id	sid	tid	token	lemma	pos
cana-4018	1	1	communications	communication	NOUN
cana-4018	1	2	on	on	ADP
cana-4018	1	3	applied	apply	VERB
cana-4018	1	4	nonlinear	nonlinear	ADJ
cana-4018	1	5	analysis	analysis	NOUN
cana-4018	1	6	issn	issn	NOUN
cana-4018	1	7	:	:	PUNCT
cana-4018	1	8	1074	1074	NUM
cana-4018	1	9	-	-	PUNCT
cana-4018	1	10	133x	133x	NUM
cana-4018	1	11	vol	vol	NOUN
cana-4018	1	12	32	32	NUM
cana-4018	1	13	no	no	NOUN
cana-4018	1	14	.	.	PUNCT
cana-4018	2	1	9s	9s	NUM
cana-4018	2	2	(	(	PUNCT
cana-4018	2	3	2025	2025	NUM
cana-4018	2	4	)	)	PUNCT
cana-4018	2	5	841	841	NUM
cana-4018	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	2	7	implementation	implementation	NOUN
cana-4018	2	8	of	of	ADP
cana-4018	2	9	r	r	NOUN
cana-4018	2	10	in	in	ADP
cana-4018	2	11	cryptographic	cryptographic	ADJ
cana-4018	2	12	algorithms	algorithm	NOUN
cana-4018	2	13	:	:	PUNCT
cana-4018	2	14	integrating	integrate	VERB
cana-4018	2	15	symmetric	symmetric	ADJ
cana-4018	2	16	matrices	matrix	NOUN
cana-4018	2	17	and	and	CCONJ
cana-4018	2	18	positive	positive	ADJ
cana-4018	2	19	integer	integer	NOUN
cana-4018	2	20	-	-	PUNCT
cana-4018	2	21	valued	value	VERB
cana-4018	2	22	functions	function	NOUN
cana-4018	2	23	1k	1k	NOUN
cana-4018	2	24	.	.	PUNCT
cana-4018	3	1	kaleeswari	kaleeswari	NOUN
cana-4018	3	2	,	,	PUNCT
cana-4018	3	3	*	*	NOUN
cana-4018	3	4	2j	2j	NOUN
cana-4018	3	5	.	.	PUNCT
cana-4018	4	1	kannan	kannan	PROPN
cana-4018	4	2	,	,	PUNCT
cana-4018	4	3	3	3	NUM
cana-4018	4	4	m.	m.	NOUN
cana-4018	4	5	mahalakshmi	mahalakshmi	PROPN
cana-4018	4	6	,	,	PUNCT
cana-4018	4	7	4a	4a	NUM
cana-4018	4	8	.	.	PUNCT
cana-4018	4	9	deepshika	deepshika	PROPN
cana-4018	4	10	,	,	PUNCT
cana-4018	4	11	5manju	5manju	NUM
cana-4018	4	12	somanath	somanath	NOUN
cana-4018	4	13	and	and	CCONJ
cana-4018	4	14	6v	6v	NOUN
cana-4018	4	15	.	.	PUNCT
cana-4018	5	1	sangeetha	sangeetha	PROPN
cana-4018	5	2	1part	1part	NUM
cana-4018	5	3	time	time	NOUN
cana-4018	5	4	ph.d	ph.d	PROPN
cana-4018	5	5	.	.	PUNCT
cana-4018	5	6	research	research	NOUN
cana-4018	5	7	scholar	scholar	NOUN
cana-4018	5	8	,	,	PUNCT
cana-4018	5	9	department	department	NOUN
cana-4018	5	10	of	of	ADP
cana-4018	5	11	mathematics	mathematics	PROPN
cana-4018	5	12	,	,	PUNCT
cana-4018	5	13	ayya	ayya	PROPN
cana-4018	5	14	nadar	nadar	PROPN
cana-4018	5	15	janaki	janaki	PROPN
cana-4018	5	16	ammal	ammal	PROPN
cana-4018	5	17	college	college	PROPN
cana-4018	5	18	(	(	PUNCT
cana-4018	5	19	autonomous	autonomous	ADJ
cana-4018	5	20	,	,	PUNCT
cana-4018	5	21	affiliated	affiliate	VERB
cana-4018	5	22	to	to	PART
cana-4018	5	23	madurai	madurai	VERB
cana-4018	5	24	kamaraj	kamaraj	ADJ
cana-4018	5	25	university	university	NOUN
cana-4018	5	26	)	)	PUNCT
cana-4018	5	27	,	,	PUNCT
cana-4018	5	28	sivakasi	sivakasi	NOUN
cana-4018	5	29	–	–	PUNCT
cana-4018	5	30	626124	626124	NUM
cana-4018	5	31	,	,	PUNCT
cana-4018	5	32	tamil	tamil	PROPN
cana-4018	5	33	nadu	nadu	PROPN
cana-4018	5	34	,	,	PUNCT
cana-4018	5	35	india	india	PROPN
cana-4018	5	36	.	.	PUNCT
cana-4018	6	1	2assistant	2assistant	NUM
cana-4018	6	2	professor	professor	NOUN
cana-4018	6	3	,	,	PUNCT
cana-4018	6	4	department	department	NOUN
cana-4018	6	5	of	of	ADP
cana-4018	6	6	mathematics	mathematics	PROPN
cana-4018	6	7	,	,	PUNCT
cana-4018	6	8	ayya	ayya	PROPN
cana-4018	6	9	nadar	nadar	PROPN
cana-4018	6	10	janaki	janaki	PROPN
cana-4018	6	11	ammal	ammal	PROPN
cana-4018	6	12	college	college	PROPN
cana-4018	6	13	(	(	PUNCT
cana-4018	6	14	autonomous	autonomous	ADJ
cana-4018	6	15	,	,	PUNCT
cana-4018	6	16	affiliated	affiliate	VERB
cana-4018	6	17	to	to	PART
cana-4018	6	18	madurai	madurai	VERB
cana-4018	6	19	kamaraj	kamaraj	ADJ
cana-4018	6	20	university	university	NOUN
cana-4018	6	21	)	)	PUNCT
cana-4018	6	22	,	,	PUNCT
cana-4018	6	23	sivakasi	sivakasi	NOUN
cana-4018	6	24	–	–	PUNCT
cana-4018	6	25	626124	626124	NUM
cana-4018	6	26	,	,	PUNCT
cana-4018	6	27	tamil	tamil	PROPN
cana-4018	6	28	nadu	nadu	PROPN
cana-4018	6	29	,	,	PUNCT
cana-4018	6	30	india	india	PROPN
cana-4018	6	31	.	.	PROPN
cana-4018	7	1	3	3	NUM
cana-4018	7	2	,	,	PUNCT
cana-4018	7	3	4full	4full	NUM
cana-4018	7	4	time	time	NOUN
cana-4018	7	5	ph.d	ph.d	PROPN
cana-4018	7	6	.	.	PUNCT
cana-4018	7	7	research	research	NOUN
cana-4018	7	8	scholar	scholar	NOUN
cana-4018	7	9	,	,	PUNCT
cana-4018	7	10	department	department	NOUN
cana-4018	7	11	of	of	ADP
cana-4018	7	12	mathematics	mathematics	PROPN
cana-4018	7	13	,	,	PUNCT
cana-4018	7	14	ayya	ayya	PROPN
cana-4018	7	15	nadar	nadar	PROPN
cana-4018	7	16	janaki	janaki	PROPN
cana-4018	7	17	ammal	ammal	PROPN
cana-4018	7	18	college	college	PROPN
cana-4018	7	19	(	(	PUNCT
cana-4018	7	20	autonomous	autonomous	ADJ
cana-4018	7	21	,	,	PUNCT
cana-4018	7	22	affiliated	affiliate	VERB
cana-4018	7	23	to	to	PART
cana-4018	7	24	madurai	madurai	VERB
cana-4018	7	25	kamaraj	kamaraj	ADJ
cana-4018	7	26	university	university	NOUN
cana-4018	7	27	)	)	PUNCT
cana-4018	7	28	,	,	PUNCT
cana-4018	7	29	sivakasi	sivakasi	NOUN
cana-4018	7	30	–	–	PUNCT
cana-4018	7	31	626124	626124	NUM
cana-4018	7	32	,	,	PUNCT
cana-4018	7	33	tamil	tamil	PROPN
cana-4018	7	34	nadu	nadu	PROPN
cana-4018	7	35	,	,	PUNCT
cana-4018	7	36	india	india	PROPN
cana-4018	7	37	.	.	PUNCT
cana-4018	8	1	5associate	5associate	NUM
cana-4018	8	2	professor	professor	NOUN
cana-4018	8	3	,	,	PUNCT
cana-4018	8	4	pg	pg	NOUN
cana-4018	8	5	and	and	CCONJ
cana-4018	8	6	research	research	PROPN
cana-4018	8	7	department	department	PROPN
cana-4018	8	8	of	of	ADP
cana-4018	8	9	mathematics	mathematics	PROPN
cana-4018	8	10	,	,	PUNCT
cana-4018	8	11	national	national	PROPN
cana-4018	8	12	college	college	PROPN
cana-4018	8	13	(	(	PUNCT
cana-4018	8	14	autonomous	autonomous	ADJ
cana-4018	8	15	,	,	PUNCT
cana-4018	8	16	affiliated	affiliate	VERB
cana-4018	8	17	to	to	PART
cana-4018	8	18	bharathidasan	bharathidasan	VERB
cana-4018	8	19	university	university	NOUN
cana-4018	8	20	)	)	PUNCT
cana-4018	8	21	,	,	PUNCT
cana-4018	8	22	trichy	trichy	NOUN
cana-4018	8	23	–	–	PUNCT
cana-4018	8	24	620	620	NUM
cana-4018	8	25	001	001	NUM
cana-4018	8	26	,	,	PUNCT
cana-4018	8	27	tamil	tamil	PROPN
cana-4018	8	28	nadu	nadu	PROPN
cana-4018	8	29	,	,	PUNCT
cana-4018	8	30	india	india	PROPN
cana-4018	8	31	.	.	PUNCT
cana-4018	9	1	6assistant	6assistant	NUM
cana-4018	9	2	professor	professor	NOUN
cana-4018	9	3	,	,	PUNCT
cana-4018	9	4	pg	pg	NOUN
cana-4018	9	5	and	and	CCONJ
cana-4018	9	6	research	research	PROPN
cana-4018	9	7	department	department	PROPN
cana-4018	9	8	of	of	ADP
cana-4018	9	9	mathematics	mathematics	PROPN
cana-4018	9	10	,	,	PUNCT
cana-4018	9	11	national	national	PROPN
cana-4018	9	12	college	college	PROPN
cana-4018	9	13	(	(	PUNCT
cana-4018	9	14	autonomous	autonomous	ADJ
cana-4018	9	15	,	,	PUNCT
cana-4018	9	16	affiliated	affiliate	VERB
cana-4018	9	17	to	to	PART
cana-4018	9	18	bharathidasan	bharathidasan	VERB
cana-4018	9	19	university	university	NOUN
cana-4018	9	20	)	)	PUNCT
cana-4018	9	21	,	,	PUNCT
cana-4018	9	22	trichy	trichy	NOUN
cana-4018	9	23	–	–	PUNCT
cana-4018	9	24	620	620	NUM
cana-4018	9	25	001	001	NUM
cana-4018	9	26	,	,	PUNCT
cana-4018	9	27	tamil	tamil	PROPN
cana-4018	9	28	nadu	nadu	PROPN
cana-4018	9	29	,	,	PUNCT
cana-4018	9	30	india	india	PROPN
cana-4018	9	31	.	.	PUNCT
cana-4018	10	1	*	*	PUNCT
cana-4018	10	2	corresponding	correspond	VERB
cana-4018	10	3	author	author	NOUN
cana-4018	10	4	’s	’s	PART
cana-4018	10	5	e	e	NOUN
cana-4018	10	6	-	-	NOUN
cana-4018	10	7	mail	mail	NOUN
cana-4018	10	8	i	i	NOUN
cana-4018	10	9	d.	d.	PROPN
cana-4018	10	10	:	:	PUNCT
cana-4018	10	11	jayram.kannan@gmail.com	jayram.kannan@gmail.com	PROPN
cana-4018	10	12	article	article	PROPN
cana-4018	10	13	history	history	NOUN
cana-4018	10	14	:	:	PUNCT
cana-4018	10	15	received	receive	VERB
cana-4018	10	16	:	:	PUNCT
cana-4018	10	17	20	20	NUM
cana-4018	10	18	-	-	SYM
cana-4018	10	19	11	11	NUM
cana-4018	10	20	-	-	PUNCT
cana-4018	10	21	2024	2024	NUM
cana-4018	10	22	revised	revise	VERB
cana-4018	10	23	:	:	PUNCT
cana-4018	10	24	22	22	NUM
cana-4018	10	25	-	-	SYM
cana-4018	10	26	12	12	NUM
cana-4018	10	27	-	-	PUNCT
cana-4018	10	28	2024	2024	NUM
cana-4018	10	29	accepted	accept	VERB
cana-4018	10	30	:	:	PUNCT
cana-4018	10	31	15	15	NUM
cana-4018	10	32	-	-	SYM
cana-4018	10	33	01	01	NUM
cana-4018	10	34	-	-	PUNCT
cana-4018	10	35	2025	2025	NUM
cana-4018	10	36	abstract	abstract	NOUN
cana-4018	10	37	:	:	PUNCT
cana-4018	10	38	in	in	ADP
cana-4018	10	39	this	this	DET
cana-4018	10	40	paper	paper	NOUN
cana-4018	10	41	,	,	PUNCT
cana-4018	10	42	algorithms	algorithm	NOUN
cana-4018	10	43	for	for	ADP
cana-4018	10	44	encryption	encryption	NOUN
cana-4018	10	45	and	and	CCONJ
cana-4018	10	46	decryption	decryption	NOUN
cana-4018	10	47	are	be	AUX
cana-4018	10	48	displayed	display	VERB
cana-4018	10	49	by	by	ADP
cana-4018	10	50	means	mean	NOUN
cana-4018	10	51	of	of	ADP
cana-4018	10	52	functions	function	NOUN
cana-4018	10	53	𝑓	𝑓	PRON
cana-4018	10	54	,	,	PUNCT
cana-4018	10	55	𝑔	𝑔	ADJ
cana-4018	10	56	:	:	PUNCT
cana-4018	10	57	ℕ	ℕ	PROPN
cana-4018	10	58	→	→	SYM
cana-4018	10	59	ℕ	ℕ	PROPN
cana-4018	10	60	and	and	CCONJ
cana-4018	10	61	a	a	DET
cana-4018	10	62	unique	unique	ADJ
cana-4018	10	63	assignment	assignment	NOUN
cana-4018	10	64	for	for	ADP
cana-4018	10	65	alphabets	alphabet	NOUN
cana-4018	10	66	.	.	PUNCT
cana-4018	11	1	in	in	ADP
cana-4018	11	2	the	the	DET
cana-4018	11	3	process	process	NOUN
cana-4018	11	4	of	of	ADP
cana-4018	11	5	encryption	encryption	NOUN
cana-4018	11	6	,	,	PUNCT
cana-4018	11	7	a	a	DET
cana-4018	11	8	cyclic	cyclic	ADJ
cana-4018	11	9	symmetric	symmetric	ADJ
cana-4018	11	10	matrix	matrix	NOUN
cana-4018	11	11	is	be	AUX
cana-4018	11	12	also	also	ADV
cana-4018	11	13	employed	employ	VERB
cana-4018	11	14	.	.	PUNCT
cana-4018	12	1	the	the	DET
cana-4018	12	2	algorithms	algorithm	NOUN
cana-4018	12	3	are	be	AUX
cana-4018	12	4	followed	follow	VERB
cana-4018	12	5	by	by	ADP
cana-4018	12	6	a	a	DET
cana-4018	12	7	few	few	ADJ
cana-4018	12	8	exemplifications	exemplification	NOUN
cana-4018	12	9	for	for	ADP
cana-4018	12	10	both	both	DET
cana-4018	12	11	processes	process	NOUN
cana-4018	12	12	.	.	PUNCT
cana-4018	13	1	in	in	ADP
cana-4018	13	2	the	the	DET
cana-4018	13	3	end	end	NOUN
cana-4018	13	4	,	,	PUNCT
cana-4018	13	5	separate	separate	ADJ
cana-4018	13	6	r	r	NOUN
cana-4018	13	7	programs	program	NOUN
cana-4018	13	8	for	for	ADP
cana-4018	13	9	encryption	encryption	NOUN
cana-4018	13	10	and	and	CCONJ
cana-4018	13	11	decryption	decryption	NOUN
cana-4018	13	12	are	be	AUX
cana-4018	13	13	provided	provide	VERB
cana-4018	13	14	with	with	ADP
cana-4018	13	15	samples	sample	NOUN
cana-4018	13	16	.	.	PUNCT
cana-4018	14	1	keywords	keyword	NOUN
cana-4018	14	2	:	:	PUNCT
cana-4018	14	3	encryption	encryption	NOUN
cana-4018	14	4	,	,	PUNCT
cana-4018	14	5	decryption	decryption	NOUN
cana-4018	14	6	,	,	PUNCT
cana-4018	14	7	cyclic	cyclic	ADJ
cana-4018	14	8	symmetric	symmetric	ADJ
cana-4018	14	9	matrix	matrix	NOUN
