id	sid	tid	token	lemma	pos
gsrj-18	1	1	gsr	gsr	PROPN
gsrj-18	1	2	journal	journal	PROPN
gsrj-18	1	3	georgetown	georgetown	PROPN
gsrj-18	1	4	scientific	scientific	PROPN
gsrj-18	1	5	research	research	PROPN
gsrj-18	1	6	journal	journal	PROPN
gsrj-18	1	7	volume	volume	NOUN
gsrj-18	1	8	1	1	NUM
gsrj-18	1	9	|	|	NOUN
gsrj-18	1	10	edition	edition	NOUN
gsrj-18	1	11	2	2	NUM
gsrj-18	1	12	july	july	PROPN
gsrj-18	1	13	31	31	NUM
gsrj-18	1	14	,	,	PUNCT
gsrj-18	1	15	2021	2021	NUM
gsrj-18	1	16	danya	danya	PROPN
gsrj-18	1	17	adams	adams	PROPN
gsrj-18	1	18	issn	issn	PROPN
gsrj-18	1	19	2767	2767	NUM
gsrj-18	1	20	-	-	PUNCT
gsrj-18	1	21	6420	6420	NUM
gsrj-18	1	22	5	5	NUM
gsrj-18	1	23	danya	danya	PROPN
gsrj-18	1	24	adams	adams	PROPN
gsrj-18	1	25	�	�	PROPN
gsrj-18	1	26	an	an	DET
gsrj-18	1	27	investigation	investigation	NOUN
gsrj-18	1	28	into	into	ADP
gsrj-18	1	29	the	the	DET
gsrj-18	1	30	mathematics	mathematic	NOUN
gsrj-18	1	31	of	of	ADP
gsrj-18	1	32	decryption	decryption	NOUN
gsrj-18	1	33	techniques	technique	NOUN
gsrj-18	1	34	in	in	ADP
gsrj-18	1	35	rsa	rsa	PROPN
gsrj-18	1	36	encryption	encryption	NOUN
gsrj-18	1	37	,	,	PUNCT
gsrj-18	1	38	with	with	ADP
gsrj-18	1	39	an	an	DET
gsrj-18	1	40	implementation	implementation	NOUN
gsrj-18	1	41	in	in	ADP
gsrj-18	1	42	python	python	PROPN
gsrj-18	1	43	sofia	sofia	PROPN
gsrj-18	1	44	flynn	flynn	PROPN
gsrj-18	1	45	volume	volume	NOUN
gsrj-18	1	46	one	one	NUM
gsrj-18	1	47	edition	edition	NOUN
gsrj-18	1	48	two	two	NUM
gsrj-18	1	49	spring	spring	NOUN
gsrj-18	1	50	2021	2021	NUM
gsrj-18	1	51	georgetown	georgetown	PROPN
gsrj-18	1	52	scientific	scientific	PROPN
gsrj-18	1	53	research	research	PROPN
gsrj-18	1	54	journal	journal	PROPN
gsrj-18	1	55	6	6	NUM
gsrj-18	1	56	georgetown	georgetown	PROPN
gsrj-18	1	57	scientific	scientific	PROPN
gsrj-18	1	58	research	research	PROPN
gsrj-18	1	59	journal	journal	NOUN
gsrj-18	1	60	an	an	DET
gsrj-18	1	61	investigation	investigation	NOUN
gsrj-18	1	62	into	into	ADP
gsrj-18	1	63	the	the	DET
gsrj-18	1	64	mathematics	mathematic	NOUN
gsrj-18	1	65	of	of	ADP
gsrj-18	1	66	decryption	decryption	NOUN
gsrj-18	1	67	techniques	technique	NOUN
gsrj-18	1	68	in	in	ADP
gsrj-18	1	69	rsa	rsa	PROPN
gsrj-18	1	70	encryption	encryption	NOUN
gsrj-18	1	71	,	,	PUNCT
gsrj-18	1	72	with	with	ADP
gsrj-18	1	73	an	an	DET
gsrj-18	1	74	implementation	implementation	NOUN
gsrj-18	1	75	in	in	ADP
gsrj-18	1	76	python	python	PROPN
gsrj-18	1	77	sofia	sofia	PROPN
gsrj-18	1	78	flynn	flynn	PROPN
gsrj-18	1	79	department	department	PROPN
gsrj-18	1	80	of	of	ADP
gsrj-18	1	81	mathematics	mathematics	PROPN
gsrj-18	1	82	,	,	PUNCT
gsrj-18	1	83	georgetown	georgetown	PROPN
gsrj-18	1	84	university	university	PROPN
gsrj-18	1	85	,	,	PUNCT
gsrj-18	1	86	washington	washington	PROPN
gsrj-18	1	87	d.c	d.c	PROPN
gsrj-18	1	88	.	.	PUNCT
gsrj-18	2	1	e	e	X
gsrj-18	2	2	-	-	NOUN
gsrj-18	2	3	mail	mail	NOUN
gsrj-18	2	4	:	:	PUNCT
gsrj-18	3	1	smf133@georgetown.edu	smf133@georgetown.edu	X
gsrj-18	3	2	https://doi.org/10.48091/gsr.v1i2.18	https://doi.org/10.48091/gsr.v1i2.18	PROPN
gsrj-18	3	3	abstract	abstract	ADV
gsrj-18	3	4	this	this	DET
gsrj-18	3	5	study	study	NOUN
gsrj-18	3	6	explores	explore	VERB
gsrj-18	3	7	the	the	DET
gsrj-18	3	8	mathematics	mathematic	NOUN
gsrj-18	3	9	of	of	ADP
gsrj-18	3	10	two	two	NUM
gsrj-18	3	11	different	different	ADJ
gsrj-18	3	12	techniques	technique	NOUN
gsrj-18	3	13	that	that	PRON
gsrj-18	3	14	can	can	AUX
gsrj-18	3	15	be	be	AUX
gsrj-18	3	16	used	use	VERB
gsrj-18	3	17	to	to	PART
gsrj-18	3	18	access	access	VERB
gsrj-18	3	19	the	the	DET
gsrj-18	3	20	decryption	decryption	NOUN
gsrj-18	3	21	key	key	NOUN
gsrj-18	3	22	in	in	ADP
gsrj-18	3	23	rsa	rsa	NOUN
gsrj-18	3	24	encryption	encryption	NOUN
gsrj-18	3	25	including	include	VERB
gsrj-18	3	26	semi	semi	ADJ
gsrj-18	3	27	-	-	ADJ
gsrj-18	3	28	prime	prime	ADJ
gsrj-18	3	29	factorization	factorization	NOUN
gsrj-18	3	30	and	and	CCONJ
gsrj-18	3	31	a	a	DET
gsrj-18	3	32	logarithmic	logarithmic	ADJ
gsrj-18	3	33	method	method	NOUN
gsrj-18	3	34	.	.	PUNCT
gsrj-18	4	1	the	the	DET
gsrj-18	4	2	study	study	NOUN
gsrj-18	4	3	then	then	ADV
gsrj-18	4	4	presents	present	VERB
gsrj-18	4	5	a	a	DET
gsrj-18	4	6	python	python	NOUN
gsrj-18	4	7	program	program	NOUN
gsrj-18	4	8	,	,	PUNCT
gsrj-18	4	9	written	write	VERB
gsrj-18	4	10	by	by	ADP
gsrj-18	4	11	the	the	DET
gsrj-18	4	12	author	author	NOUN
gsrj-18	4	13	,	,	PUNCT
gsrj-18	4	14	that	that	PRON
gsrj-18	4	15	automates	automate	VERB
gsrj-18	4	16	the	the	DET
gsrj-18	4	17	calculations	calculation	NOUN
gsrj-18	4	18	for	for	ADP
gsrj-18	4	19	either	either	PRON
gsrj-18	4	20	of	of	ADP
gsrj-18	4	21	the	the	DET
gsrj-18	4	22	decryption	decryption	NOUN
gsrj-18	4	23	techniques	technique	NOUN
gsrj-18	4	24	and	and	CCONJ
gsrj-18	4	25	also	also	ADV
gsrj-18	4	26	calculates	calculate	VERB
gsrj-18	4	27	the	the	DET
gsrj-18	4	28	number	number	NOUN
gsrj-18	4	29	of	of	ADP
gsrj-18	4	30	iterations	iteration	NOUN
gsrj-18	4	31	required	require	VERB
gsrj-18	4	32	to	to	PART
gsrj-18	4	33	determine	determine	VERB
gsrj-18	4	34	the	the	DET
gsrj-18	4	35	decryption	decryption	NOUN
gsrj-18	4	36	key	key	NOUN
gsrj-18	4	37	in	in	ADP
gsrj-18	4	38	either	either	DET
gsrj-18	4	39	circumstance	circumstance	NOUN
gsrj-18	4	40	.	.	PUNCT
gsrj-18	5	1	most	most	ADV
gsrj-18	5	2	importantly	importantly	ADV
gsrj-18	5	3	,	,	PUNCT
gsrj-18	5	4	the	the	DET
gsrj-18	5	5	program	program	NOUN
gsrj-18	5	6	utilizes	utilize	VERB
gsrj-18	5	7	only	only	ADJ
gsrj-18	5	8	values	value	NOUN
gsrj-18	5	9	of	of	ADP
gsrj-18	5	10	the	the	DET
gsrj-18	5	11	rsa	rsa	PROPN
gsrj-18	5	12	encryption	encryption	NOUN
gsrj-18	5	13	algorithm	algorithm	NOUN
gsrj-18	5	14	that	that	PRON
gsrj-18	5	15	would	would	AUX
gsrj-18	5	16	be	be	AUX
gsrj-18	5	17	made	make	VERB
gsrj-18	5	18	publicly	publicly	ADV
gsrj-18	5	19	available	available	ADJ
gsrj-18	5	20	in	in	ADP
gsrj-18	5	21	actual	actual	ADJ
gsrj-18	5	22	circumstances	circumstance	NOUN
gsrj-18	5	23	to	to	PART
gsrj-18	5	24	calculate	calculate	VERB
gsrj-18	5	25	the	the	DET
gsrj-18	5	26	decryption	decryption	NOUN
gsrj-18	5	27	key	key	NOUN
gsrj-18	5	28	so	so	SCONJ
gsrj-18	5	29	as	as	SCONJ
gsrj-18	5	30	to	to	PART
gsrj-18	5	31	mimic	mimic	VERB
gsrj-18	5	32	real	real	ADJ
gsrj-18	5	33	-	-	PUNCT
gsrj-18	5	34	life	life	NOUN
gsrj-18	5	35	occurrences	occurrence	NOUN
gsrj-18	5	36	with	with	ADP
gsrj-18	5	37	as	as	ADV
gsrj-18	5	38	much	much	ADJ
gsrj-18	5	39	integrity	integrity	NOUN
gsrj-18	5	40	and	and	CCONJ
gsrj-18	5	41	accuracy	accuracy	NOUN
gsrj-18	5	42	as	as	ADP
gsrj-18	5	43	possible	possible	ADJ
gsrj-18	5	44	.	.	PUNCT
gsrj-18	6	1	keywords	keyword	NOUN
gsrj-18	6	2	:	:	PUNCT
gsrj-18	6	3	rsa	rsa	PROPN
gsrj-18	6	4	encryption	encryption	NOUN
gsrj-18	6	5	,	,	PUNCT
gsrj-18	6	6	semi	semi	ADJ
gsrj-18	6	7	-	-	ADJ
gsrj-18	6	8	prime	prime	ADJ
gsrj-18	6	9	factorization	factorization	NOUN
gsrj-18	6	10	,	,	PUNCT
gsrj-18	6	11	decryption	decryption	NOUN
gsrj-18	6	12	,	,	PUNCT
gsrj-18	6	13	python	python	NOUN
gsrj-18	6	14	1	1	NUM
gsrj-18	6	15	.	.	PUNCT
gsrj-18	7	1	introduction	introduction	NOUN
gsrj-18	7	2	rsa	rsa	PROPN
gsrj-18	7	3	encryption	encryption	NOUN
gsrj-18	7	4	was	be	AUX
gsrj-18	7	5	created	create	VERB
gsrj-18	7	6	in	in	ADP
gsrj-18	7	7	the	the	DET
gsrj-18	7	8	1970s	1970	NOUN
gsrj-18	7	9	as	as	ADP
gsrj-18	7	10	an	an	DET
gsrj-18	7	11	asymmetric	asymmetric	ADJ
gsrj-18	7	12	(	(	PUNCT
gsrj-18	7	13	public	public	ADJ
gsrj-18	7	14	-	-	PUNCT
gsrj-18	7	15	key	key	NOUN
gsrj-18	7	16	)	)	PUNCT
gsrj-18	7	17	form	form	NOUN
gsrj-18	7	18	of	of	ADP
gsrj-18	7	19	cryptography	cryptography	NOUN
gsrj-18	7	20	that	that	PRON
gsrj-18	7	21	would	would	AUX
gsrj-18	7	22	replace	replace	VERB
gsrj-18	7	23	the	the	PRON
gsrj-18	7	24	then	then	ADV
gsrj-18	7	25	-	-	PUNCT
gsrj-18	7	26	commonly	commonly	ADV
gsrj-18	7	27	utilized	utilize	VERB
gsrj-18	7	28	and	and	CCONJ
gsrj-18	7	29	weakening	weaken	VERB
gsrj-18	7	30	symmetric	symmetric	ADJ
gsrj-18	7	31	cryptography.1	cryptography.1	NOUN
gsrj-18	7	32	in	in	ADP
gsrj-18	7	33	symmetric	symmetric	ADJ
gsrj-18	7	34	cryptography	cryptography	NOUN
gsrj-18	7	35	,	,	PUNCT
gsrj-18	7	36	in	in	ADP
gsrj-18	7	37	order	order	NOUN
gsrj-18	7	38	to	to	PART
gsrj-18	7	39	exchange	exchange	VERB
gsrj-18	7	40	secret	secret	ADJ
gsrj-18	7	41	messages	message	NOUN
gsrj-18	7	42	,	,	PUNCT
gsrj-18	7	43	two	two	NUM
gsrj-18	7	44	individuals	individual	NOUN
gsrj-18	7	45	would	would	AUX
gsrj-18	7	46	either	either	CCONJ
gsrj-18	7	47	have	have	VERB
gsrj-18	7	48	to	to	PART
gsrj-18	7	49	meet	meet	VERB
gsrj-18	7	50	beforehand	beforehand	ADV
gsrj-18	7	51	to	to	PART
gsrj-18	7	52	exchange	exchange	VERB
gsrj-18	7	53	identical	identical	ADJ
gsrj-18	7	54	keys	key	NOUN
gsrj-18	7	55	or	or	CCONJ
gsrj-18	7	56	run	run	VERB
gsrj-18	7	57	the	the	DET
gsrj-18	7	58	risk	risk	NOUN
gsrj-18	7	59	of	of	ADP
gsrj-18	7	60	their	their	PRON
gsrj-18	7	61	keys	key	NOUN
gsrj-18	7	62	being	be	AUX
gsrj-18	7	63	intercepted.2	intercepted.2	ADJ
gsrj-18	7	64	in	in	ADP
gsrj-18	7	65	a	a	DET
gsrj-18	7	66	simplified	simplified	ADJ
gsrj-18	7	67	example	example	NOUN
gsrj-18	7	68	of	of	ADP
gsrj-18	7	69	symmetric	symmetric	ADJ
gsrj-18	7	70	cryptography	cryptography	NOUN
gsrj-18	7	71	,	,	PUNCT
gsrj-18	7	72	suppose	suppose	VERB
gsrj-18	7	73	“	"	PUNCT
gsrj-18	7	74	bob	bob	PROPN
gsrj-18	7	75	”	"	PUNCT
gsrj-18	7	76	wanted	want	VERB
gsrj-18	7	77	to	to	PART
gsrj-18	7	78	send	send	VERB
gsrj-18	7	79	a	a	DET
gsrj-18	7	80	secret	secret	ADJ
gsrj-18	7	81	message	message	NOUN
gsrj-18	7	82	to	to	ADP
gsrj-18	7	83	“	"	PUNCT
gsrj-18	7	84	alice	alice	PROPN
gsrj-18	7	85	.	.	PUNCT
gsrj-18	7	86	”	"	PUNCT
gsrj-18	8	1	alice	alice	PROPN
gsrj-18	8	2	and	and	CCONJ
gsrj-18	8	3	bob	bob	PROPN
gsrj-18	8	4	would	would	AUX
gsrj-18	8	5	first	first	ADV
gsrj-18	8	6	have	have	VERB
gsrj-18	8	7	to	to	PART
gsrj-18	8	8	meet	meet	VERB
gsrj-18	8	9	each	each	DET
gsrj-18	8	10	other	other	ADJ
gsrj-18	8	11	to	to	PART
gsrj-18	8	12	share	share	VERB
gsrj-18	8	13	identical	identical	ADJ
gsrj-18	8	14	keys	key	NOUN
gsrj-18	8	15	that	that	PRON
gsrj-18	8	16	would	would	AUX
gsrj-18	8	17	be	be	AUX
gsrj-18	8	18	used	use	VERB
gsrj-18	8	19	for	for	ADP
gsrj-18	8	20	encryption	encryption	NOUN
gsrj-18	8	21	and	and	CCONJ
gsrj-18	8	22	decryption	decryption	NOUN
gsrj-18	8	23	,	,	PUNCT
gsrj-18	8	24	ensuring	ensure	VERB
gsrj-18	8	25	that	that	SCONJ
gsrj-18	8	26	each	each	DET
gsrj-18	8	27	person	person	NOUN
gsrj-18	8	28	ultimately	ultimately	ADV
gsrj-18	8	29	possesses	possess	VERB
gsrj-18	8	30	the	the	DET
gsrj-18	8	31	same	same	ADJ
gsrj-18	8	32	key	key	NOUN
gsrj-18	8	33	.	.	PUNCT
gsrj-18	9	1	using	use	VERB
gsrj-18	9	2	one	one	NUM
gsrj-18	9	3	of	of	ADP
gsrj-18	9	4	the	the	DET
gsrj-18	9	5	identical	identical	ADJ
gsrj-18	9	6	keys	key	NOUN
gsrj-18	9	7	,	,	PUNCT
gsrj-18	9	8	bob	bob	PROPN
gsrj-18	9	9	could	could	AUX
gsrj-18	9	10	then	then	ADV
gsrj-18	9	11	encrypt	encrypt	VERB
gsrj-18	9	12	his	his	PRON
gsrj-18	9	13	secret	secret	ADJ
gsrj-18	9	14	message	message	NOUN
gsrj-18	9	15	and	and	CCONJ
gsrj-18	9	16	send	send	VERB
gsrj-18	9	17	it	it	PRON
gsrj-18	9	18	to	to	ADP
gsrj-18	9	19	alice	alice	PROPN
gsrj-18	9	20	,	,	PUNCT
gsrj-18	9	21	who	who	PRON
gsrj-18	9	22	would	would	AUX
gsrj-18	9	23	then	then	ADV
gsrj-18	9	24	decrypt	decrypt	VERB
gsrj-18	9	25	the	the	DET
gsrj-18	9	26	message	message	NOUN
gsrj-18	9	27	using	use	VERB
gsrj-18	9	28	the	the	DET
gsrj-18	9	29	other	other	ADJ
gsrj-18	9	30	identical	identical	ADJ
gsrj-18	9	31	key	key	NOUN
gsrj-18	9	32	that	that	SCONJ
gsrj-18	9	33	she	she	PRON
gsrj-18	9	34	and	and	CCONJ
gsrj-18	9	35	bob	bob	PROPN
gsrj-18	9	36	had	have	AUX
gsrj-18	9	37	exchanged	exchange	VERB
gsrj-18	9	38	beforehand	beforehand	ADV
gsrj-18	9	39	.	.	PUNCT
gsrj-18	10	1	if	if	SCONJ
gsrj-18	10	2	bob	bob	PROPN
gsrj-18	10	3	and	and	CCONJ
gsrj-18	10	4	alice	alice	PROPN
gsrj-18	10	5	can	can	AUX
gsrj-18	10	6	not	not	PART
gsrj-18	10	7	meet	meet	VERB
gsrj-18	10	8	to	to	PART
gsrj-18	10	9	share	share	VERB
gsrj-18	10	10	keys	key	NOUN
gsrj-18	10	11	,	,	PUNCT
gsrj-18	10	12	then	then	ADV
gsrj-18	10	13	bob	bob	PROPN
gsrj-18	10	14	would	would	AUX
gsrj-18	10	15	have	have	VERB
gsrj-18	10	16	to	to	PART
gsrj-18	10	17	send	send	VERB
gsrj-18	10	18	the	the	DET
gsrj-18	10	19	key	key	NOUN
gsrj-18	10	20	that	that	SCONJ
gsrj-18	10	21	decrypts	decrypt	VERB
gsrj-18	10	22	his	his	PRON
gsrj-18	10	23	encrypted	encrypt	VERB
gsrj-18	10	24	message	message	NOUN
gsrj-18	10	25	along	along	ADP
gsrj-18	10	26	with	with	ADP
gsrj-18	10	27	his	his	PRON
gsrj-18	10	28	encrypted	encrypt	VERB
gsrj-18	10	29	message	message	NOUN
gsrj-18	10	30	to	to	ADP
gsrj-18	10	31	alice	alice	PROPN
gsrj-18	10	32	,	,	PUNCT
gsrj-18	10	33	running	run	VERB
gsrj-18	10	34	the	the	DET
gsrj-18	10	35	risk	risk	NOUN
gsrj-18	10	36	that	that	SCONJ
gsrj-18	10	37	a	a	DET
gsrj-18	10	38	third	third	ADJ
gsrj-18	10	39	party	party	NOUN
gsrj-18	10	40	could	could	AUX
gsrj-18	10	41	easily	easily	ADV
gsrj-18	10	42	intercept	intercept	VERB
gsrj-18	10	43	both	both	CCONJ
gsrj-18	10	44	the	the	DET
gsrj-18	10	45	encrypted	encrypt	VERB
gsrj-18	10	46	message	message	NOUN
gsrj-18	10	47	and	and	CCONJ
gsrj-18	10	48	key	key	NOUN
gsrj-18	10	49	before	before	SCONJ
gsrj-18	10	50	it	it	PRON
gsrj-18	10	51	comes	come	VERB
gsrj-18	10	52	into	into	ADP
gsrj-18	10	53	alice	alice	PROPN
gsrj-18	10	54	’s	’s	PART
gsrj-18	10	55	possession	possession	NOUN
gsrj-18	10	56	.	.	PUNCT
gsrj-18	11	1	in	in	ADP
gsrj-18	11	2	1970	1970	NUM
gsrj-18	11	3	,	,	PUNCT
gsrj-18	11	4	james	james	PROPN
gsrj-18	11	5	ellis	ellis	PROPN
gsrj-18	11	6	proposed	propose	VERB
gsrj-18	11	7	a	a	DET
gsrj-18	11	8	hypothetical	hypothetical	ADJ
gsrj-18	11	9	idea	idea	NOUN
gsrj-18	11	10	in	in	ADP
gsrj-18	11	11	which	which	PRON
gsrj-18	11	12	secret	secret	ADJ
gsrj-18	11	13	messages	message	NOUN
gsrj-18	11	14	could	could	AUX
gsrj-18	11	15	be	be	AUX
gsrj-18	11	16	exchanged	exchange	VERB
gsrj-18	11	17	between	between	ADP
gsrj-18	11	18	individuals	individual	NOUN
gsrj-18	11	19	without	without	ADP
gsrj-18	11	20	them	they	PRON
gsrj-18	11	21	having	have	VERB
gsrj-18	11	22	to	to	PART
gsrj-18	11	23	meet	meet	VERB
gsrj-18	11	24	beforehand	beforehand	ADV
gsrj-18	11	25	to	to	PART
gsrj-18	11	26	share	share	VERB
gsrj-18	11	27	identical	identical	ADJ
gsrj-18	11	28	keys	key	NOUN
gsrj-18	11	29	,	,	PUNCT
gsrj-18	11	30	thereby	thereby	ADV
gsrj-18	11	31	eliminating	eliminate	VERB
gsrj-18	11	32	dependence	dependence	NOUN
gsrj-18	11	33	on	on	ADP
gsrj-18	11	34	the	the	DET
gsrj-18	11	35	ever	ever	ADV
gsrj-18	11	36	-	-	PUNCT
gsrj-18	11	37	weakening	weaken	VERB
gsrj-18	11	38	symmetric	symmetric	ADJ
gsrj-18	11	39	cryptography.3	cryptography.3	PROPN
gsrj-18	11	40	the	the	DET
gsrj-18	11	41	premise	premise	NOUN
gsrj-18	11	42	was	be	AUX
gsrj-18	11	43	simple	simple	ADJ
gsrj-18	11	44	:	:	PUNCT
gsrj-18	11	45	if	if	SCONJ
gsrj-18	11	46	bob	bob	PROPN
gsrj-18	11	47	wished	wish	VERB
gsrj-18	11	48	to	to	PART
gsrj-18	11	49	send	send	VERB
gsrj-18	11	50	a	a	DET
gsrj-18	11	51	secret	secret	ADJ
gsrj-18	11	52	message	message	NOUN
gsrj-18	11	53	to	to	ADP
gsrj-18	11	54	alice	alice	PROPN
gsrj-18	11	55	,	,	PUNCT
gsrj-18	11	56	alice	alice	PROPN
gsrj-18	11	57	could	could	AUX
gsrj-18	11	58	create	create	VERB
gsrj-18	11	59	a	a	DET
gsrj-18	11	60	lock	lock	NOUN
gsrj-18	11	61	and	and	CCONJ
gsrj-18	11	62	a	a	DET
gsrj-18	11	63	key	key	NOUN
gsrj-18	11	64	that	that	PRON
gsrj-18	11	65	decrypted	decrypt	VERB
gsrj-18	11	66	,	,	PUNCT
gsrj-18	11	67	or	or	CCONJ
gsrj-18	11	68	“	"	PUNCT
gsrj-18	11	69	unlocked	unlocked	ADJ
gsrj-18	11	70	’	'	PUNCT
gsrj-18	11	71	,	,	PUNCT
gsrj-18	11	72	that	that	DET
gsrj-18	11	73	lock	lock	NOUN
gsrj-18	11	74	.	.	PUNCT
gsrj-18	12	1	alice	alice	PROPN
gsrj-18	12	2	could	could	AUX
gsrj-18	12	3	then	then	ADV
gsrj-18	12	4	send	send	VERB
gsrj-18	12	5	the	the	DET
gsrj-18	12	6	open	open	ADJ
gsrj-18	12	7	lock	lock	NOUN
gsrj-18	12	8	to	to	ADP
gsrj-18	12	9	bob	bob	PROPN
gsrj-18	12	10	,	,	PUNCT
gsrj-18	12	11	who	who	PRON
gsrj-18	12	12	would	would	AUX
gsrj-18	12	13	proceed	proceed	VERB
gsrj-18	12	14	to	to	PART
gsrj-18	12	15	encrypt	encrypt	VERB
gsrj-18	12	16	,	,	PUNCT
gsrj-18	12	17	or	or	CCONJ
gsrj-18	12	18	“	"	PUNCT
gsrj-18	12	19	lock	lock	NOUN
gsrj-18	12	20	”	"	PUNCT
gsrj-18	12	21	,	,	PUNCT
gsrj-18	12	22	his	his	PRON
gsrj-18	12	23	secret	secret	ADJ
gsrj-18	12	24	message	message	NOUN
gsrj-18	12	25	using	use	VERB
gsrj-18	12	26	the	the	DET
gsrj-18	12	27	open	open	ADJ
gsrj-18	12	28	lock	lock	NOUN
gsrj-18	12	29	.	.	PUNCT
gsrj-18	13	1	alice	alice	PROPN
gsrj-18	13	2	would	would	AUX
gsrj-18	13	3	retain	retain	VERB
gsrj-18	13	4	possession	possession	NOUN
gsrj-18	13	5	of	of	ADP
gsrj-18	13	6	the	the	DET
gsrj-18	13	7	key	key	NOUN
gsrj-18	13	8	that	that	PRON
gsrj-18	13	9	decrypted	decrypt	VERB
gsrj-18	13	10	the	the	DET
gsrj-18	13	11	lock	lock	NOUN
gsrj-18	13	12	.	.	PUNCT
gsrj-18	14	1	bob	bob	PROPN
gsrj-18	14	2	would	would	AUX
gsrj-18	14	3	then	then	ADV
gsrj-18	14	4	send	send	VERB
gsrj-18	14	5	his	his	PRON
gsrj-18	14	6	encrypted	encrypt	VERB
gsrj-18	14	7	message	message	NOUN
gsrj-18	14	8	to	to	ADP
gsrj-18	14	9	alice	alice	PROPN
gsrj-18	14	10	,	,	PUNCT
gsrj-18	14	11	who	who	PRON
gsrj-18	14	12	would	would	AUX
gsrj-18	14	13	decrypt	decrypt	VERB
gsrj-18	14	14	it	it	PRON
gsrj-18	14	15	using	use	VERB
gsrj-18	14	16	the	the	DET
gsrj-18	14	17	key	key	NOUN
gsrj-18	14	18	that	that	PRON
gsrj-18	14	19	remained	remain	VERB
gsrj-18	14	20	in	in	ADP
gsrj-18	14	21	her	her	PRON
gsrj-18	14	22	possession	possession	NOUN
gsrj-18	14	23	throughout	throughout	ADP
gsrj-18	14	24	the	the	DET
gsrj-18	14	25	entire	entire	ADJ
gsrj-18	14	26	process	process	NOUN
gsrj-18	14	27	.	.	PUNCT
gsrj-18	15	1	such	such	ADJ
gsrj-18	15	2	is	be	AUX
gsrj-18	15	3	the	the	DET
gsrj-18	15	4	conceptual	conceptual	ADJ
gsrj-18	15	5	idea	idea	NOUN
gsrj-18	15	6	behind	behind	ADP
gsrj-18	15	7	asymmetric	asymmetric	ADJ
gsrj-18	15	8	7	7	NUM
gsrj-18	15	9	georgetown	georgetown	PROPN
gsrj-18	15	10	scientific	scientific	PROPN
gsrj-18	15	11	research	research	PROPN
gsrj-18	15	12	journal	journal	NOUN
gsrj-18	15	13	cryptography	cryptography	NOUN
gsrj-18	15	14	;	;	PUNCT
gsrj-18	15	15	by	by	ADP
gsrj-18	15	16	preventing	prevent	VERB
gsrj-18	15	17	an	an	DET
gsrj-18	15	18	initial	initial	ADJ
gsrj-18	15	19	exchange	exchange	NOUN
gsrj-18	15	20	of	of	ADP
gsrj-18	15	21	keys	key	NOUN
gsrj-18	15	22	,	,	PUNCT
gsrj-18	15	23	one	one	PRON
gsrj-18	15	24	avoids	avoid	VERB
gsrj-18	15	25	the	the	DET
gsrj-18	15	26	risk	risk	NOUN
gsrj-18	15	27	of	of	ADP
gsrj-18	15	28	a	a	DET
gsrj-18	15	29	third	third	ADJ
gsrj-18	15	30	party	party	NOUN
gsrj-18	15	31	intercepting	intercept	VERB
gsrj-18	15	32	the	the	DET
gsrj-18	15	33	key	key	NOUN
gsrj-18	15	34	used	use	VERB
gsrj-18	15	35	to	to	PART
gsrj-18	15	36	decrypt	decrypt	VERB
gsrj-18	15	37	the	the	DET
gsrj-18	15	38	encrypted	encrypt	VERB
gsrj-18	15	39	message	message	NOUN
gsrj-18	15	40	.	.	PUNCT
gsrj-18	16	1	in	in	ADP
gsrj-18	16	2	1973	1973	NUM
gsrj-18	16	3	,	,	PUNCT
gsrj-18	16	4	clifford	clifford	PROPN
gsrj-18	16	5	cocks	cock	NOUN
gsrj-18	16	6	invented	invent	VERB
gsrj-18	16	7	a	a	DET
gsrj-18	16	8	mathematical	mathematical	ADJ
gsrj-18	16	9	implementation	implementation	NOUN
gsrj-18	16	10	of	of	ADP
gsrj-18	16	11	ellis	ellis	PROPN
gsrj-18	16	12	’	'	PUNCT
gsrj-18	16	13	idea	idea	NOUN
gsrj-18	16	14	,	,	PUNCT
gsrj-18	16	15	which	which	PRON
gsrj-18	16	16	had	have	AUX
gsrj-18	16	17	remained	remain	VERB
gsrj-18	16	18	classified	classify	VERB
gsrj-18	16	19	for	for	ADP
gsrj-18	16	20	twenty	twenty	NUM
gsrj-18	16	21	-	-	PUNCT
gsrj-18	16	22	four	four	NUM
gsrj-18	16	23	years.4	years.4	NUM
gsrj-18	16	24	later	later	ADV
gsrj-18	16	25	on	on	ADV
gsrj-18	16	26	in	in	ADP
gsrj-18	16	27	1977	1977	NUM
gsrj-18	16	28	,	,	PUNCT
gsrj-18	16	29	ron	ron	PROPN
gsrj-18	16	30	rivest	riv	ADJ
gsrj-18	16	31	,	,	PUNCT
gsrj-18	16	32	adi	adi	PROPN
gsrj-18	16	33	shamir	shamir	PROPN
gsrj-18	16	34	,	,	PUNCT
gsrj-18	16	35	and	and	CCONJ
gsrj-18	16	36	leonard	leonard	PROPN
gsrj-18	16	37	adleman	adleman	PROPN
gsrj-18	16	38	created	create	VERB
gsrj-18	16	39	the	the	DET
gsrj-18	16	40	equivalent	equivalent	NOUN
gsrj-18	16	41	of	of	ADP
gsrj-18	16	42	cocks	cock	NOUN
gsrj-18	16	43	’	'	PUNCT
gsrj-18	16	44	implementation	implementation	NOUN
gsrj-18	16	45	of	of	ADP
gsrj-18	16	46	ellis	ellis	PROPN
gsrj-18	16	47	’	'	PUNCT
gsrj-18	16	48	idea	idea	NOUN
gsrj-18	16	49	completely	completely	ADV
gsrj-18	16	50	independently.5	independently.5	PROPN
gsrj-18	16	51	the	the	DET
gsrj-18	16	52	algorithm	algorithm	NOUN
gsrj-18	16	53	they	they	PRON
gsrj-18	16	54	created	create	VERB
gsrj-18	16	55	based	base	VERB
gsrj-18	16	56	on	on	ADP
gsrj-18	16	57	ellis	ellis	PROPN
gsrj-18	16	58	’	'	PUNCT
gsrj-18	16	59	conceptual	conceptual	ADJ
gsrj-18	16	60	idea	idea	NOUN
gsrj-18	16	61	about	about	ADP
gsrj-18	16	62	asymmetric	asymmetric	ADJ
gsrj-18	16	63	cryptography	cryptography	NOUN
gsrj-18	16	64	was	be	AUX
gsrj-18	16	65	henceforth	henceforth	ADV
gsrj-18	16	66	known	know	VERB
gsrj-18	16	67	as	as	ADP
gsrj-18	16	68	rsa	rsa	PROPN
gsrj-18	16	69	(	(	PUNCT
gsrj-18	16	70	each	each	PRON
gsrj-18	16	71	of	of	ADP
gsrj-18	16	72	the	the	DET
gsrj-18	16	73	founders	founder	NOUN
gsrj-18	16	74	’	’	PART
gsrj-18	16	75	initials	initial	NOUN
gsrj-18	16	76	)	)	PUNCT
gsrj-18	16	77	encryption	encryption	NOUN
gsrj-18	16	78	and	and	CCONJ
gsrj-18	16	79	is	be	AUX
gsrj-18	16	80	widely	widely	ADV
gsrj-18	16	81	used	use	VERB
gsrj-18	16	82	today	today	NOUN
gsrj-18	16	83	.	.	PUNCT
gsrj-18	17	1	rsa	rsa	PROPN
gsrj-18	17	2	has	have	VERB
gsrj-18	17	3	formidable	formidable	ADJ
gsrj-18	17	4	strength	strength	NOUN
gsrj-18	17	5	;	;	PUNCT
gsrj-18	17	6	as	as	ADP
gsrj-18	17	7	of	of	ADP
gsrj-18	17	8	yet	yet	ADV
gsrj-18	17	9	,	,	PUNCT
gsrj-18	17	10	the	the	DET
gsrj-18	17	11	only	only	ADJ
gsrj-18	17	12	device	device	NOUN
gsrj-18	17	13	that	that	PRON
gsrj-18	17	14	is	be	AUX
gsrj-18	17	15	considered	consider	VERB
gsrj-18	17	16	to	to	PART
gsrj-18	17	17	be	be	AUX
gsrj-18	17	18	capable	capable	ADJ
gsrj-18	17	19	of	of	ADP
gsrj-18	17	20	breaking	break	VERB
gsrj-18	17	21	rsa	rsa	PROPN
gsrj-18	17	22	is	be	AUX
gsrj-18	17	23	a	a	DET
gsrj-18	17	24	quantum	quantum	ADJ
gsrj-18	17	25	computer.6	computer.6	NOUN
gsrj-18	17	26	rivest	riv	ADJ
gsrj-18	17	27	,	,	PUNCT
gsrj-18	17	28	shamir	shamir	ADJ
gsrj-18	17	29	,	,	PUNCT
gsrj-18	17	30	and	and	CCONJ
gsrj-18	17	31	adleman	adleman	PROPN
gsrj-18	17	32	’s	’s	PART
gsrj-18	17	33	algorithm	algorithm	NOUN
gsrj-18	17	34	consists	consist	VERB
gsrj-18	17	35	of	of	ADP
gsrj-18	17	36	six	six	NUM
gsrj-18	17	37	values	value	NOUN
gsrj-18	17	38	that	that	PRON
gsrj-18	17	39	correspond	correspond	VERB
gsrj-18	17	40	to	to	ADP
gsrj-18	17	41	either	either	CCONJ
gsrj-18	17	42	a	a	DET
gsrj-18	17	43	public	public	ADJ
gsrj-18	17	44	or	or	CCONJ
gsrj-18	17	45	private	private	ADJ
gsrj-18	17	46	key	key	NOUN
gsrj-18	17	47	.	.	PUNCT
gsrj-18	18	1	the	the	DET
gsrj-18	18	2	public	public	ADJ
gsrj-18	18	3	key	key	NOUN
gsrj-18	18	4	is	be	AUX
gsrj-18	18	5	released	release	VERB
gsrj-18	18	6	publicly	publicly	ADV
gsrj-18	18	7	and	and	CCONJ
gsrj-18	18	8	can	can	AUX
gsrj-18	18	9	be	be	AUX
gsrj-18	18	10	used	use	VERB
gsrj-18	18	11	by	by	ADP
gsrj-18	18	12	anyone	anyone	PRON
gsrj-18	18	13	to	to	PART
gsrj-18	18	14	encrypt	encrypt	VERB
gsrj-18	18	15	a	a	DET
gsrj-18	18	16	message	message	NOUN
gsrj-18	18	17	;	;	PUNCT
gsrj-18	18	18	the	the	DET
gsrj-18	18	19	private	private	ADJ
gsrj-18	18	20	key	key	NOUN
gsrj-18	18	21	,	,	PUNCT
gsrj-18	18	22	on	on	ADP
gsrj-18	18	23	the	the	DET
gsrj-18	18	24	other	other	ADJ
gsrj-18	18	25	hand	hand	NOUN
gsrj-18	18	26	,	,	PUNCT
gsrj-18	18	27	is	be	AUX
gsrj-18	18	28	kept	keep	VERB
gsrj-18	18	29	hidden	hide	VERB
gsrj-18	18	30	by	by	ADP
gsrj-18	18	31	the	the	DET
gsrj-18	18	32	“	"	PUNCT
gsrj-18	18	33	key	key	ADJ
gsrj-18	18	34	generator	generator	NOUN
gsrj-18	18	35	”	"	PUNCT
gsrj-18	18	36	(	(	PUNCT
gsrj-18	18	37	the	the	DET
gsrj-18	18	38	person	person	NOUN
gsrj-18	18	39	who	who	PRON
gsrj-18	18	40	creates	create	VERB
gsrj-18	18	41	the	the	DET
gsrj-18	18	42	public	public	ADJ
gsrj-18	18	43	and	and	CCONJ
gsrj-18	18	44	private	private	ADJ
gsrj-18	18	45	key	key	ADJ
gsrj-18	18	46	values	value	NOUN
gsrj-18	18	47	;	;	PUNCT
gsrj-18	18	48	the	the	DET
gsrj-18	18	49	equivalent	equivalent	NOUN
gsrj-18	18	50	of	of	ADP
gsrj-18	18	51	“	"	PUNCT
gsrj-18	18	52	alice	alice	PROPN
gsrj-18	18	53	”	"	PUNCT
gsrj-18	18	54	in	in	ADP
gsrj-18	18	55	the	the	DET
gsrj-18	18	56	latter	latter	ADJ
gsrj-18	18	57	example	example	NOUN
gsrj-18	18	58	above	above	ADP
gsrj-18	18	59	)	)	PUNCT
gsrj-18	18	60	and	and	CCONJ
gsrj-18	18	61	is	be	AUX
gsrj-18	18	62	used	use	VERB
gsrj-18	18	63	by	by	ADP
gsrj-18	18	64	the	the	DET
gsrj-18	18	65	key	key	ADJ
gsrj-18	18	66	generator	generator	NOUN
gsrj-18	18	67	to	to	PART
gsrj-18	18	68	decrypt	decrypt	VERB
gsrj-18	18	69	any	any	DET
gsrj-18	18	70	encrypted	encrypt	VERB
gsrj-18	18	71	message	message	NOUN
gsrj-18	18	72	sent	send	VERB
gsrj-18	18	73	to	to	ADP
gsrj-18	18	74	him	he	PRON
gsrj-18	18	75	or	or	CCONJ
gsrj-18	18	76	her	she	PRON
gsrj-18	18	77	.	.	PUNCT
gsrj-18	19	1	the	the	DET
gsrj-18	19	2	six	six	NUM
gsrj-18	19	3	values	value	NOUN
gsrj-18	19	4	generated	generate	VERB
gsrj-18	19	5	by	by	ADP
gsrj-18	19	6	the	the	DET
gsrj-18	19	7	key	key	ADJ
gsrj-18	19	8	generator	generator	NOUN
gsrj-18	19	9	are	be	AUX
gsrj-18	19	10	denoted	denote	VERB
gsrj-18	19	11	:	:	PUNCT
gsrj-18	20	1	p	p	X
gsrj-18	20	2	,	,	PUNCT
gsrj-18	20	3	q	q	ADJ
gsrj-18	20	4	,	,	PUNCT
gsrj-18	20	5	n	n	CCONJ
gsrj-18	20	6	,	,	PUNCT
gsrj-18	20	7	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	20	8	,	,	PUNCT
gsrj-18	20	9	e	e	NOUN
gsrj-18	20	10	,	,	PUNCT
gsrj-18	20	11	and	and	CCONJ
gsrj-18	20	12	d.	d.	PROPN
gsrj-18	20	13	p	p	PROPN
gsrj-18	20	14	,	,	PUNCT
gsrj-18	20	15	q	q	ADJ
gsrj-18	20	16	,	,	PUNCT
gsrj-18	20	17	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	20	18	,	,	PUNCT
gsrj-18	20	19	and	and	CCONJ
gsrj-18	20	20	d	d	NOUN
gsrj-18	20	21	belong	belong	VERB
gsrj-18	20	22	to	to	ADP
gsrj-18	20	23	the	the	DET
gsrj-18	20	24	private	private	ADJ
gsrj-18	20	25	key	key	NOUN
gsrj-18	20	26	and	and	CCONJ
gsrj-18	20	27	are	be	AUX
gsrj-18	20	28	kept	keep	VERB
gsrj-18	20	29	secret	secret	ADJ
gsrj-18	20	30	by	by	ADP
gsrj-18	20	31	the	the	DET
gsrj-18	20	32	key	key	ADJ
gsrj-18	20	33	generator	generator	NOUN
gsrj-18	20	34	.	.	PUNCT
gsrj-18	21	1	n	n	PROPN
gsrj-18	21	2	and	and	CCONJ
gsrj-18	21	3	e	e	PROPN
gsrj-18	21	4	belong	belong	VERB
gsrj-18	21	5	to	to	ADP
gsrj-18	21	6	the	the	DET
gsrj-18	21	7	public	public	ADJ
gsrj-18	21	8	key	key	NOUN
gsrj-18	21	9	and	and	CCONJ
gsrj-18	21	10	are	be	AUX
gsrj-18	21	11	released	release	VERB
gsrj-18	21	12	publicly	publicly	ADV
gsrj-18	21	13	.	.	PUNCT
gsrj-18	22	1	the	the	DET
gsrj-18	22	2	key	key	ADJ
gsrj-18	22	3	generator	generator	NOUN
gsrj-18	22	4	must	must	AUX
gsrj-18	22	5	generate	generate	VERB
gsrj-18	22	6	values	value	NOUN
gsrj-18	22	7	for	for	ADP
gsrj-18	22	8	p	p	NOUN
gsrj-18	22	9	,	,	PUNCT
gsrj-18	22	10	q	q	ADJ
gsrj-18	22	11	,	,	PUNCT
gsrj-18	22	12	n	n	CCONJ
gsrj-18	22	13	,	,	PUNCT
gsrj-18	22	14	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	22	15	,	,	PUNCT
gsrj-18	22	16	e	e	NOUN
gsrj-18	22	17	,	,	PUNCT
gsrj-18	22	18	and	and	CCONJ
gsrj-18	22	19	d.	d.	PROPN
gsrj-18	22	20	the	the	DET
gsrj-18	22	21	key	key	ADJ
gsrj-18	22	22	generator	generator	NOUN
gsrj-18	22	23	must	must	AUX
gsrj-18	22	24	first	first	ADV
gsrj-18	22	25	choose	choose	VERB
gsrj-18	22	26	two	two	NUM
gsrj-18	22	27	large	large	ADJ
gsrj-18	22	28	prime	prime	ADJ
gsrj-18	22	29	numbers	number	NOUN
gsrj-18	22	30	p	p	NOUN
gsrj-18	22	31	and	and	CCONJ
gsrj-18	22	32	q.	q.	PROPN
gsrj-18	22	33	in	in	ADP
gsrj-18	22	34	real	real	ADJ
gsrj-18	22	35	world	world	NOUN
gsrj-18	22	36	utilizations	utilization	NOUN
gsrj-18	22	37	of	of	ADP
gsrj-18	22	38	rsa	rsa	NOUN
gsrj-18	22	39	encryption	encryption	NOUN
gsrj-18	22	40	,	,	PUNCT
gsrj-18	22	41	these	these	DET
gsrj-18	22	42	prime	prime	ADJ
gsrj-18	22	43	numbers	number	NOUN
gsrj-18	22	44	are	be	AUX
gsrj-18	22	45	typically	typically	ADV
gsrj-18	22	46	large	large	ADJ
gsrj-18	22	47	,	,	PUNCT
gsrj-18	22	48	usually	usually	ADV
gsrj-18	22	49	hundreds	hundred	NOUN
gsrj-18	22	50	of	of	ADP
gsrj-18	22	51	digits	digit	NOUN
gsrj-18	22	52	long	long	ADV
gsrj-18	22	53	.	.	PUNCT
gsrj-18	23	1	the	the	DET
gsrj-18	23	2	key	key	ADJ
gsrj-18	23	3	generator	generator	NOUN
gsrj-18	23	4	must	must	AUX
gsrj-18	23	5	then	then	ADV
gsrj-18	23	6	multiply	multiply	VERB
gsrj-18	23	7	these	these	DET
gsrj-18	23	8	two	two	NUM
gsrj-18	23	9	prime	prime	ADJ
gsrj-18	23	10	numbers	number	NOUN
