id	sid	tid	token	lemma	pos
iajs-1805	1	1	microsoft	microsoft	PROPN
iajs-1805	1	2	word	word	NOUN
iajs-1805	1	3	404	404	NUM
iajs-1805	1	4	-	-	SYM
iajs-1805	1	5	408	408	NUM
iajs-1805	1	6	ihsciconf	ihsciconf	NOUN
iajs-1805	1	7	2017	2017	NUM
iajs-1805	1	8	special	special	ADJ
iajs-1805	1	9	issue	issue	NOUN
iajs-1805	1	10	ibn	ibn	PROPN
iajs-1805	1	11	al	al	PROPN
iajs-1805	1	12	-	-	PUNCT
iajs-1805	1	13	haitham	haitham	PROPN
iajs-1805	1	14	journal	journal	PROPN
iajs-1805	1	15	for	for	ADP
iajs-1805	1	16	pure	pure	ADJ
iajs-1805	1	17	and	and	CCONJ
iajs-1805	1	18	applied	apply	VERB
iajs-1805	1	19	science	science	NOUN
iajs-1805	1	20	https://doi.org/	https://doi.org/	NOUN
iajs-1805	1	21	10.30526/2017.ihsciconf.1805	10.30526/2017.ihsciconf.1805	NOUN
iajs-1805	1	22	for	for	ADP
iajs-1805	1	23	more	more	ADJ
iajs-1805	1	24	information	information	NOUN
iajs-1805	1	25	about	about	ADP
iajs-1805	1	26	the	the	DET
iajs-1805	1	27	conference	conference	NOUN
iajs-1805	1	28	please	please	INTJ
iajs-1805	1	29	visit	visit	VERB
iajs-1805	1	30	the	the	DET
iajs-1805	1	31	websites	website	NOUN
iajs-1805	1	32	:	:	PUNCT
iajs-1805	1	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1805	1	34	  	  	SPACE
iajs-1805	1	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1805	1	36	   	   	SPACE
iajs-1805	1	37	mathematics	mathematic	NOUN
iajs-1805	1	38	|	|	CCONJ
iajs-1805	1	39	404	404	NUM
iajs-1805	1	40	counting	counting	NOUN
iajs-1805	1	41	functions	function	NOUN
iajs-1805	1	42	to	to	PART
iajs-1805	1	43	generate	generate	VERB
iajs-1805	1	44	the	the	DET
iajs-1805	1	45	primes	prime	NOUN
iajs-1805	1	46	in	in	ADP
iajs-1805	1	47	the	the	DET
iajs-1805	1	48	rsa	rsa	PROPN
iajs-1805	1	49	algorithm	algorithm	NOUN
iajs-1805	1	50	and	and	CCONJ
iajs-1805	1	51	diffie	diffie	PROPN
iajs-1805	1	52	-	-	PUNCT
iajs-1805	1	53	hellman	hellman	PROPN
iajs-1805	1	54	key	key	PROPN
iajs-1805	1	55	exchange	exchange	PROPN
iajs-1805	1	56	    	    	SPACE
iajs-1805	1	57	faez	faez	PROPN
iajs-1805	1	58	ali	ali	PROPN
iajs-1805	1	59	al	al	PROPN
iajs-1805	1	60	-	-	PUNCT
iajs-1805	1	61	maamori	maamori	PROPN
iajs-1805	1	62	faez352013@gmail.com	faez352013@gmail.com	X
iajs-1805	2	1	mazin	mazin	PROPN
iajs-1805	2	2	saied	saie	VERB
iajs-1805	2	3	rashid	rashid	PROPN
iajs-1805	2	4	mazinalsadawy1@gmail.com	mazinalsadawy1@gmail.com	PROPN
iajs-1805	2	5	dept	dept	NOUN
iajs-1805	2	6	.	.	PROPN
iajs-1805	2	7	of	of	ADP
iajs-1805	2	8	mathematics	mathematics	PROPN
iajs-1805	2	9	/	/	SYM
iajs-1805	2	10	college	college	NOUN
iajs-1805	2	11	of	of	ADP
iajs-1805	2	12	education	education	NOUN
iajs-1805	2	13	for	for	ADP
iajs-1805	2	14	pure	pure	ADJ
iajs-1805	2	15	science/	science/	NOUN
iajs-1805	2	16	university	university	NOUN
iajs-1805	2	17	of	of	ADP
iajs-1805	2	18	babylon	babylon	PROPN
iajs-1805	2	19	         	         	SPACE
iajs-1805	2	20	abstract	abstract	ADV
iajs-1805	2	21	the	the	DET
iajs-1805	2	22	rivest	riv	ADJ
iajs-1805	2	23	–	–	PUNCT
iajs-1805	2	24	shamir	shamir	ADJ
iajs-1805	2	25	–	–	PUNCT
iajs-1805	2	26	adleman	adleman	ADJ
iajs-1805	2	27	(	(	PUNCT
iajs-1805	2	28	rsa	rsa	PROPN
iajs-1805	2	29	)	)	PUNCT
iajs-1805	2	30	and	and	CCONJ
iajs-1805	2	31	the	the	DET
iajs-1805	2	32	diffie	diffie	PROPN
iajs-1805	2	33	-	-	PUNCT
iajs-1805	2	34	hellman	hellman	PROPN
iajs-1805	2	35	(	(	PUNCT
iajs-1805	2	36	dh	dh	NOUN
iajs-1805	2	37	)	)	PUNCT
iajs-1805	2	38	key	key	ADJ
iajs-1805	2	39	exchange	exchange	NOUN
iajs-1805	2	40	are	be	AUX
iajs-1805	2	41	famous	famous	ADJ
iajs-1805	2	42	methods	method	NOUN
iajs-1805	2	43	for	for	ADP
iajs-1805	2	44	encryption	encryption	NOUN
iajs-1805	2	45	.	.	PUNCT
iajs-1805	3	1	these	these	DET
iajs-1805	3	2	methods	method	NOUN
iajs-1805	3	3	depended	depend	VERB
iajs-1805	3	4	on	on	ADP
iajs-1805	3	5	selecting	select	VERB
iajs-1805	3	6	the	the	DET
iajs-1805	3	7	primes	prime	NOUN
iajs-1805	3	8	p	p	NOUN
iajs-1805	3	9	and	and	CCONJ
iajs-1805	3	10	q	q	NOUN
iajs-1805	3	11	in	in	ADP
iajs-1805	3	12	order	order	NOUN
iajs-1805	3	13	to	to	PART
iajs-1805	3	14	be	be	AUX
iajs-1805	3	15	secure	secure	ADJ
iajs-1805	3	16	enough	enough	ADV
iajs-1805	3	17	.	.	PUNCT
iajs-1805	4	1	this	this	DET
iajs-1805	4	2	paper	paper	NOUN
iajs-1805	4	3	shows	show	VERB
iajs-1805	4	4	that	that	SCONJ
iajs-1805	4	5	the	the	DET
iajs-1805	4	6	named	name	VERB
iajs-1805	4	7	methods	method	NOUN
iajs-1805	4	8	used	use	VERB
iajs-1805	4	9	the	the	DET
iajs-1805	4	10	primes	prime	NOUN
iajs-1805	4	11	which	which	PRON
iajs-1805	4	12	are	be	AUX
iajs-1805	4	13	found	find	VERB
iajs-1805	4	14	by	by	ADP
iajs-1805	4	15	some	some	DET
iajs-1805	4	16	arithmetical	arithmetical	ADJ
iajs-1805	4	17	function	function	NOUN
iajs-1805	4	18	.in	.in	PUNCT
iajs-1805	4	19	the	the	DET
iajs-1805	4	20	other	other	ADJ
iajs-1805	4	21	sense	sense	NOUN
iajs-1805	4	22	,	,	PUNCT
iajs-1805	4	23	no	no	DET
iajs-1805	4	24	need	need	NOUN
iajs-1805	4	25	to	to	PART
iajs-1805	4	26	think	think	VERB
iajs-1805	4	27	about	about	ADP
iajs-1805	4	28	getting	get	VERB
iajs-1805	4	29	primes	prime	NOUN
iajs-1805	4	30	p	p	NOUN
iajs-1805	4	31	and	and	CCONJ
iajs-1805	4	32	q	q	PROPN
iajs-1805	4	33	and	and	CCONJ
iajs-1805	4	34	how	how	SCONJ
iajs-1805	4	35	they	they	PRON
iajs-1805	4	36	are	be	AUX
iajs-1805	4	37	secure	secure	ADJ
iajs-1805	4	38	enough	enough	ADV
iajs-1805	4	39	,	,	PUNCT
iajs-1805	4	40	since	since	SCONJ
iajs-1805	4	41	the	the	DET
iajs-1805	4	42	arithmetical	arithmetical	ADJ
iajs-1805	4	43	function	function	NOUN
iajs-1805	4	44	enable	enable	ADJ
iajs-1805	4	45	to	to	PART
iajs-1805	4	46	build	build	VERB
iajs-1805	4	47	the	the	DET
iajs-1805	4	48	primes	prime	NOUN
iajs-1805	4	49	in	in	ADP
iajs-1805	4	50	such	such	ADJ
iajs-1805	4	51	complicated	complicated	ADJ
iajs-1805	4	52	way	way	NOUN
iajs-1805	4	53	to	to	PART
iajs-1805	4	54	be	be	AUX
iajs-1805	4	55	secure	secure	ADJ
iajs-1805	4	56	.	.	PUNCT
iajs-1805	5	1	moreover	moreover	ADV
iajs-1805	5	2	,	,	PUNCT
iajs-1805	5	3	this	this	DET
iajs-1805	5	4	article	article	NOUN
iajs-1805	5	5	gives	give	VERB
iajs-1805	5	6	new	new	ADJ
iajs-1805	5	7	construction	construction	NOUN
iajs-1805	5	8	of	of	ADP
iajs-1805	5	9	the	the	DET
iajs-1805	5	10	rsa	rsa	PROPN
iajs-1805	5	11	algorithm	algorithm	NOUN
iajs-1805	5	12	and	and	CCONJ
iajs-1805	5	13	dh	dh	PROPN
iajs-1805	5	14	key	key	ADJ
iajs-1805	5	15	exchange	exchange	NOUN
iajs-1805	5	16	using	use	VERB
iajs-1805	5	17	the	the	DET
iajs-1805	5	18	primes	prime	NOUN
iajs-1805	5	19	p	p	X
iajs-1805	5	20	,	,	PUNCT
iajs-1805	5	21	qfrom	qfrom	ADP
iajs-1805	5	22	areal	areal	NOUN
iajs-1805	5	23	number	number	NOUN
iajs-1805	5	24	x.	x.	NOUN
iajs-1805	5	25	keywords	keyword	NOUN
iajs-1805	5	26	:	:	PUNCT
iajs-1805	5	27	(	(	PUNCT
iajs-1805	5	28	rsa	rsa	NOUN
iajs-1805	5	29	algorithm	algorithm	NOUN