cana-4018	14	10	,	,	PUNCT
cana-4018	14	11	positive	positive	ADJ
cana-4018	14	12	integer	integer	NOUN
cana-4018	14	13	-	-	PUNCT
cana-4018	14	14	valued	value	VERB
cana-4018	14	15	function	function	NOUN
cana-4018	14	16	.	.	PUNCT
cana-4018	15	1	2010	2010	NUM
cana-4018	15	2	msc	msc	PROPN
cana-4018	15	3	subject	subject	PROPN
cana-4018	15	4	classification	classification	NOUN
cana-4018	15	5	:	:	PUNCT
cana-4018	15	6	11a25,11t71	11a25,11t71	NUM
cana-4018	15	7	,	,	PUNCT
cana-4018	15	8	94a60	94a60	NUM
cana-4018	15	9	.	.	NOUN
cana-4018	16	1	1	1	X
cana-4018	16	2	.	.	X
cana-4018	16	3	introduction	introduction	NOUN
cana-4018	16	4	the	the	DET
cana-4018	16	5	concept	concept	NOUN
cana-4018	16	6	of	of	ADP
cana-4018	16	7	encryption	encryption	NOUN
cana-4018	16	8	is	be	AUX
cana-4018	16	9	the	the	DET
cana-4018	16	10	process	process	NOUN
cana-4018	16	11	of	of	ADP
cana-4018	16	12	transmitting	transmit	VERB
cana-4018	16	13	the	the	DET
cana-4018	16	14	original	original	ADJ
cana-4018	16	15	message	message	NOUN
cana-4018	16	16	in	in	ADP
cana-4018	16	17	a	a	DET
cana-4018	16	18	different	different	ADJ
cana-4018	16	19	form	form	NOUN
cana-4018	16	20	,	,	PUNCT
cana-4018	16	21	whereas	whereas	SCONJ
cana-4018	16	22	decryption	decryption	NOUN
cana-4018	16	23	is	be	AUX
cana-4018	16	24	the	the	DET
cana-4018	16	25	process	process	NOUN
cana-4018	16	26	of	of	ADP
cana-4018	16	27	converting	convert	VERB
cana-4018	16	28	the	the	DET
cana-4018	16	29	encrypted	encrypt	VERB
cana-4018	16	30	message	message	NOUN
cana-4018	16	31	to	to	ADP
cana-4018	16	32	its	its	PRON
cana-4018	16	33	original	original	ADJ
cana-4018	16	34	form	form	NOUN
cana-4018	16	35	.	.	PUNCT
cana-4018	17	1	there	there	PRON
cana-4018	17	2	are	be	VERB
cana-4018	17	3	a	a	DET
cana-4018	17	4	lot	lot	NOUN
cana-4018	17	5	of	of	ADP
cana-4018	17	6	algorithms	algorithm	NOUN
cana-4018	17	7	for	for	ADP
cana-4018	17	8	doing	do	VERB
cana-4018	17	9	these	these	DET
cana-4018	17	10	processes	process	NOUN
cana-4018	17	11	effectively	effectively	ADV
cana-4018	17	12	.	.	PUNCT
cana-4018	18	1	this	this	DET
cana-4018	18	2	paper	paper	NOUN
cana-4018	18	3	possesses	possess	VERB
cana-4018	18	4	such	such	ADJ
cana-4018	18	5	encryption	encryption	NOUN
cana-4018	18	6	and	and	CCONJ
cana-4018	18	7	decryption	decryption	NOUN
cana-4018	18	8	algorithms	algorithm	NOUN
cana-4018	18	9	.	.	PUNCT
cana-4018	19	1	in	in	ADP
cana-4018	19	2	recent	recent	ADJ
cana-4018	19	3	days	day	NOUN
cana-4018	19	4	,	,	PUNCT
cana-4018	19	5	researchers	researcher	NOUN
cana-4018	19	6	have	have	AUX
cana-4018	19	7	employed	employ	VERB
cana-4018	19	8	various	various	ADJ
cana-4018	19	9	unique	unique	ADJ
cana-4018	19	10	terms	term	NOUN
cana-4018	19	11	in	in	ADP
cana-4018	19	12	their	their	PRON
cana-4018	19	13	own	own	ADJ
cana-4018	19	14	encryption	encryption	NOUN
cana-4018	19	15	and	and	CCONJ
cana-4018	19	16	decryption	decryption	NOUN
cana-4018	19	17	algorithms	algorithm	NOUN
cana-4018	19	18	.	.	PUNCT
cana-4018	20	1	for	for	ADP
cana-4018	20	2	example	example	NOUN
cana-4018	20	3	,	,	PUNCT
cana-4018	20	4	(	(	PUNCT
cana-4018	20	5	dasdemir	dasdemir	NOUN
cana-4018	20	6	,	,	PUNCT
cana-4018	20	7	2011	2011	NUM
cana-4018	20	8	)	)	PUNCT
cana-4018	20	9	and	and	CCONJ
cana-4018	20	10	(	(	PUNCT
cana-4018	20	11	thiagarajan	thiagarajan	NOUN
cana-4018	20	12	,	,	PUNCT
cana-4018	20	13	2018	2018	NUM
cana-4018	20	14	)	)	PUNCT
cana-4018	20	15	used	use	VERB
cana-4018	20	16	matrices	matrix	NOUN
cana-4018	20	17	in	in	ADP
cana-4018	20	18	algorithms	algorithm	NOUN
cana-4018	20	19	.	.	PUNCT
cana-4018	21	1	basic	basic	ADJ
cana-4018	21	2	number	number	NOUN
cana-4018	21	3	theoretical	theoretical	ADJ
cana-4018	21	4	concepts	concept	NOUN
cana-4018	21	5	,	,	PUNCT
cana-4018	21	6	fibonacci	fibonacci	NOUN
cana-4018	21	7	and	and	CCONJ
cana-4018	21	8	lucas	lucas	PROPN
cana-4018	21	9	numbers	number	NOUN
cana-4018	21	10	are	be	AUX
cana-4018	21	11	also	also	ADV
cana-4018	21	12	used	use	VERB
cana-4018	21	13	in	in	ADP
cana-4018	21	14	the	the	DET
cana-4018	21	15	algorithms	algorithm	NOUN
cana-4018	21	16	provided	provide	VERB
cana-4018	21	17	in	in	ADP
cana-4018	21	18	(	(	PUNCT
cana-4018	21	19	taş	taş	NOUN
cana-4018	21	20	,	,	PUNCT
cana-4018	21	21	2018	2018	NUM
cana-4018	21	22	)	)	PUNCT
cana-4018	21	23	and	and	CCONJ
cana-4018	21	24	(	(	PUNCT
cana-4018	21	25	uçar	uçar	ADJ
cana-4018	21	26	,	,	PUNCT
cana-4018	21	27	2019	2019	NUM
cana-4018	21	28	)	)	PUNCT
cana-4018	21	29	.	.	PUNCT
cana-4018	22	1	apart	apart	ADV
cana-4018	22	2	from	from	ADP
cana-4018	22	3	these	these	PRON
cana-4018	22	4	,	,	PUNCT
cana-4018	22	5	the	the	DET
cana-4018	22	6	diophantine	diophantine	NOUN
cana-4018	22	7	equation	equation	NOUN
cana-4018	22	8	,	,	PUNCT
cana-4018	22	9	an	an	DET
cana-4018	22	10	equation	equation	NOUN
cana-4018	22	11	over	over	ADP
cana-4018	22	12	ℤ	ℤ	PROPN
cana-4018	22	13	,	,	PUNCT
cana-4018	22	14	whose	whose	DET
cana-4018	22	15	solutions	solution	NOUN
cana-4018	22	16	are	be	AUX
cana-4018	22	17	to	to	PART
cana-4018	22	18	be	be	AUX
cana-4018	22	19	found	find	VERB
cana-4018	22	20	in	in	ADP
cana-4018	22	21	ℤ	ℤ	PROPN
cana-4018	22	22	,	,	PUNCT
cana-4018	22	23	is	be	AUX
cana-4018	22	24	also	also	ADV
cana-4018	22	25	considered	consider	VERB
cana-4018	22	26	for	for	ADP
cana-4018	22	27	the	the	DET
cana-4018	22	28	conversion	conversion	NOUN
cana-4018	22	29	of	of	ADP
cana-4018	22	30	messages	message	NOUN
cana-4018	22	31	into	into	ADP
cana-4018	22	32	an	an	DET
cana-4018	22	33	alternative	alternative	ADJ
cana-4018	22	34	form	form	NOUN
cana-4018	22	35	.	.	PUNCT
cana-4018	23	1	for	for	ADP
cana-4018	23	2	instance	instance	NOUN
cana-4018	23	3	,	,	PUNCT
cana-4018	23	4	communications	communication	NOUN
cana-4018	23	5	on	on	ADP
cana-4018	23	6	applied	apply	VERB
cana-4018	23	7	nonlinear	nonlinear	ADJ
cana-4018	23	8	analysis	analysis	NOUN
cana-4018	23	9	issn	issn	NOUN
cana-4018	23	10	:	:	PUNCT
cana-4018	23	11	1074	1074	NUM
cana-4018	23	12	-	-	PUNCT
cana-4018	23	13	133x	133x	NUM
cana-4018	23	14	vol	vol	NOUN
cana-4018	23	15	32	32	NUM
cana-4018	23	16	no	no	NOUN
cana-4018	23	17	.	.	PUNCT
cana-4018	24	1	9s	9s	NUM
cana-4018	24	2	(	(	PUNCT
cana-4018	24	3	2025	2025	NUM
cana-4018	24	4	)	)	PUNCT
cana-4018	24	5	842	842	NUM
cana-4018	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	24	7	(	(	PUNCT
cana-4018	24	8	dasdemir	dasdemir	NOUN
cana-4018	24	9	,	,	PUNCT
cana-4018	24	10	2011	2011	NUM
cana-4018	24	11	)	)	PUNCT
cana-4018	24	12	and	and	CCONJ
cana-4018	24	13	(	(	PUNCT
cana-4018	24	14	kannan	kannan	PROPN
cana-4018	24	15	,	,	PUNCT
cana-4018	24	16	2022	2022	NUM
cana-4018	24	17	)	)	PUNCT
cana-4018	24	18	employ	employ	VERB
cana-4018	24	19	the	the	DET
cana-4018	24	20	well	well	ADV
cana-4018	24	21	-	-	PUNCT
cana-4018	24	22	known	know	VERB
cana-4018	24	23	pell	pell	NOUN
cana-4018	24	24	equation	equation	NOUN
cana-4018	24	25	and	and	CCONJ
cana-4018	24	26	its	its	PRON
cana-4018	24	27	solutions	solution	NOUN
cana-4018	24	28	in	in	ADP
cana-4018	24	29	recursive	recursive	ADJ
cana-4018	24	30	matrix	matrix	NOUN
cana-4018	24	31	form	form	NOUN
cana-4018	24	32	.	.	PUNCT
cana-4018	25	1	this	this	DET
cana-4018	25	2	study	study	NOUN
cana-4018	25	3	was	be	AUX
cana-4018	25	4	also	also	ADV
cana-4018	25	5	developed	develop	VERB
cana-4018	25	6	with	with	ADP
cana-4018	25	7	the	the	DET
cana-4018	25	8	thought	thought	NOUN
cana-4018	25	9	of	of	ADP
cana-4018	25	10	encrypting	encrypt	VERB
cana-4018	25	11	and	and	CCONJ
cana-4018	25	12	decrypting	decrypt	VERB
cana-4018	25	13	messages	message	NOUN
cana-4018	25	14	by	by	ADP
cana-4018	25	15	using	use	VERB
cana-4018	25	16	number	number	NOUN
cana-4018	25	17	theoretic	theoretic	ADJ
cana-4018	25	18	components	component	NOUN
cana-4018	25	19	.	.	PUNCT
cana-4018	26	1	(	(	PUNCT
cana-4018	26	2	thiagarajan	thiagarajan	NOUN
cana-4018	26	3	,	,	PUNCT
cana-4018	26	4	2018	2018	NUM
cana-4018	26	5	)	)	PUNCT
cana-4018	26	6	and	and	CCONJ
cana-4018	26	7	(	(	PUNCT
cana-4018	26	8	zeriouh	zeriouh	PROPN
cana-4018	26	9	,	,	PUNCT
cana-4018	26	10	2019	2019	NUM
cana-4018	26	11	)	)	PUNCT
cana-4018	26	12	were	be	AUX
cana-4018	26	13	utilized	utilize	VERB
cana-4018	26	14	as	as	ADP
cana-4018	26	15	a	a	DET
cana-4018	26	16	precursor	precursor	NOUN
cana-4018	26	17	to	to	ADP
cana-4018	26	18	its	its	PRON
cana-4018	26	19	creation	creation	NOUN
cana-4018	26	20	.	.	PUNCT
cana-4018	27	1	the	the	DET
cana-4018	27	2	main	main	ADJ
cana-4018	27	3	theme	theme	NOUN
cana-4018	27	4	of	of	ADP
cana-4018	27	5	this	this	DET
cana-4018	27	6	paper	paper	NOUN
cana-4018	27	7	is	be	AUX
cana-4018	27	8	to	to	PART
cana-4018	27	9	use	use	VERB
cana-4018	27	10	positive	positive	ADJ
cana-4018	27	11	integer	integer	NOUN
cana-4018	27	12	-	-	PUNCT
cana-4018	27	13	valued	value	VERB
cana-4018	27	14	function	function	NOUN
cana-4018	27	15	and	and	CCONJ
cana-4018	27	16	a	a	DET
cana-4018	27	17	cyclic	cyclic	ADJ
cana-4018	27	18	symmetric	symmetric	ADJ
cana-4018	27	19	matrix	matrix	NOUN
cana-4018	27	20	corresponding	correspond	VERB
cana-4018	27	21	to	to	ADP
cana-4018	27	22	the	the	DET
cana-4018	27	23	message	message	NOUN
cana-4018	27	24	taken	take	VERB
cana-4018	27	25	.	.	PUNCT
cana-4018	28	1	let	let	VERB
cana-4018	28	2	𝑓:ℕ	𝑓:ℕ	PROPN
cana-4018	28	3	→	→	SYM
cana-4018	28	4	ℕ	ℕ	PROPN
cana-4018	28	5	be	be	AUX
cana-4018	28	6	a	a	DET
cana-4018	28	7	function	function	NOUN
cana-4018	28	8	defined	define	VERB
cana-4018	28	9	by	by	ADP
cana-4018	28	10	𝑓(𝑛	𝑓(𝑛	NOUN
cana-4018	28	11	)	)	PUNCT
cana-4018	28	12	=	=	SYM
cana-4018	28	13	{	{	PUNCT
cana-4018	28	14	𝐴	𝐴	PROPN
cana-4018	28	15	(	(	PUNCT
cana-4018	28	16	𝑛	𝑛	PROPN
cana-4018	28	17	+	+	NUM
cana-4018	28	18	1	1	NUM
cana-4018	28	19	2	2	NUM
cana-4018	28	20	)	)	PUNCT
cana-4018	28	21	,	,	PUNCT
cana-4018	28	22	𝑖𝑓	𝑖𝑓	ADP
cana-4018	28	23	𝑛	𝑛	PRON
cana-4018	29	1	𝑖𝑠	𝑖𝑠	NOUN
cana-4018	29	2	𝑜𝑑𝑑	𝑜𝑑𝑑	PROPN
cana-4018	29	3	𝐵	𝐵	NOUN
cana-4018	29	4	(	(	PUNCT
cana-4018	29	5	𝑛	𝑛	PROPN
cana-4018	29	6	2	2	NUM
cana-4018	29	7	)	)	PUNCT
cana-4018	29	8	,	,	PUNCT
cana-4018	29	9	𝑖𝑓	𝑖𝑓	ADP
cana-4018	29	10	𝑛	𝑛	PRON
cana-4018	30	1	𝑖𝑠	𝑖𝑠	INTJ
cana-4018	30	2	𝑒𝑣𝑒𝑛	𝑒𝑣𝑒𝑛	ADJ
cana-4018	30	3	where	where	SCONJ
cana-4018	30	4	𝐴(𝑛	𝐴(𝑛	VERB
cana-4018	30	5	)	)	PUNCT
cana-4018	30	6	is	be	AUX
cana-4018	30	7	the	the	DET
cana-4018	30	8	𝑛𝑡ℎ	𝑛𝑡ℎ	NUM
cana-4018	30	9	smallest	small	ADJ
cana-4018	30	10	element	element	NOUN
cana-4018	30	11	in	in	ADP
cana-4018	30	12	the	the	DET
cana-4018	30	13	set	set	NOUN
cana-4018	30	14	𝐴	𝐴	NOUN
cana-4018	30	15	=	=	PUNCT
cana-4018	30	16	{	{	PUNCT
cana-4018	30	17	3𝑘	3𝑘	NOUN
cana-4018	31	1	+	+	NOUN
cana-4018	31	2	1	1	NUM
cana-4018	31	3	:	:	PUNCT
cana-4018	31	4	𝑘	𝑘	X
cana-4018	31	5	=	=	SYM
cana-4018	31	6	0,1,2,⋯	0,1,2,⋯	NUM
cana-4018	31	7	}	}	PUNCT
cana-4018	31	8	and	and	CCONJ
cana-4018	31	9	𝐵(𝑛	𝐵(𝑛	VERB
cana-4018	31	10	)	)	PUNCT
cana-4018	31	11	is	be	AUX
cana-4018	31	12	the	the	DET
cana-4018	31	13	𝑛𝑡ℎ	𝑛𝑡ℎ	NUM
cana-4018	31	14	smallest	small	ADJ
