id sid tid token lemma pos cana-1173 1 1 communications communication NOUN cana-1173 1 2 on on ADP cana-1173 1 3 applied apply VERB cana-1173 1 4 nonlinear nonlinear ADJ cana-1173 1 5 analysis analysis NOUN cana-1173 1 6 issn issn NOUN cana-1173 1 7 : : PUNCT cana-1173 1 8 1074 1074 NUM cana-1173 1 9 - - PUNCT cana-1173 1 10 133x 133x NUM cana-1173 1 11 vol vol NOUN cana-1173 1 12 31 31 NUM cana-1173 1 13 no no NOUN cana-1173 1 14 . . PUNCT cana-1173 2 1 6s 6s NUM cana-1173 2 2 ( ( PUNCT cana-1173 2 3 2024 2024 NUM cana-1173 2 4 ) ) PUNCT cana-1173 2 5 143 143 NUM cana-1173 2 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 2 7 encryption encryption NOUN cana-1173 2 8 and and CCONJ cana-1173 2 9 decryption decryption NOUN cana-1173 2 10 using use VERB cana-1173 2 11 hill hill NOUN cana-1173 2 12 cipher cipher ADJ cana-1173 2 13 and and CCONJ cana-1173 2 14 integral integral ADJ cana-1173 2 15 transforms transform VERB cana-1173 2 16 gobburi gobburi PROPN cana-1173 2 17 rekha1 rekha1 PROPN cana-1173 2 18 , , PUNCT cana-1173 2 19 v. v. ADP cana-1173 2 20 srinivas2 srinivas2 NOUN cana-1173 2 21 1 1 NUM cana-1173 2 22 department department NOUN cana-1173 2 23 of of ADP cana-1173 2 24 humanities humanity NOUN cana-1173 2 25 and and CCONJ cana-1173 2 26 sciences science NOUN cana-1173 2 27 , , PUNCT cana-1173 2 28 malla malla PROPN cana-1173 2 29 reddy reddy PROPN cana-1173 2 30 college college PROPN cana-1173 2 31 of of ADP cana-1173 2 32 engineering engineering NOUN cana-1173 2 33 and and CCONJ cana-1173 2 34 technology technology NOUN cana-1173 2 35 2 2 NUM cana-1173 2 36 department department NOUN cana-1173 2 37 of of ADP cana-1173 2 38 mathematics mathematics PROPN cana-1173 2 39 , , PUNCT cana-1173 2 40 osmania osmania PROPN cana-1173 2 41 university university NOUN cana-1173 2 42 article article NOUN cana-1173 2 43 history history NOUN cana-1173 2 44 : : PUNCT cana-1173 2 45 received receive VERB cana-1173 2 46 : : PUNCT cana-1173 2 47 26 26 NUM cana-1173 2 48 - - SYM cana-1173 2 49 05 05 NUM cana-1173 2 50 - - PUNCT cana-1173 2 51 2024 2024 NUM cana-1173 2 52 revised revise VERB cana-1173 2 53 : : PUNCT cana-1173 2 54 16 16 NUM cana-1173 2 55 - - SYM cana-1173 2 56 07 07 NUM cana-1173 2 57 - - PUNCT cana-1173 2 58 2024 2024 NUM cana-1173 2 59 accepted accept VERB cana-1173 2 60 : : PUNCT cana-1173 2 61 27 27 NUM cana-1173 2 62 - - SYM cana-1173 2 63 07 07 NUM cana-1173 2 64 - - PUNCT cana-1173 2 65 2024 2024 NUM cana-1173 2 66 abstract abstract NOUN cana-1173 2 67 : : PUNCT cana-1173 2 68 we we PRON cana-1173 2 69 know know VERB cana-1173 2 70 that that DET cana-1173 2 71 hill hill NOUN cana-1173 2 72 cipher cipher ADJ cana-1173 2 73 is be AUX cana-1173 2 74 one one NUM cana-1173 2 75 of of ADP cana-1173 2 76 the the DET cana-1173 2 77 regular regular ADJ cana-1173 2 78 methods method NOUN cana-1173 2 79 that that PRON cana-1173 2 80 is be AUX cana-1173 2 81 used use VERB cana-1173 2 82 in in ADP cana-1173 2 83 cryptography cryptography NOUN cana-1173 2 84 for for ADP cana-1173 2 85 encryption encryption NOUN cana-1173 2 86 and and CCONJ cana-1173 2 87 decryption decryption NOUN cana-1173 2 88 of of ADP cana-1173 2 89 data datum NOUN cana-1173 2 90 using use VERB cana-1173 2 91 modular modular ADJ cana-1173 2 92 arithmetic arithmetic NOUN cana-1173 2 93 under under ADP cana-1173 2 94 different different ADJ cana-1173 2 95 modulus modulus NOUN cana-1173 2 96 . . PUNCT cana-1173 3 1 moreover moreover ADV cana-1173 3 2 , , PUNCT cana-1173 3 3 we we PRON cana-1173 3 4 have have AUX cana-1173 3 5 seen see VERB cana-1173 3 6 results result NOUN cana-1173 3 7 using use VERB cana-1173 3 8 some some DET cana-1173 3 9 integral integral ADJ cana-1173 3 10 transforms transform NOUN cana-1173 3 11 like like ADP cana-1173 3 12 laplace laplace NOUN cana-1173 3 13 transforms transform VERB cana-1173 3 14 , , PUNCT cana-1173 3 15 aboodh aboodh PROPN cana-1173 3 16 transforms transform VERB cana-1173 3 17 and and CCONJ cana-1173 3 18 many many ADJ cana-1173 3 19 more more ADJ cana-1173 3 20 . . PUNCT cana-1173 4 1 this this DET cana-1173 4 2 paper paper NOUN cana-1173 4 3 extracts extract VERB cana-1173 4 4 the the DET cana-1173 4 5 result result NOUN cana-1173 4 6 of of ADP cana-1173 4 7 dual dual ADJ cana-1173 4 8 encryption encryption NOUN cana-1173 4 9 and and CCONJ cana-1173 4 10 decryption decryption NOUN cana-1173 4 11 with with ADP cana-1173 4 12 a a DET cana-1173 4 13 combination combination NOUN cana-1173 4 14 of of ADP cana-1173 4 15 hill hill NOUN cana-1173 4 16 cipher cipher ADJ cana-1173 4 17 and and CCONJ cana-1173 4 18 few few ADJ cana-1173 4 19 integral integral ADJ cana-1173 4 20 transforms transform NOUN cana-1173 4 21 . . PUNCT cana-1173 5 1 introduction introduction NOUN cana-1173 5 2 : : PUNCT cana-1173 5 3 in in ADP cana-1173 5 4 many many ADJ cana-1173 