iajs-1805	5	30	and	and	CCONJ
iajs-1805	5	31	diffie	diffie	PROPN
iajs-1805	5	32	-	-	PUNCT
iajs-1805	5	33	hellman	hellman	PROPN
iajs-1805	5	34	exchange	exchange	PROPN
iajs-1805	5	35	,	,	PUNCT
iajs-1805	5	36	beurling	beurle	VERB
iajs-1805	5	37	primes	prime	NOUN
iajs-1805	5	38	,	,	PUNCT
iajs-1805	5	39	analytic	analytic	ADJ
iajs-1805	5	40	number	number	NOUN
iajs-1805	5	41	theory	theory	NOUN
iajs-1805	5	42	)	)	PUNCT
iajs-1805	5	43	.	.	PUNCT
iajs-1805	5	44	                	                	SPACE
iajs-1805	5	45	ihsciconf	ihsciconf	PROPN
iajs-1805	5	46	2017	2017	NUM
iajs-1805	5	47	special	special	ADJ
iajs-1805	5	48	issue	issue	NOUN
iajs-1805	5	49	ibn	ibn	PROPN
iajs-1805	5	50	al	al	PROPN
iajs-1805	5	51	-	-	PUNCT
iajs-1805	5	52	haitham	haitham	PROPN
iajs-1805	5	53	journal	journal	PROPN
iajs-1805	5	54	for	for	ADP
iajs-1805	5	55	pure	pure	ADJ
iajs-1805	5	56	and	and	CCONJ
iajs-1805	5	57	applied	apply	VERB
iajs-1805	5	58	science	science	NOUN
iajs-1805	5	59	https://doi.org/	https://doi.org/	NOUN
iajs-1805	5	60	10.30526/2017.ihsciconf.1805	10.30526/2017.ihsciconf.1805	NOUN
iajs-1805	5	61	for	for	ADP
iajs-1805	5	62	more	more	ADJ
iajs-1805	5	63	information	information	NOUN
iajs-1805	5	64	about	about	ADP
iajs-1805	5	65	the	the	DET
iajs-1805	5	66	conference	conference	NOUN
iajs-1805	5	67	please	please	INTJ
iajs-1805	5	68	visit	visit	VERB
iajs-1805	5	69	the	the	DET
iajs-1805	5	70	websites	website	NOUN
iajs-1805	5	71	:	:	PUNCT
iajs-1805	5	72	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1805	5	73	  	  	SPACE
iajs-1805	5	74	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1805	5	75	   	   	SPACE
iajs-1805	5	76	mathematics	mathematic	NOUN
iajs-1805	6	1	|	|	ADV
iajs-1805	6	2	405	405	NUM
iajs-1805	6	3	1	1	NUM
iajs-1805	6	4	.	.	PUNCT
iajs-1805	7	1	introduction	introduction	NOUN
iajs-1805	7	2	since	since	SCONJ
iajs-1805	7	3	the	the	DET
iajs-1805	7	4	seventieth	seventieth	NOUN
iajs-1805	7	5	of	of	ADP
iajs-1805	7	6	the	the	DET
iajs-1805	7	7	last	last	ADJ
iajs-1805	7	8	century	century	NOUN
iajs-1805	8	1	,	,	PUNCT
iajs-1805	8	2	several	several	ADJ
iajs-1805	8	3	authors	author	NOUN
iajs-1805	8	4	introduced	introduce	VERB
iajs-1805	8	5	a	a	DET
iajs-1805	8	6	cryptographic	cryptographic	ADJ
iajs-1805	8	7	algorithm	algorithm	NOUN
iajs-1805	8	8	in	in	ADP
iajs-1805	8	9	order	order	NOUN
iajs-1805	8	10	to	to	PART
iajs-1805	8	11	replace	replace	VERB
iajs-1805	8	12	the	the	DET
iajs-1805	8	13	less	less	ADV
iajs-1805	8	14	secure	secure	ADJ
iajs-1805	8	15	algorithms	algorithm	NOUN
iajs-1805	8	16	“	"	PUNCT
iajs-1805	8	17	diffie	diffie	PROPN
iajs-1805	8	18	and	and	CCONJ
iajs-1805	8	19	hellman	hellman	PROPN
iajs-1805	8	20	”	"	PUNCT
iajs-1805	8	21	,	,	PUNCT
iajs-1805	8	22	who	who	PRON
iajs-1805	8	23	described	describe	VERB
iajs-1805	8	24	the	the	DET
iajs-1805	8	25	idea	idea	NOUN
iajs-1805	8	26	of	of	ADP
iajs-1805	8	27	such	such	DET
iajs-1805	8	28	an	an	DET
iajs-1805	8	29	algorithm	algorithm	NOUN
iajs-1805	8	30	,	,	PUNCT
iajs-1805	8	31	but	but	CCONJ
iajs-1805	8	32	never	never	ADV
iajs-1805	8	33	truly	truly	ADV
iajs-1805	8	34	developed	develop	VERB
iajs-1805	8	35	it	it	PRON
iajs-1805	8	36	.	.	PUNCT
iajs-1805	9	1	the	the	DET
iajs-1805	9	2	rsa	rsa	PROPN
iajs-1805	9	3	algorithm	algorithm	NOUN
iajs-1805	9	4	and	and	CCONJ
iajs-1805	9	5	dh	dh	NOUN
iajs-1805	9	6	-	-	PUNCT
iajs-1805	9	7	key	key	ADJ
iajs-1805	9	8	exchange	exchange	NOUN
iajs-1805	9	9	cryptosystems	cryptosystem	NOUN
iajs-1805	9	10	(	(	PUNCT
iajs-1805	9	11	as	as	ADV
iajs-1805	9	12	well	well	ADV
iajs-1805	9	13	as	as	ADP
iajs-1805	9	14	digital	digital	ADJ
iajs-1805	9	15	signatures	signature	NOUN
iajs-1805	9	16	)	)	PUNCT
iajs-1805	9	17	are	be	AUX
iajs-1805	9	18	regarded	regard	VERB
iajs-1805	9	19	as	as	ADP
iajs-1805	9	20	the	the	DET
iajs-1805	9	21	important	important	ADJ
iajs-1805	9	22	security	security	NOUN
iajs-1805	9	23	schemes	scheme	NOUN
iajs-1805	9	24	(	(	PUNCT
iajs-1805	9	25	see	see	VERB
iajs-1805	9	26	for	for	ADP
iajs-1805	9	27	instance	instance	NOUN
iajs-1805	9	28	(	(	PUNCT
iajs-1805	9	29	a.	a.	NOUN
iajs-1805	9	30	salomaa.[8	salomaa.[8	NUM
iajs-1805	9	31	]	]	PUNCT
iajs-1805	9	32	)	)	PUNCT
iajs-1805	9	33	,	,	PUNCT
iajs-1805	9	34	(	(	PUNCT
iajs-1805	9	35	j.	j.	PROPN
iajs-1805	9	36	coron	coron	PROPN
iajs-1805	9	37	.[5	.[5	X
iajs-1805	9	38	]	]	PUNCT
iajs-1805	9	39	)	)	PUNCT
iajs-1805	9	40	and	and	CCONJ
iajs-1805	9	41	(	(	PUNCT
iajs-1805	9	42	s.d	s.d	PROPN
iajs-1805	9	43	.	.	PROPN
iajs-1805	9	44	galbraith.[6	galbraith.[6	PROPN
iajs-1805	9	45	]	]	PUNCT
iajs-1805	9	46	)	)	PUNCT
iajs-1805	9	47	.	.	PUNCT
iajs-1805	10	1	the	the	DET
iajs-1805	10	2	majority	majority	NOUN
iajs-1805	10	3	is	be	AUX
iajs-1805	10	4	to	to	PART
iajs-1805	10	5	know	know	VERB
iajs-1805	10	6	the	the	DET
iajs-1805	10	7	security	security	NOUN
iajs-1805	10	8	algorithms	algorithm	NOUN
iajs-1805	10	9	that	that	PRON
iajs-1805	10	10	focused	focus	VERB
iajs-1805	10	11	on	on	ADP
iajs-1805	10	12	generating	generate	VERB
iajs-1805	10	13	the	the	DET
iajs-1805	10	14	primes	prime	NOUN
iajs-1805	10	15	which	which	PRON
iajs-1805	10	16	is	be	AUX
iajs-1805	10	17	called	call	VERB
iajs-1805	10	18	the	the	DET
iajs-1805	10	19	code	code	NOUN
iajs-1805	10	20	of	of	ADP
iajs-1805	10	21	the	the	DET
iajs-1805	10	22	encryption	encryption	NOUN
iajs-1805	10	23	.	.	PUNCT
iajs-1805	11	1	the	the	DET
iajs-1805	11	2	main	main	ADJ
iajs-1805	11	3	aim	aim	NOUN
iajs-1805	11	4	of	of	ADP
iajs-1805	11	5	this	this	DET
iajs-1805	11	6	work	work	NOUN
iajs-1805	11	7	is	be	AUX
iajs-1805	11	8	to	to	PART
iajs-1805	11	9	secure	secure	VERB
iajs-1805	11	10	enough	enough	ADV
iajs-1805	11	11	the	the	DET
iajs-1805	11	12	mentioned	mention	VERB
iajs-1805	11	13	algorithms	algorithm	NOUN
iajs-1805	11	14	and	and	CCONJ
iajs-1805	11	15	the	the	DET
iajs-1805	11	16	way	way	NOUN
iajs-1805	11	17	for	for	ADP
iajs-1805	11	18	building	build	VERB
iajs-1805	11	19	the	the	DET
iajs-1805	11	20	prime	prime	NOUN
iajs-1805	11	21	from	from	ADP
iajs-1805	11	22	a	a	DET
iajs-1805	11	23	challenging	challenging	ADJ
iajs-1805	11	24	way	way	NOUN
iajs-1805	11	25	that	that	PRON
iajs-1805	11	26	no	no	DET
iajs-1805	11	27	one	one	NOUN
iajs-1805	11	28	can	can	AUX
iajs-1805	11	29	predict	predict	VERB
iajs-1805	11	30	it	it	PRON
iajs-1805	11	31	.	.	PUNCT
iajs-1805	12	1	here	here	ADV
iajs-1805	12	2	,	,	PUNCT
iajs-1805	12	3	the	the	DET
iajs-1805	12	4	principle	principle	ADJ
iajs-1805	12	5	objective	objective	NOUN
iajs-1805	12	6	is	be	AUX
iajs-1805	12	7	to	to	PART
iajs-1805	12	8	overlook	overlook	VERB
iajs-1805	12	9	the	the	DET
iajs-1805	12	10	utilization	utilization	NOUN
iajs-1805	12	11	of	of	ADP
iajs-1805	12	12	the	the	DET
iajs-1805	12	13	messenger	messenger	NOUN
iajs-1805	12	14	with	with	ADP
