,	,	PUNCT
fcis-6343	105	14	b	b	NOUN
fcis-6343	105	15	)	)	PUNCT
fcis-6343	105	16	:	:	PUNCT
fcis-6343	105	17	zqn	zqn	PROPN
fcis-6343	106	1	一	一	PUNCT
fcis-6343	106	2	zq	zq	PROPN
fcis-6343	106	3	are	be	AUX
fcis-6343	106	4	given	give	VERB
fcis-6343	106	5	by	by	ADP
fcis-6343	106	6	f(a	f(a	PROPN
fcis-6343	106	7	,	,	PUNCT
fcis-6343	106	8	b)(x	b)(x	PROPN
fcis-6343	106	9	)	)	PUNCT
fcis-6343	106	10	=	=	SYM
fcis-6343	106	11	b−	b−	PROPN
fcis-6343	106	12	<	<	X
fcis-6343	106	13	a	a	X
fcis-6343	106	14	,	,	PUNCT
fcis-6343	106	15	x	x	X
fcis-6343	106	16	>	>	X
fcis-6343	106	17	(	(	PUNCT
fcis-6343	106	18	mod	mod	PROPN
fcis-6343	106	19	q	q	NOUN
fcis-6343	106	20	)	)	PUNCT
fcis-6343	106	21	=	=	SYM
fcis-6343	107	1	b	b	PROPN
fcis-6343	107	2	−	−	PROPN
fcis-6343	107	3	σ	σ	PROPN
fcis-6343	107	4	a[i]x[i	a[i]x[i	PROPN
fcis-6343	107	5	]	]	X
fcis-6343	107	6	∈	∈	PROPN
fcis-6343	107	7	zq	zq	PROPN
fcis-6343	107	8	.	.	PUNCT
fcis-6343	108	1	the	the	DET
fcis-6343	108	2	addition	addition	NOUN
fcis-6343	108	3	of	of	ADP
fcis-6343	108	4	the	the	DET
fcis-6343	108	5	ciphertext	ciphertext	NOUN
fcis-6343	108	6	corresponds	correspond	VERB
fcis-6343	108	7	to	to	ADP
fcis-6343	108	8	the	the	DET
fcis-6343	108	9	addition	addition	NOUN
fcis-6343	108	10	of	of	ADP
fcis-6343	108	11	the	the	DET
fcis-6343	108	12	linear	linear	ADJ
fcis-6343	108	13	function	function	NOUN
fcis-6343	108	14	:	:	PUNCT
fcis-6343	108	15	f(a+a\	f(a+a\	NUM
fcis-6343	108	16	,	,	PUNCT
fcis-6343	108	17	b+b\	b+b\	NOUN
fcis-6343	108	18	)	)	PUNCT
fcis-6343	108	19	(	(	PUNCT
fcis-6343	108	20	x	x	X
fcis-6343	108	21	)	)	PUNCT
fcis-6343	108	22	=	=	SYM
fcis-6343	108	23	f(a	f(a	NOUN
fcis-6343	108	24	,	,	PUNCT
fcis-6343	108	25	b)(x	b)(x	PROPN
fcis-6343	108	26	)	)	PUNCT
fcis-6343	108	27	+	+	CCONJ
fcis-6343	108	28	f(a\	f(a\	NOUN
fcis-6343	108	29	,	,	PUNCT
fcis-6343	108	30	b\	b\	PUNCT
fcis-6343	108	31	)	)	PUNCT
fcis-6343	108	32	(	(	PUNCT
fcis-6343	108	33	x	x	NOUN
fcis-6343	108	34	)	)	PUNCT
fcis-6343	108	35	.	.	PUNCT
fcis-6343	109	1	this	this	PRON
fcis-6343	109	2	is	be	AUX
fcis-6343	109	3	another	another	DET
fcis-6343	109	4	linear	linear	ADJ
fcis-6343	109	5	function	function	NOUN
fcis-6343	109	6	corresponding	correspond	VERB
fcis-6343	109	7	to	to	ADP
fcis-6343	109	8	the	the	DET
fcis-6343	109	9	ciphertext	ciphertext	NOUN
fcis-6343	109	10	(	(	PUNCT
fcis-6343	109	11	a	a	DET
fcis-6343	109	12	+	+	X
fcis-6343	110	1	a\	a\	NOUN
fcis-6343	110	2	,	,	PUNCT
fcis-6343	110	3	b	b	NOUN
fcis-6343	110	4	+	+	CCONJ
fcis-6343	110	5	b\	b\	NUM
fcis-6343	110	6	)	)	PUNCT
fcis-6343	110	7	.	.	PUNCT
fcis-6343	111	1	the	the	DET
fcis-6343	111	2	multiplication	multiplication	NOUN
fcis-6343	111	3	of	of	ADP
fcis-6343	111	4	the	the	DET
fcis-6343	111	5	two	two	NUM
fcis-6343	111	6	ciphertexts	ciphertexts	NOUN
fcis-6343	111	7	is	be	AUX
fcis-6343	111	8	:	:	PUNCT
fcis-6343	111	9	f(a	f(a	NOUN
fcis-6343	111	10	,	,	PUNCT
fcis-6343	111	11	b)(x)f(a\	b)(x)f(a\	NOUN
fcis-6343	111	12	,	,	PUNCT
fcis-6343	111	13	b\	b\	PUNCT
fcis-6343	111	14	)	)	PUNCT
fcis-6343	111	15	(	(	PUNCT