5 5 circumstances circumstance NOUN cana-1173 5 6 , , PUNCT cana-1173 5 7 the the DET cana-1173 5 8 sender sender NOUN cana-1173 5 9 wants want VERB cana-1173 5 10 to to PART cana-1173 5 11 keep keep VERB cana-1173 5 12 the the DET cana-1173 5 13 message message NOUN cana-1173 5 14 private private ADJ cana-1173 5 15 from from ADP cana-1173 5 16 the the DET cana-1173 5 17 public public NOUN cana-1173 5 18 or or CCONJ cana-1173 5 19 from from ADP cana-1173 5 20 unauthorized unauthorized ADJ cana-1173 5 21 users user NOUN cana-1173 5 22 . . PUNCT cana-1173 6 1 here here ADV cana-1173 6 2 , , PUNCT cana-1173 6 3 we we PRON cana-1173 6 4 combine combine VERB cana-1173 6 5 hill hill NOUN cana-1173 6 6 cipher cipher ADJ cana-1173 6 7 with with ADP cana-1173 6 8 laplace laplace NOUN cana-1173 6 9 and and CCONJ cana-1173 6 10 kamal kamal PROPN cana-1173 6 11 transforms transform VERB cana-1173 6 12 to to PART cana-1173 6 13 encrypt encrypt VERB cana-1173 6 14 the the DET cana-1173 6 15 message message NOUN cana-1173 6 16 and and CCONJ cana-1173 6 17 apply apply VERB cana-1173 6 18 their their PRON cana-1173 6 19 inverse inverse NOUN cana-1173 6 20 transforms transform VERB cana-1173 6 21 to to PART cana-1173 6 22 decrypt decrypt VERB cana-1173 6 23 it it PRON cana-1173 6 24 . . PUNCT cana-1173 7 1 in in ADP cana-1173 7 2 contrast contrast NOUN cana-1173 7 3 to to ADP cana-1173 7 4 cipher cipher ADJ cana-1173 7 5 text text NOUN cana-1173 7 6 , , PUNCT cana-1173 7 7 which which PRON cana-1173 7 8 is be AUX cana-1173 7 9 a a DET cana-1173 7 10 coded code VERB cana-1173 7 11 version version NOUN cana-1173 7 12 of of ADP cana-1173 7 13 plaintext plaintext NOUN cana-1173 7 14 , , PUNCT cana-1173 7 15 the the DET cana-1173 7 16 original original ADJ cana-1173 7 17 message message NOUN cana-1173 7 18 written write VERB cana-1173 7 19 by by ADP cana-1173 7 20 the the DET cana-1173 7 21 user user NOUN cana-1173 7 22 is be AUX cana-1173 7 23 referred refer VERB cana-1173 7 24 to to ADP cana-1173 7 25 as as ADP cana-1173 7 26 plaintext plaintext NOUN cana-1173 7 27 . . PUNCT cana-1173 8 1 objectives objective NOUN cana-1173 8 2 : : PUNCT cana-1173 8 3 in in ADP cana-1173 8 4 this this DET cana-1173 8 5 paper paper NOUN cana-1173 8 6 , , PUNCT cana-1173 8 7 we we PRON cana-1173 8 8 focus focus VERB cana-1173 8 9 on on ADP cana-1173 8 10 two two NUM cana-1173 8 11 stages stage NOUN cana-1173 8 12 of of ADP cana-1173 8 13 encryption encryption NOUN cana-1173 8 14 and and CCONJ cana-1173 8 15 two two NUM cana-1173 8 16 stages stage NOUN cana-1173 8 17 of of ADP cana-1173 8 18 decryption decryption NOUN cana-1173 8 19 under under ADP cana-1173 8 20 modulo modulo NOUN cana-1173 8 21 255 255 NUM cana-1173 8 22 . . PUNCT cana-1173 9 1 methods method NOUN cana-1173 9 2 : : PUNCT cana-1173 9 3 using use VERB cana-1173 9 4 hill hill NOUN cana-1173 9 5 cipher cipher ADJ cana-1173 9 6 with with ADP cana-1173 9 7 different different ADJ cana-1173 9 8 transformation transformation NOUN cana-1173 9 9 techniques technique NOUN cana-1173 9 10 , , PUNCT cana-1173 9 11 we we PRON cana-1173 9 12 have have AUX cana-1173 9 13 encrypted encrypt VERB cana-1173 9 14 and and CCONJ cana-1173 9 15 decrypted decrypt VERB cana-1173 9 16 the the DET cana-1173 9 17 data datum NOUN cana-1173 9 18 . . PUNCT cana-1173 10 1 one one NUM cana-1173 10 2 is be AUX cana-1173 10 3 hill hill NOUN cana-1173 10 4 cipher cipher ADJ cana-1173 10 5 with with ADP cana-1173 10 6 laplace laplace NOUN cana-1173 10 7 transform transform NOUN cana-1173 10 8 technique technique NOUN cana-1173 10 9 while while SCONJ cana-1173 10 10 the the DET cana-1173 10 11 other other ADJ cana-1173 10 12 is be AUX cana-1173 10 13 hill hill NOUN cana-1173 10 14 cipher cipher ADJ cana-1173 10 15 with with ADP cana-1173 10 16 kamal kamal PROPN cana-1173 10 17 transform transform NOUN cana-1173 10 18 technique technique NOUN cana-1173 10 19 . . PUNCT cana-1173 11 1 results result NOUN cana-1173 11 2 : : PUNCT cana-1173 11 3 in in ADP cana-1173 11 4 this this DET cana-1173 11 5 paper paper NOUN cana-1173 11 6 , , PUNCT cana-1173 11 7 we we PRON cana-1173 11 8 see see VERB cana-1173 11 9 that that SCONJ cana-1173 11 10 the the DET cana-1173 11 11 original original ADJ cana-1173 11 12 text text NOUN cana-1173 11 13 is be AUX cana-1173 11 14 transformed transform VERB cana-1173 11 15 to to ADP cana-1173 11 16 cipher cipher ADJ cana-1173 11 17 text text NOUN cana-1173 11 18 which which PRON cana-1173 11 19 could could AUX cana-1173 11 20 be be AUX cana-1173 11 21 retrievable retrievable ADJ cana-1173 11 22 using use VERB cana-1173 11 23 some some DET cana-1173 11 24 techniques technique NOUN cana-1173 11 25 . . PUNCT cana-1173 12 1 conclusions conclusion NOUN cana-1173 12 2 : : PUNCT cana-1173 12 3 this this PRON cana-1173 12 4 is be AUX cana-1173 12 5 a a DET