iajs-1805	12	15	a	a	DET
iajs-1805	12	16	specific	specific	ADJ
iajs-1805	12	17	end	end	NOUN
iajs-1805	12	18	goal	goal	NOUN
iajs-1805	12	19	to	to	PART
iajs-1805	12	20	convey	convey	VERB
iajs-1805	12	21	keys	key	NOUN
iajs-1805	12	22	to	to	ADP
iajs-1805	12	23	the	the	DET
iajs-1805	12	24	recipient	recipient	NOUN
iajs-1805	12	25	over	over	ADP
iajs-1805	12	26	another	another	DET
iajs-1805	12	27	protected	protect	VERB
iajs-1805	12	28	channel	channel	NOUN
iajs-1805	12	29	before	before	ADP
iajs-1805	12	30	transmitting	transmit	VERB
iajs-1805	12	31	the	the	DET
iajs-1805	12	32	initially	initially	ADV
iajs-1805	12	33	planned	plan	VERB
iajs-1805	12	34	data	datum	NOUN
iajs-1805	12	35	or	or	CCONJ
iajs-1805	12	36	message	message	NOUN
iajs-1805	12	37	.	.	PUNCT
iajs-1805	13	1	the	the	DET
iajs-1805	13	2	more	more	ADV
iajs-1805	13	3	vital	vital	ADJ
iajs-1805	13	4	thing	thing	NOUN
iajs-1805	13	5	here	here	ADV
iajs-1805	13	6	is	be	AUX
iajs-1805	13	7	that	that	SCONJ
iajs-1805	13	8	the	the	DET
iajs-1805	13	9	keys	key	NOUN
iajs-1805	13	10	ought	ought	AUX
iajs-1805	13	11	to	to	PART
iajs-1805	13	12	be	be	AUX
iajs-1805	13	13	worked	work	VERB
iajs-1805	13	14	in	in	ADP
iajs-1805	13	15	such	such	DET
iajs-1805	13	16	a	a	DET
iajs-1805	13	17	way	way	NOUN
iajs-1805	13	18	that	that	PRON
iajs-1805	13	19	the	the	DET
iajs-1805	13	20	unscrambling	unscrambling	ADJ
iajs-1805	13	21	key	key	NOUN
iajs-1805	13	22	may	may	AUX
iajs-1805	13	23	not	not	PART
iajs-1805	13	24	be	be	AUX
iajs-1805	13	25	effortlessly	effortlessly	ADV
iajs-1805	13	26	found	find	VERB
iajs-1805	13	27	from	from	ADP
iajs-1805	13	28	the	the	DET
iajs-1805	13	29	rsa	rsa	PROPN
iajs-1805	13	30	calculation	calculation	NOUN
iajs-1805	13	31	and	and	CCONJ
iajs-1805	13	32	dh	dh	NOUN
iajs-1805	13	33	-	-	PUNCT
iajs-1805	13	34	key	key	NOUN
iajs-1805	13	35	.	.	PUNCT
iajs-1805	14	1	in	in	ADP
iajs-1805	14	2	this	this	DET
iajs-1805	14	3	article	article	NOUN
iajs-1805	14	4	,	,	PUNCT
iajs-1805	14	5	the	the	DET
iajs-1805	14	6	work	work	NOUN
iajs-1805	14	7	has	have	AUX
iajs-1805	14	8	been	be	AUX
iajs-1805	14	9	done	do	VERB
iajs-1805	14	10	concentrated	concentrate	VERB
iajs-1805	14	11	on	on	ADP
iajs-1805	14	12	how	how	SCONJ
iajs-1805	14	13	could	could	AUX
iajs-1805	14	14	we	we	PRON
iajs-1805	14	15	make	make	VERB
iajs-1805	14	16	the	the	DET
iajs-1805	14	17	algorithm	algorithm	NOUN
iajs-1805	14	18	secure	secure	VERB
iajs-1805	14	19	strongly	strongly	ADV
iajs-1805	14	20	such	such	ADJ
iajs-1805	14	21	that	that	SCONJ
iajs-1805	14	22	one	one	PRON
iajs-1805	14	23	can	can	AUX
iajs-1805	14	24	say	say	VERB
iajs-1805	14	25	it	it	PRON
iajs-1805	14	26	breaks	break	VERB
iajs-1805	14	27	down	down	ADP
iajs-1805	14	28	it	it	PRON
iajs-1805	14	29	.	.	PUNCT
iajs-1805	15	1	the	the	DET
iajs-1805	15	2	main	main	ADJ
iajs-1805	15	3	body	body	NOUN
iajs-1805	15	4	of	of	ADP
iajs-1805	15	5	this	this	DET
iajs-1805	15	6	work	work	NOUN
iajs-1805	15	7	shows	show	VERB
iajs-1805	15	8	that	that	SCONJ
iajs-1805	15	9	,	,	PUNCT
iajs-1805	15	10	there	there	PRON
iajs-1805	15	11	is	be	VERB
iajs-1805	15	12	an	an	DET
iajs-1805	15	13	arithmetical	arithmetical	ADJ
iajs-1805	15	14	function	function	NOUN
iajs-1805	15	15	which	which	PRON
iajs-1805	15	16	generates	generate	VERB
iajs-1805	15	17	a	a	DET
iajs-1805	15	18	prime	prime	ADJ
iajs-1805	15	19	number	number	NOUN
iajs-1805	15	20	p	p	NOUN
iajs-1805	15	21	from	from	ADP
iajs-1805	15	22	a	a	DET
iajs-1805	15	23	large	large	ADJ
iajs-1805	15	24	enough	enough	ADJ
iajs-1805	15	25	real	real	ADJ
iajs-1805	15	26	number	number	NOUN
iajs-1805	15	27	x	x	PUNCT
iajs-1805	15	28	and	and	CCONJ
iajs-1805	15	29	uses	use	VERB
iajs-1805	15	30	that	that	DET
iajs-1805	15	31	prime	prime	NOUN
iajs-1805	15	32	in	in	ADP
iajs-1805	15	33	the	the	DET
iajs-1805	15	34	code	code	NOUN
iajs-1805	15	35	of	of	ADP
iajs-1805	15	36	the	the	DET
iajs-1805	15	37	algorithm	algorithm	NOUN
iajs-1805	15	38	.	.	PUNCT
iajs-1805	16	1	in	in	ADP
iajs-1805	16	2	this	this	DET
iajs-1805	16	3	work	work	NOUN
iajs-1805	16	4	,	,	PUNCT
iajs-1805	16	5	we	we	PRON
iajs-1805	16	6	generate	generate	VERB
iajs-1805	16	7	the	the	DET
iajs-1805	16	8	prime	prime	NOUN
iajs-1805	16	9	p	p	NOUN
iajs-1805	16	10	by	by	ADP
iajs-1805	16	11	using	use	VERB
iajs-1805	16	12	the	the	DET
iajs-1805	16	13	arithmetical	arithmetical	ADJ
iajs-1805	16	14	function	function	NOUN
iajs-1805	16	15	f*(x	f*(x	NOUN
iajs-1805	16	16	)	)	PUNCT
iajs-1805	16	17	.	.	PUNCT
iajs-1805	17	1	2	2	X
iajs-1805	17	2	.	.	X
iajs-1805	17	3	materials	material	NOUN
iajs-1805	17	4	and	and	CCONJ
iajs-1805	17	5	methods	method	NOUN
iajs-1805	17	6	the	the	DET
iajs-1805	17	7	generating	generate	VERB
iajs-1805	17	8	function	function	NOUN
iajs-1805	17	9	f*(x	f*(x	NOUN
iajs-1805	17	10	)	)	PUNCT
iajs-1805	17	11	.	.	PUNCT
iajs-1805	18	1	let	let	VERB
iajs-1805	18	2	ƥ	ƥ	PRON
iajs-1805	18	3	2,3,5,7	2,3,5,7	NUM
iajs-1805	18	4	,	,	PUNCT
iajs-1805	18	5	…	…	PUNCT
iajs-1805	18	6	be	be	AUX
iajs-1805	18	7	a	a	DET
iajs-1805	18	8	set	set	NOUN
iajs-1805	18	9	of	of	ADP
iajs-1805	18	10	primes	prime	NOUN
iajs-1805	18	11	,	,	PUNCT
iajs-1805	18	12	while	while	SCONJ
iajs-1805	18	13	the	the	DET
iajs-1805	18	14	set	set	NOUN
iajs-1805	18	15	of	of	ADP
iajs-1805	18	16	natural	natural	ADJ
iajs-1805	18	17	number	number	NOUN
iajs-1805	18	18	is	be	AUX
iajs-1805	18	19	𝒩	𝒩	PROPN
iajs-1805	18	20	1,2,3,4,5,6,7	1,2,3,4,5,6,7	NUM
iajs-1805	18	21	,	,	PUNCT
iajs-1805	18	22	.	.	PUNCT
iajs-1805	18	23	.	.	PUNCT
iajs-1805	18	24	.	.	PUNCT
iajs-1805	19	1	.	.	PUNCT
iajs-1805	20	1	.	.	PUNCT
iajs-1805	21	1	the	the	DET
iajs-1805	21	2	counting	counting	NOUN
iajs-1805	21	3	functions	function	NOUN
iajs-1805	21	4	of	of	ADP
iajs-1805	21	5	prime	prime	NOUN
iajs-1805	21	6	and	and	CCONJ
iajs-1805	21	7	integers	integer	NOUN
iajs-1805	21	8	are	be	AUX
iajs-1805	21	9	defined	define	VERB
iajs-1805	21	10	as	as	SCONJ
iajs-1805	21	11	follows	follow	VERB
iajs-1805	21	12	:	:	PUNCT
iajs-1805	21	13	definition	definition	NOUN
iajs-1805	21	14	let	let	VERB
iajs-1805	21	15	ƥ	ƥ	PRON
iajs-1805	21	16	2,3,5,7	2,3,5,7	NUM
iajs-1805	21	17	,	,	PUNCT
iajs-1805	21	18	.	.	PUNCT
iajs-1805	21	19	.	.	PUNCT
iajs-1805	21	20	.	.	PUNCT
iajs-1805	21	21	.	.	PUNCT
iajs-1805	21	22	.	.	PUNCT
iajs-1805	22	1	.	.	PUNCT
iajs-1805	23	1	the	the	DET
iajs-1805	23	2	counting	counting	NOUN
iajs-1805	23	3	function	function	NOUN
iajs-1805	23	4	for	for	ADP
iajs-1805	23	5	any	any	DET
iajs-1805	23	6	positive	positive	ADJ
iajs-1805	23	7	real	real	NOUN
iajs-1805	23	8	x	x	VERB
iajs-1805	23	9	is	be	AUX
iajs-1805	23	10	defined	define	VERB
iajs-1805	23	11	to	to	PART
iajs-1805	23	12	be	be	AUX
iajs-1805	23	13	:	:	PUNCT
iajs-1805	23	14	𝐻	𝐻	PROPN
iajs-1805	23	15	𝑥	𝑥	PRON
iajs-1805	23	16	∑	∑	PUNCT