fcis-6343	111	16	x	x	X
fcis-6343	111	17	)	)	PUNCT
fcis-6343	111	18	=	=	SYM
fcis-6343	111	19	(	(	PUNCT
fcis-6343	111	20	b	b	X
fcis-6343	111	21	−	−	PROPN
fcis-6343	111	22	σ	σ	PROPN
fcis-6343	111	23	a[i]x[i])(b\	a[i]x[i])(b\	PROPN
fcis-6343	111	24	−	−	PROPN
fcis-6343	112	1	σ	σ	NOUN
fcis-6343	113	1	a\	a\	PROPN
fcis-6343	114	1	[	[	X
fcis-6343	114	2	i]x[i	i]x[i	NOUN
fcis-6343	114	3	]	]	X
fcis-6343	114	4	)	)	PUNCT
fcis-6343	114	5	=	=	SYM
fcis-6343	114	6	h0	h0	PROPN
fcis-6343	114	7	+	+	X
fcis-6343	114	8	σhix[i	σhix[i	NOUN
fcis-6343	114	9	]	]	PUNCT
fcis-6343	115	1	+	+	CCONJ
fcis-6343	115	2	σxi	σxi	PROPN
fcis-6343	115	3	,	,	PUNCT
fcis-6343	115	4	jx[i]x[j	jx[i]x[j	PROPN
fcis-6343	115	5	]	]	PUNCT
fcis-6343	115	6	.	.	PUNCT
fcis-6343	116	1	it	it	PRON
fcis-6343	116	2	can	can	AUX
fcis-6343	116	3	be	be	AUX
fcis-6343	116	4	found	find	VERB
fcis-6343	116	5	that	that	SCONJ
fcis-6343	116	6	the	the	DET
fcis-6343	116	7	result	result	NOUN
fcis-6343	116	8	is	be	AUX
fcis-6343	116	9	a	a	DET
fcis-6343	116	10	quadratic	quadratic	ADJ
fcis-6343	116	11	polynomial	polynomial	NOUN
fcis-6343	116	12	about	about	ADP
fcis-6343	116	13	the	the	DET
fcis-6343	116	14	variable	variable	ADJ
fcis-6343	116	15	x.	x.	NOUN
fcis-6343	116	16	therefore	therefore	ADV
fcis-6343	116	17	,	,	PUNCT
fcis-6343	116	18	a	a	DET
fcis-6343	116	19	serious	serious	ADJ
fcis-6343	116	20	problem	problem	NOUN
fcis-6343	116	21	is	be	AUX
fcis-6343	116	22	encountered	encounter	VERB
fcis-6343	116	23	,	,	PUNCT
fcis-6343	116	24	that	that	ADV
fcis-6343	116	25	is	is	ADV
fcis-6343	116	26	,	,	PUNCT
fcis-6343	116	27	the	the	DET
fcis-6343	116	28	coefficient	coefficient	NOUN
fcis-6343	116	29	of	of	ADP
fcis-6343	116	30	the	the	DET
fcis-6343	116	31	quadratic	quadratic	ADJ
fcis-6343	116	32	polynomial	polynomial	NOUN
fcis-6343	116	33	has	have	VERB
fcis-6343	116	34	to	to	PART
fcis-6343	116	35	be	be	AUX
fcis-6343	116	36	calculated	calculate	VERB
fcis-6343	116	37	.	.	PUNCT
fcis-6343	117	1	to	to	PART
fcis-6343	117	2	narrow	narrow	VERB
fcis-6343	117	3	the	the	DET
fcis-6343	117	4	scale	scale	NOUN
fcis-6343	117	5	of	of	ADP
fcis-6343	117	6	the	the	DET
fcis-6343	117	7	ciphertext	ciphertext	NOUN
fcis-6343	117	8	,	,	PUNCT
fcis-6343	117	9	the	the	DET
fcis-6343	117	10	technology	technology	NOUN
fcis-6343	117	11	of	of	ADP
fcis-6343	117	12	relinearization	relinearization	NOUN
fcis-6343	117	13	is	be	AUX
fcis-6343	117	14	adopted	adopt	VERB
fcis-6343	117	15	.	.	PUNCT
fcis-6343	118	1	in	in	ADP
fcis-6343	118	2	case	case	NOUN
fcis-6343	118	3	of	of	ADP
fcis-6343	118	4	the	the	DET
fcis-6343	118	5	new	new	ADJ
fcis-6343	118	6	secret	secret	ADJ
fcis-6343	118	7	key	key	PROPN
fcis-6343	118	8	t	t	PROPN
fcis-6343	118	9	,	,	PUNCT
fcis-6343	118	10	h0	h0	NOUN
fcis-6343	118	11	+	+	CCONJ
fcis-6343	118	12	σhis[i	σhis[i	PROPN
fcis-6343	118	13	]	]	PUNCT
fcis-6343	118	14	+	+	CCONJ
fcis-6343	118	15	σhi	σhi	X
fcis-6343	118	16	,	,	PUNCT
fcis-6343	118	17	js[i]s[j	js[i]s[j	PROPN
fcis-6343	118	18	]	]	PUNCT
fcis-6343	118	19	is	be	AUX
fcis-6343	118	20	approximately	approximately	ADV