cana-1173 12 6 novel novel ADJ cana-1173 12 7 method method NOUN cana-1173 12 8 that that PRON cana-1173 12 9 uses use VERB cana-1173 12 10 dual dual ADJ cana-1173 12 11 techniques technique NOUN cana-1173 12 12 to to PART cana-1173 12 13 safeguard safeguard VERB cana-1173 12 14 data datum NOUN cana-1173 12 15 : : PUNCT cana-1173 12 16 first first ADV cana-1173 12 17 , , PUNCT cana-1173 12 18 it it PRON cana-1173 12 19 encrypts encrypt VERB cana-1173 12 20 the the DET cana-1173 12 21 encrypted encrypt VERB cana-1173 12 22 cipher cipher ADJ cana-1173 12 23 text text NOUN cana-1173 12 24 , , PUNCT cana-1173 12 25 and and CCONJ cana-1173 12 26 then then ADV cana-1173 12 27 it it PRON cana-1173 12 28 decrypts decrypt VERB cana-1173 12 29 it it PRON cana-1173 12 30 again again ADV cana-1173 12 31 . . PUNCT cana-1173 13 1 the the DET cana-1173 13 2 data datum NOUN cana-1173 13 3 is be AUX cana-1173 13 4 protected protect VERB cana-1173 13 5 all all ADV cana-1173 13 6 along along ADP cana-1173 13 7 the the DET cana-1173 13 8 way way NOUN cana-1173 13 9 because because SCONJ cana-1173 13 10 the the DET cana-1173 13 11 key key NOUN cana-1173 13 12 that that PRON cana-1173 13 13 is be AUX cana-1173 13 14 transmitted transmit VERB cana-1173 13 15 to to ADP cana-1173 13 16 the the DET cana-1173 13 17 recipient recipient NOUN cana-1173 13 18 is be AUX cana-1173 13 19 very very ADV cana-1173 13 20 big big ADJ cana-1173 13 21 and and CCONJ cana-1173 13 22 difficult difficult ADJ cana-1173 13 23 to to PART cana-1173 13 24 crack crack VERB cana-1173 13 25 . . PUNCT cana-1173 14 1 keywords keyword NOUN cana-1173 14 2 : : PUNCT cana-1173 14 3 encryption encryption NOUN cana-1173 14 4 , , PUNCT cana-1173 14 5 decryption decryption NOUN cana-1173 14 6 , , PUNCT cana-1173 14 7 hill hill NOUN cana-1173 14 8 cipher cipher ADJ cana-1173 14 9 , , PUNCT cana-1173 14 10 laplace laplace NOUN cana-1173 14 11 transform transform NOUN cana-1173 14 12 , , PUNCT cana-1173 14 13 inverse inverse ADJ cana-1173 14 14 laplace laplace NOUN cana-1173 14 15 transform transform NOUN cana-1173 14 16 , , PUNCT cana-1173 14 17 kamal kamal PROPN cana-1173 14 18 transform transform VERB cana-1173 14 19 and and CCONJ cana-1173 14 20 inverse inverse NOUN cana-1173 14 21 kamal kamal PROPN cana-1173 14 22 transform transform NOUN cana-1173 14 23 . . PUNCT cana-1173 15 1 1 1 X cana-1173 15 2 . . X cana-1173 15 3 introduction introduction NOUN cana-1173 15 4 as as ADP cana-1173 15 5 security security NOUN cana-1173 15 6 of of ADP cana-1173 15 7 information information NOUN cana-1173 15 8 plays play VERB cana-1173 15 9 a a DET cana-1173 15 10 crucial crucial ADJ cana-1173 15 11 role role NOUN cana-1173 15 12 , , PUNCT cana-1173 15 13 we we PRON cana-1173 15 14 discuss discuss VERB cana-1173 15 15 a a DET cana-1173 15 16 dual dual ADJ cana-1173 15 17 encryption encryption NOUN cana-1173 15 18 and and CCONJ cana-1173 15 19 decryption decryption NOUN cana-1173 15 20 of of ADP cana-1173 15 21 data datum NOUN cana-1173 15 22 using use VERB cana-1173 15 23 hill hill NOUN cana-1173 15 24 cipher cipher ADJ cana-1173 15 25 with with ADP cana-1173 15 26 combination combination NOUN cana-1173 15 27 of of ADP cana-1173 15 28 laplace laplace NOUN cana-1173 15 29 transform transform NOUN cana-1173 15 30 and and CCONJ cana-1173 15 31 kamal kamal PROPN cana-1173 15 32 transform transform NOUN cana-1173 15 33 . . PUNCT cana-1173 16 1 the the DET cana-1173 16 2 study study NOUN cana-1173 16 3 of of ADP cana-1173 16 4 encrypted encrypt VERB cana-1173 16 5 messages message NOUN cana-1173 16 6 is be AUX cana-1173 16 7 known know VERB cana-1173 16 8 as as ADP cana-1173 16 9 cryptography cryptography NOUN cana-1173 16 10 . . PUNCT cana-1173 17 1 in in ADP cana-1173 17 2 many many ADJ cana-1173 17 3 circumstances circumstance NOUN cana-1173 17 4 , , PUNCT cana-1173 17 5 the the DET cana-1173 17 6 sender sender NOUN cana-1173 17 7 wants want VERB cana-1173 17 8 to to PART cana-1173 17 9 keep keep VERB cana-1173 17 10 the the DET cana-1173 17 11 message message NOUN cana-1173 17 12 private private ADJ cana-1173 17 13 from from ADP cana-1173 17 14 the the DET cana-1173 17 15 public public NOUN cana-1173 17 16 or or CCONJ cana-1173 17 17 from from ADP cana-1173 17 18 unauthorized unauthorized ADJ cana-1173 17 19 users user NOUN cana-1173 17 20 . . PUNCT cana-1173 18 1 information information NOUN cana-1173 18 2 is be AUX cana-1173 18 3 protected protect VERB cana-1173 18 4 using use VERB cana-1173 18 5 encryption encryption NOUN cana-1173 18 6 , , PUNCT cana-1173 18 7 and and CCONJ cana-1173 18 8 the the DET cana-1173 18 9 original original ADJ cana-1173 18 10 message message NOUN cana-1173 18 11 is be AUX cana-1173 18 12 unlocked unlock VERB cana-1173 18 13 using use VERB cana-1173 18 14 decryption decryption NOUN cana-1173 18 15 . . PUNCT cana-1173 