iajs-1805	23	17	log	log	VERB
iajs-1805	23	18	𝑝	𝑝	NOUN
iajs-1805	23	19	,	,	PUNCT
iajs-1805	23	20	where	where	SCONJ
iajs-1805	23	21	𝑘	𝑘	PRON
iajs-1805	23	22	∈	∈	NOUN
iajs-1805	23	23	𝑁	𝑁	PROPN
iajs-1805	23	24	and	and	CCONJ
iajs-1805	23	25	𝑝	𝑝	NOUN
iajs-1805	23	26	∈	∈	PROPN
iajs-1805	24	1	ƥ	ƥ	VERB
iajs-1805	24	2	.	.	PUNCT
iajs-1805	25	1	we	we	PRON
iajs-1805	25	2	can	can	AUX
iajs-1805	25	3	write	write	VERB
iajs-1805	25	4	𝐻	𝐻	PROPN
iajs-1805	25	5	𝑥	𝑥	NOUN
iajs-1805	25	6	as	as	SCONJ
iajs-1805	25	7	follows	follow	VERB
iajs-1805	25	8	:	:	PUNCT
iajs-1805	25	9	𝐻	𝐻	PROPN
iajs-1805	25	10	𝑥	𝑥	PART
iajs-1805	25	11	∑	∑	PUNCT
iajs-1805	25	12	∑	∑	VERB
iajs-1805	25	13	log	log	VERB
iajs-1805	25	14	𝑝	𝑝	NOUN
iajs-1805	25	15	∑	∑	PROPN
iajs-1805	25	16	ℎ	ℎ	X
iajs-1805	25	17	𝑥	𝑥	PROPN
iajs-1805	25	18	,	,	PUNCT
iajs-1805	25	19	(	(	PUNCT
iajs-1805	25	20	see[1]for	see[1]for	ADP
iajs-1805	25	21	more	more	ADJ
iajs-1805	25	22	details	detail	NOUN
iajs-1805	25	23	)	)	PUNCT
iajs-1805	25	24	.	.	PUNCT
iajs-1805	26	1	𝑊ℎ𝑒𝑟𝑒	𝑊ℎ𝑒𝑟𝑒	NOUN
iajs-1805	26	2	ℎ	ℎ	PART
iajs-1805	26	3	𝑥	𝑥	DET
iajs-1805	26	4	∑	∑	PUNCT
iajs-1805	26	5	log	log	VERB
iajs-1805	26	6	𝑝.	𝑝.	NOUN
iajs-1805	26	7	now	now	ADV
iajs-1805	26	8	using	use	VERB
iajs-1805	26	9	the	the	DET
iajs-1805	26	10	mobiusinversion	mobiusinversion	NOUN
iajs-1805	26	11	formula	formula	NOUN
iajs-1805	26	12	,	,	PUNCT
iajs-1805	26	13	we	we	PRON
iajs-1805	26	14	get	get	VERB
iajs-1805	26	15	𝐹	𝐹	PROPN
iajs-1805	26	16	𝑥	𝑥	INTJ
iajs-1805	26	17	∑	∑	ADV
iajs-1805	26	18	𝜇	𝜇	ADP
iajs-1805	26	19	𝑛	𝑛	DET
iajs-1805	26	20	𝐻	𝐻	NOUN
iajs-1805	26	21	𝑥	𝑥	NOUN
iajs-1805	26	22	,	,	PUNCT
iajs-1805	26	23	where	where	SCONJ
iajs-1805	26	24	𝜇	𝜇	ADP
iajs-1805	26	25	𝑛	𝑛	PROPN
iajs-1805	26	26	is	be	AUX
iajs-1805	26	27	𝑚𝑎𝑏𝑖𝑢𝑠	𝑚𝑎𝑏𝑖𝑢𝑠	ADJ
iajs-1805	26	28	function	function	NOUN
iajs-1805	26	29	.	.	PUNCT
iajs-1805	27	1	the	the	DET
iajs-1805	27	2	counting	counting	NOUN
iajs-1805	27	3	function	function	NOUN
iajs-1805	27	4	h(x	h(x	PROPN
iajs-1805	27	5	)	)	PUNCT
iajs-1805	27	6	is	be	AUX
iajs-1805	27	7	represented	represent	VERB
iajs-1805	27	8	as	as	ADP
iajs-1805	27	9	the	the	DET
iajs-1805	27	10	integer	integer	NOUN
iajs-1805	27	11	part	part	NOUN
iajs-1805	27	12	of	of	ADP
iajs-1805	27	13	and	and	CCONJ
iajs-1805	27	14	positive	positive	ADJ
iajs-1805	27	15	x	x	NOUN
iajs-1805	27	16	minus	minus	ADP
iajs-1805	27	17	1,this	1,this	NUM
iajs-1805	27	18	tells	tell	VERB
iajs-1805	27	19	us	we	PRON
iajs-1805	27	20	that	that	SCONJ
iajs-1805	27	21	the	the	DET
iajs-1805	27	22	f(x	f(x	PROPN
iajs-1805	27	23	)	)	PUNCT
iajs-1805	27	24	would	would	AUX
iajs-1805	27	25	be	be	AUX
iajs-1805	27	26	the	the	DET
iajs-1805	27	27	sum	sum	NOUN
iajs-1805	27	28	of	of	ADP
iajs-1805	27	29	product	product	NOUN
iajs-1805	27	30	𝜇	𝜇	ADP
iajs-1805	27	31	𝑥	𝑥	PROPN
iajs-1805	27	32	and	and	CCONJ
iajs-1805	27	33	the	the	DET
iajs-1805	27	34	integer	integer	NOUN
iajs-1805	27	35	part	part	NOUN
iajs-1805	27	36	of	of	ADP
iajs-1805	27	37	and	and	CCONJ
iajs-1805	27	38	positive	positive	ADJ
iajs-1805	27	39	x	x	NOUN
iajs-1805	27	40	minus	minus	ADP
iajs-1805	27	41	1	1	NUM
iajs-1805	27	42	.	.	PUNCT
iajs-1805	27	43	where	where	SCONJ
iajs-1805	27	44	the	the	DET
iajs-1805	27	45	sum	sum	NOUN
iajs-1805	27	46	is	be	AUX
iajs-1805	27	47	running	run	VERB
iajs-1805	27	48	from	from	ADP
iajs-1805	27	49	1	1	NUM
iajs-1805	27	50	to	to	ADP
iajs-1805	27	51	infinity	infinity	NOUN
iajs-1805	27	52	.	.	PUNCT
iajs-1805	28	1	we	we	PRON
iajs-1805	28	2	note	note	VERB
iajs-1805	28	3	that	that	SCONJ
iajs-1805	28	4	the	the	DET
iajs-1805	28	5	sum	sum	NOUN
iajs-1805	28	6	is	be	AUX
iajs-1805	28	7	vanished	vanish	VERB
iajs-1805	28	8	when	when	SCONJ
iajs-1805	28	9	the	the	DET
iajs-1805	28	10	index	index	NOUN
iajs-1805	28	11	is	be	AUX
iajs-1805	28	12	greater	great	ADJ
iajs-1805	28	13	than	than	ADP
iajs-1805	28	14	.in	.in	PUNCT
iajs-1805	28	15	the	the	DET
iajs-1805	28	16	other	other	ADJ
iajs-1805	28	17	words	word	NOUN
iajs-1805	28	18	,	,	PUNCT
iajs-1805	28	19	f(x	f(x	PROPN
iajs-1805	28	20	)	)	PUNCT
iajs-1805	29	1	=	=	SYM
iajs-1805	29	2	g(x	g(x	NOUN
iajs-1805	29	3	)	)	PUNCT
iajs-1805	30	1	+	+	NOUN
iajs-1805	30	2	zero	zero	NUM
iajs-1805	30	3	,	,	PUNCT
iajs-1805	30	4	where	where	SCONJ
iajs-1805	30	5	the	the	DET
iajs-1805	30	6	g(x	g(x	NOUN
iajs-1805	30	7	)	)	PUNCT
iajs-1805	30	8	means	mean	VERB
iajs-1805	30	9	the	the	DET
iajs-1805	30	10	sum	sum	NOUN
iajs-1805	30	11	of	of	ADP
iajs-1805	30	12	product	product	NOUN
iajs-1805	30	13	𝜇	𝜇	ADP
iajs-1805	30	14	𝑥	𝑥	PROPN
iajs-1805	30	15	and	and	CCONJ
iajs-1805	30	16	the	the	DET
iajs-1805	30	17	integer	integer	NOUN
iajs-1805	30	18	part	part	NOUN
iajs-1805	30	19	of	of	ADP
iajs-1805	30	20	positive	positive	ADJ
iajs-1805	30	21	x	x	NOUN
iajs-1805	30	22	minus	minus	ADP
iajs-1805	30	23	1	1	NUM
iajs-1805	30	24	for	for	ADP
iajs-1805	30	25	the	the	DET
iajs-1805	30	26	index	index	NOUN
iajs-1805	30	27	is	be	AUX
iajs-1805	30	28	less	less	ADJ
iajs-1805	30	29	than	than	ADP
iajs-1805	30	30	or	or	CCONJ
iajs-1805	30	31	equal	equal	ADJ
iajs-1805	30	32	to	to	ADP
iajs-1805	30	33	.	.	PUNCT
iajs-1805	31	1	ihsciconf	ihsciconf	PROPN
iajs-1805	31	2	2017	2017	NUM
iajs-1805	31	3	special	special	ADJ
iajs-1805	31	4	issue	issue	NOUN
iajs-1805	31	5	ibn	ibn	PROPN
iajs-1805	31	6	al	al	PROPN
iajs-1805	31	7	-	-	PUNCT
iajs-1805	31	8	haitham	haitham	PROPN
iajs-1805	31	9	journal	journal	PROPN
iajs-1805	31	10	for	for	ADP
iajs-1805	31	11	pure	pure	ADJ
iajs-1805	31	12	and	and	CCONJ
iajs-1805	31	13	applied	apply	VERB
iajs-1805	31	14	science	science	NOUN
iajs-1805	31	15	https://doi.org/	https://doi.org/	NOUN
iajs-1805	31	16	10.30526/2017.ihsciconf.1805	10.30526/2017.ihsciconf.1805	NOUN
iajs-1805	31	17	for	for	ADP
iajs-1805	31	18	more	more	ADJ
iajs-1805	31	19	information	information	NOUN
iajs-1805	31	20	about	about	ADP
iajs-1805	31	21	the	the	DET
iajs-1805	31	22	conference	conference	NOUN
iajs-1805	31	23	please	please	INTJ
iajs-1805	31	24	visit	visit	VERB
iajs-1805	31	25	the	the	DET
iajs-1805	31	26	websites	website	NOUN
iajs-1805	31	27	:	:	PUNCT
iajs-1805	31	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1805	31	29	  	  	SPACE
iajs-1805	31	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1805	31	31	   	   	SPACE
iajs-1805	31	32	mathematics	mathematic	NOUN
iajs-1805	31	33	|	|	ADV
iajs-1805	31	34	406	406	NUM
iajs-1805	31	35	the	the	DET
iajs-1805	31	36	function	function	NOUN
iajs-1805	31	37	f(x	f(x	PROPN
iajs-1805	31	38	)	)	PUNCT
iajs-1805	31	39	is	be	AUX
iajs-1805	31	40	increasing	increase	VERB
iajs-1805	31	41	step	step	NOUN
iajs-1805	31	42	function	function	NOUN
iajs-1805	31	43	.	.	PUNCT
iajs-1805	32	1	so	so	ADV
iajs-1805	32	2	,	,	PUNCT
iajs-1805	32	3	choosing	choose	VERB
iajs-1805	32	4	a	a	DET