fcis-6343	118	21	equal	equal	ADJ
fcis-6343	118	22	to	to	PART
fcis-6343	118	23	h0	h0	VERB
fcis-6343	118	24	+	+	CCONJ
fcis-6343	118	25	σhi(bi−	σhi(bi−	NOUN
fcis-6343	118	26	<	<	X
fcis-6343	118	27	ai	ai	PROPN
fcis-6343	118	28	,	,	PUNCT
fcis-6343	118	29	t	t	NOUN
fcis-6343	118	30	>	>	PUNCT
fcis-6343	118	31	)	)	PUNCT
fcis-6343	119	1	+	+	CCONJ
fcis-6343	119	2	σhi	σhi	X
fcis-6343	119	3	,	,	PUNCT
fcis-6343	119	4	j(bi	j(bi	PROPN
fcis-6343	119	5	,	,	PUNCT
fcis-6343	119	6	j−	j−	VERB
fcis-6343	119	7	<	<	X
fcis-6343	119	8	ai	ai	PROPN
fcis-6343	119	9	,	,	PUNCT
fcis-6343	119	10	j	j	PROPN
fcis-6343	119	11	,	,	PUNCT
fcis-6343	119	12	t	t	PROPN
fcis-6343	119	13	>	>	PUNCT
fcis-6343	119	14	)	)	PUNCT
fcis-6343	119	15	.	.	PUNCT
fcis-6343	120	1	this	this	PRON
fcis-6343	120	2	is	be	AUX
fcis-6343	120	3	the	the	DET
fcis-6343	120	4	linear	linear	ADJ
fcis-6343	120	5	function	function	NOUN
fcis-6343	120	6	about	about	ADP
fcis-6343	120	7	the	the	DET
fcis-6343	120	8	secret	secret	ADJ
fcis-6343	120	9	key	key	PROPN
fcis-6343	120	10	t	t	PROPN
fcis-6343	120	11	,	,	PUNCT
fcis-6343	120	12	with	with	ADP
fcis-6343	120	13	bi	bi	PROPN
fcis-6343	120	14	,	,	PUNCT
fcis-6343	120	15	j	j	PROPN
fcis-6343	121	1	=	=	X
fcis-6343	121	2	<	<	X
fcis-6343	121	3	ai	ai	PROPN
fcis-6343	121	4	,	,	PUNCT
fcis-6343	121	5	j	j	PROPN
fcis-6343	121	6	,	,	PUNCT
fcis-6343	121	7	t	t	PROPN
fcis-6343	121	8	>	>	X
fcis-6343	121	9	+2ei	+2ei	PROPN
fcis-6343	121	10	,	,	PUNCT
fcis-6343	121	11	j	j	PROPN
fcis-6343	121	12	+	+	NUM
fcis-6343	121	13	s[i]s[j	s[i]s[j	PROPN
fcis-6343	121	14	]	]	PUNCT
fcis-6343	121	15	≈	≈	PROPN
fcis-6343	121	16	<	<	X
fcis-6343	121	17	ai	ai	PROPN
fcis-6343	121	18	,	,	PUNCT
fcis-6343	121	19	j	j	PROPN
fcis-6343	121	20	,	,	PUNCT
fcis-6343	121	21	t	t	PROPN
fcis-6343	121	22	>	>	X
fcis-6343	122	1	+	+	NOUN
fcis-6343	122	2	s[i]s[j	s[i]s[j	NOUN
fcis-6343	122	3	]	]	PUNCT
fcis-6343	122	4	.	.	PUNCT
fcis-6343	123	1	therefore	therefore	ADV
fcis-6343	123	2	,	,	PUNCT
fcis-6343	123	3	the	the	DET
fcis-6343	123	4	re	re	NOUN
fcis-6343	123	5	-	-	NOUN
fcis-6343	123	6	linearization	linearization	NOUN
fcis-6343	123	7	technology	technology	NOUN
fcis-6343	123	8	reduces	reduce	VERB
fcis-6343	123	9	the	the	DET
fcis-6343	123	10	ciphertext	ciphertext	NOUN
fcis-6343	123	11	to	to	ADP
fcis-6343	123	12	n	n	PROPN
fcis-6343	123	13	+	+	CCONJ
fcis-6343	123	14	1	1	NUM
fcis-6343	123	15	,	,	PUNCT
fcis-6343	123	16	which	which	PRON
fcis-6343	123	17	eliminates	eliminate	VERB
fcis-6343	123	18	the	the	DET
fcis-6343	123	19	dependence	dependence	NOUN
fcis-6343	123	20	on	on	ADP
fcis-6343	123	21	the	the	DET
fcis-6343	123	22	assumption	assumption	NOUN
fcis-6343	123	23	of	of	ADP
fcis-6343	123	24	ideal	ideal	ADJ
fcis-6343	123	25	cases	case	NOUN
fcis-6343	123	26	,	,	PUNCT
fcis-6343	123	27	and	and	CCONJ
fcis-6343	123	28	a	a	DET
fcis-6343	123	29	part	part	NOUN
fcis-6343	123	30	of	of	ADP
fcis-6343	123	31	homomorphic	homomorphic	ADJ
fcis-6343	123	32	encryp	encryp	NOUN
fcis-6343	123	33	tions	tion	NOUN
fcis-6343	123	34	is	be	AUX