cana-4018	31	15	element	element	NOUN
cana-4018	31	16	in	in	ADP
cana-4018	31	17	the	the	DET
cana-4018	31	18	set	set	ADJ
cana-4018	31	19	𝐵	𝐵	NOUN
cana-4018	32	1	=	=	PUNCT
cana-4018	32	2	ℕ\𝐴.	ℕ\𝐴.	NOUN
cana-4018	32	3	this	this	PRON
cana-4018	32	4	is	be	AUX
cana-4018	32	5	the	the	DET
cana-4018	32	6	positive	positive	ADJ
cana-4018	32	7	integer	integer	NOUN
cana-4018	32	8	-	-	PUNCT
cana-4018	32	9	valued	value	VERB
cana-4018	32	10	function	function	NOUN
cana-4018	32	11	used	use	VERB
cana-4018	32	12	for	for	ADP
cana-4018	32	13	the	the	DET
cana-4018	32	14	conversion	conversion	NOUN
cana-4018	32	15	of	of	ADP
cana-4018	32	16	messages	message	NOUN
cana-4018	32	17	in	in	ADP
cana-4018	32	18	this	this	DET
cana-4018	32	19	paper	paper	NOUN
cana-4018	32	20	.	.	PUNCT
cana-4018	33	1	also	also	ADV
cana-4018	33	2	,	,	PUNCT
cana-4018	33	3	the	the	DET
cana-4018	33	4	alphabets	alphabet	NOUN
cana-4018	33	5	are	be	AUX
cana-4018	33	6	assigned	assign	VERB
cana-4018	33	7	uniquely	uniquely	ADV
cana-4018	33	8	.	.	PUNCT
cana-4018	34	1	this	this	DET
cana-4018	34	2	article	article	NOUN
cana-4018	34	3	comprises	comprise	VERB
cana-4018	34	4	various	various	ADJ
cana-4018	34	5	components	component	NOUN
cana-4018	34	6	,	,	PUNCT
cana-4018	34	7	such	such	ADJ
cana-4018	34	8	as	as	ADP
cana-4018	34	9	sections	section	NOUN
cana-4018	34	10	and	and	CCONJ
cana-4018	34	11	subsections	subsection	NOUN
cana-4018	34	12	.	.	PUNCT
cana-4018	35	1	notations	notation	NOUN
cana-4018	35	2	and	and	CCONJ
cana-4018	35	3	positions	position	NOUN
cana-4018	35	4	are	be	AUX
cana-4018	35	5	the	the	DET
cana-4018	35	6	major	major	ADJ
cana-4018	35	7	requirements	requirement	NOUN
cana-4018	35	8	of	of	ADP
cana-4018	35	9	this	this	DET
cana-4018	35	10	paper	paper	NOUN
cana-4018	35	11	,	,	PUNCT
cana-4018	35	12	and	and	CCONJ
cana-4018	35	13	they	they	PRON
cana-4018	35	14	follow	follow	VERB
cana-4018	35	15	the	the	DET
cana-4018	35	16	section	section	NOUN
cana-4018	35	17	“	"	PUNCT
cana-4018	35	18	introduction	introduction	NOUN
cana-4018	35	19	”	"	PUNCT
cana-4018	35	20	.	.	PUNCT
cana-4018	36	1	the	the	DET
cana-4018	36	2	section	section	NOUN
cana-4018	36	3	“	"	PUNCT
cana-4018	36	4	procedures	procedure	NOUN
cana-4018	36	5	for	for	ADP
cana-4018	36	6	encryption	encryption	NOUN
cana-4018	36	7	and	and	CCONJ
cana-4018	36	8	decryption	decryption	NOUN
cana-4018	36	9	”	"	PUNCT
cana-4018	36	10	displays	display	VERB
cana-4018	36	11	the	the	DET
cana-4018	36	12	algorithms	algorithm	NOUN
cana-4018	36	13	of	of	ADP
cana-4018	36	14	encryption	encryption	NOUN
cana-4018	36	15	and	and	CCONJ
cana-4018	36	16	decryption	decryption	NOUN
cana-4018	36	17	,	,	PUNCT
cana-4018	36	18	along	along	ADP
cana-4018	36	19	with	with	ADP
cana-4018	36	20	examples	example	NOUN
cana-4018	36	21	in	in	ADP
cana-4018	36	22	the	the	DET
cana-4018	36	23	subsection	subsection	NOUN
cana-4018	36	24	“	"	PUNCT
cana-4018	36	25	few	few	ADJ
cana-4018	36	26	exemplifications	exemplification	NOUN
cana-4018	36	27	”	"	PUNCT
cana-4018	36	28	.	.	PUNCT
cana-4018	37	1	after	after	ADP
cana-4018	37	2	that	that	PRON
cana-4018	37	3	,	,	PUNCT
cana-4018	37	4	the	the	DET
cana-4018	37	5	section	section	NOUN
cana-4018	37	6	“	"	PUNCT
cana-4018	37	7	r	r	NOUN
cana-4018	37	8	code	code	NOUN
cana-4018	37	9	for	for	ADP
cana-4018	37	10	encryption	encryption	NOUN
cana-4018	37	11	and	and	CCONJ
cana-4018	37	12	decryption	decryption	NOUN
cana-4018	37	13	”	"	PUNCT
cana-4018	37	14	is	be	AUX
cana-4018	37	15	placed	place	VERB
cana-4018	37	16	.	.	PUNCT
cana-4018	38	1	this	this	DET
cana-4018	38	2	section	section	NOUN
cana-4018	38	3	provides	provide	VERB
cana-4018	38	4	r	r	NOUN
cana-4018	38	5	programs	program	NOUN
cana-4018	38	6	for	for	ADP
cana-4018	38	7	both	both	DET
cana-4018	38	8	processes	process	NOUN
cana-4018	38	9	with	with	ADP
cana-4018	38	10	an	an	DET
cana-4018	38	11	illustration	illustration	NOUN
cana-4018	38	12	.	.	PUNCT
cana-4018	39	1	finally	finally	ADV
cana-4018	39	2	,	,	PUNCT
cana-4018	39	3	there	there	PRON
cana-4018	39	4	is	be	VERB
cana-4018	39	5	a	a	DET
cana-4018	39	6	conclusion	conclusion	NOUN
cana-4018	39	7	to	to	ADP
cana-4018	39	8	this	this	DET
cana-4018	39	9	article	article	NOUN
cana-4018	39	10	.	.	PUNCT
cana-4018	40	1	1.1	1.1	NUM
cana-4018	40	2	.	.	PUNCT
cana-4018	40	3	notations	notation	NOUN
cana-4018	40	4	the	the	DET
cana-4018	40	5	following	follow	VERB
cana-4018	40	6	are	be	AUX
cana-4018	40	7	the	the	DET
cana-4018	40	8	basic	basic	ADJ
cana-4018	40	9	notations	notation	NOUN
cana-4018	40	10	used	use	VERB
cana-4018	40	11	in	in	ADP
cana-4018	40	12	this	this	DET
cana-4018	40	13	paper	paper	NOUN
cana-4018	40	14	:	:	PUNCT
cana-4018	40	15	•	•	NUM
cana-4018	40	16	𝑊𝑖	𝑊𝑖	PROPN
cana-4018	40	17	:	:	PUNCT
cana-4018	40	18	𝑖	𝑖	NUM
cana-4018	40	19	𝑡ℎ	𝑡ℎ	NOUN
cana-4018	40	20	word	word	NOUN
cana-4018	40	21	in	in	ADP
cana-4018	40	22	the	the	DET
cana-4018	40	23	message	message	NOUN
cana-4018	40	24	to	to	PART
cana-4018	40	25	be	be	AUX
cana-4018	40	26	sent	send	VERB
cana-4018	40	27	•	•	PRON
cana-4018	40	28	𝑛(𝑊𝑖	𝑛(𝑊𝑖	PROPN
cana-4018	40	29	):	):	PUNCT
cana-4018	40	30	number	number	NOUN
cana-4018	40	31	of	of	ADP
cana-4018	40	32	letters	letter	NOUN
cana-4018	40	33	in	in	ADP
cana-4018	40	34	the	the	DET
cana-4018	40	35	word	word	NOUN
cana-4018	40	36	𝑊𝑖	𝑊𝑖	PROPN
cana-4018	40	37	•	•	NOUN
cana-4018	40	38	ℕ	ℕ	PROPN
cana-4018	40	39	:	:	PUNCT
cana-4018	40	40	the	the	DET
cana-4018	40	41	set	set	NOUN
cana-4018	40	42	of	of	ADP
cana-4018	40	43	all	all	DET
cana-4018	40	44	natural	natural	ADJ
cana-4018	40	45	numbers	number	NOUN
cana-4018	40	46	•	•	PRON
cana-4018	40	47	𝐴	𝐴	PROPN
cana-4018	40	48	:	:	PUNCT
cana-4018	40	49	the	the	DET
cana-4018	40	50	set	set	NOUN
cana-4018	40	51	of	of	ADP
cana-4018	40	52	all	all	DET
cana-4018	40	53	natural	natural	ADJ
cana-4018	40	54	numbers	number	NOUN
cana-4018	40	55	of	of	ADP
cana-4018	40	56	the	the	DET
cana-4018	40	57	form	form	NOUN
cana-4018	40	58	3𝑘	3𝑘	NOUN
cana-4018	40	59	+	+	CCONJ
cana-4018	40	60	1	1	NUM
cana-4018	40	61	,	,	PUNCT
cana-4018	40	62	𝑘	𝑘	X
cana-4018	40	63	=	=	SYM
cana-4018	40	64	0,1,2,⋯	0,1,2,⋯	NUM
cana-4018	40	65	•	•	NUM
cana-4018	40	66	𝐵	𝐵	NOUN
cana-4018	40	67	:	:	PUNCT
cana-4018	40	68	the	the	DET
cana-4018	40	69	set	set	NOUN
cana-4018	40	70	of	of	ADP
cana-4018	40	71	all	all	DET
cana-4018	40	72	natural	natural	ADJ
cana-4018	40	73	numbers	number	NOUN
cana-4018	40	74	not	not	PART
cana-4018	40	75	in	in	ADP
cana-4018	40	76	the	the	DET
cana-4018	40	77	set	set	NOUN
cana-4018	40	78	𝐴	𝐴	PROPN
cana-4018	40	79	•	•	NOUN
cana-4018	40	80	𝐴(𝑛	𝐴(𝑛	NUM
cana-4018	40	81	):	):	PUNCT
cana-4018	40	82	𝑛𝑡ℎ	𝑛𝑡ℎ	PRON
cana-4018	40	83	smallest	small	ADJ
cana-4018	40	84	element	element	NOUN
cana-4018	40	85	in	in	ADP
cana-4018	40	86	the	the	DET
cana-4018	40	87	set	set	NOUN
cana-4018	40	88	𝐴	𝐴	PROPN
cana-4018	40	89	•	•	ADP
cana-4018	40	90	𝐵(𝑛	𝐵(𝑛	NUM
cana-4018	40	91	):	):	PUNCT
cana-4018	40	92	𝑛𝑡ℎ	𝑛𝑡ℎ	PRON
cana-4018	40	93	smallest	small	ADJ
cana-4018	40	94	element	element	NOUN
cana-4018	40	95	in	in	ADP
cana-4018	40	96	the	the	DET
cana-4018	40	97	set	set	ADJ
cana-4018	40	98	𝐵	𝐵	NOUN
cana-4018	40	99	•	•	NOUN
cana-4018	40	100	𝑓	𝑓	X
cana-4018	40	101	:	:	PUNCT
cana-4018	40	102	a	a	DET
cana-4018	40	103	positive	positive	ADJ
cana-4018	40	104	integer	integer	NOUN
cana-4018	40	105	-	-	PUNCT
cana-4018	40	106	valued	value	VERB
cana-4018	40	107	function	function	NOUN
cana-4018	40	108	defined	define	VERB
cana-4018	40	109	on	on	ADP
cana-4018	40	110	ℕ	ℕ	PROPN
cana-4018	40	111	by	by	ADP
cana-4018	40	112	𝑓(𝑛	𝑓(𝑛	NOUN
cana-4018	40	113	)	)	PUNCT
cana-4018	40	114	=	=	SYM
cana-4018	40	115	{	{	PUNCT
cana-4018	40	116	𝐴	𝐴	PROPN
cana-4018	40	117	(	(	PUNCT
cana-4018	40	118	𝑛	𝑛	PROPN
cana-4018	40	119	+	+	NUM
cana-4018	40	120	1	1	NUM
cana-4018	40	121	2	2	NUM
cana-4018	40	122	)	)	PUNCT
cana-4018	40	123	,	,	PUNCT
cana-4018	40	124	𝑖𝑓	𝑖𝑓	ADP
cana-4018	41	1	𝑛	𝑛	PRON
cana-4018	41	2	𝑖𝑠	𝑖𝑠	NOUN
cana-4018	41	3	𝑜𝑑𝑑	𝑜𝑑𝑑	PROPN
cana-4018	41	4	𝐵	𝐵	NOUN
cana-4018	41	5	(	(	PUNCT
cana-4018	41	6	𝑛	𝑛	PROPN
cana-4018	41	7	2	2	NUM
cana-4018	41	8	)	)	PUNCT
cana-4018	41	9	,	,	PUNCT
cana-4018	41	10	𝑖𝑓	𝑖𝑓	ADP
cana-4018	41	11	𝑛	𝑛	PRON
cana-4018	41	12	𝑖𝑠	𝑖𝑠	INTJ
cana-4018	41	13	𝑒𝑣𝑒𝑛	𝑒𝑣𝑒𝑛	ADJ
cana-4018	42	1	•	•	ADP
cana-4018	42	2	𝑔	𝑔	NOUN
cana-4018	42	3	:	:	PUNCT
cana-4018	42	4	a	a	DET
cana-4018	42	5	positive	positive	ADJ
cana-4018	42	6	integer	integer	NOUN
cana-4018	42	7	-	-	PUNCT
cana-4018	42	8	valued	value	VERB
cana-4018	42	9	function	function	NOUN
cana-4018	42	10	defined	define	VERB
cana-4018	42	11	on	on	ADP
cana-4018	42	12	ℕ	ℕ	PROPN
cana-4018	42	13	by	by	ADP
cana-4018	42	14	𝑔(𝑛	𝑔(𝑛	NOUN
cana-4018	42	15	)	)	PUNCT
cana-4018	42	16	=	=	PRON
cana-4018	42	17	{	{	PUNCT
cana-4018	42	18	𝑛	𝑛	PROPN
cana-4018	43	1	+	+	NUM
cana-4018	43	2	1	1	NUM
cana-4018	43	3	2	2	NUM
cana-4018	43	4	,	,	PUNCT
cana-4018	43	5	𝑖𝑓	𝑖𝑓	ADP
cana-4018	43	6	𝑛	𝑛	DET
cana-4018	43	7	𝑖𝑠	𝑖𝑠	NOUN
cana-4018	43	8	𝑜𝑑𝑑	𝑜𝑑𝑑	NOUN
cana-4018	43	9	𝑛	𝑛	DET
cana-4018	43	10	2	2	NUM
cana-4018	43	11	,	,	PUNCT
cana-4018	43	12	𝑖𝑓	𝑖𝑓	ADP
cana-4018	43	13	𝑛	𝑛	DET
cana-4018	43	14	𝑖𝑠	𝑖𝑠	INTJ
cana-4018	43	15	𝑒𝑣𝑒𝑛	𝑒𝑣𝑒𝑛	ADJ
cana-4018	43	16	•	•	ADP
cana-4018	43	17	𝑀𝑖	𝑀𝑖	NOUN
cana-4018	43	18	:	:	PUNCT
cana-4018	43	19	cyclic	cyclic	ADJ
cana-4018	43	20	symmetric	symmetric	ADJ
cana-4018	43	21	matrix	matrix	NOUN
cana-4018	43	22	for	for	ADP
cana-4018	43	23	𝑊𝑖	𝑊𝑖	PROPN
cana-4018	43	24	communications	communication	NOUN
cana-4018	43	25	on	on	ADP
cana-4018	43	26	applied	apply	VERB
cana-4018	43	27	nonlinear	nonlinear	ADJ
cana-4018	43	28	analysis	analysis	NOUN
cana-4018	43	29	issn	issn	NOUN
cana-4018	43	30	:	:	PUNCT
cana-4018	43	31	1074	1074	NUM
cana-4018	43	32	-	-	PUNCT
cana-4018	43	33	133x	133x	NUM
cana-4018	43	34	vol	vol	NOUN
cana-4018	43	35	32	32	NUM
cana-4018	43	36	no	no	NOUN
cana-4018	43	37	.	.	PUNCT
cana-4018	44	1	9s	9s	NUM
cana-4018	44	2	(	(	PUNCT
cana-4018	44	3	2025	2025	NUM
cana-4018	44	4	)	)	PUNCT
cana-4018	44	5	843	843	NUM
cana-4018	44	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	44	7	•	•	NUM
cana-4018	44	8	𝐼𝑖	𝐼𝑖	PROPN
cana-4018	44	9	:	:	PUNCT
cana-4018	44	10	identity	identity	NOUN
cana-4018	44	11	matrix	matrix	NOUN
cana-4018	44	12	of	of	ADP
cana-4018	44	13	order	order	NOUN
cana-4018	44	14	𝑖	𝑖	SYM
cana-4018	44	15	•	•	NUM
cana-4018	44	16	𝑅𝑖	𝑅𝑖	PROPN
cana-4018	44	17	:	:	PUNCT
cana-4018	44	18	𝑔(𝑛(𝑊𝑖	𝑔(𝑛(𝑊𝑖	NOUN
cana-4018	44	19	)	)	PUNCT
cana-4018	44	20	)	)	PUNCT
cana-4018	44	21	𝑡ℎ	𝑡ℎ	PROPN
cana-4018	44	22	row	row	NOUN
cana-4018	44	23	of	of	ADP
cana-4018	44	24	the	the	DET
cana-4018	44	25	cyclic	cyclic	ADJ
cana-4018	44	26	matrix	matrix	NOUN
cana-4018	44	27	𝑀𝑖	𝑀𝑖	PROPN
cana-4018	44	28	•	•	NUM
cana-4018	44	29	𝐷(𝑅𝑖	𝐷(𝑅𝑖	NOUN
cana-4018	44	30	):	):	PUNCT
cana-4018	44	31	diagonal	diagonal	ADJ
cana-4018	44	32	matrix	matrix	NOUN
cana-4018	44	33	with	with	ADP
cana-4018	44	34	entries	entry	NOUN
cana-4018	44	35	in	in	ADP
cana-4018	44	36	𝑅𝑖	𝑅𝑖	PROPN