iajs-1805	32	5	(	(	PUNCT
iajs-1805	32	6	large	large	ADJ
iajs-1805	32	7	enough	enough	ADV
iajs-1805	32	8	)	)	PUNCT
iajs-1805	32	9	real	real	ADJ
iajs-1805	32	10	number	number	NOUN
iajs-1805	32	11	x	x	PUNCT
iajs-1805	32	12	gives	give	VERB
iajs-1805	32	13	two	two	NUM
iajs-1805	32	14	options	option	NOUN
iajs-1805	32	15	on	on	ADP
iajs-1805	32	16	the	the	DET
iajs-1805	32	17	f(x	f(x	PROPN
iajs-1805	32	18	)	)	PUNCT
iajs-1805	32	19	which	which	PRON
iajs-1805	32	20	are	be	AUX
iajs-1805	32	21	given	give	VERB
iajs-1805	32	22	as	as	SCONJ
iajs-1805	32	23	follows	follow	VERB
iajs-1805	32	24	:	:	PUNCT
iajs-1805	32	25	either	either	CCONJ
iajs-1805	32	26	the	the	DET
iajs-1805	32	27	output	output	NOUN
iajs-1805	32	28	of	of	ADP
iajs-1805	32	29	f(x	f(x	PROPN
iajs-1805	32	30	)	)	PUNCT
iajs-1805	32	31	is	be	AUX
iajs-1805	32	32	a	a	DET
iajs-1805	32	33	prime	prime	ADJ
iajs-1805	32	34	number	number	NOUN
iajs-1805	32	35	or	or	CCONJ
iajs-1805	32	36	a	a	DET
iajs-1805	32	37	natural	natural	ADJ
iajs-1805	32	38	number	number	NOUN
iajs-1805	32	39	.	.	PUNCT
iajs-1805	33	1	the	the	DET
iajs-1805	33	2	reader	reader	NOUN
iajs-1805	33	3	must	must	AUX
iajs-1805	33	4	be	be	AUX
iajs-1805	33	5	familiar	familiar	ADJ
iajs-1805	33	6	with	with	ADP
iajs-1805	33	7	proof	proof	NOUN
iajs-1805	33	8	of	of	ADP
iajs-1805	33	9	f(x	f(x	PROPN
iajs-1805	33	10	)	)	PUNCT
iajs-1805	33	11	being	be	AUX
iajs-1805	33	12	increased	increase	VERB
iajs-1805	33	13	and	and	CCONJ
iajs-1805	33	14	step	step	NOUN
iajs-1805	33	15	function	function	NOUN
iajs-1805	33	16	.	.	PUNCT
iajs-1805	34	1	for	for	ADP
iajs-1805	34	2	more	more	ADJ
iajs-1805	34	3	details	detail	NOUN
iajs-1805	34	4	,	,	PUNCT
iajs-1805	34	5	one	one	PRON
iajs-1805	34	6	can	can	AUX
iajs-1805	34	7	see	see	VERB
iajs-1805	34	8	[	[	X
iajs-1805	34	9	2	2	NUM
iajs-1805	34	10	]	]	PUNCT
iajs-1805	34	11	.	.	PUNCT
iajs-1805	35	1	moreover	moreover	ADV
iajs-1805	35	2	,	,	PUNCT
iajs-1805	35	3	if	if	SCONJ
iajs-1805	35	4	we	we	PRON
iajs-1805	35	5	define	define	VERB
iajs-1805	35	6	df=	df=	PROPN
iajs-1805	35	7	f(x)-f(x-1	f(x)-f(x-1	NOUN
iajs-1805	35	8	)	)	PUNCT
iajs-1805	35	9	,	,	PUNCT
iajs-1805	35	10	then	then	ADV
iajs-1805	35	11	df	df	PROPN
iajs-1805	35	12	must	must	AUX
iajs-1805	35	13	be	be	AUX
iajs-1805	35	14	either	either	PRON
iajs-1805	35	15	1	1	NUM
iajs-1805	35	16	or	or	CCONJ
iajs-1805	35	17	0	0	NUM
iajs-1805	35	18	.	.	PUNCT
iajs-1805	36	1	if	if	SCONJ
iajs-1805	36	2	one	one	PRON
iajs-1805	36	3	can	can	AUX
iajs-1805	36	4	calculatethe	calculatethe	VERB
iajs-1805	36	5	jump	jump	NOUN
iajs-1805	36	6	of	of	ADP
iajs-1805	36	7	f(x	f(x	PROPN
iajs-1805	36	8	)	)	PUNCT
iajs-1805	36	9	he	he	PRON
iajs-1805	36	10	can	can	AUX
iajs-1805	36	11	see	see	VERB
iajs-1805	36	12	that	that	PRON
iajs-1805	36	13	,	,	PUNCT
iajs-1805	36	14	𝐹	𝐹	PROPN
iajs-1805	36	15	𝑑	𝑑	PROPN
iajs-1805	36	16	𝐹	𝐹	PROPN
iajs-1805	36	17	𝑑	𝑑	PROPN
iajs-1805	36	18	1	1	NUM
iajs-1805	36	19	1	1	NUM
iajs-1805	36	20	𝑖𝑓	𝑖𝑓	ADP
iajs-1805	36	21	𝑑	𝑑	PROPN
iajs-1805	36	22	𝑛	𝑛	PROPN
iajs-1805	36	23	,	,	PUNCT
iajs-1805	36	24	𝑛	𝑛	PROPN
iajs-1805	36	25	,	,	PUNCT
iajs-1805	36	26	𝑘	𝑘	DET
iajs-1805	36	27	1	1	NUM
iajs-1805	36	28	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
iajs-1805	36	29	𝑑	𝑑	PROPN
iajs-1805	36	30	2	2	NUM
iajs-1805	36	31	0	0	NUM
iajs-1805	36	32	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
iajs-1805	36	33	.	.	PUNCT
iajs-1805	37	1	more	more	ADJ
iajs-1805	37	2	details	detail	NOUN
iajs-1805	37	3	,	,	PUNCT
iajs-1805	37	4	one	one	PRON
iajs-1805	37	5	can	can	AUX
iajs-1805	37	6	see	see	VERB
iajs-1805	37	7	[	[	X
iajs-1805	37	8	1	1	NUM
iajs-1805	37	9	]	]	PUNCT
iajs-1805	37	10	.	.	PUNCT
iajs-1805	38	1	therefore	therefore	ADV
iajs-1805	38	2	,	,	PUNCT
iajs-1805	38	3	getting	get	VERB
iajs-1805	38	4	a	a	DET
iajs-1805	38	5	prime	prime	NOUN
iajs-1805	38	6	p	p	NOUN
iajs-1805	38	7	from	from	ADP
iajs-1805	38	8	a	a	DET
iajs-1805	38	9	real	real	NOUN
iajs-1805	38	10	x	x	VERB
iajs-1805	38	11	is	be	AUX
iajs-1805	38	12	guaranteed	guarantee	VERB
iajs-1805	38	13	by	by	ADP
iajs-1805	38	14	taking	take	VERB
iajs-1805	38	15	the	the	DET
iajs-1805	38	16	power	power	NOUN
iajs-1805	38	17	,	,	PUNCT
iajs-1805	38	18	which	which	PRON
iajs-1805	38	19	is	be	AUX
iajs-1805	38	20	the	the	DET
iajs-1805	38	21	characteristic	characteristic	ADJ
iajs-1805	38	22	function	function	NOUN
iajs-1805	38	23	mf(x	mf(x	NOUN
iajs-1805	38	24	)	)	PUNCT
iajs-1805	38	25	,	,	PUNCT
iajs-1805	38	26	of	of	ADP
iajs-1805	38	27	the	the	DET
iajs-1805	38	28	output	output	NOUN
iajs-1805	38	29	of	of	ADP
iajs-1805	38	30	f(x)to	f(x)to	PROPN
iajs-1805	38	31	the	the	DET
iajs-1805	38	32	characteristic	characteristic	ADJ
iajs-1805	38	33	function	function	NOUN
iajs-1805	38	34	mf(x	mf(x	PROPN
iajs-1805	38	35	)	)	PUNCT
iajs-1805	38	36	.	.	PUNCT
iajs-1805	39	1	this	this	PRON
iajs-1805	39	2	means	mean	VERB
iajs-1805	39	3	that	that	SCONJ
iajs-1805	39	4	𝐹∗	𝐹∗	VERB
iajs-1805	39	5	𝑥	𝑥	NOUN
iajs-1805	39	6	f	f	X
iajs-1805	39	7	x	x	X
iajs-1805	39	8	𝒎𝑭	𝒎𝑭	PROPN
iajs-1805	39	9	,	,	PUNCT
iajs-1805	39	10	where	where	SCONJ
iajs-1805	39	11	the	the	DET
iajs-1805	39	12	characteristic	characteristic	ADJ
iajs-1805	39	13	function	function	NOUN
iajs-1805	39	14	is	be	AUX
iajs-1805	39	15	defined	define	VERB
iajs-1805	39	16	by	by	ADP
iajs-1805	39	17	𝒎	𝒎	PROPN
iajs-1805	39	18	∙	∙	PROPN
iajs-1805	39	19	,	,	PUNCT
iajs-1805	39	20	,	,	PUNCT
iajs-1805	39	21	∙	∙	PROPN
iajs-1805	39	22	,	,	PUNCT
iajs-1805	39	23	.	.	PUNCT
iajs-1805	40	1	therefore	therefore	ADV
iajs-1805	40	2	,	,	PUNCT
iajs-1805	40	3	the	the	DET
iajs-1805	40	4	step	step	NOUN
iajs-1805	40	5	function	function	NOUN
iajs-1805	40	6	𝐹∗	𝐹∗	X
iajs-1805	40	7	𝑥	𝑥	NOUN
iajs-1805	40	8	is	be	AUX
iajs-1805	40	9	either	either	PRON
iajs-1805	40	10	zero	zero	NUM
iajs-1805	40	11	or	or	CCONJ
iajs-1805	40	12	prime	prime	ADJ
iajs-1805	40	13	number	number	NOUN
iajs-1805	40	14	.	.	PUNCT
iajs-1805	41	1	the	the	DET
iajs-1805	41	2	mathematical	mathematical	ADJ
iajs-1805	41	3	technique	technique	NOUN
iajs-1805	41	4	shows	show	VERB
iajs-1805	41	5	that	that	SCONJ
iajs-1805	41	6	picking	pick	VERB
iajs-1805	41	7	a	a	DET
iajs-1805	41	8	prime	prime	ADJ
iajs-1805	41	9	number	number	NOUN
iajs-1805	41	10	from	from	ADP
iajs-1805	41	11	a	a	DET
iajs-1805	41	12	large	large	ADJ
iajs-1805	41	13	real	real	ADJ
iajs-1805	41	14	number	number	NOUN
iajs-1805	41	15	is	be	AUX
iajs-1805	41	16	not	not	PART
iajs-1805	41	17	easy	easy	ADJ
iajs-1805	41	18	without	without	ADP
iajs-1805	41	19	knowing	know	VERB
iajs-1805	41	20	the	the	DET
iajs-1805	41	21	function	function	NOUN
iajs-1805	41	22	f(x	f(x	PROPN
iajs-1805	41	23	)	)	PUNCT
iajs-1805	41	24	.	.	PUNCT
iajs-1805	42	1	3	3	X
iajs-1805	42	2	.	.	NOUN
iajs-1805	42	3	example	example	NOUN