gsrj-18	23	11	together	together	ADV
gsrj-18	23	12	to	to	PART
gsrj-18	23	13	attain	attain	VERB
gsrj-18	23	14	the	the	DET
gsrj-18	23	15	value	value	NOUN
gsrj-18	23	16	of	of	ADP
gsrj-18	23	17	n	n	CCONJ
gsrj-18	23	18	,	,	PUNCT
gsrj-18	23	19	that	that	ADV
gsrj-18	23	20	is	be	AUX
gsrj-18	23	21	,	,	PUNCT
gsrj-18	23	22	p	p	X
gsrj-18	24	1	x	x	X
gsrj-18	24	2	q	q	NOUN
gsrj-18	24	3	=	=	PUNCT
gsrj-18	24	4	n.	n.	NOUN
gsrj-18	24	5	n	n	VERB
gsrj-18	24	6	is	be	AUX
gsrj-18	24	7	a	a	DET
gsrj-18	24	8	semi	semi	ADJ
gsrj-18	24	9	-	-	ADJ
gsrj-18	24	10	prime	prime	ADJ
gsrj-18	24	11	number	number	NOUN
gsrj-18	24	12	,	,	PUNCT
gsrj-18	24	13	or	or	CCONJ
gsrj-18	24	14	the	the	DET
gsrj-18	24	15	product	product	NOUN
gsrj-18	24	16	of	of	ADP
gsrj-18	24	17	two	two	NUM
gsrj-18	24	18	prime	prime	ADJ
gsrj-18	24	19	numbers	number	NOUN
gsrj-18	24	20	.	.	PUNCT
gsrj-18	25	1	next	next	ADV
gsrj-18	25	2	,	,	PUNCT
gsrj-18	25	3	the	the	DET
gsrj-18	25	4	key	key	ADJ
gsrj-18	25	5	generator	generator	NOUN
gsrj-18	25	6	calculates	calculate	VERB
gsrj-18	25	7	the	the	DET
gsrj-18	25	8	𝜑𝜑	𝜑𝜑	NOUN
gsrj-18	25	9	or	or	CCONJ
gsrj-18	25	10	“	"	PUNCT
gsrj-18	25	11	phi	phi	NOUN
gsrj-18	25	12	”	"	PUNCT
gsrj-18	25	13	of	of	ADP
gsrj-18	25	14	n.	n.	NOUN
gsrj-18	25	15	the	the	DET
gsrj-18	25	16	phi	phi	NOUN
gsrj-18	25	17	of	of	ADP
gsrj-18	25	18	a	a	DET
gsrj-18	25	19	number	number	NOUN
gsrj-18	25	20	outputs	output	NOUN
gsrj-18	25	21	how	how	SCONJ
gsrj-18	25	22	many	many	ADJ
gsrj-18	25	23	positive	positive	ADJ
gsrj-18	25	24	integers	integer	NOUN
gsrj-18	25	25	are	be	AUX
gsrj-18	25	26	less	less	ADJ
gsrj-18	25	27	than	than	ADP
gsrj-18	25	28	that	that	DET
gsrj-18	25	29	number	number	NOUN
gsrj-18	25	30	that	that	PRON
gsrj-18	25	31	do	do	AUX
gsrj-18	25	32	not	not	PART
gsrj-18	25	33	share	share	VERB
gsrj-18	25	34	any	any	DET
gsrj-18	25	35	common	common	ADJ
gsrj-18	25	36	factors	factor	NOUN
gsrj-18	25	37	greater	great	ADJ
gsrj-18	25	38	than	than	ADP
gsrj-18	25	39	one	one	NUM
gsrj-18	25	40	with	with	ADP
gsrj-18	25	41	the	the	DET
gsrj-18	25	42	number	number	NOUN
gsrj-18	25	43	.	.	PUNCT
gsrj-18	26	1	for	for	ADP
gsrj-18	26	2	example	example	NOUN
gsrj-18	26	3	,	,	PUNCT
gsrj-18	26	4	to	to	PART
gsrj-18	26	5	find	find	VERB
gsrj-18	26	6	the	the	DET
gsrj-18	26	7	phi	phi	NOUN
gsrj-18	26	8	of	of	ADP
gsrj-18	26	9	nine	nine	NUM
gsrj-18	26	10	,	,	PUNCT
gsrj-18	26	11	a	a	DET
gsrj-18	26	12	key	key	ADJ
gsrj-18	26	13	generator	generator	NOUN
gsrj-18	26	14	would	would	AUX
gsrj-18	26	15	list	list	VERB
gsrj-18	26	16	all	all	PRON
gsrj-18	26	17	of	of	ADP
gsrj-18	26	18	the	the	DET
gsrj-18	26	19	integers	integer	NOUN
gsrj-18	26	20	less	less	ADJ
gsrj-18	26	21	than	than	ADP
gsrj-18	26	22	nine	nine	NUM
gsrj-18	26	23	but	but	CCONJ
gsrj-18	26	24	greater	great	ADJ
gsrj-18	26	25	than	than	ADP
gsrj-18	26	26	or	or	CCONJ
gsrj-18	26	27	equal	equal	ADJ
gsrj-18	26	28	to	to	ADP
gsrj-18	26	29	one	one	NUM
gsrj-18	26	30	(	(	PUNCT
gsrj-18	26	31	eight	eight	NUM
gsrj-18	26	32	,	,	PUNCT
gsrj-18	26	33	seven	seven	NUM
gsrj-18	26	34	,	,	PUNCT
gsrj-18	26	35	six	six	NUM
gsrj-18	26	36	,	,	PUNCT
gsrj-18	26	37	five	five	NUM
gsrj-18	26	38	,	,	PUNCT
gsrj-18	26	39	four	four	NUM
gsrj-18	26	40	,	,	PUNCT
gsrj-18	26	41	three	three	NUM
gsrj-18	26	42	,	,	PUNCT
gsrj-18	26	43	two	two	NUM
gsrj-18	26	44	,	,	PUNCT
gsrj-18	26	45	one	one	NUM
gsrj-18	26	46	)	)	PUNCT
gsrj-18	26	47	.	.	PUNCT
gsrj-18	27	1	from	from	ADP
gsrj-18	27	2	this	this	DET
gsrj-18	27	3	list	list	NOUN
gsrj-18	27	4	,	,	PUNCT
gsrj-18	27	5	they	they	PRON
gsrj-18	27	6	would	would	AUX
gsrj-18	27	7	then	then	ADV
gsrj-18	27	8	evaluate	evaluate	VERB
gsrj-18	27	9	which	which	PRON
gsrj-18	27	10	integers	integer	NOUN
gsrj-18	27	11	share	share	VERB
gsrj-18	27	12	common	common	ADJ
gsrj-18	27	13	factors	factor	NOUN
gsrj-18	27	14	with	with	ADP
gsrj-18	27	15	nine	nine	NUM
gsrj-18	27	16	that	that	PRON
gsrj-18	27	17	are	be	AUX
gsrj-18	27	18	greater	great	ADJ
gsrj-18	27	19	than	than	ADP
gsrj-18	27	20	one	one	NUM
gsrj-18	27	21	.	.	PUNCT
gsrj-18	28	1	six	six	NUM
gsrj-18	28	2	and	and	CCONJ
gsrj-18	28	3	three	three	NUM
gsrj-18	28	4	both	both	PRON
gsrj-18	28	5	share	share	VERB
gsrj-18	28	6	common	common	ADJ
gsrj-18	28	7	factors	factor	NOUN
gsrj-18	28	8	greater	great	ADJ
gsrj-18	28	9	than	than	ADP
gsrj-18	28	10	one	one	NUM
gsrj-18	28	11	with	with	ADP
gsrj-18	28	12	nine	nine	NUM
gsrj-18	28	13	while	while	SCONJ
gsrj-18	28	14	eight	eight	NUM
gsrj-18	28	15	,	,	PUNCT
gsrj-18	28	16	seven	seven	NUM
gsrj-18	28	17	,	,	PUNCT
gsrj-18	28	18	five	five	NUM
gsrj-18	28	19	,	,	PUNCT
gsrj-18	28	20	four	four	NUM
gsrj-18	28	21	,	,	PUNCT
gsrj-18	28	22	two	two	NUM
gsrj-18	28	23	,	,	PUNCT
gsrj-18	28	24	and	and	CCONJ
gsrj-18	28	25	one	one	NUM
gsrj-18	28	26	do	do	AUX
gsrj-18	28	27	not	not	PART
gsrj-18	28	28	share	share	VERB
gsrj-18	28	29	any	any	DET
gsrj-18	28	30	common	common	ADJ
gsrj-18	28	31	factors	factor	NOUN
gsrj-18	28	32	greater	great	ADJ
gsrj-18	28	33	than	than	ADP
gsrj-18	28	34	one	one	NUM
gsrj-18	28	35	with	with	ADP
gsrj-18	28	36	nine	nine	NUM
gsrj-18	28	37	.	.	PUNCT
gsrj-18	29	1	the	the	DET
gsrj-18	29	2	phi	phi	NOUN
gsrj-18	29	3	of	of	ADP
gsrj-18	29	4	nine	nine	NUM
gsrj-18	29	5	is	be	AUX
gsrj-18	29	6	six	six	NUM
gsrj-18	29	7	because	because	SCONJ
gsrj-18	29	8	there	there	PRON
gsrj-18	29	9	are	be	VERB
gsrj-18	29	10	six	six	NUM
gsrj-18	29	11	integers	integer	NOUN
gsrj-18	29	12	less	less	ADJ
gsrj-18	29	13	than	than	ADP
gsrj-18	29	14	nine	nine	NUM
gsrj-18	29	15	that	that	PRON
gsrj-18	29	16	do	do	AUX
gsrj-18	29	17	not	not	PART
gsrj-18	29	18	share	share	VERB
gsrj-18	29	19	any	any	DET
gsrj-18	29	20	common	common	ADJ
gsrj-18	29	21	factors	factor	NOUN
gsrj-18	29	22	greater	great	ADJ
gsrj-18	29	23	than	than	ADP
gsrj-18	29	24	one	one	NUM
gsrj-18	29	25	with	with	ADP
gsrj-18	29	26	nine	nine	NUM
gsrj-18	29	27	.	.	PUNCT
gsrj-18	30	1	calculating	calculate	VERB
gsrj-18	30	2	the	the	DET
gsrj-18	30	3	phi	phi	NOUN
gsrj-18	30	4	of	of	ADP
gsrj-18	30	5	n	n	NUM
gsrj-18	30	6	is	be	AUX
gsrj-18	30	7	straightforward	straightforward	ADJ
gsrj-18	30	8	for	for	ADP
gsrj-18	30	9	the	the	DET
gsrj-18	30	10	key	key	ADJ
gsrj-18	30	11	generator	generator	NOUN
gsrj-18	30	12	due	due	ADP
gsrj-18	30	13	to	to	ADP
gsrj-18	30	14	the	the	DET
gsrj-18	30	15	fact	fact	NOUN
gsrj-18	30	16	that	that	SCONJ
gsrj-18	30	17	the	the	DET
gsrj-18	30	18	phi	phi	NOUN
gsrj-18	30	19	function	function	NOUN
gsrj-18	30	20	is	be	AUX
gsrj-18	30	21	multiplicative	multiplicative	ADJ
gsrj-18	30	22	,	,	PUNCT
gsrj-18	30	23	meaning	mean	VERB
gsrj-18	30	24	that	that	SCONJ
gsrj-18	30	25	:	:	PUNCT
gsrj-18	30	26	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	30	27	=	=	SYM
gsrj-18	30	28	𝜑𝜑p	𝜑𝜑p	PROPN
gsrj-18	30	29	x	x	X
gsrj-18	30	30	𝜑𝜑q	𝜑𝜑q	NOUN
gsrj-18	30	31	(	(	PUNCT
gsrj-18	30	32	equation	equation	NOUN
gsrj-18	30	33	1	1	NUM
gsrj-18	30	34	)	)	PUNCT
gsrj-18	30	35	or	or	CCONJ
gsrj-18	30	36	the	the	DET
gsrj-18	30	37	phi	phi	NOUN
gsrj-18	30	38	of	of	ADP
gsrj-18	30	39	n	n	PRON
gsrj-18	30	40	is	be	AUX
gsrj-18	30	41	equivalent	equivalent	ADJ
gsrj-18	30	42	to	to	ADP
gsrj-18	30	43	the	the	DET
gsrj-18	30	44	phi	phi	NOUN
gsrj-18	30	45	of	of	SCONJ
gsrj-18	30	46	each	each	PRON
gsrj-18	30	47	of	of	ADP
gsrj-18	30	48	n	n	CCONJ
gsrj-18	30	49	’s	’s	PART
gsrj-18	30	50	factors	factor	NOUN
gsrj-18	30	51	multiplied	multiply	VERB
gsrj-18	30	52	together	together	ADV
gsrj-18	30	53	.	.	PUNCT
gsrj-18	31	1	this	this	DET
gsrj-18	31	2	property	property	NOUN
gsrj-18	31	3	can	can	AUX
gsrj-18	31	4	be	be	AUX
gsrj-18	31	5	proved	prove	VERB
gsrj-18	31	6	using	use	VERB
gsrj-18	31	7	the	the	DET
gsrj-18	31	8	chinese	chinese	ADJ
gsrj-18	31	9	remainder	remainder	NOUN
gsrj-18	31	10	theorem	theorem	NOUN
gsrj-18	31	11	but	but	CCONJ
gsrj-18	31	12	such	such	DET
gsrj-18	31	13	a	a	DET
gsrj-18	31	14	proof	proof	NOUN
gsrj-18	31	15	is	be	AUX
gsrj-18	31	16	omitted	omit	VERB
gsrj-18	31	17	in	in	ADP
gsrj-18	31	18	this	this	DET
gsrj-18	31	19	paper.7	paper.7	PROPN
gsrj-18	31	20	thus	thus	ADV
gsrj-18	31	21	,	,	PUNCT
gsrj-18	31	22	the	the	DET
gsrj-18	31	23	key	key	ADJ
gsrj-18	31	24	generator	generator	NOUN
gsrj-18	31	25	can	can	AUX
gsrj-18	31	26	calculate	calculate	VERB
gsrj-18	31	27	the	the	DET
gsrj-18	31	28	phi	phi	NOUN
gsrj-18	31	29	of	of	ADP
gsrj-18	31	30	p	p	NOUN
gsrj-18	31	31	and	and	CCONJ
gsrj-18	31	32	the	the	DET
gsrj-18	31	33	phi	phi	NOUN
gsrj-18	31	34	of	of	ADP
gsrj-18	31	35	q	q	NOUN
gsrj-18	31	36	and	and	CCONJ
gsrj-18	31	37	multiply	multiply	VERB
gsrj-18	31	38	these	these	DET
gsrj-18	31	39	two	two	NUM
gsrj-18	31	40	values	value	NOUN
gsrj-18	31	41	together	together	ADV
gsrj-18	31	42	to	to	PART
gsrj-18	31	43	attain	attain	VERB
gsrj-18	31	44	the	the	DET
gsrj-18	31	45	phi	phi	NOUN
gsrj-18	31	46	of	of	ADP
gsrj-18	31	47	n.	n.	VERB
gsrj-18	31	48	the	the	DET
gsrj-18	31	49	phi	phi	NOUN
gsrj-18	31	50	of	of	ADP
gsrj-18	31	51	any	any	DET
gsrj-18	31	52	prime	prime	ADJ
gsrj-18	31	53	number	number	NOUN
gsrj-18	31	54	is	be	AUX
gsrj-18	31	55	simply	simply	ADV
gsrj-18	31	56	one	one	NUM
gsrj-18	31	57	less	less	ADJ
gsrj-18	31	58	than	than	ADP
gsrj-18	31	59	the	the	DET
gsrj-18	31	60	original	original	ADJ
gsrj-18	31	61	prime	prime	ADJ
gsrj-18	31	62	number	number	NOUN
gsrj-18	31	63	because	because	SCONJ
gsrj-18	31	64	the	the	DET
gsrj-18	31	65	only	only	ADJ
gsrj-18	31	66	factors	factor	NOUN
gsrj-18	31	67	that	that	SCONJ
gsrj-18	31	68	prime	prime	ADJ
gsrj-18	31	69	numbers	number	NOUN
gsrj-18	31	70	have	have	AUX
gsrj-18	31	71	are	be	AUX
gsrj-18	31	72	one	one	NUM
gsrj-18	31	73	and	and	CCONJ
gsrj-18	31	74	itself.8	itself.8	INTJ
gsrj-18	31	75	for	for	ADP
gsrj-18	31	76	example	example	NOUN
gsrj-18	31	77	,	,	PUNCT
gsrj-18	31	78	the	the	DET
gsrj-18	31	79	phi	phi	NOUN
gsrj-18	31	80	of	of	ADP
gsrj-18	31	81	five	five	NUM
gsrj-18	31	82	(	(	PUNCT
gsrj-18	31	83	a	a	DET
gsrj-18	31	84	prime	prime	ADJ
gsrj-18	31	85	number	number	NOUN
gsrj-18	31	86	)	)	PUNCT
gsrj-18	31	87	is	be	AUX
gsrj-18	31	88	four	four	NUM
gsrj-18	31	89	because	because	SCONJ
gsrj-18	31	90	there	there	PRON
gsrj-18	31	91	are	be	VERB
gsrj-18	31	92	four	four	NUM
gsrj-18	31	93	positive	positive	ADJ
gsrj-18	31	94	integers	integer	NOUN
gsrj-18	31	95	less	less	ADJ
gsrj-18	31	96	than	than	ADP
gsrj-18	31	97	five	five	NUM
gsrj-18	31	98	that	that	PRON
gsrj-18	31	99	do	do	AUX
gsrj-18	31	100	not	not	PART
gsrj-18	31	101	share	share	VERB
gsrj-18	31	102	any	any	DET
gsrj-18	31	103	common	common	ADJ
gsrj-18	31	104	factors	factor	NOUN
gsrj-18	31	105	greater	great	ADJ
gsrj-18	31	106	than	than	ADP
gsrj-18	31	107	one	one	NUM
gsrj-18	31	108	with	with	ADP
gsrj-18	31	109	five	five	NUM
gsrj-18	31	110	.	.	PUNCT
gsrj-18	32	1	thus	thus	ADV
gsrj-18	32	2	,	,	PUNCT
gsrj-18	32	3	the	the	DET
gsrj-18	32	4	phi	phi	NOUN
gsrj-18	32	5	of	of	ADP
gsrj-18	32	6	the	the	DET
gsrj-18	32	7	prime	prime	ADJ
gsrj-18	32	8	number	number	NOUN
gsrj-18	32	9	p	p	NOUN
gsrj-18	32	10	is	be	AUX
gsrj-18	32	11	(	(	PUNCT
gsrj-18	32	12	p	p	X
gsrj-18	32	13	–	–	PUNCT
gsrj-18	32	14	1	1	NUM
gsrj-18	32	15	)	)	PUNCT
gsrj-18	32	16	and	and	CCONJ
gsrj-18	32	17	the	the	DET
gsrj-18	32	18	phi	phi	NOUN
gsrj-18	32	19	of	of	ADP
gsrj-18	32	20	the	the	DET
gsrj-18	32	21	prime	prime	ADJ
gsrj-18	32	22	number	number	NOUN
gsrj-18	32	23	q	q	PUNCT
gsrj-18	32	24	is	be	AUX
gsrj-18	32	25	(	(	PUNCT
gsrj-18	32	26	q	q	NOUN
gsrj-18	32	27	–	–	PUNCT
gsrj-18	32	28	1	1	NUM
gsrj-18	32	29	)	)	PUNCT
gsrj-18	32	30	.	.	PUNCT
gsrj-18	33	1	thus	thus	ADV
gsrj-18	33	2	,	,	PUNCT
gsrj-18	33	3	the	the	DET
gsrj-18	33	4	phi	phi	NOUN
gsrj-18	33	5	of	of	ADP
gsrj-18	33	6	the	the	DET
gsrj-18	33	7	semi	semi	ADJ
gsrj-18	33	8	-	-	ADJ
gsrj-18	33	9	prime	prime	ADJ
gsrj-18	33	10	n	n	NOUN
gsrj-18	33	11	is	be	AUX
gsrj-18	33	12	(	(	PUNCT
gsrj-18	33	13	p	p	X
gsrj-18	33	14	–	–	PUNCT
gsrj-18	33	15	1)*(q	1)*(q	NUM
gsrj-18	33	16	–	–	PUNCT
gsrj-18	33	17	1	1	NUM
gsrj-18	33	18	)	)	PUNCT
gsrj-18	33	19	.	.	PUNCT
gsrj-18	34	1	to	to	PART
gsrj-18	34	2	generate	generate	VERB
gsrj-18	34	3	e	e	NOUN
gsrj-18	34	4	,	,	PUNCT
gsrj-18	34	5	the	the	DET
gsrj-18	34	6	key	key	ADJ
gsrj-18	34	7	generator	generator	NOUN
gsrj-18	34	8	must	must	AUX
gsrj-18	34	9	pick	pick	VERB
gsrj-18	34	10	an	an	DET
gsrj-18	34	11	integer	integer	NOUN
gsrj-18	34	12	that	that	PRON
gsrj-18	34	13	satisfies	satisfy	VERB
gsrj-18	34	14	the	the	DET
gsrj-18	34	15	requirement	requirement	NOUN
gsrj-18	34	16	:	:	PUNCT
gsrj-18	34	17	1	1	NUM
gsrj-18	34	18	<	<	X
gsrj-18	34	19	e	e	X
gsrj-18	34	20	<	<	X
gsrj-18	34	21	𝜑𝜑n	𝜑𝜑n	PROPN
gsrj-18	34	22	;	;	PUNCT
gsrj-18	34	23	e	e	NOUN
gsrj-18	34	24	shares	share	VERB
gsrj-18	34	25	no	no	DET
gsrj-18	34	26	common	common	ADJ
gsrj-18	34	27	factors	factor	NOUN
gsrj-18	34	28	with	with	ADP
gsrj-18	34	29	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	34	30	.	.	PUNCT
gsrj-18	35	1	finally	finally	ADV
gsrj-18	35	2	,	,	PUNCT
gsrj-18	35	3	to	to	PART
gsrj-18	35	4	generate	generate	VERB
gsrj-18	35	5	d	d	PROPN
gsrj-18	35	6	,	,	PUNCT
gsrj-18	35	7	the	the	DET
gsrj-18	35	8	key	key	ADJ
gsrj-18	35	9	generator	generator	NOUN
gsrj-18	35	10	must	must	AUX
gsrj-18	35	11	pick	pick	VERB
gsrj-18	35	12	an	an	DET
gsrj-18	35	13	integer	integer	NOUN
gsrj-18	35	14	that	that	PRON
gsrj-18	35	15	satisfies	satisfy	VERB
gsrj-18	35	16	the	the	DET
gsrj-18	35	17	requirement	requirement	NOUN
gsrj-18	35	18	:	:	PUNCT
gsrj-18	35	19	(	(	PUNCT
gsrj-18	35	20	e*d	e*d	PROPN
gsrj-18	35	21	)	)	PUNCT
gsrj-18	35	22	mod	mod	PROPN
gsrj-18	35	23	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	35	24	=	=	SYM
gsrj-18	35	25	1	1	X
gsrj-18	35	26	(	(	PUNCT
gsrj-18	35	27	equation	equation	NOUN
gsrj-18	35	28	2	2	NUM
gsrj-18	35	29	)	)	PUNCT
gsrj-18	35	30	the	the	DET
gsrj-18	35	31	operation	operation	NOUN
gsrj-18	35	32	“	"	PUNCT
gsrj-18	35	33	mod	mod	ADJ
gsrj-18	35	34	”	"	PUNCT
gsrj-18	35	35	outputs	output	NOUN
gsrj-18	35	36	the	the	DET
gsrj-18	35	37	remainder	remainder	NOUN
gsrj-18	35	38	of	of	ADP
gsrj-18	35	39	a	a	DET
gsrj-18	35	40	division	division	NOUN
gsrj-18	35	41	.	.	PUNCT
gsrj-18	36	1	for	for	ADP
gsrj-18	36	2	example	example	NOUN
gsrj-18	36	3	,	,	PUNCT
gsrj-18	36	4	8	8	NUM
gsrj-18	36	5	mod	mod	NOUN
gsrj-18	36	6	6	6	NUM
gsrj-18	36	7	=	=	SYM
gsrj-18	36	8	2	2	NUM
gsrj-18	36	9	because	because	SCONJ
gsrj-18	36	10	the	the	DET
gsrj-18	36	11	remainder	remainder	NOUN
gsrj-18	36	12	of	of	ADP
gsrj-18	36	13	the	the	DET
gsrj-18	36	14	division	division	NOUN
gsrj-18	36	15	eight	eight	NUM
gsrj-18	36	16	divided	divide	VERB
gsrj-18	36	17	by	by	ADP
gsrj-18	36	18	six	six	NUM
gsrj-18	36	19	is	be	AUX
gsrj-18	36	20	two	two	NUM
gsrj-18	36	21	.	.	PUNCT
gsrj-18	37	1	once	once	ADV
gsrj-18	37	2	the	the	DET
gsrj-18	37	3	key	key	ADJ
gsrj-18	37	4	generator	generator	NOUN
gsrj-18	37	5	has	have	AUX
gsrj-18	37	6	generated	generate	VERB
gsrj-18	37	7	values	value	NOUN
gsrj-18	37	8	for	for	ADP
gsrj-18	37	9	p	p	NOUN
gsrj-18	37	10	,	,	PUNCT
gsrj-18	37	11	q	q	ADJ
gsrj-18	37	12	,	,	PUNCT
gsrj-18	37	13	n	n	CCONJ
gsrj-18	37	14	,	,	PUNCT
gsrj-18	37	15	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	37	16	,	,	PUNCT
gsrj-18	37	17	e	e	NOUN
gsrj-18	37	18	,	,	PUNCT
gsrj-18	37	19	and	and	CCONJ
gsrj-18	37	20	d	d	X
gsrj-18	37	21	,	,	PUNCT
gsrj-18	37	22	they	they	PRON
gsrj-18	37	23	must	must	AUX
gsrj-18	37	24	release	release	VERB
gsrj-18	37	25	the	the	DET
gsrj-18	37	26	values	value	NOUN
gsrj-18	37	27	of	of	ADP
gsrj-18	37	28	n	n	NOUN
gsrj-18	37	29	and	and	CCONJ
gsrj-18	37	30	e	e	PROPN
gsrj-18	37	31	(	(	PUNCT
gsrj-18	37	32	the	the	DET
gsrj-18	37	33	public	public	ADJ
gsrj-18	37	34	key	key	ADJ
gsrj-18	37	35	values	value	NOUN
gsrj-18	37	36	)	)	PUNCT
gsrj-18	37	37	to	to	ADP
gsrj-18	37	38	the	the	DET
gsrj-18	37	39	8	8	NUM
gsrj-18	37	40	georgetown	georgetown	PROPN
gsrj-18	37	41	scientific	scientific	PROPN
gsrj-18	37	42	research	research	NOUN
gsrj-18	37	43	journal	journal	NOUN
gsrj-18	37	44	public	public	ADJ
gsrj-18	37	45	but	but	CCONJ
gsrj-18	37	46	retain	retain	VERB
gsrj-18	37	47	the	the	DET
gsrj-18	37	48	values	value	NOUN
gsrj-18	37	49	of	of	ADP
gsrj-18	37	50	p	p	X
gsrj-18	37	51	,	,	PUNCT
gsrj-18	37	52	q	q	ADJ
gsrj-18	37	53	,	,	PUNCT
gsrj-18	37	54	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	37	55	,	,	PUNCT
gsrj-18	37	56	and	and	CCONJ
gsrj-18	37	57	d	d	X
gsrj-18	37	58	(	(	PUNCT
gsrj-18	37	59	the	the	DET
gsrj-18	37	60	private	private	ADJ
gsrj-18	37	61	key	key	ADJ
gsrj-18	37	62	values	value	NOUN
gsrj-18	37	63	)	)	PUNCT
gsrj-18	37	64	.	.	PUNCT
gsrj-18	38	1	if	if	SCONJ
gsrj-18	38	2	a	a	DET
gsrj-18	38	3	person	person	NOUN
gsrj-18	38	4	(	(	PUNCT
gsrj-18	38	5	the	the	DET
gsrj-18	38	6	“	"	PUNCT
gsrj-18	38	7	sender	sender	NOUN
gsrj-18	38	8	”	"	PUNCT
gsrj-18	38	9	;	;	PUNCT
gsrj-18	38	10	the	the	DET
gsrj-18	38	11	equivalent	equivalent	NOUN
gsrj-18	38	12	of	of	ADP
gsrj-18	38	13	“	"	PUNCT
gsrj-18	38	14	bob	bob	PROPN
gsrj-18	38	15	”	"	PUNCT
gsrj-18	38	16	in	in	ADP
gsrj-18	38	17	the	the	DET
gsrj-18	38	18	latter	latter	ADJ
gsrj-18	38	19	example	example	NOUN
gsrj-18	38	20	above	above	ADP
gsrj-18	38	21	)	)	PUNCT
gsrj-18	38	22	wishes	wish	VERB
gsrj-18	38	23	to	to	PART
gsrj-18	38	24	send	send	VERB
gsrj-18	38	25	a	a	DET
gsrj-18	38	26	secret	secret	ADJ
gsrj-18	38	27	message	message	NOUN
gsrj-18	38	28	to	to	ADP
gsrj-18	38	29	the	the	DET
gsrj-18	38	30	key	key	ADJ
gsrj-18	38	31	generator	generator	NOUN
gsrj-18	38	32	,	,	PUNCT
gsrj-18	38	33	they	they	PRON
gsrj-18	38	34	can	can	AUX
gsrj-18	38	35	use	use	VERB
gsrj-18	38	36	the	the	DET
gsrj-18	38	37	values	value	NOUN
gsrj-18	38	38	of	of	ADP
gsrj-18	38	39	n	n	NOUN
gsrj-18	38	40	and	and	CCONJ
gsrj-18	38	41	e	e	NOUN
gsrj-18	38	42	to	to	PART
gsrj-18	38	43	encrypt	encrypt	VERB
gsrj-18	38	44	their	their	PRON
gsrj-18	38	45	message	message	NOUN
gsrj-18	38	46	using	use	VERB
gsrj-18	38	47	the	the	DET
gsrj-18	38	48	expression	expression	NOUN
gsrj-18	38	49	:	:	PUNCT
gsrj-18	38	50	!	!	PUNCT
gsrj-18	39	1	mod	mod	PROPN
gsrj-18	40	1	n	n	CCONJ
gsrj-18	40	2	,	,	PUNCT
gsrj-18	40	3	where	where	SCONJ
gsrj-18	40	4	m	m	NOUN
gsrj-18	40	5	is	be	AUX
gsrj-18	40	6	the	the	DET
gsrj-18	40	7	secret	secret	ADJ
gsrj-18	40	8	message	message	NOUN
gsrj-18	40	9	to	to	PART
gsrj-18	40	10	be	be	AUX
gsrj-18	40	11	encrypted	encrypt	VERB
gsrj-18	40	12	.	.	PUNCT
gsrj-18	41	1	the	the	DET
gsrj-18	41	2	sender	sender	NOUN
gsrj-18	41	3	would	would	AUX
gsrj-18	41	4	then	then	ADV
gsrj-18	41	5	send	send	VERB
gsrj-18	41	6	this	this	DET
gsrj-18	41	7	encrypted	encrypt	VERB
gsrj-18	41	8	message	message	NOUN
gsrj-18	41	9	!	!	PUNCT
gsrj-18	42	1	mod	mod	PROPN
gsrj-18	43	1	n	n	CCONJ
gsrj-18	43	2	(	(	PUNCT
gsrj-18	43	3	the	the	DET
gsrj-18	43	4	result	result	NOUN
gsrj-18	43	5	of	of	ADP
gsrj-18	43	6	which	which	PRON
gsrj-18	43	7	is	be	AUX
gsrj-18	43	8	known	know	VERB
gsrj-18	43	9	as	as	ADP
gsrj-18	43	10	“	"	PUNCT
gsrj-18	43	11	c	c	NOUN
gsrj-18	43	12	”	"	PUNCT
gsrj-18	43	13	,	,	PUNCT
gsrj-18	43	14	for	for	ADP
gsrj-18	43	15	ciphertext	ciphertext	NOUN
gsrj-18	43	16	message	message	NOUN
gsrj-18	43	17	)	)	PUNCT
gsrj-18	43	18	to	to	ADP
gsrj-18	43	19	the	the	DET
gsrj-18	43	20	key	key	ADJ
gsrj-18	43	21	generator	generator	NOUN
gsrj-18	43	22	.	.	PUNCT
gsrj-18	44	1	the	the	DET
gsrj-18	44	2	key	key	ADJ
gsrj-18	44	3	generator	generator	NOUN
gsrj-18	44	4	can	can	AUX
gsrj-18	44	5	then	then	ADV
gsrj-18	44	6	decrypt	decrypt	VERB
gsrj-18	44	7	the	the	DET
gsrj-18	44	8	encrypted	encrypt	VERB
gsrj-18	44	9	message	message	NOUN
gsrj-18	44	10	c	c	NOUN
gsrj-18	44	11	by	by	ADP
gsrj-18	44	12	using	use	VERB
gsrj-18	44	13	the	the	DET
gsrj-18	44	14	private	private	ADJ
gsrj-18	44	15	key	key	ADJ
gsrj-18	44	16	value	value	NOUN
gsrj-18	44	17	of	of	ADP
gsrj-18	44	18	d	d	PROPN
gsrj-18	44	19	through	through	ADP
gsrj-18	44	20	the	the	DET
gsrj-18	44	21	expression	expression	NOUN
gsrj-18	44	22	:	:	PUNCT
gsrj-18	44	23	"	"	PUNCT
gsrj-18	44	24	mod	mod	PROPN
gsrj-18	44	25	n.	n.	NOUN
gsrj-18	44	26	the	the	DET
gsrj-18	44	27	result	result	NOUN
gsrj-18	44	28	of	of	ADP
gsrj-18	44	29	"	"	PUNCT
gsrj-18	44	30	mod	mod	PROPN
gsrj-18	44	31	n	n	PROPN
gsrj-18	44	32	yields	yield	VERB
gsrj-18	44	33	the	the	DET
gsrj-18	44	34	original	original	ADJ
gsrj-18	44	35	message	message	NOUN
gsrj-18	44	36	m.	m.	NOUN
gsrj-18	44	37	thus	thus	ADV
gsrj-18	44	38	,	,	PUNCT
gsrj-18	44	39	in	in	ADP
gsrj-18	44	40	summary	summary	NOUN
gsrj-18	44	41	:	:	PUNCT
gsrj-18	44	42	!	!	PUNCT
gsrj-18	45	1	mod	mod	PROPN
gsrj-18	46	1	n	n	PROPN
gsrj-18	46	2	=	=	SYM
gsrj-18	46	3	c	c	PROPN
gsrj-18	46	4	(	(	PUNCT
gsrj-18	46	5	equation	equation	NOUN
gsrj-18	46	6	3	3	NUM
gsrj-18	46	7	)	)	PUNCT
gsrj-18	46	8	and	and	CCONJ
gsrj-18	46	9	"	"	PUNCT
gsrj-18	46	10	mod	mod	PROPN
gsrj-18	46	11	n	n	PROPN
gsrj-18	46	12	=	=	SYM
gsrj-18	46	13	m	m	PROPN
gsrj-18	46	14	(	(	PUNCT
gsrj-18	46	15	equation	equation	NOUN
gsrj-18	46	16	4	4	NUM
gsrj-18	46	17	)	)	PUNCT
gsrj-18	46	18	with	with	ADP
gsrj-18	46	19	proof	proof	NOUN
gsrj-18	46	20	of	of	ADP
gsrj-18	46	21	correctness	correctness	NOUN
gsrj-18	46	22	derived	derive	VERB
gsrj-18	46	23	by	by	ADP
gsrj-18	46	24	rivest	riv	ADJ
gsrj-18	46	25	,	,	PUNCT
gsrj-18	46	26	shamir	shamir	ADJ
gsrj-18	46	27	,	,	PUNCT
gsrj-18	46	28	and	and	CCONJ
gsrj-18	46	29	adleman	adleman	NOUN
gsrj-18	46	30	using	use	VERB
gsrj-18	46	31	fermat	fermat	PROPN
gsrj-18	46	32	’s	’s	PART
gsrj-18	46	33	little	little	ADJ
gsrj-18	46	34	theorem	theorem	NOUN
gsrj-18	46	35	in	in	ADP
gsrj-18	46	36	their	their	PRON
gsrj-18	46	37	publication	publication	NOUN
gsrj-18	46	38	.	.	PUNCT
gsrj-18	47	1	as	as	SCONJ
gsrj-18	47	2	can	can	AUX
gsrj-18	47	3	be	be	AUX
gsrj-18	47	4	seen	see	VERB
gsrj-18	47	5	,	,	PUNCT
gsrj-18	47	6	rsa	rsa	NOUN
gsrj-18	47	7	encryption	encryption	NOUN
gsrj-18	47	8	functions	function	NOUN
gsrj-18	47	9	similarly	similarly	ADV
gsrj-18	47	10	to	to	ADP
gsrj-18	47	11	the	the	DET
gsrj-18	47	12	simplified	simplified	ADJ
gsrj-18	47	13	example	example	NOUN
gsrj-18	47	14	of	of	ADP
gsrj-18	47	15	asymmetric	asymmetric	ADJ
gsrj-18	47	16	encryption	encryption	NOUN
gsrj-18	47	17	given	give	VERB
gsrj-18	47	18	earlier	early	ADV
gsrj-18	47	19	(	(	PUNCT
gsrj-18	47	20	introduction	introduction	NOUN
gsrj-18	47	21	,	,	PUNCT
gsrj-18	47	22	paragraph	paragraph	NOUN
gsrj-18	47	23	two	two	NUM
gsrj-18	47	24	)	)	PUNCT
gsrj-18	47	25	.	.	PUNCT
gsrj-18	48	1	alice	alice	PROPN
gsrj-18	48	2	,	,	PUNCT
gsrj-18	48	3	the	the	DET
gsrj-18	48	4	key	key	ADJ
gsrj-18	48	5	generator	generator	NOUN
gsrj-18	48	6	,	,	PUNCT
gsrj-18	48	7	creates	create	VERB
gsrj-18	48	8	a	a	DET
gsrj-18	48	9	public	public	ADJ
gsrj-18	48	10	and	and	CCONJ
gsrj-18	48	11	private	private	ADJ
gsrj-18	48	12	key	key	NOUN
gsrj-18	48	13	containing	contain	VERB
gsrj-18	48	14	the	the	DET
gsrj-18	48	15	values	value	NOUN
gsrj-18	48	16	of	of	ADP
gsrj-18	48	17	p	p	X
gsrj-18	48	18	,	,	PUNCT
gsrj-18	48	19	q	q	ADJ
gsrj-18	48	20	,	,	PUNCT
gsrj-18	48	21	n	n	CCONJ
gsrj-18	48	22	,	,	PUNCT
gsrj-18	48	23	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	48	24	,	,	PUNCT
gsrj-18	48	25	e	e	NOUN
gsrj-18	48	26	,	,	PUNCT
gsrj-18	48	27	and	and	CCONJ
gsrj-18	48	28	d.	d.	PROPN
gsrj-18	48	29	n	n	PROPN
gsrj-18	48	30	and	and	CCONJ
gsrj-18	48	31	e	e	NOUN
gsrj-18	48	32	function	function	NOUN
gsrj-18	48	33	as	as	ADP
gsrj-18	48	34	the	the	DET
gsrj-18	48	35	values	value	NOUN
gsrj-18	48	36	that	that	PRON
gsrj-18	48	37	bob	bob	PROPN
gsrj-18	48	38	uses	use	VERB
gsrj-18	48	39	to	to	PART
gsrj-18	48	40	lock	lock	VERB
gsrj-18	48	41	the	the	DET
gsrj-18	48	42	open	open	ADJ
gsrj-18	48	43	lock	lock	NOUN
gsrj-18	48	44	that	that	PRON
gsrj-18	48	45	alice	alice	PROPN
gsrj-18	48	46	created	create	VERB
gsrj-18	48	47	and	and	CCONJ
gsrj-18	48	48	sent	send	VERB
gsrj-18	48	49	to	to	ADP
gsrj-18	48	50	him	he	PRON
gsrj-18	48	51	,	,	PUNCT
gsrj-18	48	52	while	while	SCONJ
gsrj-18	48	53	the	the	DET
gsrj-18	48	54	values	value	NOUN
gsrj-18	48	55	of	of	ADP
gsrj-18	48	56	p	p	X
gsrj-18	48	57	,	,	PUNCT
gsrj-18	48	58	q	q	ADJ
gsrj-18	48	59	,	,	PUNCT
gsrj-18	48	60	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	48	61	,	,	PUNCT
gsrj-18	48	62	and	and	CCONJ
gsrj-18	48	63	d	d	ADP
gsrj-18	48	64	function	function	NOUN
gsrj-18	48	65	as	as	ADP
gsrj-18	48	66	the	the	DET
gsrj-18	48	67	key	key	NOUN
gsrj-18	48	68	that	that	PRON
gsrj-18	48	69	opens	open	VERB
gsrj-18	48	70	the	the	DET
gsrj-18	48	71	lock	lock	NOUN
gsrj-18	48	72	once	once	SCONJ
gsrj-18	48	73	bob	bob	PROPN
gsrj-18	48	74	locks	lock	VERB
gsrj-18	48	75	it	it	PRON
gsrj-18	48	76	with	with	ADP
gsrj-18	48	77	his	his	PRON
gsrj-18	48	78	message	message	NOUN
gsrj-18	48	79	and	and	CCONJ
gsrj-18	48	80	sends	send	VERB
gsrj-18	48	81	it	it	PRON
gsrj-18	48	82	to	to	ADP
gsrj-18	48	83	alice	alice	PROPN
gsrj-18	48	84	.	.	PUNCT
gsrj-18	49	1	although	although	SCONJ
gsrj-18	49	2	publicly	publicly	ADV
gsrj-18	49	3	releasing	release	VERB
gsrj-18	49	4	the	the	DET
gsrj-18	49	5	values	value	NOUN
gsrj-18	49	6	of	of	ADP
gsrj-18	49	7	n	n	NOUN
gsrj-18	49	8	and	and	CCONJ
gsrj-18	49	9	e	e	NOUN
gsrj-18	49	10	does	do	AUX
gsrj-18	49	11	not	not	PART
gsrj-18	49	12	detract	detract	VERB
gsrj-18	49	13	from	from	ADP
gsrj-18	49	14	the	the	DET
gsrj-18	49	15	strength	strength	NOUN
gsrj-18	49	16	of	of	ADP
gsrj-18	49	17	asymmetric	asymmetric	ADJ
gsrj-18	49	18	rsa	rsa	PROPN
gsrj-18	49	19	encryption	encryption	NOUN
gsrj-18	49	20	,	,	PUNCT
gsrj-18	49	21	it	it	PRON
gsrj-18	49	22	is	be	AUX
gsrj-18	49	23	integral	integral	ADJ
gsrj-18	49	24	that	that	SCONJ
gsrj-18	49	25	the	the	DET
gsrj-18	49	26	values	value	NOUN
gsrj-18	49	27	of	of	ADP
gsrj-18	49	28	p	p	X
gsrj-18	49	29	,	,	PUNCT
gsrj-18	49	30	q	q	ADJ
gsrj-18	49	31	,	,	PUNCT
gsrj-18	49	32	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	49	33	,	,	PUNCT
gsrj-18	49	34	and	and	CCONJ
gsrj-18	49	35	d	d	AUX
gsrj-18	49	36	remain	remain	VERB
gsrj-18	49	37	hidden	hidden	ADJ
gsrj-18	49	38	and	and	CCONJ
gsrj-18	49	39	can	can	AUX
gsrj-18	49	40	only	only	ADV
gsrj-18	49	41	be	be	AUX
gsrj-18	49	42	accessed	access	VERB
gsrj-18	49	43	by	by	ADP
gsrj-18	49	44	the	the	DET
gsrj-18	49	45	key	key	ADJ
gsrj-18	49	46	generator	generator	NOUN
gsrj-18	49	47	:	:	PUNCT
gsrj-18	49	48	this	this	PRON
gsrj-18	49	49	is	be	AUX
gsrj-18	49	50	because	because	SCONJ
gsrj-18	49	51	rsa	rsa	NOUN
gsrj-18	49	52	encryption	encryption	NOUN
gsrj-18	49	53	was	be	AUX
gsrj-18	49	54	built	build	VERB
gsrj-18	49	55	around	around	ADP
gsrj-18	49	56	two	two	NUM
gsrj-18	49	57	main	main	ADJ
gsrj-18	49	58	assumptions	assumption	NOUN
gsrj-18	49	59	that	that	PRON
gsrj-18	49	60	make	make	VERB
gsrj-18	49	61	it	it	PRON
gsrj-18	49	62	safe	safe	ADJ
gsrj-18	49	63	and	and	CCONJ
gsrj-18	49	64	acceptable	acceptable	ADJ
gsrj-18	49	65	to	to	PART
gsrj-18	49	66	release	release	VERB
gsrj-18	49	67	the	the	DET
gsrj-18	49	68	values	value	NOUN
gsrj-18	49	69	of	of	ADP
gsrj-18	49	70	n	n	NOUN
gsrj-18	49	71	and	and	CCONJ
gsrj-18	49	72	e	e	NOUN
gsrj-18	49	73	publicly	publicly	ADV
gsrj-18	49	74	.	.	PUNCT
gsrj-18	50	1	first	first	ADV
gsrj-18	50	2	,	,	PUNCT
gsrj-18	50	3	it	it	PRON
gsrj-18	50	4	is	be	AUX
gsrj-18	50	5	exceedingly	exceedingly	ADV
gsrj-18	50	6	time	time	NOUN
gsrj-18	50	7	-	-	PUNCT
gsrj-18	50	8	consuming	consume	VERB
gsrj-18	50	9	to	to	PART
gsrj-18	50	10	calculate	calculate	VERB
gsrj-18	50	11	the	the	DET
gsrj-18	50	12	decryption	decryption	NOUN
gsrj-18	50	13	key	key	NOUN
gsrj-18	50	14	(	(	PUNCT
gsrj-18	50	15	d	d	NOUN
gsrj-18	50	16	)	)	PUNCT
gsrj-18	50	17	by	by	ADP
gsrj-18	50	18	factoring	factor	VERB
gsrj-18	50	19	large	large	ADJ
gsrj-18	50	20	semi	semi	ADJ
gsrj-18	50	21	-	-	ADJ
gsrj-18	50	22	prime	prime	ADJ
gsrj-18	50	23	numbers	number	NOUN
gsrj-18	50	24	.	.	PUNCT
gsrj-18	51	1	second	second	ADJ
gsrj-18	51	2	,	,	PUNCT
gsrj-18	51	3	it	it	PRON
gsrj-18	51	4	is	be	AUX
gsrj-18	51	5	exceedingly	exceedingly	ADV
gsrj-18	51	6	timeconsuming	timeconsuming	ADJ
gsrj-18	51	7	to	to	PART
gsrj-18	51	8	calculate	calculate	VERB
gsrj-18	51	9	the	the	DET
gsrj-18	51	10	decryption	decryption	NOUN
gsrj-18	51	11	key	key	NOUN
gsrj-18	51	12	(	(	PUNCT
gsrj-18	51	13	d	d	NOUN
gsrj-18	51	14	)	)	PUNCT
gsrj-18	51	15	using	use	VERB
gsrj-18	51	16	properties	property	NOUN
gsrj-18	51	17	of	of	ADP
gsrj-18	51	18	logarithms	logarithm	NOUN
gsrj-18	51	19	because	because	SCONJ
gsrj-18	51	20	of	of	ADP
gsrj-18	51	21	the	the	DET
gsrj-18	51	22	discrete	discrete	ADJ
gsrj-18	51	23	logarithm	logarithm	NOUN
gsrj-18	51	24	problem	problem	NOUN
gsrj-18	51	25	.	.	PUNCT
gsrj-18	52	1	if	if	SCONJ
gsrj-18	52	2	the	the	DET
gsrj-18	52	3	decryption	decryption	NOUN
gsrj-18	52	4	key	key	NOUN
gsrj-18	52	5	d	d	NOUN
gsrj-18	52	6	was	be	AUX
gsrj-18	52	7	accessed	access	VERB
gsrj-18	52	8	by	by	ADP
gsrj-18	52	9	a	a	DET
gsrj-18	52	10	person	person	NOUN
gsrj-18	52	11	other	other	ADJ
gsrj-18	52	12	than	than	ADP