cana-4018	44	37	1.2	1.2	NUM
cana-4018	44	38	.	.	PUNCT
cana-4018	45	1	positions	position	NOUN
cana-4018	45	2	the	the	DET
cana-4018	45	3	following	follow	VERB
cana-4018	45	4	is	be	AUX
cana-4018	45	5	the	the	DET
cana-4018	45	6	table	table	NOUN
cana-4018	45	7	for	for	ADP
cana-4018	45	8	position	position	NOUN
cana-4018	45	9	of	of	ADP
cana-4018	45	10	alphabets	alphabet	NOUN
cana-4018	45	11	:	:	PUNCT
cana-4018	46	1	a	a	DET
cana-4018	46	2	b	b	X
cana-4018	46	3	c	c	NOUN
cana-4018	46	4	d	d	X
cana-4018	46	5	e	e	X
cana-4018	46	6	f	f	PROPN
cana-4018	46	7	g	g	PROPN
cana-4018	46	8	h	h	NOUN
cana-4018	47	1	i	i	PRON
cana-4018	47	2	j	j	PROPN
cana-4018	48	1	k	k	PROPN
cana-4018	48	2	l	l	PROPN
cana-4018	48	3	m	m	VERB
cana-4018	48	4	7	7	NUM
cana-4018	48	5	13	13	NUM
cana-4018	48	6	21	21	NUM
cana-4018	48	7	31	31	NUM
cana-4018	48	8	43	43	NUM
cana-4018	48	9	57	57	NUM
cana-4018	48	10	73	73	NUM
cana-4018	48	11	91	91	NUM
cana-4018	48	12	111	111	NUM
cana-4018	48	13	133	133	NUM
cana-4018	48	14	157	157	NUM
cana-4018	48	15	183	183	NUM
cana-4018	48	16	211	211	NUM
cana-4018	49	1	n	n	PRON
cana-4018	49	2	o	o	NOUN
cana-4018	49	3	p	p	X
cana-4018	49	4	q	q	NOUN
cana-4018	49	5	r	r	NOUN
cana-4018	49	6	s	s	PROPN
cana-4018	49	7	t	t	NOUN
cana-4018	49	8	u	u	NOUN
cana-4018	49	9	v	v	PROPN
cana-4018	49	10	w	w	NOUN
cana-4018	49	11	x	x	X
cana-4018	49	12	y	y	PROPN
cana-4018	49	13	z	z	PROPN
cana-4018	49	14	241	241	NUM
cana-4018	50	1	273	273	NUM
cana-4018	50	2	307	307	NUM
cana-4018	50	3	343	343	NUM
cana-4018	50	4	381	381	NUM
cana-4018	50	5	421	421	NUM
cana-4018	50	6	463	463	NUM
cana-4018	50	7	507	507	NUM
cana-4018	50	8	553	553	NUM
cana-4018	50	9	601	601	NUM
cana-4018	50	10	651	651	NUM
cana-4018	50	11	703	703	NUM
cana-4018	50	12	757	757	NUM
cana-4018	50	13	table	table	NOUN
cana-4018	50	14	1	1	NUM
cana-4018	50	15	:	:	PUNCT
cana-4018	50	16	numerical	numerical	ADJ
cana-4018	50	17	assignments	assignment	NOUN
cana-4018	50	18	for	for	ADP
cana-4018	50	19	alphabets	alphabet	NOUN
cana-4018	50	20	2	2	NUM
cana-4018	50	21	.	.	PUNCT
cana-4018	50	22	procedures	procedure	NOUN
cana-4018	50	23	for	for	ADP
cana-4018	50	24	encryption	encryption	NOUN
cana-4018	50	25	and	and	CCONJ
cana-4018	50	26	decryption	decryption	NOUN
cana-4018	50	27	this	this	DET
cana-4018	50	28	section	section	NOUN
cana-4018	50	29	covers	cover	VERB
cana-4018	50	30	the	the	DET
cana-4018	50	31	steps	step	NOUN
cana-4018	50	32	for	for	ADP
cana-4018	50	33	the	the	DET
cana-4018	50	34	processes	process	NOUN
cana-4018	50	35	of	of	ADP
cana-4018	50	36	encryption	encryption	NOUN
cana-4018	50	37	and	and	CCONJ
cana-4018	50	38	decryption	decryption	NOUN
cana-4018	50	39	for	for	ADP
cana-4018	50	40	a	a	DET
cana-4018	50	41	given	give	VERB
cana-4018	50	42	message	message	NOUN
cana-4018	50	43	.	.	PUNCT
cana-4018	51	1	2.1	2.1	NUM
cana-4018	51	2	.	.	PUNCT
cana-4018	51	3	encryption	encryption	NOUN
cana-4018	51	4	in	in	ADP
cana-4018	51	5	this	this	DET
cana-4018	51	6	encryption	encryption	NOUN
cana-4018	51	7	process	process	NOUN
cana-4018	51	8	,	,	PUNCT
cana-4018	51	9	each	each	DET
cana-4018	51	10	word	word	NOUN
cana-4018	51	11	has	have	VERB
cana-4018	51	12	to	to	PART
cana-4018	51	13	be	be	AUX
cana-4018	51	14	encrypted	encrypt	VERB
cana-4018	51	15	separately	separately	ADV
cana-4018	51	16	.	.	PUNCT
cana-4018	52	1	first	first	ADV
cana-4018	52	2	,	,	PUNCT
cana-4018	52	3	split	split	VERB
cana-4018	52	4	the	the	DET
cana-4018	52	5	message	message	NOUN
cana-4018	52	6	(	(	PUNCT
cana-4018	52	7	assume	assume	VERB
cana-4018	52	8	it	it	PRON
cana-4018	52	9	has	have	VERB
cana-4018	52	10	𝑛	𝑛	DET
cana-4018	52	11	words	word	NOUN
cana-4018	52	12	)	)	PUNCT
cana-4018	52	13	to	to	PART
cana-4018	52	14	be	be	AUX
cana-4018	52	15	sent	send	VERB
cana-4018	52	16	into	into	ADP
cana-4018	52	17	𝑊1,𝑊2	𝑊1,𝑊2	NOUN
cana-4018	52	18	,	,	PUNCT
cana-4018	52	19	⋯	⋯	X
cana-4018	52	20	,	,	PUNCT
cana-4018	52	21	𝑊𝑛	𝑊𝑛	PROPN
cana-4018	52	22	(	(	PUNCT
cana-4018	52	23	omit	omit	NOUN
cana-4018	52	24	spaces	space	NOUN
cana-4018	52	25	)	)	PUNCT
cana-4018	52	26	.	.	PUNCT
cana-4018	53	1	then	then	ADV
cana-4018	53	2	do	do	VERB
cana-4018	53	3	the	the	DET
cana-4018	53	4	same	same	ADJ
cana-4018	53	5	steps	step	NOUN
cana-4018	53	6	given	give	VERB
cana-4018	53	7	below	below	ADP
cana-4018	53	8	for	for	ADP
cana-4018	53	9	each	each	DET
cana-4018	53	10	𝑖	𝑖	X
cana-4018	53	11	(	(	PUNCT
cana-4018	53	12	the	the	DET
cana-4018	53	13	following	follow	VERB
cana-4018	53	14	steps	step	NOUN
cana-4018	53	15	are	be	AUX
cana-4018	53	16	provided	provide	VERB
cana-4018	53	17	for	for	ADP
cana-4018	53	18	the	the	DET
cana-4018	53	19	word	word	NOUN
cana-4018	53	20	𝑊𝑖	𝑊𝑖	PROPN
cana-4018	53	21	)	)	PUNCT
cana-4018	53	22	(	(	PUNCT
cana-4018	53	23	e1	e1	PROPN
cana-4018	53	24	)	)	PUNCT
cana-4018	53	25	using	use	VERB
cana-4018	53	26	the	the	DET
cana-4018	53	27	table	table	NOUN
cana-4018	53	28	1	1	NUM
cana-4018	53	29	,	,	PUNCT
cana-4018	53	30	find	find	VERB
cana-4018	53	31	the	the	DET
cana-4018	53	32	position	position	NOUN
cana-4018	53	33	for	for	ADP
cana-4018	53	34	each	each	DET
cana-4018	53	35	letter	letter	NOUN
cana-4018	53	36	in	in	ADP
cana-4018	53	37	the	the	DET
cana-4018	53	38	word	word	NOUN
cana-4018	53	39	𝑊𝑖.	𝑊𝑖.	PROPN
cana-4018	53	40	(	(	PUNCT
cana-4018	53	41	e2	e2	PROPN
cana-4018	53	42	)	)	PUNCT
cana-4018	53	43	apply	apply	VERB
cana-4018	53	44	the	the	DET
cana-4018	53	45	function	function	NOUN
cana-4018	53	46	𝑓	𝑓	PRON
cana-4018	53	47	for	for	ADP
cana-4018	53	48	each	each	PRON
cana-4018	53	49	of	of	ADP
cana-4018	53	50	these	these	DET
cana-4018	53	51	numerical	numerical	ADJ
cana-4018	53	52	positions	position	NOUN
cana-4018	53	53	.	.	PUNCT
cana-4018	54	1	(	(	PUNCT
cana-4018	54	2	e3	e3	NOUN
cana-4018	54	3	)	)	PUNCT
cana-4018	54	4	construct	construct	VERB
cana-4018	54	5	a	a	DET
cana-4018	54	6	cyclic	cyclic	ADJ
cana-4018	54	7	symmetric	symmetric	ADJ
cana-4018	54	8	matrix	matrix	NOUN
cana-4018	54	9	𝑀𝑖	𝑀𝑖	PROPN
cana-4018	54	10	of	of	ADP
cana-4018	54	11	order	order	NOUN
cana-4018	55	1	𝑖	𝑖	SYM
cana-4018	55	2	×	×	VERB
cana-4018	55	3	𝑖	𝑖	ADP
cana-4018	55	4	using	use	VERB
cana-4018	55	5	the	the	DET
cana-4018	55	6	values	value	NOUN
cana-4018	55	7	obtained	obtain	VERB
cana-4018	55	8	in	in	ADP
cana-4018	55	9	(	(	PUNCT
cana-4018	55	10	𝐸2	𝐸2	ADJ
cana-4018	55	11	)	)	PUNCT
cana-4018	55	12	.	.	PUNCT
cana-4018	56	1	(	(	PUNCT
cana-4018	56	2	e4	e4	PROPN
cana-4018	56	3	)	)	PUNCT
cana-4018	56	4	calculate	calculate	NOUN
cana-4018	56	5	𝑛(𝑊𝑖	𝑛(𝑊𝑖	PROPN
cana-4018	56	6	)	)	PUNCT
cana-4018	56	7	.	.	PUNCT
cana-4018	57	1	(	(	PUNCT
cana-4018	57	2	e5	e5	NOUN
cana-4018	57	3	)	)	PUNCT
cana-4018	57	4	calculate	calculate	NOUN
cana-4018	57	5	𝑔(𝑛(𝑊𝑖	𝑔(𝑛(𝑊𝑖	PROPN
cana-4018	57	6	)	)	PUNCT
cana-4018	57	7	)	)	PUNCT
cana-4018	57	8	.	.	PUNCT
cana-4018	58	1	(	(	PUNCT
cana-4018	58	2	e6	e6	PROPN
cana-4018	58	3	)	)	PUNCT
cana-4018	58	4	construct	construct	VERB
cana-4018	58	5	the	the	DET
cana-4018	58	6	diagonal	diagonal	ADJ
cana-4018	58	7	matrix	matrix	NOUN
cana-4018	58	8	𝐷(𝑅𝑖	𝐷(𝑅𝑖	NUM
cana-4018	58	9	)	)	PUNCT
cana-4018	58	10	.	.	PUNCT
cana-4018	59	1	(	(	PUNCT
cana-4018	59	2	e7	e7	PROPN
cana-4018	59	3	)	)	PUNCT
cana-4018	59	4	find	find	VERB
cana-4018	59	5	𝐷(𝑅𝑖	𝐷(𝑅𝑖	NUM
cana-4018	59	6	)	)	PUNCT
cana-4018	59	7	−	−	PROPN
cana-4018	59	8	𝑛(𝑊𝑖)𝐼𝑛(𝑊𝑖	𝑛(𝑊𝑖)𝐼𝑛(𝑊𝑖	NOUN
cana-4018	59	9	)	)	PUNCT
cana-4018	59	10	,	,	PUNCT
cana-4018	59	11	which	which	PRON
cana-4018	59	12	is	be	AUX
cana-4018	59	13	the	the	DET
cana-4018	59	14	encrypted	encrypt	VERB
cana-4018	59	15	key	key	NOUN
cana-4018	59	16	.	.	PUNCT
cana-4018	60	1	this	this	DET
cana-4018	60	2	encrypted	encrypt	VERB
cana-4018	60	3	key	key	NOUN
cana-4018	60	4	is	be	AUX
cana-4018	60	5	to	to	PART
cana-4018	60	6	be	be	AUX
cana-4018	60	7	sent	send	VERB
cana-4018	60	8	as	as	ADP
cana-4018	60	9	𝐸𝑖	𝐸𝑖	PROPN
cana-4018	60	10	=	=	SYM
cana-4018	60	11	(	(	PUNCT
cana-4018	60	12	𝑒𝑖1	𝑒𝑖1	NOUN
cana-4018	60	13	𝑒𝑖2	𝑒𝑖2	NOUN
cana-4018	60	14	⋯	⋯	PROPN
cana-4018	60	15	𝑒𝑖𝑘𝑖	𝑒𝑖𝑘𝑖	PROPN
cana-4018	60	16	)	)	PUNCT
cana-4018	60	17	where	where	SCONJ
cana-4018	60	18	𝑒𝑖𝑘𝑖′𝑠	𝑒𝑖𝑘𝑖′𝑠	PROPN
cana-4018	60	19	are	be	AUX
cana-4018	60	20	the	the	DET
cana-4018	60	21	diagonal	diagonal	ADJ
cana-4018	60	22	entries	entry	NOUN
cana-4018	60	23	of	of	ADP
cana-4018	60	24	𝐷(𝑅𝑖	𝐷(𝑅𝑖	NOUN
cana-4018	60	25	)	)	PUNCT
cana-4018	60	26	−	−	PROPN
cana-4018	60	27	𝑛(𝑊𝑖)𝐼𝑛(𝑊𝑖	𝑛(𝑊𝑖)𝐼𝑛(𝑊𝑖	NOUN
cana-4018	60	28	)	)	PUNCT
cana-4018	60	29	.	.	PUNCT
cana-4018	61	1	2.2	2.2	NUM
cana-4018	61	2	.	.	PUNCT
cana-4018	61	3	decryption	decryption	NOUN
cana-4018	61	4	for	for	ADP
cana-4018	61	5	each	each	PRON
cana-4018	61	6	𝑖	𝑖	NOUN
cana-4018	61	7	do	do	AUX
cana-4018	61	8	the	the	DET
cana-4018	61	9	following	follow	VERB
cana-4018	61	10	steps	step	NOUN
cana-4018	61	11	for	for	ADP
cana-4018	61	12	the	the	DET
cana-4018	61	13	decryption	decryption	NOUN
cana-4018	61	14	of	of	ADP
cana-4018	61	15	the	the	DET
cana-4018	61	16	encrypted	encrypt	VERB
cana-4018	61	17	key	key	NOUN
cana-4018	61	18	𝐸𝑖.	𝐸𝑖.	PROPN
cana-4018	61	19	(	(	PUNCT
cana-4018	61	20	d1	d1	PROPN
cana-4018	61	21	)	)	PUNCT
cana-4018	61	22	calculate	calculate	NOUN
cana-4018	61	23	𝐶𝑖	𝐶𝑖	PROPN
cana-4018	61	24	=	=	PUNCT
cana-4018	61	25	(	(	PUNCT
cana-4018	61	26	𝑐𝑖1	𝑐𝑖1	NOUN
cana-4018	61	27	𝑐𝑖2	𝑐𝑖2	NOUN
cana-4018	61	28	⋯	⋯	VERB
cana-4018	61	29	𝑐𝑖𝑘𝑖	𝑐𝑖𝑘𝑖	PROPN
cana-4018	61	30	)	)	PUNCT
cana-4018	62	1	=	=	SYM
cana-4018	62	2	𝐷(𝐸𝑖	𝐷(𝐸𝑖	PROPN
cana-4018	62	3	)	)	PUNCT
cana-4018	63	1	+	+	CCONJ
cana-4018	63	2	𝑘𝑖𝐼𝑘𝑖.	𝑘𝑖𝐼𝑘𝑖.	ADJ
cana-4018	63	3	(	(	PUNCT
cana-4018	63	4	d2	d2	PROPN
cana-4018	63	5	)	)	PUNCT
cana-4018	63	6	find	find	VERB
cana-4018	63	7	𝑔(𝑘𝑖	𝑔(𝑘𝑖	NOUN
cana-4018	63	8	)	)	PUNCT
cana-4018	63	9	.	.	PUNCT
cana-4018	64	1	(	(	PUNCT
cana-4018	64	2	d3	d3	PROPN
cana-4018	64	3	)	)	PUNCT
cana-4018	64	4	construct	construct	NOUN
cana-4018	64	5	𝑆𝑖	𝑆𝑖	PROPN
cana-4018	64	6	=	=	PUNCT
cana-4018	64	7	(	(	PUNCT
cana-4018	64	8	𝑠𝑖1	𝑠𝑖1	PROPN
cana-4018	64	9	𝑠𝑖2	𝑠𝑖2	PROPN
cana-4018	64	10	⋯	⋯	PROPN
cana-4018	64	11	𝑠𝑖𝑘𝑖	𝑠𝑖𝑘𝑖	PROPN
cana-4018	64	12	)	)	PUNCT
cana-4018	64	13	where	where	SCONJ
cana-4018	64	14	𝑠𝑖𝑔(𝑘𝑖	𝑠𝑖𝑔(𝑘𝑖	NOUN
cana-4018	64	15	)	)	PUNCT
cana-4018	64	16	is	be	AUX
cana-4018	64	17	𝑐𝑖1	𝑐𝑖1	NOUN
cana-4018	64	18	,	,	PUNCT
cana-4018	64	19	𝑠𝑖(𝑔(𝑘𝑖)+1	𝑠𝑖(𝑔(𝑘𝑖)+1	NUM
cana-4018	64	20	)	)	PUNCT
cana-4018	64	21	is	be	AUX
cana-4018	64	22	𝑐𝑖2	𝑐𝑖2	NOUN
cana-4018	64	23	,	,	PUNCT
cana-4018	64	24	⋯	⋯	VERB
cana-4018	64	25	(	(	PUNCT
cana-4018	64	26	occurs	occur	VERB
cana-4018	64	27	in	in	ADP
cana-4018	64	28	cyclic	cyclic	ADJ
cana-4018	64	29	order	order	NOUN
cana-4018	64	30	)	)	PUNCT
cana-4018	64	31	.	.	PUNCT
cana-4018	65	1	(	(	PUNCT
cana-4018	65	2	d4	d4	PROPN
cana-4018	65	3	)	)	PUNCT
cana-4018	65	4	for	for	ADP
cana-4018	65	5	each	each	DET
cana-4018	65	6	𝑠𝑖𝑗(1	𝑠𝑖𝑗(1	NOUN
cana-4018	65	7	≤	≤	PUNCT
cana-4018	65	8	𝑗	𝑗	PRON
cana-4018	65	9	≤	≤	NUM
cana-4018	65	10	𝑘𝑖	𝑘𝑖	NOUN
cana-4018	65	11	)	)	PUNCT
cana-4018	65	12	,	,	PUNCT
cana-4018	65	13	calculate	calculate	VERB