iajs-1805	42	4	and	and	CCONJ
iajs-1805	42	5	its	its	PRON
iajs-1805	42	6	applicable	applicable	ADJ
iajs-1805	42	7	algorithm	algorithm	NOUN
iajs-1805	42	8	here	here	ADV
iajs-1805	42	9	,	,	PUNCT
iajs-1805	42	10	we	we	PRON
iajs-1805	42	11	give	give	VERB
iajs-1805	42	12	a	a	DET
iajs-1805	42	13	very	very	ADV
iajs-1805	42	14	simple	simple	ADJ
iajs-1805	42	15	example	example	NOUN
iajs-1805	42	16	in	in	ADP
iajs-1805	42	17	order	order	NOUN
iajs-1805	42	18	to	to	PART
iajs-1805	42	19	show	show	VERB
iajs-1805	42	20	how	how	SCONJ
iajs-1805	42	21	the	the	DET
iajs-1805	42	22	method	method	NOUN
iajs-1805	42	23	works	work	VERB
iajs-1805	42	24	:	:	PUNCT
iajs-1805	42	25	choice	choice	NOUN
iajs-1805	42	26	x	x	X
iajs-1805	42	27	=	=	SYM
iajs-1805	42	28	41.5	41.5	NUM
iajs-1805	42	29	.	.	PUNCT
iajs-1805	43	1	by	by	ADP
iajs-1805	43	2	definition	definition	NOUN
iajs-1805	43	3	2.1	2.1	NUM
iajs-1805	43	4	,	,	PUNCT
iajs-1805	43	5	we	we	PRON
iajs-1805	43	6	get	get	VERB
iajs-1805	43	7	f	f	X
iajs-1805	43	8	(	(	PUNCT
iajs-1805	43	9	41.5	41.5	NUM
iajs-1805	43	10	)	)	PUNCT
iajs-1805	43	11	=	=	SYM
iajs-1805	43	12	m(1	m(1	NOUN
iajs-1805	43	13	)	)	PUNCT
iajs-1805	43	14	(	(	PUNCT
iajs-1805	43	15	[	[	X
iajs-1805	43	16	41.51/1]-1	41.51/1]-1	X
iajs-1805	43	17	)	)	PUNCT
iajs-1805	43	18	+	+	CCONJ
iajs-1805	43	19	m(2	m(2	NOUN
iajs-1805	43	20	)	)	PUNCT
iajs-1805	43	21	(	(	PUNCT
iajs-1805	43	22	[	[	X
iajs-1805	43	23	41.51/2]-1	41.51/2]-1	NOUN
iajs-1805	43	24	)	)	PUNCT
iajs-1805	43	25	+	+	CCONJ
iajs-1805	43	26	m(3	m(3	NOUN
iajs-1805	43	27	)	)	PUNCT
iajs-1805	43	28	(	(	PUNCT
iajs-1805	44	1	[	[	X
iajs-1805	44	2	41.51/3	41.51/3	X
iajs-1805	44	3	]	]	X
iajs-1805	44	4	-1	-1	PUNCT
iajs-1805	44	5	)	)	PUNCT
iajs-1805	44	6	+	+	CCONJ
iajs-1805	44	7	m(4	m(4	PROPN
iajs-1805	44	8	)	)	PUNCT
iajs-1805	44	9	(	(	PUNCT
iajs-1805	44	10	[	[	PUNCT
iajs-1805	44	11	41.51/4	41.51/4	NUM
iajs-1805	44	12	]	]	X
iajs-1805	44	13	-1	-1	PUNCT
iajs-1805	44	14	)	)	PUNCT
iajs-1805	45	1	+	+	X
iajs-1805	45	2	m(5	m(5	NOUN
iajs-1805	45	3	)	)	PUNCT
iajs-1805	45	4	(	(	PUNCT
iajs-1805	46	1	[	[	X
iajs-1805	46	2	41.51/5	41.51/5	X
iajs-1805	46	3	]	]	X
iajs-1805	46	4	-1	-1	NOUN
iajs-1805	46	5	)	)	PUNCT
iajs-1805	46	6	(	(	PUNCT
iajs-1805	46	7	the	the	DET
iajs-1805	46	8	function	function	NOUN
iajs-1805	46	9	f	f	PROPN
iajs-1805	46	10	x	x	AUX
iajs-1805	46	11	is	be	AUX
iajs-1805	46	12	vanished	vanish	VERB
iajs-1805	46	13	for	for	ADP
iajs-1805	46	14	n	n	X
iajs-1805	46	15	>	>	X
iajs-1805	46	16	.	.	PUNCT
iajs-1805	47	1	=	=	PUNCT
iajs-1805	47	2	40	40	NUM
iajs-1805	47	3	–	–	SYM
iajs-1805	47	4	5	5	NUM
iajs-1805	47	5	–	–	SYM
iajs-1805	47	6	2	2	NUM
iajs-1805	47	7	+	+	SYM
iajs-1805	47	8	0	0	NUM
iajs-1805	47	9	–	–	SYM
iajs-1805	47	10	1	1	NUM
iajs-1805	47	11	=	=	SYM
iajs-1805	47	12	32	32	NUM
iajs-1805	47	13	not	not	PART
iajs-1805	47	14	prime	prime	ADJ
iajs-1805	47	15	.	.	PUNCT
iajs-1805	48	1	by	by	ADP
iajs-1805	48	2	corollary	corollary	ADJ
iajs-1805	48	3	2.7	2.7	NUM
iajs-1805	48	4	,	,	PUNCT
iajs-1805	48	5	we	we	PRON
iajs-1805	48	6	get	get	VERB
iajs-1805	48	7	f(41.5	f(41.5	NOUN
iajs-1805	48	8	)	)	PUNCT
iajs-1805	48	9	=	=	NUM
iajs-1805	48	10	32	32	NUM
iajs-1805	48	11	,	,	PUNCT
iajs-1805	48	12	where	where	SCONJ
iajs-1805	48	13	γ	γ	X
iajs-1805	48	14	=	=	SYM
iajs-1805	48	15	0	0	NOUN
iajs-1805	48	16	=	=	SYM
iajs-1805	48	17	(	(	PUNCT
iajs-1805	48	18	32)0	32)0	NUM
iajs-1805	48	19	=	=	SYM
iajs-1805	48	20	1	1	NUM
iajs-1805	48	21	.	.	X
iajs-1805	48	22	ihsciconf	ihsciconf	PROPN
iajs-1805	48	23	2017	2017	NUM
iajs-1805	48	24	special	special	ADJ
iajs-1805	48	25	issue	issue	NOUN
iajs-1805	48	26	ibn	ibn	PROPN
iajs-1805	48	27	al	al	PROPN
iajs-1805	48	28	-	-	PUNCT
iajs-1805	48	29	haitham	haitham	PROPN
iajs-1805	48	30	journal	journal	PROPN
iajs-1805	48	31	for	for	ADP
iajs-1805	48	32	pure	pure	ADJ
iajs-1805	48	33	and	and	CCONJ
iajs-1805	48	34	applied	apply	VERB
iajs-1805	48	35	science	science	NOUN
iajs-1805	48	36	https://doi.org/	https://doi.org/	NOUN
iajs-1805	48	37	10.30526/2017.ihsciconf.1805	10.30526/2017.ihsciconf.1805	NOUN
iajs-1805	48	38	for	for	ADP
iajs-1805	48	39	more	more	ADJ
iajs-1805	48	40	information	information	NOUN
iajs-1805	48	41	about	about	ADP
iajs-1805	48	42	the	the	DET
iajs-1805	48	43	conference	conference	NOUN
iajs-1805	48	44	please	please	INTJ
iajs-1805	48	45	visit	visit	VERB
iajs-1805	48	46	the	the	DET
iajs-1805	48	47	websites	website	NOUN
iajs-1805	48	48	:	:	PUNCT
iajs-1805	48	49	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1805	48	50	  	  	SPACE
iajs-1805	48	51	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1805	48	52	   	   	SPACE
iajs-1805	48	53	mathematics	mathematic	NOUN
iajs-1805	48	54	|	|	ADV
iajs-1805	48	55	407	407	NUM
iajs-1805	48	56	program	program	NOUN
iajs-1805	48	57	(	(	PUNCT
iajs-1805	48	58	1	1	NUM
iajs-1805	48	59	):	):	PUNCT
iajs-1805	48	60	shows	show	NOUN
iajs-1805	48	61	generating	generate	VERB
iajs-1805	48	62	the	the	DET
iajs-1805	48	63	prime	prime	NOUN
iajs-1805	48	64	p	p	NOUN
iajs-1805	48	65	from	from	ADP
iajs-1805	48	66	a	a	DET
iajs-1805	48	67	real	real	ADJ
iajs-1805	48	68	number	number	NOUN
iajs-1805	48	69	x	x	NOUN
iajs-1805	48	70	:	:	PUNCT
iajs-1805	48	71	clear	clear	ADJ
iajs-1805	48	72	clc	clc	PROPN
iajs-1805	48	73	x=24.5	x=24.5	PROPN
iajs-1805	48	74	;	;	PUNCT
iajs-1805	48	75	n=1	n=1	PROPN
iajs-1805	48	76	;	;	PUNCT
iajs-1805	48	77	t=1	t=1	PROPN
iajs-1805	48	78	;	;	PUNCT
iajs-1805	48	79	sum=0	sum=0	PROPN
iajs-1805	48	80	;	;	PUNCT
iajs-1805	48	81	while	while	SCONJ
iajs-1805	48	82	(	(	PUNCT
iajs-1805	48	83	t	t	NOUN
iajs-1805	48	84	)	)	PUNCT
iajs-1805	48	85	n	n	NOUN
iajs-1805	48	86	)	)	PUNCT
iajs-1805	48	87	)	)	PUNCT
iajs-1805	49	1	if	if	SCONJ
iajs-1805	49	2	n>(log2(x)/log2(2	n>(log2(x)/log2(2	PROPN
iajs-1805	49	3	break	break	VERB
iajs-1805	49	4	end	end	NOUN
iajs-1805	49	5	if	if	SCONJ
iajs-1805	49	6	n==1	n==1	PROPN
iajs-1805	49	7	mobn=1	mobn=1	PROPN
iajs-1805	49	8	;	;	PUNCT
iajs-1805	49	9	else	else	ADV
iajs-1805	49	10	if	if	SCONJ
iajs-1805	49	11	isprime(n	isprime(n	PROPN
iajs-1805	49	12	)	)	PUNCT
iajs-1805	49	13	mobn=-1	mobn=-1	PROPN
iajs-1805	49	14	;	;	PUNCT
iajs-1805	49	15	else	else	ADV
iajs-1805	49	16	n1	n1	PROPN
iajs-1805	49	17	=	=	SYM
iajs-1805	49	18	n	n	NUM
iajs-1805	49	19	;	;	PUNCT
iajs-1805	49	20	base=2	base=2	NUM
iajs-1805	49	21	;	;	PUNCT
iajs-1805	49	22	k=1	k=1	X
iajs-1805	49	23	;	;	PUNCT
iajs-1805	49	24	while	while	SCONJ
iajs-1805	49	25	n1>1	n1>1	NOUN
iajs-1805	49	26	while	while	SCONJ
iajs-1805	49	27	mod(n1,base)~=0	mod(n1,base)~=0	NOUN
iajs-1805	49	28	base	base	NOUN
iajs-1805	49	29	=	=	SYM
iajs-1805	49	30	base+1	base+1	NOUN
iajs-1805	49	31	;	;	PUNCT
iajs-1805	49	32	end	end	NOUN
iajs-1805	49	33	a(k)=base	a(k)=base	PROPN
iajs-1805	49	34	;	;	PUNCT