gsrj-18	52	13	the	the	DET
gsrj-18	52	14	key	key	ADJ
gsrj-18	52	15	generator	generator	NOUN
gsrj-18	52	16	,	,	PUNCT
gsrj-18	52	17	then	then	ADV
gsrj-18	52	18	this	this	DET
gsrj-18	52	19	person	person	NOUN
gsrj-18	52	20	would	would	AUX
gsrj-18	52	21	be	be	AUX
gsrj-18	52	22	able	able	ADJ
gsrj-18	52	23	to	to	PART
gsrj-18	52	24	intercept	intercept	VERB
gsrj-18	52	25	secret	secret	ADJ
gsrj-18	52	26	encrypted	encrypt	VERB
gsrj-18	52	27	messages	message	NOUN
gsrj-18	52	28	meant	mean	VERB
gsrj-18	52	29	for	for	ADP
gsrj-18	52	30	the	the	DET
gsrj-18	52	31	key	key	ADJ
gsrj-18	52	32	generator	generator	NOUN
gsrj-18	52	33	and	and	CCONJ
gsrj-18	52	34	decrypt	decrypt	VERB
gsrj-18	52	35	them	they	PRON
gsrj-18	52	36	using	use	VERB
gsrj-18	52	37	the	the	DET
gsrj-18	52	38	intercepted	intercept	VERB
gsrj-18	52	39	value	value	NOUN
gsrj-18	52	40	of	of	ADP
gsrj-18	52	41	d.	d.	PROPN
gsrj-18	52	42	in	in	ADP
gsrj-18	52	43	short	short	PROPN
gsrj-18	52	44	,	,	PUNCT
gsrj-18	52	45	rsa	rsa	PROPN
gsrj-18	52	46	is	be	AUX
gsrj-18	52	47	a	a	DET
gsrj-18	52	48	secure	secure	ADJ
gsrj-18	52	49	cryptosystem	cryptosystem	NOUN
gsrj-18	52	50	because	because	SCONJ
gsrj-18	52	51	accessing	access	VERB
gsrj-18	52	52	the	the	DET
gsrj-18	52	53	decryption	decryption	NOUN
gsrj-18	52	54	key	key	NOUN
gsrj-18	52	55	by	by	ADP
gsrj-18	52	56	semi	semi	ADJ
gsrj-18	52	57	-	-	ADJ
gsrj-18	52	58	prime	prime	ADJ
gsrj-18	52	59	factorization	factorization	NOUN
gsrj-18	52	60	or	or	CCONJ
gsrj-18	52	61	logarithmic	logarithmic	ADJ
gsrj-18	52	62	properties	property	NOUN
gsrj-18	52	63	both	both	PRON
gsrj-18	52	64	prove	prove	VERB
gsrj-18	52	65	to	to	PART
gsrj-18	52	66	be	be	AUX
gsrj-18	52	67	too	too	ADV
gsrj-18	52	68	time	time	NOUN
gsrj-18	52	69	-	-	PUNCT
gsrj-18	52	70	consuming	consume	VERB
gsrj-18	52	71	to	to	PART
gsrj-18	52	72	be	be	AUX
gsrj-18	52	73	pursued	pursue	VERB
gsrj-18	52	74	realistically	realistically	ADV
gsrj-18	52	75	,	,	PUNCT
gsrj-18	52	76	at	at	ADP
gsrj-18	52	77	least	least	ADJ
gsrj-18	52	78	until	until	ADP
gsrj-18	52	79	the	the	DET
gsrj-18	52	80	advent	advent	NOUN
gsrj-18	52	81	of	of	ADP
gsrj-18	52	82	quantum	quantum	NOUN
gsrj-18	52	83	computing	computing	NOUN
gsrj-18	52	84	.	.	PUNCT
gsrj-18	53	1	if	if	SCONJ
gsrj-18	53	2	a	a	DET
gsrj-18	53	3	“	"	PUNCT
gsrj-18	53	4	message	message	NOUN
gsrj-18	53	5	-	-	PUNCT
gsrj-18	53	6	interceptor	interceptor	NOUN
gsrj-18	53	7	”	"	PUNCT
gsrj-18	53	8	(	(	PUNCT
gsrj-18	53	9	the	the	DET
gsrj-18	53	10	equivalent	equivalent	NOUN
gsrj-18	53	11	of	of	ADP
gsrj-18	53	12	a	a	DET
gsrj-18	53	13	“	"	PUNCT
gsrj-18	53	14	hacker	hacker	NOUN
gsrj-18	53	15	”	"	PUNCT
gsrj-18	53	16	)	)	PUNCT
gsrj-18	53	17	wants	want	VERB
gsrj-18	53	18	to	to	PART
gsrj-18	53	19	calculate	calculate	VERB
gsrj-18	53	20	the	the	DET
gsrj-18	53	21	value	value	NOUN
gsrj-18	53	22	of	of	ADP
gsrj-18	53	23	the	the	DET
gsrj-18	53	24	decryption	decryption	NOUN
gsrj-18	53	25	key	key	NOUN
gsrj-18	53	26	using	use	VERB
gsrj-18	53	27	only	only	ADV
gsrj-18	53	28	the	the	DET
gsrj-18	53	29	publicly	publicly	ADV
gsrj-18	53	30	-	-	PUNCT
gsrj-18	53	31	available	available	ADJ
gsrj-18	53	32	values	value	NOUN
gsrj-18	53	33	of	of	ADP
gsrj-18	53	34	n	n	PROPN
gsrj-18	53	35	and	and	CCONJ
gsrj-18	53	36	e	e	NOUN
gsrj-18	53	37	,	,	PUNCT
gsrj-18	53	38	they	they	PRON
gsrj-18	53	39	have	have	VERB
gsrj-18	53	40	two	two	NUM
gsrj-18	53	41	options	option	NOUN
gsrj-18	53	42	,	,	PUNCT
gsrj-18	53	43	with	with	ADP
gsrj-18	53	44	the	the	DET
gsrj-18	53	45	first	first	ADJ
gsrj-18	53	46	being	be	AUX
gsrj-18	53	47	semi	semi	ADJ
gsrj-18	53	48	-	-	ADJ
gsrj-18	53	49	prime	prime	ADJ
gsrj-18	53	50	factorization.9	factorization.9	PROPN
gsrj-18	53	51	when	when	SCONJ
gsrj-18	53	52	semiprime	semiprime	NOUN
gsrj-18	53	53	factorization	factorization	NOUN
gsrj-18	53	54	is	be	AUX
gsrj-18	53	55	used	use	VERB
gsrj-18	53	56	by	by	ADP
gsrj-18	53	57	a	a	DET
gsrj-18	53	58	messageinterceptor	messageinterceptor	NOUN
gsrj-18	53	59	in	in	ADP
gsrj-18	53	60	an	an	DET
gsrj-18	53	61	attempt	attempt	NOUN
gsrj-18	53	62	to	to	PART
gsrj-18	53	63	gain	gain	VERB
gsrj-18	53	64	access	access	NOUN
gsrj-18	53	65	to	to	ADP
gsrj-18	53	66	the	the	DET
gsrj-18	53	67	decryption	decryption	NOUN
gsrj-18	53	68	key	key	NOUN
gsrj-18	53	69	,	,	PUNCT
gsrj-18	53	70	the	the	DET
gsrj-18	53	71	magnitude	magnitude	NOUN
gsrj-18	53	72	of	of	ADP
gsrj-18	53	73	the	the	DET
gsrj-18	53	74	semi	semi	ADJ
gsrj-18	53	75	-	-	ADJ
gsrj-18	53	76	prime	prime	ADJ
gsrj-18	53	77	number	number	NOUN
gsrj-18	53	78	proves	prove	VERB
gsrj-18	53	79	to	to	PART
gsrj-18	53	80	be	be	AUX
gsrj-18	53	81	of	of	ADP
gsrj-18	53	82	paramount	paramount	ADJ
gsrj-18	53	83	importance	importance	NOUN
gsrj-18	53	84	in	in	ADP
gsrj-18	53	85	preventing	prevent	VERB
gsrj-18	53	86	the	the	DET
gsrj-18	53	87	message	message	NOUN
gsrj-18	53	88	-	-	PUNCT
gsrj-18	53	89	interceptor	interceptor	NOUN
gsrj-18	53	90	from	from	ADP
gsrj-18	53	91	calculating	calculate	VERB
gsrj-18	53	92	the	the	DET
gsrj-18	53	93	decryption	decryption	NOUN
gsrj-18	53	94	key	key	NOUN
gsrj-18	53	95	.	.	PUNCT
gsrj-18	54	1	in	in	ADP
gsrj-18	54	2	the	the	DET
gsrj-18	54	3	case	case	NOUN
gsrj-18	54	4	of	of	ADP
gsrj-18	54	5	rsa	rsa	PROPN
gsrj-18	54	6	encryption	encryption	NOUN
gsrj-18	54	7	,	,	PUNCT
gsrj-18	54	8	the	the	DET
gsrj-18	54	9	semi	semi	ADJ
gsrj-18	54	10	-	-	ADJ
gsrj-18	54	11	prime	prime	ADJ
gsrj-18	54	12	number	number	NOUN
gsrj-18	54	13	is	be	AUX
gsrj-18	54	14	n	n	PRON
gsrj-18	54	15	(	(	PUNCT
gsrj-18	54	16	the	the	DET
gsrj-18	54	17	product	product	NOUN
gsrj-18	54	18	of	of	ADP
gsrj-18	54	19	the	the	DET
gsrj-18	54	20	two	two	NUM
gsrj-18	54	21	prime	prime	ADJ
gsrj-18	54	22	numbers	number	NOUN
gsrj-18	54	23	p	p	NOUN
gsrj-18	54	24	and	and	CCONJ
gsrj-18	54	25	q	q	NOUN
gsrj-18	54	26	)	)	PUNCT
gsrj-18	54	27	,	,	PUNCT
gsrj-18	54	28	whose	whose	DET
gsrj-18	54	29	value	value	NOUN
gsrj-18	54	30	is	be	AUX
gsrj-18	54	31	publicly	publicly	ADV
gsrj-18	54	32	available	available	ADJ
gsrj-18	54	33	to	to	ADP
gsrj-18	54	34	the	the	DET
gsrj-18	54	35	messageinterceptor	messageinterceptor	NOUN
gsrj-18	54	36	.	.	PUNCT
gsrj-18	55	1	the	the	DET
gsrj-18	55	2	message	message	NOUN
gsrj-18	55	3	-	-	PUNCT
gsrj-18	55	4	interceptor	interceptor	NOUN
gsrj-18	55	5	must	must	AUX
gsrj-18	55	6	factor	factor	VERB
gsrj-18	55	7	the	the	DET
gsrj-18	55	8	semi	semi	ADJ
gsrj-18	55	9	-	-	ADJ
gsrj-18	55	10	prime	prime	ADJ
gsrj-18	55	11	number	number	NOUN
gsrj-18	55	12	n	n	NOUN
gsrj-18	55	13	into	into	ADP
gsrj-18	55	14	its	its	PRON
gsrj-18	55	15	constituent	constituent	ADJ
gsrj-18	55	16	factors	factor	NOUN
gsrj-18	55	17	p	p	NOUN
gsrj-18	55	18	and	and	CCONJ
gsrj-18	55	19	q.	q.	NOUN
gsrj-18	55	20	from	from	ADP
gsrj-18	55	21	there	there	ADV
gsrj-18	55	22	,	,	PUNCT
gsrj-18	55	23	the	the	DET
gsrj-18	55	24	messageinterceptor	messageinterceptor	NOUN
gsrj-18	55	25	can	can	AUX
gsrj-18	55	26	plug	plug	VERB
gsrj-18	55	27	in	in	ADP
gsrj-18	55	28	the	the	DET
gsrj-18	55	29	values	value	NOUN
gsrj-18	55	30	of	of	ADP
gsrj-18	55	31	p	p	NOUN
gsrj-18	55	32	and	and	CCONJ
gsrj-18	55	33	q	q	NOUN
gsrj-18	55	34	into	into	ADP
gsrj-18	55	35	the	the	DET
gsrj-18	55	36	expression	expression	NOUN
gsrj-18	55	37	(	(	PUNCT
gsrj-18	55	38	p	p	X
gsrj-18	55	39	–	–	PUNCT
gsrj-18	55	40	1)*(q	1)*(q	NUM
gsrj-18	55	41	–	–	PUNCT
gsrj-18	55	42	1	1	NUM
gsrj-18	55	43	)	)	PUNCT
gsrj-18	55	44	to	to	PART
gsrj-18	55	45	find	find	VERB
gsrj-18	55	46	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	55	47	.	.	PUNCT
gsrj-18	56	1	after	after	ADP
gsrj-18	56	2	having	having	AUX
gsrj-18	56	3	attained	attain	VERB
gsrj-18	56	4	the	the	DET
gsrj-18	56	5	value	value	NOUN
gsrj-18	56	6	of	of	ADP
gsrj-18	56	7	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	56	8	,	,	PUNCT
gsrj-18	56	9	the	the	DET
gsrj-18	56	10	messageinterceptor	messageinterceptor	NOUN
gsrj-18	56	11	,	,	PUNCT
gsrj-18	56	12	knowing	know	VERB
gsrj-18	56	13	that	that	SCONJ
gsrj-18	56	14	(	(	PUNCT
gsrj-18	56	15	e*d	e*d	PROPN
gsrj-18	56	16	)	)	PUNCT
gsrj-18	56	17	must	must	AUX
gsrj-18	56	18	equal	equal	VERB
gsrj-18	56	19	1	1	NUM
gsrj-18	56	20	more	more	ADJ
gsrj-18	56	21	than	than	ADP
gsrj-18	56	22	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	56	23	in	in	ADP
gsrj-18	56	24	order	order	NOUN
gsrj-18	56	25	to	to	PART
gsrj-18	56	26	achieve	achieve	VERB
gsrj-18	56	27	a	a	DET
gsrj-18	56	28	modular	modular	ADJ
gsrj-18	56	29	relationship	relationship	NOUN
gsrj-18	56	30	with	with	ADP
gsrj-18	56	31	1	1	NUM
gsrj-18	56	32	as	as	ADP
gsrj-18	56	33	a	a	DET
gsrj-18	56	34	remainder	remainder	NOUN
gsrj-18	56	35	,	,	PUNCT
gsrj-18	56	36	can	can	AUX
gsrj-18	56	37	plug	plug	VERB
gsrj-18	56	38	this	this	DET
gsrj-18	56	39	value	value	NOUN
gsrj-18	56	40	along	along	ADP
gsrj-18	56	41	with	with	ADP
gsrj-18	56	42	the	the	DET
gsrj-18	56	43	public	public	ADJ
gsrj-18	56	44	key	key	ADJ
gsrj-18	56	45	value	value	NOUN
gsrj-18	56	46	of	of	ADP
gsrj-18	56	47	e	e	NOUN
gsrj-18	56	48	into	into	ADP
gsrj-18	56	49	equation	equation	NOUN
gsrj-18	56	50	2	2	NUM
gsrj-18	56	51	and	and	CCONJ
gsrj-18	56	52	solve	solve	VERB
gsrj-18	56	53	for	for	ADP
gsrj-18	56	54	d.	d.	PROPN
gsrj-18	56	55	for	for	ADP
gsrj-18	56	56	example	example	NOUN
gsrj-18	56	57	,	,	PUNCT
gsrj-18	56	58	if	if	SCONJ
gsrj-18	56	59	e	e	NOUN
gsrj-18	56	60	is	be	AUX
gsrj-18	56	61	7	7	NUM
gsrj-18	56	62	and	and	CCONJ
gsrj-18	56	63	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	56	64	is	be	AUX
gsrj-18	56	65	3120	3120	NUM
gsrj-18	56	66	,	,	PUNCT
gsrj-18	56	67	then	then	ADV
gsrj-18	56	68	the	the	DET
gsrj-18	56	69	formula	formula	NOUN
gsrj-18	56	70	would	would	AUX
gsrj-18	56	71	be	be	AUX
gsrj-18	56	72	:	:	PUNCT
gsrj-18	56	73	7d	7d	NUM
gsrj-18	56	74	mod	mod	NOUN
gsrj-18	56	75	3120	3120	NUM
gsrj-18	56	76	=	=	SYM
gsrj-18	56	77	1	1	NUM
gsrj-18	56	78	,	,	PUNCT
gsrj-18	56	79	and	and	CCONJ
gsrj-18	56	80	thus	thus	ADV
gsrj-18	56	81	,	,	PUNCT
gsrj-18	56	82	7d	7d	NUM
gsrj-18	56	83	must	must	AUX
gsrj-18	56	84	equal	equal	VERB
gsrj-18	56	85	3121	3121	NUM
gsrj-18	56	86	for	for	SCONJ
gsrj-18	56	87	the	the	DET
gsrj-18	56	88	relationship	relationship	NOUN
gsrj-18	56	89	to	to	PART
gsrj-18	56	90	work	work	VERB
gsrj-18	56	91	.	.	PUNCT
gsrj-18	57	1	with	with	ADP
gsrj-18	57	2	this	this	PRON
gsrj-18	57	3	in	in	ADP
gsrj-18	57	4	mind	mind	NOUN
gsrj-18	57	5	,	,	PUNCT
gsrj-18	57	6	the	the	DET
gsrj-18	57	7	message	message	NOUN
gsrj-18	57	8	-	-	PUNCT
gsrj-18	57	9	interceptor	interceptor	NOUN
gsrj-18	57	10	can	can	AUX
gsrj-18	57	11	easily	easily	ADV
gsrj-18	57	12	solve	solve	VERB
gsrj-18	57	13	for	for	ADP
gsrj-18	57	14	d	d	NOUN
gsrj-18	57	15	:	:	PUNCT
gsrj-18	57	16	7d	7d	NUM
gsrj-18	57	17	=	=	SYM
gsrj-18	57	18	3121	3121	NUM
gsrj-18	57	19	d	d	NOUN
gsrj-18	57	20	=	=	SYM
gsrj-18	57	21	445.857143	445.857143	NUM
gsrj-18	57	22	.	.	PUNCT
gsrj-18	57	23	.	.	PUNCT
gsrj-18	57	24	.	.	PUNCT
gsrj-18	58	1	d	d	X
gsrj-18	58	2	,	,	PUNCT
gsrj-18	58	3	however	however	ADV
gsrj-18	58	4	,	,	PUNCT
gsrj-18	58	5	must	must	AUX
gsrj-18	58	6	be	be	AUX
gsrj-18	58	7	an	an	DET
gsrj-18	58	8	integer	integer	NOUN
gsrj-18	58	9	value	value	NOUN
gsrj-18	58	10	.	.	PUNCT
gsrj-18	59	1	in	in	ADP
gsrj-18	59	2	order	order	NOUN
gsrj-18	59	3	to	to	PART
gsrj-18	59	4	satisfy	satisfy	VERB
gsrj-18	59	5	this	this	DET
gsrj-18	59	6	rule	rule	NOUN
gsrj-18	59	7	,	,	PUNCT
gsrj-18	59	8	the	the	DET
gsrj-18	59	9	message	message	NOUN
gsrj-18	59	10	-	-	PUNCT
gsrj-18	59	11	interceptor	interceptor	NOUN
gsrj-18	59	12	can	can	AUX
gsrj-18	59	13	look	look	VERB
gsrj-18	59	14	for	for	ADP
gsrj-18	59	15	other	other	ADJ
gsrj-18	59	16	modular	modular	ADJ
gsrj-18	59	17	relationships	relationship	NOUN
gsrj-18	59	18	that	that	PRON
gsrj-18	59	19	yield	yield	VERB
gsrj-18	59	20	a	a	DET
gsrj-18	59	21	remainder	remainder	NOUN
gsrj-18	59	22	of	of	ADP
gsrj-18	59	23	1	1	NUM
gsrj-18	59	24	.	.	PUNCT
gsrj-18	60	1	for	for	ADP
gsrj-18	60	2	example	example	NOUN
gsrj-18	60	3	,	,	PUNCT
gsrj-18	60	4	6241	6241	NUM
gsrj-18	60	5	mod	mod	NOUN
gsrj-18	60	6	6240	6240	NUM
gsrj-18	60	7	=	=	SYM
gsrj-18	60	8	1	1	NUM
gsrj-18	60	9	.	.	NOUN
gsrj-18	60	10	9	9	NUM
gsrj-18	60	11	georgetown	georgetown	PROPN
gsrj-18	60	12	scientific	scientific	PROPN
gsrj-18	60	13	research	research	NOUN
gsrj-18	60	14	journal	journal	NOUN
gsrj-18	60	15	similarly	similarly	ADV
gsrj-18	60	16	,	,	PUNCT
gsrj-18	60	17	9361	9361	NUM
gsrj-18	60	18	mod	mod	PROPN
gsrj-18	60	19	9360	9360	NUM
gsrj-18	60	20	=	=	SYM
gsrj-18	60	21	1	1	X
gsrj-18	60	22	.	.	PUNCT
gsrj-18	61	1	the	the	DET
gsrj-18	61	2	messageinterceptor	messageinterceptor	NOUN
gsrj-18	61	3	can	can	AUX
gsrj-18	61	4	keep	keep	VERB
gsrj-18	61	5	on	on	ADP
gsrj-18	61	6	multiplying	multiply	VERB
gsrj-18	61	7	the	the	DET
gsrj-18	61	8	value	value	NOUN
gsrj-18	61	9	of	of	ADP
gsrj-18	61	10	3120	3120	NUM
gsrj-18	61	11	by	by	ADP
gsrj-18	61	12	increasing	increase	VERB
gsrj-18	61	13	integers	integer	NOUN
gsrj-18	61	14	to	to	PART
gsrj-18	61	15	achieve	achieve	VERB
gsrj-18	61	16	different	different	ADJ
gsrj-18	61	17	modular	modular	ADJ
gsrj-18	61	18	relationships	relationship	NOUN
gsrj-18	61	19	that	that	PRON
gsrj-18	61	20	will	will	AUX
gsrj-18	61	21	still	still	ADV
gsrj-18	61	22	yield	yield	VERB
gsrj-18	61	23	1	1	NUM
gsrj-18	61	24	as	as	ADP
gsrj-18	61	25	a	a	DET
gsrj-18	61	26	remainder	remainder	NOUN
gsrj-18	61	27	until	until	SCONJ
gsrj-18	61	28	d	d	PROPN
gsrj-18	61	29	is	be	AUX
gsrj-18	61	30	an	an	DET
gsrj-18	61	31	integer	integer	NOUN
gsrj-18	61	32	value	value	NOUN
gsrj-18	61	33	.	.	PUNCT
gsrj-18	62	1	example	example	NOUN
gsrj-18	62	2	:	:	PUNCT
gsrj-18	62	3	7d	7d	NUM
gsrj-18	62	4	mod	mod	NOUN
gsrj-18	62	5	(	(	PUNCT
gsrj-18	62	6	3120	3120	NUM
gsrj-18	62	7	*	*	SYM
gsrj-18	62	8	1	1	NUM
gsrj-18	62	9	)	)	PUNCT
gsrj-18	62	10	=	=	SYM
gsrj-18	62	11	1	1	NUM
gsrj-18	62	12	;	;	PUNCT
gsrj-18	62	13	7d	7d	NUM
gsrj-18	62	14	=	=	SYM
gsrj-18	62	15	3120	3120	NUM
gsrj-18	62	16	*	*	SYM
gsrj-18	62	17	1	1	NUM
gsrj-18	62	18	+	+	NUM
gsrj-18	62	19	1	1	NUM
gsrj-18	62	20	;	;	PUNCT
gsrj-18	63	1	d	d	X
gsrj-18	63	2	=	=	PUNCT
gsrj-18	63	3	(	(	PUNCT
gsrj-18	63	4	3120	3120	NUM
gsrj-18	63	5	*	*	SYM
gsrj-18	63	6	1	1	NUM
gsrj-18	63	7	+	+	CCONJ
gsrj-18	63	8	1)/7	1)/7	NUM
gsrj-18	63	9	;	;	PUNCT
gsrj-18	63	10	d	d	NOUN
gsrj-18	63	11	=	=	PUNCT
gsrj-18	63	12	decimal	decimal	ADJ
gsrj-18	63	13	7d	7d	NUM
gsrj-18	63	14	mod	mod	NOUN
gsrj-18	63	15	(	(	PUNCT
gsrj-18	63	16	3120	3120	NUM
gsrj-18	63	17	*	*	SYM
gsrj-18	63	18	2	2	NUM
gsrj-18	63	19	)	)	PUNCT
gsrj-18	63	20	=	=	SYM
gsrj-18	63	21	1	1	NUM
gsrj-18	63	22	;	;	PUNCT
gsrj-18	63	23	7d	7d	NUM
gsrj-18	63	24	=	=	SYM
gsrj-18	63	25	3120	3120	NUM
gsrj-18	63	26	*	*	SYM
gsrj-18	63	27	2	2	NUM
gsrj-18	63	28	+	+	NUM
gsrj-18	63	29	1	1	NUM
gsrj-18	63	30	;	;	PUNCT
gsrj-18	63	31	d	d	X
gsrj-18	63	32	=	=	PUNCT
gsrj-18	63	33	(	(	PUNCT
gsrj-18	63	34	3120	3120	NUM
gsrj-18	63	35	*	*	SYM
gsrj-18	63	36	2	2	NUM
gsrj-18	63	37	+	+	SYM
gsrj-18	63	38	1)/7	1)/7	NUM
gsrj-18	63	39	;	;	PUNCT
gsrj-18	63	40	d	d	NOUN
gsrj-18	63	41	=	=	PUNCT
gsrj-18	63	42	decimal	decimal	ADJ
gsrj-18	63	43	7d	7d	NUM
gsrj-18	63	44	mod	mod	NOUN
gsrj-18	63	45	(	(	PUNCT
gsrj-18	63	46	3120	3120	NUM
gsrj-18	63	47	*	*	SYM
gsrj-18	63	48	3	3	NUM
gsrj-18	63	49	)	)	PUNCT
gsrj-18	63	50	=	=	SYM
gsrj-18	63	51	1	1	NUM
gsrj-18	63	52	;	;	PUNCT
gsrj-18	63	53	7d	7d	NUM
gsrj-18	63	54	=	=	SYM
gsrj-18	63	55	3120	3120	NUM
gsrj-18	63	56	*	*	SYM
gsrj-18	63	57	3	3	NUM
gsrj-18	63	58	+	+	SYM
gsrj-18	63	59	1	1	NUM
gsrj-18	63	60	;	;	PUNCT
gsrj-18	63	61	d	d	X
gsrj-18	63	62	=	=	PUNCT
gsrj-18	63	63	(	(	PUNCT
gsrj-18	63	64	3120	3120	NUM
gsrj-18	63	65	*	*	SYM
gsrj-18	63	66	3	3	NUM
gsrj-18	63	67	+	+	SYM
gsrj-18	63	68	1)/7	1)/7	NUM
gsrj-18	63	69	;	;	PUNCT
gsrj-18	63	70	d	d	NOUN
gsrj-18	63	71	=	=	PUNCT
gsrj-18	63	72	decimal	decimal	ADJ
gsrj-18	63	73	7d	7d	NUM
gsrj-18	63	74	mod	mod	NOUN
gsrj-18	63	75	(	(	PUNCT
gsrj-18	63	76	3120	3120	NUM
gsrj-18	63	77	*	*	SYM
gsrj-18	63	78	4	4	NUM
gsrj-18	63	79	)	)	PUNCT
gsrj-18	63	80	=	=	SYM
gsrj-18	63	81	1	1	NUM
gsrj-18	63	82	;	;	PUNCT
gsrj-18	63	83	7d	7d	NUM
gsrj-18	63	84	=	=	SYM
gsrj-18	63	85	3120	3120	NUM
gsrj-18	63	86	*	*	SYM
gsrj-18	63	87	4	4	NUM
gsrj-18	63	88	+	+	SYM
gsrj-18	63	89	1	1	NUM
gsrj-18	63	90	;	;	PUNCT
gsrj-18	63	91	d	d	X
gsrj-18	63	92	=	=	PUNCT
gsrj-18	63	93	(	(	PUNCT
gsrj-18	63	94	3120	3120	NUM
gsrj-18	63	95	*	*	SYM
gsrj-18	63	96	4	4	NUM
gsrj-18	63	97	+	+	NOUN
gsrj-18	63	98	1)/7	1)/7	NUM
gsrj-18	63	99	;	;	PUNCT
gsrj-18	63	100	d	d	NOUN
gsrj-18	63	101	=	=	PUNCT
gsrj-18	63	102	integer	integer	NOUN
gsrj-18	63	103	here	here	ADV
gsrj-18	63	104	,	,	PUNCT
gsrj-18	63	105	solving	solve	VERB
gsrj-18	63	106	for	for	ADP
gsrj-18	63	107	d	d	NOUN
gsrj-18	63	108	only	only	ADV
gsrj-18	63	109	requires	require	VERB
gsrj-18	63	110	4	4	NUM
gsrj-18	63	111	iterations	iteration	NOUN
gsrj-18	63	112	.	.	PUNCT
gsrj-18	64	1	the	the	DET
gsrj-18	64	2	formula	formula	NOUN
gsrj-18	64	3	for	for	ADP
gsrj-18	64	4	solving	solve	VERB
gsrj-18	64	5	for	for	ADP
gsrj-18	64	6	d	d	PROPN
gsrj-18	64	7	simplifies	simplifie	NOUN
gsrj-18	64	8	to	to	PART
gsrj-18	64	9	:	:	PUNCT
gsrj-18	64	10	d	d	X
gsrj-18	64	11	=	=	PUNCT
gsrj-18	64	12	𝜑𝜑n	𝜑𝜑n	PROPN
gsrj-18	64	13	*	*	X
gsrj-18	64	14	𝜑𝜑nmultiplier	𝜑𝜑nmultiplier	NOUN
gsrj-18	64	15	+	+	X
gsrj-18	64	16	1)/e	1)/e	NUM
gsrj-18	64	17	(	(	PUNCT
gsrj-18	64	18	equation	equation	NOUN
gsrj-18	64	19	5	5	NUM
gsrj-18	64	20	)	)	PUNCT
gsrj-18	64	21	where	where	SCONJ
gsrj-18	64	22	𝜑𝜑nmultiplier	𝜑𝜑nmultipli	ADJ
gsrj-18	64	23	”	"	PUNCT
gsrj-18	64	24	is	be	AUX
gsrj-18	64	25	a	a	DET
gsrj-18	64	26	specific	specific	ADJ
gsrj-18	64	27	integer	integer	NOUN
gsrj-18	64	28	value	value	NOUN
gsrj-18	64	29	that	that	PRON
gsrj-18	64	30	the	the	DET
gsrj-18	64	31	message	message	NOUN
gsrj-18	64	32	-	-	PUNCT
gsrj-18	64	33	interceptor	interceptor	NOUN
gsrj-18	64	34	multiplies	multiplie	NOUN
gsrj-18	64	35	𝜑𝜑n	𝜑𝜑n	VERB
gsrj-18	64	36	by	by	ADP
gsrj-18	64	37	to	to	PART
gsrj-18	64	38	achieve	achieve	VERB
gsrj-18	64	39	different	different	ADJ
gsrj-18	64	40	modular	modular	ADJ
gsrj-18	64	41	relationships	relationship	NOUN
gsrj-18	64	42	that	that	PRON
gsrj-18	64	43	yield	yield	VERB
gsrj-18	64	44	1	1	NUM
gsrj-18	64	45	.	.	PUNCT
gsrj-18	64	46	with	with	ADP
gsrj-18	64	47	knowledge	knowledge	NOUN
gsrj-18	64	48	of	of	ADP
gsrj-18	64	49	the	the	DET
gsrj-18	64	50	publicly	publicly	ADV
gsrj-18	64	51	-	-	PUNCT
gsrj-18	64	52	available	available	ADJ
gsrj-18	64	53	value	value	NOUN
gsrj-18	64	54	of	of	ADP
gsrj-18	64	55	e	e	NOUN
gsrj-18	64	56	as	as	ADV
gsrj-18	64	57	well	well	ADV
gsrj-18	64	58	as	as	ADP
gsrj-18	64	59	the	the	DET
gsrj-18	64	60	value	value	NOUN
gsrj-18	64	61	of	of	ADP
gsrj-18	64	62	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	64	63	,	,	PUNCT
gsrj-18	64	64	the	the	DET
gsrj-18	64	65	messageinterceptor	messageinterceptor	NOUN
gsrj-18	64	66	can	can	AUX
gsrj-18	64	67	easily	easily	ADV
gsrj-18	64	68	calculate	calculate	VERB
gsrj-18	64	69	the	the	DET
gsrj-18	64	70	value	value	NOUN
gsrj-18	64	71	of	of	ADP
gsrj-18	64	72	the	the	DET
gsrj-18	64	73	decryption	decryption	NOUN
gsrj-18	64	74	key	key	NOUN
gsrj-18	64	75	,	,	PUNCT
gsrj-18	64	76	d	d	X
gsrj-18	64	77	,	,	PUNCT
gsrj-18	64	78	having	having	AUX
gsrj-18	64	79	created	create	VERB
gsrj-18	64	80	one	one	NUM
gsrj-18	64	81	equation	equation	NOUN
gsrj-18	64	82	with	with	ADP
gsrj-18	64	83	only	only	ADV
gsrj-18	64	84	one	one	NUM
gsrj-18	64	85	unknown	unknown	ADJ
gsrj-18	64	86	value	value	NOUN
gsrj-18	64	87	.	.	PUNCT
gsrj-18	65	1	however	however	ADV
gsrj-18	65	2	,	,	PUNCT
gsrj-18	65	3	one	one	NUM
gsrj-18	65	4	problem	problem	NOUN
gsrj-18	65	5	exists	exist	VERB
gsrj-18	65	6	:	:	PUNCT
gsrj-18	65	7	factoring	factor	VERB
gsrj-18	65	8	n	n	X
gsrj-18	65	9	into	into	ADP
gsrj-18	65	10	its	its	PRON
gsrj-18	65	11	constituent	constituent	ADJ
gsrj-18	65	12	factors	factor	NOUN
gsrj-18	65	13	p	p	NOUN
gsrj-18	65	14	and	and	CCONJ
gsrj-18	65	15	q	q	NOUN
gsrj-18	65	16	becomes	become	VERB
gsrj-18	65	17	increasingly	increasingly	ADV
gsrj-18	65	18	timeconsuming	timeconsuming	ADJ
gsrj-18	65	19	as	as	SCONJ
gsrj-18	65	20	n	n	PRON
gsrj-18	65	21	grows	grow	NOUN
gsrj-18	65	22	.	.	PUNCT
gsrj-18	66	1	this	this	PRON
gsrj-18	66	2	is	be	AUX
gsrj-18	66	3	why	why	SCONJ
gsrj-18	66	4	large	large	ADJ
gsrj-18	66	5	prime	prime	ADJ
gsrj-18	66	6	numbers	number	NOUN
gsrj-18	66	7	had	have	VERB
gsrj-18	66	8	to	to	PART
gsrj-18	66	9	be	be	AUX
gsrj-18	66	10	chosen	choose	VERB
gsrj-18	66	11	by	by	ADP
gsrj-18	66	12	the	the	DET
gsrj-18	66	13	key	key	ADJ
gsrj-18	66	14	generator	generator	NOUN
gsrj-18	66	15	as	as	ADP
gsrj-18	66	16	values	value	NOUN
gsrj-18	66	17	for	for	ADP
gsrj-18	66	18	p	p	PROPN
gsrj-18	66	19	and	and	CCONJ
gsrj-18	66	20	q.	q.	NOUN
gsrj-18	66	21	the	the	DET
gsrj-18	66	22	larger	large	ADJ
gsrj-18	66	23	n	n	NOUN
gsrj-18	66	24	is	be	AUX
gsrj-18	66	25	(	(	PUNCT
gsrj-18	66	26	the	the	DET
gsrj-18	66	27	product	product	NOUN
gsrj-18	66	28	of	of	ADP
gsrj-18	66	29	the	the	DET
gsrj-18	66	30	already	already	ADV
gsrj-18	66	31	large	large	ADJ
gsrj-18	66	32	values	value	NOUN
gsrj-18	66	33	of	of	ADP
gsrj-18	66	34	p	p	NOUN
gsrj-18	66	35	and	and	CCONJ
gsrj-18	66	36	q	q	NOUN
gsrj-18	66	37	)	)	PUNCT
gsrj-18	66	38	,	,	PUNCT
gsrj-18	66	39	the	the	DET
gsrj-18	66	40	more	more	ADJ
gsrj-18	66	41	time	time	NOUN
gsrj-18	66	42	it	it	PRON
gsrj-18	66	43	will	will	AUX
gsrj-18	66	44	take	take	VERB
gsrj-18	66	45	to	to	PART
gsrj-18	66	46	factor	factor	VERB
gsrj-18	66	47	it	it	PRON
gsrj-18	66	48	.	.	PUNCT
gsrj-18	67	1	in	in	ADP
gsrj-18	67	2	rsa	rsa	PROPN
gsrj-18	67	3	,	,	PUNCT
gsrj-18	67	4	the	the	DET
gsrj-18	67	5	types	type	NOUN
gsrj-18	67	6	of	of	ADP
gsrj-18	67	7	semi	semi	ADJ
gsrj-18	67	8	-	-	ADJ
gsrj-18	67	9	prime	prime	ADJ
gsrj-18	67	10	numbers	number	NOUN
gsrj-18	67	11	utilized	utilize	VERB
gsrj-18	67	12	are	be	AUX
gsrj-18	67	13	typically	typically	ADV
gsrj-18	67	14	around	around	ADV
gsrj-18	67	15	600	600	NUM
gsrj-18	67	16	digits	digit	NOUN
gsrj-18	67	17	long	long	ADJ
gsrj-18	67	18	.	.	PUNCT
gsrj-18	68	1	semi	semi	ADJ
gsrj-18	68	2	-	-	ADJ
gsrj-18	68	3	prime	prime	ADJ
gsrj-18	68	4	numbers	number	NOUN
gsrj-18	68	5	of	of	ADP
gsrj-18	68	6	such	such	ADJ
gsrj-18	68	7	magnitudes	magnitude	NOUN
gsrj-18	68	8	take	take	VERB
gsrj-18	68	9	a	a	DET
gsrj-18	68	10	huge	huge	ADJ
gsrj-18	68	11	amount	amount	NOUN
gsrj-18	68	12	of	of	ADP
gsrj-18	68	13	time	time	NOUN
gsrj-18	68	14	to	to	PART
gsrj-18	68	15	factor	factor	NOUN
gsrj-18	68	16	using	use	VERB
gsrj-18	68	17	current	current	ADJ
gsrj-18	68	18	technologies	technology	NOUN
gsrj-18	68	19	.	.	PUNCT
gsrj-18	69	1	in	in	ADP
gsrj-18	69	2	fact	fact	NOUN
gsrj-18	69	3	,	,	PUNCT
gsrj-18	69	4	in	in	ADP
gsrj-18	69	5	1978	1978	NUM
gsrj-18	69	6	,	,	PUNCT
gsrj-18	69	7	rivest	riv	ADJ
gsrj-18	69	8	,	,	PUNCT
gsrj-18	69	9	shamir	shamir	ADJ
gsrj-18	69	10	,	,	PUNCT
gsrj-18	69	11	and	and	CCONJ
gsrj-18	69	12	adleman	adleman	NOUN
gsrj-18	69	13	predicted	predict	VERB
gsrj-18	69	14	that	that	SCONJ
gsrj-18	69	15	factoring	factor	VERB
gsrj-18	69	16	a	a	DET
gsrj-18	69	17	500	500	NUM
gsrj-18	69	18	-	-	PUNCT
gsrj-18	69	19	digit	digit	NOUN
gsrj-18	69	20	semi	semi	ADJ
gsrj-18	69	21	-	-	ADJ
gsrj-18	69	22	prime	prime	ADJ
gsrj-18	69	23	number	number	NOUN
gsrj-18	69	24	would	would	AUX
gsrj-18	69	25	take	take	VERB
gsrj-18	69	26	approximately	approximately	ADV
gsrj-18	69	27	4.2	4.2	NUM
gsrj-18	69	28	x	x	NOUN
gsrj-18	69	29	years	year	NOUN
gsrj-18	69	30	to	to	PART
gsrj-18	69	31	factor	factor	VERB
gsrj-18	69	32	using	use	VERB
gsrj-18	69	33	the	the	DET
gsrj-18	69	34	schroeppel	schroeppel	NOUN
gsrj-18	69	35	factoring	factoring	NOUN
gsrj-18	69	36	algorithm.10	algorithm.10	NOUN
gsrj-18	69	37	therefore	therefore	ADV
gsrj-18	69	38	,	,	PUNCT
gsrj-18	69	39	due	due	ADP
gsrj-18	69	40	to	to	ADP
gsrj-18	69	41	the	the	DET
gsrj-18	69	42	immense	immense	ADJ
gsrj-18	69	43	amount	amount	NOUN
gsrj-18	69	44	of	of	ADP
gsrj-18	69	45	time	time	NOUN
gsrj-18	69	46	needed	need	VERB
gsrj-18	69	47	to	to	PART
gsrj-18	69	48	factor	factor	VERB
gsrj-18	69	49	n	n	NOUN
gsrj-18	69	50	into	into	ADP
gsrj-18	69	51	its	its	PRON
gsrj-18	69	52	constituent	constituent	ADJ
gsrj-18	69	53	factors	factor	NOUN
gsrj-18	69	54	p	p	NOUN
gsrj-18	69	55	and	and	CCONJ
gsrj-18	69	56	q	q	X
gsrj-18	69	57	,	,	PUNCT
gsrj-18	69	58	it	it	PRON
gsrj-18	69	59	is	be	AUX
gsrj-18	69	60	impractical	impractical	ADJ
gsrj-18	69	61	for	for	SCONJ
gsrj-18	69	62	a	a	DET
gsrj-18	69	63	message	message	NOUN
gsrj-18	69	64	-	-	PUNCT
gsrj-18	69	65	interceptor	interceptor	NOUN
gsrj-18	69	66	to	to	PART
gsrj-18	69	67	use	use	VERB
gsrj-18	69	68	semiprime	semiprime	NOUN
gsrj-18	69	69	factorization	factorization	NOUN
gsrj-18	69	70	to	to	PART
gsrj-18	69	71	calculate	calculate	VERB
gsrj-18	69	72	the	the	DET
gsrj-18	69	73	decryption	decryption	NOUN
gsrj-18	69	74	key	key	NOUN
gsrj-18	69	75	,	,	PUNCT
gsrj-18	69	76	d.11	d.11	VERB
gsrj-18	69	77	the	the	DET
gsrj-18	69	78	second	second	ADJ
gsrj-18	69	79	option	option	NOUN
gsrj-18	69	80	that	that	PRON
gsrj-18	69	81	the	the	DET
gsrj-18	69	82	messageinterceptor	messageinterceptor	NOUN
gsrj-18	69	83	has	have	VERB
gsrj-18	69	84	if	if	SCONJ
gsrj-18	69	85	he	he	PRON
gsrj-18	69	86	wishes	wish	VERB
gsrj-18	69	87	to	to	PART
gsrj-18	69	88	calculate	calculate	VERB
gsrj-18	69	89	the	the	DET
gsrj-18	69	90	value	value	NOUN
gsrj-18	69	91	of	of	ADP
gsrj-18	69	92	the	the	DET
gsrj-18	69	93	decryption	decryption	NOUN
gsrj-18	69	94	key	key	NOUN
gsrj-18	69	95	using	use	VERB
gsrj-18	69	96	only	only	ADV
gsrj-18	69	97	the	the	DET
gsrj-18	69	98	publicly	publicly	ADV
gsrj-18	69	99	available	available	ADJ
gsrj-18	69	100	values	value	NOUN
gsrj-18	69	101	of	of	ADP
gsrj-18	69	102	n	n	NOUN
gsrj-18	69	103	and	and	CCONJ
gsrj-18	69	104	e	e	NOUN
gsrj-18	69	105	is	be	AUX
gsrj-18	69	106	to	to	PART
gsrj-18	69	107	use	use	VERB
gsrj-18	69	108	the	the	DET
gsrj-18	69	109	properties	property	NOUN
gsrj-18	69	110	of	of	ADP
gsrj-18	69	111	logarithms	logarithm	NOUN
gsrj-18	69	112	.	.	PUNCT
gsrj-18	70	1	recall	recall	VERB
gsrj-18	70	2	that	that	SCONJ
gsrj-18	70	3	encrypting	encrypt	VERB
gsrj-18	70	4	a	a	DET
gsrj-18	70	5	message	message	NOUN
gsrj-18	70	6	requires	require	VERB
gsrj-18	70	7	plugging	plug	VERB
gsrj-18	70	8	a	a	DET
gsrj-18	70	9	secret	secret	ADJ
gsrj-18	70	10	message	message	NOUN
gsrj-18	70	11	m	m	VERB
gsrj-18	70	12	into	into	ADP
gsrj-18	70	13	the	the	DET
gsrj-18	70	14	expression	expression	NOUN
gsrj-18	70	15	!	!	PUNCT
gsrj-18	71	1	mod	mod	PROPN
gsrj-18	71	2	n	n	CCONJ
gsrj-18	71	3	,	,	PUNCT
gsrj-18	71	4	and	and	CCONJ
gsrj-18	71	5	thus	thus	ADV
gsrj-18	71	6	decrypting	decrypt	VERB
gsrj-18	71	7	that	that	DET
gsrj-18	71	8	message	message	NOUN
gsrj-18	71	9	requires	require	VERB
gsrj-18	71	10	plugging	plug	VERB
gsrj-18	71	11	in	in	ADP
gsrj-18	71	12	the	the	DET
gsrj-18	71	13	result	result	NOUN
gsrj-18	71	14	of	of	ADP
gsrj-18	71	15	!	!	PUNCT
gsrj-18	71	16	mod	mod	PROPN
gsrj-18	72	1	n	n	PROPN
gsrj-18	72	2	(	(	PUNCT
gsrj-18	72	3	which	which	PRON
gsrj-18	72	4	is	be	AUX
gsrj-18	72	5	c	c	NOUN
gsrj-18	72	6	)	)	PUNCT
gsrj-18	72	7	into	into	ADP
gsrj-18	72	8	the	the	DET
gsrj-18	72	9	expression	expression	NOUN
gsrj-18	72	10	"	"	PUNCT
gsrj-18	72	11	mod	mod	NOUN
gsrj-18	72	12	n	n	PART
gsrj-18	72	13	to	to	PART
gsrj-18	72	14	attain	attain	VERB
gsrj-18	72	15	the	the	DET
gsrj-18	72	16	original	original	ADJ
gsrj-18	72	17	message	message	NOUN
gsrj-18	72	18	m.	m.	NOUN
gsrj-18	72	19	the	the	DET
gsrj-18	72	20	messageinterceptor	messageinterceptor	NOUN
gsrj-18	72	21	,	,	PUNCT
gsrj-18	72	22	like	like	ADP
gsrj-18	72	23	all	all	DET
gsrj-18	72	24	others	other	NOUN
gsrj-18	72	25	,	,	PUNCT
gsrj-18	72	26	has	have	VERB
gsrj-18	72	27	access	access	NOUN
gsrj-18	72	28	to	to	ADP
gsrj-18	72	29	the	the	DET
gsrj-18	72	30	public	public	ADJ
gsrj-18	72	31	key	key	ADJ
gsrj-18	72	32	values	value	NOUN
gsrj-18	72	33	of	of	ADP
gsrj-18	72	34	n	n	PRON
gsrj-18	72	35	and	and	CCONJ
gsrj-18	72	36	e.	e.	PROPN
gsrj-18	72	37	he	he	PRON
gsrj-18	72	38	can	can	AUX
gsrj-18	72	39	generate	generate	VERB
gsrj-18	72	40	a	a	DET
gsrj-18	72	41	secret	secret	ADJ
gsrj-18	72	42	integer	integer	NOUN
gsrj-18	72	43	message	message	NOUN
gsrj-18	72	44	m	m	VERB
gsrj-18	72	45	and	and	CCONJ
gsrj-18	72	46	plug	plug	VERB
gsrj-18	72	47	it	it	PRON
gsrj-18	72	48	into	into	ADP
gsrj-18	72	49	the	the	DET
gsrj-18	72	50	expression	expression	NOUN
gsrj-18	72	51	!	!	PUNCT
gsrj-18	73	1	mod	mod	PROPN
gsrj-18	74	1	n	n	PRON
gsrj-18	74	2	to	to	PART
gsrj-18	74	3	attain	attain	VERB
gsrj-18	74	4	the	the	DET
gsrj-18	74	5	ciphertext	ciphertext	NOUN
gsrj-18	74	6	/	/	SYM
gsrj-18	74	7	encrypted	encrypt	VERB
gsrj-18	74	8	message	message	NOUN
gsrj-18	74	9	c.	c.	PROPN