fcis-6343	123	35	acquired	acquire	VERB
fcis-6343	123	36	through	through	ADP
fcis-6343	123	37	learning	learn	VERB
fcis-6343	123	38	with	with	ADP
fcis-6343	123	39	errors	error	NOUN
fcis-6343	123	40	,	,	PUNCT
fcis-6343	123	41	which	which	PRON
fcis-6343	123	42	becomes	become	VERB
fcis-6343	123	43	the	the	DET
fcis-6343	123	44	basis	basis	NOUN
fcis-6343	123	45	of	of	ADP
fcis-6343	123	46	realizing	realize	VERB
fcis-6343	123	47	fully	fully	ADV
fcis-6343	123	48	homomorphic	homomorphic	ADJ
fcis-6343	123	49	encryption	encryption	NOUN
fcis-6343	123	50	.	.	PUNCT
fcis-6343	124	1	5.2	5.2	NUM
fcis-6343	124	2	.	.	PUNCT
fcis-6343	124	3	application	application	NOUN
fcis-6343	124	4	of	of	ADP
fcis-6343	124	5	privacy	privacy	NOUN
fcis-6343	124	6	computing	computing	NOUN
fcis-6343	124	7	in	in	ADP
fcis-6343	124	8	the	the	DET
fcis-6343	124	9	field	field	NOUN
fcis-6343	124	10	of	of	ADP
fcis-6343	124	11	blockchains	blockchain	NOUN
fcis-6343	124	12	the	the	DET
fcis-6343	124	13	combination	combination	NOUN
fcis-6343	124	14	of	of	ADP
fcis-6343	124	15	technologies	technology	NOUN
fcis-6343	124	16	of	of	ADP
fcis-6343	124	17	privacy	privacy	NOUN
fcis-6343	124	18	computing	computing	NOUN
fcis-6343	124	19	and	and	CCONJ
fcis-6343	124	20	blockchains	blockchain	NOUN
fcis-6343	124	21	produces	produce	VERB
fcis-6343	124	22	the	the	DET
fcis-6343	124	23	advantages	advantage	NOUN
fcis-6343	124	24	of	of	ADP
fcis-6343	124	25	the	the	DET
fcis-6343	124	26	two	two	NUM
fcis-6343	124	27	,	,	PUNCT
fcis-6343	124	28	thus	thus	ADV
fcis-6343	124	29	realizing	realize	VERB
fcis-6343	124	30	data	datum	NOUN
fcis-6343	124	31	security	security	NOUN
fcis-6343	124	32	in	in	ADP
fcis-6343	124	33	the	the	DET
fcis-6343	124	34	whole	whole	ADJ
fcis-6343	124	35	process	process	NOUN
fcis-6343	124	36	of	of	ADP
fcis-6343	124	37	computing	computing	NOUN
fcis-6343	124	38	and	and	CCONJ
fcis-6343	124	39	applications	application	NOUN
fcis-6343	124	40	.	.	PUNCT
fcis-6343	125	1	data	datum	NOUN
fcis-6343	125	2	privacy	privacy	NOUN
fcis-6343	125	3	receives	receive	VERB
fcis-6343	125	4	great	great	ADJ
fcis-6343	125	5	attention	attention	NOUN
fcis-6343	125	6	during	during	ADP
fcis-6343	125	7	the	the	DET
fcis-6343	125	8	process	process	NOUN
fcis-6343	125	9	of	of	ADP
fcis-6343	125	10	blockchain	blockchain	PROPN
fcis-6343	125	11	application	application	NOUN
fcis-6343	125	12	.	.	PUNCT
fcis-6343	126	1	one	one	NUM
fcis-6343	126	2	of	of	ADP
fcis-6343	126	3	the	the	DET
fcis-6343	126	4	schemes	scheme	NOUN
fcis-6343	126	5	to	to	PART
fcis-6343	126	6	protect	protect	VERB
fcis-6343	126	7	privacy	privacy	NOUN
fcis-6343	126	8	is	be	AUX
fcis-6343	126	9	to	to	PART
fcis-6343	126	10	produce	produce	VERB
fcis-6343	126	11	links	link	NOUN
fcis-6343	126	12	after	after	ADP
fcis-6343	126	13	the	the	DET
fcis-6343	126	14	desensitization	desensitization	NOUN
fcis-6343	126	15	of	of	ADP
fcis-6343	126	16	data	data	PROPN
fcis-6343	126	17	.	.	PUNCT
fcis-6343	127	1	however	however	ADV
fcis-6343	127	2	,	,	PUNCT
fcis-6343	127	3	the	the	DET