iajs-1805	49	35	n1	n1	NOUN
iajs-1805	49	36	=	=	SYM
iajs-1805	49	37	n1	n1	NOUN
iajs-1805	49	38	/	/	SYM
iajs-1805	49	39	base	base	NOUN
iajs-1805	49	40	;	;	PUNCT
iajs-1805	49	41	base=2	base=2	NUM
iajs-1805	49	42	;	;	PUNCT
iajs-1805	49	43	k	k	X
iajs-1805	49	44	=	=	X
iajs-1805	49	45	k+1	k+1	X
iajs-1805	49	46	;	;	PUNCT
iajs-1805	49	47	end	end	NOUN
iajs-1805	49	48	t=1	t=1	ADP
iajs-1805	49	49	;	;	PUNCT
iajs-1805	49	50	for	for	ADP
iajs-1805	49	51	i=1	i=1	PROPN
iajs-1805	49	52	:	:	PUNCT
iajs-1805	49	53	k-1	k-1	PROPN
iajs-1805	49	54	if	if	SCONJ
iajs-1805	49	55	a(i)~=a(1	a(i)~=a(1	ADV
iajs-1805	49	56	)	)	PUNCT
iajs-1805	49	57	t=2	t=2	VERB
iajs-1805	49	58	;	;	PUNCT
iajs-1805	49	59	end	end	NOUN
iajs-1805	49	60	end	end	NOUN
iajs-1805	49	61	if	if	SCONJ
iajs-1805	49	62	t==1	t==1	PRON
iajs-1805	49	63	mobn=0	mobn=0	NUM
iajs-1805	49	64	;	;	PUNCT
iajs-1805	49	65	else	else	ADV
iajs-1805	49	66	if	if	SCONJ
iajs-1805	49	67	mod(k,2)==0	mod(k,2)==0	PROPN
iajs-1805	49	68	mobn=1	mobn=1	PROPN
iajs-1805	49	69	;	;	PUNCT
iajs-1805	49	70	else	else	ADV
iajs-1805	49	71	mobn=-1	mobn=-1	PROPN
iajs-1805	49	72	end	end	NOUN
iajs-1805	49	73	end	end	NOUN
iajs-1805	49	74	end	end	NOUN
iajs-1805	49	75	end	end	NOUN
iajs-1805	49	76	mobn	mobn	PROPN
iajs-1805	49	77	xn	xn	PUNCT
iajs-1805	50	1	=	=	NOUN
iajs-1805	50	2	fix(x^(1	fix(x^(1	NOUN
iajs-1805	50	3	/	/	SYM
iajs-1805	50	4	n	n	CCONJ
iajs-1805	50	5	)	)	PUNCT
iajs-1805	50	6	)	)	PUNCT
iajs-1805	50	7	;	;	PUNCT
iajs-1805	50	8	sum	sum	NOUN
iajs-1805	50	9	=	=	SYM
iajs-1805	50	10	sum+(mobn*(xn-1	sum+(mobn*(xn-1	NOUN
iajs-1805	50	11	)	)	PUNCT
iajs-1805	50	12	)	)	PUNCT
iajs-1805	50	13	;	;	PUNCT
iajs-1805	51	1	n	n	CCONJ
iajs-1805	51	2	=	=	SYM
iajs-1805	51	3	n+1	n+1	PROPN
iajs-1805	51	4	;	;	PUNCT
iajs-1805	51	5	ihsciconf	ihsciconf	PROPN
iajs-1805	51	6	2017	2017	NUM
iajs-1805	51	7	special	special	ADJ
iajs-1805	51	8	issue	issue	NOUN
iajs-1805	51	9	ibn	ibn	PROPN
iajs-1805	51	10	al	al	PROPN
iajs-1805	51	11	-	-	PUNCT
iajs-1805	51	12	haitham	haitham	PROPN
iajs-1805	51	13	journal	journal	PROPN
iajs-1805	51	14	for	for	ADP
iajs-1805	51	15	pure	pure	ADJ
iajs-1805	51	16	and	and	CCONJ
iajs-1805	51	17	applied	apply	VERB
iajs-1805	51	18	science	science	NOUN
iajs-1805	51	19	https://doi.org/	https://doi.org/	NOUN
iajs-1805	51	20	10.30526/2017.ihsciconf.1805	10.30526/2017.ihsciconf.1805	NOUN
iajs-1805	51	21	for	for	ADP
iajs-1805	51	22	more	more	ADJ
iajs-1805	51	23	information	information	NOUN
iajs-1805	51	24	about	about	ADP
iajs-1805	51	25	the	the	DET
iajs-1805	51	26	conference	conference	NOUN
iajs-1805	51	27	please	please	INTJ
iajs-1805	51	28	visit	visit	VERB
iajs-1805	51	29	the	the	DET
iajs-1805	51	30	websites	website	NOUN
iajs-1805	51	31	:	:	PUNCT
iajs-1805	51	32	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1805	51	33	  	  	SPACE
iajs-1805	51	34	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1805	51	35	   	   	SPACE
iajs-1805	51	36	mathematics	mathematic	NOUN
iajs-1805	51	37	|	|	ADV
iajs-1805	51	38	408	408	NUM
iajs-1805	51	39	end	end	VERB
iajs-1805	51	40	4	4	NUM
iajs-1805	51	41	.	.	PUNCT
iajs-1805	51	42	discussion	discussion	NOUN
iajs-1805	51	43	of	of	ADP
iajs-1805	51	44	the	the	DET
iajs-1805	51	45	results	result	NOUN
iajs-1805	51	46	and	and	CCONJ
iajs-1805	51	47	future	future	ADJ
iajs-1805	51	48	works	work	NOUN
iajs-1805	51	49	:	:	PUNCT
iajs-1805	51	50	the	the	DET
iajs-1805	51	51	simple	simple	ADJ
iajs-1805	51	52	example	example	NOUN
iajs-1805	51	53	given	give	VERB
iajs-1805	51	54	above	above	ADV
iajs-1805	51	55	was	be	AUX
iajs-1805	51	56	just	just	ADV
iajs-1805	51	57	to	to	PART
iajs-1805	51	58	reflect	reflect	VERB
iajs-1805	51	59	the	the	DET
iajs-1805	51	60	hard	hard	ADJ
iajs-1805	51	61	work	work	NOUN
iajs-1805	51	62	of	of	ADP
iajs-1805	51	63	building	build	VERB
iajs-1805	51	64	the	the	DET
iajs-1805	51	65	prime	prime	NOUN
iajs-1805	51	66	p	p	NOUN
iajs-1805	51	67	from	from	ADP
iajs-1805	51	68	a	a	DET
iajs-1805	51	69	large	large	ADJ
iajs-1805	51	70	real	real	ADJ
iajs-1805	51	71	x.	x.	NOUN
iajs-1805	51	72	one	one	PRON
iajs-1805	51	73	could	could	AUX
iajs-1805	51	74	use	use	VERB
iajs-1805	51	75	this	this	DET
iajs-1805	51	76	approach	approach	NOUN
iajs-1805	51	77	in	in	ADP
iajs-1805	51	78	various	various	ADJ
iajs-1805	51	79	manners	manner	NOUN
iajs-1805	51	80	and	and	CCONJ
iajs-1805	51	81	subject	subject	NOUN
iajs-1805	51	82	especially	especially	ADV
iajs-1805	51	83	in	in	ADP
iajs-1805	51	84	security	security	NOUN
iajs-1805	51	85	branches	branch	NOUN
iajs-1805	51	86	.	.	PUNCT
iajs-1805	52	1	references	reference	NOUN
iajs-1805	52	2	[	[	X
iajs-1805	52	3	1	1	X
iajs-1805	52	4	]	]	PUNCT
iajs-1805	52	5	t.	t.	PROPN
iajs-1805	52	6	m.	m.	NOUN
iajs-1805	52	7	apostol	apostol	PROPN
iajs-1805	52	8	,	,	PUNCT
iajs-1805	52	9	mathematical	mathematical	ADJ
iajs-1805	52	10	analysis	analysis	NOUN
iajs-1805	52	11	second	second	ADJ
iajs-1805	52	12	edition	edition	NOUN
iajs-1805	52	13	,	,	PUNCT
iajs-1805	52	14	addison	addison	PROPN
iajs-1805	52	15	-	-	PUNCT
iajs-1805	52	16	wesley	wesley	PROPN
iajs-1805	52	17	,	,	PUNCT
iajs-1805	52	18	1974	1974	NUM
iajs-1805	52	19	.	.	PUNCT
iajs-1805	53	1	[	[	X
iajs-1805	53	2	2	2	NUM
iajs-1805	53	3	]	]	SYM
iajs-1805	53	4	   	   	SPACE
iajs-1805	53	5	luma	luma	NOUN
iajs-1805	53	6	.	.	PUNCT
iajs-1805	54	1	n.m	n.m	PROPN
iajs-1805	54	2	.	.	PROPN
iajs-1805	54	3	tawfiq	tawfiq	PROPN
iajs-1805	54	4	,	,	PUNCT
iajs-1805	54	5	 	 	SPACE
iajs-1805	54	6	numerical	numerical	ADJ
iajs-1805	54	7	solution	solution	NOUN
iajs-1805	54	8	of	of	ADP
iajs-1805	54	9	singular	singular	ADJ
iajs-1805	54	10	perturbation	perturbation	NOUN
iajs-1805	54	11	problems	problem	NOUN
iajs-1805	54	12	by	by	ADP
iajs-1805	54	13	using	use	VERB
iajs-1805	54	14	collocation	collocation	NOUN
iajs-1805	54	15	neural	neural	ADJ
iajs-1805	54	16	networks	network	NOUN
iajs-1805	54	17	,	,	PUNCT
iajs-1805	54	18	mj	mj	PROPN
iajs-1805	54	19	journal	journal	PROPN
iajs-1805	54	20	on	on	ADP
iajs-1805	54	21	numerical	numerical	ADJ
iajs-1805	54	22	analysis	analysis	NOUN
iajs-1805	54	23	,	,	PUNCT
iajs-1805	54	24	1	1	NUM
iajs-1805	54	25	(	(	PUNCT
iajs-1805	54	26	1	1	NUM
iajs-1805	54	27	)	)	PUNCT
iajs-1805	54	28	(	(	PUNCT
iajs-1805	54	29	2017	2017	NUM
iajs-1805	54	30	)	)	PUNCT
iajs-1805	54	31	1	1	NUM
iajs-1805	54	32	-	-	SYM
iajs-1805	54	33	7	7	NUM
iajs-1805	54	34	.	.	PUNCT
iajs-1805	55	1	[	[	X
iajs-1805	55	2	3	3	NUM
iajs-1805	55	3	]	]	X
iajs-1805	55	4	q.	q.	PROPN
iajs-1805	55	5	baodong	baodong	PROPN
iajs-1805	55	6	,	,	PUNCT
iajs-1805	55	7	"	"	PUNCT
iajs-1805	55	8	leakage	leakage	NOUN
iajs-1805	55	9	-	-	PUNCT
iajs-1805	55	10	resilient	resilient	ADJ
iajs-1805	55	11	lossy	lossy	ADJ
iajs-1805	55	12	trapdoor	trapdoor	NOUN
iajs-1805	55	13	functions	function	NOUN