19 1 integral integral ADJ cana-1173 19 2 transformations transformation NOUN cana-1173 19 3 have have VERB cana-1173 19 4 a a DET cana-1173 19 5 wide wide ADJ cana-1173 19 6 range range NOUN cana-1173 19 7 of of ADP cana-1173 19 8 uses use NOUN cana-1173 19 9 , , PUNCT cana-1173 19 10 especially especially ADV cana-1173 19 11 in in ADP cana-1173 19 12 the the DET cana-1173 19 13 realm realm NOUN cana-1173 19 14 of of ADP cana-1173 19 15 cryptography cryptography NOUN cana-1173 19 16 . . PUNCT cana-1173 20 1 in in ADP cana-1173 20 2 cryptography cryptography NOUN cana-1173 20 3 , , PUNCT cana-1173 20 4 hyperbolic hyperbolic ADJ cana-1173 20 5 functions function NOUN cana-1173 20 6 such such ADJ cana-1173 20 7 as as ADP cana-1173 20 8 sine sine NOUN cana-1173 20 9 , , PUNCT cana-1173 20 10 cosine cosine NOUN cana-1173 20 11 , , PUNCT cana-1173 20 12 communications communication NOUN cana-1173 20 13 on on ADP cana-1173 20 14 applied apply VERB cana-1173 20 15 nonlinear nonlinear ADJ cana-1173 20 16 analysis analysis NOUN cana-1173 20 17 issn issn NOUN cana-1173 20 18 : : PUNCT cana-1173 20 19 1074 1074 NUM cana-1173 20 20 - - PUNCT cana-1173 20 21 133x 133x NUM cana-1173 20 22 vol vol NOUN cana-1173 20 23 31 31 NUM cana-1173 20 24 no no NOUN cana-1173 20 25 . . PUNCT cana-1173 21 1 6s 6s NUM cana-1173 21 2 ( ( PUNCT cana-1173 21 3 2024 2024 NUM cana-1173 21 4 ) ) PUNCT cana-1173 22 1 144 144 NUM cana-1173 22 2 https://internationalpubls.com https://internationalpubls.com X cana-1173 22 3 exponential exponential NOUN cana-1173 22 4 , , PUNCT cana-1173 22 5 polynomial polynomial ADJ cana-1173 22 6 , , PUNCT cana-1173 22 7 etc etc X cana-1173 22 8 . . X cana-1173 22 9 are be AUX cana-1173 22 10 transformed transform VERB cana-1173 22 11 using use VERB cana-1173 22 12 the the DET cana-1173 22 13 laplace laplace NOUN cana-1173 22 14 , , PUNCT cana-1173 22 15 elzaki elzaki NOUN cana-1173 22 16 , , PUNCT cana-1173 22 17 and and CCONJ cana-1173 22 18 kamal kamal ADJ cana-1173 22 19 methods method NOUN cana-1173 22 20 . . PUNCT cana-1173 23 1 while while SCONJ cana-1173 23 2 elzaki elzaki NOUN cana-1173 23 3 transform transform NOUN cana-1173 23 4 is be AUX cana-1173 23 5 used use VERB cana-1173 23 6 by by ADP cana-1173 23 7 [ [ X cana-1173 23 8 2 2 NUM cana-1173 23 9 ] ] PUNCT cana-1173 23 10 and and CCONJ cana-1173 23 11 kamal kamal PROPN cana-1173 23 12 transform transform VERB cana-1173 23 13 [ [ X cana-1173 23 14 9 9 NUM cana-1173 23 15 ] ] PUNCT cana-1173 23 16 , , PUNCT cana-1173 24 1 [ [ X cana-1173 24 2 5 5 NUM cana-1173 24 3 , , PUNCT cana-1173 24 4 6 6 NUM cana-1173 24 5 ] ] PUNCT cana-1173 24 6 , , PUNCT cana-1173 24 7 [ [ X cana-1173 24 8 1 1 NUM cana-1173 24 9 ] ] PUNCT cana-1173 24 10 employ employ NOUN cana-1173 24 11 laplace laplace NOUN cana-1173 24 12 transform transform NOUN cana-1173 24 13 . . PUNCT cana-1173 25 1 here here ADV cana-1173 25 2 , , PUNCT cana-1173 25 3 we we PRON cana-1173 25 4 combine combine VERB cana-1173 25 5 hill hill NOUN cana-1173 25 6 cipher cipher ADJ cana-1173 25 7 with with ADP cana-1173 25 8 laplace laplace NOUN cana-1173 25 9 and and CCONJ cana-1173 25 10 kamal kamal PROPN cana-1173 25 11 transforms transform VERB cana-1173 25 12 to to PART cana-1173 25 13 encrypt encrypt VERB cana-1173 25 14 the the DET cana-1173 25 15 message message NOUN cana-1173 25 16 and and CCONJ cana-1173 25 17 apply apply VERB cana-1173 25 18 their their PRON cana-1173 25 19 inverse inverse NOUN cana-1173 25 20 transforms transform VERB cana-1173 25 21 to to PART cana-1173 25 22 decrypt decrypt VERB cana-1173 25 23 it it PRON cana-1173 25 24 . . PUNCT cana-1173 26 1 in in ADP cana-1173 26 2 contrast contrast NOUN cana-1173 26 3 to to ADP cana-1173 26 4 cipher cipher ADJ cana-1173 26 5 text text NOUN cana-1173 26 6 , , PUNCT cana-1173 26 7 which which PRON cana-1173 26 8 is be AUX cana-1173 26 9 a a DET cana-1173 26 10 coded code VERB cana-1173 26 11 version version NOUN cana-1173 26 12 of of ADP cana-1173 26 13 plaintext plaintext NOUN cana-1173 26 14 , , PUNCT cana-1173 26 15 the the DET cana-1173 26 16 original original ADJ cana-1173 26 17 message message NOUN cana-1173 26 18 written write VERB cana-1173 26 19 by by ADP cana-1173 26 20 the the DET cana-1173 26 21 user user NOUN cana-1173 26 22 is be AUX cana-1173 26 23 referred refer VERB cana-1173 26 24 to to ADP cana-1173 26 25 as as ADP cana-1173 26 26 plaintext plaintext NOUN cana-1173 26 27 . . PUNCT cana-1173 27 1 encryption encryption NOUN cana-1173 27 2 , , PUNCT cana-1173 27 3 also also ADV cana-1173 27 4 known know VERB cana-1173 27 5 as as ADP cana-1173 27 6 the the DET cana-1173 27 7 process process NOUN cana-1173 27 8 of of ADP cana-1173 27 9 rendering render VERB cana-1173 27 10 information information NOUN cana-1173 27 11 unintelligible unintelligible ADJ cana-1173 27 12 , , PUNCT cana-1173 