fcis-6343	127	4	desensitization	desensitization	NOUN
fcis-6343	127	5	of	of	ADP
fcis-6343	127	6	data	datum	NOUN
fcis-6343	127	7	will	will	AUX
fcis-6343	127	8	lead	lead	VERB
fcis-6343	127	9	to	to	ADP
fcis-6343	127	10	the	the	DET
fcis-6343	127	11	incompleteness	incompleteness	NOUN
fcis-6343	127	12	of	of	ADP
fcis-6343	127	13	data	data	PROPN
fcis-6343	127	14	,	,	PUNCT
fcis-6343	127	15	which	which	PRON
fcis-6343	127	16	can	can	AUX
fcis-6343	127	17	affect	affect	VERB
fcis-6343	127	18	the	the	DET
fcis-6343	127	19	integrity	integrity	NOUN
fcis-6343	127	20	and	and	CCONJ
fcis-6343	127	21	processing	processing	NOUN
fcis-6343	127	22	of	of	ADP
fcis-6343	127	23	data	data	PROPN
fcis-6343	127	24	.	.	PUNCT
fcis-6343	128	1	privacy	privacy	NOUN
fcis-6343	128	2	computing	computing	NOUN
fcis-6343	128	3	plays	play	VERB
fcis-6343	128	4	a	a	DET
fcis-6343	128	5	role	role	NOUN
fcis-6343	128	6	in	in	ADP
fcis-6343	128	7	this	this	DET
fcis-6343	128	8	process	process	NOUN
fcis-6343	128	9	.	.	PUNCT
fcis-6343	129	1	it	it	PRON
fcis-6343	129	2	makes	make	VERB
fcis-6343	129	3	data	datum	NOUN
fcis-6343	129	4	to	to	PART
fcis-6343	129	5	be	be	AUX
fcis-6343	129	6	processed	process	VERB
fcis-6343	129	7	and	and	CCONJ
fcis-6343	129	8	verified	verify	VERB
fcis-6343	129	9	,	,	PUNCT
fcis-6343	129	10	and	and	CCONJ
fcis-6343	129	11	keep	keep	VERB
fcis-6343	129	12	invisible	invisible	ADJ
fcis-6343	129	13	with	with	ADP
fcis-6343	129	14	the	the	DET
fcis-6343	129	15	premise	premise	NOUN
fcis-6343	129	16	of	of	ADP
fcis-6343	129	17	ensuring	ensure	VERB
fcis-6343	129	18	the	the	DET
fcis-6343	129	19	integrity	integrity	NOUN
fcis-6343	129	20	of	of	ADP
fcis-6343	129	21	data	data	PROPN
fcis-6343	129	22	.	.	PUNCT
fcis-6343	130	1	the	the	DET
fcis-6343	130	2	application	application	NOUN
fcis-6343	130	3	of	of	ADP
fcis-6343	130	4	the	the	DET
fcis-6343	130	5	privacy	privacy	NOUN
fcis-6343	130	6	computing	compute	VERB
fcis-6343	130	7	technology	technology	NOUN
fcis-6343	130	8	in	in	ADP
fcis-6343	130	9	the	the	DET
fcis-6343	130	10	field	field	NOUN
fcis-6343	130	11	of	of	ADP
fcis-6343	130	12	blockchains	blockchain	NOUN
fcis-6343	130	13	includes	include	VERB
fcis-6343	130	14	two	two	NUM
fcis-6343	130	15	extremely	extremely	ADV
fcis-6343	130	16	crucial	crucial	ADJ
fcis-6343	130	17	areas	area	NOUN
fcis-6343	130	18	,	,	PUNCT
fcis-6343	130	19	namely	namely	ADV
fcis-6343	130	20	privacy	privacy	NOUN
fcis-6343	130	21	transaction	transaction	NOUN
fcis-6343	130	22	protocol	protocol	NOUN
fcis-6343	130	23	and	and	CCONJ
fcis-6343	130	24	privacy	privacy	NOUN
fcis-6343	130	25	computing	computing	NOUN
fcis-6343	130	26	protocol	protocol	NOUN
fcis-6343	130	27	.	.	PUNCT
fcis-6343	131	1	these	these	DET
fcis-6343	131	2	two	two	NUM
fcis-6343	131	3	forms	form	NOUN
fcis-6343	131	4	of	of	ADP
fcis-6343	131	5	application	application	NOUN
fcis-6343	131	6	mainly	mainly	ADV
fcis-6343	131	7	solve	solve	VERB
fcis-6343	131	8	the	the	DET
fcis-6343	131	9	problems	problem	NOUN
fcis-6343	131	10	in	in	ADP
fcis-6343	131	11	the	the	DET