gsrj-18	74	10	then	then	ADV
gsrj-18	74	11	,	,	PUNCT
gsrj-18	74	12	they	they	PRON
gsrj-18	74	13	can	can	AUX
gsrj-18	74	14	plug	plug	VERB
gsrj-18	74	15	the	the	DET
gsrj-18	74	16	value	value	NOUN
gsrj-18	74	17	of	of	ADP
gsrj-18	74	18	c	c	PROPN
gsrj-18	74	19	along	along	ADP
gsrj-18	74	20	with	with	ADP
gsrj-18	74	21	the	the	DET
gsrj-18	74	22	public	public	ADJ
gsrj-18	74	23	key	key	ADJ
gsrj-18	74	24	value	value	NOUN
gsrj-18	74	25	of	of	ADP
gsrj-18	74	26	n	n	CCONJ
gsrj-18	74	27	into	into	ADP
gsrj-18	74	28	the	the	DET
gsrj-18	74	29	expression	expression	NOUN
gsrj-18	74	30	"	"	PUNCT
gsrj-18	74	31	mod	mod	PROPN
gsrj-18	74	32	n.	n.	PROPN
gsrj-18	74	33	the	the	DET
gsrj-18	74	34	message	message	NOUN
gsrj-18	74	35	-	-	PUNCT
gsrj-18	74	36	interceptor	interceptor	NOUN
gsrj-18	74	37	knows	know	VERB
gsrj-18	74	38	that	that	SCONJ
gsrj-18	74	39	the	the	DET
gsrj-18	74	40	result	result	NOUN
gsrj-18	74	41	of	of	ADP
gsrj-18	74	42	"	"	PUNCT
gsrj-18	74	43	mod	mod	PROPN
gsrj-18	74	44	n	n	PRON
gsrj-18	74	45	must	must	AUX
gsrj-18	74	46	equal	equal	VERB
gsrj-18	74	47	his	his	PRON
gsrj-18	74	48	original	original	ADJ
gsrj-18	74	49	message	message	NOUN
gsrj-18	74	50	m	m	PROPN
gsrj-18	74	51	(	(	PUNCT
gsrj-18	74	52	see	see	VERB
gsrj-18	74	53	equation	equation	NOUN
gsrj-18	74	54	4	4	NUM
gsrj-18	74	55	)	)	PUNCT
gsrj-18	74	56	.	.	PUNCT
gsrj-18	75	1	the	the	DET
gsrj-18	75	2	message	message	NOUN
gsrj-18	75	3	-	-	PUNCT
gsrj-18	75	4	interceptor	interceptor	NOUN
gsrj-18	75	5	has	have	VERB
gsrj-18	75	6	knowledge	knowledge	NOUN
gsrj-18	75	7	of	of	ADP
gsrj-18	75	8	the	the	DET
gsrj-18	75	9	value	value	NOUN
gsrj-18	75	10	of	of	ADP
gsrj-18	75	11	n	n	PROPN
gsrj-18	75	12	(	(	PUNCT
gsrj-18	75	13	a	a	DET
gsrj-18	75	14	public	public	ADJ
gsrj-18	75	15	value	value	NOUN
gsrj-18	75	16	)	)	PUNCT
gsrj-18	75	17	as	as	ADV
gsrj-18	75	18	well	well	ADV
gsrj-18	75	19	as	as	ADP
gsrj-18	75	20	c	c	PROPN
gsrj-18	75	21	and	and	CCONJ
gsrj-18	75	22	m	m	PROPN
gsrj-18	75	23	,	,	PUNCT
gsrj-18	75	24	because	because	SCONJ
gsrj-18	75	25	he	he	PRON
gsrj-18	75	26	generated	generate	VERB
gsrj-18	75	27	these	these	DET
gsrj-18	75	28	values	value	NOUN
gsrj-18	75	29	.	.	PUNCT
gsrj-18	76	1	therefore	therefore	ADV
gsrj-18	76	2	,	,	PUNCT
gsrj-18	76	3	the	the	DET
gsrj-18	76	4	messageinterceptor	messageinterceptor	NOUN
gsrj-18	76	5	has	have	AUX
gsrj-18	76	6	created	create	VERB
gsrj-18	76	7	an	an	DET
gsrj-18	76	8	equation	equation	NOUN
gsrj-18	76	9	in	in	ADP
gsrj-18	76	10	which	which	PRON
gsrj-18	76	11	only	only	ADV
gsrj-18	76	12	one	one	NUM
gsrj-18	76	13	unknown	unknown	ADJ
gsrj-18	76	14	,	,	PUNCT
gsrj-18	76	15	d	d	X
gsrj-18	76	16	,	,	PUNCT
gsrj-18	76	17	the	the	DET
gsrj-18	76	18	decryption	decryption	NOUN
gsrj-18	76	19	key	key	NOUN
gsrj-18	76	20	,	,	PUNCT
gsrj-18	76	21	exists	exist	VERB
gsrj-18	76	22	.	.	PUNCT
gsrj-18	77	1	for	for	ADP
gsrj-18	77	2	example	example	NOUN
gsrj-18	77	3	,	,	PUNCT
gsrj-18	77	4	if	if	SCONJ
gsrj-18	77	5	n	n	PRON
gsrj-18	77	6	is	be	AUX
gsrj-18	77	7	143	143	NUM
gsrj-18	77	8	and	and	CCONJ
gsrj-18	77	9	e	e	NOUN
gsrj-18	77	10	is	be	AUX
gsrj-18	77	11	7	7	NUM
gsrj-18	77	12	,	,	PUNCT
gsrj-18	77	13	and	and	CCONJ
gsrj-18	77	14	the	the	DET
gsrj-18	77	15	messageinterceptor	messageinterceptor	NOUN
gsrj-18	77	16	picks	pick	VERB
gsrj-18	77	17	his	his	PRON
gsrj-18	77	18	secret	secret	ADJ
gsrj-18	77	19	message	message	NOUN
gsrj-18	77	20	m	m	VERB
gsrj-18	77	21	to	to	PART
gsrj-18	77	22	be	be	AUX
gsrj-18	77	23	24	24	NUM
gsrj-18	77	24	,	,	PUNCT
gsrj-18	77	25	then	then	ADV
gsrj-18	77	26	the	the	DET
gsrj-18	77	27	enciphered	enciphered	ADJ
gsrj-18	77	28	message	message	NOUN
gsrj-18	77	29	would	would	AUX
gsrj-18	77	30	be	be	AUX
gsrj-18	77	31	mod	mod	PROPN
gsrj-18	77	32	143	143	NUM
gsrj-18	77	33	,	,	PUNCT
gsrj-18	77	34	or	or	CCONJ
gsrj-18	77	35	106	106	NUM
gsrj-18	77	36	.	.	PUNCT
gsrj-18	78	1	the	the	DET
gsrj-18	78	2	message	message	NOUN
gsrj-18	78	3	-	-	PUNCT
gsrj-18	78	4	interceptor	interceptor	NOUN
gsrj-18	78	5	can	can	AUX
gsrj-18	78	6	plug	plug	VERB
gsrj-18	78	7	in	in	ADP
gsrj-18	78	8	the	the	DET
gsrj-18	78	9	values	value	NOUN
gsrj-18	78	10	of	of	ADP
gsrj-18	78	11	143	143	NUM
gsrj-18	78	12	(	(	PUNCT
gsrj-18	78	13	n	n	CCONJ
gsrj-18	78	14	)	)	PUNCT
gsrj-18	78	15	,	,	PUNCT
gsrj-18	78	16	24	24	NUM
gsrj-18	78	17	(	(	PUNCT
gsrj-18	78	18	m	m	NOUN
gsrj-18	78	19	)	)	PUNCT
gsrj-18	78	20	and	and	CCONJ
gsrj-18	78	21	106	106	NUM
gsrj-18	78	22	(	(	PUNCT
gsrj-18	78	23	c	c	NOUN
gsrj-18	78	24	)	)	PUNCT
gsrj-18	78	25	into	into	ADP
gsrj-18	78	26	equation	equation	NOUN
gsrj-18	78	27	4	4	NUM
gsrj-18	78	28	,	,	PUNCT
gsrj-18	78	29	yielding	yield	VERB
gsrj-18	78	30	"	"	PUNCT
gsrj-18	78	31	mod	mod	ADJ
gsrj-18	78	32	143	143	NUM
gsrj-18	78	33	=	=	SYM
gsrj-18	78	34	24	24	NUM
gsrj-18	78	35	,	,	PUNCT
gsrj-18	78	36	and	and	CCONJ
gsrj-18	78	37	subsequently	subsequently	ADV
gsrj-18	78	38	solve	solve	VERB
gsrj-18	78	39	for	for	ADP
gsrj-18	78	40	d.	d.	PROPN
gsrj-18	78	41	knowing	know	VERB
gsrj-18	78	42	that	that	SCONJ
gsrj-18	78	43	"	"	PUNCT
gsrj-18	78	44	must	must	AUX
gsrj-18	78	45	equal	equal	VERB
gsrj-18	78	46	to	to	ADP
gsrj-18	78	47	143	143	NUM
gsrj-18	78	48	+	+	NUM
gsrj-18	78	49	24	24	NUM
gsrj-18	78	50	,	,	PUNCT
gsrj-18	78	51	or	or	CCONJ
gsrj-18	78	52	167	167	NUM
gsrj-18	78	53	,	,	PUNCT
gsrj-18	78	54	for	for	SCONJ
gsrj-18	78	55	the	the	DET
gsrj-18	78	56	above	above	ADJ
gsrj-18	78	57	equation	equation	NOUN
gsrj-18	78	58	to	to	PART
gsrj-18	78	59	work	work	VERB
gsrj-18	78	60	due	due	ADP
gsrj-18	78	61	to	to	ADP
gsrj-18	78	62	modular	modular	ADJ
gsrj-18	78	63	arithmetic	arithmetic	ADJ
gsrj-18	78	64	(	(	PUNCT
gsrj-18	78	65	167	167	NUM
gsrj-18	78	66	mod	mod	NOUN
gsrj-18	79	1	143	143	NUM
gsrj-18	79	2	=	=	SYM
gsrj-18	79	3	24	24	NUM
gsrj-18	79	4	)	)	PUNCT
gsrj-18	80	1	,	,	PUNCT
gsrj-18	80	2	the	the	DET
gsrj-18	80	3	message	message	NOUN
gsrj-18	80	4	-	-	PUNCT
gsrj-18	80	5	interceptor	interceptor	NOUN
gsrj-18	80	6	can	can	AUX
gsrj-18	80	7	set	set	VERB
gsrj-18	80	8	"	"	PUNCT
gsrj-18	80	9	to	to	ADP
gsrj-18	80	10	167	167	NUM
gsrj-18	80	11	.	.	PUNCT
gsrj-18	81	1	knowing	know	VERB
gsrj-18	81	2	that	that	SCONJ
gsrj-18	81	3	"	"	PUNCT
gsrj-18	81	4	=	=	SYM
gsrj-18	81	5	167	167	NUM
gsrj-18	81	6	,	,	PUNCT
gsrj-18	81	7	the	the	DET
gsrj-18	81	8	message	message	NOUN
gsrj-18	81	9	-	-	PUNCT
gsrj-18	81	10	interceptor	interceptor	NOUN
gsrj-18	81	11	can	can	AUX
gsrj-18	81	12	easily	easily	ADV
gsrj-18	81	13	solve	solve	VERB
gsrj-18	81	14	for	for	ADP
gsrj-18	81	15	d	d	NOUN
gsrj-18	81	16	using	use	VERB
gsrj-18	81	17	the	the	DET
gsrj-18	81	18	properties	property	NOUN
gsrj-18	81	19	of	of	ADP
gsrj-18	81	20	logarithms	logarithm	NOUN
gsrj-18	81	21	:	:	PUNCT
gsrj-18	81	22	"	"	PUNCT
gsrj-18	81	23	=	=	SYM
gsrj-18	81	24	167	167	NUM
gsrj-18	81	25	log	log	NOUN
gsrj-18	81	26	"	"	PUNCT
gsrj-18	81	27	=	=	SYM
gsrj-18	81	28	log	log	VERB
gsrj-18	81	29	167	167	NUM
gsrj-18	81	30	d	d	NOUN
gsrj-18	81	31	(	(	PUNCT
gsrj-18	81	32	log	log	NOUN
gsrj-18	81	33	106	106	NUM
gsrj-18	81	34	)	)	PUNCT
gsrj-18	82	1	=	=	PRON
gsrj-18	82	2	log	log	VERB
gsrj-18	82	3	167	167	NUM
gsrj-18	82	4	d	d	NOUN
gsrj-18	82	5	=	=	PRON
gsrj-18	82	6	log	log	NOUN
gsrj-18	82	7	167	167	NUM
gsrj-18	82	8	/	/	SYM
gsrj-18	82	9	log	log	NOUN
gsrj-18	82	10	106	106	NUM
gsrj-18	82	11	d	d	NOUN
gsrj-18	82	12	=	=	SYM
gsrj-18	82	13	1.09747	1.09747	NUM
gsrj-18	82	14	.	.	PUNCT
gsrj-18	82	15	.	.	PUNCT
gsrj-18	83	1	.	.	PUNCT
gsrj-18	84	1	10	10	NUM
gsrj-18	85	1	i	i	PRON
gsrj-18	85	2	i	i	PRON
gsrj-18	86	1	i	i	PRON
gsrj-18	86	2	i	i	PRON
gsrj-18	87	1	i	i	PRON
gsrj-18	87	2	i	i	PRON
gsrj-18	88	1	i	i	PRON
gsrj-18	89	1	i	i	PRON
gsrj-18	89	2	georgetown	georgetown	VERB
gsrj-18	89	3	scientific	scientific	ADJ
gsrj-18	89	4	research	research	PROPN
gsrj-18	89	5	journal	journal	PROPN
gsrj-18	89	6	however	however	ADV
gsrj-18	89	7	,	,	PUNCT
gsrj-18	89	8	d	d	PROPN
gsrj-18	89	9	has	have	VERB
gsrj-18	89	10	the	the	DET
gsrj-18	89	11	restriction	restriction	NOUN
gsrj-18	89	12	that	that	SCONJ
gsrj-18	89	13	it	it	PRON
gsrj-18	89	14	must	must	AUX
gsrj-18	89	15	be	be	AUX
gsrj-18	89	16	an	an	DET
gsrj-18	89	17	integer	integer	NOUN
gsrj-18	89	18	value	value	NOUN
gsrj-18	89	19	,	,	PUNCT
gsrj-18	89	20	which	which	PRON
gsrj-18	89	21	the	the	DET
gsrj-18	89	22	above	above	ADJ
gsrj-18	89	23	value	value	NOUN
gsrj-18	89	24	is	be	AUX
gsrj-18	89	25	not	not	PART
gsrj-18	89	26	.	.	PUNCT
gsrj-18	90	1	thus	thus	ADV
gsrj-18	90	2	,	,	PUNCT
gsrj-18	90	3	the	the	DET
gsrj-18	90	4	message	message	NOUN
gsrj-18	90	5	-	-	PUNCT
gsrj-18	90	6	interceptor	interceptor	NOUN
gsrj-18	90	7	needs	need	NOUN
gsrj-18	90	8	to	to	PART
gsrj-18	90	9	come	come	VERB
gsrj-18	90	10	up	up	ADP
gsrj-18	90	11	with	with	ADP
gsrj-18	90	12	another	another	DET
gsrj-18	90	13	way	way	NOUN
gsrj-18	90	14	to	to	PART
gsrj-18	90	15	calculate	calculate	VERB
gsrj-18	90	16	d	d	NOUN
gsrj-18	90	17	using	use	VERB
gsrj-18	90	18	this	this	DET
gsrj-18	90	19	method	method	NOUN
gsrj-18	90	20	.	.	PUNCT
gsrj-18	91	1	the	the	DET
gsrj-18	91	2	message	message	NOUN
gsrj-18	91	3	-	-	PUNCT
gsrj-18	91	4	interceptor	interceptor	NOUN
gsrj-18	91	5	knows	know	VERB
gsrj-18	91	6	that	that	SCONJ
gsrj-18	91	7	167	167	NUM
gsrj-18	91	8	mod	mod	NOUN
gsrj-18	91	9	143	143	NUM
gsrj-18	91	10	=	=	SYM
gsrj-18	91	11	24	24	NUM
gsrj-18	91	12	,	,	PUNCT
gsrj-18	91	13	but	but	CCONJ
gsrj-18	91	14	there	there	PRON
gsrj-18	91	15	are	be	VERB
gsrj-18	91	16	other	other	ADJ
gsrj-18	91	17	values	value	NOUN
gsrj-18	91	18	that	that	PRON
gsrj-18	91	19	,	,	PUNCT
gsrj-18	91	20	when	when	SCONJ
gsrj-18	91	21	divided	divide	VERB
gsrj-18	91	22	by	by	ADP
gsrj-18	91	23	each	each	DET
gsrj-18	91	24	other	other	ADJ
gsrj-18	91	25	,	,	PUNCT
gsrj-18	91	26	will	will	AUX
gsrj-18	91	27	yield	yield	VERB
gsrj-18	91	28	a	a	DET
gsrj-18	91	29	remainder	remainder	NOUN
gsrj-18	91	30	of	of	ADP
gsrj-18	91	31	24	24	NUM
gsrj-18	91	32	.	.	PUNCT
gsrj-18	92	1	143	143	NUM
gsrj-18	92	2	multiplied	multiply	VERB
gsrj-18	92	3	by	by	ADP
gsrj-18	92	4	2	2	NUM
gsrj-18	92	5	is	be	AUX
gsrj-18	92	6	286	286	NUM
gsrj-18	92	7	.	.	PUNCT
gsrj-18	93	1	286	286	NUM
gsrj-18	93	2	plus	plus	CCONJ
gsrj-18	93	3	24	24	NUM
gsrj-18	93	4	is	be	AUX
gsrj-18	93	5	310	310	NUM
gsrj-18	93	6	.	.	PUNCT
gsrj-18	94	1	thus	thus	ADV
gsrj-18	94	2	,	,	PUNCT
gsrj-18	94	3	310	310	NUM
gsrj-18	94	4	mod	mod	ADJ
gsrj-18	94	5	286	286	NUM
gsrj-18	94	6	=	=	SYM
gsrj-18	94	7	24	24	NUM
gsrj-18	94	8	.	.	PUNCT
gsrj-18	95	1	similarly	similarly	ADV
gsrj-18	95	2	,	,	PUNCT
gsrj-18	95	3	143	143	NUM
gsrj-18	95	4	multiplied	multiply	VERB
gsrj-18	95	5	by	by	ADP
gsrj-18	95	6	3	3	NUM
gsrj-18	95	7	is	be	AUX
gsrj-18	95	8	429	429	NUM
gsrj-18	95	9	.	.	PUNCT
gsrj-18	96	1	429	429	NUM
gsrj-18	96	2	plus	plus	CCONJ
gsrj-18	96	3	24	24	NUM
gsrj-18	96	4	is	be	AUX
gsrj-18	96	5	453	453	NUM
gsrj-18	96	6	.	.	PUNCT
gsrj-18	97	1	thus	thus	ADV
gsrj-18	97	2	,	,	PUNCT
gsrj-18	97	3	453	453	NUM
gsrj-18	97	4	mod	mod	NOUN
gsrj-18	97	5	429	429	NUM
gsrj-18	97	6	=	=	SYM
gsrj-18	97	7	24	24	NUM
gsrj-18	97	8	.	.	PUNCT
gsrj-18	98	1	the	the	DET
gsrj-18	98	2	message	message	NOUN
gsrj-18	98	3	-	-	PUNCT
gsrj-18	98	4	interceptor	interceptor	NOUN
gsrj-18	98	5	can	can	AUX
gsrj-18	98	6	keep	keep	VERB
gsrj-18	98	7	on	on	ADP
gsrj-18	98	8	multiplying	multiply	VERB
gsrj-18	98	9	the	the	DET
gsrj-18	98	10	value	value	NOUN
gsrj-18	98	11	of	of	ADP
gsrj-18	98	12	143	143	NUM
gsrj-18	98	13	by	by	ADP
gsrj-18	98	14	increasing	increase	VERB
gsrj-18	98	15	integers	integer	NOUN
gsrj-18	98	16	to	to	PART
gsrj-18	98	17	achieve	achieve	VERB
gsrj-18	98	18	different	different	ADJ
gsrj-18	98	19	modular	modular	ADJ
gsrj-18	98	20	relationships	relationship	NOUN
gsrj-18	98	21	that	that	PRON
gsrj-18	98	22	will	will	AUX
gsrj-18	98	23	still	still	ADV
gsrj-18	98	24	yield	yield	VERB
gsrj-18	98	25	24	24	NUM
gsrj-18	98	26	as	as	ADP
gsrj-18	98	27	a	a	DET
gsrj-18	98	28	remainder	remainder	NOUN
gsrj-18	98	29	until	until	SCONJ
gsrj-18	98	30	d	d	PROPN
gsrj-18	98	31	is	be	AUX
gsrj-18	98	32	an	an	DET
gsrj-18	98	33	integer	integer	NOUN
gsrj-18	98	34	value	value	NOUN
gsrj-18	98	35	.	.	PUNCT
gsrj-18	99	1	example	example	NOUN
gsrj-18	99	2	:	:	PUNCT
gsrj-18	99	3	"	"	PUNCT
gsrj-18	99	4	mod	mod	X
gsrj-18	99	5	(	(	PUNCT
gsrj-18	99	6	143	143	NUM
gsrj-18	99	7	*	*	NUM
gsrj-18	99	8	1	1	NUM
gsrj-18	99	9	)	)	PUNCT
gsrj-18	99	10	=	=	SYM
gsrj-18	99	11	24	24	NUM
gsrj-18	99	12	;	;	PUNCT
gsrj-18	99	13	"	"	PUNCT
gsrj-18	99	14	=	=	SYM
gsrj-18	99	15	(	(	PUNCT
gsrj-18	99	16	143	143	NUM
gsrj-18	99	17	*	*	NUM
gsrj-18	99	18	1	1	NUM
gsrj-18	99	19	)	)	PUNCT
gsrj-18	99	20	+	+	CCONJ
gsrj-18	99	21	24	24	NUM
gsrj-18	99	22	;	;	PUNCT
gsrj-18	99	23	log	log	NOUN
gsrj-18	99	24	(	(	PUNCT
gsrj-18	99	25	"	"	PUNCT
gsrj-18	99	26	=	=	SYM
gsrj-18	99	27	log(143	log(143	PROPN
gsrj-18	99	28	*	*	PROPN
gsrj-18	99	29	1	1	NUM
gsrj-18	99	30	+24	+24	NUM
gsrj-18	99	31	)	)	PUNCT
gsrj-18	99	32	;	;	PUNCT
gsrj-18	100	1	d	d	X
gsrj-18	100	2	=	=	SYM
gsrj-18	100	3	log(143	log(143	PROPN
gsrj-18	100	4	*	*	PROPN
gsrj-18	100	5	1	1	PROPN
gsrj-18	100	6	+	+	NUM
gsrj-18	100	7	24)/log(106	24)/log(106	NUM
gsrj-18	100	8	)	)	PUNCT
gsrj-18	100	9	;	;	PUNCT
gsrj-18	100	10	d	d	X
gsrj-18	100	11	=	=	PUNCT
gsrj-18	100	12	decimal	decimal	ADJ
gsrj-18	100	13	"	"	PUNCT
gsrj-18	100	14	mod	mod	NOUN
gsrj-18	100	15	(	(	PUNCT
gsrj-18	100	16	143	143	NUM
gsrj-18	100	17	*	*	SYM
gsrj-18	100	18	2	2	NUM
gsrj-18	100	19	)	)	PUNCT
gsrj-18	100	20	=	=	SYM
gsrj-18	100	21	24	24	NUM
gsrj-18	100	22	;	;	PUNCT
gsrj-18	100	23	"	"	PUNCT
gsrj-18	100	24	=	=	SYM
gsrj-18	100	25	(	(	PUNCT
gsrj-18	100	26	143	143	NUM
gsrj-18	100	27	*	*	SYM
gsrj-18	100	28	2	2	NUM
gsrj-18	100	29	)	)	PUNCT
gsrj-18	100	30	+	+	CCONJ
gsrj-18	100	31	24	24	NUM
gsrj-18	100	32	;	;	PUNCT
gsrj-18	100	33	log	log	NOUN
gsrj-18	100	34	(	(	PUNCT
gsrj-18	100	35	"	"	PUNCT
gsrj-18	100	36	=	=	SYM
gsrj-18	100	37	log(143	log(143	PROPN
gsrj-18	100	38	*	*	PROPN
gsrj-18	100	39	2	2	NUM
gsrj-18	100	40	+24	+24	NUM
gsrj-18	100	41	)	)	PUNCT
gsrj-18	100	42	;	;	PUNCT
gsrj-18	100	43	d	d	X
gsrj-18	100	44	=	=	SYM
gsrj-18	100	45	log(143	log(143	PROPN
gsrj-18	100	46	*	*	PROPN
gsrj-18	100	47	2	2	NUM
gsrj-18	100	48	+	+	NUM
gsrj-18	100	49	24)/log(106	24)/log(106	NUM
gsrj-18	100	50	)	)	PUNCT
gsrj-18	100	51	;	;	PUNCT
gsrj-18	100	52	d	d	X
gsrj-18	100	53	=	=	PUNCT
gsrj-18	100	54	decimal	decimal	ADJ
gsrj-18	100	55	"	"	PUNCT
gsrj-18	100	56	mod	mod	NOUN
gsrj-18	100	57	(	(	PUNCT
gsrj-18	100	58	143	143	NUM
gsrj-18	100	59	*	*	SYM
gsrj-18	100	60	3	3	NUM
gsrj-18	100	61	)	)	PUNCT
gsrj-18	100	62	=	=	SYM
gsrj-18	100	63	24	24	NUM
gsrj-18	100	64	;	;	PUNCT
gsrj-18	100	65	"	"	PUNCT
gsrj-18	100	66	=	=	SYM
gsrj-18	100	67	(	(	PUNCT
gsrj-18	100	68	143	143	NUM
gsrj-18	100	69	*	*	SYM
gsrj-18	100	70	3	3	NUM
gsrj-18	100	71	)	)	PUNCT
gsrj-18	100	72	+	+	CCONJ
gsrj-18	100	73	24	24	NUM
gsrj-18	100	74	;	;	PUNCT
gsrj-18	100	75	log	log	NOUN
gsrj-18	100	76	(	(	PUNCT
gsrj-18	100	77	"	"	PUNCT
gsrj-18	100	78	=	=	SYM
gsrj-18	100	79	log(143	log(143	PROPN
gsrj-18	100	80	*	*	PROPN
gsrj-18	100	81	3	3	NUM
gsrj-18	100	82	+24	+24	NUM
gsrj-18	100	83	)	)	PUNCT
gsrj-18	100	84	;	;	PUNCT
gsrj-18	100	85	d	d	X
gsrj-18	100	86	=	=	SYM
gsrj-18	100	87	log(143	log(143	PROPN
gsrj-18	100	88	*	*	PROPN
gsrj-18	100	89	3	3	NUM
gsrj-18	100	90	+	+	SYM
gsrj-18	100	91	24)/log(106	24)/log(106	NUM
gsrj-18	100	92	)	)	PUNCT
gsrj-18	100	93	;	;	PUNCT
gsrj-18	100	94	d	d	X
gsrj-18	100	95	=	=	PRON
gsrj-18	100	96	decimal	decimal	VERB
gsrj-18	100	97	the	the	DET
gsrj-18	100	98	formula	formula	NOUN
gsrj-18	100	99	for	for	ADP
gsrj-18	100	100	solving	solve	VERB
gsrj-18	100	101	for	for	ADP
gsrj-18	100	102	d	d	PROPN
gsrj-18	100	103	in	in	ADP
gsrj-18	100	104	this	this	DET
gsrj-18	100	105	way	way	NOUN
gsrj-18	100	106	can	can	AUX
gsrj-18	100	107	be	be	AUX
gsrj-18	100	108	simplified	simplify	VERB
gsrj-18	100	109	to	to	ADP
gsrj-18	100	110	:	:	PUNCT
gsrj-18	100	111	d	d	X
gsrj-18	100	112	=	=	SYM
gsrj-18	100	113	log(n*nmultiplier	log(n*nmultipli	ADJ
gsrj-18	100	114	+	+	NOUN
gsrj-18	100	115	m)/log(c	m)/log(c	NOUN
gsrj-18	100	116	)	)	PUNCT
gsrj-18	100	117	(	(	PUNCT
gsrj-18	100	118	equation	equation	NOUN
gsrj-18	100	119	6	6	NUM
gsrj-18	100	120	)	)	PUNCT
gsrj-18	100	121	where	where	SCONJ
gsrj-18	100	122	“	"	PUNCT
gsrj-18	100	123	nmultiplier	nmultiplier	NOUN
gsrj-18	100	124	”	"	PUNCT
gsrj-18	100	125	is	be	AUX
gsrj-18	100	126	the	the	DET
gsrj-18	100	127	increasing	increase	VERB
gsrj-18	100	128	integer	integer	NOUN
gsrj-18	100	129	by	by	ADP
gsrj-18	100	130	which	which	PRON
gsrj-18	100	131	the	the	DET
gsrj-18	100	132	message	message	NOUN
gsrj-18	100	133	-	-	PUNCT
gsrj-18	100	134	interceptor	interceptor	NOUN
gsrj-18	100	135	multiplies	multiplie	NOUN
gsrj-18	100	136	n	n	PART
gsrj-18	100	137	to	to	PART
gsrj-18	100	138	achieve	achieve	VERB
gsrj-18	100	139	different	different	ADJ
gsrj-18	100	140	modular	modular	ADJ
gsrj-18	100	141	relationships	relationship	NOUN
gsrj-18	100	142	that	that	PRON
gsrj-18	100	143	will	will	AUX
gsrj-18	100	144	still	still	ADV
gsrj-18	100	145	yield	yield	VERB
gsrj-18	100	146	the	the	DET
gsrj-18	100	147	secret	secret	ADJ
gsrj-18	100	148	message	message	NOUN
gsrj-18	100	149	,	,	PUNCT
gsrj-18	100	150	m.	m.	NOUN
gsrj-18	100	151	even	even	ADV
gsrj-18	100	152	though	though	SCONJ
gsrj-18	100	153	the	the	DET
gsrj-18	100	154	message	message	NOUN
gsrj-18	100	155	-	-	PUNCT
gsrj-18	100	156	interceptor	interceptor	NOUN
gsrj-18	100	157	can	can	AUX
gsrj-18	100	158	keep	keep	VERB
gsrj-18	100	159	on	on	ADP
gsrj-18	100	160	running	run	VERB
gsrj-18	100	161	this	this	DET
gsrj-18	100	162	type	type	NOUN
gsrj-18	100	163	of	of	ADP
gsrj-18	100	164	sequence	sequence	NOUN
gsrj-18	100	165	to	to	PART
gsrj-18	100	166	achieve	achieve	VERB
gsrj-18	100	167	an	an	DET
gsrj-18	100	168	integer	integer	NOUN
gsrj-18	100	169	value	value	NOUN
gsrj-18	100	170	for	for	ADP
gsrj-18	100	171	d	d	PROPN
gsrj-18	100	172	,	,	PUNCT
gsrj-18	100	173	the	the	DET
gsrj-18	100	174	amount	amount	NOUN
gsrj-18	100	175	of	of	ADP
gsrj-18	100	176	iterations	iteration	NOUN
gsrj-18	100	177	it	it	PRON
gsrj-18	100	178	would	would	AUX
gsrj-18	100	179	take	take	VERB
gsrj-18	100	180	to	to	PART
gsrj-18	100	181	finally	finally	ADV
gsrj-18	100	182	attain	attain	VERB
gsrj-18	100	183	an	an	DET
gsrj-18	100	184	integer	integer	NOUN
gsrj-18	100	185	value	value	NOUN
gsrj-18	100	186	for	for	ADP
gsrj-18	100	187	d	d	PROPN
gsrj-18	100	188	is	be	AUX
gsrj-18	100	189	astronomical	astronomical	ADJ
gsrj-18	100	190	,	,	PUNCT
gsrj-18	100	191	making	make	VERB
gsrj-18	100	192	the	the	DET
gsrj-18	100	193	logarithmic	logarithmic	ADJ
gsrj-18	100	194	decryption	decryption	NOUN
gsrj-18	100	195	key	key	NOUN
gsrj-18	100	196	calculations	calculation	NOUN
gsrj-18	100	197	just	just	ADV
gsrj-18	100	198	as	as	ADP
gsrj-18	100	199	impractical	impractical	ADJ
gsrj-18	100	200	and	and	CCONJ
gsrj-18	100	201	time	time	NOUN
gsrj-18	100	202	-	-	PUNCT
gsrj-18	100	203	consuming	consume	VERB
gsrj-18	100	204	as	as	ADP
gsrj-18	100	205	semi	semi	ADJ
gsrj-18	100	206	-	-	ADJ
gsrj-18	100	207	prime	prime	ADJ
gsrj-18	100	208	factorization	factorization	NOUN
gsrj-18	100	209	.	.	PUNCT
gsrj-18	101	1	the	the	DET
gsrj-18	101	2	difficulty	difficulty	NOUN
gsrj-18	101	3	of	of	ADP
gsrj-18	101	4	calculating	calculate	VERB
gsrj-18	101	5	the	the	DET
gsrj-18	101	6	exponent	exponent	NOUN
gsrj-18	101	7	d	d	NOUN
gsrj-18	101	8	in	in	ADP
gsrj-18	101	9	this	this	DET
gsrj-18	101	10	way	way	NOUN
gsrj-18	101	11	is	be	AUX
gsrj-18	101	12	known	know	VERB
gsrj-18	101	13	as	as	ADP
gsrj-18	101	14	the	the	DET
gsrj-18	101	15	discrete	discrete	ADJ
gsrj-18	101	16	logarithm	logarithm	NOUN
gsrj-18	101	17	problem	problem	NOUN
gsrj-18	101	18	,	,	PUNCT
gsrj-18	101	19	or	or	CCONJ
gsrj-18	101	20	the	the	DET
gsrj-18	101	21	“	"	PUNCT
gsrj-18	101	22	rsa	rsa	PROPN
gsrj-18	101	23	problem	problem	NOUN
gsrj-18	101	24	.	.	PUNCT
gsrj-18	101	25	”	"	PUNCT
gsrj-18	102	1	decryption	decryption	NOUN
gsrj-18	102	2	through	through	ADP
gsrj-18	102	3	semi	semi	ADJ
gsrj-18	102	4	-	-	ADJ
gsrj-18	102	5	prime	prime	ADJ
gsrj-18	102	6	factorization	factorization	NOUN
gsrj-18	102	7	and	and	CCONJ
gsrj-18	102	8	decryption	decryption	NOUN
gsrj-18	102	9	through	through	ADP
gsrj-18	102	10	logarithmic	logarithmic	ADJ
gsrj-18	102	11	properties	property	NOUN
gsrj-18	102	12	are	be	AUX
gsrj-18	102	13	both	both	PRON
gsrj-18	102	14	processes	process	NOUN
gsrj-18	102	15	that	that	PRON
gsrj-18	102	16	are	be	AUX
gsrj-18	102	17	referred	refer	VERB
gsrj-18	102	18	to	to	ADP
gsrj-18	102	19	as	as	SCONJ
gsrj-18	102	20	“	"	PUNCT
gsrj-18	102	21	trapdoor	trapdoor	PROPN
gsrj-18	102	22	one	one	NUM
gsrj-18	102	23	-	-	PUNCT
gsrj-18	102	24	way	way	NOUN
gsrj-18	102	25	functions”.12	functions”.12	PUNCT
gsrj-18	102	26	trapdoor	trapdoor	PROPN
gsrj-18	102	27	one	one	NUM
gsrj-18	102	28	-	-	PUNCT
gsrj-18	102	29	way	way	NOUN
gsrj-18	102	30	functions	function	NOUN
gsrj-18	102	31	are	be	AUX
gsrj-18	102	32	easy	easy	ADJ
gsrj-18	102	33	to	to	PART
gsrj-18	102	34	compute	compute	VERB
gsrj-18	102	35	in	in	ADP
gsrj-18	102	36	one	one	NUM
gsrj-18	102	37	direction	direction	NOUN
gsrj-18	102	38	but	but	CCONJ
gsrj-18	102	39	difficult	difficult	ADJ
gsrj-18	102	40	to	to	PART
gsrj-18	102	41	compute	compute	VERB
gsrj-18	102	42	in	in	ADP
gsrj-18	102	43	the	the	DET
gsrj-18	102	44	other	other	ADJ
gsrj-18	102	45	direction	direction	NOUN
gsrj-18	102	46	unless	unless	SCONJ
gsrj-18	102	47	special	special	ADJ
gsrj-18	102	48	“	"	PUNCT
gsrj-18	102	49	trapdoor	trapdoor	PROPN
gsrj-18	102	50	”	"	PUNCT
gsrj-18	102	51	information	information	NOUN
gsrj-18	102	52	is	be	AUX
gsrj-18	102	53	known	know	VERB
gsrj-18	102	54	.	.	PUNCT
gsrj-18	103	1	in	in	ADP
gsrj-18	103	2	the	the	DET
gsrj-18	103	3	case	case	NOUN
gsrj-18	103	4	of	of	ADP
gsrj-18	103	5	decryption	decryption	NOUN
gsrj-18	103	6	through	through	ADP
gsrj-18	103	7	semi	semi	ADJ
gsrj-18	103	8	-	-	ADJ
gsrj-18	103	9	prime	prime	ADJ
gsrj-18	103	10	factorization	factorization	NOUN
gsrj-18	103	11	,	,	PUNCT
gsrj-18	103	12	rivest	riv	ADJ
gsrj-18	103	13	,	,	PUNCT
gsrj-18	103	14	shamir	shamir	ADJ
gsrj-18	103	15	,	,	PUNCT
gsrj-18	103	16	and	and	CCONJ
gsrj-18	103	17	aldeman	aldeman	NOUN
gsrj-18	103	18	realized	realize	VERB
gsrj-18	103	19	that	that	SCONJ
gsrj-18	103	20	it	it	PRON
gsrj-18	103	21	was	be	AUX
gsrj-18	103	22	trivially	trivially	ADV
gsrj-18	103	23	easy	easy	ADJ
gsrj-18	103	24	to	to	PART
gsrj-18	103	25	multiply	multiply	VERB
gsrj-18	103	26	two	two	NUM
gsrj-18	103	27	large	large	ADJ
gsrj-18	103	28	prime	prime	ADJ
gsrj-18	103	29	numbers	number	NOUN
gsrj-18	103	30	p	p	NOUN
gsrj-18	103	31	and	and	CCONJ
gsrj-18	103	32	q	q	NOUN
gsrj-18	103	33	together	together	ADV
gsrj-18	103	34	yet	yet	ADV
gsrj-18	103	35	infinitely	infinitely	ADV
gsrj-18	103	36	more	more	ADV
gsrj-18	103	37	difficult	difficult	ADJ
gsrj-18	103	38	and	and	CCONJ
gsrj-18	103	39	time	time	NOUN
gsrj-18	103	40	-	-	PUNCT
gsrj-18	103	41	consuming	consume	VERB
gsrj-18	103	42	to	to	PART
gsrj-18	103	43	factor	factor	VERB
gsrj-18	103	44	the	the	DET
gsrj-18	103	45	resulting	result	VERB
gsrj-18	103	46	semi	semi	ADJ
gsrj-18	103	47	-	-	ADJ
gsrj-18	103	48	prime	prime	ADJ
gsrj-18	103	49	number	number	NOUN
gsrj-18	103	50	,	,	PUNCT
gsrj-18	103	51	n.	n.	NOUN
gsrj-18	103	52	similarly	similarly	ADV
gsrj-18	103	53	,	,	PUNCT
gsrj-18	103	54	they	they	PRON
gsrj-18	103	55	realized	realize	VERB
gsrj-18	103	56	that	that	SCONJ
gsrj-18	103	57	it	it	PRON
gsrj-18	103	58	was	be	AUX
gsrj-18	103	59	easy	easy	ADJ
gsrj-18	103	60	to	to	PART
gsrj-18	103	61	calculate	calculate	VERB
gsrj-18	103	62	m	m	PROPN
gsrj-18	103	63	in	in	ADP
gsrj-18	103	64	equation	equation	NOUN
gsrj-18	103	65	4	4	NUM
gsrj-18	103	66	given	give	VERB
gsrj-18	103	67	the	the	DET
gsrj-18	103	68	values	value	NOUN
gsrj-18	103	69	of	of	ADP
gsrj-18	103	70	c	c	NOUN
gsrj-18	103	71	,	,	PUNCT
gsrj-18	103	72	n	n	CCONJ
gsrj-18	103	73	,	,	PUNCT
gsrj-18	103	74	and	and	CCONJ
gsrj-18	103	75	most	most	ADV
gsrj-18	103	76	importantly	importantly	ADV
gsrj-18	103	77	,	,	PUNCT
gsrj-18	104	1	d	d	NOUN
gsrj-18	104	2	,	,	PUNCT
gsrj-18	104	3	but	but	CCONJ
gsrj-18	104	4	far	far	ADV
gsrj-18	104	5	more	more	ADV
gsrj-18	104	6	arduous	arduous	ADJ
gsrj-18	104	7	to	to	PART
gsrj-18	104	8	calculate	calculate	VERB
gsrj-18	104	9	the	the	DET
gsrj-18	104	10	value	value	NOUN
gsrj-18	104	11	of	of	ADP
gsrj-18	104	12	d	d	PROPN
gsrj-18	104	13	in	in	ADP
gsrj-18	104	14	equation	equation	NOUN
gsrj-18	104	15	4	4	NUM
gsrj-18	104	16	given	give	VERB
gsrj-18	104	17	the	the	DET
gsrj-18	104	18	values	value	NOUN
gsrj-18	104	19	of	of	ADP
gsrj-18	104	20	c	c	NOUN
gsrj-18	104	21	,	,	PUNCT
gsrj-18	104	22	n	n	CCONJ
gsrj-18	104	23	,	,	PUNCT
gsrj-18	104	24	and	and	CCONJ
gsrj-18	104	25	m.	m.	NOUN
gsrj-18	104	26	these	these	DET
gsrj-18	104	27	two	two	NUM
gsrj-18	104	28	utilizations	utilization	NOUN
gsrj-18	104	29	of	of	ADP
gsrj-18	104	30	trapdoor	trapdoor	PROPN
gsrj-18	104	31	oneway	oneway	PROPN
gsrj-18	104	32	functions	function	NOUN
gsrj-18	104	33	in	in	ADP
gsrj-18	104	34	rsa	rsa	NOUN
gsrj-18	104	35	encryption	encryption	NOUN
gsrj-18	104	36	are	be	AUX
gsrj-18	104	37	what	what	PRON
gsrj-18	104	38	make	make	VERB
gsrj-18	104	39	it	it	PRON
gsrj-18	104	40	so	so	ADV
gsrj-18	104	41	formidably	formidably	ADV
gsrj-18	104	42	strong	strong	ADJ
gsrj-18	104	43	and	and	CCONJ
gsrj-18	104	44	currently	currently	ADV
gsrj-18	104	45	unbreakable	unbreakable	ADJ
gsrj-18	104	46	without	without	ADP
gsrj-18	104	47	a	a	DET
gsrj-18	104	48	quantum	quantum	ADJ
gsrj-18	104	49	computer.13	computer.13	NOUN
gsrj-18	104	50	in	in	ADP
gsrj-18	104	51	the	the	DET
gsrj-18	104	52	case	case	NOUN
gsrj-18	104	53	of	of	ADP
gsrj-18	104	54	decryption	decryption	NOUN
gsrj-18	104	55	through	through	ADP
gsrj-18	104	56	either	either	DET
gsrj-18	104	57	semiprime	semiprime	NOUN
gsrj-18	104	58	factorization	factorization	NOUN
gsrj-18	104	59	or	or	CCONJ
gsrj-18	104	60	logarithmic	logarithmic	ADJ
gsrj-18	104	61	properties	property	NOUN
gsrj-18	104	62	,	,	PUNCT
gsrj-18	104	63	an	an	DET
gsrj-18	104	64	immense	immense	ADJ
gsrj-18	104	65	number	number	NOUN
gsrj-18	104	66	of	of	ADP
gsrj-18	104	67	iterations	iteration	NOUN
gsrj-18	104	68	are	be	AUX
gsrj-18	104	69	required	require	VERB
gsrj-18	104	70	to	to	PART
gsrj-18	104	71	finally	finally	ADV
gsrj-18	104	72	attain	attain	VERB
gsrj-18	104	73	the	the	DET
gsrj-18	104	74	decryption	decryption	NOUN
gsrj-18	104	75	key	key	NOUN
gsrj-18	104	76	,	,	PUNCT
gsrj-18	104	77	d.	d.	PROPN
gsrj-18	104	78	in	in	ADP
gsrj-18	104	79	the	the	DET
gsrj-18	104	80	case	case	NOUN
gsrj-18	104	81	of	of	ADP
gsrj-18	104	82	semi	semi	ADJ
gsrj-18	104	83	-	-	ADJ
gsrj-18	104	84	prime	prime	ADJ
gsrj-18	104	85	factorization	factorization	NOUN
gsrj-18	104	86	,	,	PUNCT
gsrj-18	104	87	if	if	SCONJ
gsrj-18	104	88	every	every	DET
gsrj-18	104	89	integer	integer	NOUN
gsrj-18	104	90	less	less	ADJ
gsrj-18	104	91	than	than	ADP
gsrj-18	104	92	the	the	DET
gsrj-18	104	93	semi	semi	ADJ
gsrj-18	104	94	-	-	ADJ
gsrj-18	104	95	prime	prime	ADJ
gsrj-18	104	96	number	number	NOUN
gsrj-18	104	97	,	,	PUNCT
gsrj-18	104	98	n	n	CCONJ
gsrj-18	104	99	,	,	PUNCT
gsrj-18	104	100	and	and	CCONJ
gsrj-18	104	101	greater	great	ADJ
gsrj-18	104	102	than	than	ADP
gsrj-18	104	103	or	or	CCONJ
gsrj-18	104	104	equal	equal	ADJ
gsrj-18	104	105	to	to	ADP
gsrj-18	104	106	two	two	NUM
gsrj-18	104	107	was	be	AUX
gsrj-18	104	108	tested	test	VERB
gsrj-18	104	109	to	to	PART
gsrj-18	104	110	see	see	VERB
gsrj-18	104	111	if	if	SCONJ
gsrj-18	104	112	it	it	PRON
gsrj-18	104	113	divided	divide	VERB
gsrj-18	104	114	evenly	evenly	ADV
gsrj-18	104	115	into	into	ADP
gsrj-18	104	116	n	n	CCONJ
gsrj-18	104	117	,	,	PUNCT
gsrj-18	104	118	the	the	DET
gsrj-18	104	119	number	number	NOUN
gsrj-18	104	120	of	of	ADP
gsrj-18	104	121	iterations	iteration	NOUN
gsrj-18	104	122	required	require	VERB
gsrj-18	104	123	would	would	AUX
gsrj-18	104	124	be	be	AUX
gsrj-18	104	125	n	n	PRON
gsrj-18	104	126	–	–	PUNCT
gsrj-18	104	127	2	2	X
gsrj-18	104	128	.	.	X
gsrj-18	105	1	if	if	SCONJ
gsrj-18	105	2	n	n	PRON
gsrj-18	105	3	is	be	AUX
gsrj-18	105	4	a	a	DET
gsrj-18	105	5	huge	huge	ADJ
gsrj-18	105	6	semi	semi	ADJ
gsrj-18	105	7	-	-	ADJ
gsrj-18	105	8	prime	prime	ADJ
gsrj-18	105	9	number	number	NOUN
gsrj-18	105	10	that	that	PRON
gsrj-18	105	11	is	be	AUX
gsrj-18	105	12	hundreds	hundred	NOUN
gsrj-18	105	13	of	of	ADP
gsrj-18	105	14	digits	digit	NOUN
gsrj-18	105	15	long	long	ADV
gsrj-18	105	16	,	,	PUNCT
gsrj-18	105	17	the	the	DET
gsrj-18	105	18	number	number	NOUN
gsrj-18	105	19	of	of	ADP
gsrj-18	105	20	iterations	iteration	NOUN
gsrj-18	105	21	required	require	VERB
gsrj-18	105	22	to	to	PART
gsrj-18	105	23	factor	factor	NOUN