cana-4018	65	14	𝑦(𝑠𝑖𝑗	𝑦(𝑠𝑖𝑗	PROPN
cana-4018	65	15	)	)	PUNCT
cana-4018	65	16	=	=	SYM
cana-4018	66	1	2(𝑠𝑖𝑗−1	2(𝑠𝑖𝑗−1	NUM
cana-4018	66	2	)	)	PUNCT
cana-4018	66	3	3	3	NUM
cana-4018	66	4	+	+	SYM
cana-4018	66	5	1	1	NUM
cana-4018	66	6	.	.	X
cana-4018	66	7	(	(	PUNCT
cana-4018	66	8	d5	d5	NOUN
cana-4018	66	9	)	)	PUNCT
cana-4018	66	10	replacing	replace	VERB
cana-4018	66	11	𝑦(𝑠𝑖𝑗	𝑦(𝑠𝑖𝑗	PROPN
cana-4018	66	12	)	)	PUNCT
cana-4018	66	13	for	for	ADP
cana-4018	66	14	all	all	DET
cana-4018	66	15	1	1	NUM
cana-4018	66	16	≤	≤	NUM
cana-4018	66	17	𝑗	𝑗	PRON
cana-4018	66	18	≤	≤	NOUN
cana-4018	66	19	𝑘𝑖	𝑘𝑖	NOUN
cana-4018	66	20	by	by	ADP
cana-4018	66	21	its	its	PRON
cana-4018	66	22	corresponding	corresponding	ADJ
cana-4018	66	23	alphabet	alphabet	NOUN
cana-4018	66	24	,	,	PUNCT
cana-4018	66	25	the	the	DET
cana-4018	66	26	required	require	VERB
cana-4018	66	27	word	word	NOUN
cana-4018	66	28	is	be	AUX
cana-4018	66	29	obtained	obtain	VERB
cana-4018	66	30	.	.	PUNCT
cana-4018	67	1	communications	communication	NOUN
cana-4018	67	2	on	on	ADP
cana-4018	67	3	applied	apply	VERB
cana-4018	67	4	nonlinear	nonlinear	ADJ
cana-4018	67	5	analysis	analysis	NOUN
cana-4018	67	6	issn	issn	NOUN
cana-4018	67	7	:	:	PUNCT
cana-4018	67	8	1074	1074	NUM
cana-4018	67	9	-	-	PUNCT
cana-4018	67	10	133x	133x	NUM
cana-4018	67	11	vol	vol	NOUN
cana-4018	67	12	32	32	NUM
cana-4018	67	13	no	no	NOUN
cana-4018	67	14	.	.	PUNCT
cana-4018	68	1	9s	9s	NUM
cana-4018	68	2	(	(	PUNCT
cana-4018	68	3	2025	2025	NUM
cana-4018	68	4	)	)	PUNCT
cana-4018	68	5	844	844	NUM
cana-4018	68	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	68	7	2.3	2.3	NUM
cana-4018	68	8	.	.	PUNCT
cana-4018	69	1	few	few	ADJ
cana-4018	69	2	exemplifications	exemplification	NOUN
cana-4018	69	3	here	here	ADV
cana-4018	69	4	are	be	AUX
cana-4018	69	5	two	two	NUM
cana-4018	69	6	examples	example	NOUN
cana-4018	69	7	for	for	ADP
cana-4018	69	8	the	the	DET
cana-4018	69	9	above	above	ADV
cana-4018	69	10	given	give	VERB
cana-4018	69	11	encryption	encryption	NOUN
cana-4018	69	12	and	and	CCONJ
cana-4018	69	13	decryption	decryption	NOUN
cana-4018	69	14	processes	process	NOUN
cana-4018	69	15	.	.	PUNCT
cana-4018	69	16	example	example	NOUN
cana-4018	69	17	2.1	2.1	NUM
cana-4018	69	18	.	.	PUNCT
cana-4018	70	1	encrypt	encrypt	VERB
cana-4018	70	2	and	and	CCONJ
cana-4018	70	3	decrypt	decrypt	VERB
cana-4018	70	4	the	the	DET
cana-4018	70	5	message	message	NOUN
cana-4018	70	6	“	"	PUNCT
cana-4018	70	7	primes	prime	NOUN
cana-4018	70	8	”	"	PUNCT
cana-4018	70	9	.	.	PUNCT
cana-4018	71	1	here	here	ADV
cana-4018	71	2	we	we	PRON
cana-4018	71	3	have	have	VERB
cana-4018	71	4	only	only	ADV
cana-4018	71	5	one	one	NUM
cana-4018	71	6	word	word	NOUN
cana-4018	71	7	to	to	ADP
cana-4018	71	8	process	process	NOUN
cana-4018	71	9	.	.	PUNCT
cana-4018	72	1	so	so	ADV
cana-4018	72	2	𝑊1	𝑊1	PROPN
cana-4018	73	1	=	=	SYM
cana-4018	73	2	𝑃𝑅𝐼𝑀𝐸𝑆.	𝑃𝑅𝐼𝑀𝐸𝑆.	NOUN
cana-4018	73	3	encryption	encryption	NOUN
cana-4018	73	4	:	:	PUNCT
cana-4018	73	5	(	(	PUNCT
cana-4018	73	6	e1	e1	PROPN
cana-4018	73	7	)	)	PUNCT
cana-4018	73	8	(	(	PUNCT
cana-4018	73	9	e2	e2	PROPN
cana-4018	73	10	)	)	PUNCT
cana-4018	73	11	(	(	PUNCT
cana-4018	73	12	e3	e3	NOUN
cana-4018	73	13	)	)	PUNCT
cana-4018	73	14	𝑀1	𝑀1	NOUN
cana-4018	73	15	=	=	PUNCT
cana-4018	73	16	(	(	PUNCT
cana-4018	73	17	460	460	NUM
cana-4018	73	18	571	571	NUM
cana-4018	73	19	166	166	NUM
cana-4018	73	20	316	316	NUM
cana-4018	73	21	64	64	NUM
cana-4018	73	22	631	631	NUM
cana-4018	73	23	571	571	NUM
cana-4018	73	24	166	166	NUM
cana-4018	73	25	316	316	NUM
cana-4018	73	26	64	64	NUM
cana-4018	73	27	631	631	NUM
cana-4018	73	28	460	460	NUM
cana-4018	73	29	166	166	NUM
cana-4018	73	30	316	316	NUM
cana-4018	73	31	64	64	NUM
cana-4018	73	32	631	631	NUM
cana-4018	73	33	460	460	NUM
cana-4018	73	34	571	571	NUM
cana-4018	73	35	316	316	NUM
cana-4018	73	36	64	64	NUM
cana-4018	73	37	631	631	NUM
cana-4018	73	38	460	460	NUM
cana-4018	73	39	571	571	NUM
cana-4018	73	40	166	166	NUM
cana-4018	73	41	64	64	NUM
cana-4018	73	42	631	631	NUM
cana-4018	73	43	460	460	NUM
cana-4018	73	44	571	571	NUM
cana-4018	73	45	166	166	NUM
cana-4018	73	46	316	316	NUM
cana-4018	73	47	631	631	NUM
cana-4018	73	48	460	460	NUM
cana-4018	73	49	571	571	NUM
cana-4018	73	50	166	166	NUM
cana-4018	73	51	316	316	NUM
cana-4018	73	52	64	64	NUM
cana-4018	73	53	)	)	PUNCT
cana-4018	73	54	(	(	PUNCT
cana-4018	73	55	e4	e4	PROPN
cana-4018	73	56	)	)	PUNCT
cana-4018	73	57	𝑛(𝑊1	𝑛(𝑊1	PROPN
cana-4018	73	58	)	)	PUNCT
cana-4018	73	59	=	=	SYM
cana-4018	73	60	6	6	NUM
cana-4018	73	61	(	(	PUNCT
cana-4018	73	62	e5	e5	PROPN
cana-4018	73	63	)	)	PUNCT
cana-4018	73	64	𝑔(𝑛(𝑊1	𝑔(𝑛(𝑊1	PROPN
cana-4018	73	65	)	)	PUNCT
cana-4018	73	66	)	)	PUNCT
cana-4018	73	67	=	=	SYM
cana-4018	73	68	3	3	NUM
cana-4018	73	69	(	(	PUNCT
cana-4018	73	70	e6	e6	PROPN
cana-4018	73	71	)	)	PUNCT
cana-4018	73	72	𝐷(𝑅1	𝐷(𝑅1	X
cana-4018	73	73	)	)	PUNCT
cana-4018	73	74	=	=	PUNCT
cana-4018	73	75	(	(	PUNCT
cana-4018	73	76	166	166	NUM
cana-4018	73	77	0	0	NUM
cana-4018	73	78	0	0	NUM
cana-4018	73	79	0	0	NUM
cana-4018	73	80	0	0	NUM
cana-4018	73	81	0	0	NUM
cana-4018	73	82	0	0	NUM
cana-4018	74	1	316	316	NUM
cana-4018	74	2	0	0	NUM
cana-4018	74	3	0	0	NUM
cana-4018	74	4	0	0	NUM
cana-4018	74	5	0	0	NUM
cana-4018	74	6	0	0	NUM
cana-4018	74	7	0	0	NUM
cana-4018	74	8	64	64	NUM
cana-4018	74	9	0	0	NUM
cana-4018	74	10	0	0	NUM
cana-4018	74	11	0	0	NUM
cana-4018	74	12	0	0	NUM
cana-4018	74	13	0	0	NUM
cana-4018	74	14	0	0	NUM
cana-4018	74	15	631	631	NUM
cana-4018	74	16	0	0	NUM
cana-4018	74	17	0	0	NUM
cana-4018	74	18	0	0	NUM
cana-4018	74	19	0	0	NUM
cana-4018	74	20	0	0	NUM
cana-4018	74	21	0	0	NUM
cana-4018	74	22	460	460	NUM
cana-4018	74	23	0	0	NUM
cana-4018	74	24	0	0	NUM
cana-4018	74	25	0	0	NUM
cana-4018	74	26	0	0	NUM
cana-4018	74	27	0	0	NUM
cana-4018	74	28	0	0	NUM
cana-4018	74	29	571	571	NUM
cana-4018	74	30	)	)	PUNCT
cana-4018	74	31	(	(	PUNCT
cana-4018	74	32	e7	e7	PROPN
cana-4018	74	33	)	)	PUNCT
cana-4018	74	34	𝐷(𝑅1	𝐷(𝑅1	PROPN
cana-4018	74	35	)	)	PUNCT
cana-4018	75	1	−	−	PROPN
cana-4018	75	2	𝑛(𝑊1)𝐼𝑛(𝑊1	𝑛(𝑊1)𝐼𝑛(𝑊1	X
cana-4018	75	3	)	)	PUNCT
cana-4018	75	4	=	=	PUNCT
cana-4018	75	5	(	(	PUNCT
cana-4018	75	6	166	166	NUM
cana-4018	75	7	0	0	NUM
cana-4018	75	8	0	0	NUM
cana-4018	75	9	0	0	NUM
cana-4018	75	10	0	0	NUM
cana-4018	75	11	0	0	NUM
cana-4018	75	12	0	0	NUM
cana-4018	76	1	316	316	NUM
cana-4018	76	2	0	0	NUM
cana-4018	76	3	0	0	NUM
cana-4018	76	4	0	0	NUM
cana-4018	76	5	0	0	NUM
cana-4018	76	6	0	0	NUM
cana-4018	76	7	0	0	NUM
cana-4018	76	8	64	64	NUM
cana-4018	76	9	0	0	NUM
cana-4018	76	10	0	0	NUM
cana-4018	76	11	0	0	NUM
cana-4018	76	12	0	0	NUM
cana-4018	76	13	0	0	NUM
cana-4018	76	14	0	0	NUM
cana-4018	76	15	631	631	NUM
cana-4018	76	16	0	0	NUM
cana-4018	76	17	0	0	NUM
cana-4018	76	18	0	0	NUM
cana-4018	76	19	0	0	NUM
cana-4018	76	20	0	0	NUM
cana-4018	76	21	0	0	NUM
cana-4018	76	22	460	460	NUM
cana-4018	76	23	0	0	NUM
cana-4018	76	24	0	0	NUM
cana-4018	76	25	0	0	NUM
cana-4018	76	26	0	0	NUM
cana-4018	76	27	0	0	NUM
cana-4018	76	28	0	0	NUM
cana-4018	76	29	571	571	NUM
cana-4018	76	30	)	)	PUNCT
cana-4018	76	31	−	−	PROPN
cana-4018	76	32	(	(	PUNCT
cana-4018	76	33	6	6	NUM
cana-4018	76	34	0	0	NUM
cana-4018	76	35	0	0	NUM
cana-4018	76	36	0	0	NUM
cana-4018	76	37	0	0	NUM
cana-4018	76	38	0	0	NUM
cana-4018	76	39	0	0	NUM
cana-4018	76	40	6	6	NUM
cana-4018	76	41	0	0	NUM
cana-4018	76	42	0	0	NUM
cana-4018	76	43	0	0	NUM
cana-4018	76	44	0	0	NUM
cana-4018	76	45	0	0	NUM
cana-4018	76	46	0	0	NUM
cana-4018	76	47	6	6	NUM
cana-4018	76	48	0	0	NUM
cana-4018	76	49	0	0	NUM
cana-4018	76	50	0	0	NUM
cana-4018	76	51	0	0	NUM
cana-4018	76	52	0	0	NUM
cana-4018	76	53	0	0	NUM
cana-4018	76	54	6	6	NUM
cana-4018	76	55	0	0	NUM
cana-4018	76	56	0	0	NUM
cana-4018	76	57	0	0	NUM
cana-4018	76	58	0	0	NUM
cana-4018	76	59	0	0	NUM
cana-4018	76	60	0	0	NUM
cana-4018	76	61	6	6	NUM
cana-4018	76	62	0	0	NUM
cana-4018	76	63	0	0	NUM
cana-4018	76	64	0	0	NUM
cana-4018	76	65	0	0	NUM
cana-4018	76	66	0	0	NUM
cana-4018	76	67	0	0	NUM
cana-4018	76	68	6	6	NUM
cana-4018	76	69	)	)	PUNCT
cana-4018	76	70	p	p	NOUN
cana-4018	76	71	r	r	NOUN
cana-4018	77	1	i	i	PRON
cana-4018	77	2	m	m	VERB
cana-4018	77	3	e	e	NOUN
cana-4018	77	4	s	s	VERB
cana-4018	77	5	307	307	NUM
cana-4018	77	6	381	381	NUM
cana-4018	77	7	111	111	NUM
cana-4018	77	8	211	211	NUM
cana-4018	77	9	43	43	NUM
cana-4018	77	10	421	421	NUM
cana-4018	77	11	𝑛	𝑛	DET
cana-4018	77	12	307	307	NUM
cana-4018	77	13	381	381	NUM
cana-4018	77	14	111	111	NUM
cana-4018	77	15	211	211	NUM
cana-4018	77	16	43	43	NUM
cana-4018	77	17	421	421	NUM
cana-4018	77	18	𝑓(𝑛	𝑓(𝑛	NOUN
cana-4018	77	19	)	)	PUNCT
cana-4018	77	20	460	460	NUM
cana-4018	77	21	571	571	NUM
cana-4018	77	22	166	166	NUM
cana-4018	77	23	316	316	NUM
cana-4018	77	24	64	64	NUM
cana-4018	77	25	631	631	NUM
cana-4018	77	26	communications	communication	NOUN
cana-4018	77	27	on	on	ADP
cana-4018	77	28	applied	apply	VERB
cana-4018	77	29	nonlinear	nonlinear	ADJ
cana-4018	77	30	analysis	analysis	NOUN
cana-4018	77	31	issn	issn	NOUN
cana-4018	77	32	:	:	PUNCT
cana-4018	77	33	1074	1074	NUM
cana-4018	77	34	-	-	PUNCT
cana-4018	77	35	133x	133x	NUM
cana-4018	77	36	vol	vol	NOUN
cana-4018	77	37	32	32	NUM
cana-4018	77	38	no	no	NOUN
cana-4018	77	39	.	.	PUNCT
cana-4018	78	1	9s	9s	NUM
cana-4018	78	2	(	(	PUNCT
cana-4018	78	3	2025	2025	NUM
cana-4018	78	4	)	)	PUNCT
cana-4018	78	5	845	845	NUM
cana-4018	78	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	78	7	=	=	PUNCT
cana-4018	78	8	(	(	PUNCT
cana-4018	78	9	160	160	NUM
cana-4018	78	10	0	0	NUM
cana-4018	78	11	0	0	NUM
cana-4018	78	12	0	0	NUM
cana-4018	78	13	0	0	NUM
cana-4018	78	14	0	0	NUM
cana-4018	78	15	0	0	NUM
cana-4018	79	1	310	310	NUM
cana-4018	79	2	0	0	NUM
cana-4018	79	3	0	0	NUM
cana-4018	79	4	0	0	NUM
cana-4018	79	5	0	0	NUM
cana-4018	79	6	0	0	NUM
cana-4018	79	7	0	0	NUM
cana-4018	80	1	58	58	NUM
cana-4018	80	2	0	0	NUM
cana-4018	80	3	0	0	NUM
cana-4018	80	4	0	0	NUM
cana-4018	80	5	0	0	NUM
cana-4018	80	6	0	0	NUM
cana-4018	80	7	0	0	NUM
cana-4018	80	8	625	625	NUM
cana-4018	80	9	0	0	NUM
cana-4018	80	10	0	0	NUM
cana-4018	80	11	0	0	NUM
cana-4018	80	12	0	0	NUM
cana-4018	80	13	0	0	NUM
cana-4018	80	14	0	0	NUM
cana-4018	80	15	454	454	NUM
cana-4018	80	16	0	0	NUM
cana-4018	80	17	0	0	NUM
cana-4018	80	18	0	0	NUM
cana-4018	80	19	0	0	NUM
cana-4018	80	20	0	0	NUM
cana-4018	80	21	0	0	NUM
cana-4018	80	22	565	565	NUM
cana-4018	80	23	)	)	PUNCT
cana-4018	80	24	the	the	DET
cana-4018	80	25	encrypted	encrypt	VERB
cana-4018	80	26	key	key	NOUN
cana-4018	80	27	is	be	AUX
cana-4018	80	28	𝐸1	𝐸1	NOUN
cana-4018	80	29	=	=	PUNCT
cana-4018	80	30	(	(	PUNCT
cana-4018	80	31	160	160	NUM
cana-4018	80	32	310	310	NUM
cana-4018	80	33	58	58	NUM
cana-4018	80	34	625	625	NUM
cana-4018	80	35	454	454	NUM
cana-4018	80	36	565	565	NUM
cana-4018	80	37	)	)	PUNCT
cana-4018	80	38	decryption	decryption	NOUN
cana-4018	80	39	:	:	PUNCT
cana-4018	80	40	here	here	ADV
cana-4018	80	41	𝑘1	𝑘1	PROPN