27 13 decryption decryption NOUN cana-1173 27 14 , , PUNCT cana-1173 27 15 or or CCONJ cana-1173 27 16 the the DET cana-1173 27 17 process process NOUN cana-1173 27 18 of of ADP cana-1173 27 19 creating create VERB cana-1173 27 20 cipher cipher ADJ cana-1173 27 21 , , PUNCT cana-1173 27 22 is be AUX cana-1173 27 23 referred refer VERB cana-1173 27 24 to to ADP cana-1173 27 25 as as ADP cana-1173 27 26 cryptography cryptography NOUN cana-1173 27 27 . . PUNCT cana-1173 28 1 there there PRON cana-1173 28 2 are be VERB cana-1173 28 3 two two NUM cana-1173 28 4 components component NOUN cana-1173 28 5 to to ADP cana-1173 28 6 the the DET cana-1173 28 7 encryption encryption NOUN cana-1173 28 8 and and CCONJ cana-1173 28 9 decryption decryption NOUN cana-1173 28 10 process process NOUN cana-1173 28 11 : : PUNCT cana-1173 28 12 the the DET cana-1173 28 13 algorithm algorithm NOUN cana-1173 28 14 and and CCONJ cana-1173 28 15 the the DET cana-1173 28 16 key key NOUN cana-1173 28 17 . . PUNCT cana-1173 29 1 the the DET cana-1173 29 2 use use NOUN cana-1173 29 3 of of ADP cana-1173 29 4 the the DET cana-1173 29 5 key key NOUN cana-1173 29 6 for for ADP cana-1173 29 7 encryption encryption NOUN cana-1173 29 8 and and CCONJ cana-1173 29 9 decryption decryption NOUN cana-1173 29 10 makes make VERB cana-1173 29 11 cryptography cryptography NOUN cana-1173 29 12 safer safe ADJ cana-1173 29 13 . . PUNCT cana-1173 30 1 we we PRON cana-1173 30 2 need need VERB cana-1173 30 3 the the DET cana-1173 30 4 following follow VERB cana-1173 30 5 well well ADV cana-1173 30 6 - - PUNCT cana-1173 30 7 known know VERB cana-1173 30 8 formulas formula NOUN cana-1173 30 9 because because SCONJ cana-1173 30 10 in in ADP cana-1173 30 11 this this DET cana-1173 30 12 study study NOUN cana-1173 30 13 we we PRON cana-1173 30 14 will will AUX cana-1173 30 15 cover cover VERB cana-1173 30 16 the the DET cana-1173 30 17 uses use NOUN cana-1173 30 18 of of ADP cana-1173 30 19 laplace laplace NOUN cana-1173 30 20 transforms transform VERB cana-1173 30 21 and and CCONJ cana-1173 30 22 kamal kamal ADJ cana-1173 30 23 transform transform NOUN cana-1173 30 24 . . PUNCT cana-1173 31 1 2 2 X cana-1173 31 2 . . X cana-1173 31 3 definitions definition NOUN cana-1173 31 4 laplace laplace NOUN cana-1173 31 5 transform transform NOUN cana-1173 31 6 : : PUNCT cana-1173 31 7 if if SCONJ cana-1173 31 8 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 31 9 ) ) PUNCT cana-1173 31 10 is be AUX cana-1173 31 11 a a DET cana-1173 31 12 function function NOUN cana-1173 31 13 defined define VERB cana-1173 31 14 for for ADP cana-1173 31 15 all all DET cana-1173 31 16 positive positive ADJ cana-1173 31 17 values value NOUN cana-1173 31 18 of of ADP cana-1173 31 19 t t PROPN cana-1173 31 20 , , PUNCT cana-1173 31 21 then then ADV cana-1173 31 22 the the DET cana-1173 31 23 laplace laplace NOUN cana-1173 31 24 transform transform NOUN cana-1173 31 25 of of ADP cana-1173 31 26 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 31 27 ) ) PUNCT cana-1173 31 28 is be AUX cana-1173 31 29 defined define VERB cana-1173 31 30 as as ADP cana-1173 31 31 : : PUNCT cana-1173 31 32 𝐿 𝐿 PROPN cana-1173 31 33 { { PUNCT cana-1173 31 34 𝑓(𝑑 𝑓(𝑑 PROPN cana-1173 31 35 ) ) PUNCT cana-1173 31 36 } } PUNCT cana-1173 32 1 = = SYM cana-1173 32 2 𝐹(𝑠 𝐹(𝑠 NUM cana-1173 32 3 ) ) PUNCT cana-1173 32 4 = = NOUN cana-1173 32 5 ∫ ∫ PROPN cana-1173 32 6 e e NOUN cana-1173 32 7 ∞ ∞ PROPN cana-1173 32 8 0 0 NUM cana-1173 32 9 βˆ’π‘ π‘‘ βˆ’π‘ π‘‘ PROPN cana-1173 32 10 𝑓(𝑑)𝑑𝑑 𝑓(𝑑)𝑑𝑑 NOUN cana-1173 32 11 , , PUNCT cana-1173 32 12 provided provide VERB cana-1173 32 13 that that SCONJ cana-1173 32 14 the the DET cana-1173 32 15 integral integral ADJ cana-1173 32 16 exists exist VERB cana-1173 32 17 . . PUNCT cana-1173 33 1 here here ADV cana-1173 33 2 the the DET cana-1173 33 3 parameter parameter NOUN cana-1173 33 4 s s PART cana-1173 33 5 is be AUX cana-1173 33 6 a a DET cana-1173 33 7 real real ADJ cana-1173 33 8 or or CCONJ cana-1173 33 9 complex complex ADJ cana-1173 33 10 number number NOUN cana-1173 33 11 . . PUNCT cana-1173 34 1 the the DET cana-1173 34 2 corresponding corresponding ADJ cana-1173 34 3 inverse inverse NOUN cana-1173 34 4 laplace laplace NOUN cana-1173 34 5 transform transform NOUN cana-1173 34 6 is be AUX cana-1173 34 7 πΏβˆ’1{𝐹(𝑠 πΏβˆ’1{𝐹(𝑠 ADJ cana-1173 34 8 ) ) PUNCT cana-1173 34 9 } } PUNCT cana-1173 34 10 = = SYM cana-1173 34 11 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 34 12 ) ) PUNCT cana-1173 34 13 . . PUNCT cana-1173 35 1 some some DET cana-1173 35 2 standard standard ADJ cana-1173 35 3 results result NOUN cana-1173 35 4 of of ADP cana-1173 35 5 laplace laplace NOUN cana-1173 35 6 transform transform VERB cana-1173 35 7 𝐿 𝐿 PROPN cana-1173 35 8 { { PUNCT cana-1173 35 9 1 1 NUM cana-1173 35 10 } } PUNCT cana-1173 35 11 = = SYM cana-1173 36 1 1 1 NUM cana-1173 36 2 s s X cana-1173 36 3 πΏβˆ’1 πΏβˆ’1 NOUN cana-1173 36 4 { { PUNCT cana-1173 36 5 1 1 NUM cana-1173 36 6 s s PART cana-1173 36 7 } } PUNCT cana-1173 36 8 = = SYM cana-1173 36 9 1 1 NUM cana-1173 36 10 𝐿{𝑑 𝐿{𝑑 NUM cana-1173 36 11 𝑛 𝑛 NOUN cana-1173 36 12 } } PUNCT cana-1173 36 13 = = SYM cana-1173 36 14 n n X cana-1173 36 15 ! ! PUNCT cana-1173 36 16 s s PART cana-1173 37 1 n+1 n+1 PROPN cana-1173 37 2 πΏβˆ’1 πΏβˆ’1 NOUN cana-1173 37 3 { { PUNCT cana-1173 37 4 1 1 NUM cana-1173 37 5 s s NOUN cana-1173 37 6 n+1 n+1 PROPN cana-1173 37 7 } } PUNCT cana-1173 37 8 = = SYM cana-1173 37 9 tn tn PROPN cana-1173 37 10 n n NOUN cana-1173 37 11 ! ! PUNCT cana-1173 38 1 𝐿{π‘’π‘Žπ‘‘ 𝐿{π‘’π‘Žπ‘‘ ADP cana-1173 38 2 } } PUNCT cana-1173 38 3 = = SYM cana-1173 38 4 1 1 NUM cana-1173 38 5 s s NOUN cana-1173 38 6 βˆ’a βˆ’a NOUN cana-1173 38 7 πΏβˆ’1 πΏβˆ’1 NOUN cana-1173 38 8 { { PUNCT cana-1173 38 9 1 1 NUM cana-1173 38 10 sβˆ’ sβˆ’ PROPN cana-1173 38 11 a a DET cana-1173 38 12 } } PUNCT cana-1173 38 13 = = PUNCT cana-1173 38 14 π‘’π‘Žπ‘‘ π‘’π‘Žπ‘‘ ADP cana-1173 38 15 𝐿 𝐿 PROPN cana-1173 38 16 { { PUNCT cana-1173 38 17 𝑑 𝑑 PROPN cana-1173 38 18 𝑛𝑓(𝑑 𝑛𝑓(𝑑 ADJ cana-1173 38 19 ) ) PUNCT cana-1173 38 20 } } PUNCT cana-1173 38 21 = = SYM cana-1173 38 22 ( ( PUNCT cana-1173 38 23 βˆ’1 βˆ’1 NOUN cana-1173 38 24 ) ) PUNCT cana-1173 38 25 𝑛 𝑛 PART cana-1173 39 1 d d NOUN cana-1173 39 2 n n CCONJ cana-1173 39 3 ds ds VERB cana-1173 39 4 n n NOUN cana-1173 39 5 𝐹(𝑠 𝐹(𝑠 NUM cana-1173 39 6 ) ) PUNCT cana-1173 39 7 πΏβˆ’1 πΏβˆ’1 NOUN cana-1173 39 8 { { PUNCT cana-1173 40 1 d d NOUN cana-1173 40 2 n n CCONJ cana-1173 40 3 ds ds VERB cana-1173 40 4 n n NOUN cana-1173 40 5 𝐹(𝑠 𝐹(𝑠 NUM cana-1173 40 6 ) ) PUNCT cana-1173 40 7 } } PUNCT cana-1173 40 8 = = SYM cana-1173 40 9 tn𝑓(𝑑 tn𝑓(𝑑 NUM cana-1173 40 10 ) ) PUNCT cana-1173 40 11 𝑑𝑠 𝑑𝑠 PRON cana-1173 40 12 kamal kamal PROPN cana-1173 40 13 transform transform PROPN cana-1173 40 14 : : PUNCT cana-1173 40 15 the the DET cana-1173 40 16 kamal kamal PROPN cana-1173 40 17 transforms transform VERB cana-1173 40 18 defined define VERB cana-1173 40 19 by by ADP cana-1173 40 20 the the DET cana-1173 40 21 integral integral ADJ cana-1173 40 22 equation equation NOUN cana-1173 40 23 : : PUNCT cana-1173 40 24 𝐾[𝑓(𝑑 𝐾[𝑓(𝑑 ADJ cana-1173 40 25 ) ) PUNCT cana-1173 40 26 ] ] PUNCT cana-1173 41 1 = = PUNCT cana-1173 41 2 𝐺(𝑣 𝐺(𝑣 X cana-1173 41 3 ) ) PUNCT cana-1173 41 4 = = SYM cana-1173 41 5 ∫ ∫ PROPN cana-1173 41 6 f(t f(t PROPN cana-1173 41 7 ) ) PUNCT cana-1173 42 1 ∞ ∞ NOUN cana-1173 42 2 0 0 NUM cana-1173 43 1 e e NOUN cana-1173 43 2 βˆ’t βˆ’t NOUN cana-1173 43 3 v v ADP cana-1173 43 4 𝑑𝑑 𝑑𝑑 ADP cana-1173 43 5 , , PUNCT cana-1173 43 6 𝑑 𝑑 X cana-1173 43 7 β‰₯ β‰₯ NOUN cana-1173 43 8 0 0 NUM cana-1173 43 9 , , PUNCT cana-1173 43 10 π‘˜1 π‘˜1 ADJ cana-1173 43 11 ≀ ≀ NOUN cana-1173 43 12 𝑣 𝑣 DET cana-1173 43 13 ≀ ≀ ADJ cana-1173 43 14 π‘˜2 π‘˜2 PROPN cana-1173 43 15 , , PUNCT cana-1173 43 16 where where SCONJ cana-1173 43 17 π‘˜1 π‘˜1 NOUN cana-1173 43 18 , , PUNCT cana-1173 43 19 π‘˜2 π‘˜2 PROPN cana-1173 43 20 may may AUX cana-1173 43 21 be be AUX cana-1173 43 22 finite finite ADJ cana-1173 43 23 or or CCONJ cana-1173 43 24 infinite infinite VERB cana-1173 43 25 . . PUNCT cana-1173 44 1 some some DET cana-1173 44 2 standard standard ADJ cana-1173 44 3 results result NOUN cana-1173 44 4 of of ADP cana-1173 44 5 kamal kamal PROPN cana-1173 44 6 transform transform VERB cana-1173 44 7 𝐾 𝐾 PROPN cana-1173 44 8 [ [ X cana-1173 44 9 1 1 NUM cana-1173 44 10 ] ] PUNCT cana-1173 44 11 = = PUNCT cana-1173 44 12 𝑣 𝑣 X cana-1173 44 13 πΎβˆ’1[𝑣 πΎβˆ’1[𝑣 NOUN cana-1173 44 14 ] ] X cana-1173 44 15 = = SYM cana-1173 44 16 1 1 NUM cana-1173 44 17 𝐾[𝑑 𝐾[𝑑 NOUN cana-1173 44 18 ] ] X cana-1173 44 19 = = X cana-1173 44 20 𝑣2 𝑣2 X cana-1173 44 21 πΎβˆ’1[𝑣2 πΎβˆ’1[𝑣2 NOUN cana-1173 44 22 ] ] X cana-1173 44 23 = = SYM cana-1173 44 24 𝑑 𝑑 PROPN cana-1173 44 25 𝐾[𝑑 𝐾[𝑑 NOUN cana-1173 44 26 𝑛 𝑛 X cana-1173 44 27 ] ] X cana-1173 44 28 = = SYM cana-1173 44 29 𝑛 𝑛 PROPN cana-1173 44 30 ! ! NOUN cana-1173 44 31 𝑣𝑛+1 𝑣𝑛+1 NUM cana-1173 44 32 πΎβˆ’1[𝑣 πΎβˆ’1[𝑣 PRON cana-1173 44 33 𝑛+1 𝑛+1 PROPN cana-1173 44 34 ] ] PUNCT cana-1173 44 35 = = SYM cana-1173 44 36 t t PROPN cana-1173 44 37 n n NOUN cana-1173 44 38 n n CCONJ cana-1173 44 39 ! ! PUNCT cana-1173 44 40 𝐾[π‘‘π‘’π‘Žπ‘‘ 𝐾[π‘‘π‘’π‘Žπ‘‘ NOUN cana-1173 44 41 ] ] X cana-1173 44 42 = = SYM cana-1173 44 43 v v NUM cana-1173 44 44 2 2 NUM cana-1173 44 45 ( ( PUNCT cana-1173 44 46 1 1 NUM cana-1173 44 47 βˆ’ βˆ’ PROPN cana-1173 44 48 av av NOUN cana-1173 44 49 ) ) PUNCT cana-1173 44 50 2 2 NUM cana-1173 44 51 πΎβˆ’1 πΎβˆ’1 NOUN cana-1173 44 52 [ [ PUNCT cana-1173 44 53 v v NUM cana-1173 44 54 2 2 NUM cana-1173 44 55 ( ( PUNCT cana-1173 44 56 1 1 NUM cana-1173 44 57 βˆ’ βˆ’ PROPN cana-1173 44 58 av av NOUN