gsrj-18	105	24	n	n	PRON
gsrj-18	105	25	would	would	AUX
gsrj-18	105	26	be	be	AUX
gsrj-18	105	27	two	two	NUM
gsrj-18	105	28	subtracted	subtract	VERB
gsrj-18	105	29	from	from	ADP
gsrj-18	105	30	the	the	DET
gsrj-18	105	31	huge	huge	ADJ
gsrj-18	105	32	semi	semi	ADJ
gsrj-18	105	33	-	-	ADJ
gsrj-18	105	34	prime	prime	ADJ
gsrj-18	105	35	number	number	NOUN
gsrj-18	105	36	.	.	PUNCT
gsrj-18	106	1	while	while	SCONJ
gsrj-18	106	2	it	it	PRON
gsrj-18	106	3	is	be	AUX
gsrj-18	106	4	true	true	ADJ
gsrj-18	106	5	that	that	SCONJ
gsrj-18	106	6	not	not	PART
gsrj-18	106	7	all	all	DET
gsrj-18	106	8	the	the	DET
gsrj-18	106	9	numbers	number	NOUN
gsrj-18	106	10	less	less	ADJ
gsrj-18	106	11	than	than	ADP
gsrj-18	106	12	n	n	PRON
gsrj-18	106	13	would	would	AUX
gsrj-18	106	14	have	have	VERB
gsrj-18	106	15	to	to	PART
gsrj-18	106	16	be	be	AUX
gsrj-18	106	17	assessed	assess	VERB
gsrj-18	106	18	if	if	SCONJ
gsrj-18	106	19	it	it	PRON
gsrj-18	106	20	was	be	AUX
gsrj-18	106	21	certain	certain	ADJ
gsrj-18	106	22	that	that	SCONJ
gsrj-18	106	23	n	n	NOUN
gsrj-18	106	24	was	be	AUX
gsrj-18	106	25	semi	semi	ADJ
gsrj-18	106	26	-	-	ADJ
gsrj-18	106	27	prime	prime	ADJ
gsrj-18	106	28	(	(	PUNCT
gsrj-18	106	29	because	because	SCONJ
gsrj-18	106	30	this	this	PRON
gsrj-18	106	31	would	would	AUX
gsrj-18	106	32	narrow	narrow	VERB
gsrj-18	106	33	the	the	DET
gsrj-18	106	34	numbers	number	NOUN
gsrj-18	106	35	that	that	PRON
gsrj-18	106	36	needed	need	VERB
gsrj-18	106	37	to	to	PART
gsrj-18	106	38	be	be	AUX
gsrj-18	106	39	tested	test	VERB
gsrj-18	106	40	down	down	ADP
gsrj-18	106	41	to	to	ADP
gsrj-18	106	42	only	only	ADJ
gsrj-18	106	43	prime	prime	ADJ
gsrj-18	106	44	numbers	number	NOUN
gsrj-18	106	45	)	)	PUNCT
gsrj-18	106	46	,	,	PUNCT
gsrj-18	106	47	if	if	SCONJ
gsrj-18	106	48	access	access	NOUN
gsrj-18	106	49	to	to	ADP
gsrj-18	106	50	a	a	DET
gsrj-18	106	51	large	large	ADJ
gsrj-18	106	52	bank	bank	NOUN
gsrj-18	106	53	of	of	ADP
gsrj-18	106	54	prime	prime	ADJ
gsrj-18	106	55	numbers	number	NOUN
gsrj-18	106	56	is	be	AUX
gsrj-18	106	57	not	not	PART
gsrj-18	106	58	unattainable	unattainable	ADJ
gsrj-18	106	59	(	(	PUNCT
gsrj-18	106	60	as	as	ADP
gsrj-18	106	61	in	in	ADP
gsrj-18	106	62	this	this	DET
gsrj-18	106	63	project	project	NOUN
gsrj-18	106	64	)	)	PUNCT
gsrj-18	106	65	,	,	PUNCT
gsrj-18	106	66	all	all	PRON
gsrj-18	106	67	integers	integer	NOUN
gsrj-18	106	68	greater	great	ADJ
gsrj-18	106	69	than	than	ADP
gsrj-18	106	70	or	or	CCONJ
gsrj-18	106	71	equal	equal	ADJ
gsrj-18	106	72	to	to	ADP
gsrj-18	106	73	two	two	NUM
gsrj-18	106	74	and	and	CCONJ
gsrj-18	106	75	less	less	ADJ
gsrj-18	106	76	than	than	ADP
gsrj-18	106	77	n	n	PRON
gsrj-18	106	78	would	would	AUX
gsrj-18	106	79	still	still	ADV
gsrj-18	106	80	have	have	VERB
gsrj-18	106	81	to	to	PART
gsrj-18	106	82	be	be	AUX
gsrj-18	106	83	tested	test	VERB
gsrj-18	106	84	to	to	PART
gsrj-18	106	85	see	see	VERB
gsrj-18	106	86	if	if	SCONJ
gsrj-18	106	87	they	they	PRON
gsrj-18	106	88	divide	divide	VERB
gsrj-18	106	89	evenly	evenly	ADV
gsrj-18	106	90	into	into	ADP
gsrj-18	106	91	n	n	CCONJ
gsrj-18	106	92	,	,	PUNCT
gsrj-18	106	93	making	make	VERB
gsrj-18	106	94	the	the	DET
gsrj-18	106	95	expression	expression	NOUN
gsrj-18	106	96	for	for	ADP
gsrj-18	106	97	the	the	DET
gsrj-18	106	98	amount	amount	NOUN
gsrj-18	106	99	of	of	ADP
gsrj-18	106	100	iterations	iteration	NOUN
gsrj-18	106	101	needed	need	VERB
gsrj-18	106	102	to	to	PART
gsrj-18	106	103	factor	factor	VERB
gsrj-18	106	104	n	n	NOUN
gsrj-18	106	105	in	in	ADP
gsrj-18	106	106	this	this	DET
gsrj-18	106	107	project	project	NOUN
gsrj-18	106	108	n	n	CCONJ
gsrj-18	106	109	–	–	PUNCT
gsrj-18	106	110	2	2	X
gsrj-18	106	111	.	.	X
gsrj-18	107	1	in	in	ADP
gsrj-18	107	2	the	the	DET
gsrj-18	107	3	algorithm	algorithm	NOUN
gsrj-18	107	4	presented	present	VERB
gsrj-18	107	5	for	for	ADP
gsrj-18	107	6	factoring	factor	VERB
gsrj-18	107	7	n	n	CCONJ
gsrj-18	107	8	in	in	ADP
gsrj-18	107	9	this	this	DET
gsrj-18	107	10	manner	manner	NOUN
gsrj-18	107	11	,	,	PUNCT
gsrj-18	107	12	time	time	NOUN
gsrj-18	107	13	complexity	complexity	NOUN
gsrj-18	107	14	is	be	AUX
gsrj-18	107	15	o(n	o(n	NUM
gsrj-18	107	16	)	)	PUNCT
gsrj-18	107	17	.	.	PUNCT
gsrj-18	108	1	in	in	ADP
gsrj-18	108	2	the	the	DET
gsrj-18	108	3	case	case	NOUN
gsrj-18	108	4	of	of	ADP
gsrj-18	108	5	decryption	decryption	NOUN
gsrj-18	108	6	through	through	ADP
gsrj-18	108	7	logarithmic	logarithmic	ADJ
gsrj-18	108	8	properties	property	NOUN
gsrj-18	108	9	,	,	PUNCT
gsrj-18	108	10	(	(	PUNCT
gsrj-18	108	11	"	"	PUNCT
gsrj-18	108	12	#	#	SYM
gsrj-18	108	13	$	$	SYM
gsrj-18	108	14	%	%	NOUN
gsrj-18	108	15	)	)	PUNCT
gsrj-18	108	16	∗	∗	NOUN
gsrj-18	108	17	(	(	PUNCT
gsrj-18	108	18	iterations	iteration	NOUN
gsrj-18	108	19	are	be	AUX
gsrj-18	108	20	required	require	VERB
gsrj-18	108	21	to	to	PART
gsrj-18	108	22	acquire	acquire	VERB
gsrj-18	108	23	d.	d.	PROPN
gsrj-18	108	24	because	because	SCONJ
gsrj-18	108	25	the	the	DET
gsrj-18	108	26	formula	formula	NOUN
gsrj-18	108	27	for	for	ADP
gsrj-18	108	28	solving	solve	VERB
gsrj-18	108	29	for	for	ADP
gsrj-18	108	30	d	d	PROPN
gsrj-18	108	31	through	through	ADP
gsrj-18	108	32	11	11	NUM
gsrj-18	108	33	i	i	PRON
gsrj-18	109	1	i	i	PRON
gsrj-18	109	2	i	i	PRON
gsrj-18	110	1	i	i	PRON
gsrj-18	110	2	i	i	PRON
gsrj-18	111	1	i	i	PRON
gsrj-18	111	2	i	i	PRON
gsrj-18	112	1	i	i	PRON
gsrj-18	112	2	i	i	PRON
gsrj-18	113	1	i	i	PRON
gsrj-18	113	2	i	i	PRON
gsrj-18	114	1	i	i	PRON
gsrj-18	114	2	georgetown	georgetown	VERB
gsrj-18	114	3	scientific	scientific	ADJ
gsrj-18	114	4	research	research	NOUN
gsrj-18	114	5	journal	journal	NOUN
gsrj-18	114	6	logarithmic	logarithmic	ADJ
gsrj-18	114	7	techniques	technique	NOUN
gsrj-18	114	8	can	can	AUX
gsrj-18	114	9	be	be	AUX
gsrj-18	114	10	simplified	simplify	VERB
gsrj-18	114	11	to	to	ADP
gsrj-18	114	12	equation	equation	NOUN
gsrj-18	114	13	6	6	NUM
gsrj-18	114	14	,	,	PUNCT
gsrj-18	114	15	where	where	SCONJ
gsrj-18	114	16	“	"	PUNCT
gsrj-18	114	17	nmultiplier	nmultiplier	NOUN
gsrj-18	114	18	”	"	PUNCT
gsrj-18	114	19	is	be	AUX
gsrj-18	114	20	the	the	DET
gsrj-18	114	21	increasing	increase	VERB
gsrj-18	114	22	integers	integer	NOUN
gsrj-18	114	23	the	the	DET
gsrj-18	114	24	message	message	NOUN
gsrj-18	114	25	-	-	PUNCT
gsrj-18	114	26	interceptor	interceptor	NOUN
gsrj-18	114	27	multiplies	multiplie	NOUN
gsrj-18	114	28	n	n	ADV
gsrj-18	114	29	by	by	ADP
gsrj-18	114	30	to	to	PART
gsrj-18	114	31	achieve	achieve	VERB
gsrj-18	114	32	different	different	ADJ
gsrj-18	114	33	modular	modular	ADJ
gsrj-18	114	34	relationships	relationship	NOUN
gsrj-18	114	35	that	that	PRON
gsrj-18	114	36	will	will	AUX
gsrj-18	114	37	still	still	ADV
gsrj-18	114	38	yield	yield	VERB
gsrj-18	114	39	the	the	DET
gsrj-18	114	40	secret	secret	ADJ
gsrj-18	114	41	message	message	NOUN
gsrj-18	114	42	,	,	PUNCT
gsrj-18	114	43	m	m	PRON
gsrj-18	114	44	,	,	PUNCT
gsrj-18	114	45	“	"	PUNCT
gsrj-18	114	46	nmultiplier	nmultiplier	NOUN
gsrj-18	114	47	”	"	PUNCT
gsrj-18	114	48	can	can	AUX
gsrj-18	114	49	be	be	AUX
gsrj-18	114	50	isolated	isolate	VERB
gsrj-18	114	51	and	and	CCONJ
gsrj-18	114	52	solved	solve	VERB
gsrj-18	114	53	for	for	ADP
gsrj-18	114	54	to	to	PART
gsrj-18	114	55	attain	attain	VERB
gsrj-18	114	56	the	the	DET
gsrj-18	114	57	number	number	NOUN
gsrj-18	114	58	of	of	ADP
gsrj-18	114	59	iterations	iteration	NOUN
gsrj-18	114	60	it	it	PRON
gsrj-18	114	61	would	would	AUX
gsrj-18	114	62	take	take	VERB
gsrj-18	114	63	to	to	PART
gsrj-18	114	64	solve	solve	VERB
gsrj-18	114	65	for	for	ADP
gsrj-18	114	66	d.	d.	PROPN
gsrj-18	114	67	the	the	DET
gsrj-18	114	68	following	following	NOUN
gsrj-18	114	69	demonstrates	demonstrate	VERB
gsrj-18	114	70	the	the	DET
gsrj-18	114	71	process	process	NOUN
gsrj-18	114	72	of	of	ADP
gsrj-18	114	73	isolating	isolate	VERB
gsrj-18	114	74	“	"	PUNCT
gsrj-18	114	75	nmultiplier	nmultiplier	NOUN
gsrj-18	114	76	”	"	PUNCT
gsrj-18	114	77	from	from	ADP
gsrj-18	114	78	the	the	DET
gsrj-18	114	79	equation	equation	NOUN
gsrj-18	114	80	d	d	NOUN
gsrj-18	114	81	=	=	SYM
gsrj-18	114	82	log(n*nmultiplier	log(n*nmultipli	ADJ
gsrj-18	114	83	+	+	CCONJ
gsrj-18	114	84	m)/log(c	m)/log(c	NOUN
gsrj-18	114	85	):	):	PUNCT
gsrj-18	114	86	d	d	NOUN
gsrj-18	114	87	=	=	SYM
gsrj-18	114	88	log(n*nmultiplier	log(n*nmultipli	ADJ
gsrj-18	114	89	+	+	CCONJ
gsrj-18	114	90	m)/log(c	m)/log(c	NOUN
gsrj-18	114	91	)	)	PUNCT
gsrj-18	114	92	d*[log(c	d*[log(c	NOUN
gsrj-18	114	93	)	)	PUNCT
gsrj-18	114	94	]	]	PUNCT
gsrj-18	115	1	=	=	PUNCT
gsrj-18	115	2	log(n*nmultiplier	log(n*nmultipli	ADJ
gsrj-18	115	3	+	+	CCONJ
gsrj-18	115	4	m	m	VERB
gsrj-18	115	5	)	)	PUNCT
gsrj-18	116	1	=	=	SYM
gsrj-18	117	1	n*nmultiplier	n*nmultiplier	ADJ
gsrj-18	117	2	+	+	NUM
gsrj-18	117	3	m	m	VERB
gsrj-18	117	4	–	–	PUNCT
gsrj-18	117	5	m	m	VERB
gsrj-18	117	6	=	=	SYM
gsrj-18	117	7	n*nmultiplier	n*nmultiplier	ADJ
gsrj-18	117	8	nmultiplier	nmultiplier	NOUN
gsrj-18	117	9	=	=	NOUN
gsrj-18	117	10	∗	∗	NOUN
gsrj-18	117	11	(	(	PUNCT
gsrj-18	117	12	)	)	PUNCT
gsrj-18	117	13	(	(	PUNCT
gsrj-18	117	14	equation	equation	NOUN
gsrj-18	117	15	7	7	NUM
gsrj-18	117	16	)	)	PUNCT
gsrj-18	117	17	by	by	ADP
gsrj-18	117	18	solving	solve	VERB
gsrj-18	117	19	for	for	ADP
gsrj-18	117	20	“	"	PUNCT
gsrj-18	117	21	nmultiplier	nmultiplier	NOUN
gsrj-18	117	22	”	"	PUNCT
gsrj-18	117	23	,	,	PUNCT
gsrj-18	117	24	the	the	DET
gsrj-18	117	25	number	number	NOUN
gsrj-18	117	26	of	of	ADP
gsrj-18	117	27	iterations	iteration	NOUN
gsrj-18	117	28	needed	need	VERB
gsrj-18	117	29	to	to	PART
gsrj-18	117	30	calculate	calculate	VERB
gsrj-18	117	31	d	d	PROPN
gsrj-18	117	32	through	through	ADP
gsrj-18	117	33	logarithmic	logarithmic	ADJ
gsrj-18	117	34	techniques	technique	NOUN
gsrj-18	117	35	has	have	AUX
gsrj-18	117	36	been	be	AUX
gsrj-18	117	37	calculated	calculate	VERB
gsrj-18	117	38	to	to	PART
gsrj-18	117	39	be	be	AUX
gsrj-18	117	40	∗	∗	NOUN
gsrj-18	117	41	(	(	PUNCT
gsrj-18	117	42	)	)	PUNCT
gsrj-18	117	43	.	.	PUNCT
gsrj-18	118	1	because	because	SCONJ
gsrj-18	118	2	this	this	DET
gsrj-18	118	3	program	program	NOUN
gsrj-18	118	4	allows	allow	VERB
gsrj-18	118	5	a	a	DET
gsrj-18	118	6	maximum	maximum	NOUN
gsrj-18	118	7	of	of	ADP
gsrj-18	118	8	one	one	NUM
gsrj-18	118	9	million	million	NUM
gsrj-18	118	10	iterations	iteration	NOUN
gsrj-18	118	11	to	to	PART
gsrj-18	118	12	compute	compute	VERB
gsrj-18	118	13	d	d	NOUN
gsrj-18	118	14	in	in	ADP
gsrj-18	118	15	this	this	DET
gsrj-18	118	16	manner	manner	NOUN
gsrj-18	118	17	,	,	PUNCT
gsrj-18	118	18	the	the	DET
gsrj-18	118	19	associated	associate	VERB
gsrj-18	118	20	time	time	NOUN
gsrj-18	118	21	complexity	complexity	NOUN
gsrj-18	118	22	is	be	AUX
gsrj-18	118	23	less	less	ADJ
gsrj-18	118	24	than	than	ADP
gsrj-18	118	25	o(1000000	o(1000000	NUM
gsrj-18	118	26	)	)	PUNCT
gsrj-18	118	27	.	.	PUNCT
gsrj-18	119	1	the	the	DET
gsrj-18	119	2	purpose	purpose	NOUN
gsrj-18	119	3	of	of	ADP
gsrj-18	119	4	this	this	DET
gsrj-18	119	5	research	research	NOUN
gsrj-18	119	6	study	study	NOUN
gsrj-18	119	7	is	be	AUX
gsrj-18	119	8	to	to	PART
gsrj-18	119	9	discuss	discuss	VERB
gsrj-18	119	10	the	the	DET
gsrj-18	119	11	function	function	NOUN
gsrj-18	119	12	of	of	ADP
gsrj-18	119	13	a	a	DET
gsrj-18	119	14	program	program	NOUN
gsrj-18	119	15	built	build	VERB
gsrj-18	119	16	using	use	VERB
gsrj-18	119	17	python	python	NOUN
gsrj-18	119	18	that	that	PRON
gsrj-18	119	19	calculates	calculate	VERB
gsrj-18	119	20	the	the	DET
gsrj-18	119	21	decryption	decryption	NOUN
gsrj-18	119	22	key	key	NOUN
gsrj-18	119	23	using	use	VERB
gsrj-18	119	24	semi	semi	ADJ
gsrj-18	119	25	-	-	ADJ
gsrj-18	119	26	prime	prime	ADJ
gsrj-18	119	27	factorization	factorization	NOUN
gsrj-18	119	28	as	as	ADV
gsrj-18	119	29	well	well	ADV
gsrj-18	119	30	as	as	ADP
gsrj-18	119	31	the	the	DET
gsrj-18	119	32	logarithmic	logarithmic	ADJ
gsrj-18	119	33	method	method	NOUN
gsrj-18	119	34	.	.	PUNCT
gsrj-18	120	1	further	far	ADV
gsrj-18	120	2	,	,	PUNCT
gsrj-18	120	3	the	the	DET
gsrj-18	120	4	program	program	NOUN
gsrj-18	120	5	calculates	calculate	VERB
gsrj-18	120	6	the	the	DET
gsrj-18	120	7	number	number	NOUN
gsrj-18	120	8	of	of	ADP
gsrj-18	120	9	iterations	iteration	NOUN
gsrj-18	120	10	required	require	VERB
gsrj-18	120	11	to	to	PART
gsrj-18	120	12	calculate	calculate	VERB
gsrj-18	120	13	d	d	NOUN
gsrj-18	120	14	using	use	VERB
gsrj-18	120	15	either	either	PRON
gsrj-18	120	16	of	of	ADP
gsrj-18	120	17	these	these	DET
gsrj-18	120	18	methods	method	NOUN
gsrj-18	120	19	,	,	PUNCT
gsrj-18	120	20	indicating	indicate	VERB
gsrj-18	120	21	the	the	DET
gsrj-18	120	22	efficacy	efficacy	NOUN
gsrj-18	120	23	and	and	CCONJ
gsrj-18	120	24	advantageousness	advantageousness	NOUN
gsrj-18	120	25	of	of	ADP
gsrj-18	120	26	using	use	VERB
gsrj-18	120	27	one	one	NUM
gsrj-18	120	28	method	method	NOUN
gsrj-18	120	29	over	over	ADP
gsrj-18	120	30	the	the	DET
gsrj-18	120	31	other	other	ADJ
gsrj-18	120	32	in	in	ADP
gsrj-18	120	33	different	different	ADJ
gsrj-18	120	34	circumstances	circumstance	NOUN
gsrj-18	120	35	.	.	PUNCT
gsrj-18	121	1	this	this	DET
gsrj-18	121	2	research	research	NOUN
gsrj-18	121	3	study	study	NOUN
gsrj-18	121	4	will	will	AUX
gsrj-18	121	5	delve	delve	VERB
gsrj-18	121	6	into	into	ADP
gsrj-18	121	7	explaining	explain	VERB
gsrj-18	121	8	the	the	DET
gsrj-18	121	9	code	code	NOUN
gsrj-18	121	10	written	write	VERB
gsrj-18	121	11	in	in	ADP
gsrj-18	121	12	the	the	DET
gsrj-18	121	13	program	program	NOUN
gsrj-18	121	14	and	and	CCONJ
gsrj-18	121	15	how	how	SCONJ
gsrj-18	121	16	it	it	PRON
gsrj-18	121	17	contributes	contribute	VERB
gsrj-18	121	18	to	to	ADP
gsrj-18	121	19	achieving	achieve	VERB
gsrj-18	121	20	the	the	DET
gsrj-18	121	21	end	end	NOUN
gsrj-18	121	22	result	result	NOUN
gsrj-18	121	23	of	of	ADP
gsrj-18	121	24	decryption	decryption	NOUN
gsrj-18	121	25	as	as	ADV
gsrj-18	121	26	well	well	ADV
gsrj-18	121	27	as	as	ADP
gsrj-18	121	28	the	the	DET
gsrj-18	121	29	number	number	NOUN
gsrj-18	121	30	of	of	ADP
gsrj-18	121	31	iterations	iteration	NOUN
gsrj-18	121	32	derived	derive	VERB
gsrj-18	121	33	necessary	necessary	ADJ
gsrj-18	121	34	to	to	PART
gsrj-18	121	35	calculate	calculate	VERB
gsrj-18	121	36	d	d	NOUN
gsrj-18	121	37	using	use	VERB
gsrj-18	121	38	either	either	PRON
gsrj-18	121	39	of	of	ADP
gsrj-18	121	40	the	the	DET
gsrj-18	121	41	aforementioned	aforementioned	ADJ
gsrj-18	121	42	methods	method	NOUN
gsrj-18	121	43	,	,	PUNCT
gsrj-18	121	44	being	be	AUX
gsrj-18	121	45	that	that	PRON
gsrj-18	121	46	of	of	ADP
gsrj-18	121	47	semi	semi	ADJ
gsrj-18	121	48	-	-	ADJ
gsrj-18	121	49	prime	prime	ADJ
gsrj-18	121	50	factorization	factorization	NOUN
gsrj-18	121	51	or	or	CCONJ
gsrj-18	121	52	logarithms	logarithm	NOUN
gsrj-18	121	53	.	.	PUNCT
gsrj-18	122	1	2	2	X
gsrj-18	122	2	.	.	X
gsrj-18	122	3	materials	material	NOUN
gsrj-18	122	4	2.1	2.1	NUM
gsrj-18	122	5	required	require	VERB
gsrj-18	122	6	materials	material	NOUN
gsrj-18	122	7	:	:	PUNCT
gsrj-18	122	8	python	python	NOUN
gsrj-18	122	9	programming	programming	NOUN
gsrj-18	122	10	system	system	NOUN
gsrj-18	122	11	installed	instal	VERB
gsrj-18	122	12	on	on	ADP
gsrj-18	122	13	macbook	macbook	NOUN
gsrj-18	122	14	laptop	laptop	NOUN
gsrj-18	122	15	or	or	CCONJ
gsrj-18	122	16	other	other	ADJ
gsrj-18	122	17	personal	personal	ADJ
gsrj-18	122	18	computer	computer	NOUN
gsrj-18	122	19	,	,	PUNCT
gsrj-18	122	20	complete	complete	ADJ
gsrj-18	122	21	with	with	ADP
gsrj-18	122	22	idle	idle	ADJ
gsrj-18	122	23	and	and	CCONJ
gsrj-18	122	24	running	running	NOUN
gsrj-18	122	25	module	module	NOUN
gsrj-18	122	26	.	.	PUNCT
gsrj-18	123	1	access	access	NOUN
gsrj-18	123	2	to	to	ADP
gsrj-18	123	3	python	python	PROPN
gsrj-18	123	4	’s	’s	PART
gsrj-18	123	5	“	"	PUNCT
gsrj-18	123	6	math	math	NOUN
gsrj-18	123	7	”	"	PUNCT
gsrj-18	123	8	module	module	NOUN
gsrj-18	123	9	located	locate	VERB
gsrj-18	123	10	in	in	ADP
gsrj-18	123	11	python	python	PROPN
gsrj-18	123	12	’s	’s	PART
gsrj-18	123	13	standard	standard	ADJ
gsrj-18	123	14	library	library	NOUN
gsrj-18	123	15	.	.	PUNCT
gsrj-18	124	1	the	the	DET
gsrj-18	124	2	module	module	NOUN
gsrj-18	124	3	includes	include	VERB
gsrj-18	124	4	mathematical	mathematical	ADJ
gsrj-18	124	5	functions	function	NOUN
gsrj-18	124	6	necessary	necessary	ADJ
gsrj-18	124	7	to	to	ADP
gsrj-18	124	8	the	the	DET
gsrj-18	124	9	operation	operation	NOUN
gsrj-18	124	10	of	of	ADP
gsrj-18	124	11	the	the	DET
gsrj-18	124	12	program	program	NOUN
gsrj-18	124	13	.	.	PUNCT
gsrj-18	125	1	2.1	2.1	NUM
gsrj-18	125	2	recommended	recommend	VERB
gsrj-18	125	3	materials	material	NOUN
gsrj-18	125	4	:	:	PUNCT
gsrj-18	125	5	access	access	NOUN
gsrj-18	125	6	to	to	ADP
gsrj-18	125	7	a	a	DET
gsrj-18	125	8	computational	computational	ADJ
gsrj-18	125	9	knowledge	knowledge	NOUN
gsrj-18	125	10	/	/	SYM
gsrj-18	125	11	answer	answer	NOUN
gsrj-18	125	12	engine	engine	NOUN
gsrj-18	125	13	like	like	ADP
gsrj-18	125	14	wolfram	wolfram	PROPN
gsrj-18	125	15	alpha	alpha	PROPN
gsrj-18	125	16	used	use	VERB
gsrj-18	125	17	to	to	PART
gsrj-18	125	18	initially	initially	ADV
gsrj-18	125	19	verify	verify	VERB
gsrj-18	125	20	the	the	DET
gsrj-18	125	21	accuracy	accuracy	NOUN
gsrj-18	125	22	of	of	ADP
gsrj-18	125	23	the	the	DET
gsrj-18	125	24	results	result	NOUN
gsrj-18	125	25	obtained	obtain	VERB
gsrj-18	125	26	from	from	ADP
gsrj-18	125	27	the	the	DET
gsrj-18	125	28	program.14	program.14	PROPN
gsrj-18	125	29	12	12	NUM
gsrj-18	125	30	georgetown	georgetown	PROPN
gsrj-18	125	31	scientific	scientific	PROPN
gsrj-18	125	32	research	research	NOUN
gsrj-18	125	33	journal	journal	NOUN
gsrj-18	125	34	2	2	NUM
gsrj-18	125	35	.	.	PUNCT
gsrj-18	125	36	methods	method	NOUN
gsrj-18	125	37	/	/	SYM
gsrj-18	125	38	procedures	procedure	NOUN
gsrj-18	125	39	figure	figure	VERB
gsrj-18	125	40	1	1	NUM
gsrj-18	125	41	.	.	PUNCT
gsrj-18	125	42	code	code	NOUN
gsrj-18	125	43	script	script	VERB
gsrj-18	125	44	3.1	3.1	NUM
gsrj-18	125	45	the	the	DET
gsrj-18	125	46	code	code	NOUN
gsrj-18	125	47	behind	behind	ADP
gsrj-18	125	48	semi	semi	ADJ
gsrj-18	125	49	-	-	ADJ
gsrj-18	125	50	prime	prime	ADJ
gsrj-18	125	51	factorization	factorization	NOUN
gsrj-18	125	52	to	to	PART
gsrj-18	125	53	calculate	calculate	VERB
gsrj-18	125	54	d	d	PROPN
gsrj-18	125	55	(	(	PUNCT
gsrj-18	125	56	lines	line	NOUN
gsrj-18	125	57	1	1	NUM
gsrj-18	125	58	-	-	SYM
gsrj-18	125	59	47	47	NUM
gsrj-18	125	60	)	)	PUNCT
gsrj-18	125	61	3.1.1	3.1.1	NUM
gsrj-18	125	62	factoring	factoring	NOUN
gsrj-18	125	63	n	n	NOUN
gsrj-18	125	64	in	in	ADP
gsrj-18	125	65	lines	line	NOUN
gsrj-18	125	66	3	3	NUM
gsrj-18	125	67	–	–	PUNCT
gsrj-18	125	68	9	9	NUM
gsrj-18	125	69	,	,	PUNCT
gsrj-18	125	70	the	the	DET
gsrj-18	125	71	program	program	NOUN
gsrj-18	125	72	asks	ask	VERB
gsrj-18	125	73	for	for	ADP
gsrj-18	125	74	a	a	DET
gsrj-18	125	75	semiprime	semiprime	NOUN
gsrj-18	125	76	input	input	NOUN
gsrj-18	125	77	which	which	PRON
gsrj-18	125	78	it	it	PRON
gsrj-18	125	79	then	then	ADV
gsrj-18	125	80	sets	set	VERB
gsrj-18	125	81	to	to	ADP
gsrj-18	125	82	the	the	DET
gsrj-18	125	83	variable	variable	ADJ
gsrj-18	125	84	n.	n.	NOUN
gsrj-18	125	85	the	the	DET
gsrj-18	125	86	program	program	NOUN
gsrj-18	125	87	is	be	AUX
gsrj-18	125	88	designed	design	VERB
gsrj-18	125	89	to	to	PART
gsrj-18	125	90	test	test	VERB
gsrj-18	125	91	all	all	DET
gsrj-18	125	92	integers	integer	NOUN
gsrj-18	125	93	less	less	ADJ
gsrj-18	125	94	than	than	ADP
gsrj-18	125	95	n	n	NOUN
gsrj-18	125	96	but	but	CCONJ
gsrj-18	125	97	greater	great	ADJ
gsrj-18	125	98	than	than	ADP
gsrj-18	125	99	or	or	CCONJ
gsrj-18	125	100	equal	equal	ADJ
gsrj-18	125	101	to	to	ADP
gsrj-18	125	102	two	two	NUM
gsrj-18	125	103	to	to	PART
gsrj-18	125	104	determine	determine	VERB
gsrj-18	125	105	whether	whether	SCONJ
gsrj-18	125	106	they	they	PRON
gsrj-18	125	107	divide	divide	VERB
gsrj-18	125	108	evenly	evenly	ADV
gsrj-18	125	109	into	into	ADP
gsrj-18	125	110	n.	n.	NOUN
gsrj-18	125	111	an	an	DET
gsrj-18	125	112	integer	integer	NOUN
gsrj-18	125	113	is	be	AUX
gsrj-18	125	114	a	a	DET
gsrj-18	125	115	factor	factor	NOUN
gsrj-18	125	116	of	of	ADP
gsrj-18	125	117	n	n	NOUN
gsrj-18	125	118	if	if	SCONJ
gsrj-18	125	119	the	the	DET
gsrj-18	125	120	remainder	remainder	NOUN
gsrj-18	125	121	of	of	ADP
gsrj-18	125	122	n	n	PRON
gsrj-18	125	123	divided	divide	VERB
gsrj-18	125	124	by	by	ADP
gsrj-18	125	125	said	say	VERB
gsrj-18	125	126	integer	integer	NOUN
gsrj-18	125	127	equals	equal	VERB
gsrj-18	125	128	zero	zero	NUM
gsrj-18	125	129	.	.	PUNCT
gsrj-18	126	1	the	the	DET
gsrj-18	126	2	integers	integer	NOUN
gsrj-18	126	3	that	that	PRON
gsrj-18	126	4	do	do	AUX
gsrj-18	126	5	divide	divide	VERB
gsrj-18	126	6	evenly	evenly	ADV
gsrj-18	126	7	into	into	ADP
gsrj-18	126	8	n	n	NUM
gsrj-18	126	9	are	be	AUX
gsrj-18	126	10	deemed	deem	VERB
gsrj-18	126	11	to	to	PART
gsrj-18	126	12	be	be	AUX
gsrj-18	126	13	factors	factor	NOUN
gsrj-18	126	14	of	of	ADP
gsrj-18	126	15	n	n	NUM
gsrj-18	126	16	and	and	CCONJ
gsrj-18	126	17	are	be	AUX
gsrj-18	126	18	appended	append	VERB
gsrj-18	126	19	to	to	ADP
gsrj-18	126	20	a	a	DET
gsrj-18	126	21	list	list	NOUN
gsrj-18	126	22	called	call	VERB
gsrj-18	126	23	“	"	PUNCT
gsrj-18	126	24	nfactorslist	nfactorslist	NOUN
gsrj-18	126	25	”	"	PUNCT
gsrj-18	126	26	.	.	PUNCT
gsrj-18	127	1	in	in	ADP
gsrj-18	127	2	lines	line	NOUN
gsrj-18	127	3	10	10	NUM
gsrj-18	127	4	–	–	SYM
gsrj-18	127	5	20	20	NUM
gsrj-18	127	6	,	,	PUNCT
gsrj-18	127	7	the	the	DET
gsrj-18	127	8	program	program	NOUN
gsrj-18	127	9	forces	force	VERB
gsrj-18	127	10	another	another	DET
gsrj-18	127	11	input	input	NOUN
gsrj-18	127	12	to	to	PART
gsrj-18	127	13	be	be	AUX
gsrj-18	127	14	given	give	VERB
gsrj-18	127	15	for	for	ADP
gsrj-18	127	16	n	n	PRON
gsrj-18	127	17	if	if	SCONJ
gsrj-18	127	18	the	the	DET
gsrj-18	127	19	first	first	ADJ
gsrj-18	127	20	input	input	NOUN
gsrj-18	127	21	is	be	AUX
gsrj-18	127	22	not	not	PART
gsrj-18	127	23	a	a	DET
gsrj-18	127	24	semi	semi	ADJ
gsrj-18	127	25	-	-	ADJ
gsrj-18	127	26	prime	prime	ADJ
gsrj-18	127	27	number	number	NOUN
gsrj-18	127	28	.	.	PUNCT
gsrj-18	128	1	if	if	SCONJ
gsrj-18	128	2	the	the	DET
gsrj-18	128	3	length	length	NOUN
gsrj-18	128	4	of	of	ADP
gsrj-18	128	5	nfactorslist	nfactorslist	NOUN
gsrj-18	128	6	is	be	AUX
gsrj-18	128	7	only	only	ADV
gsrj-18	128	8	four	four	NUM
gsrj-18	128	9	,	,	PUNCT
gsrj-18	128	10	this	this	PRON
gsrj-18	128	11	indicates	indicate	VERB
gsrj-18	128	12	that	that	SCONJ
gsrj-18	128	13	n	n	X
gsrj-18	128	14	is	be	AUX
gsrj-18	128	15	a	a	DET
gsrj-18	128	16	semi	semi	ADJ
gsrj-18	128	17	-	-	ADJ
gsrj-18	128	18	prime	prime	ADJ
gsrj-18	128	19	number	number	NOUN
gsrj-18	128	20	because	because	SCONJ
gsrj-18	128	21	semi	semi	ADJ
gsrj-18	128	22	-	-	ADJ
gsrj-18	128	23	prime	prime	ADJ
gsrj-18	128	24	numbers	number	NOUN
gsrj-18	128	25	only	only	ADV
gsrj-18	128	26	have	have	VERB
gsrj-18	128	27	four	four	NUM
gsrj-18	128	28	factors	factor	NOUN
gsrj-18	128	29	:	:	PUNCT
gsrj-18	128	30	one	one	NUM
gsrj-18	128	31	,	,	PUNCT
gsrj-18	128	32	the	the	DET
gsrj-18	128	33	semi	semi	ADJ
gsrj-18	128	34	-	-	ADJ
gsrj-18	128	35	prime	prime	ADJ
gsrj-18	128	36	itself	itself	PRON
gsrj-18	128	37	,	,	PUNCT
gsrj-18	128	38	and	and	CCONJ
gsrj-18	128	39	the	the	DET
gsrj-18	128	40	two	two	NUM
gsrj-18	128	41	prime	prime	ADJ
gsrj-18	128	42	numbers	number	NOUN
gsrj-18	128	43	multiplied	multiply	VERB
gsrj-18	128	44	together	together	ADV
gsrj-18	128	45	to	to	PART
gsrj-18	128	46	attain	attain	VERB
gsrj-18	128	47	the	the	DET
gsrj-18	128	48	semi	semi	ADJ
gsrj-18	128	49	-	-	ADJ
gsrj-18	128	50	prime	prime	ADJ
gsrj-18	128	51	number	number	NOUN
gsrj-18	128	52	.	.	PUNCT
gsrj-18	129	1	in	in	ADP
gsrj-18	129	2	lines	line	NOUN
gsrj-18	129	3	21	21	NUM
gsrj-18	129	4	–	–	PUNCT
gsrj-18	129	5	25	25	NUM
gsrj-18	129	6	,	,	PUNCT
gsrj-18	129	7	after	after	ADP
gsrj-18	129	8	ensuring	ensure	VERB
gsrj-18	129	9	a	a	DET
gsrj-18	129	10	semi	semi	ADJ
gsrj-18	129	11	-	-	ADJ
gsrj-18	129	12	prime	prime	ADJ
gsrj-18	129	13	input	input	NOUN
gsrj-18	129	14	for	for	ADP
gsrj-18	129	15	n	n	CCONJ
gsrj-18	129	16	,	,	PUNCT
gsrj-18	129	17	the	the	DET
gsrj-18	129	18	program	program	NOUN
gsrj-18	129	19	sets	set	VERB
gsrj-18	129	20	the	the	DET
gsrj-18	129	21	variables	variable	NOUN
gsrj-18	129	22	p	p	NOUN
gsrj-18	129	23	and	and	CCONJ
gsrj-18	129	24	q	q	NOUN
gsrj-18	129	25	to	to	ADP
gsrj-18	129	26	the	the	DET
gsrj-18	129	27	two	two	NUM
gsrj-18	129	28	prime	prime	ADJ
gsrj-18	129	29	numbers	number	NOUN
gsrj-18	129	30	that	that	PRON
gsrj-18	129	31	n	n	VERB
gsrj-18	129	32	is	be	AUX
gsrj-18	129	33	divisible	divisible	ADJ
gsrj-18	129	34	by	by	ADP
gsrj-18	129	35	.	.	PUNCT
gsrj-18	130	1	3.1.2	3.1.2	NUM
gsrj-18	130	2	factoring	factor	VERB
gsrj-18	130	3	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	130	4	in	in	ADP
gsrj-18	130	5	lines	line	NOUN
gsrj-18	130	6	26	26	NUM
gsrj-18	130	7	–	–	PUNCT
gsrj-18	130	8	27	27	NUM
gsrj-18	130	9	,	,	PUNCT
gsrj-18	130	10	the	the	DET
gsrj-18	130	11	program	program	NOUN
gsrj-18	130	12	sets	set	VERB
gsrj-18	130	13	the	the	DET
gsrj-18	130	14	variable	variable	ADJ
gsrj-18	130	15	phin	phin	PROPN
gsrj-18	130	16	to	to	ADP
gsrj-18	130	17	(	(	PUNCT
gsrj-18	130	18	p	p	X
gsrj-18	130	19	–	–	PUNCT
gsrj-18	130	20	1)*(q	1)*(q	NUM
gsrj-18	130	21	–	–	PUNCT
gsrj-18	130	22	1	1	NUM
gsrj-18	130	23	)	)	PUNCT
gsrj-18	130	24	based	base	VERB
gsrj-18	130	25	on	on	ADP
gsrj-18	130	26	the	the	DET
gsrj-18	130	27	mathematics	mathematic	NOUN
gsrj-18	130	28	described	describe	VERB
gsrj-18	130	29	in	in	ADP
gsrj-18	130	30	the	the	DET
gsrj-18	130	31	introduction	introduction	NOUN
gsrj-18	130	32	for	for	ADP
gsrj-18	130	33	the	the	DET
gsrj-18	130	34	calculation	calculation	NOUN
gsrj-18	130	35	of	of	ADP
gsrj-18	130	36	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	130	37	.	.	PUNCT
gsrj-18	131	1	3.1.3	3.1.3	NUM
gsrj-18	131	2	generating	generate	VERB
gsrj-18	131	3	a	a	DET
gsrj-18	131	4	public	public	ADJ
gsrj-18	131	5	key	key	ADJ
gsrj-18	131	6	value	value	NOUN
gsrj-18	131	7	for	for	ADP
gsrj-18	131	8	e	e	PROPN
gsrj-18	131	9	in	in	ADP
gsrj-18	131	10	lines	line	NOUN
gsrj-18	131	11	34	34	NUM
gsrj-18	131	12	–	–	SYM
gsrj-18	131	13	40	40	NUM
gsrj-18	131	14	,	,	PUNCT
gsrj-18	131	15	the	the	DET
gsrj-18	131	16	program	program	NOUN
gsrj-18	131	17	initializes	initialize	VERB
gsrj-18	131	18	a	a	DET
gsrj-18	131	19	list	list	NOUN
gsrj-18	131	20	called	call	VERB
gsrj-18	131	21	“	"	PUNCT
gsrj-18	131	22	phinfactorslist	phinfactorslist	NOUN
gsrj-18	131	23	”	"	PUNCT
gsrj-18	131	24	that	that	PRON
gsrj-18	131	25	lists	list	VERB
gsrj-18	131	26	the	the	DET
gsrj-18	131	27	factors	factor	NOUN
gsrj-18	131	28	of	of	ADP
gsrj-18	131	29	the	the	DET
gsrj-18	131	30	value	value	NOUN
gsrj-18	131	31	of	of	ADP
gsrj-18	131	32	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	131	33	by	by	ADP
gsrj-18	131	34	testing	testing	NOUN
gsrj-18	131	35	which	which	PRON
gsrj-18	131	36	integers	integer	NOUN
gsrj-18	131	37	are	be	AUX
gsrj-18	131	38	greater	great	ADJ
gsrj-18	131	39	than	than	ADP
gsrj-18	131	40	two	two	NUM
gsrj-18	131	41	but	but	CCONJ
gsrj-18	131	42	less	less	ADJ
gsrj-18	131	43	than	than	ADP
gsrj-18	131	44	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	131	45	and	and	CCONJ
gsrj-18	131	46	yield	yield	VERB
gsrj-18	131	47	a	a	DET
gsrj-18	131	48	remainder	remainder	NOUN
gsrj-18	131	49	of	of	ADP
gsrj-18	131	50	zero	zero	NUM
gsrj-18	131	51	when	when	SCONJ
gsrj-18	131	52	divided	divide	VERB
gsrj-18	131	53	into	into	ADP
gsrj-18	131	54	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	131	55	.	.	PUNCT
gsrj-18	132	1	in	in	ADP
gsrj-18	132	2	lines	line	NOUN
gsrj-18	132	3	41	41	NUM
gsrj-18	132	4	–	–	SYM
gsrj-18	132	5	42	42	NUM
gsrj-18	132	6	,	,	PUNCT
gsrj-18	132	7	the	the	DET
gsrj-18	132	8	program	program	NOUN
gsrj-18	132	9	initializes	initialize	VERB
gsrj-18	132	10	a	a	DET
gsrj-18	132	11	list	list	NOUN
gsrj-18	132	12	called	call	VERB
gsrj-18	132	13	“	"	PUNCT
gsrj-18	132	14	primeslessthan100list	primeslessthan100list	NOUN
gsrj-18	132	15	”	"	PUNCT
gsrj-18	132	16	which	which	PRON
gsrj-18	132	17	lists	list	VERB
gsrj-18	132	18	all	all	PRON
gsrj-18	132	19	of	of	ADP
gsrj-18	132	20	the	the	DET
gsrj-18	132	21	prime	prime	ADJ
gsrj-18	132	22	numbers	number	NOUN
gsrj-18	132	23	less	less	ADJ
gsrj-18	132	24	than	than	ADP
gsrj-18	132	25	100	100	NUM
gsrj-18	132	26	and	and	CCONJ
gsrj-18	132	27	also	also	ADV
gsrj-18	132	28	initializes	initialize	VERB
gsrj-18	132	29	that	that	DET
gsrj-18	132	30	variable	variable	ADJ
gsrj-18	132	31	e	e	NOUN
gsrj-18	132	32	by	by	ADP
gsrj-18	132	33	setting	set	VERB
gsrj-18	132	34	it	it	PRON
gsrj-18	132	35	to	to	ADP
gsrj-18	132	36	a	a	DET
gsrj-18	132	37	placeholder	placeholder	NOUN
gsrj-18	132	38	value	value	NOUN