fcis-6343	131	12	aspect	aspect	NOUN
fcis-6343	131	13	of	of	ADP
fcis-6343	131	14	privacy	privacy	NOUN
fcis-6343	131	15	.	.	PUNCT
fcis-6343	132	1	the	the	DET
fcis-6343	132	2	privacy	privacy	NOUN
fcis-6343	132	3	transaction	transaction	NOUN
fcis-6343	132	4	protocol	protocol	NOUN
fcis-6343	132	5	refers	refer	VERB
fcis-6343	132	6	to	to	ADP
fcis-6343	132	7	the	the	DET
fcis-6343	132	8	encryption	encryption	NOUN
fcis-6343	132	9	of	of	ADP
fcis-6343	132	10	the	the	DET
fcis-6343	132	11	transaction	transaction	NOUN
fcis-6343	132	12	data	datum	NOUN
fcis-6343	132	13	on	on	ADP
fcis-6343	132	14	the	the	DET
fcis-6343	132	15	blockchain	blockchain	NOUN
fcis-6343	132	16	,	,	PUNCT
fcis-6343	132	17	and	and	CCONJ
fcis-6343	132	18	the	the	DET
fcis-6343	132	19	verification	verification	NOUN
fcis-6343	132	20	of	of	ADP
fcis-6343	132	21	the	the	DET
fcis-6343	132	22	relationship	relationship	NOUN
fcis-6343	132	23	between	between	ADP
fcis-6343	132	24	transaction	transaction	NOUN
fcis-6343	132	25	data	datum	NOUN
fcis-6343	132	26	can	can	AUX
fcis-6343	132	27	be	be	AUX
fcis-6343	132	28	ensured	ensure	VERB
fcis-6343	132	29	at	at	ADP
fcis-6343	132	30	the	the	DET
fcis-6343	132	31	same	same	ADJ
fcis-6343	132	32	time	time	NOUN
fcis-6343	132	33	,	,	PUNCT
fcis-6343	132	34	that	that	PRON
fcis-6343	132	35	is	be	AUX
fcis-6343	132	36	to	to	PART
fcis-6343	132	37	say	say	VERB
fcis-6343	132	38	,	,	PUNCT
fcis-6343	132	39	it	it	PRON
fcis-6343	132	40	can	can	AUX
fcis-6343	132	41	conduct	conduct	VERB
fcis-6343	132	42	audit	audit	NOUN
fcis-6343	132	43	accounts	account	NOUN
fcis-6343	132	44	in	in	ADP
fcis-6343	132	45	the	the	DET
fcis-6343	132	46	situation	situation	NOUN
fcis-6343	132	47	of	of	ADP
fcis-6343	132	48	keeping	keep	VERB
fcis-6343	132	49	accounts	account	NOUN
fcis-6343	132	50	private	private	ADJ
fcis-6343	132	51	.	.	PUNCT
fcis-6343	133	1	at	at	ADP
fcis-6343	133	2	present	present	ADJ
fcis-6343	133	3	,	,	PUNCT
fcis-6343	133	4	multiple	multiple	ADJ
fcis-6343	133	5	blockchain	blockchain	NOUN
fcis-6343	133	6	projects	project	NOUN
fcis-6343	133	7	adopt	adopt	VERB
fcis-6343	133	8	the	the	DET
fcis-6343	133	9	privacy	privacy	NOUN
fcis-6343	133	10	transaction	transaction	NOUN
fcis-6343	133	11	protocol	protocol	NOUN
fcis-6343	133	12	.	.	PUNCT
fcis-6343	134	1	the	the	DET
fcis-6343	134	2	privacy	privacy	NOUN
fcis-6343	134	3	computing	computing	NOUN
fcis-6343	134	4	protocol	protocol	NOUN
fcis-6343	134	5	realizes	realize	VERB
fcis-6343	134	6	the	the	DET
fcis-6343	134	7	protection	protection	NOUN
fcis-6343	134	8	of	of	ADP
fcis-6343	134	9	privacy	privacy	NOUN
fcis-6343	134	10	during	during	ADP
fcis-6343	134	11	the	the	DET
fcis-6343	134	12	whole	whole	ADJ
fcis-6343	134	13	process	process	NOUN
fcis-6343	134	14	from	from	ADP
fcis-6343	134	15	the	the	DET
fcis-6343	134	16	generation	generation	NOUN
fcis-6343	134	17	,	,	PUNCT
fcis-6343	134	18	storage	storage	NOUN
fcis-6343	134	19	to	to	ADP
fcis-6343	134	20	analysis	analysis	NOUN
fcis-6343	134	21	,	,	PUNCT
fcis-6343	134	22	calculation	calculation	NOUN