cana-1173 44 59 ) ) PUNCT cana-1173 44 60 2 2 NUM cana-1173 44 61 ] ] PUNCT cana-1173 44 62 = = PRON cana-1173 44 63 π‘‘π‘’π‘Žπ‘‘ π‘‘π‘’π‘Žπ‘‘ VERB cana-1173 44 64 3 3 NUM cana-1173 44 65 . . PUNCT cana-1173 44 66 methods method NOUN cana-1173 44 67 in in ADP cana-1173 44 68 this this PRON cana-1173 44 69 we we PRON cana-1173 44 70 discuss discuss VERB cana-1173 44 71 how how SCONJ cana-1173 44 72 to to PART cana-1173 44 73 encrypt encrypt VERB cana-1173 44 74 the the DET cana-1173 44 75 original original ADJ cana-1173 44 76 text text NOUN cana-1173 44 77 into into ADP cana-1173 44 78 cipher cipher ADJ cana-1173 44 79 text text NOUN cana-1173 44 80 using use VERB cana-1173 44 81 the the DET cana-1173 44 82 following follow VERB cana-1173 44 83 steps step NOUN cana-1173 44 84 . . PUNCT cana-1173 45 1 encryption encryption NOUN cana-1173 45 2 algorithm algorithm NOUN cana-1173 45 3 : : PUNCT cana-1173 45 4 step step NOUN cana-1173 45 5 1 1 NUM cana-1173 45 6 : : PUNCT cana-1173 45 7 select select VERB cana-1173 45 8 the the DET cana-1173 45 9 plain plain ADJ cana-1173 45 10 text text NOUN cana-1173 45 11 and and CCONJ cana-1173 45 12 convert convert VERB cana-1173 45 13 the the DET cana-1173 45 14 text text NOUN cana-1173 45 15 into into ADP cana-1173 45 16 numbers number NOUN cana-1173 45 17 by by ADP cana-1173 45 18 assigning assign VERB cana-1173 45 19 the the DET cana-1173 45 20 values value NOUN cana-1173 45 21 as as ADP cana-1173 45 22 a=1 a=1 NOUN cana-1173 45 23 , , PUNCT cana-1173 45 24 b=2 b=2 NOUN cana-1173 45 25 … … PUNCT cana-1173 45 26 . . PUNCT cana-1173 46 1 z=26 z=26 NOUN cana-1173 46 2 , , PUNCT cana-1173 46 3 space=27 space=27 ADJ cana-1173 46 4 , , PUNCT cana-1173 46 5 a=28 a=28 VERB cana-1173 46 6 , , PUNCT cana-1173 46 7 b=29 b=29 NOUN cana-1173 46 8 , , PUNCT cana-1173 46 9 z=53.arrange z=53.arrange VERB cana-1173 46 10 the the DET cana-1173 46 11 plain plain ADJ cana-1173 46 12 text text NOUN cana-1173 46 13 which which PRON cana-1173 46 14 transformed transform VERB cana-1173 46 15 in in ADP cana-1173 46 16 numbers number NOUN cana-1173 46 17 in in ADP cana-1173 46 18 matrix matrix NOUN cana-1173 46 19 form form NOUN cana-1173 46 20 of of ADP cana-1173 46 21 order order NOUN cana-1173 46 22 nxn nxn PROPN cana-1173 46 23 or or CCONJ cana-1173 46 24 mxn mxn PROPN cana-1173 47 1 . . PUNCT cana-1173 47 2 communications communication NOUN cana-1173 47 3 on on ADP cana-1173 47 4 applied apply VERB cana-1173 47 5 nonlinear nonlinear ADJ cana-1173 47 6 analysis analysis NOUN cana-1173 47 7 issn issn NOUN cana-1173 47 8 : : PUNCT cana-1173 47 9 1074 1074 NUM cana-1173 47 10 - - PUNCT cana-1173 47 11 133x 133x NUM cana-1173 47 12 vol vol NOUN cana-1173 47 13 31 31 NUM cana-1173 47 14 no no NOUN cana-1173 47 15 . . PUNCT cana-1173 48 1 6s 6s NUM cana-1173 48 2 ( ( PUNCT cana-1173 48 3 2024 2024 NUM cana-1173 48 4 ) ) PUNCT cana-1173 48 5 145 145 NUM cana-1173 48 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 48 7 step step NOUN cana-1173 48 8 2 2 NUM cana-1173 48 9 : : PUNCT cana-1173 48 10 let let VERB cana-1173 48 11 the the DET cana-1173 48 12 matrix matrix NOUN cana-1173 48 13 be be AUX cana-1173 48 14 denoted denote VERB cana-1173 48 15 by by ADP cana-1173 48 16 p. p. NOUN cana-1173 48 17 step step NOUN cana-1173 48 18 3 3 NUM cana-1173 48 19 : : PUNCT cana-1173 48 20 define define VERB cana-1173 48 21 a a DET cana-1173 48 22 key key ADJ cana-1173 48 23 matrix matrix NOUN cana-1173 48 24 whose whose DET cana-1173 48 25 inverse inverse NOUN cana-1173 48 26 exists exist VERB cana-1173 48 27 . . PUNCT cana-1173 49 1 let let VERB cana-1173 49 2 a a PRON cana-1173 49 3 be be AUX cana-1173 49 4 the the DET cana-1173 49 5 key key ADJ cana-1173 49 6 matrix matrix NOUN cana-1173 49 7 of of ADP cana-1173 49 8 order order NOUN cana-1173 49 9 nxn nxn PROPN cana-1173 49 10 which which PRON cana-1173 49 11 acts act VERB cana-1173 49 12 as as ADP cana-1173 49 13 encryption encryption NOUN cana-1173 49 14 key key NOUN cana-1173 49 15 and and CCONJ cana-1173 49 16 the the DET cana-1173 49 17 inverse inverse NOUN cana-1173 49 18 of of ADP cana-1173 49 19 the the DET cana-1173 49 20 matrix matrix NOUN cana-1173 49 21 a a DET cana-1173 49 22 acts act NOUN cana-1173 49 23 as as ADP cana-1173 49 24 decryption decryption NOUN cana-1173 49 25 key key NOUN cana-1173 49 26 . . PUNCT cana-1173 50 1 step step NOUN cana-1173 50 2 4 4 NUM cana-1173 50 3 : : PUNCT cana-1173 50 4 let let VERB cana-1173 50 5 us we PRON cana-1173 50 6 define define VERB cana-1173 50 7 𝐸 𝐸 PROPN cana-1173 50 8 ≑ ≑ PROPN cana-1173 50 9 𝐴𝑃(π‘šπ‘œπ‘‘ 𝐴𝑃(π‘šπ‘œπ‘‘ NOUN cana-1173 50 10 53 53 NUM cana-1173 50 11 ) ) PUNCT cana-1173 50 12 which which PRON cana-1173 50 13 is be AUX cana-1173 50 14 the the DET cana-1173 50 15 first first ADJ cana-1173 50 16 stage stage NOUN cana-1173 50 17 of of ADP