gsrj-18	132	39	of	of	ADP
gsrj-18	132	40	1	1	NUM
gsrj-18	132	41	.	.	NOUN
gsrj-18	132	42	13	13	NUM
gsrj-18	132	43	11"	11"	NUM
gsrj-18	132	44	°	°	PROPN
gsrj-18	132	45	"'1	"'1	NOUN
gsrj-18	132	46	m	m	NOUN
gsrj-18	132	47	"	"	PUNCT
gsrj-18	132	48	"	"	PUNCT
gsrj-18	132	49	"	"	PUNCT
gsrj-18	132	50	2	2	NUM
gsrj-18	132	51	l'nnl	l'nnl	PROPN
gsrj-18	132	52	"	"	PUNCT
gsrj-18	132	53	ijiutyl'l1o	ijiutyl'l1o	PROPN
gsrj-18	132	54	,	,	PUNCT
gsrj-18	132	55	lllllouuji	lllllouuji	PROPN
gsrj-18	132	56	sl'.mj	sl'.mj	PROPN
gsrj-18	132	57	-	-	PUNCT
gsrj-18	132	58	l'iu.\ie	l'iu.\ie	NOUN
gsrj-18	132	59	fat	fat	NOUN
gsrj-18	132	60	:	:	PUNCT
gsrj-18	132	61	l'orjza'llo~	l'orjza'llo~	PROPN
gsrj-18	132	62	l	l	NOUN
gsrj-18	132	63	lnltl21l2tvl!uble	lnltl21l2tvl!uble	ADJ
gsrj-18	132	64	,	,	PUNCT
gsrj-18	132	65	•u	•u	PROPN
gsrj-18	132	66	<	<	X
gsrj-18	132	67	er-!lmd	er-!lmd	ADJ
gsrj-18	132	68	imojlorinpn	imojlorinpn	NOUN
gsrj-18	132	69	4	4	NUM
gsrj-18	132	70	lmtiali	lmtiali	VERB
gsrj-18	132	71	:	:	PUNCT
gsrj-18	132	72	a	a	X
gsrj-18	132	73	:	:	PUNCT
gsrj-18	132	74	li	li	PROPN
gsrj-18	132	75	>	>	PROPN
gsrj-18	132	76	l.	l.	PROPN
gsrj-18	132	77	•-li	•-li	PROPN
gsrj-18	132	78	>	>	X
gsrj-18	132	79	t•	t•	NOUN
gsrj-18	132	80	1	1	NUM
gsrj-18	132	81	,	,	PUNCT
gsrj-18	132	82	n	n	PROPN
gsrj-18	132	83	5slartlooo	5slartlooo	NUM
gsrj-18	132	84	6	6	NUM
gsrj-18	132	85	7	7	NUM
gsrj-18	132	86	8	8	NUM
gsrj-18	132	87	forllll-,1m111utc{2.nl	forllll-,1m111utc{2.nl	NOUN
gsrj-18	132	88	lfnm	lfnm	X
gsrj-18	132	89	>	>	X
gsrj-18	132	90	di•o	di•o	PROPN
gsrj-18	132	91	addllo	addllo	PROPN
gsrj-18	132	92	:	:	PUNCT
gsrj-18	132	93	f	f	X
gsrj-18	132	94	>	>	PUNCT
gsrj-18	132	95	aonl.j	aonl.j	PROPN
gsrj-18	132	96	<	<	X
gsrj-18	132	97	t	t	PROPN
gsrj-18	132	98	9	9	NUM
gsrj-18	132	99	end	end	NOUN
gsrj-18	132	100	loco	loco	NOUN
gsrj-18	132	101	ios!anlooo	ios!anlooo	NOUN
gsrj-18	132	102	11	11	NUM
gsrj-18	132	103	\\bile	\\bile	NOUN
gsrj-18	132	104	1eqiib	1eqiib	PROPN
gsrj-18	132	105	ofnfoctcnljg	ofnfoctcnljg	NOUN
gsrj-18	132	106	,	,	PUNCT
gsrj-18	132	107	4	4	NUM
gsrj-18	132	108	12	12	NUM
gsrj-18	132	109	ll	ll	NOUN
gsrj-18	132	110	n	n	ADV
gsrj-18	132	111	•	•	ADJ
gsrj-18	132	112	"	"	PUNCT
gsrj-18	132	113	"	"	PUNCT
gsrj-18	132	114	"	"	PUNCT
gsrj-18	132	115	-¢	-¢	PROPN
gsrj-18	132	116	>	>	PUNCT
gsrj-18	132	117	"	"	PUNCT
gsrj-18	132	118	"	"	PUNCT
gsrj-18	132	119	'	'	PUNCT
gsrj-18	132	120	in"!l"i	in"!l"i	PROPN
gsrj-18	132	121	'	'	PUNCT
gsrj-18	132	122	&	&	CCONJ
gsrj-18	132	123	,	,	PUNCT
gsrj-18	132	124	pa	pa	PROPN
gsrj-18	132	125	dclc	dclc	VERB
gsrj-18	132	126	,	,	PUNCT
gsrj-18	132	127	c	c	PROPN
gsrj-18	132	128	nfa	nfa	PROPN
gsrj-18	132	129	:	:	PUNCT
gsrj-18	132	130	unli	unli	ADJ
gsrj-18	132	131	,	,	PUNCT
gsrj-18	132	132	i	i	PRON
gsrj-18	132	133	u	u	VERB
gsrj-18	132	134	15	15	NUM
gsrj-18	132	135	addl	addl	NOUN
gsrj-18	132	136	,	,	PUNCT
gsrj-18	132	137	nionfaamlist	nionfaamlist	NOUN
gsrj-18	132	138	sbnloop	sbnloop	NOUN
gsrj-18	132	139	16	16	NUM
gsrj-18	132	140	17	17	NUM
gsrj-18	132	141	18	18	NUM
gsrj-18	132	142	19	19	NUM
gsrj-18	132	143	20endloop	20endloop	NUM
gsrj-18	132	144	21	21	NUM
gsrj-18	132	145	siar	siar	NOUN
gsrj-18	132	146	,	,	PUNCT
gsrj-18	132	147	b	b	X
gsrj-18	132	148	-	-	PUNCT
gsrj-18	132	149	c	c	NOUN
gsrj-18	132	150	,	,	PUNCT
gsrj-18	132	151	?	?	NUM
gsrj-18	132	152	2	2	NUM
gsrj-18	132	153	23	23	NUM
gsrj-18	132	154	24	24	NUM
gsrj-18	132	155	2.1	2.1	NUM
gsrj-18	132	156	endloop	endloop	NOUN
gsrj-18	132	157	for	for	ADP
gsrj-18	132	158	inlq	inlq	ADV
gsrj-18	132	159	,	,	PUNCT
gsrj-18	132	160	cn	cn	PROPN
gsrj-18	132	161	i	i	PRON
gsrj-18	132	162	in	in	ADP
gsrj-18	132	163	n1f1p.c	n1f1p.c	PROPN
gsrj-18	132	164	(	(	PUNCT
gsrj-18	132	165	2	2	NUM
gsrj-18	132	166	.	.	NUM
gsrj-18	132	167	n	n	CCONJ
gsrj-18	132	168	)	)	PUNCT
gsrj-18	132	169	if	if	SCONJ
gsrj-18	132	170	modi	modi	PROPN
gsrj-18	132	171	0	0	PUNCT
gsrj-18	132	172	for	for	ADP
gsrj-18	132	173	lm'll'ff	lm'll'ff	ADJ
gsrj-18	132	174	i	i	PRON
gsrj-18	132	175	in	in	ADP
gsrj-18	132	176	111¥tc	111¥tc	NUM
gsrj-18	132	177	(	(	PUNCT
gsrj-18	132	178	2	2	NUM
gsrj-18	132	179	,	,	PUNCT
gsrj-18	132	180	n	n	CCONJ
gsrj-18	132	181	)	)	PUNCT
gsrj-18	132	182	if	if	SCONJ
gsrj-18	132	183	"	"	PUNCT
gsrj-18	132	184	"	"	PUNCT
gsrj-18	132	185	'	'	PUNCT
gsrj-18	132	186	1i	1i	NUM
gsrj-18	132	187	-	-	PUNCT
gsrj-18	132	188	o	o	NOUN
gsrj-18	132	189	lnitiolize\'•riollleq	lnitiolize\'•riollleq	NOUN
gsrj-18	132	190	i	i	PRON
gsrj-18	132	191	fni1lltlin	fni1lltlin	PROPN
gsrj-18	132	192	:	:	PUNCT
gsrj-18	132	193	,	,	PUNCT
gsrj-18	132	194	.uiate	.uiate	VERB
gsrj-18	132	195	p	p	NOUN
gsrj-18	132	196	•	•	NUM
gsrj-18	132	197	nk	nk	NOUN
gsrj-18	132	198	)	)	PUNCT
gsrj-18	132	199	add	add	VERB
gsrj-18	132	200	i	i	PROPN
gsrj-18	132	201	io	io	PROPN
gsrj-18	132	202	nfanli	nfanli	PROPN
gsrj-18	132	203	>	>	PROPN
gsrj-18	132	204	t	t	PROPN
gsrj-18	132	205	26	26	NUM
gsrj-18	132	206	lrumlrze	lrumlrze	NOUN
gsrj-18	132	207	,	,	PUNCT
gsrj-18	132	208	onollle	onollle	ADJ
gsrj-18	132	209	l'hln	l'hln	PROPN
gsrj-18	132	210	(	(	PUNCT
gsrj-18	132	211	p	p	PROPN
gsrj-18	132	212	1)'(0	1)'(0	NUM
gsrj-18	132	213	i	i	NOUN
gsrj-18	132	214	)	)	PUNCT
gsrj-18	132	215	27	27	NUM
gsrj-18	132	216	end	end	NOUN
gsrj-18	132	217	loop	loop	NOUN
gsrj-18	132	218	28	28	NUM
gsrj-18	132	219	lcitimr	lcitimr	NOUN
gsrj-18	132	220	"	"	PUNCT
gsrj-18	132	221	'	'	PUNCT
gsrj-18	132	222	w1h	w1h	NOUN
gsrj-18	132	223	pt	pt	NOUN
gsrj-18	132	224	-	-	PUNCT
gsrj-18	132	225	quals	qual	NOUN
gsrj-18	132	226	•	•	NOUN
gsrj-18	132	227	"	"	PUNCT
gsrj-18	132	228	p	p	NOUN
gsrj-18	132	229	•	•	NOUN
gsrj-18	132	230	"	"	PUNCT
gsrj-18	132	231	291citimr"'"'m~-"q-	291citimr"'"'m~-"q-	NUM
gsrj-18	132	232	"	"	PUNCT
gsrj-18	132	233	jo	jo	PROPN
gsrj-18	132	234	lru1labz£	lru1labz£	PROPN
gsrj-18	132	235	sl!102	sl!102	DET
gsrj-18	132	236	i,_,~.	i,_,~.	NOUN
gsrj-18	132	237	-,'in	-,'in	PUNCT
gsrj-18	132	238	n	n	PRON
gsrj-18	132	239	••	••	NOUN
gsrj-18	132	240	ji	ji	PROPN
gsrj-18	132	241	1'nn1	1'nn1	NUM
gsrj-18	132	242	l'lxilals	l'lxilal	NOUN
gsrj-18	132	243	followed	follow	VERB
gsrj-18	132	244	by	by	ADP
gsrj-18	132	245	i	i	PRON
gsrj-18	132	246	'	'	PART
gsrj-18	132	247	32primq	32primq	NUM
gsrj-18	132	248	,	,	PUNCT
gsrj-18	132	249	quakfol1	quakfol1	NOUN
gsrj-18	132	250	-	-	PUNCT
gsrj-18	132	251	dbyq	dbyq	NOUN
gsrj-18	132	252	jl	jl	NOUN
gsrj-18	132	253	prim	prim	PROPN
gsrj-18	132	254	plu,~ual	plu,~ual	PROPN
gsrj-18	132	255	,	,	PUNCT
gsrj-18	132	256	fol	fol	NOUN
gsrj-18	132	257	..	..	PUNCT
gsrj-18	132	258	_	_	PUNCT
gsrj-18	132	259	..	..	PUNCT
gsrj-18	132	260	by	by	ADP
gsrj-18	132	261	pili	pili	NOUN
gsrj-18	132	262	:	:	PUNCT
gsrj-18	132	263	34	34	NUM
gsrj-18	132	264	lnitializc	lnitializc	PROPN
gsrj-18	132	265	li	li	PROPN
gsrj-18	132	266	,	,	PUNCT
gsrj-18	132	267	t	t	PROPN
gsrj-18	132	268	l'llinfiicionli	l'llinfiicionli	PROPN
gsrj-18	132	269	,	,	PUNCT
gsrj-18	132	270	t	t	PROPN
gsrj-18	132	271	i.	i.	NOUN
gsrj-18	132	272	l'bil	l'bil	PROPN
gsrj-18	132	273	351jcktc	351jcktc	PROPN
gsrj-18	132	274	clanall	clanall	NOUN
gsrj-18	132	275	,	,	PUNCT
gsrj-18	132	276	0	0	NUM
gsrj-18	132	277	-	-	SYM
gsrj-18	132	278	2	2	NUM
gsrj-18	132	279	m	m	NOUN
gsrj-18	132	280	l'lnnfllda'sll5	l'lnnfllda'sll5	PROPN
gsrj-18	132	281	t	t	PROPN
gsrj-18	132	282	.16sun	.16sun	PROPN
gsrj-18	132	283	loop	loop	PROPN
gsrj-18	132	284	17	17	NUM
gsrj-18	132	285	38	38	NUM
gsrj-18	132	286	forim'!p'lln~(2,l'l!in	forim'!p'lln~(2,l'l!in	NOUN
gsrj-18	132	287	)	)	PUNCT
gsrj-18	132	288	lfl'h,,"lmodi•o	lfl'h,,"lmodi•o	NOUN
gsrj-18	132	289	39	39	NUM
gsrj-18	132	290	40endloop	40endloop	NUM
gsrj-18	132	291	addilol'bil	addilol'bil	PROPN
gsrj-18	132	292	ic10rw5i	ic10rw5i	VERB
gsrj-18	132	293	41	41	NUM
gsrj-18	132	294	lnitlallzc	lnitlallzc	NOUN
gsrj-18	132	295	(	(	PUNCT
gsrj-18	132	296	jg	jg	PROPN
gsrj-18	132	297	pr!meslestlb	pr!meslestlb	NOUN
gsrj-18	132	298	:	:	PUNCT
gsrj-18	132	299	lnlootjg	lnlootjg	NOUN
gsrj-18	132	300	•	•	NUM
gsrj-18	132	301	2	2	NUM
gsrj-18	132	302	,	,	PUNCT
gsrj-18	132	303	3	3	NUM
gsrj-18	132	304	,	,	PUNCT
gsrj-18	132	305	5	5	NUM
gsrj-18	132	306	,	,	PUNCT
gsrj-18	132	307	7	7	NUM
gsrj-18	132	308	,	,	PUNCT
gsrj-18	132	309	ii	ii	NOUN
gsrj-18	132	310	,	,	PUNCT
gsrj-18	132	311	13	13	NUM
gsrj-18	132	312	,	,	PUNCT
gsrj-18	132	313	17	17	NUM
gsrj-18	132	314	,	,	PUNCT
gsrj-18	132	315	19	19	NUM
gsrj-18	132	316	,	,	PUNCT
gsrj-18	132	317	23	23	NUM
gsrj-18	132	318	,	,	PUNCT
gsrj-18	132	319	29	29	NUM
gsrj-18	132	320	,	,	PUNCT
gsrj-18	132	321	31	31	NUM
gsrj-18	132	322	,	,	PUNCT
gsrj-18	132	323	37	37	NUM
gsrj-18	132	324	,	,	PUNCT
gsrj-18	132	325	41	41	NUM
gsrj-18	132	326	,	,	PUNCT
gsrj-18	132	327	43	43	NUM
gsrj-18	132	328	,	,	PUNCT
gsrj-18	132	329	47	47	NUM
gsrj-18	132	330	,	,	PUNCT
gsrj-18	132	331	53	53	NUM
gsrj-18	132	332	,	,	PUNCT
gsrj-18	132	333	59	59	NUM
gsrj-18	132	334	,	,	PUNCT
gsrj-18	132	335	61	61	NUM
gsrj-18	132	336	,	,	PUNCT
gsrj-18	132	337	71	71	NUM
gsrj-18	132	338	,	,	PUNCT
gsrj-18	132	339	73	73	NUM
gsrj-18	132	340	,	,	PUNCT
gsrj-18	132	341	79	79	NUM
gsrj-18	132	342	,	,	PUNCT
gsrj-18	132	343	83	83	NUM
gsrj-18	132	344	,	,	PUNCT
gsrj-18	132	345	89	89	NUM
gsrj-18	132	346	,	,	PUNCT
gsrj-18	132	347	97	97	NUM
gsrj-18	132	348	42	42	NUM
gsrj-18	132	349	lnitialw	lnitialw	NOUN
gsrj-18	132	350	:	:	PUNCT
gsrj-18	132	351	m.tblc	m.tblc	PROPN
gsrj-18	132	352	e-1	e-1	PROPN
gsrj-18	132	353	-osian	-osian	PROPN
gsrj-18	132	354	loco	loco	PROPN
gsrj-18	132	355	44	44	NUM
gsrj-18	132	356	4.~	4.~	NUM
gsrj-18	132	357	46	46	NUM
gsrj-18	132	358	,	,	PUNCT
gsrj-18	132	359	fl	fl	PROPN
gsrj-18	132	360	48	48	NUM
gsrj-18	132	361	49fm•up	49fm•up	NUM
gsrj-18	132	362	ll'bilee•i	ll'bilee•i	PROPN
gsrj-18	132	363	lffln	lffln	VERB
gsrj-18	132	364	dcmcnof'prina.f	dcmcnof'prina.f	PROPN
gsrj-18	132	365	~,thant(k)(jsi	~,thant(k)(jsi	PUNCT
gsrj-18	132	366	is	be	AUX
gsrj-18	132	367	nn1	nn1	PROPN
gsrj-18	132	368	in	in	ADP
gsrj-18	132	369	phi1'"factordi~	phi1'"factordi~	NOUN
gsrj-18	132	370	efirq	efirq	PROPN
gsrj-18	132	371	clara11	clara11	NOUN
gsrj-18	132	372	rlprimcd	rlprimcd	NOUN
gsrj-18	132	373	°	°	NUM
gsrj-18	132	374	''	''	PUNCT
gsrj-18	132	375	thlnlool	thlnlool	NOUN
gsrj-18	132	376	j~	j~	PROPN
gsrj-18	132	377	else	else	ADV
gsrj-18	132	378	delele	delele	PROPN
gsrj-18	132	379	lir.;t	lir.;t	PROPN
gsrj-18	132	380	elemolll	elemolll	NOUN
gsrj-18	132	381	of	of	ADP
gsrj-18	132	382	primoslesslbonloolist	primoslesslbonloolist	NOUN
gsrj-18	132	383	!	!	PUNCT
gsrj-18	133	1	:	:	PUNCT
gsrj-18	133	2	4	4	X
gsrj-18	133	3	)	)	PUNCT
gsrj-18	133	4	lnitiali1e	lnitiali1e	NOUN
gsrj-18	133	5	51:~	51:~	NOUN
gsrj-18	133	6	r-.a	r-.a	NOUN
gsrj-18	133	7	,	,	PUNCT
gsrj-18	133	8	nk	nk	PROPN
gsrj-18	133	9	-~-	-~-	PROPN
gsrj-18	133	10	,	,	PUNCT
gsrj-18	133	11	.	.	PUNCT
gsrj-18	134	1	51	51	NUM
gsrj-18	134	2	l'nnl	l'nnl	NOUN
gsrj-18	134	3	!	!	PUNCT
gsrj-18	135	1	:	:	PUNCT
gsrj-18	135	2	,	,	PUNCT
gsrj-18	135	3	cpols	cpol	NOUN
gsrj-18	135	4	followed	follow	VERB
gsrj-18	135	5	by	by	ADP
gsrj-18	135	6	e	e	PROPN
gsrj-18	135	7	52	52	NUM
gsrj-18	135	8	lnitializc	lnitializc	NOUN
gsrj-18	135	9	,	,	PUNCT
gsrj-18	135	10	'	'	PUNCT
gsrj-18	135	11	driable	driable	ADJ
gsrj-18	135	12	p!u,~1u!tipller	p!u,~1u!tipller	PROPN
gsrj-18	135	13	sls	sls	PROPN
gsrj-18	135	14	..	..	PUNCT
gsrj-18	135	15	t~	t~	PUNCT
gsrj-18	135	16	~	~	PUNCT
gsrj-18	136	1	5s	5s	NUM
gsrj-18	136	2	561	561	NUM
gsrj-18	136	3	:	:	PUNCT
gsrj-18	136	4	ndloop	ndloop	ADV
gsrj-18	136	5	111,ilc	111,ilc	NUM
gsrj-18	136	6	:	:	PUNCT
gsrj-18	136	7	(	(	PUNCT
gsrj-18	136	8	(	(	PUNCT
gsrj-18	136	9	(	(	PUNCT
gsrj-18	136	10	l'h;s:',lull	l'h;s:',lull	X
gsrj-18	136	11	~	~	SYM
gsrj-18	136	12	ia'phn	ia'phn	ADJ
gsrj-18	136	13	)	)	PUNCT
gsrj-18	136	14	+	+	PUNCT
gsrj-18	136	15	l)if	l)if	NOUN
gsrj-18	136	16	.	.	PUNCT
gsrj-18	136	17	)	)	PUNCT
gsrj-18	136	18	m-.1	m-.1	VERB
gsrj-18	136	19	1	1	NUM
gsrj-18	136	20	dur	dur	X
gsrj-18	136	21	,	,	PUNCT
gsrj-18	136	22	;	;	PUNCT
gsrj-18	136	23	rwl	rwl	VERB
gsrj-18	136	24	apnl	apnl	NOUN
gsrj-18	136	25	0	0	NUM
gsrj-18	136	26	p!u,'c\tllll	p!u,'c\tllll	PROPN
gsrj-18	136	27	>	>	X
gsrj-18	136	28	her	her	PRON
gsrj-18	136	29	plu.~mulbpbor+	plu.~mulbpbor+	NOUN
gsrj-18	137	1	i	i	PRON
gsrj-18	137	2	~	~	PUNCT
gsrj-18	137	3	lcitimr	lcitimr	NOUN
gsrj-18	137	4	ma1bk	ma1bk	NUM
gsrj-18	137	5	d	d	SYM
gsrj-18	137	6	•	•	NUM
gsrj-18	137	7	(	(	PUNCT
gsrj-18	137	8	(	(	PUNCT
gsrj-18	137	9	p!,l"mdtiplicr'pbi),,i	p!,l"mdtiplicr'pbi),,i	NOUN
gsrj-18	137	10	+	+	CCONJ
gsrj-18	138	1	i	i	NOUN
gsrj-18	138	2	)	)	PUNCT
gsrj-18	138	3	'	'	NUM
gsrj-18	139	1	1	1	NUM
gsrj-18	139	2	!	!	NUM
gsrj-18	139	3	58	58	NUM
gsrj-18	139	4	lcitimr	lcitimr	NOUN
gsrj-18	139	5	"	"	PUNCT
gsrj-18	139	6	'	'	PUNCT
gsrj-18	139	7	w1h	w1h	NOUN
gsrj-18	139	8	~--o-	~--o-	NUM
gsrj-18	139	9	"	"	PUNCT
gsrj-18	139	10	'	'	PUNCT
gsrj-18	139	11	!	!	PUNCT
gsrj-18	140	1	d	d	X
gsrj-18	140	2	l'nnl	l'nnl	PROPN
gsrj-18	140	3	uoquab	uoquab	NOUN
gsrj-18	140	4	fol1	fol1	PROPN
gsrj-18	140	5	-	-	PUNCT
gsrj-18	140	6	d	d	PROPN
gsrj-18	140	7	by	by	ADP
gsrj-18	140	8	u	u	NOUN
gsrj-18	140	9	60	60	NUM
gsrj-18	140	10	l'nnl	l'nnl	PROPN
gsrj-18	140	11	"	"	PUNCT
gsrj-18	140	12	ooulyl'llo	ooulyl'llo	NOUN
gsrj-18	140	13	:	:	PUNCT
gsrj-18	140	14	s	s	PART
gsrj-18	140	15	'	'	PUNCT
gsrj-18	140	16	lllr()ij(j]i	lllr()ij(j]i	ADJ
gsrj-18	140	17	lugariul\l!>~	lugariul\l!>~	PROPN
gsrj-18	140	18	61	61	NUM
gsrj-18	140	19	lnitlallzcwrublc	lnitlallzcwrublc	NOUN
gsrj-18	140	20	m	m	NOUN
gsrj-18	140	21	=	=	NOUN
gsrj-18	140	22	u!ff-¢,ffllm	u!ff-¢,ffllm	ADJ
gsrj-18	140	23	-	-	PUNCT
gsrj-18	140	24	lnpn	lnpn	NOUN
gsrj-18	140	25	61	61	NUM
gsrj-18	140	26	lmtiilli	lmtiilli	NOUN
gsrj-18	140	27	:	:	PUNCT
gsrj-18	140	28	«	«	PUNCT
gsrj-18	140	29	v&bltc	v&bltc	ADJ
gsrj-18	140	30	•	•	NOUN
gsrj-18	140	31	m	m	VERB
gsrj-18	140	32	r.mt'd	r.mt'd	PROPN
gsrj-18	140	33	tu	tu	PROPN
gsrj-18	140	34	i.ir	i.ir	PROPN
gsrj-18	140	35	e	e	PROPN
gsrj-18	140	36	pw	pw	PROPN
gsrj-18	140	37	,	,	PUNCT
gsrj-18	140	38	aall	aall	PROPN
gsrj-18	140	39	au	au	PROPN
gsrj-18	140	40	!	!	PROPN
gsrj-18	140	41	n	n	PROPN
gsrj-18	140	42	6l	6l	NUM
gsrj-18	140	43	lnitializc	lnitializc	NOUN
gsrj-18	140	44	lllrinr	lllrinr	PROPN
gsrj-18	140	45	moctuab	moctuab	ADJ
gsrj-18	140	46	•	•	PRON
gsrj-18	140	47	"	"	PUNCT
gsrj-18	140	48	scatt	scatt	NOUN
gsrj-18	140	49	mcssa,;c	mcssa,;c	NOUN
gsrj-18	140	50	•	•	NOUN
gsrj-18	140	51	•	•	NUM
gsrj-18	140	52	641mlabz£	641mlabz£	NUM
gsrj-18	140	53	sl!102ccciual,•"l	sl!102ccciual,•"l	NOUN
gsrj-18	140	54	:	:	PUNCT
gsrj-18	140	55	nc	nc	ADJ
gsrj-18	140	56	:	:	PUNCT
gsrj-18	140	57	mllodlllwllllc	mllodlllwllllc	ADJ
gsrj-18	140	58	••	••	NOUN
gsrj-18	140	59	65	65	NUM
gsrj-18	140	60	prim~	prim~	NOUN
gsrj-18	140	61	fblmod	fblmod	NOUN
gsrj-18	140	62	by	by	ADP
gsrj-18	140	63	m	m	PROPN
gsrj-18	140	64	<	<	X
gsrj-18	140	65	,	,	PUNCT
gsrj-18	140	66	6	6	NUM
gsrj-18	140	67	prim	prim	ADJ
gsrj-18	140	68	caiwl	caiwl	NOUN
gsrj-18	140	69	,	,	PUNCT
gsrj-18	140	70	folk	folk	NOUN
gsrj-18	140	71	>	>	X
gsrj-18	140	72	wod	wod	VERB
gsrj-18	140	73	by	by	ADP
gsrj-18	140	74	c	c	PROPN
gsrj-18	140	75	67	67	NUM
gsrj-18	140	76	lnitializc	lnitializc	NOUN
gsrj-18	140	77	wt	wt	ADP
gsrj-18	140	78	noo!ntc,.adli31	noo!ntc,.adli31	NOUN
gsrj-18	140	79	•	•	PROPN
gsrj-18	140	80	i	i	NOUN
gsrj-18	140	81	,	,	PUNCT
gsrj-18	140	82	2	2	NUM
gsrj-18	140	83	68	68	NUM
gsrj-18	140	84	delde	delde	VERB
gsrj-18	140	85	all	all	DET
gsrj-18	140	86	elemom	elemom	NOUN
gsrj-18	140	87	or	or	CCONJ
gsrj-18	140	88	nonlnlqpl)li	nonlnlqpl)li	ADP
gsrj-18	140	89	<	<	X
gsrj-18	140	90	l	l	NOUN
gsrj-18	140	91	69	69	NUM
gsrj-18	140	92	lnitlallzc	lnitlallzc	NOUN
gsrj-18	140	93	wrublc	wrublc	NOUN
gsrj-18	140	94	:	:	PUNCT
gsrj-18	140	95	multiplier•	multiplier•	VERB
gsrj-18	140	96	i	i	PRON
gsrj-18	140	97	10	10	NUM
gsrj-18	140	98	lnitiali	lnitiali	PROPN
gsrj-18	140	99	,	,	PUNCT
gsrj-18	140	100	c	c	NOUN
gsrj-18	140	101	..	..	PUNCT
gsrj-18	140	102	,	,	PUNCT
gsrj-18	140	103	;	;	PUNCT
gsrj-18	140	104	.,i-	.,i-	NUM
gsrj-18	140	105	,	,	PUNCT
gsrj-18	140	106	io	io	NOUN
gsrj-18	140	107	,	,	PUNCT
gsrj-18	140	108	j)lr.-lop{c	j)lr.-lop{c	NOUN
gsrj-18	140	109	)	)	PUNCT
gsrj-18	140	110	71	71	NUM
gsrj-18	140	111	slanlooo	slanlooo	NOUN
gsrj-18	140	112	72	72	NUM
gsrj-18	140	113	1111ile	1111ile	NUM
gsrj-18	140	114	lultiplierdoesoot~	lultiplierdoesoot~	NOUN
gsrj-18	140	115	ioixxkx	ioixxkx	NOUN
gsrj-18	140	116	>	>	X
gsrj-18	140	117	73	73	NUM
gsrj-18	140	118	lf((loj(n•	lf((loj(n•	NOUN
gsrj-18	140	119	,	,	PUNCT
gsrj-18	140	120	.!ultiplier+m))'!ior()jc))mod	.!ultiplier+m))'!ior()jc))mod	PUNCT
gsrj-18	141	1	i	i	PRON
gsrj-18	141	2	doesdoioqualo	doesdoioqualo	VERB
gsrj-18	141	3	74	74	NUM
gsrj-18	141	4	am((icftn	am((icftn	PROPN
gsrj-18	141	5	'	'	PUNCT
gsrj-18	141	6	.fultiplia+m)~)10	.fultiplia+m)~)10	PROPN
gsrj-18	141	7	l	l	PROPN
gsrj-18	141	8	..	..	PUNCT
gsrj-18	141	9	_nl.is1	_nl.is1	PUNCT
gsrj-18	141	10	'	'	PUNCT
gsrj-18	141	11	is	be	AUX
gsrj-18	141	12	iltiplia-1,'\luhiplia	iltiplia-1,'\luhiplia	ADV
gsrj-18	141	13	+	+	ADV
gsrj-18	141	14	1	1	NUM
gsrj-18	141	15	71	71	NUM
gsrj-18	141	16	>	>	X
gsrj-18	141	17	else	else	PROPN
gsrj-18	141	18	d2	d2	PROPN
gsrj-18	141	19	(	(	PUNCT
gsrj-18	141	20	(	(	PUNCT
gsrj-18	141	21	iot(n'nmultiplier•m)}~	iot(n'nmultiplier•m)}~	X
gsrj-18	141	22	)	)	PUNCT
gsrj-18	141	23	77	77	NUM
gsrj-18	142	1	711fmh~	711fmh~	NUM
gsrj-18	142	2	791f02	791f02	NUM
gsrj-18	142	3	-	-	SYM
gsrj-18	142	4	1	1	NUM
gsrj-18	142	5	iio	iio	NOUN
gsrj-18	142	6	pnnl	pnnl	VERB
gsrj-18	142	7	·	·	PUNCT
gsrj-18	142	8	u	u	NOUN
gsrj-18	142	9	more	more	ADV
gsrj-18	142	10	thoo	thoo	ADJ
gsrj-18	142	11	•	•	ADJ
gsrj-18	142	12	rmllm	rmllm	NOUN
gsrj-18	142	13	11er.111ms	11er.111ms	PROPN
gsrj-18	142	14	io	io	PROPN
gsrj-18	142	15	col	col	PROPN
gsrj-18	142	16	......	......	PROPN
gsrj-18	142	17	_	_	NOUN
gsrj-18	142	18	.	.	PUNCT
gsrj-18	143	1	81	81	NUM
gsrj-18	143	2	else	else	ADV
gsrj-18	143	3	82	82	NUM
gsrj-18	143	4	printd2	printd2	NOUN
gsrj-18	143	5	ill	ill	ADJ
gsrj-18	143	6	pri	pri	NOUN
gsrj-18	143	7	,	,	PUNCT
gsrj-18	143	8	.	.	PUNCT
gsrj-18	143	9	,	,	PUNCT
gsrj-18	143	10	iow	iow	PROPN
gsrj-18	143	11	ma	ma	PROPN
gsrj-18	143	12	rmra11c1'	rmra11c1'	PROPN
gsrj-18	143	13	.	.	PUNCT
gsrj-18	143	14	"l	"l	PUNCT
gsrj-18	143	15	"	"	PUNCT
gsrj-18	143	16	"	"	PUNCT
gsrj-18	143	17	84	84	NUM
gsrj-18	143	18	lrutlall2o	lrutlall2o	PROPN
gsrj-18	143	19	stnn2	stnn2	PUNCT
gsrj-18	143	20	lbrouobsan1l'runol'iict"'120b0n	lbrouobsan1l'runol'iict"'120b0n	NOUN
gsrj-18	144	1	"	"	PUNCT
gsrj-18	144	2	lleraoons	lleraoon	NOUN
gsrj-18	144	3	uswt	uswt	PROPN
gsrj-18	144	4	sam	sam	PROPN
gsrj-18	144	5	oruno	oruno	PROPN
gsrj-18	144	6	fac1onzlwon	fac1onzlwon	PROPN
gsrj-18	144	7	•	•	PUNCT
gsrj-18	144	8	as	as	ADP
gsrj-18	144	9	l!!ltl2ll2r	l!!ltl2ll2r	PROPN
gsrj-18	144	10	rridj	rridj	NOUN
gsrj-18	144	11	!	!	PUNCT
gsrj-18	145	1	~	~	PUNCT
gsrj-18	145	2	=	=	PUNCT
gsrj-18	145	3	·	·	PUNCT
gsrj-18	145	4	,	,	PUNCT
gsrj-18	145	5	u!fflll	u!fflll	PRON
gsrj-18	145	6	lotlarithms	lotlarithm	NOUN
gsrj-18	145	7	=	=	PUNCT
gsrj-18	145	8	•	•	NUM
gsrj-18	145	9	86	86	NUM
gsrj-18	145	10	lcitimr	lcitimr	NOUN
gsrj-18	145	11	.-.-ia	.-.-ia	NOUN
gsrj-18	145	12	,	,	PUNCT
gsrj-18	145	13	blc	blc	PROPN
gsrj-18	145	14	l1er,6tnm•sc	l1er,6tnm•sc	PROPN
gsrj-18	145	15	:	:	PUNCT
gsrj-18	145	16	uiprim	uiprim	ADJ
gsrj-18	145	17	:	:	PUNCT
gsrj-18	145	18	faruriatiw	faruriatiw	NOUN
gsrj-18	145	19	•	•	ADP
gsrj-18	145	20	n	n	NUM
gsrj-18	145	21	-2	-2	NOUN
gsrj-18	145	22	117	117	NUM
gsrj-18	145	23	l'nnl	l'nnl	PROPN
gsrj-18	145	24	11rcqd	11rcqd	NUM
gsrj-18	145	25	,	,	PUNCT
gsrj-18	145	26	samj'nm	samj'nm	ADP
gsrj-18	145	27	:	:	PUNCT
gsrj-18	145	28	l'icionlll!joo	l'icionlll!joo	NOUN
gsrj-18	145	29	follov,,:d	follov,,:d	NOUN
gsrj-18	145	30	by	by	ADP
gsrj-18	145	31	l1a11kmviiscmj'nm	l1a11kmviiscmj'nm	PROPN
gsrj-18	145	32	:	:	PUNCT
gsrj-18	145	33	l'aclaulllloll	l'aclaulllloll	NOUN
gsrj-18	145	34	8111mlabz£v1nblcl1a0110mvi&lol>•{(i0ioux:(ioltoll,~un	8111mlabz£v1nblcl1a0110mvi&lol>•{(i0ioux:(ioltoll,~un	NOUN
gsrj-18	145	35	-	-	PUNCT
gsrj-18	145	36	ml'n	ml'n	VERB
gsrj-18	145	37	89	89	NUM
gsrj-18	145	38	prim	prim	ADJ
gsrj-18	145	39	lll'ouj!hu	lll'ouj!hu	PROPN
gsrj-18	145	40	,	,	PUNCT
gsrj-18	145	41	pllhm	pllhm	ADJ
gsrj-18	145	42	fblm'ed	fblm'ed	NOUN
gsrj-18	145	43	by	by	ADP
gsrj-18	145	44	ltmdoosvijloll	ltmdoosvijloll	NOUN
gsrj-18	145	45	'	'	PUNCT
gsrj-18	145	46	georgetown	georgetown	PROPN
gsrj-18	145	47	scientific	scientific	PROPN
gsrj-18	145	48	research	research	PROPN
gsrj-18	145	49	journal	journal	NOUN
gsrj-18	145	50	in	in	ADP
gsrj-18	145	51	lines	line	NOUN
gsrj-18	145	52	43	43	NUM
gsrj-18	145	53	–	–	SYM
gsrj-18	145	54	49	49	NUM
gsrj-18	145	55	,	,	PUNCT
gsrj-18	145	56	the	the	DET
gsrj-18	145	57	program	program	NOUN
gsrj-18	145	58	generates	generate	VERB
gsrj-18	145	59	a	a	DET
gsrj-18	145	60	value	value	NOUN
gsrj-18	145	61	for	for	ADP
gsrj-18	145	62	e	e	NOUN
gsrj-18	145	63	,	,	PUNCT
gsrj-18	145	64	which	which	PRON
gsrj-18	145	65	must	must	AUX
gsrj-18	145	66	be	be	AUX
gsrj-18	145	67	greater	great	ADJ
gsrj-18	145	68	than	than	ADP
gsrj-18	145	69	1	1	NUM
gsrj-18	145	70	,	,	PUNCT
gsrj-18	145	71	less	less	ADJ
gsrj-18	145	72	than	than	ADP
gsrj-18	145	73	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	145	74	,	,	PUNCT
gsrj-18	145	75	and	and	CCONJ
gsrj-18	145	76	share	share	VERB
gsrj-18	145	77	no	no	DET
gsrj-18	145	78	common	common	ADJ
gsrj-18	145	79	factors	factor	NOUN
gsrj-18	145	80	with	with	ADP
gsrj-18	145	81	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	145	82	.	.	PUNCT
gsrj-18	146	1	the	the	DET
gsrj-18	146	2	program	program	NOUN
gsrj-18	146	3	cross	cross	NOUN
gsrj-18	146	4	-	-	ADJ
gsrj-18	146	5	checks	checks	ADJ
gsrj-18	146	6	values	value	NOUN
gsrj-18	146	7	in	in	ADP
gsrj-18	146	8	the	the	DET
gsrj-18	146	9	primeslessthan100list	primeslessthan100list	NOUN
gsrj-18	146	10	against	against	ADP
gsrj-18	146	11	values	value	NOUN
gsrj-18	146	12	in	in	ADP
gsrj-18	146	13	the	the	DET
gsrj-18	146	14	phinfactorslist	phinfactorslist	NOUN
gsrj-18	146	15	until	until	SCONJ
gsrj-18	146	16	it	it	PRON
gsrj-18	146	17	finds	find	VERB
gsrj-18	146	18	a	a	DET
gsrj-18	146	19	value	value	NOUN
gsrj-18	146	20	in	in	ADP
gsrj-18	146	21	the	the	DET
gsrj-18	146	22	primeslessthan100list	primeslessthan100list	NOUN
gsrj-18	146	23	that	that	PRON
gsrj-18	146	24	is	be	AUX
gsrj-18	146	25	not	not	PART
gsrj-18	146	26	in	in	ADP
gsrj-18	146	27	the	the	DET
gsrj-18	146	28	phinfactorslist	phinfactorslist	NOUN
gsrj-18	146	29	,	,	PUNCT
gsrj-18	146	30	which	which	PRON
gsrj-18	146	31	it	it	PRON
gsrj-18	146	32	then	then	ADV
gsrj-18	146	33	sets	set	VERB
gsrj-18	146	34	it	it	PRON
gsrj-18	146	35	to	to	ADP
gsrj-18	146	36	the	the	DET
gsrj-18	146	37	variable	variable	NOUN
gsrj-18	146	38	e.	e.	PROPN
gsrj-18	146	39	by	by	ADP
gsrj-18	146	40	checking	check	VERB
gsrj-18	146	41	primes	prime	NOUN
gsrj-18	146	42	as	as	ADP
gsrj-18	146	43	possible	possible	ADJ
gsrj-18	146	44	values	value	NOUN
gsrj-18	146	45	for	for	ADP
gsrj-18	146	46	e	e	NOUN
gsrj-18	146	47	against	against	ADP
gsrj-18	146	48	the	the	DET
gsrj-18	146	49	factors	factor	NOUN
gsrj-18	146	50	of	of	ADP
gsrj-18	146	51	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	146	52	,	,	PUNCT
gsrj-18	146	53	the	the	DET
gsrj-18	146	54	program	program	NOUN
gsrj-18	146	55	ensures	ensure	VERB
gsrj-18	146	56	that	that	SCONJ
gsrj-18	146	57	whatever	whatever	DET
gsrj-18	146	58	value	value	NOUN
gsrj-18	146	59	it	it	PRON
gsrj-18	146	60	picks	pick	VERB
gsrj-18	146	61	for	for	ADP
gsrj-18	146	62	e	e	NOUN
gsrj-18	146	63	shares	share	NOUN
gsrj-18	146	64	no	no	DET
gsrj-18	146	65	common	common	ADJ
gsrj-18	146	66	factors	factor	NOUN
gsrj-18	146	67	with	with	ADP
gsrj-18	146	68	𝜑𝜑n	𝜑𝜑n	NOUN
gsrj-18	146	69	.	.	PUNCT
gsrj-18	147	1	3.1.4	3.1.4	NUM
gsrj-18	147	2	generating	generating	NOUN
gsrj-18	147	3	d	d	PROPN
gsrj-18	147	4	in	in	ADP
gsrj-18	147	5	lines	line	NOUN
gsrj-18	147	6	52	52	NUM
gsrj-18	147	7	–	–	SYM
gsrj-18	147	8	56	56	NUM
gsrj-18	147	9	,	,	PUNCT
gsrj-18	147	10	the	the	DET
gsrj-18	147	11	program	program	NOUN
gsrj-18	147	12	sets	set	VERB
gsrj-18	147	13	a	a	DET
gsrj-18	147	14	variable	variable	NOUN
gsrj-18	147	15	called	call	VERB
gsrj-18	147	16	“	"	PUNCT
gsrj-18	147	17	phinmultiplier	phinmultiplier	NOUN
gsrj-18	147	18	”	"	PUNCT
gsrj-18	147	19	to	to	ADP
gsrj-18	147	20	1	1	NUM
gsrj-18	147	21	,	,	PUNCT
gsrj-18	147	22	which	which	PRON
gsrj-18	147	23	will	will	AUX
gsrj-18	147	24	act	act	VERB
gsrj-18	147	25	as	as	ADP
gsrj-18	147	26	𝜑𝜑nmultiplier	𝜑𝜑nmultiplier	ADJ
gsrj-18	147	27	in	in	ADP
gsrj-18	147	28	equation	equation	NOUN
gsrj-18	147	29	5	5	NUM
gsrj-18	147	30	.	.	PUNCT
gsrj-18	148	1	while	while	SCONJ
gsrj-18	148	2	d	d	NOUN
gsrj-18	148	3	does	do	AUX
gsrj-18	148	4	not	not	PART
gsrj-18	148	5	equal	equal	VERB
gsrj-18	148	6	an	an	DET
gsrj-18	148	7	integer	integer	NOUN
gsrj-18	148	8	solution	solution	NOUN
gsrj-18	148	9	,	,	PUNCT
gsrj-18	148	10	the	the	DET
gsrj-18	148	11	program	program	NOUN
gsrj-18	148	12	continuously	continuously	ADV
gsrj-18	148	13	adds	add	VERB
gsrj-18	148	14	1	1	NUM
gsrj-18	148	15	to	to	ADP
gsrj-18	148	16	the	the	DET
gsrj-18	148	17	value	value	NOUN
gsrj-18	148	18	of	of	ADP
gsrj-18	148	19	phinmultiplier	phinmultiplier	NOUN
gsrj-18	148	20	.	.	PUNCT
gsrj-18	149	1	when	when	SCONJ
gsrj-18	149	2	phinmultiplier	phinmultiplier	NOUN
gsrj-18	149	3	iterates	iterate	VERB
gsrj-18	149	4	enough	enough	ADV
gsrj-18	149	5	that	that	SCONJ
gsrj-18	149	6	it	it	PRON
gsrj-18	149	7	yields	yield	VERB
gsrj-18	149	8	an	an	DET
gsrj-18	149	9	integer	integer	NOUN
gsrj-18	149	10	value	value	NOUN
gsrj-18	149	11	for	for	ADP
gsrj-18	149	12	d	d	PROPN
gsrj-18	149	13	,	,	PUNCT
gsrj-18	149	14	the	the	DET
gsrj-18	149	15	program	program	NOUN
gsrj-18	149	16	sets	set	VERB
gsrj-18	149	17	d	d	NOUN
gsrj-18	149	18	to	to	PART
gsrj-18	149	19	𝜑𝜑n	𝜑𝜑n	VERB
gsrj-18	149	20	*	*	NOUN
gsrj-18	149	21	𝜑𝜑nmultiplier	𝜑𝜑nmultiplier	NOUN
gsrj-18	149	22	+	+	X
gsrj-18	149	23	1)/e	1)/e	NUM
gsrj-18	149	24	,	,	PUNCT
gsrj-18	149	25	where	where	SCONJ
gsrj-18	149	26	𝜑𝜑nmultiplier	𝜑𝜑nmultiplier	NOUN
gsrj-18	149	27	represents	represent	VERB
gsrj-18	149	28	the	the	DET
gsrj-18	149	29	number	number	NOUN
gsrj-18	149	30	of	of	ADP
gsrj-18	149	31	iterations	iteration	NOUN
gsrj-18	149	32	it	it	PRON
gsrj-18	149	33	took	take	VERB
gsrj-18	149	34	to	to	PART
gsrj-18	149	35	yield	yield	VERB
gsrj-18	149	36	an	an	DET
gsrj-18	149	37	integer	integer	NOUN
gsrj-18	149	38	solution	solution	NOUN
gsrj-18	149	39	for	for	ADP
gsrj-18	149	40	d.	d.	PROPN
gsrj-18	149	41	3.2	3.2	NUM
gsrj-18	149	42	the	the	DET
gsrj-18	149	43	code	code	NOUN
gsrj-18	149	44	behind	behind	ADP
gsrj-18	149	45	logarithmic	logarithmic	ADJ
gsrj-18	149	46	techniques	technique	NOUN
gsrj-18	149	47	to	to	PART
gsrj-18	149	48	calculate	calculate	VERB
gsrj-18	149	49	d	d	PROPN
gsrj-18	149	50	(	(	PUNCT
gsrj-18	149	51	lines	line	NOUN
gsrj-18	149	52	48	48	NUM
gsrj-18	149	53	–	–	SYM
gsrj-18	149	54	71	71	NUM
gsrj-18	149	55	)	)	PUNCT
gsrj-18	149	56	in	in	ADP
gsrj-18	149	57	lines	line	NOUN
gsrj-18	149	58	61	61	NUM
gsrj-18	149	59	–	–	PUNCT
gsrj-18	149	60	62	62	NUM
gsrj-18	149	61	,	,	PUNCT
gsrj-18	149	62	the	the	DET
gsrj-18	149	63	program	program	NOUN
gsrj-18	149	64	asks	ask	VERB
gsrj-18	149	65	for	for	ADP
gsrj-18	149	66	an	an	DET
gsrj-18	149	67	integer	integer	NOUN
gsrj-18	149	68	input	input	NOUN
gsrj-18	149	69	and	and	CCONJ
gsrj-18	149	70	sets	set	VERB
gsrj-18	149	71	it	it	PRON
gsrj-18	149	72	to	to	ADP
gsrj-18	149	73	the	the	DET
gsrj-18	149	74	variable	variable	ADJ
gsrj-18	149	75	m.	m.	NOUN
gsrj-18	149	76	it	it	PRON
gsrj-18	149	77	then	then	ADV
gsrj-18	149	78	encrypts	encrypt	VERB
gsrj-18	149	79	m	m	VERB
gsrj-18	149	80	by	by	ADP
gsrj-18	149	81	raising	raise	VERB
gsrj-18	149	82	it	it	PRON
gsrj-18	149	83	to	to	ADP
gsrj-18	149	84	the	the	DET
gsrj-18	149	85	value	value	NOUN
gsrj-18	149	86	of	of	ADP
gsrj-18	149	87	e	e	NOUN
gsrj-18	149	88	,	,	PUNCT
gsrj-18	149	89	dividing	divide	VERB
gsrj-18	149	90	the	the	DET
gsrj-18	149	91	entire	entire	ADJ
gsrj-18	149	92	expression	expression	NOUN
gsrj-18	149	93	by	by	ADP
gsrj-18	149	94	n	n	CCONJ
gsrj-18	149	95	,	,	PUNCT
gsrj-18	149	96	and	and	CCONJ
gsrj-18	149	97	taking	take	VERB
gsrj-18	149	98	the	the	DET
gsrj-18	149	99	modulus	modulus	NOUN
gsrj-18	149	100	of	of	ADP
gsrj-18	149	101	the	the	DET
gsrj-18	149	102	division	division	NOUN
gsrj-18	149	103	,	,	PUNCT
gsrj-18	149	104	which	which	PRON
gsrj-18	149	105	is	be	AUX
gsrj-18	149	106	c	c	NOUN
gsrj-18	149	107	,	,	PUNCT
gsrj-18	149	108	the	the	DET
gsrj-18	149	109	ciphertext	ciphertext	ADJ
gsrj-18	149	110	message	message	NOUN