fcis-6343	134	23	,	,	PUNCT
fcis-6343	134	24	application	application	NOUN
fcis-6343	134	25	,	,	PUNCT
fcis-6343	134	26	and	and	CCONJ
fcis-6343	134	27	deletion	deletion	NOUN
fcis-6343	134	28	at	at	ADP
fcis-6343	134	29	last	last	ADV
fcis-6343	134	30	,	,	PUNCT
fcis-6343	134	31	guaranteeing	guarantee	VERB
fcis-6343	134	32	the	the	DET
fcis-6343	134	33	safety	safety	NOUN
fcis-6343	134	34	of	of	ADP
fcis-6343	134	35	users	user	NOUN
fcis-6343	134	36	’	’	PART
fcis-6343	134	37	data	datum	NOUN
fcis-6343	134	38	to	to	ADP
fcis-6343	134	39	the	the	DET
fcis-6343	134	40	greatest	great	ADJ
fcis-6343	134	41	extent	extent	NOUN
fcis-6343	134	42	.	.	PUNCT
fcis-6343	135	1	it	it	PRON
fcis-6343	135	2	is	be	AUX
fcis-6343	135	3	different	different	ADJ
fcis-6343	135	4	from	from	ADP
fcis-6343	135	5	the	the	DET
fcis-6343	135	6	preservation	preservation	NOUN
fcis-6343	135	7	of	of	ADP
fcis-6343	135	8	data	datum	NOUN
fcis-6343	135	9	security	security	NOUN
fcis-6343	135	10	through	through	ADP
fcis-6343	135	11	the	the	DET
fcis-6343	135	12	encryption	encryption	NOUN
fcis-6343	135	13	and	and	CCONJ
fcis-6343	135	14	transcoding	transcoding	NOUN
fcis-6343	135	15	conducted	conduct	VERB
fcis-6343	135	16	by	by	ADP
fcis-6343	135	17	the	the	DET
fcis-6343	135	18	original	original	ADJ
fcis-6343	135	19	blockchain	blockchain	NOUN
fcis-6343	135	20	.	.	PUNCT
fcis-6343	136	1	references	reference	NOUN
fcis-6343	136	2	[	[	X
fcis-6343	136	3	1	1	NUM
fcis-6343	136	4	]	]	PUNCT
fcis-6343	136	5	adleman	adleman	NOUN
fcis-6343	136	6	l.	l.	PROPN
fcis-6343	136	7	rivest	riv	ADJ
fcis-6343	136	8	r	r	PROPN
fcis-6343	136	9	l	l	NOUN
fcis-6343	136	10	,	,	PUNCT
fcis-6343	136	11	shamir	shamir	PROPN
fcis-6343	136	12	a.	a.	PROPN
fcis-6343	136	13	a	a	DET
fcis-6343	136	14	method	method	NOUN
fcis-6343	136	15	for	for	ADP
fcis-6343	136	16	obtaining	obtain	VERB
fcis-6343	136	17	digital	digital	ADJ
fcis-6343	136	18	signatures	signature	NOUN
fcis-6343	136	19	and	and	CCONJ
fcis-6343	136	20	public	public	ADJ
fcis-6343	136	21	-	-	PUNCT
fcis-6343	136	22	key	key	NOUN
fcis-6343	136	23	cryptosystems	cryptosystem	NOUN
fcis-6343	136	24	.	.	PUNCT
fcis-6343	137	1	communications	communication	NOUN
fcis-6343	137	2	of	of	ADP
fcis-6343	137	3	the	the	DET
fcis-6343	137	4	acm	acm	NOUN
fcis-6343	137	5	,	,	PUNCT
fcis-6343	137	6	21	21	NUM
fcis-6343	137	7	,	,	PUNCT
fcis-6343	137	8	1978	1978	NUM
fcis-6343	137	9	.	.	PUNCT
fcis-6343	138	1	[	[	X
fcis-6343	138	2	2	2	NUM
fcis-6343	138	3	]	]	PUNCT
fcis-6343	138	4	gentry	gentry	NOUN
fcis-6343	138	5	c.	c.	PROPN
fcis-6343	138	6	fully	fully	ADV
fcis-6343	138	7	homomorphic	homomorphic	ADJ
fcis-6343	138	8	encryption	encryption	NOUN
fcis-6343	138	9	using	use	VERB
fcis-6343	138	10	ideal	ideal	ADJ
fcis-6343	138	11	lattices	lattice	NOUN
fcis-6343	138	12	.	.	PUNCT
fcis-6343	139	1	proceedings	proceeding	NOUN
fcis-6343	139	2	of	of	ADP
fcis-6343	139	3	the	the	DET
fcis-6343	139	4	forty	forty	NUM
fcis-6343	139	5	-	-	PUNCT
fcis-6343	139	6	first	first	ADJ
fcis-6343	139	7	annual	annual	ADJ
fcis-6343	139	8	acm	acm	NOUN