iajs-1805	55	14	and	and	CCONJ
iajs-1805	55	15	public	public	ADJ
iajs-1805	55	16	-	-	PUNCT
iajs-1805	55	17	key	key	NOUN
iajs-1805	55	18	encryption	encryption	NOUN
iajs-1805	55	19	.	.	PUNCT
iajs-1805	55	20	"	"	PUNCT
iajs-1805	56	1	proceedings	proceeding	NOUN
iajs-1805	56	2	of	of	ADP
iajs-1805	56	3	the	the	DET
iajs-1805	56	4	first	first	ADJ
iajs-1805	56	5	acm	acm	NOUN
iajs-1805	56	6	workshop	workshop	NOUN
iajs-1805	56	7	on	on	ADP
iajs-1805	56	8	asia	asia	PROPN
iajs-1805	56	9	public	public	ADJ
iajs-1805	56	10	-	-	PUNCT
iajs-1805	56	11	key	key	NOUN
iajs-1805	56	12	cryptography	cryptography	NOUN
iajs-1805	56	13	.	.	PUNCT
iajs-1805	56	14	acm	acm	PROPN
iajs-1805	56	15	,	,	PUNCT
iajs-1805	56	16	2013	2013	NUM
iajs-1805	56	17	.	.	PUNCT
iajs-1805	57	1	[	[	X
iajs-1805	57	2	4	4	NUM
iajs-1805	57	3	]	]	X
iajs-1805	57	4	q.	q.	PROPN
iajs-1805	57	5	baodong	baodong	PROPN
iajs-1805	57	6	,	,	PUNCT
iajs-1805	57	7	and	and	CCONJ
iajs-1805	57	8	s.	s.	PROPN
iajs-1805	57	9	liu	liu	PROPN
iajs-1805	57	10	,	,	PUNCT
iajs-1805	57	11	"	"	PUNCT
iajs-1805	57	12	leakage	leakage	NOUN
iajs-1805	57	13	-	-	PUNCT
iajs-1805	57	14	flexible	flexible	ADJ
iajs-1805	57	15	cca	cca	VERB
iajs-1805	57	16	-	-	PUNCT
iajs-1805	57	17	secure	secure	ADJ
iajs-1805	57	18	public	public	ADJ
iajs-1805	57	19	-	-	PUNCT
iajs-1805	57	20	key	key	NOUN
iajs-1805	57	21	encryption	encryption	NOUN
iajs-1805	57	22	:	:	PUNCT
iajs-1805	57	23	simple	simple	ADJ
iajs-1805	57	24	construction	construction	NOUN
iajs-1805	57	25	and	and	CCONJ
iajs-1805	57	26	free	free	ADJ
iajs-1805	57	27	of	of	ADP
iajs-1805	57	28	pairing	pair	VERB
iajs-1805	57	29	.	.	PUNCT
iajs-1805	57	30	"	"	PUNCT
iajs-1805	58	1	international	international	ADJ
iajs-1805	58	2	workshop	workshop	NOUN
iajs-1805	58	3	on	on	ADP
iajs-1805	58	4	public	public	ADJ
iajs-1805	58	5	key	key	ADJ
iajs-1805	58	6	cryptography	cryptography	NOUN
iajs-1805	58	7	.	.	PUNCT
iajs-1805	59	1	springer	springer	PROPN
iajs-1805	59	2	berlin	berlin	PROPN
iajs-1805	59	3	heidelberg	heidelberg	PROPN
iajs-1805	59	4	,	,	PUNCT
iajs-1805	59	5	2014	2014	NUM
iajs-1805	59	6	.	.	PUNCT
iajs-1805	60	1	[	[	X
iajs-1805	60	2	5	5	X
iajs-1805	60	3	]	]	PUNCT
iajs-1805	60	4	j.	j.	PROPN
iajs-1805	60	5	coron	coron	PROPN
iajs-1805	60	6	,	,	PUNCT
iajs-1805	60	7	"	"	PUNCT
iajs-1805	60	8	fully	fully	ADV
iajs-1805	60	9	homomorphic	homomorphic	ADJ
iajs-1805	60	10	encryption	encryption	NOUN
iajs-1805	60	11	over	over	ADP
iajs-1805	60	12	the	the	DET
iajs-1805	60	13	integers	integer	NOUN
iajs-1805	60	14	with	with	ADP
iajs-1805	60	15	shorter	short	ADJ
iajs-1805	60	16	public	public	ADJ
iajs-1805	60	17	keys	key	NOUN
iajs-1805	60	18	.	.	PUNCT
iajs-1805	60	19	"	"	PUNCT
iajs-1805	60	20	annual	annual	ADJ
iajs-1805	60	21	cryptology	cryptology	NOUN
iajs-1805	60	22	conference	conference	NOUN
iajs-1805	60	23	.	.	PUNCT
iajs-1805	61	1	springer	springer	PROPN
iajs-1805	61	2	berlin	berlin	PROPN
iajs-1805	61	3	heidelberg	heidelberg	PROPN
iajs-1805	61	4	,	,	PUNCT
iajs-1805	61	5	2011	2011	NUM
iajs-1805	61	6	.	.	PUNCT
iajs-1805	62	1	[	[	X
iajs-1805	62	2	6	6	NUM
iajs-1805	62	3	]	]	X
iajs-1805	62	4	s.d	s.d	PROPN
iajs-1805	62	5	.	.	PROPN
iajs-1805	62	6	galbraith	galbraith	PROPN
iajs-1805	62	7	.	.	PUNCT
iajs-1805	63	1	mathematics	mathematic	NOUN
iajs-1805	63	2	of	of	ADP
iajs-1805	63	3	public	public	ADJ
iajs-1805	63	4	key	key	ADJ
iajs-1805	63	5	cryptography	cryptography	NOUN
iajs-1805	63	6	.	.	PUNCT
iajs-1805	64	1	cambridge	cambridge	PROPN
iajs-1805	64	2	university	university	PROPN
iajs-1805	64	3	press	press	NOUN
iajs-1805	64	4	,	,	PUNCT
iajs-1805	64	5	2012	2012	NUM
iajs-1805	64	6	.	.	PUNCT
iajs-1805	65	1	[	[	X
iajs-1805	65	2	7	7	X
iajs-1805	65	3	]	]	PUNCT
iajs-1805	65	4	b.	b.	PROPN
iajs-1805	65	5	persis	persis	PROPN
iajs-1805	65	6	urbana	urbana	PROPN
iajs-1805	65	7	,	,	PUNCT
iajs-1805	65	8	purshotam	purshotam	PROPN
iajs-1805	65	9	mandiwa	mandiwa	PROPN
iajs-1805	65	10	,	,	PUNCT
iajs-1805	65	11	and	and	CCONJ
iajs-1805	65	12	m.	m.	PROPN
iajs-1805	65	13	kumar	kumar	PROPN
iajs-1805	65	14	,	,	PUNCT
iajs-1805	65	15	"	"	PUNCT
iajs-1805	65	16	a	a	DET
iajs-1805	65	17	modified	modified	ADJ
iajs-1805	65	18	rsa	rsa	NOUN
iajs-1805	65	19	cryptosystem	cryptosystem	NOUN
iajs-1805	65	20	based	base	VERB
iajs-1805	65	21	on	on	ADP
iajs-1805	65	22	‘	'	PUNCT
iajs-1805	65	23	n’prime	n’prime	ADJ
iajs-1805	65	24	numbers	number	NOUN
iajs-1805	65	25	.	.	PUNCT
iajs-1805	65	26	"	"	PUNCT
iajs-1805	66	1	international	international	ADJ
iajs-1805	66	2	journal	journal	NOUN
iajs-1805	66	3	of	of	ADP
iajs-1805	66	4	engineering	engineering	NOUN
iajs-1805	66	5	and	and	CCONJ
iajs-1805	66	6	computer	computer	NOUN
iajs-1805	66	7	science	science	NOUN
iajs-1805	66	8	1	1	NUM
iajs-1805	66	9	(	(	PUNCT
iajs-1805	66	10	2012	2012	NUM
iajs-1805	66	11	):	):	PUNCT
iajs-1805	66	12	63	63	NUM
iajs-1805	66	13	-	-	SYM
iajs-1805	66	14	66	66	NUM
iajs-1805	66	15	.	.	PUNCT
iajs-1805	67	1	[	[	X
iajs-1805	67	2	8	8	NUM
iajs-1805	67	3	]	]	PUNCT
iajs-1805	67	4	a.	a.	NOUN
iajs-1805	67	5	salomaa	salomaa	PROPN
iajs-1805	67	6	,	,	PUNCT
iajs-1805	67	7	public	public	ADJ
iajs-1805	67	8	-	-	PUNCT
iajs-1805	67	9	key	key	NOUN
iajs-1805	67	10	cryptography	cryptography	NOUN
iajs-1805	67	11	.	.	PUNCT
iajs-1805	68	1	springer	springer	NOUN
iajs-1805	68	2	science	science	PROPN
iajs-1805	68	3	&	&	CCONJ
iajs-1805	68	4	business	business	NOUN
iajs-1805	68	5	media	medium	NOUN
iajs-1805	68	6	,	,	PUNCT
iajs-1805	68	7	2013	2013	NUM
iajs-1805	68	8	.	.	PUNCT
iajs-1805	69	1	[	[	X
iajs-1805	69	2	9	9	NUM
iajs-1805	69	3	]	]	X
iajs-1805	69	4	l.n.m.tawfiq	l.n.m.tawfiq	PROPN
iajs-1805	69	5	and	and	CCONJ
iajs-1805	69	6	r.s.naoum	r.s.naoum	NOUN
iajs-1805	69	7	,	,	PUNCT
iajs-1805	69	8	(	(	PUNCT
iajs-1805	69	9	2007	2007	NUM
iajs-1805	69	10	)	)	PUNCT
iajs-1805	69	11	.	.	PUNCT
iajs-1805	70	1	density	density	NOUN
iajs-1805	70	2	and	and	CCONJ
iajs-1805	70	3	approximation	approximation	NOUN
iajs-1805	70	4	by	by	ADP
iajs-1805	70	5	using	use	VERB
iajs-1805	70	6	feed	feed	NOUN
iajs-1805	70	7	forward	forward	ADV
iajs-1805	70	8	artificial	artificial	ADJ
iajs-1805	70	9	neural	neural	ADJ
iajs-1805	70	10	networks	network	NOUN
iajs-1805	70	11	,	,	PUNCT
iajs-1805	70	12	ibn	ibn	PROPN
iajs-1805	70	13	al	al	PROPN
iajs-1805	70	14	-	-	PUNCT
iajs-1805	70	15	haitham	haitham	PROPN
iajs-1805	70	16	journal	journal	PROPN
iajs-1805	70	17	for	for	ADP
iajs-1805	70	18	pure	pure	ADJ
iajs-1805	70	19	&	&	CCONJ
iajs-1805	70	20	applied	applied	ADJ
iajs-1805	70	21	sciences	science	NOUN
iajs-1805	70	22	,	,	PUNCT
iajs-1805	70	23	20(1	20(1	NUM
iajs-1805	70	24	):	):	PUNCT
iajs-1805	70	25	67	67	NUM
iajs-1805	70	26	-	-	SYM
iajs-1805	70	27	81	81	NUM
iajs-1805	70	28	.	.	PUNCT
iajs-1805	70	29	  	  	SPACE