gsrj-18	149	111	.	.	PUNCT
gsrj-18	150	1	in	in	ADP
gsrj-18	150	2	lines	line	NOUN
gsrj-18	150	3	67	67	NUM
gsrj-18	150	4	–	–	SYM
gsrj-18	150	5	82	82	NUM
gsrj-18	150	6	,	,	PUNCT
gsrj-18	150	7	the	the	DET
gsrj-18	150	8	program	program	NOUN
gsrj-18	150	9	initializes	initialize	VERB
gsrj-18	150	10	a	a	DET
gsrj-18	150	11	variable	variable	NOUN
gsrj-18	150	12	called	call	VERB
gsrj-18	150	13	“	"	PUNCT
gsrj-18	150	14	nmultiplier	nmultiplier	NOUN
gsrj-18	150	15	”	"	PUNCT
gsrj-18	150	16	to	to	ADP
gsrj-18	150	17	1	1	NUM
gsrj-18	150	18	which	which	PRON
gsrj-18	150	19	acts	act	VERB
gsrj-18	150	20	as	as	ADP
gsrj-18	150	21	nmultiplier	nmultiplier	NOUN
gsrj-18	150	22	in	in	ADP
gsrj-18	150	23	equation	equation	NOUN
gsrj-18	150	24	6	6	NUM
gsrj-18	150	25	.	.	PUNCT
gsrj-18	151	1	because	because	SCONJ
gsrj-18	151	2	python	python	PROPN
gsrj-18	151	3	has	have	VERB
gsrj-18	151	4	a	a	DET
gsrj-18	151	5	limited	limited	ADJ
gsrj-18	151	6	capacity	capacity	NOUN
gsrj-18	151	7	for	for	ADP
gsrj-18	151	8	running	run	VERB
gsrj-18	151	9	large	large	ADJ
gsrj-18	151	10	numbers	number	NOUN
gsrj-18	151	11	of	of	ADP
gsrj-18	151	12	iterations	iteration	NOUN
gsrj-18	151	13	,	,	PUNCT
gsrj-18	151	14	the	the	DET
gsrj-18	151	15	program	program	NOUN
gsrj-18	151	16	continuously	continuously	ADV
gsrj-18	151	17	adds	add	VERB
gsrj-18	151	18	1	1	NUM
gsrj-18	151	19	to	to	PART
gsrj-18	151	20	nmultiplier	nmultiplier	VERB
gsrj-18	151	21	until	until	ADP
gsrj-18	151	22	nmultiplier	nmultiplier	NOUN
gsrj-18	151	23	=	=	SYM
gsrj-18	151	24	1000000	1000000	NUM
gsrj-18	151	25	(	(	PUNCT
gsrj-18	151	26	the	the	DET
gsrj-18	151	27	first	first	ADJ
gsrj-18	151	28	million	million	NUM
gsrj-18	151	29	iterations	iteration	NOUN
gsrj-18	151	30	)	)	PUNCT
gsrj-18	151	31	instead	instead	ADV
gsrj-18	151	32	of	of	ADP
gsrj-18	151	33	until	until	SCONJ
gsrj-18	151	34	d	d	PROPN
gsrj-18	151	35	is	be	AUX
gsrj-18	151	36	an	an	DET
gsrj-18	151	37	integer	integer	NOUN
gsrj-18	151	38	.	.	PUNCT
gsrj-18	152	1	when	when	SCONJ
gsrj-18	152	2	nmultiplier	nmultiplier	NOUN
gsrj-18	152	3	=	=	SYM
gsrj-18	152	4	1000000	1000000	NUM
gsrj-18	152	5	,	,	PUNCT
gsrj-18	152	6	although	although	SCONJ
gsrj-18	152	7	d	d	PRON
gsrj-18	152	8	might	might	AUX
gsrj-18	152	9	not	not	PART
gsrj-18	152	10	be	be	AUX
gsrj-18	152	11	an	an	DET
gsrj-18	152	12	integer	integer	NOUN
gsrj-18	152	13	,	,	PUNCT
gsrj-18	152	14	the	the	DET
gsrj-18	152	15	program	program	NOUN
gsrj-18	152	16	still	still	ADV
gsrj-18	152	17	cuts	cut	VERB
gsrj-18	152	18	off	off	ADP
gsrj-18	152	19	at	at	ADP
gsrj-18	152	20	this	this	DET
gsrj-18	152	21	point	point	NOUN
gsrj-18	152	22	and	and	CCONJ
gsrj-18	152	23	prints	print	NOUN
gsrj-18	152	24	that	that	PRON
gsrj-18	152	25	d	d	NOUN
gsrj-18	152	26	takes	take	VERB
gsrj-18	152	27	more	more	ADJ
gsrj-18	152	28	than	than	ADP
gsrj-18	152	29	one	one	NUM
gsrj-18	152	30	million	million	NUM
gsrj-18	152	31	iterations	iteration	NOUN
gsrj-18	152	32	to	to	PART
gsrj-18	152	33	calculate	calculate	VERB
gsrj-18	152	34	.	.	PUNCT
gsrj-18	153	1	all	all	DET
gsrj-18	153	2	non	non	ADJ
gsrj-18	153	3	-	-	ADJ
gsrj-18	153	4	integer	integer	ADJ
gsrj-18	153	5	numbers	number	NOUN
gsrj-18	153	6	resulting	result	VERB
gsrj-18	153	7	from	from	ADP
gsrj-18	153	8	log(n*nmultiplier	log(n*nmultipli	ADJ
gsrj-18	153	9	+	+	CCONJ
gsrj-18	153	10	m)/log(c	m)/log(c	NOUN
gsrj-18	153	11	)	)	PUNCT
gsrj-18	153	12	are	be	AUX
gsrj-18	153	13	appended	append	VERB
gsrj-18	153	14	to	to	ADP
gsrj-18	153	15	the	the	DET
gsrj-18	153	16	list	list	NOUN
gsrj-18	153	17	“	"	PUNCT
gsrj-18	153	18	nonintegerdlist	nonintegerdlist	NOUN
gsrj-18	153	19	”	"	PUNCT
gsrj-18	153	20	and	and	CCONJ
gsrj-18	153	21	stored	store	VERB
gsrj-18	153	22	.	.	PUNCT
gsrj-18	154	1	3.3	3.3	NUM
gsrj-18	154	2	the	the	DET
gsrj-18	154	3	code	code	NOUN
gsrj-18	154	4	behind	behind	ADP
gsrj-18	154	5	iterations	iteration	NOUN
gsrj-18	154	6	for	for	ADP
gsrj-18	154	7	semi	semi	ADJ
gsrj-18	154	8	-	-	ADJ
gsrj-18	154	9	prime	prime	ADJ
gsrj-18	154	10	factorization	factorization	NOUN
gsrj-18	154	11	to	to	PART
gsrj-18	154	12	calculate	calculate	VERB
gsrj-18	154	13	d	d	NOUN
gsrj-18	154	14	and	and	CCONJ
gsrj-18	154	15	logarithmic	logarithmic	ADJ
gsrj-18	154	16	techniques	technique	NOUN
gsrj-18	154	17	to	to	PART
gsrj-18	154	18	calculate	calculate	VERB
gsrj-18	154	19	d	d	PROPN
gsrj-18	154	20	(	(	PUNCT
gsrj-18	154	21	lines	line	NOUN
gsrj-18	154	22	72	72	NUM
gsrj-18	154	23	–	–	PUNCT
gsrj-18	154	24	80	80	NUM
gsrj-18	154	25	)	)	PUNCT
gsrj-18	154	26	in	in	ADP
gsrj-18	154	27	lines	line	NOUN
gsrj-18	154	28	86	86	NUM
gsrj-18	154	29	–	–	SYM
gsrj-18	154	30	89	89	NUM
gsrj-18	154	31	,	,	PUNCT
gsrj-18	154	32	the	the	DET
gsrj-18	154	33	iterations	iteration	NOUN
gsrj-18	154	34	for	for	ADP
gsrj-18	154	35	decryption	decryption	NOUN
gsrj-18	154	36	using	use	VERB
gsrj-18	154	37	semi	semi	ADJ
gsrj-18	154	38	-	-	ADJ
gsrj-18	154	39	prime	prime	ADJ
gsrj-18	154	40	factorization	factorization	NOUN
gsrj-18	154	41	and	and	CCONJ
gsrj-18	154	42	for	for	ADP
gsrj-18	154	43	decryption	decryption	NOUN
gsrj-18	154	44	using	use	VERB
gsrj-18	154	45	logarithmic	logarithmic	ADJ
gsrj-18	154	46	techniques	technique	NOUN
gsrj-18	154	47	are	be	AUX
gsrj-18	154	48	both	both	PRON
gsrj-18	154	49	calculated	calculate	VERB
gsrj-18	154	50	using	use	VERB
gsrj-18	154	51	the	the	DET
gsrj-18	154	52	expressions	expression	NOUN
gsrj-18	154	53	n	n	CCONJ
gsrj-18	154	54	–	–	PUNCT
gsrj-18	154	55	2	2	NUM
gsrj-18	154	56	and	and	CCONJ
gsrj-18	154	57	(	(	PUNCT
gsrj-18	154	58	"	"	PUNCT
gsrj-18	154	59	#	#	SYM
gsrj-18	154	60	$	$	SYM
gsrj-18	154	61	%	%	NOUN
gsrj-18	154	62	)	)	PUNCT
gsrj-18	154	63	∗	∗	NOUN
gsrj-18	154	64	(	(	PUNCT
gsrj-18	154	65	,	,	PUNCT
gsrj-18	154	66	respectively	respectively	ADV
gsrj-18	154	67	(	(	PUNCT
gsrj-18	154	68	see	see	VERB
gsrj-18	154	69	introduction	introduction	NOUN
gsrj-18	154	70	of	of	ADP
gsrj-18	154	71	derivation	derivation	NOUN
gsrj-18	154	72	of	of	ADP
gsrj-18	154	73	iterations	iteration	NOUN
gsrj-18	154	74	)	)	PUNCT
gsrj-18	154	75	.	.	PUNCT
gsrj-18	155	1	the	the	DET
gsrj-18	155	2	program	program	NOUN
gsrj-18	155	3	then	then	ADV
gsrj-18	155	4	prints	print	VERB
gsrj-18	155	5	the	the	DET
gsrj-18	155	6	number	number	NOUN
gsrj-18	155	7	of	of	ADP
gsrj-18	155	8	iterations	iteration	NOUN
gsrj-18	155	9	needed	need	VERB
gsrj-18	155	10	in	in	ADP
gsrj-18	155	11	either	either	DET
gsrj-18	155	12	case	case	NOUN
gsrj-18	155	13	,	,	PUNCT
gsrj-18	155	14	allowing	allow	VERB
gsrj-18	155	15	for	for	ADP
gsrj-18	155	16	quick	quick	ADJ
gsrj-18	155	17	comparison	comparison	NOUN
gsrj-18	155	18	of	of	ADP
gsrj-18	155	19	either	either	DET
gsrj-18	155	20	method	method	NOUN
gsrj-18	155	21	’s	’s	PART
gsrj-18	155	22	effectiveness	effectiveness	NOUN
gsrj-18	155	23	in	in	ADP
gsrj-18	155	24	different	different	ADJ
gsrj-18	155	25	circumstances	circumstance	NOUN
gsrj-18	155	26	.	.	PUNCT
gsrj-18	156	1	4	4	X
gsrj-18	156	2	.	.	X
gsrj-18	156	3	results	result	NOUN
gsrj-18	156	4	figure	figure	VERB
gsrj-18	156	5	2	2	NUM
gsrj-18	156	6	.	.	PUNCT
gsrj-18	156	7	program	program	NOUN
gsrj-18	156	8	yield	yield	VERB
gsrj-18	156	9	the	the	DET
gsrj-18	156	10	creation	creation	NOUN
gsrj-18	156	11	of	of	ADP
gsrj-18	156	12	the	the	DET
gsrj-18	156	13	python	python	PROPN
gsrj-18	156	14	code	code	NOUN
gsrj-18	156	15	described	describe	VERB
gsrj-18	156	16	on	on	ADP
gsrj-18	156	17	the	the	DET
gsrj-18	156	18	previous	previous	ADJ
gsrj-18	156	19	pages	page	NOUN
gsrj-18	156	20	(	(	PUNCT
gsrj-18	156	21	figure	figure	NOUN
gsrj-18	156	22	1	1	NUM
gsrj-18	156	23	)	)	PUNCT
gsrj-18	156	24	resulted	result	VERB
gsrj-18	156	25	in	in	ADP
gsrj-18	156	26	a	a	DET
gsrj-18	156	27	program	program	NOUN
gsrj-18	156	28	that	that	PRON
gsrj-18	156	29	,	,	PUNCT
gsrj-18	156	30	when	when	SCONJ
gsrj-18	156	31	run	run	NOUN
gsrj-18	156	32	,	,	PUNCT
gsrj-18	156	33	yielded	yield	VERB
gsrj-18	156	34	the	the	DET
gsrj-18	156	35	above	above	ADJ
gsrj-18	156	36	result	result	NOUN
gsrj-18	156	37	(	(	PUNCT
gsrj-18	156	38	figure	figure	NOUN
gsrj-18	156	39	2	2	NUM
gsrj-18	156	40	)	)	PUNCT
gsrj-18	156	41	.	.	PUNCT
gsrj-18	157	1	lines	line	NOUN
gsrj-18	157	2	1	1	NUM
gsrj-18	157	3	–	–	SYM
gsrj-18	157	4	9	9	NUM
gsrj-18	157	5	print	print	NOUN
gsrj-18	157	6	each	each	PRON
gsrj-18	157	7	of	of	ADP
gsrj-18	157	8	the	the	DET
gsrj-18	157	9	values	value	NOUN
gsrj-18	157	10	necessary	necessary	ADJ
gsrj-18	157	11	to	to	PART
gsrj-18	157	12	calculate	calculate	VERB
gsrj-18	157	13	the	the	DET
gsrj-18	157	14	decryption	decryption	NOUN
gsrj-18	157	15	key	key	NOUN
gsrj-18	157	16	,	,	PUNCT
gsrj-18	157	17	d	d	X
gsrj-18	157	18	,	,	PUNCT
gsrj-18	157	19	through	through	ADP
gsrj-18	157	20	semiprime	semiprime	NOUN
gsrj-18	157	21	factorization	factorization	NOUN
gsrj-18	157	22	.	.	PUNCT
gsrj-18	158	1	in	in	ADP
gsrj-18	158	2	line	line	NOUN
gsrj-18	158	3	2	2	NUM
gsrj-18	158	4	,	,	PUNCT
gsrj-18	158	5	the	the	DET
gsrj-18	158	6	program	program	NOUN
gsrj-18	158	7	asks	ask	VERB
gsrj-18	158	8	for	for	ADP
gsrj-18	158	9	a	a	DET
gsrj-18	158	10	semi	semi	ADJ
gsrj-18	158	11	-	-	ADJ
gsrj-18	158	12	prime	prime	ADJ
gsrj-18	158	13	number	number	NOUN
gsrj-18	158	14	input	input	NOUN
gsrj-18	158	15	.	.	PUNCT
gsrj-18	159	1	if	if	SCONJ
gsrj-18	159	2	a	a	DET
gsrj-18	159	3	number	number	NOUN
gsrj-18	159	4	that	that	PRON
gsrj-18	159	5	is	be	AUX
gsrj-18	159	6	not	not	PART
gsrj-18	159	7	semi	semi	ADJ
gsrj-18	159	8	-	-	ADJ
gsrj-18	159	9	prime	prime	ADJ
gsrj-18	159	10	is	be	AUX
gsrj-18	159	11	inputted	inputte	VERB
gsrj-18	159	12	,	,	PUNCT
gsrj-18	159	13	as	as	ADP
gsrj-18	159	14	in	in	ADP
gsrj-18	159	15	figure	figure	NOUN
gsrj-18	159	16	2	2	NUM
gsrj-18	159	17	when	when	SCONJ
gsrj-18	159	18	1500	1500	NUM
gsrj-18	159	19	was	be	AUX
gsrj-18	159	20	inputted	inputte	VERB
gsrj-18	159	21	,	,	PUNCT
gsrj-18	159	22	the	the	DET
gsrj-18	159	23	program	program	NOUN
gsrj-18	159	24	asks	ask	VERB
gsrj-18	159	25	for	for	ADP
gsrj-18	159	26	another	another	DET
gsrj-18	159	27	semi	semi	ADJ
gsrj-18	159	28	-	-	ADJ
gsrj-18	159	29	prime	prime	ADJ
gsrj-18	159	30	value	value	NOUN
gsrj-18	159	31	instead	instead	ADV
gsrj-18	159	32	,	,	PUNCT
gsrj-18	159	33	displaying	display	VERB
gsrj-18	159	34	the	the	DET
gsrj-18	159	35	message	message	NOUN
gsrj-18	159	36	“	"	PUNCT
gsrj-18	159	37	your	your	PRON
gsrj-18	159	38	prior	prior	ADJ
gsrj-18	159	39	input	input	NOUN
gsrj-18	159	40	was	be	AUX
gsrj-18	159	41	not	not	PART
gsrj-18	159	42	a	a	DET
gsrj-18	159	43	semi	semi	ADJ
gsrj-18	159	44	-	-	ADJ
gsrj-18	159	45	prime	prime	ADJ
gsrj-18	159	46	number	number	NOUN
gsrj-18	159	47	.	.	PUNCT
gsrj-18	160	1	14	14	NUM
gsrj-18	160	2	0	0	NUM
gsrj-18	160	3	decryption	decryption	NOUN
gsrj-18	160	4	through	through	ADP
gsrj-18	160	5	semi	semi	ADJ
gsrj-18	160	6	-	-	ADJ
gsrj-18	160	7	prime	prime	ADJ
gsrj-18	160	8	factorization	factorization	NOUN
gsrj-18	160	9	0	0	PUNCT
gsrj-18	160	10	enter	enter	VERB
gsrj-18	160	11	a	a	DET
gsrj-18	160	12	semi	semi	ADJ
gsrj-18	160	13	-	-	ADJ
gsrj-18	160	14	prime	prime	ADJ
gsrj-18	160	15	number	number	NOUN
gsrj-18	160	16	:	:	PUNCT
gsrj-18	160	17	1500	1500	NUM
gsrj-18	160	18	0	0	NUM
gsrj-18	160	19	your	your	PRON
gsrj-18	160	20	prior	prior	ADJ
gsrj-18	160	21	input	input	NOUN
gsrj-18	160	22	was	be	AUX
gsrj-18	160	23	not	not	PART
gsrj-18	160	24	a	a	DET
gsrj-18	160	25	semi	semi	ADJ
gsrj-18	160	26	-	-	ADJ
gsrj-18	160	27	prime	prime	ADJ
gsrj-18	160	28	number	number	NOUN
gsrj-18	160	29	.	.	PUNCT
gsrj-18	161	1	enter	enter	VERB
gsrj-18	161	2	a	a	DET
gsrj-18	161	3	semi	semi	ADJ
gsrj-18	161	4	-	-	ADJ
gsrj-18	161	5	prime	prime	ADJ
gsrj-18	161	6	number	number	NOUN
gsrj-18	161	7	:	:	PUNCT
gsrj-18	161	8	1820	1820	NUM
gsrj-18	161	9	g	g	NOUN
gsrj-18	161	10	your	your	PRON
gsrj-18	161	11	prior	prior	ADJ
gsrj-18	161	12	input	input	NOUN
gsrj-18	161	13	was	be	AUX
gsrj-18	161	14	not	not	PART
gsrj-18	161	15	a	a	DET
gsrj-18	161	16	semi	semi	ADJ
gsrj-18	161	17	-	-	ADJ
gsrj-18	161	18	prime	prime	ADJ
gsrj-18	161	19	number	number	NOUN
gsrj-18	161	20	.	.	PUNCT
gsrj-18	162	1	enter	enter	VERB
gsrj-18	162	2	a	a	DET
gsrj-18	162	3	semi	semi	ADJ
gsrj-18	162	4	-	-	ADJ
gsrj-18	162	5	prime	prime	ADJ
gsrj-18	162	6	number	number	NOUN
gsrj-18	162	7	:	:	PUNCT
gsrj-18	162	8	143	143	NUM
gsrj-18	162	9	•	•	NOUN
gsrj-18	162	10	p	p	X
gsrj-18	162	11	■	■	PUNCT
gsrj-18	162	12	11	11	NUM
gsrj-18	162	13	•	•	NUM
gsrj-18	162	14	q.	q.	NOUN
gsrj-18	162	15	13	13	NUM
gsrj-18	162	16	q	q	NOUN
gsrj-18	162	17	phi	phi	NOUN
gsrj-18	162	18	n	n	NOUN
gsrj-18	162	19	•	•	NOUN
gsrj-18	162	20	120	120	NUM
gsrj-18	162	21	0	0	NUM
gsrj-18	162	22	e	e	NOUN
gsrj-18	162	23	•	•	NOUN
gsrj-18	162	24	7	7	NUM
gsrj-18	162	25	0	0	NUM
gsrj-18	162	26	d	d	NOUN
gsrj-18	162	27	•	•	NUM
gsrj-18	162	28	103	103	NUM
gsrj-18	162	29	g	g	NOUN
gsrj-18	162	30	)	)	PUNCT
gsrj-18	162	31	decryption	decryption	NOUN
gsrj-18	162	32	through	through	ADP
gsrj-18	162	33	logarithms	logarithm	NOUN
gsrj-18	162	34	4d	4d	NUM
gsrj-18	162	35	enter	enter	VERB
gsrj-18	162	36	a	a	DET
gsrj-18	162	37	secret	secret	ADJ
gsrj-18	162	38	message	message	NOUN
gsrj-18	162	39	to	to	PART
gsrj-18	162	40	encrypt	encrypt	VERB
gsrj-18	162	41	:	:	PUNCT
gsrj-18	162	42	24	24	NUM
gsrj-18	162	43	g	g	NOUN
gsrj-18	162	44	secret	secret	ADJ
gsrj-18	162	45	message	message	NOUN
gsrj-18	162	46	•	•	ADP
gsrj-18	162	47	24	24	NUM
gsrj-18	162	48	0	0	NUM
gsrj-18	162	49	encrypted	encrypt	VERB
gsrj-18	162	50	message	message	NOUN
gsrj-18	162	51	•	•	ADP
gsrj-18	162	52	106	106	NUM
gsrj-18	162	53	g	g	NOUN
gsrj-18	162	54	,	,	PUNCT
gsrj-18	163	1	d	d	NOUN
gsrj-18	163	2	•	•	ADV
gsrj-18	163	3	more	more	ADJ
gsrj-18	163	4	than	than	ADP
gsrj-18	163	5	o	o	NOUN
gsrj-18	163	6	million	million	NUM
gsrj-18	163	7	iterations	iteration	NOUN
gsrj-18	163	8	to	to	PART
gsrj-18	163	9	calculate	calculate	VERB
gsrj-18	163	10	fd	fd	PROPN
gsrj-18	163	11	how	how	SCONJ
gsrj-18	163	12	many	many	ADJ
gsrj-18	163	13	iterations	iteration	NOUN
gsrj-18	163	14	?	?	PUNCT
gsrj-18	164	1	g	g	NOUN
gsrj-18	164	2	iterations	iteration	NOUN
gsrj-18	164	3	using	use	VERB
gsrj-18	164	4	semi	semi	ADJ
gsrj-18	164	5	-	-	ADJ
gsrj-18	164	6	prime	prime	ADJ
gsrj-18	164	7	factorization	factorization	NOUN
gsrj-18	164	8	■	■	PUNCT
gsrj-18	164	9	141	141	NUM
gsrj-18	164	10	4d	4d	NUM
gsrj-18	164	11	iterations	iteration	NOUN
gsrj-18	164	12	using	use	VERB
gsrj-18	164	13	logarithms	logarithm	NOUN
gsrj-18	164	14	•	•	NUM
gsrj-18	164	15	2.8z597349859519e+z06	2.8z597349859519e+z06	NUM
gsrj-18	164	16	georgetown	georgetown	PROPN
gsrj-18	164	17	scientific	scientific	PROPN
gsrj-18	164	18	research	research	NOUN
gsrj-18	164	19	journal	journal	PROPN
gsrj-18	164	20	enter	enter	VERB
gsrj-18	164	21	a	a	DET
gsrj-18	164	22	semi	semi	ADJ
gsrj-18	164	23	-	-	ADJ
gsrj-18	164	24	prime	prime	ADJ
gsrj-18	164	25	number	number	NOUN
gsrj-18	164	26	:	:	PUNCT
gsrj-18	164	27	”	"	PUNCT
gsrj-18	164	28	until	until	SCONJ
gsrj-18	164	29	a	a	DET
gsrj-18	164	30	semi	semi	ADJ
gsrj-18	164	31	-	-	ADJ
gsrj-18	164	32	prime	prime	ADJ
gsrj-18	164	33	value	value	NOUN
gsrj-18	164	34	has	have	AUX
gsrj-18	164	35	been	be	AUX
gsrj-18	164	36	given	give	VERB
gsrj-18	164	37	.	.	PUNCT
gsrj-18	165	1	when	when	SCONJ
gsrj-18	165	2	a	a	DET
gsrj-18	165	3	semi	semi	ADJ
gsrj-18	165	4	-	-	ADJ
gsrj-18	165	5	prime	prime	ADJ
gsrj-18	165	6	value	value	NOUN
gsrj-18	165	7	is	be	AUX
gsrj-18	165	8	given	give	VERB
gsrj-18	165	9	,	,	PUNCT
gsrj-18	165	10	this	this	DET
gsrj-18	165	11	number	number	NOUN
gsrj-18	165	12	is	be	AUX
gsrj-18	165	13	factored	factor	VERB
gsrj-18	165	14	into	into	ADP
gsrj-18	165	15	its	its	PRON
gsrj-18	165	16	constituent	constituent	NOUN
gsrj-18	165	17	factors	factor	NOUN
gsrj-18	165	18	,	,	PUNCT
gsrj-18	165	19	p	p	NOUN
gsrj-18	165	20	and	and	CCONJ
gsrj-18	165	21	q	q	NOUN
gsrj-18	165	22	,	,	PUNCT
gsrj-18	165	23	which	which	PRON
gsrj-18	165	24	are	be	AUX
gsrj-18	165	25	then	then	ADV
gsrj-18	165	26	printed	print	VERB
gsrj-18	165	27	.	.	PUNCT
gsrj-18	166	1	𝜑𝜑n	𝜑𝜑n	PROPN
gsrj-18	166	2	is	be	AUX
gsrj-18	166	3	then	then	ADV
gsrj-18	166	4	calculated	calculate	VERB
gsrj-18	166	5	by	by	ADP
gsrj-18	166	6	plugging	plug	VERB
gsrj-18	166	7	p	p	NOUN
gsrj-18	166	8	and	and	CCONJ
gsrj-18	166	9	q	q	NOUN
gsrj-18	166	10	into	into	ADP
gsrj-18	166	11	the	the	DET
gsrj-18	166	12	expression	expression	NOUN
gsrj-18	166	13	(	(	PUNCT
gsrj-18	166	14	p	p	X
gsrj-18	166	15	–	–	PUNCT
gsrj-18	166	16	1)*(q	1)*(q	NUM
gsrj-18	166	17	–	–	PUNCT
gsrj-18	166	18	1	1	NUM
gsrj-18	166	19	)	)	PUNCT
gsrj-18	166	20	and	and	CCONJ
gsrj-18	166	21	subsequently	subsequently	ADV
gsrj-18	166	22	printed	print	VERB
gsrj-18	166	23	.	.	PUNCT
gsrj-18	167	1	once	once	ADV
gsrj-18	167	2	a	a	DET
gsrj-18	167	3	public	public	ADJ
gsrj-18	167	4	key	key	ADJ
gsrj-18	167	5	value	value	NOUN
gsrj-18	167	6	e	e	NOUN
gsrj-18	167	7	is	be	AUX
gsrj-18	167	8	generated	generate	VERB
gsrj-18	167	9	and	and	CCONJ
gsrj-18	167	10	printed	print	VERB
gsrj-18	167	11	,	,	PUNCT
gsrj-18	167	12	d	d	PROPN
gsrj-18	167	13	is	be	AUX
gsrj-18	167	14	solved	solve	VERB
gsrj-18	167	15	for	for	ADP
gsrj-18	167	16	in	in	ADP
gsrj-18	167	17	equation	equation	NOUN
gsrj-18	167	18	2	2	NUM
gsrj-18	167	19	and	and	CCONJ
gsrj-18	167	20	printed	print	VERB
gsrj-18	167	21	.	.	PUNCT
gsrj-18	168	1	lines	line	NOUN
gsrj-18	168	2	10	10	NUM
gsrj-18	168	3	–	–	PUNCT
gsrj-18	168	4	14	14	NUM
gsrj-18	168	5	print	print	NOUN
gsrj-18	168	6	the	the	DET
gsrj-18	168	7	necessary	necessary	ADJ
gsrj-18	168	8	information	information	NOUN
gsrj-18	168	9	to	to	PART
gsrj-18	168	10	calculate	calculate	VERB
gsrj-18	168	11	d	d	PROPN
gsrj-18	168	12	through	through	ADP
gsrj-18	168	13	logarithms	logarithm	NOUN
gsrj-18	168	14	.	.	PUNCT
gsrj-18	169	1	in	in	ADP
gsrj-18	169	2	line	line	NOUN
gsrj-18	169	3	11	11	NUM
gsrj-18	169	4	,	,	PUNCT
gsrj-18	169	5	the	the	DET
gsrj-18	169	6	program	program	NOUN
gsrj-18	169	7	asks	ask	VERB
gsrj-18	169	8	for	for	ADP
gsrj-18	169	9	an	an	DET
gsrj-18	169	10	integer	integer	NOUN
gsrj-18	169	11	message	message	NOUN
gsrj-18	169	12	m	m	PROPN
gsrj-18	169	13	,	,	PUNCT
gsrj-18	169	14	prints	print	NOUN
gsrj-18	169	15	m	m	VERB
gsrj-18	169	16	in	in	ADP
gsrj-18	169	17	line	line	NOUN
gsrj-18	169	18	12	12	NUM
gsrj-18	169	19	,	,	PUNCT
gsrj-18	169	20	prints	print	NOUN
gsrj-18	169	21	c	c	NOUN
gsrj-18	169	22	(	(	PUNCT
gsrj-18	169	23	the	the	DET
gsrj-18	169	24	value	value	NOUN
gsrj-18	169	25	of	of	ADP
gsrj-18	169	26	m	m	PROPN
gsrj-18	169	27	,	,	PUNCT
gsrj-18	169	28	encrypted	encrypt	VERB
gsrj-18	169	29	)	)	PUNCT
gsrj-18	169	30	in	in	ADP
gsrj-18	169	31	line	line	NOUN
gsrj-18	169	32	13	13	NUM
gsrj-18	169	33	,	,	PUNCT
gsrj-18	169	34	and	and	CCONJ
gsrj-18	169	35	prints	print	NOUN
gsrj-18	169	36	d	d	NOUN
gsrj-18	169	37	in	in	ADP
gsrj-18	169	38	line	line	NOUN
gsrj-18	169	39	14	14	NUM
gsrj-18	169	40	by	by	ADP
gsrj-18	169	41	solving	solve	VERB
gsrj-18	169	42	for	for	ADP
gsrj-18	169	43	it	it	PRON
gsrj-18	169	44	in	in	ADP
gsrj-18	169	45	equation	equation	NOUN
gsrj-18	169	46	4	4	NUM
gsrj-18	169	47	.	.	PUNCT
gsrj-18	170	1	however	however	ADV
gsrj-18	170	2	,	,	PUNCT
gsrj-18	170	3	in	in	ADP
gsrj-18	170	4	all	all	DET
gsrj-18	170	5	the	the	DET
gsrj-18	170	6	times	time	NOUN
gsrj-18	170	7	that	that	SCONJ
gsrj-18	170	8	the	the	DET
gsrj-18	170	9	program	program	NOUN
gsrj-18	170	10	has	have	AUX
gsrj-18	170	11	been	be	AUX
gsrj-18	170	12	run	run	VERB
gsrj-18	170	13	,	,	PUNCT
gsrj-18	170	14	it	it	PRON
gsrj-18	170	15	has	have	AUX
gsrj-18	170	16	never	never	ADV
gsrj-18	170	17	been	be	AUX
gsrj-18	170	18	able	able	ADJ
gsrj-18	170	19	to	to	PART
gsrj-18	170	20	calculate	calculate	VERB
gsrj-18	170	21	d	d	PROPN
gsrj-18	170	22	through	through	ADP
gsrj-18	170	23	logarithms	logarithm	NOUN
gsrj-18	170	24	due	due	ADP
gsrj-18	170	25	to	to	ADP
gsrj-18	170	26	the	the	DET
gsrj-18	170	27	fact	fact	NOUN
gsrj-18	170	28	that	that	SCONJ
gsrj-18	170	29	it	it	PRON
gsrj-18	170	30	would	would	AUX
gsrj-18	170	31	take	take	VERB
gsrj-18	170	32	an	an	DET
gsrj-18	170	33	incredible	incredible	ADJ
gsrj-18	170	34	amount	amount	NOUN
gsrj-18	170	35	of	of	ADP
gsrj-18	170	36	iterations	iteration	NOUN
gsrj-18	170	37	to	to	PART
gsrj-18	170	38	do	do	VERB
gsrj-18	170	39	this	this	PRON
gsrj-18	170	40	.	.	PUNCT
gsrj-18	171	1	instead	instead	ADV
gsrj-18	171	2	,	,	PUNCT
gsrj-18	171	3	the	the	DET
gsrj-18	171	4	program	program	NOUN
gsrj-18	171	5	prints	print	NOUN
gsrj-18	171	6	,	,	PUNCT
gsrj-18	171	7	“	"	PUNCT
gsrj-18	171	8	d	d	NOUN
gsrj-18	171	9	=	=	PUNCT
gsrj-18	171	10	more	more	ADJ
gsrj-18	171	11	than	than	ADP
gsrj-18	171	12	a	a	DET
gsrj-18	171	13	million	million	NUM
gsrj-18	171	14	iterations	iteration	NOUN
gsrj-18	171	15	to	to	PART
gsrj-18	171	16	calculate	calculate	VERB
gsrj-18	171	17	”	"	PUNCT
gsrj-18	171	18	if	if	SCONJ
gsrj-18	171	19	it	it	PRON
gsrj-18	171	20	can	can	AUX
gsrj-18	171	21	not	not	PART
gsrj-18	171	22	calculate	calculate	VERB
gsrj-18	171	23	d	d	PROPN
gsrj-18	171	24	through	through	ADP
gsrj-18	171	25	logarithms	logarithm	NOUN
gsrj-18	171	26	in	in	ADP
gsrj-18	171	27	under	under	ADP
gsrj-18	171	28	a	a	DET
gsrj-18	171	29	million	million	NUM
gsrj-18	171	30	iterations	iteration	NOUN
gsrj-18	171	31	.	.	PUNCT
gsrj-18	172	1	finally	finally	ADV
gsrj-18	172	2	,	,	PUNCT
gsrj-18	172	3	in	in	ADP
gsrj-18	172	4	lines	line	NOUN
gsrj-18	172	5	15	15	NUM
gsrj-18	172	6	–	–	SYM
gsrj-18	172	7	17	17	NUM
gsrj-18	172	8	,	,	PUNCT
gsrj-18	172	9	the	the	DET
gsrj-18	172	10	program	program	NOUN
gsrj-18	172	11	prints	print	VERB
gsrj-18	172	12	the	the	DET
gsrj-18	172	13	number	number	NOUN
gsrj-18	172	14	of	of	ADP
gsrj-18	172	15	iterations	iteration	NOUN
gsrj-18	172	16	that	that	SCONJ
gsrj-18	172	17	the	the	DET
gsrj-18	172	18	program	program	NOUN
gsrj-18	172	19	needs	need	VERB
gsrj-18	172	20	to	to	PART
gsrj-18	172	21	calculate	calculate	VERB
gsrj-18	172	22	d	d	NOUN
gsrj-18	172	23	in	in	ADP
gsrj-18	172	24	either	either	DET
gsrj-18	172	25	instance	instance	NOUN
gsrj-18	172	26	.	.	PUNCT
gsrj-18	173	1	on	on	ADP
gsrj-18	173	2	occasion	occasion	NOUN
gsrj-18	173	3	,	,	PUNCT
gsrj-18	173	4	the	the	DET
gsrj-18	173	5	program	program	NOUN
gsrj-18	173	6	will	will	AUX
gsrj-18	173	7	experience	experience	VERB
gsrj-18	173	8	an	an	DET
gsrj-18	173	9	overflow	overflow	NOUN
gsrj-18	173	10	error	error	NOUN
gsrj-18	173	11	when	when	SCONJ
gsrj-18	173	12	it	it	PRON
gsrj-18	173	13	tries	try	VERB
gsrj-18	173	14	to	to	PART
gsrj-18	173	15	calculate	calculate	VERB
gsrj-18	173	16	the	the	DET
gsrj-18	173	17	iterations	iteration	NOUN
gsrj-18	173	18	for	for	ADP
gsrj-18	173	19	decryption	decryption	NOUN
gsrj-18	173	20	through	through	ADP
gsrj-18	173	21	logarithms	logarithm	NOUN
gsrj-18	173	22	because	because	SCONJ
gsrj-18	173	23	python	python	PROPN
gsrj-18	173	24	does	do	AUX
gsrj-18	173	25	not	not	PART
gsrj-18	173	26	have	have	VERB
gsrj-18	173	27	the	the	DET
gsrj-18	173	28	capacity	capacity	NOUN
gsrj-18	173	29	for	for	ADP
gsrj-18	173	30	such	such	ADJ
gsrj-18	173	31	huge	huge	ADJ
gsrj-18	173	32	calculations	calculation	NOUN
gsrj-18	173	33	.	.	PUNCT
gsrj-18	174	1	this	this	DET
gsrj-18	174	2	project	project	NOUN
gsrj-18	174	3	would	would	AUX
gsrj-18	174	4	be	be	AUX
gsrj-18	174	5	economically	economically	ADV
gsrj-18	174	6	feasible	feasible	ADJ
gsrj-18	174	7	to	to	PART
gsrj-18	174	8	implement	implement	VERB
gsrj-18	174	9	as	as	SCONJ
gsrj-18	174	10	it	it	PRON
gsrj-18	174	11	would	would	AUX
gsrj-18	174	12	not	not	PART
gsrj-18	174	13	cost	cost	VERB
gsrj-18	174	14	anything	anything	PRON
gsrj-18	174	15	to	to	PART
gsrj-18	174	16	download	download	VERB
gsrj-18	174	17	an	an	DET
gsrj-18	174	18	app	app	NOUN
gsrj-18	174	19	version	version	NOUN
gsrj-18	174	20	of	of	ADP
gsrj-18	174	21	this	this	DET
gsrj-18	174	22	program	program	NOUN
gsrj-18	174	23	onto	onto	ADP
gsrj-18	174	24	a	a	DET
gsrj-18	174	25	mobile	mobile	ADJ
gsrj-18	174	26	device	device	NOUN
gsrj-18	174	27	once	once	SCONJ
gsrj-18	174	28	a	a	DET
gsrj-18	174	29	graphical	graphical	ADJ
gsrj-18	174	30	user	user	NOUN
gsrj-18	174	31	interface	interface	NOUN
gsrj-18	174	32	has	have	AUX
gsrj-18	174	33	been	be	AUX
gsrj-18	174	34	created	create	VERB
gsrj-18	174	35	for	for	ADP
gsrj-18	174	36	all	all	PRON
gsrj-18	174	37	of	of	ADP
gsrj-18	174	38	the	the	DET
gsrj-18	174	39	code	code	NOUN
gsrj-18	174	40	that	that	PRON
gsrj-18	174	41	has	have	AUX
gsrj-18	174	42	been	be	AUX
gsrj-18	174	43	written	write	VERB
gsrj-18	174	44	.	.	PUNCT
gsrj-18	175	1	5	5	X
gsrj-18	175	2	.	.	X
gsrj-18	175	3	discussion	discussion	NOUN
gsrj-18	175	4	and	and	CCONJ
gsrj-18	175	5	conclusions	conclusion	NOUN
gsrj-18	175	6	the	the	DET
gsrj-18	175	7	research	research	NOUN
gsrj-18	175	8	study	study	NOUN
gsrj-18	175	9	undertaken	undertake	VERB
gsrj-18	175	10	was	be	AUX
gsrj-18	175	11	largely	largely	ADV
gsrj-18	175	12	successful	successful	ADJ
gsrj-18	175	13	because	because	SCONJ
gsrj-18	175	14	it	it	PRON
gsrj-18	175	15	met	meet	VERB
gsrj-18	175	16	all	all	PRON
gsrj-18	175	17	of	of	ADP
gsrj-18	175	18	the	the	DET
gsrj-18	175	19	objectives	objective	NOUN
gsrj-18	175	20	defined	define	VERB
gsrj-18	175	21	in	in	ADP
gsrj-18	175	22	the	the	DET
gsrj-18	175	23	introduction	introduction	NOUN
gsrj-18	175	24	:	:	PUNCT
gsrj-18	175	25	to	to	PART
gsrj-18	175	26	describe	describe	VERB
gsrj-18	175	27	the	the	DET
gsrj-18	175	28	mathematics	mathematic	NOUN
gsrj-18	175	29	of	of	ADP
gsrj-18	175	30	decryption	decryption	NOUN
gsrj-18	175	31	techniques	technique	NOUN
gsrj-18	175	32	,	,	PUNCT
gsrj-18	175	33	to	to	PART
gsrj-18	175	34	create	create	VERB
gsrj-18	175	35	a	a	DET
gsrj-18	175	36	program	program	NOUN
gsrj-18	175	37	capable	capable	ADJ
gsrj-18	175	38	of	of	ADP
gsrj-18	175	39	calculating	calculate	VERB
gsrj-18	175	40	the	the	DET
gsrj-18	175	41	decryption	decryption	NOUN
gsrj-18	175	42	key	key	NOUN
gsrj-18	175	43	in	in	ADP
gsrj-18	175	44	rsa	rsa	PROPN
gsrj-18	175	45	using	use	VERB
gsrj-18	175	46	two	two	NUM
gsrj-18	175	47	different	different	ADJ
gsrj-18	175	48	methods	method	NOUN
gsrj-18	175	49	and	and	CCONJ
gsrj-18	175	50	calculating	calculate	VERB
gsrj-18	175	51	the	the	DET
gsrj-18	175	52	number	number	NOUN
gsrj-18	175	53	of	of	ADP
gsrj-18	175	54	iterations	iteration	NOUN
gsrj-18	175	55	required	require	VERB
gsrj-18	175	56	to	to	PART
gsrj-18	175	57	accomplish	accomplish	VERB
gsrj-18	175	58	this	this	PRON
gsrj-18	175	59	in	in	ADP
gsrj-18	175	60	either	either	DET
gsrj-18	175	61	instance	instance	NOUN
gsrj-18	175	62	,	,	PUNCT
gsrj-18	175	63	and	and	CCONJ
gsrj-18	175	64	to	to	PART
gsrj-18	175	65	explain	explain	VERB
gsrj-18	175	66	the	the	DET
gsrj-18	175	67	code	code	NOUN
gsrj-18	175	68	written	write	VERB
gsrj-18	175	69	in	in	ADP
gsrj-18	175	70	the	the	DET
gsrj-18	175	71	program	program	NOUN
gsrj-18	175	72	and	and	CCONJ
gsrj-18	175	73	its	its	PRON
gsrj-18	175	74	roles	role	NOUN
gsrj-18	175	75	in	in	ADP
gsrj-18	175	76	ultimately	ultimately	ADV
gsrj-18	175	77	achieving	achieve	VERB
gsrj-18	175	78	the	the	DET
gsrj-18	175	79	end	end	NOUN
gsrj-18	175	80	result	result	NOUN
gsrj-18	175	81	of	of	ADP
gsrj-18	175	82	decryption	decryption	NOUN
gsrj-18	175	83	.	.	PUNCT
gsrj-18	176	1	the	the	DET
gsrj-18	176	2	program	program	NOUN
gsrj-18	176	3	has	have	VERB
gsrj-18	176	4	the	the	DET
gsrj-18	176	5	capacity	capacity	NOUN
gsrj-18	176	6	to	to	PART
gsrj-18	176	7	calculate	calculate	VERB
gsrj-18	176	8	the	the	DET
gsrj-18	176	9	decryption	decryption	NOUN
gsrj-18	176	10	key	key	NOUN
gsrj-18	176	11	through	through	ADP
gsrj-18	176	12	both	both	DET
gsrj-18	176	13	semi	semi	ADJ
gsrj-18	176	14	-	-	ADJ
gsrj-18	176	15	prime	prime	ADJ
gsrj-18	176	16	factorization	factorization	NOUN
gsrj-18	176	17	and	and	CCONJ
gsrj-18	176	18	through	through	ADP
gsrj-18	176	19	the	the	DET
gsrj-18	176	20	logarithmic	logarithmic	ADJ
gsrj-18	176	21	method	method	NOUN
gsrj-18	176	22	.	.	PUNCT
gsrj-18	177	1	that	that	PRON
gsrj-18	177	2	being	be	AUX
gsrj-18	177	3	said	say	VERB
gsrj-18	177	4	,	,	PUNCT
gsrj-18	177	5	the	the	DET
gsrj-18	177	6	logarithmic	logarithmic	ADJ
gsrj-18	177	7	method	method	NOUN
gsrj-18	177	8	almost	almost	ADV
gsrj-18	177	9	always	always	ADV
gsrj-18	177	10	takes	take	VERB
gsrj-18	177	11	too	too	ADV
gsrj-18	177	12	many	many	ADJ
gsrj-18	177	13	iterations	iteration	NOUN
gsrj-18	177	14	to	to	PART
gsrj-18	177	15	feasibly	feasibly	ADV
gsrj-18	177	16	calculate	calculate	VERB
gsrj-18	177	17	the	the	DET
gsrj-18	177	18	decryption	decryption	NOUN
gsrj-18	177	19	key	key	NOUN
gsrj-18	177	20	because	because	SCONJ
gsrj-18	177	21	of	of	ADP
gsrj-18	177	22	the	the	DET
gsrj-18	177	23	exponentiation	exponentiation	NOUN
gsrj-18	177	24	operations	operation	NOUN
gsrj-18	177	25	involved	involve	VERB
gsrj-18	177	26	.	.	PUNCT
gsrj-18	178	1	however	however	ADV