fcis-6343	139	9	symposium	symposium	NOUN
fcis-6343	139	10	on	on	ADP
fcis-6343	139	11	theory	theory	NOUN
fcis-6343	139	12	of	of	ADP
fcis-6343	139	13	computing	computing	NOUN
fcis-6343	139	14	,	,	PUNCT
fcis-6343	139	15	pages	page	NOUN
fcis-6343	139	16	169	169	NUM
fcis-6343	139	17	–	–	PUNCT
fcis-6343	139	18	178	178	NUM
fcis-6343	139	19	,	,	PUNCT
fcis-6343	139	20	2009	2009	NUM
fcis-6343	139	21	.	.	PUNCT
fcis-6343	140	1	[	[	X
fcis-6343	140	2	3	3	X
fcis-6343	140	3	]	]	X
fcis-6343	140	4	vercauteren	vercauteren	PROPN
fcis-6343	140	5	f.	f.	PROPN
fcis-6343	140	6	fan	fan	PROPN
fcis-6343	140	7	j.	j.	PROPN
fcis-6343	140	8	somewhat	somewhat	ADV
fcis-6343	140	9	practical	practical	ADJ
fcis-6343	140	10	fully	fully	ADV
fcis-6343	140	11	homomorphic	homomorphic	ADJ
fcis-6343	140	12	encryption	encryption	NOUN
fcis-6343	140	13	.	.	PUNCT
fcis-6343	141	1	iacr	iacr	ADJ
fcis-6343	141	2	cryptology	cryptology	NOUN
fcis-6343	141	3	eprint	eprint	NOUN
fcis-6343	141	4	archive	archive	NOUN
fcis-6343	141	5	,	,	PUNCT
fcis-6343	141	6	2012	2012	NUM
fcis-6343	141	7	.	.	PUNCT
fcis-6343	142	1	[	[	X
fcis-6343	142	2	4	4	X
fcis-6343	142	3	]	]	X
fcis-6343	142	4	kim	kim	PROPN
fcis-6343	142	5	m	m	PROPN
fcis-6343	142	6	et	et	PROPN
fcis-6343	142	7	al	al	PROPN
fcis-6343	142	8	.	.	PUNCT
fcis-6343	143	1	cheon	cheon	PROPN
fcis-6343	143	2	h	h	PROPN
fcis-6343	143	3	j	j	PROPN
fcis-6343	143	4	,	,	PUNCT
fcis-6343	143	5	kim	kim	PROPN
fcis-6343	143	6	a.	a.	PROPN
fcis-6343	143	7	homomorphic	homomorphic	ADJ
fcis-6343	143	8	encryption	encryption	NOUN
fcis-6343	143	9	for	for	ADP
fcis-6343	143	10	arithmetic	arithmetic	NOUN
fcis-6343	143	11	of	of	ADP
fcis-6343	143	12	approx	approx	PROPN
fcis-6343	143	13	-	-	PUNCT
fcis-6343	143	14	imate	imate	PROPN
fcis-6343	143	15	numbers	number	NOUN
fcis-6343	143	16	.	.	PUNCT
fcis-6343	144	1	advances	advance	NOUN
fcis-6343	144	2	in	in	ADP
fcis-6343	144	3	cryptology	cryptology	NOUN
fcis-6343	144	4	asiacrypt	asiacrypt	NOUN
fcis-6343	144	5	,	,	PUNCT
fcis-6343	144	6	2017	2017	NUM
fcis-6343	144	7	pt	pt	NOUN
fcis-6343	144	8	i	i	PROPN
fcis-6343	144	9	,	,	PUNCT
fcis-6343	144	10	pages	page	NOUN
fcis-6343	144	11	409–437	409–437	NUM
fcis-6343	144	12	,	,	PUNCT
fcis-6343	144	13	2017	2017	NUM
fcis-6343	144	14	.	.	PUNCT
fcis-6343	145	1	[	[	X
fcis-6343	145	2	5	5	X
fcis-6343	145	3	]	]	PUNCT
fcis-6343	145	4	vaikuntanathan	vaikuntanathan	ADV
fcis-6343	145	5	v.	v.	ADP
fcis-6343	145	6	brakerski	brakerski	PROPN
fcis-6343	145	7	z	z	NOUN
fcis-6343	145	8	,	,	PUNCT
fcis-6343	145	9	gentry	gentry	NOUN
fcis-6343	145	10	c.	c.	PROPN
fcis-6343	145	11	fully	fully	ADV
fcis-6343	145	12	homomorphic	homomorphic	ADJ
fcis-6343	145	13	encryption	encryption	NOUN
fcis-6343	145	14	without	without	ADP
fcis-6343	145	15	bootstrapping	bootstrappe	VERB
fcis-6343	145	16	.	.	PUNCT
fcis-6343	146	1	iacr	iacr	ADJ
fcis-6343	146	2	cryptology	cryptology	NOUN
fcis-6343	146	3	eprint	eprint	NOUN
fcis-6343	146	4	archive	archive	NOUN
fcis-6343	146	5	,	,	PUNCT
fcis-6343	146	6	2011	2011	NUM
fcis-6343	146	7	.	.	PUNCT