cana-4018	80	42	=	=	NOUN
cana-4018	80	43	6	6	NUM
cana-4018	80	44	.	.	PUNCT
cana-4018	81	1	(	(	PUNCT
cana-4018	81	2	d1	d1	NOUN
cana-4018	81	3	)	)	PUNCT
cana-4018	81	4	𝐶1	𝐶1	NOUN
cana-4018	81	5	=	=	PUNCT
cana-4018	81	6	𝐷(𝐸1	𝐷(𝐸1	PROPN
cana-4018	81	7	)	)	PUNCT
cana-4018	82	1	+	+	CCONJ
cana-4018	82	2	𝑘1𝐼𝑘1	𝑘1𝐼𝑘1	INTJ
cana-4018	82	3	=	=	SYM
cana-4018	82	4	(	(	PUNCT
cana-4018	82	5	166	166	NUM
cana-4018	82	6	316	316	NUM
cana-4018	82	7	64	64	NUM
cana-4018	82	8	631	631	NUM
cana-4018	82	9	460	460	NUM
cana-4018	82	10	571	571	NUM
cana-4018	82	11	)	)	PUNCT
cana-4018	82	12	(	(	PUNCT
cana-4018	82	13	d2	d2	PROPN
cana-4018	82	14	)	)	PUNCT
cana-4018	82	15	𝑔(𝑘1	𝑔(𝑘1	NOUN
cana-4018	82	16	)	)	PUNCT
cana-4018	82	17	=	=	SYM
cana-4018	82	18	3	3	NUM
cana-4018	82	19	(	(	PUNCT
cana-4018	82	20	d3	d3	PROPN
cana-4018	82	21	)	)	PUNCT
cana-4018	82	22	𝑆1	𝑆1	NOUN
cana-4018	82	23	=	=	PUNCT
cana-4018	82	24	(	(	PUNCT
cana-4018	82	25	460	460	NUM
cana-4018	82	26	571	571	NUM
cana-4018	82	27	166	166	NUM
cana-4018	82	28	316	316	NUM
cana-4018	82	29	64	64	NUM
cana-4018	82	30	631	631	NUM
cana-4018	82	31	)	)	PUNCT
cana-4018	82	32	𝑠11	𝑠11	ADJ
cana-4018	82	33	𝑠12	𝑠12	NOUN
cana-4018	82	34	𝑠13	𝑠13	NOUN
cana-4018	82	35	𝑠14	𝑠14	NOUN
cana-4018	82	36	𝑠15	𝑠15	PROPN
cana-4018	82	37	𝑠16	𝑠16	PROPN
cana-4018	82	38	𝑠𝑖𝑗	𝑠𝑖𝑗	PROPN
cana-4018	82	39	460	460	NUM
cana-4018	82	40	571	571	NUM
cana-4018	82	41	166	166	NUM
cana-4018	82	42	316	316	NUM
cana-4018	82	43	64	64	NUM
cana-4018	82	44	631	631	NUM
cana-4018	82	45	𝑦(𝑠𝑖𝑗	𝑦(𝑠𝑖𝑗	PROPN
cana-4018	82	46	)	)	PUNCT
cana-4018	82	47	307	307	NUM
cana-4018	82	48	381	381	NUM
cana-4018	82	49	111	111	NUM
cana-4018	82	50	211	211	NUM
cana-4018	82	51	43	43	NUM
cana-4018	82	52	421	421	NUM
cana-4018	82	53	(	(	PUNCT
cana-4018	82	54	d4	d4	PROPN
cana-4018	82	55	)	)	PUNCT
cana-4018	82	56	the	the	DET
cana-4018	82	57	required	require	VERB
cana-4018	82	58	word	word	NOUN
cana-4018	82	59	is	be	AUX
cana-4018	82	60	“	"	PUNCT
cana-4018	82	61	primes	prime	NOUN
cana-4018	82	62	”	"	PUNCT
cana-4018	82	63	.	.	PUNCT
cana-4018	83	1	example	example	NOUN
cana-4018	83	2	2.2	2.2	NUM
cana-4018	83	3	.	.	PUNCT
cana-4018	84	1	encrypt	encrypt	VERB
cana-4018	84	2	and	and	CCONJ
cana-4018	84	3	decrypt	decrypt	VERB
cana-4018	84	4	the	the	DET
cana-4018	84	5	message	message	NOUN
cana-4018	84	6	“	"	PUNCT
cana-4018	84	7	she	she	PRON
cana-4018	84	8	drives	drive	VERB
cana-4018	84	9	a	a	DET
cana-4018	84	10	car	car	NOUN
cana-4018	84	11	”	"	PUNCT
cana-4018	84	12	.	.	PUNCT
cana-4018	85	1	encryption	encryption	NOUN
cana-4018	85	2	:	:	PUNCT
cana-4018	85	3	the	the	DET
cana-4018	85	4	following	follow	VERB
cana-4018	85	5	table	table	NOUN
cana-4018	85	6	presents	present	VERB
cana-4018	85	7	the	the	DET
cana-4018	85	8	encryption	encryption	NOUN
cana-4018	85	9	process	process	NOUN
cana-4018	85	10	.	.	PUNCT
cana-4018	86	1	𝑊𝑖	𝑊𝑖	PROPN
cana-4018	86	2	she	she	PRON
cana-4018	86	3	drives	drive	VERB
cana-4018	86	4	a	a	DET
cana-4018	86	5	car	car	NOUN
cana-4018	86	6	(	(	PUNCT
cana-4018	86	7	𝐸1	𝐸1	NOUN
cana-4018	86	8	)	)	PUNCT
cana-4018	86	9	•	•	NUM
cana-4018	86	10	𝑆	𝑆	PROPN
cana-4018	86	11	=	=	PUNCT
cana-4018	86	12	421	421	NUM
cana-4018	86	13	•	•	NOUN
cana-4018	87	1	𝐻	𝐻	NOUN
cana-4018	87	2	=	=	SYM
cana-4018	87	3	91	91	NUM
cana-4018	87	4	•	•	NUM
cana-4018	87	5	𝐸	𝐸	NOUN
cana-4018	87	6	=	=	SYM
cana-4018	87	7	43	43	NUM
cana-4018	87	8	•	•	NUM
cana-4018	87	9	𝐷	𝐷	NOUN
cana-4018	87	10	=	=	NOUN
cana-4018	87	11	31	31	NUM
cana-4018	87	12	•	•	NUM
cana-4018	87	13	𝑅	𝑅	PROPN
cana-4018	87	14	=	=	PROPN
cana-4018	87	15	381	381	NUM
cana-4018	87	16	•	•	NOUN
cana-4018	87	17	𝐼	𝐼	PROPN
cana-4018	87	18	=	=	SYM
cana-4018	87	19	111	111	NUM
cana-4018	87	20	•	•	NUM
cana-4018	87	21	𝑉	𝑉	PROPN
cana-4018	87	22	=	=	NOUN
cana-4018	87	23	553	553	NUM
cana-4018	87	24	•	•	NUM
cana-4018	87	25	𝐸	𝐸	NOUN
cana-4018	87	26	=	=	SYM
cana-4018	87	27	43	43	NUM
cana-4018	87	28	•	•	NUM
cana-4018	87	29	𝑆	𝑆	PROPN
cana-4018	87	30	=	=	PUNCT
cana-4018	87	31	421	421	NUM
cana-4018	87	32	•	•	NUM
cana-4018	87	33	𝐴	𝐴	PROPN
cana-4018	87	34	=	=	NOUN
cana-4018	87	35	7	7	NUM
cana-4018	87	36	•	•	NUM
cana-4018	87	37	𝐶	𝐶	PROPN
cana-4018	87	38	=	=	SYM
cana-4018	87	39	21	21	NUM
cana-4018	87	40	•	•	NUM
cana-4018	87	41	𝐴	𝐴	NOUN
cana-4018	87	42	=	=	NOUN
cana-4018	87	43	7	7	NUM
cana-4018	87	44	•	•	NUM
cana-4018	87	45	𝑅	𝑅	PROPN
cana-4018	87	46	=	=	PROPN
cana-4018	87	47	381	381	NUM
cana-4018	87	48	(	(	PUNCT
cana-4018	87	49	𝐸2	𝐸2	ADJ
cana-4018	87	50	)	)	PUNCT
cana-4018	87	51	•	•	NUM
cana-4018	87	52	𝑓(421	𝑓(421	NOUN
cana-4018	87	53	)	)	PUNCT
cana-4018	87	54	=	=	PUNCT
cana-4018	88	1	631	631	NUM
cana-4018	88	2	•	•	NUM
cana-4018	88	3	𝑓(91	𝑓(91	PROPN
cana-4018	88	4	)	)	PUNCT
cana-4018	88	5	=	=	SYM
cana-4018	88	6	136	136	NUM
cana-4018	88	7	•	•	NUM
cana-4018	88	8	𝑓(43	𝑓(43	NUM
cana-4018	88	9	)	)	PUNCT
cana-4018	89	1	=	=	SYM
cana-4018	89	2	64	64	NUM
cana-4018	89	3	•	•	NUM
cana-4018	89	4	𝑓(31	𝑓(31	NOUN
cana-4018	89	5	)	)	PUNCT
cana-4018	89	6	=	=	SYM
cana-4018	89	7	46	46	NUM
cana-4018	89	8	•	•	NUM
cana-4018	89	9	𝑓(381	𝑓(381	NOUN
cana-4018	89	10	)	)	PUNCT
cana-4018	89	11	=	=	SYM
cana-4018	89	12	571	571	NUM
cana-4018	89	13	•	•	NUM
cana-4018	89	14	𝑓(111	𝑓(111	NOUN
cana-4018	89	15	)	)	PUNCT
cana-4018	89	16	=	=	SYM
cana-4018	90	1	166	166	NUM
cana-4018	90	2	•	•	NUM
cana-4018	90	3	𝑓(553	𝑓(553	PROPN
cana-4018	90	4	)	)	PUNCT
cana-4018	90	5	=	=	SYM
cana-4018	90	6	829	829	NUM
cana-4018	90	7	•	•	NUM
cana-4018	90	8	𝑓(43	𝑓(43	NUM
cana-4018	90	9	)	)	PUNCT
cana-4018	91	1	=	=	SYM
cana-4018	91	2	64	64	NUM
cana-4018	91	3	•	•	NUM
cana-4018	91	4	𝑓(421	𝑓(421	NOUN
cana-4018	91	5	)	)	PUNCT
cana-4018	91	6	=	=	PUNCT
cana-4018	92	1	631	631	NUM
cana-4018	92	2	•	•	NUM
cana-4018	92	3	𝑓(7	𝑓(7	PROPN
cana-4018	92	4	)	)	PUNCT
cana-4018	92	5	=	=	PUNCT
cana-4018	93	1	10	10	NUM
cana-4018	93	2	•	•	NUM
cana-4018	93	3	𝑓(21	𝑓(21	ADJ
cana-4018	93	4	)	)	PUNCT
cana-4018	93	5	=	=	SYM
cana-4018	93	6	31	31	NUM
cana-4018	93	7	•	•	NUM
cana-4018	93	8	𝑓(7	𝑓(7	PROPN
cana-4018	93	9	)	)	PUNCT
cana-4018	93	10	=	=	SYM
cana-4018	93	11	10	10	NUM
cana-4018	93	12	•	•	NUM
cana-4018	93	13	𝑓(381	𝑓(381	NOUN
cana-4018	93	14	)	)	PUNCT
cana-4018	93	15	=	=	SYM
cana-4018	94	1	571	571	NUM
cana-4018	94	2	(	(	PUNCT
cana-4018	94	3	𝐸3	𝐸3	NOUN
cana-4018	94	4	)	)	PUNCT
cana-4018	94	5	(	(	PUNCT
cana-4018	94	6	631	631	NUM
cana-4018	94	7	136	136	NUM
cana-4018	94	8	64	64	NUM
cana-4018	94	9	136	136	NUM
cana-4018	94	10	64	64	NUM
cana-4018	94	11	631	631	NUM
cana-4018	94	12	64	64	NUM
cana-4018	94	13	631	631	NUM
cana-4018	94	14	136	136	NUM
cana-4018	94	15	)	)	PUNCT
cana-4018	94	16	(	(	PUNCT
cana-4018	94	17	46	46	NUM
cana-4018	94	18	571	571	NUM
cana-4018	94	19	166	166	NUM
cana-4018	94	20	829	829	NUM
cana-4018	94	21	64	64	NUM
cana-4018	94	22	631	631	NUM
cana-4018	94	23	571	571	NUM
cana-4018	94	24	166	166	NUM
cana-4018	94	25	829	829	NUM
cana-4018	94	26	64	64	NUM
cana-4018	94	27	631	631	NUM
cana-4018	94	28	46	46	NUM
cana-4018	94	29	166	166	NUM
cana-4018	94	30	829	829	NUM
cana-4018	94	31	64	64	NUM
cana-4018	94	32	631	631	NUM
cana-4018	94	33	46	46	NUM
cana-4018	94	34	571	571	NUM
cana-4018	94	35	829	829	NUM
cana-4018	94	36	64	64	NUM
cana-4018	94	37	631	631	NUM
cana-4018	94	38	46	46	NUM
cana-4018	94	39	571	571	NUM
cana-4018	94	40	166	166	NUM
cana-4018	94	41	64	64	NUM
cana-4018	94	42	631	631	NUM
cana-4018	94	43	46	46	NUM
cana-4018	94	44	571	571	NUM
cana-4018	94	45	166	166	NUM
cana-4018	94	46	829	829	NUM
cana-4018	94	47	631	631	NUM
cana-4018	94	48	46	46	NUM
cana-4018	94	49	571	571	NUM
cana-4018	94	50	166	166	NUM
cana-4018	94	51	829	829	NUM
cana-4018	94	52	64	64	NUM
cana-4018	94	53	)	)	PUNCT
cana-4018	94	54	(	(	PUNCT
cana-4018	94	55	10	10	NUM
cana-4018	94	56	)	)	PUNCT
cana-4018	94	57	(	(	PUNCT
cana-4018	94	58	31	31	NUM
cana-4018	94	59	10	10	NUM
cana-4018	94	60	571	571	NUM
cana-4018	94	61	10	10	NUM
cana-4018	94	62	571	571	NUM
cana-4018	94	63	31	31	NUM
cana-4018	94	64	571	571	NUM
cana-4018	94	65	31	31	NUM
cana-4018	94	66	10	10	NUM
cana-4018	94	67	)	)	PUNCT
cana-4018	94	68	(	(	PUNCT
cana-4018	94	69	𝐸4	𝐸4	NOUN
cana-4018	94	70	)	)	PUNCT
cana-4018	94	71	𝑛(𝑊1	𝑛(𝑊1	PROPN
cana-4018	94	72	)	)	PUNCT
cana-4018	94	73	=	=	SYM
cana-4018	94	74	3	3	NUM
cana-4018	94	75	𝑛(𝑊2	𝑛(𝑊2	PROPN
cana-4018	94	76	)	)	PUNCT
cana-4018	94	77	=	=	PUNCT
cana-4018	95	1	6	6	NUM
cana-4018	95	2	𝑛(𝑊3	𝑛(𝑊3	NOUN
cana-4018	95	3	)	)	PUNCT
cana-4018	95	4	=	=	SYM
cana-4018	95	5	1	1	NUM
cana-4018	95	6	𝑛(𝑊4	𝑛(𝑊4	NUM
cana-4018	95	7	)	)	PUNCT
cana-4018	95	8	=	=	SYM
cana-4018	95	9	3	3	NUM
cana-4018	95	10	(	(	PUNCT
cana-4018	95	11	𝐸5	𝐸5	ADJ
cana-4018	95	12	)	)	PUNCT
cana-4018	95	13	𝑔(𝑛(𝑊1	𝑔(𝑛(𝑊1	NOUN
cana-4018	95	14	)	)	PUNCT
cana-4018	95	15	)	)	PUNCT
cana-4018	96	1	=	=	SYM
cana-4018	96	2	2	2	NUM
cana-4018	96	3	𝑔(𝑛(𝑊2	𝑔(𝑛(𝑊2	NOUN
cana-4018	96	4	)	)	PUNCT
cana-4018	96	5	)	)	PUNCT
cana-4018	97	1	=	=	SYM
cana-4018	97	2	3	3	NUM
cana-4018	97	3	𝑔(𝑛(𝑊3	𝑔(𝑛(𝑊3	NOUN
cana-4018	97	4	)	)	PUNCT
cana-4018	97	5	)	)	PUNCT
cana-4018	98	1	=	=	SYM
cana-4018	98	2	1	1	NUM
cana-4018	98	3	𝑔(𝑛(𝑊4	𝑔(𝑛(𝑊4	NOUN
cana-4018	98	4	)	)	PUNCT
cana-4018	98	5	)	)	PUNCT
cana-4018	99	1	=	=	SYM
cana-4018	99	2	2	2	NUM
cana-4018	99	3	communications	communication	NOUN
cana-4018	99	4	on	on	ADP
cana-4018	99	5	applied	apply	VERB
cana-4018	99	6	nonlinear	nonlinear	ADJ
cana-4018	99	7	analysis	analysis	NOUN
cana-4018	99	8	issn	issn	NOUN
cana-4018	99	9	:	:	PUNCT
cana-4018	99	10	1074	1074	NUM
cana-4018	99	11	-	-	PUNCT
cana-4018	99	12	133x	133x	NUM
cana-4018	99	13	vol	vol	NOUN
cana-4018	99	14	32	32	NUM
cana-4018	99	15	no	no	NOUN
cana-4018	99	16	.	.	PUNCT
cana-4018	100	1	9s	9s	NUM
cana-4018	100	2	(	(	PUNCT
cana-4018	100	3	2025	2025	NUM
cana-4018	100	4	)	)	PUNCT
cana-4018	100	5	846	846	NUM
cana-4018	100	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	100	7	(	(	PUNCT
cana-4018	100	8	𝐸6	𝐸6	PROPN
cana-4018	100	9	)	)	PUNCT
cana-4018	100	10	(	(	PUNCT
cana-4018	100	11	136	136	NUM
cana-4018	100	12	0	0	NUM
cana-4018	100	13	0	0	NUM
cana-4018	100	14	0	0	NUM
cana-4018	101	1	64	64	NUM
cana-4018	101	2	0	0	NUM
cana-4018	101	3	0	0	NUM
cana-4018	101	4	0	0	NUM
cana-4018	101	5	631	631	NUM
cana-4018	101	6	)	)	PUNCT
cana-4018	101	7	(	(	PUNCT
cana-4018	101	8	166	166	NUM
cana-4018	101	9	0	0	NUM
cana-4018	101	10	0	0	NUM
cana-4018	101	11	0	0	NUM
cana-4018	101	12	0	0	NUM
cana-4018	101	13	0	0	NUM
cana-4018	101	14	0	0	NUM
cana-4018	101	15	829	829	NUM
cana-4018	101	16	0	0	NUM
cana-4018	101	17	0	0	NUM
cana-4018	101	18	0	0	NUM
cana-4018	101	19	0	0	NUM
cana-4018	101	20	0	0	NUM
cana-4018	101	21	0	0	NUM
cana-4018	102	1	64	64	NUM
cana-4018	102	2	0	0	NUM
cana-4018	102	3	0	0	NUM
cana-4018	102	4	0	0	NUM
cana-4018	102	5	0	0	NUM
cana-4018	102	6	0	0	NUM
cana-4018	102	7	0	0	NUM
cana-4018	102	8	631	631	NUM
cana-4018	102	9	0	0	NUM
cana-4018	102	10	0	0	NUM
cana-4018	102	11	0	0	NUM
cana-4018	102	12	0	0	NUM
cana-4018	102	13	0	0	NUM
cana-4018	102	14	0	0	NUM
cana-4018	102	15	46	46	NUM