gsrj-18	178	2	,	,	PUNCT
gsrj-18	178	3	the	the	DET
gsrj-18	178	4	program	program	NOUN
gsrj-18	178	5	is	be	AUX
gsrj-18	178	6	still	still	ADV
gsrj-18	178	7	theoretically	theoretically	ADV
gsrj-18	178	8	capable	capable	ADJ
gsrj-18	178	9	of	of	ADP
gsrj-18	178	10	calculating	calculate	VERB
gsrj-18	178	11	the	the	DET
gsrj-18	178	12	decryption	decryption	NOUN
gsrj-18	178	13	key	key	NOUN
gsrj-18	178	14	through	through	ADP
gsrj-18	178	15	the	the	DET
gsrj-18	178	16	logarithmic	logarithmic	ADJ
gsrj-18	178	17	method	method	NOUN
gsrj-18	178	18	.	.	PUNCT
gsrj-18	179	1	the	the	DET
gsrj-18	179	2	program	program	NOUN
gsrj-18	179	3	is	be	AUX
gsrj-18	179	4	also	also	ADV
gsrj-18	179	5	capable	capable	ADJ
gsrj-18	179	6	of	of	ADP
gsrj-18	179	7	calculating	calculate	VERB
gsrj-18	179	8	the	the	DET
gsrj-18	179	9	number	number	NOUN
gsrj-18	179	10	of	of	ADP
gsrj-18	179	11	iterations	iteration	NOUN
gsrj-18	179	12	needed	need	VERB
gsrj-18	179	13	to	to	PART
gsrj-18	179	14	calculate	calculate	VERB
gsrj-18	179	15	d	d	PROPN
gsrj-18	179	16	through	through	ADP
gsrj-18	179	17	either	either	CCONJ
gsrj-18	179	18	method	method	NOUN
gsrj-18	179	19	but	but	CCONJ
gsrj-18	179	20	will	will	AUX
gsrj-18	179	21	at	at	ADP
gsrj-18	179	22	times	time	NOUN
gsrj-18	179	23	experience	experience	VERB
gsrj-18	179	24	an	an	DET
gsrj-18	179	25	overflow	overflow	NOUN
gsrj-18	179	26	error	error	NOUN
gsrj-18	179	27	if	if	SCONJ
gsrj-18	179	28	the	the	DET
gsrj-18	179	29	number	number	NOUN
gsrj-18	179	30	of	of	ADP
gsrj-18	179	31	iterations	iteration	NOUN
gsrj-18	179	32	needed	need	VERB
gsrj-18	179	33	to	to	PART
gsrj-18	179	34	calculate	calculate	VERB
gsrj-18	179	35	d	d	PROPN
gsrj-18	179	36	through	through	ADP
gsrj-18	179	37	logarithmic	logarithmic	ADJ
gsrj-18	179	38	techniques	technique	NOUN
gsrj-18	179	39	exceeds	exceed	VERB
gsrj-18	179	40	python	python	PROPN
gsrj-18	179	41	’s	’s	PART
gsrj-18	179	42	programming	programming	NOUN
gsrj-18	179	43	capacity	capacity	NOUN
gsrj-18	179	44	.	.	PUNCT
gsrj-18	180	1	if	if	SCONJ
gsrj-18	180	2	the	the	DET
gsrj-18	180	3	code	code	NOUN
gsrj-18	180	4	in	in	ADP
gsrj-18	180	5	this	this	DET
gsrj-18	180	6	study	study	NOUN
gsrj-18	180	7	can	can	AUX
gsrj-18	180	8	be	be	AUX
gsrj-18	180	9	replicated	replicate	VERB
gsrj-18	180	10	using	use	VERB
gsrj-18	180	11	more	more	ADV
gsrj-18	180	12	powerful	powerful	ADJ
gsrj-18	180	13	and	and	CCONJ
gsrj-18	180	14	faster	fast	ADJ
gsrj-18	180	15	programs	program	NOUN
gsrj-18	180	16	,	,	PUNCT
gsrj-18	180	17	it	it	PRON
gsrj-18	180	18	would	would	AUX
gsrj-18	180	19	be	be	AUX
gsrj-18	180	20	surmised	surmise	VERB
gsrj-18	180	21	that	that	SCONJ
gsrj-18	180	22	d	d	NOUN
gsrj-18	180	23	would	would	AUX
gsrj-18	180	24	be	be	AUX
gsrj-18	180	25	calculated	calculate	VERB
gsrj-18	180	26	with	with	ADP
gsrj-18	180	27	more	more	ADJ
gsrj-18	180	28	rapidity	rapidity	NOUN
gsrj-18	180	29	through	through	ADP
gsrj-18	180	30	the	the	DET
gsrj-18	180	31	logarithmic	logarithmic	ADJ
gsrj-18	180	32	technique	technique	NOUN
gsrj-18	180	33	and	and	CCONJ
gsrj-18	180	34	the	the	DET
gsrj-18	180	35	program	program	NOUN
gsrj-18	180	36	would	would	AUX
gsrj-18	180	37	not	not	PART
gsrj-18	180	38	experience	experience	VERB
gsrj-18	180	39	overflow	overflow	NOUN
gsrj-18	180	40	errors	error	NOUN
gsrj-18	180	41	.	.	PUNCT
gsrj-18	181	1	when	when	SCONJ
gsrj-18	181	2	such	such	ADJ
gsrj-18	181	3	errors	error	NOUN
gsrj-18	181	4	occur	occur	VERB
gsrj-18	181	5	,	,	PUNCT
gsrj-18	181	6	exception	exception	NOUN
gsrj-18	181	7	handling	handling	NOUN
gsrj-18	181	8	can	can	AUX
gsrj-18	181	9	be	be	AUX
gsrj-18	181	10	used	use	VERB
gsrj-18	181	11	to	to	PART
gsrj-18	181	12	catch	catch	VERB
gsrj-18	181	13	the	the	DET
gsrj-18	181	14	errors	error	NOUN
gsrj-18	181	15	using	use	VERB
gsrj-18	181	16	python	python	PROPN
gsrj-18	181	17	’s	’s	PART
gsrj-18	181	18	overflowerror	overflowerror	NOUN
gsrj-18	181	19	.	.	PUNCT
gsrj-18	182	1	such	such	DET
gsrj-18	182	2	an	an	DET
gsrj-18	182	3	implementation	implementation	NOUN
gsrj-18	182	4	is	be	AUX
gsrj-18	182	5	provided	provide	VERB
gsrj-18	182	6	in	in	ADP
gsrj-18	182	7	the	the	DET
gsrj-18	182	8	appendix	appendix	NOUN
gsrj-18	182	9	.	.	PUNCT
gsrj-18	183	1	additionally	additionally	ADV
gsrj-18	183	2	,	,	PUNCT
gsrj-18	183	3	there	there	PRON
gsrj-18	183	4	are	be	VERB
gsrj-18	183	5	many	many	ADJ
gsrj-18	183	6	other	other	ADJ
gsrj-18	183	7	techniques	technique	NOUN
gsrj-18	183	8	in	in	ADP
gsrj-18	183	9	existence	existence	NOUN
gsrj-18	183	10	to	to	PART
gsrj-18	183	11	factor	factor	VERB
gsrj-18	183	12	large	large	ADJ
gsrj-18	183	13	semi	semi	ADJ
gsrj-18	183	14	-	-	ADJ
gsrj-18	183	15	prime	prime	ADJ
gsrj-18	183	16	numbers	number	NOUN
gsrj-18	183	17	,	,	PUNCT
gsrj-18	183	18	though	though	SCONJ
gsrj-18	183	19	this	this	DET
gsrj-18	183	20	program	program	NOUN
gsrj-18	183	21	only	only	ADV
gsrj-18	183	22	makes	make	VERB
gsrj-18	183	23	use	use	NOUN
gsrj-18	183	24	of	of	ADP
gsrj-18	183	25	one	one	NUM
gsrj-18	183	26	of	of	ADP
gsrj-18	183	27	the	the	DET
gsrj-18	183	28	most	most	ADV
gsrj-18	183	29	rudimentary	rudimentary	ADJ
gsrj-18	183	30	such	such	ADJ
gsrj-18	183	31	techniques	technique	NOUN
gsrj-18	183	32	.	.	PUNCT
gsrj-18	184	1	the	the	DET
gsrj-18	184	2	quadratic	quadratic	ADJ
gsrj-18	184	3	sieve	sieve	NOUN
gsrj-18	184	4	and	and	CCONJ
gsrj-18	184	5	the	the	DET
gsrj-18	184	6	general	general	ADJ
gsrj-18	184	7	number	number	NOUN
gsrj-18	184	8	field	field	NOUN
gsrj-18	184	9	sieve	sieve	NOUN
gsrj-18	184	10	are	be	AUX
gsrj-18	184	11	two	two	NUM
gsrj-18	184	12	such	such	ADJ
gsrj-18	184	13	integer	integer	NOUN
gsrj-18	184	14	factorization	factorization	NOUN
gsrj-18	184	15	algorithms	algorithm	NOUN
gsrj-18	184	16	that	that	PRON
gsrj-18	184	17	far	far	ADV
gsrj-18	184	18	outstrip	outstrip	VERB
gsrj-18	184	19	the	the	DET
gsrj-18	184	20	technique	technique	NOUN
gsrj-18	184	21	presented	present	VERB
gsrj-18	184	22	in	in	ADP
gsrj-18	184	23	this	this	DET
gsrj-18	184	24	research.15	research.15	NOUN
gsrj-18	184	25	further	far	ADV
gsrj-18	184	26	,	,	PUNCT
gsrj-18	184	27	this	this	DET
gsrj-18	184	28	program	program	NOUN
gsrj-18	184	29	could	could	AUX
gsrj-18	184	30	have	have	VERB
gsrj-18	184	31	possible	possible	ADJ
gsrj-18	184	32	implementations	implementation	NOUN
gsrj-18	184	33	in	in	ADP
gsrj-18	184	34	the	the	DET
gsrj-18	184	35	future	future	NOUN
gsrj-18	184	36	.	.	PUNCT
gsrj-18	185	1	because	because	SCONJ
gsrj-18	185	2	it	it	PRON
gsrj-18	185	3	is	be	AUX
gsrj-18	185	4	capable	capable	ADJ
gsrj-18	185	5	of	of	ADP
gsrj-18	185	6	calculating	calculate	VERB
gsrj-18	185	7	the	the	DET
gsrj-18	185	8	number	number	NOUN
gsrj-18	185	9	of	of	ADP
gsrj-18	185	10	iterations	iteration	NOUN
gsrj-18	185	11	needed	need	VERB
gsrj-18	185	12	to	to	PART
gsrj-18	185	13	obtain	obtain	VERB
gsrj-18	185	14	the	the	DET
gsrj-18	185	15	decryption	decryption	NOUN
gsrj-18	185	16	key	key	NOUN
gsrj-18	185	17	through	through	ADP
gsrj-18	185	18	either	either	CCONJ
gsrj-18	185	19	semi	semi	ADJ
gsrj-18	185	20	-	-	ADJ
gsrj-18	185	21	prime	prime	ADJ
gsrj-18	185	22	factorization	factorization	NOUN
gsrj-18	185	23	or	or	CCONJ
gsrj-18	185	24	logarithms	logarithm	NOUN
gsrj-18	185	25	,	,	PUNCT
gsrj-18	185	26	the	the	DET
gsrj-18	185	27	program	program	NOUN
gsrj-18	185	28	could	could	AUX
gsrj-18	185	29	potentially	potentially	ADV
gsrj-18	185	30	be	be	AUX
gsrj-18	185	31	used	use	VERB
gsrj-18	185	32	as	as	ADP
gsrj-18	185	33	a	a	DET
gsrj-18	185	34	starting	starting	NOUN
gsrj-18	185	35	point	point	NOUN
gsrj-18	185	36	to	to	PART
gsrj-18	185	37	create	create	VERB
gsrj-18	185	38	an	an	DET
gsrj-18	185	39	entirely	entirely	ADV
gsrj-18	185	40	new	new	ADJ
gsrj-18	185	41	study	study	NOUN
gsrj-18	185	42	in	in	ADP
gsrj-18	185	43	which	which	PRON
gsrj-18	185	44	the	the	DET
gsrj-18	185	45	efficacy	efficacy	NOUN
gsrj-18	185	46	of	of	ADP
gsrj-18	185	47	either	either	DET
gsrj-18	185	48	decryption	decryption	NOUN
gsrj-18	185	49	method	method	NOUN
gsrj-18	185	50	is	be	AUX
gsrj-18	185	51	compared	compare	VERB
gsrj-18	185	52	when	when	SCONJ
gsrj-18	185	53	certain	certain	ADJ
gsrj-18	185	54	variables	variable	NOUN
gsrj-18	185	55	like	like	ADP
gsrj-18	185	56	the	the	DET
gsrj-18	185	57	length	length	NOUN
gsrj-18	185	58	of	of	ADP
gsrj-18	185	59	the	the	DET
gsrj-18	185	60	semiprime	semiprime	NOUN
gsrj-18	185	61	number	number	NOUN
gsrj-18	185	62	n	n	ADP
gsrj-18	185	63	or	or	CCONJ
gsrj-18	185	64	the	the	DET
gsrj-18	185	65	public	public	ADJ
gsrj-18	185	66	exponent	exponent	NOUN
gsrj-18	185	67	e	e	PRON
gsrj-18	185	68	are	be	AUX
gsrj-18	185	69	varied	varied	ADJ
gsrj-18	185	70	.	.	PUNCT
gsrj-18	186	1	15	15	NUM
gsrj-18	186	2	georgetown	georgetown	PROPN
gsrj-18	186	3	scientific	scientific	PROPN
gsrj-18	186	4	research	research	NOUN
gsrj-18	186	5	journal	journal	NOUN
gsrj-18	186	6	acknowledgements	acknowledgement	NOUN
gsrj-18	186	7	i	i	PRON
gsrj-18	186	8	would	would	AUX
gsrj-18	186	9	like	like	VERB
gsrj-18	186	10	to	to	PART
gsrj-18	186	11	offer	offer	VERB
gsrj-18	186	12	my	my	PRON
gsrj-18	186	13	thanks	thank	NOUN
gsrj-18	186	14	to	to	ADP
gsrj-18	186	15	dr	dr	PROPN
gsrj-18	186	16	.	.	PROPN
gsrj-18	186	17	michal	michal	PROPN
gsrj-18	186	18	kolpak	kolpak	PROPN
gsrj-18	186	19	and	and	CCONJ
gsrj-18	186	20	mr	mr	PROPN
gsrj-18	186	21	.	.	PROPN
gsrj-18	186	22	quillian	quillian	PROPN
gsrj-18	186	23	haralson	haralson	PROPN
gsrj-18	186	24	for	for	ADP
gsrj-18	186	25	inspiring	inspire	VERB
gsrj-18	186	26	this	this	DET
gsrj-18	186	27	project	project	NOUN
gsrj-18	186	28	,	,	PUNCT
gsrj-18	186	29	as	as	ADV
gsrj-18	186	30	well	well	ADV
gsrj-18	186	31	as	as	ADP
gsrj-18	186	32	to	to	ADP
gsrj-18	186	33	the	the	DET
gsrj-18	186	34	myriad	myriad	ADJ
gsrj-18	186	35	other	other	ADJ
gsrj-18	186	36	friends	friend	NOUN
gsrj-18	186	37	,	,	PUNCT
gsrj-18	186	38	educators	educator	NOUN
gsrj-18	186	39	,	,	PUNCT
gsrj-18	186	40	and	and	CCONJ
gsrj-18	186	41	family	family	NOUN
gsrj-18	186	42	who	who	PRON
gsrj-18	186	43	have	have	AUX
gsrj-18	186	44	given	give	VERB
gsrj-18	186	45	their	their	PRON
gsrj-18	186	46	encouragement	encouragement	NOUN
gsrj-18	186	47	and	and	CCONJ
gsrj-18	186	48	support	support	NOUN
gsrj-18	186	49	in	in	ADP
gsrj-18	186	50	the	the	DET
gsrj-18	186	51	creation	creation	NOUN
gsrj-18	186	52	of	of	ADP
gsrj-18	186	53	this	this	PRON
gsrj-18	186	54	and	and	CCONJ
gsrj-18	186	55	many	many	ADJ
gsrj-18	186	56	other	other	ADJ
gsrj-18	186	57	projects	project	NOUN
gsrj-18	186	58	.	.	PUNCT
gsrj-18	187	1	references	reference	NOUN
gsrj-18	187	2	1	1	NUM
gsrj-18	187	3	.	.	PUNCT
gsrj-18	187	4	luciano	luciano	PROPN
gsrj-18	187	5	,	,	PUNCT
gsrj-18	187	6	d.	d.	PROPN
gsrj-18	187	7	,	,	PUNCT
gsrj-18	187	8	prichett	prichett	PROPN
gsrj-18	187	9	,	,	PUNCT
gsrj-18	187	10	g.	g.	PROPN
gsrj-18	187	11	(	(	PUNCT
gsrj-18	187	12	1987	1987	NUM
gsrj-18	187	13	)	)	PUNCT
gsrj-18	187	14	.	.	PUNCT
gsrj-18	188	1	cryptology	cryptology	NOUN
gsrj-18	188	2	:	:	PUNCT
gsrj-18	188	3	from	from	ADP
gsrj-18	188	4	caesar	caesar	PROPN
gsrj-18	188	5	ciphers	cipher	NOUN
gsrj-18	188	6	to	to	ADP
gsrj-18	188	7	public	public	ADJ
gsrj-18	188	8	-	-	PUNCT
gsrj-18	188	9	key	key	NOUN
gsrj-18	188	10	cryptosystems	cryptosystem	NOUN
gsrj-18	188	11	.	.	PUNCT
gsrj-18	189	1	the	the	DET
gsrj-18	189	2	college	college	NOUN
gsrj-18	189	3	mathematics	mathematics	PROPN
gsrj-18	189	4	journal	journal	NOUN
gsrj-18	189	5	,	,	PUNCT
gsrj-18	189	6	18(1	18(1	NUM
gsrj-18	189	7	)	)	PUNCT
gsrj-18	189	8	,	,	PUNCT
gsrj-18	189	9	2	2	NUM
gsrj-18	189	10	-	-	SYM
gsrj-18	189	11	17	17	NUM
gsrj-18	189	12	.	.	PUNCT
gsrj-18	190	1	https://doi.org/10.2307/2686311	https://doi.org/10.2307/2686311	NOUN
gsrj-18	190	2	.	.	NOUN
gsrj-18	190	3	2	2	NUM
gsrj-18	190	4	.	.	X
gsrj-18	190	5	deffs	deff	NOUN
gsrj-18	190	6	,	,	PUNCT
gsrj-18	190	7	h.	h.	PROPN
gsrj-18	190	8	,	,	PUNCT
gsrj-18	190	9	helmut	helmut	PROPN
gsrj-18	190	10	,	,	PUNCT
gsrj-18	190	11	k.	k.	PROPN
gsrj-18	190	12	introduction	introduction	NOUN
gsrj-18	190	13	to	to	ADP
gsrj-18	190	14	cryptography	cryptography	NOUN
gsrj-18	190	15	,	,	PUNCT
gsrj-18	190	16	principles	principle	NOUN
gsrj-18	190	17	and	and	CCONJ
gsrj-18	190	18	applications	application	NOUN
gsrj-18	191	1	2nd	2nd	PROPN
gsrj-18	191	2	ed	ed	NOUN
gsrj-18	191	3	.	.	PUNCT
gsrj-18	192	1	(	(	PUNCT
gsrj-18	192	2	2007	2007	NUM
gsrj-18	192	3	)	)	PUNCT
gsrj-18	192	4	.	.	PUNCT
gsrj-18	193	1	springer	springer	NOUN
gsrj-18	193	2	.	.	PUNCT
gsrj-18	194	1	11	11	NUM
gsrj-18	194	2	-	-	SYM
gsrj-18	194	3	31	31	NUM
gsrj-18	194	4	.	.	PUNCT
gsrj-18	195	1	3	3	X
gsrj-18	195	2	.	.	X
gsrj-18	195	3	ellis	ellis	PROPN
gsrj-18	195	4	,	,	PUNCT
gsrj-18	195	5	j.	j.	PROPN
gsrj-18	195	6	h.	h.	PROPN
gsrj-18	195	7	(	(	PUNCT
gsrj-18	195	8	1970	1970	NUM
gsrj-18	195	9	)	)	PUNCT
gsrj-18	195	10	.	.	PUNCT
gsrj-18	196	1	the	the	DET
gsrj-18	196	2	possibility	possibility	NOUN
gsrj-18	196	3	of	of	ADP
gsrj-18	196	4	secure	secure	ADJ
gsrj-18	196	5	nonsecret	nonsecret	ADJ
gsrj-18	196	6	digital	digital	ADJ
gsrj-18	196	7	encryption	encryption	NOUN
gsrj-18	196	8	.	.	PUNCT
gsrj-18	197	1	uk	uk	PROPN
gsrj-18	197	2	communications	communication	NOUN
gsrj-18	197	3	electronics	electronic	NOUN
gsrj-18	197	4	security	security	NOUN
gsrj-18	197	5	group	group	NOUN
gsrj-18	197	6	.	.	PUNCT
gsrj-18	198	1	www.cesg.gov.uk/site/publications/media/possnse	www.cesg.gov.uk/site/publications/media/possnse	NOUN
gsrj-18	198	2	.	.	PUNCT
gsrj-18	198	3	pdf	pdf	NOUN
gsrj-18	198	4	.	.	PUNCT
gsrj-18	199	1	_	_	PUNCT
gsrj-18	200	1	_	_	PUNCT
gsrj-18	201	1	_	_	PUNCT
gsrj-18	202	1	_	_	PUNCT
gsrj-18	203	1	_	_	PUNCT
gsrj-18	204	1	_	_	PUNCT
gsrj-18	205	1	_	_	PUNCT
gsrj-18	206	1	_	_	PUNCT
gsrj-18	207	1	_	_	PUNCT
gsrj-18	207	2	.	.	PUNCT
gsrj-18	208	1	(	(	PUNCT
gsrj-18	208	2	1999	1999	NUM
gsrj-18	208	3	)	)	PUNCT
gsrj-18	208	4	.	.	PUNCT
gsrj-18	209	1	the	the	DET
gsrj-18	209	2	history	history	NOUN
gsrj-18	209	3	of	of	ADP
gsrj-18	209	4	non	non	ADJ
gsrj-18	209	5	-	-	ADJ
gsrj-18	209	6	secret	secret	ADJ
gsrj-18	209	7	encryption	encryption	NOUN
gsrj-18	209	8	.	.	PUNCT
gsrj-18	210	1	cryptologia	cryptologia	PROPN
gsrj-18	210	2	23(3	23(3	NUM
gsrj-18	210	3	)	)	PUNCT
gsrj-18	210	4	267–73	267–73	NOUN
gsrj-18	210	5	.	.	PUNCT
gsrj-18	211	1	http://	http://	PROPN
gsrj-18	211	2	www.informaworld.com/10.1080/0161119991887919	www.informaworld.com/10.1080/0161119991887919	X
gsrj-18	211	3	.	.	PUNCT
gsrj-18	212	1	4	4	X
gsrj-18	212	2	.	.	X
gsrj-18	212	3	cocks	cock	NOUN
gsrj-18	212	4	,	,	PUNCT
gsrj-18	212	5	c.	c.	PROPN
gsrj-18	212	6	c.	c.	PROPN
gsrj-18	212	7	(	(	PUNCT
gsrj-18	212	8	1973	1973	NUM
gsrj-18	212	9	)	)	PUNCT
gsrj-18	212	10	.	.	PUNCT
gsrj-18	213	1	a	a	DET
gsrj-18	213	2	note	note	NOUN
gsrj-18	213	3	on	on	ADP
gsrj-18	213	4	non	non	ADJ
gsrj-18	213	5	-	-	ADJ
gsrj-18	213	6	secret	secret	ADJ
gsrj-18	213	7	encryption	encryption	NOUN
gsrj-18	213	8	.	.	PUNCT
gsrj-18	214	1	uk	uk	PROPN
gsrj-18	214	2	communications	communication	NOUN
gsrj-18	214	3	electronics	electronic	NOUN
gsrj-18	214	4	security	security	NOUN
gsrj-18	214	5	group	group	NOUN
gsrj-18	214	6	.	.	PUNCT
gsrj-18	215	1	http://www.cesg.gov.uk/publications/media	http://www.cesg.gov.uk/publications/media	PROPN
gsrj-18	216	1	/notense.pdf	/notense.pdf	PUNCT
gsrj-18	216	2	.	.	PUNCT
gsrj-18	217	1	5	5	X
gsrj-18	217	2	.	.	X
gsrj-18	217	3	rivest	riv	ADJ
gsrj-18	217	4	,	,	PUNCT
gsrj-18	217	5	r.	r.	PROPN
gsrj-18	217	6	l.	l.	PROPN
gsrj-18	217	7	,	,	PUNCT
gsrj-18	217	8	shamir	shamir	PROPN
gsrj-18	217	9	,	,	PUNCT
gsrj-18	217	10	a.	a.	NOUN
gsrj-18	217	11	,	,	PUNCT
gsrj-18	217	12	adleman	adleman	NOUN
gsrj-18	217	13	,	,	PUNCT
gsrj-18	217	14	l.	l.	PROPN
gsrj-18	217	15	(	(	PUNCT
gsrj-18	217	16	1977	1977	NUM
gsrj-18	217	17	)	)	PUNCT
gsrj-18	217	18	.	.	PUNCT
gsrj-18	218	1	a	a	DET
gsrj-18	218	2	method	method	NOUN
gsrj-18	218	3	for	for	ADP
gsrj-18	218	4	obtaining	obtain	VERB
gsrj-18	218	5	digital	digital	ADJ
gsrj-18	218	6	signatures	signature	NOUN
gsrj-18	218	7	and	and	CCONJ
gsrj-18	218	8	publickey	publickey	ADJ
gsrj-18	218	9	cryptosystems	cryptosystem	NOUN
gsrj-18	218	10	.	.	PUNCT
gsrj-18	219	1	technical	technical	ADJ
gsrj-18	219	2	memo	memo	NOUN
gsrj-18	219	3	number	number	NOUN
gsrj-18	219	4	mit	mit	PROPN
gsrj-18	219	5	-	-	PUNCT
gsrj-18	219	6	lcs	lcs	NOUN
gsrj-18	219	7	-	-	PUNCT
gsrj-18	219	8	tm-082	tm-082	PROPN
gsrj-18	219	9	.	.	PUNCT
gsrj-18	220	1	mit	mit	PROPN
gsrj-18	220	2	.	.	PUNCT
gsrj-18	221	1	http://publications	http://publication	NOUN
gsrj-18	221	2	.csail.mit.edu	.csail.mit.edu	PUNCT
gsrj-18	221	3	/	/	SYM
gsrj-18	221	4	lcs	lcs	PROPN
gsrj-18	221	5	/	/	SYM
gsrj-18	221	6	specpub.php?id=81	specpub.php?id=81	PROPN
gsrj-18	221	7	.	.	PROPN
gsrj-18	222	1	6	6	X
gsrj-18	222	2	.	.	X
gsrj-18	222	3	holden	holden	PROPN
gsrj-18	222	4	,	,	PUNCT
gsrj-18	222	5	j.	j.	PROPN
gsrj-18	222	6	(	(	PUNCT
gsrj-18	222	7	2017	2017	NUM
gsrj-18	222	8	)	)	PUNCT
gsrj-18	222	9	.	.	PUNCT
gsrj-18	223	1	the	the	DET
gsrj-18	223	2	mathematics	mathematic	NOUN
gsrj-18	223	3	of	of	ADP
gsrj-18	223	4	secrets	secret	NOUN
gsrj-18	223	5	:	:	PUNCT
gsrj-18	223	6	cryptography	cryptography	NOUN
gsrj-18	223	7	from	from	ADP
gsrj-18	223	8	caesar	caesar	PROPN
gsrj-18	223	9	ciphers	cipher	NOUN
gsrj-18	223	10	to	to	ADP
gsrj-18	223	11	digital	digital	ADJ
gsrj-18	223	12	encryption	encryption	NOUN
gsrj-18	223	13	.	.	PUNCT
gsrj-18	224	1	princeton	princeton	PROPN
gsrj-18	224	2	university	university	PROPN
gsrj-18	224	3	press	press	NOUN
gsrj-18	224	4	.	.	PUNCT
gsrj-18	225	1	216	216	NUM
gsrj-18	225	2	.	.	X
gsrj-18	225	3	7	7	X
gsrj-18	225	4	.	.	X
gsrj-18	225	5	dence	dence	NOUN
gsrj-18	225	6	,	,	PUNCT
gsrj-18	225	7	j.	j.	PROPN
gsrj-18	225	8	b.	b.	PROPN
gsrj-18	225	9	,	,	PUNCT
gsrj-18	225	10	dence	dence	NOUN
gsrj-18	225	11	,	,	PUNCT
gsrj-18	225	12	t.	t.	PROPN
gsrj-18	225	13	p.	p.	PROPN
gsrj-18	225	14	(	(	PUNCT
gsrj-18	225	15	1999	1999	NUM
gsrj-18	225	16	)	)	PUNCT
gsrj-18	225	17	.	.	PUNCT
gsrj-18	226	1	elements	element	NOUN
gsrj-18	226	2	of	of	ADP
gsrj-18	226	3	the	the	DET
gsrj-18	226	4	theory	theory	NOUN
gsrj-18	226	5	of	of	ADP
gsrj-18	226	6	numbers	number	NOUN
gsrj-18	226	7	.	.	PUNCT
gsrj-18	227	1	harcourt	harcourt	PROPN
gsrj-18	227	2	academic	academic	ADJ
gsrj-18	227	3	press	press	NOUN
gsrj-18	227	4	.	.	PUNCT
gsrj-18	228	1	156	156	NUM
gsrj-18	228	2	.	.	NOUN
gsrj-18	228	3	8	8	X
gsrj-18	228	4	.	.	X
gsrj-18	229	1	https://mathworld.wolfram.com/primenumber.ht	https://mathworld.wolfram.com/primenumber.ht	PROPN
gsrj-18	229	2	ml	ml	VERB
gsrj-18	229	3	.	.	PUNCT
gsrj-18	230	1	retrieved	retrieve	VERB
gsrj-18	230	2	march	march	PROPN
gsrj-18	230	3	1	1	NUM
gsrj-18	230	4	,	,	PUNCT
gsrj-18	230	5	2021	2021	NUM
gsrj-18	230	6	.	.	PUNCT
gsrj-18	231	1	9	9	X
gsrj-18	231	2	.	.	X
gsrj-18	231	3	wagstaff	wagstaff	NOUN
gsrj-18	231	4	,	,	PUNCT
gsrj-18	231	5	s.	s.	PROPN
gsrj-18	231	6	(	(	PUNCT
gsrj-18	231	7	2013	2013	NUM
gsrj-18	231	8	)	)	PUNCT
gsrj-18	231	9	.	.	PUNCT
gsrj-18	232	1	the	the	DET
gsrj-18	232	2	joy	joy	NOUN
gsrj-18	232	3	of	of	ADP
gsrj-18	232	4	factoring	factoring	NOUN
gsrj-18	232	5	.	.	PUNCT
gsrj-18	233	1	american	american	PROPN
gsrj-18	233	2	mathematical	mathematical	PROPN
gsrj-18	233	3	society	society	NOUN
gsrj-18	233	4	.	.	PUNCT
gsrj-18	234	1	195–202	195–202	NUM
gsrj-18	234	2	.	.	PUNCT
gsrj-18	235	1	10	10	NUM
gsrj-18	235	2	.	.	PUNCT
gsrj-18	236	1	rivest	riv	ADJ
gsrj-18	236	2	,	,	PUNCT
gsrj-18	236	3	r.	r.	PROPN
gsrj-18	236	4	l.	l.	PROPN
gsrj-18	236	5	,	,	PUNCT
gsrj-18	236	6	shamir	shamir	PROPN
gsrj-18	236	7	,	,	PUNCT
gsrj-18	236	8	a.	a.	NOUN
gsrj-18	236	9	,	,	PUNCT
gsrj-18	236	10	adleman	adleman	NOUN
gsrj-18	236	11	,	,	PUNCT
gsrj-18	236	12	l.	l.	PROPN
gsrj-18	236	13	(	(	PUNCT
gsrj-18	236	14	1978	1978	NUM
gsrj-18	236	15	)	)	PUNCT
gsrj-18	236	16	.	.	PUNCT
gsrj-18	237	1	a	a	DET
gsrj-18	237	2	method	method	NOUN
gsrj-18	237	3	for	for	ADP
gsrj-18	237	4	obtaining	obtain	VERB
gsrj-18	237	5	digital	digital	ADJ
gsrj-18	237	6	signatures	signature	NOUN
gsrj-18	237	7	and	and	CCONJ
gsrj-18	237	8	publickey	publickey	ADJ
gsrj-18	237	9	cryptosystems	cryptosystem	NOUN
gsrj-18	237	10	.	.	PUNCT
gsrj-18	238	1	communications	communication	NOUN
gsrj-18	238	2	of	of	ADP
gsrj-18	238	3	the	the	DET
gsrj-18	238	4	association	association	NOUN
gsrj-18	238	5	for	for	ADP
gsrj-18	238	6	computing	computing	NOUN
gsrj-18	238	7	machinery	machinery	NOUN
gsrj-18	238	8	,	,	PUNCT
gsrj-18	238	9	21(2	21(2	NUM
gsrj-18	238	10	)	)	PUNCT
gsrj-18	238	11	.	.	PUNCT
gsrj-18	239	1	11	11	NUM
gsrj-18	239	2	.	.	X
gsrj-18	239	3	gardner	gardner	NOUN
gsrj-18	239	4	,	,	PUNCT
gsrj-18	239	5	martin	martin	PROPN
gsrj-18	239	6	.	.	PUNCT
gsrj-18	240	1	(	(	PUNCT
gsrj-18	240	2	1977	1977	NUM
gsrj-18	240	3	)	)	PUNCT
gsrj-18	240	4	.	.	PUNCT
gsrj-18	241	1	mathematical	mathematical	ADJ
gsrj-18	241	2	games	game	NOUN
gsrj-18	241	3	:	:	PUNCT
gsrj-18	241	4	a	a	DET
gsrj-18	241	5	new	new	ADJ
gsrj-18	241	6	kind	kind	NOUN
gsrj-18	241	7	of	of	ADP
gsrj-18	241	8	cipher	cipher	ADJ
gsrj-18	241	9	that	that	PRON
gsrj-18	241	10	would	would	AUX
gsrj-18	241	11	take	take	VERB
gsrj-18	241	12	millions	million	NOUN
gsrj-18	241	13	of	of	ADP
gsrj-18	241	14	years	year	NOUN
gsrj-18	241	15	to	to	PART
gsrj-18	241	16	break	break	VERB
gsrj-18	241	17	.	.	PUNCT
gsrj-18	242	1	scientific	scientific	ADJ
gsrj-18	242	2	american	american	ADJ
gsrj-18	242	3	237(2	237(2	NUM
gsrj-18	242	4	)	)	PUNCT
gsrj-18	242	5	120–24	120–24	NUM
gsrj-18	242	6	.	.	PUNCT
gsrj-18	243	1	https://simson.net/ref/1977/gardner_rsa.pdf	https://simson.net/ref/1977/gardner_rsa.pdf	PROPN
gsrj-18	243	2	.	.	PUNCT
gsrj-18	244	1	12	12	NUM
gsrj-18	244	2	.	.	PUNCT
gsrj-18	245	1	diffie	diffie	PROPN
gsrj-18	245	2	,	,	PUNCT
gsrj-18	245	3	w.	w.	PROPN
gsrj-18	245	4	,	,	PUNCT
gsrj-18	245	5	hellman	hellman	NOUN
gsrj-18	245	6	,	,	PUNCT
gsrj-18	245	7	m.	m.	NOUN
gsrj-18	245	8	(	(	PUNCT
gsrj-18	245	9	1976	1976	NUM
gsrj-18	245	10	)	)	PUNCT
gsrj-18	245	11	.	.	PUNCT
gsrj-18	246	1	new	new	ADJ
gsrj-18	246	2	directions	direction	NOUN
gsrj-18	246	3	in	in	ADP
gsrj-18	246	4	cryptography	cryptography	NOUN
gsrj-18	246	5	.	.	PUNCT
gsrj-18	247	1	ieee	ieee	NOUN
gsrj-18	247	2	transactions	transaction	NOUN
gsrj-18	247	3	on	on	ADP
gsrj-18	247	4	information	information	NOUN
gsrj-18	247	5	theory	theory	NOUN
gsrj-18	247	6	,	,	PUNCT
gsrj-18	247	7	22	22	NUM
gsrj-18	247	8	(	(	PUNCT
gsrj-18	247	9	6	6	NUM
gsrj-18	247	10	):	):	PUNCT
gsrj-18	247	11	644–654	644–654	NUM
gsrj-18	247	12	.	.	PUNCT
gsrj-18	248	1	https://doi.org/10.1109/tit.1976.1055638	https://doi.org/10.1109/tit.1976.1055638	NOUN
gsrj-18	248	2	13	13	NUM
gsrj-18	248	3	.	.	PUNCT
gsrj-18	249	1	gidney	gidney	PROPN
gsrj-18	249	2	,	,	PUNCT
gsrj-18	249	3	c.	c.	NOUN
gsrj-18	249	4	,	,	PUNCT
gsrj-18	249	5	ekerå	ekerå	NOUN
gsrj-18	249	6	,	,	PUNCT
gsrj-18	249	7	m.	m.	NOUN
gsrj-18	249	8	(	(	PUNCT
gsrj-18	249	9	2021	2021	NUM
gsrj-18	249	10	)	)	PUNCT
gsrj-18	249	11	.	.	PUNCT
gsrj-18	250	1	how	how	SCONJ
gsrj-18	250	2	to	to	PART
gsrj-18	250	3	factor	factor	VERB
gsrj-18	250	4	2048	2048	NUM
gsrj-18	250	5	bit	bit	NOUN
gsrj-18	250	6	rsa	rsa	NOUN
gsrj-18	250	7	integers	integer	NOUN
gsrj-18	250	8	in	in	ADP
gsrj-18	250	9	8	8	NUM
gsrj-18	250	10	hours	hour	NOUN
gsrj-18	250	11	using	use	VERB
gsrj-18	250	12	20	20	NUM
gsrj-18	250	13	million	million	NUM
gsrj-18	250	14	noisy	noisy	ADJ
gsrj-18	250	15	qubits	qubit	NOUN
gsrj-18	250	16	.	.	PUNCT
gsrj-18	251	1	quantum	quantum	PROPN
gsrj-18	251	2	5	5	NUM
gsrj-18	251	3	.	.	PUNCT
gsrj-18	251	4	(	(	PUNCT
gsrj-18	251	5	433	433	NUM
gsrj-18	251	6	)	)	PUNCT
gsrj-18	251	7	.	.	PUNCT
gsrj-18	252	1	arxvix	arxvix	PROPN
gsrj-18	252	2	:	:	PUNCT
gsrj-18	253	1	1905.09749v3	1905.09749v3	PROPN
gsrj-18	253	2	.	.	PUNCT
gsrj-18	254	1	https://doi.org/10.22331/q-202104-15-433	https://doi.org/10.22331/q-202104-15-433	PROPN
gsrj-18	254	2	.	.	PUNCT
gsrj-18	255	1	14	14	NUM
gsrj-18	255	2	.	.	PUNCT
gsrj-18	255	3	https://www.wolframalpha.com/	https://www.wolframalpha.com/	PROPN
gsrj-18	255	4	15	15	NUM
gsrj-18	255	5	.	.	PUNCT
gsrj-18	255	6	pomerance	pomerance	NOUN
gsrj-18	255	7	,	,	PUNCT
gsrj-18	255	8	c.	c.	PROPN
gsrj-18	255	9	(	(	PUNCT
gsrj-18	255	10	1996	1996	NUM
gsrj-18	255	11	)	)	PUNCT
gsrj-18	255	12	.	.	PUNCT
gsrj-18	256	1	a	a	DET
gsrj-18	256	2	tale	tale	NOUN
gsrj-18	256	3	of	of	ADP
gsrj-18	256	4	two	two	NUM
gsrj-18	256	5	sieves	sieve	NOUN
gsrj-18	256	6	.	.	PUNCT
gsrj-18	257	1	notices	notice	NOUN
gsrj-18	257	2	of	of	ADP
gsrj-18	257	3	the	the	DET
gsrj-18	257	4	american	american	PROPN
gsrj-18	257	5	mathematical	mathematical	PROPN
gsrj-18	257	6	society	society	NOUN
gsrj-18	257	7	.	.	PUNCT
gsrj-18	258	1	43	43	NUM
gsrj-18	258	2	(	(	PUNCT
gsrj-18	258	3	12	12	NUM
gsrj-18	258	4	)	)	PUNCT
gsrj-18	258	5	.	.	PUNCT
gsrj-18	259	1	1473–1485	1473–1485	NUM
gsrj-18	259	2	.	.	PUNCT
gsrj-18	260	1	16	16	NUM
gsrj-18	260	2	georgetown	georgetown	PROPN
gsrj-18	260	3	scientific	scientific	PROPN
gsrj-18	260	4	research	research	NOUN
gsrj-18	260	5	journal	journal	NOUN
gsrj-18	260	6	17	17	NUM
gsrj-18	260	7	appendix	appendix	VERB
gsrj-18	260	8	an	an	DET
gsrj-18	260	9	implementation	implementation	NOUN
gsrj-18	260	10	of	of	ADP
gsrj-18	260	11	the	the	DET
gsrj-18	260	12	program	program	NOUN
gsrj-18	260	13	in	in	ADP
gsrj-18	260	14	pseudocode	pseudocode	NOUN
gsrj-18	260	15	is	be	AUX
gsrj-18	260	16	provided	provide	VERB
gsrj-18	260	17	below	below	ADP
gsrj-18	260	18	in	in	ADP
gsrj-18	260	19	which	which	DET
gsrj-18	260	20	exception	exception	NOUN
gsrj-18	260	21	handling	handling	NOUN
gsrj-18	260	22	is	be	AUX
gsrj-18	260	23	used	use	VERB
gsrj-18	260	24	to	to	PART
gsrj-18	260	25	handle	handle	VERB
gsrj-18	260	26	overflow	overflow	ADJ
gsrj-18	260	27	errors	error	NOUN
gsrj-18	260	28	.	.	PUNCT
gsrj-18	261	1	georgetown	georgetown	PROPN
gsrj-18	261	2	scientific	scientific	PROPN
gsrj-18	261	3	research	research	PROPN
gsrj-18	261	4	journal	journal	NOUN
gsrj-18	261	5	18	18	NUM
gsrj-18	261	6	73	73	NUM
gsrj-18	261	7	danya	danya	PROPN
gsrj-18	261	8	adams	adams	PROPN
gsrj-18	261	9	danya	danya	PROPN
gsrj-18	261	10	adams	adams	PROPN
gsrj-18	261	11	�	�	PROPN
gsrj-18	261	12	gsr	gsr	PROPN
gsrj-18	261	13	journal	journal	PROPN
gsrj-18	261	14	georgetown	georgetown	PROPN
gsrj-18	261	15	scientific	scientific	PROPN
gsrj-18	261	16	research	research	PROPN
gsrj-18	261	17	journal	journal	NOUN
gsrj-18	261	18	table	table	NOUN
gsrj-18	261	19	of	of	ADP
gsrj-18	261	20	contents	content	NOUN
gsrj-18	261	21	letter	letter	NOUN
gsrj-18	261	22	from	from	ADP
gsrj-18	261	23	the	the	DET
gsrj-18	261	24	editors	editor	NOUN
gsrj-18	261	25	an	an	DET
gsrj-18	261	26	investigation	investigation	NOUN
gsrj-18	261	27	into	into	ADP
gsrj-18	261	28	themathematics	themathematic	NOUN
gsrj-18	261	29	of	of	ADP
gsrj-18	261	30	decryptiontechniques	decryptiontechnique	NOUN
gsrj-18	261	31	in	in	ADP
gsrj-18	261	32	rsa	rsa	NOUN
gsrj-18	261	33	encryption	encryption	NOUN
gsrj-18	261	34	,	,	PUNCT
gsrj-18	261	35	with	with	ADP
gsrj-18	261	36	an	an	DET
gsrj-18	261	37	implementation	implementation	NOUN
gsrj-18	261	38	in	in	ADP
gsrj-18	261	39	python	python	PROPN
gsrj-18	261	40	gpr40	gpr40	PROPN
gsrj-18	261	41	and	and	CCONJ
gsrj-18	261	42	postsynaptic	postsynaptic	ADJ
gsrj-18	261	43	nmdareceptors	nmdareceptor	NOUN
gsrj-18	261	44	:	:	PUNCT
gsrj-18	261	45	a	a	DET
gsrj-18	261	46	pair	pair	NOUN
gsrj-18	261	47	againstepilepsy	againstepilepsy	ADJ
gsrj-18	261	48	the	the	DET
gsrj-18	261	49	burn	burn	NOUN
gsrj-18	261	50	behind	behind	ADP
gsrj-18	261	51	the	the	DET
gsrj-18	261	52	bullet	bullet	NOUN
gsrj-18	261	53	:	:	PUNCT
gsrj-18	261	54	understanding	understand	VERB
gsrj-18	261	55	black	black	ADJ
gsrj-18	261	56	mothers’experiences	mothers’experience	NOUN
gsrj-18	261	57	after	after	ADP
gsrj-18	261	58	losing	lose	VERB
gsrj-18	261	59	a	a	DET
gsrj-18	261	60	childto	childto	ADJ
gsrj-18	261	61	gun	gun	NOUN
gsrj-18	261	62	violence	violence	NOUN
gsrj-18	261	63	in	in	ADP
gsrj-18	261	64	washington	washington	PROPN
gsrj-18	261	65	,	,	PUNCT
gsrj-18	261	66	dc	dc	PROPN
gsrj-18	261	67	-	-	PUNCT
gsrj-18	261	68	baltimore	baltimore	PROPN
gsrj-18	261	69	city	city	PROPN
gsrj-18	261	70	metropolitanregion	metropolitanregion	NOUN
gsrj-18	261	71	cancer	cancer	NOUN
gsrj-18	261	72	models	model	NOUN
gsrj-18	261	73	to	to	PART
gsrj-18	261	74	defeat	defeat	VERB
gsrj-18	261	75	therapyresistance	therapyresistance	NOUN
gsrj-18	261	76	in	in	ADP
gsrj-18	261	77	pancreatic	pancreatic	ADJ
gsrj-18	261	78	ductaladenocarcinoma	ductaladenocarcinoma	NOUN
gsrj-18	261	79	meet	meet	NOUN
gsrj-18	261	80	the	the	DET
gsrj-18	261	81	authors	author	NOUN
gsrj-18	261	82	meet	meet	VERB
gsrj-18	261	83	the	the	DET
gsrj-18	261	84	staff	staff	NOUN
gsrj-18	261	85	acknowledgments	acknowledgment	NOUN