cana-4018	102	16	0	0	NUM
cana-4018	102	17	0	0	NUM
cana-4018	102	18	0	0	NUM
cana-4018	102	19	0	0	NUM
cana-4018	102	20	0	0	NUM
cana-4018	102	21	0	0	NUM
cana-4018	102	22	571	571	NUM
cana-4018	102	23	)	)	PUNCT
cana-4018	102	24	(	(	PUNCT
cana-4018	102	25	10	10	NUM
cana-4018	102	26	)	)	PUNCT
cana-4018	102	27	(	(	PUNCT
cana-4018	102	28	10	10	NUM
cana-4018	102	29	0	0	NUM
cana-4018	102	30	0	0	NUM
cana-4018	102	31	0	0	NUM
cana-4018	102	32	571	571	NUM
cana-4018	102	33	0	0	NUM
cana-4018	102	34	0	0	NUM
cana-4018	102	35	0	0	NUM
cana-4018	102	36	31	31	NUM
cana-4018	102	37	)	)	PUNCT
cana-4018	102	38	(	(	PUNCT
cana-4018	102	39	𝐸7	𝐸7	NOUN
cana-4018	102	40	)	)	PUNCT
cana-4018	102	41	(	(	PUNCT
cana-4018	102	42	133	133	NUM
cana-4018	102	43	0	0	NUM
cana-4018	102	44	0	0	NUM
cana-4018	102	45	0	0	NUM
cana-4018	102	46	61	61	NUM
cana-4018	102	47	0	0	NUM
cana-4018	102	48	0	0	NUM
cana-4018	102	49	0	0	NUM
cana-4018	102	50	628	628	NUM
cana-4018	102	51	)	)	PUNCT
cana-4018	102	52	(	(	PUNCT
cana-4018	102	53	160	160	NUM
cana-4018	102	54	0	0	NUM
cana-4018	102	55	0	0	NUM
cana-4018	102	56	0	0	NUM
cana-4018	102	57	0	0	NUM
cana-4018	102	58	0	0	NUM
cana-4018	102	59	0	0	NUM
cana-4018	102	60	823	823	NUM
cana-4018	102	61	0	0	NUM
cana-4018	102	62	0	0	NUM
cana-4018	102	63	0	0	NUM
cana-4018	102	64	0	0	NUM
cana-4018	102	65	0	0	NUM
cana-4018	102	66	0	0	NUM
cana-4018	103	1	58	58	NUM
cana-4018	103	2	0	0	NUM
cana-4018	103	3	0	0	NUM
cana-4018	103	4	0	0	NUM
cana-4018	103	5	0	0	NUM
cana-4018	103	6	0	0	NUM
cana-4018	103	7	0	0	NUM
cana-4018	103	8	625	625	NUM
cana-4018	103	9	0	0	NUM
cana-4018	103	10	0	0	NUM
cana-4018	103	11	0	0	NUM
cana-4018	103	12	0	0	NUM
cana-4018	103	13	0	0	NUM
cana-4018	103	14	0	0	NUM
cana-4018	103	15	40	40	NUM
cana-4018	103	16	0	0	NUM
cana-4018	103	17	0	0	NUM
cana-4018	103	18	0	0	NUM
cana-4018	103	19	0	0	NUM
cana-4018	103	20	0	0	NUM
cana-4018	103	21	0	0	NUM
cana-4018	103	22	565	565	NUM
cana-4018	103	23	)	)	PUNCT
cana-4018	103	24	(	(	PUNCT
cana-4018	103	25	9	9	NUM
cana-4018	103	26	)	)	PUNCT
cana-4018	103	27	(	(	PUNCT
cana-4018	103	28	7	7	NUM
cana-4018	103	29	0	0	NUM
cana-4018	103	30	0	0	NUM
cana-4018	103	31	0	0	NUM
cana-4018	103	32	568	568	NUM
cana-4018	103	33	0	0	NUM
cana-4018	103	34	0	0	NUM
cana-4018	103	35	0	0	NUM
cana-4018	103	36	28	28	NUM
cana-4018	103	37	)	)	PUNCT
cana-4018	104	1	𝐸𝑖	𝐸𝑖	PROPN
cana-4018	104	2	(	(	PUNCT
cana-4018	104	3	133	133	NUM
cana-4018	104	4	61	61	NUM
cana-4018	104	5	628	628	NUM
cana-4018	104	6	)	)	PUNCT
cana-4018	104	7	(	(	PUNCT
cana-4018	104	8	160	160	NUM
cana-4018	104	9	823	823	NUM
cana-4018	104	10	58	58	NUM
cana-4018	104	11	625	625	NUM
cana-4018	104	12	40	40	NUM
cana-4018	104	13	565	565	NUM
cana-4018	104	14	)	)	PUNCT
cana-4018	104	15	(	(	PUNCT
cana-4018	104	16	9	9	NUM
cana-4018	104	17	)	)	PUNCT
cana-4018	104	18	(	(	PUNCT
cana-4018	104	19	7	7	NUM
cana-4018	104	20	568	568	NUM
cana-4018	104	21	28	28	NUM
cana-4018	104	22	)	)	PUNCT
cana-4018	104	23	table	table	NOUN
cana-4018	104	24	2	2	NUM
cana-4018	104	25	.	.	X
cana-4018	104	26	encryption	encryption	NOUN
cana-4018	104	27	for	for	ADP
cana-4018	104	28	“	"	PUNCT
cana-4018	104	29	she	she	PRON
cana-4018	104	30	drives	drive	VERB
cana-4018	104	31	a	a	DET
cana-4018	104	32	car	car	NOUN
cana-4018	104	33	”	"	PUNCT
cana-4018	104	34	decryption	decryption	NOUN
cana-4018	104	35	:	:	PUNCT
cana-4018	104	36	the	the	DET
cana-4018	104	37	following	follow	VERB
cana-4018	104	38	table	table	NOUN
cana-4018	104	39	presents	present	VERB
cana-4018	104	40	the	the	DET
cana-4018	104	41	decryption	decryption	NOUN
cana-4018	104	42	process	process	NOUN
cana-4018	104	43	.	.	PUNCT
cana-4018	105	1	𝐸𝑖	𝐸𝑖	PROPN
cana-4018	105	2	(	(	PUNCT
cana-4018	105	3	133	133	NUM
cana-4018	105	4	61	61	NUM
cana-4018	105	5	628	628	NUM
cana-4018	105	6	)	)	PUNCT
cana-4018	105	7	(	(	PUNCT
cana-4018	105	8	160	160	NUM
cana-4018	105	9	823	823	NUM
cana-4018	105	10	58	58	NUM
cana-4018	105	11	625	625	NUM
cana-4018	105	12	40	40	NUM
cana-4018	105	13	565	565	NUM
cana-4018	105	14	)	)	PUNCT
cana-4018	105	15	(	(	PUNCT
cana-4018	105	16	9	9	NUM
cana-4018	105	17	)	)	PUNCT
cana-4018	105	18	(	(	PUNCT
cana-4018	105	19	7	7	NUM
cana-4018	105	20	568	568	NUM
cana-4018	105	21	28	28	NUM
cana-4018	105	22	)	)	PUNCT
cana-4018	105	23	𝑘𝑖	𝑘𝑖	NOUN
cana-4018	105	24	𝑘1	𝑘1	NOUN
cana-4018	105	25	=	=	SYM
cana-4018	105	26	3	3	NUM
cana-4018	105	27	𝑘2	𝑘2	NOUN
cana-4018	105	28	=	=	PUNCT
cana-4018	105	29	6	6	NUM
cana-4018	105	30	𝑘3	𝑘3	NOUN
cana-4018	105	31	=	=	SYM
cana-4018	105	32	1	1	NUM
cana-4018	105	33	𝑘4	𝑘4	NOUN
cana-4018	105	34	=	=	SYM
cana-4018	105	35	3	3	NUM
cana-4018	105	36	(	(	PUNCT
cana-4018	105	37	𝐷1	𝐷1	PROPN
cana-4018	105	38	)	)	PUNCT
cana-4018	105	39	(	(	PUNCT
cana-4018	105	40	136	136	NUM
cana-4018	105	41	64	64	NUM
cana-4018	105	42	631	631	NUM
cana-4018	105	43	)	)	PUNCT
cana-4018	105	44	(	(	PUNCT
cana-4018	105	45	166	166	NUM
cana-4018	105	46	829	829	NUM
cana-4018	105	47	64	64	NUM
cana-4018	105	48	631	631	NUM
cana-4018	105	49	46	46	NUM
cana-4018	105	50	571	571	NUM
cana-4018	105	51	)	)	PUNCT
cana-4018	105	52	(	(	PUNCT
cana-4018	105	53	10	10	NUM
cana-4018	105	54	)	)	PUNCT
cana-4018	105	55	(	(	PUNCT
cana-4018	105	56	10	10	NUM
cana-4018	105	57	571	571	NUM
cana-4018	105	58	31	31	NUM
cana-4018	105	59	)	)	PUNCT
cana-4018	105	60	(	(	PUNCT
cana-4018	105	61	𝐷2	𝐷2	PROPN
cana-4018	105	62	)	)	PUNCT
cana-4018	105	63	𝑔(𝑘1	𝑔(𝑘1	NOUN
cana-4018	105	64	)	)	PUNCT
cana-4018	105	65	=	=	SYM
cana-4018	105	66	2	2	NUM
cana-4018	105	67	𝑔(𝑘2	𝑔(𝑘2	NOUN
cana-4018	105	68	)	)	PUNCT
cana-4018	105	69	=	=	SYM
cana-4018	105	70	3	3	NUM
cana-4018	105	71	𝑔(𝑘3	𝑔(𝑘3	NOUN
cana-4018	105	72	)	)	PUNCT
cana-4018	105	73	=	=	SYM
cana-4018	105	74	1	1	NUM
cana-4018	105	75	𝑔(𝑘4	𝑔(𝑘4	NOUN
cana-4018	105	76	)	)	PUNCT
cana-4018	105	77	=	=	SYM
cana-4018	105	78	2	2	NUM
cana-4018	105	79	(	(	PUNCT
cana-4018	105	80	𝐷3	𝐷3	PROPN
cana-4018	105	81	)	)	PUNCT
cana-4018	105	82	(	(	PUNCT
cana-4018	105	83	631	631	NUM
cana-4018	105	84	136	136	NUM
cana-4018	105	85	64	64	NUM
cana-4018	105	86	)	)	PUNCT
cana-4018	105	87	(	(	PUNCT
cana-4018	105	88	46	46	NUM
cana-4018	105	89	571	571	NUM
cana-4018	105	90	166	166	NUM
cana-4018	105	91	829	829	NUM
cana-4018	105	92	64	64	NUM
cana-4018	105	93	631	631	NUM
cana-4018	105	94	)	)	PUNCT
cana-4018	105	95	(	(	PUNCT
cana-4018	105	96	10	10	NUM
cana-4018	105	97	)	)	PUNCT
cana-4018	105	98	(	(	PUNCT
cana-4018	105	99	31	31	NUM
cana-4018	105	100	10	10	NUM
cana-4018	105	101	571	571	NUM
cana-4018	105	102	)	)	PUNCT
cana-4018	105	103	(	(	PUNCT
cana-4018	105	104	𝐷4	𝐷4	NOUN
cana-4018	105	105	)	)	PUNCT
cana-4018	105	106	𝑠11	𝑠11	ADJ
cana-4018	105	107	𝑠12	𝑠12	NOUN
cana-4018	105	108	𝑠13	𝑠13	NOUN
cana-4018	105	109	𝑠1𝑗	𝑠1𝑗	NOUN
cana-4018	105	110	631	631	NUM
cana-4018	105	111	136	136	NUM
cana-4018	105	112	64	64	NUM
cana-4018	105	113	𝑦(𝑠1𝑗	𝑦(𝑠1𝑗	NUM
cana-4018	105	114	)	)	PUNCT
cana-4018	105	115	421	421	NUM
cana-4018	105	116	91	91	NUM
cana-4018	105	117	43	43	NUM
cana-4018	105	118	𝑠21	𝑠21	NOUN
cana-4018	105	119	𝑠22	𝑠22	NOUN
cana-4018	105	120	𝑠23	𝑠23	NUM
cana-4018	105	121	𝑠24	𝑠24	VERB
cana-4018	105	122	𝑠25	𝑠25	NOUN
cana-4018	105	123	𝑠26	𝑠26	NOUN
cana-4018	105	124	𝑠2𝑗	𝑠2𝑗	PUNCT
cana-4018	105	125	46	46	NUM
cana-4018	105	126	571	571	NUM
cana-4018	105	127	166	166	NUM
cana-4018	105	128	829	829	NUM
cana-4018	105	129	64	64	NUM
cana-4018	105	130	631	631	NUM
cana-4018	105	131	𝑦(𝑠2𝑗	𝑦(𝑠2𝑗	NOUN
cana-4018	105	132	)	)	PUNCT
cana-4018	105	133	31	31	NUM
cana-4018	105	134	381	381	NUM
cana-4018	105	135	111	111	NUM
cana-4018	105	136	553	553	NUM
cana-4018	105	137	43	43	NUM
cana-4018	105	138	421	421	NUM
cana-4018	105	139	𝑠31	𝑠31	NOUN
cana-4018	105	140	𝑠3𝑗	𝑠3𝑗	PROPN
cana-4018	105	141	10	10	NUM
cana-4018	105	142	𝑦(𝑠3𝑗	𝑦(𝑠3𝑗	NOUN
cana-4018	105	143	)	)	PUNCT
cana-4018	105	144	7	7	NUM
cana-4018	105	145	𝑠41	𝑠41	NOUN
cana-4018	105	146	𝑠42	𝑠42	PROPN
cana-4018	105	147	𝑠43	𝑠43	NOUN
cana-4018	105	148	𝑠4𝑗	𝑠4𝑗	PROPN
cana-4018	105	149	31	31	NUM
cana-4018	105	150	10	10	NUM
cana-4018	105	151	571	571	NUM
cana-4018	105	152	𝑦(𝑠4𝑗	𝑦(𝑠4𝑗	NOUN
cana-4018	105	153	)	)	PUNCT
cana-4018	105	154	21	21	NUM
cana-4018	105	155	7	7	NUM
cana-4018	105	156	381	381	NUM
cana-4018	105	157	(	(	PUNCT
cana-4018	105	158	𝐷5	𝐷5	PROPN
cana-4018	105	159	)	)	PUNCT
cana-4018	105	160	she	she	PRON
cana-4018	105	161	drives	drive	VERB
cana-4018	105	162	a	a	DET
cana-4018	105	163	car	car	NOUN
cana-4018	105	164	table	table	NOUN
cana-4018	105	165	3	3	NUM
cana-4018	105	166	.	.	X
cana-4018	105	167	decryption	decryption	NOUN
cana-4018	105	168	for	for	ADP
cana-4018	105	169	“	"	PUNCT
cana-4018	105	170	she	she	PRON
cana-4018	105	171	drives	drive	VERB
cana-4018	105	172	a	a	DET
cana-4018	105	173	car	car	NOUN
cana-4018	105	174	”	"	PUNCT
cana-4018	105	175	communications	communication	NOUN
cana-4018	105	176	on	on	ADP
cana-4018	105	177	applied	apply	VERB
cana-4018	105	178	nonlinear	nonlinear	ADJ
cana-4018	105	179	analysis	analysis	NOUN
cana-4018	105	180	issn	issn	NOUN
cana-4018	105	181	:	:	PUNCT
cana-4018	105	182	1074	1074	NUM
cana-4018	105	183	-	-	PUNCT
cana-4018	105	184	133x	133x	NUM
cana-4018	105	185	vol	vol	NOUN
cana-4018	105	186	32	32	NUM
cana-4018	105	187	no	no	NOUN
cana-4018	105	188	.	.	PUNCT
cana-4018	106	1	9s	9s	NUM
cana-4018	106	2	(	(	PUNCT
cana-4018	106	3	2025	2025	NUM
cana-4018	106	4	)	)	PUNCT
cana-4018	106	5	847	847	NUM
cana-4018	106	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	106	7	3	3	X
cana-4018	106	8	.	.	PUNCT
cana-4018	107	1	r	r	NOUN
cana-4018	107	2	code	code	NOUN
cana-4018	107	3	for	for	ADP
cana-4018	107	4	encryption	encryption	NOUN
cana-4018	107	5	and	and	CCONJ
cana-4018	107	6	decryption	decryption	NOUN
cana-4018	107	7	of	of	ADP
cana-4018	107	8	words	word	NOUN
cana-4018	107	9	with	with	ADP
cana-4018	107	10	four	four	NUM
cana-4018	107	11	letters	letter	NOUN
cana-4018	107	12	figure	figure	VERB
cana-4018	107	13	1	1	NUM
cana-4018	107	14	.	.	PUNCT
cana-4018	107	15	code	code	NOUN
cana-4018	107	16	for	for	ADP
cana-4018	107	17	encryption	encryption	NOUN
cana-4018	107	18	communications	communication	NOUN
cana-4018	107	19	on	on	ADP
cana-4018	107	20	applied	apply	VERB
cana-4018	107	21	nonlinear	nonlinear	ADJ
cana-4018	107	22	analysis	analysis	NOUN
cana-4018	107	23	issn	issn	NOUN
cana-4018	107	24	:	:	PUNCT
cana-4018	107	25	1074	1074	NUM
cana-4018	107	26	-	-	PUNCT
cana-4018	107	27	133x	133x	NUM
cana-4018	107	28	vol	vol	NOUN
cana-4018	107	29	32	32	NUM
cana-4018	107	30	no	no	NOUN
cana-4018	107	31	.	.	PUNCT
cana-4018	108	1	9s	9s	NUM
cana-4018	108	2	(	(	PUNCT
cana-4018	108	3	2025	2025	NUM
cana-4018	108	4	)	)	PUNCT
cana-4018	108	5	848	848	NUM
cana-4018	108	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	108	7	figure	figure	NOUN
cana-4018	108	8	2	2	NUM
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cana-4018	108	10	continuation	continuation	NOUN
cana-4018	108	11	of	of	ADP
cana-4018	108	12	figure	figure	NOUN
cana-4018	108	13	1	1	NUM
cana-4018	108	14	sample	sample	NOUN
cana-4018	108	15	output	output	NOUN
cana-4018	108	16	for	for	ADP
cana-4018	108	17	encryption	encryption	NOUN
cana-4018	108	18	figure	figure	NOUN
cana-4018	108	19	3	3	NUM
cana-4018	108	20	.	.	PUNCT
cana-4018	108	21	encryption	encryption	NOUN
cana-4018	108	22	of	of	ADP
cana-4018	108	23	rock	rock	NOUN
cana-4018	108	24	communications	communication	NOUN
cana-4018	108	25	on	on	ADP
cana-4018	108	26	applied	apply	VERB
cana-4018	108	27	nonlinear	nonlinear	ADJ
cana-4018	108	28	analysis	analysis	NOUN
cana-4018	108	29	issn	issn	NOUN
cana-4018	108	30	:	:	PUNCT
cana-4018	108	31	1074	1074	NUM
cana-4018	108	32	-	-	PUNCT
cana-4018	108	33	133x	133x	NUM
cana-4018	108	34	vol	vol	NOUN
cana-4018	108	35	32	32	NUM
cana-4018	108	36	no	no	NOUN
cana-4018	108	37	.	.	PUNCT
cana-4018	109	1	9s	9s	NUM
cana-4018	109	2	(	(	PUNCT
cana-4018	109	3	2025	2025	NUM
cana-4018	109	4	)	)	PUNCT
cana-4018	109	5	849	849	NUM
cana-4018	109	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	109	7	figure	figure	NOUN
cana-4018	109	8	4	4	NUM
cana-4018	109	9	.	.	PUNCT
cana-4018	109	10	code	code	NOUN
cana-4018	109	11	for	for	ADP
cana-4018	109	12	decryption	decryption	NOUN
cana-4018	109	13	output	output	NOUN
cana-4018	109	14	for	for	ADP
cana-4018	109	15	decrypting	decrypt	VERB
cana-4018	109	16	“	"	PUNCT
cana-4018	109	17	rock	rock	NOUN
cana-4018	109	18	”	"	PUNCT
cana-4018	109	19	figure	figure	NOUN
cana-4018	109	20	5	5	NUM
cana-4018	109	21	.	.	PUNCT
cana-4018	109	22	decryption	decryption	NOUN
cana-4018	109	23	of	of	ADP
cana-4018	109	24	rock	rock	NOUN
cana-4018	109	25	communications	communication	NOUN
cana-4018	109	26	on	on	ADP
cana-4018	109	27	applied	apply	VERB
cana-4018	109	28	nonlinear	nonlinear	ADJ
cana-4018	109	29	analysis	analysis	NOUN
cana-4018	109	30	issn	issn	NOUN
cana-4018	109	31	:	:	PUNCT
cana-4018	109	32	1074	1074	NUM
cana-4018	109	33	-	-	PUNCT
cana-4018	109	34	133x	133x	NUM
cana-4018	109	35	vol	vol	NOUN
cana-4018	109	36	32	32	NUM
cana-4018	109	37	no	no	NOUN
cana-4018	109	38	.	.	PUNCT
cana-4018	110	1	9s	9s	NUM
cana-4018	110	2	(	(	PUNCT
cana-4018	110	3	2025	2025	NUM
cana-4018	110	4	)	)	PUNCT
cana-4018	110	5	850	850	NUM
cana-4018	110	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4018	110	7	4	4	NUM
cana-4018	110	8	.	.	X
cana-4018	110	9	conclusion	conclusion	NOUN
cana-4018	110	10	this	this	DET
cana-4018	110	11	paper	paper	NOUN
cana-4018	110	12	presents	present	VERB
cana-4018	110	13	encryption	encryption	NOUN
cana-4018	110	14	and	and	CCONJ
cana-4018	110	15	decryption	decryption	NOUN
cana-4018	110	16	algorithms	algorithm	NOUN
cana-4018	110	17	employing	employ	VERB
cana-4018	110	18	positive	positive	ADJ
cana-4018	110	19	integer	integer	NOUN
cana-4018	110	20	-	-	PUNCT
cana-4018	110	21	valued	value	VERB
cana-4018	110	22	functions	function	NOUN
cana-4018	110	23	and	and	CCONJ
cana-4018	110	24	cyclic	cyclic	ADJ
cana-4018	110	25	symmetric	symmetric	ADJ
cana-4018	110	26	matrices	matrix	NOUN
cana-4018	110	27	.	.	PUNCT
cana-4018	111	1	these	these	DET
cana-4018	111	2	algorithms	algorithm	NOUN
cana-4018	111	3	are	be	AUX
cana-4018	111	4	successfully	successfully	ADV
cana-4018	111	5	verified	verify	VERB
cana-4018	111	6	by	by	ADP
cana-4018	111	7	means	mean	NOUN
cana-4018	111	8	of	of	ADP
cana-4018	111	9	examples	example	NOUN
cana-4018	111	10	and	and	CCONJ
cana-4018	111	11	r	r	NOUN
cana-4018	111	12	codes	code	NOUN
cana-4018	111	13	for	for	ADP
cana-4018	111	14	words	word	NOUN
cana-4018	111	15	with	with	ADP
cana-4018	111	16	four	four	NUM
cana-4018	111	17	letters	letter	NOUN
cana-4018	111	18	.	.	PUNCT
cana-4018	112	1	one	one	PRON
cana-4018	112	2	may	may	AUX
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cana-4018	112	4	those	those	DET
cana-4018	112	5	r	r	NOUN
cana-4018	112	6	codes	code	NOUN
cana-4018	112	7	for	for	ADP
cana-4018	112	8	more	more	ADJ
cana-4018	112	9	than	than	ADP
cana-4018	112	10	four	four	NUM
cana-4018	112	11	lettered	lettered	ADJ
cana-4018	112	12	word	word	NOUN
cana-4018	112	13	.	.	PUNCT
cana-4018	113	1	also	also	ADV
cana-4018	113	2	,	,	PUNCT
cana-4018	113	3	this	this	DET
cana-4018	113	4	article	article	NOUN
cana-4018	113	5	paves	pave	VERB
cana-4018	113	6	the	the	DET
cana-4018	113	7	way	way	NOUN
cana-4018	113	8	to	to	PART
cana-4018	113	9	create	create	VERB
cana-4018	113	10	new	new	ADJ
cana-4018	113	11	such	such	ADJ
cana-4018	113	12	algorithms	algorithm	NOUN
cana-4018	113	13	by	by	ADP
cana-4018	113	14	effectively	effectively	ADV
cana-4018	113	15	changing	change	VERB
cana-4018	113	16	the	the	DET
cana-4018	113	17	arithmetic	arithmetic	ADJ
cana-4018	113	18	functions	function	NOUN
cana-4018	113	19	given	give	VERB
cana-4018	113	20	here	here	ADV
cana-4018	113	21	.	.	PUNCT
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cana-4018	114	2	[	[	X
cana-4018	114	3	1	1	NUM
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cana-4018	114	7	a.	a.	NOUN
cana-4018	114	8	(	(	PUNCT
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cana-4018	114	10	)	)	PUNCT
cana-4018	114	11	.	.	PUNCT
cana-4018	115	1	on	on	ADP
cana-4018	115	2	the	the	DET
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cana-4018	115	4	,	,	PUNCT
cana-4018	115	5	pelllucas	pellluca	NOUN
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cana-4018	115	8	pell	pell	NOUN
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cana-4018	115	12	method	method	NOUN
cana-4018	115	13	.	.	PUNCT
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cana-4018	116	2	mathematical	mathematical	ADJ
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cana-4018	116	6	)	)	PUNCT
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cana-4018	116	11	.	.	PUNCT
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cana-4018	117	11	,	,	PUNCT
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cana-4018	117	18	)	)	PUNCT
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cana-4018	118	2	algorithm	algorithm	NOUN
cana-4018	118	3	involving	involve	VERB
cana-4018	118	4	the	the	DET
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cana-4018	118	6	𝑄𝑝	𝑄𝑝	NOUN
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cana-4018	119	10	-	-	SYM
cana-4018	119	11	538	538	NUM
cana-4018	119	12	.	.	PUNCT
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cana-4018	120	2	3	3	NUM
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cana-4018	122	9	10(1	10(1	NUM
cana-4018	122	10	)	)	PUNCT
cana-4018	122	11	,	,	PUNCT
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cana-4018	122	13	-	-	SYM
cana-4018	122	14	8	8	NUM
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cana-4018	123	1	[	[	X
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cana-4018	123	20	ö.	ö.	PROPN
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cana-4018	123	24	)	)	PUNCT
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cana-4018	124	3	coding	coding	NOUN
cana-4018	124	4	/	/	SYM
cana-4018	124	5	decoding	decode	VERB
cana-4018	124	6	algorithm	algorithm	NOUN
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cana-4018	124	8	fibonacci	fibonacci	NOUN
cana-4018	124	9	numbers	number	NOUN
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cana-4018	125	1	discrete	discrete	ADJ
cana-4018	125	2	mathematics	mathematic	NOUN
cana-4018	125	3	,	,	PUNCT
cana-4018	125	4	algorithms	algorithm	NOUN
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cana-4018	125	8	10(2	10(2	NUM
cana-4018	125	9	)	)	PUNCT
cana-4018	125	10	,	,	PUNCT
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cana-4018	126	11	,	,	PUNCT
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cana-4018	126	13	,	,	PUNCT
cana-4018	126	14	j.	j.	PROPN
cana-4018	126	15	,	,	PUNCT
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cana-4018	126	17	padmashree	padmashree	PROPN
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cana-4018	126	19	j.	j.	PROPN
cana-4018	126	20	(	(	PUNCT
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cana-4018	126	22	)	)	PUNCT
cana-4018	126	23	.	.	PUNCT
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cana-4018	127	3	decryption	decryption	NOUN
cana-4018	127	4	algorithm	algorithm	NOUN
cana-4018	127	5	using	use	VERB
cana-4018	127	6	algebraic	algebraic	ADJ
cana-4018	127	7	matrix	matrix	NOUN
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cana-4018	128	2	of	of	ADP
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cana-4018	128	4	:	:	PUNCT
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cana-4018	128	6	series	series	NOUN
cana-4018	128	7	,	,	PUNCT
cana-4018	128	8	1000(1	1000(1	PROPN
cana-4018	128	9	)	)	PUNCT
cana-4018	128	10	,	,	PUNCT
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cana-4018	129	2	6	6	NUM
cana-4018	129	3	]	]	X
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cana-4018	129	5	,	,	PUNCT
cana-4018	129	6	s.	s.	PROPN
cana-4018	129	7	,	,	PUNCT
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cana-4018	129	9	,	,	PUNCT
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cana-4018	129	11	,	,	PUNCT
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cana-4018	129	19	)	)	PUNCT
cana-4018	129	20	.	.	PUNCT
cana-4018	130	1	a	a	DET
cana-4018	130	2	new	new	ADJ
cana-4018	130	3	application	application	NOUN
cana-4018	130	4	to	to	ADP
cana-4018	130	5	coding	code	VERB
cana-4018	130	6	theory	theory	NOUN
cana-4018	130	7	via	via	ADP
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cana-4018	130	9	and	and	CCONJ
cana-4018	130	10	lucas	lucas	PROPN
cana-4018	130	11	numbers	number	NOUN
cana-4018	130	12	.	.	PUNCT
cana-4018	131	1	mathematical	mathematical	ADJ
cana-4018	131	2	sciences	science	NOUN
cana-4018	131	3	and	and	CCONJ
cana-4018	131	4	applications	application	NOUN
cana-4018	131	5	e	e	NOUN
cana-4018	131	6	-	-	NOUN
cana-4018	131	7	notes	note	NOUN
cana-4018	131	8	,	,	PUNCT
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cana-4018	131	10	)	)	PUNCT
cana-4018	131	11	,	,	PUNCT
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cana-4018	131	13	-	-	SYM
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cana-4018	131	15	.	.	PUNCT
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cana-4018	132	2	7	7	NUM
cana-4018	132	3	]	]	SYM
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cana-4018	132	16	(	(	PUNCT
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cana-4018	132	18	)	)	PUNCT
cana-4018	132	19	.	.	PUNCT
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cana-4018	133	2	based	base	VERB
cana-4018	133	3	on	on	ADP
cana-4018	133	4	the	the	DET
cana-4018	133	5	matrices	matrix	NOUN
cana-4018	133	6	.	.	PUNCT
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cana-4018	134	2	,	,	PUNCT
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cana-4018	134	4	)	)	PUNCT
cana-4018	134	5	,	,	PUNCT
cana-4018	134	6	75	75	NUM
cana-4018	134	7	-	-	SYM
cana-4018	134	8	83	83	NUM
cana-4018	134	9	.	.	PUNCT