cana-1173 50 18 encryption encryption NOUN cana-1173 50 19 . . PUNCT cana-1173 51 1 step step NOUN cana-1173 51 2 5 5 NUM cana-1173 51 3 : : PUNCT cana-1173 51 4 let let VERB cana-1173 51 5 us we PRON cana-1173 51 6 define define VERB cana-1173 51 7 the the DET cana-1173 51 8 function function NOUN cana-1173 51 9 f(t f(t NOUN cana-1173 51 10 ) ) PUNCT cana-1173 51 11 = = PUNCT cana-1173 51 12 βˆ‘ βˆ‘ PUNCT cana-1173 51 13 gi gi PROPN cana-1173 51 14 n n PRON cana-1173 51 15 i=0 i=0 PROPN cana-1173 51 16 t2cosht t2cosht VERB cana-1173 51 17 , , PUNCT cana-1173 51 18 where where SCONJ cana-1173 51 19 gi gi PRON cana-1173 51 20 are be AUX cana-1173 51 21 constants.the constants.the DET cana-1173 51 22 values value NOUN cana-1173 51 23 in in ADP cana-1173 51 24 e e PROPN cana-1173 51 25 are be AUX cana-1173 51 26 taken take VERB cana-1173 51 27 as as ADP cana-1173 51 28 the the DET cana-1173 51 29 coefficients coefficient NOUN cana-1173 51 30 in in ADP cana-1173 51 31 the the DET cana-1173 51 32 function function NOUN cana-1173 51 33 . . PUNCT cana-1173 52 1 step step NOUN cana-1173 52 2 6 6 NUM cana-1173 52 3 : : PUNCT cana-1173 52 4 apply apply VERB cana-1173 52 5 laplace laplace NOUN cana-1173 52 6 transform transform NOUN cana-1173 52 7 for for ADP cana-1173 52 8 the the DET cana-1173 52 9 function function NOUN cana-1173 52 10 f(t f(t PROPN cana-1173 52 11 ) ) PUNCT cana-1173 52 12 . . PUNCT cana-1173 53 1 that that PRON cana-1173 53 2 is be AUX cana-1173 53 3 , , PUNCT cana-1173 53 4 𝐿{𝑓(𝑑 𝐿{𝑓(𝑑 CCONJ cana-1173 53 5 ) ) PUNCT cana-1173 53 6 } } PUNCT cana-1173 54 1 = = SYM cana-1173 54 2 𝐺(𝑠 𝐺(𝑠 X cana-1173 54 3 ) ) PUNCT cana-1173 54 4 which which PRON cana-1173 54 5 is be AUX cana-1173 54 6 the the DET cana-1173 54 7 second second ADJ cana-1173 54 8 level level NOUN cana-1173 54 9 of of ADP cana-1173 54 10 encryption encryption NOUN cana-1173 54 11 and and CCONJ cana-1173 54 12 adjust adjust VERB cana-1173 54 13 the the DET cana-1173 54 14 coefficients coefficient NOUN cana-1173 54 15 in in ADP cana-1173 54 16 g(s g(s NOUN cana-1173 54 17 ) ) PUNCT cana-1173 54 18 under under ADP cana-1173 54 19 modulo modulo NOUN cana-1173 54 20 255 255 NUM cana-1173 54 21 and and CCONJ cana-1173 54 22 transform transform VERB cana-1173 54 23 them they PRON cana-1173 54 24 into into ADP cana-1173 54 25 symbols symbol NOUN cana-1173 54 26 using use VERB cana-1173 54 27 the the DET cana-1173 54 28 ascii ascii ADJ cana-1173 54 29 values value NOUN cana-1173 54 30 . . PUNCT cana-1173 55 1 hence hence ADV cana-1173 55 2 , , PUNCT cana-1173 55 3 the the DET cana-1173 55 4 sender sender NOUN cana-1173 55 5 sends send VERB cana-1173 55 6 the the DET cana-1173 55 7 cipher cipher ADJ cana-1173 55 8 text text NOUN cana-1173 55 9 along along ADP cana-1173 55 10 with with ADP cana-1173 55 11 the the DET cana-1173 55 12 key key ADJ cana-1173 55 13 π‘Ÿi π‘Ÿi ADP cana-1173 55 14 , , PUNCT cana-1173 55 15 where where SCONJ cana-1173 55 16 π‘Ÿi= π‘Ÿi= PROPN cana-1173 55 17 ( ( PUNCT cana-1173 55 18 fi fi NOUN cana-1173 55 19 – – PUNCT cana-1173 55 20 π‘ži π‘ži NOUN cana-1173 55 21 ) ) PUNCT cana-1173 55 22 / / SYM cana-1173 55 23 255 255 NUM cana-1173 55 24 . . PUNCT cana-1173 56 1 now now ADV cana-1173 56 2 , , PUNCT cana-1173 56 3 we we PRON cana-1173 56 4 discuss discuss VERB cana-1173 56 5 how how SCONJ cana-1173 56 6 to to PART cana-1173 56 7 decrypt decrypt VERB cana-1173 56 8 the the DET cana-1173 56 9 cipher cipher ADJ cana-1173 56 10 text text NOUN cana-1173 56 11 to to ADP cana-1173 56 12 original original ADJ cana-1173 56 13 text text NOUN cana-1173 56 14 using use VERB cana-1173 56 15 the the DET cana-1173 56 16 following follow VERB cana-1173 56 17 steps step NOUN cana-1173 56 18 . . PUNCT cana-1173 57 1 decryption decryption NOUN cana-1173 57 2 algorithm algorithm NOUN cana-1173 57 3 : : PUNCT cana-1173 57 4 step step NOUN cana-1173 57 5 1 1 NUM cana-1173 57 6 : : PUNCT cana-1173 57 7 transform transform VERB cana-1173 57 8 the the DET cana-1173 57 9 cipher cipher ADJ cana-1173 57 10 text text NOUN cana-1173 57 11 into into ADP cana-1173 57 12 numbers number NOUN cana-1173 57 13 using use VERB cana-1173 57 14 the the DET cana-1173 57 15 ascii ascii ADJ cana-1173 57 16 values value NOUN cana-1173 57 17 . . PUNCT cana-1173 58 1 now now ADV cana-1173 58 2 , , PUNCT cana-1173 58 3 using use VERB cana-1173 58 4 the the DET cana-1173 58 5 cipher cipher ADJ cana-1173 58 6 text text NOUN cana-1173 58 7 which which PRON cana-1173 58 8 are be AUX cana-1173 58 9 transformed transform VERB cana-1173 58 10 into into ADP cana-1173 58 11 numbers number NOUN cana-1173 58 12 and and CCONJ cana-1173 58 13 the the DET cana-1173 58 14 key key NOUN cana-1173 58 15 we we PRON cana-1173 58 16 find find VERB cana-1173 58 17 the the DET cana-1173 58 18 coefficients coefficient NOUN cana-1173 58 19 π‘ži π‘ži NOUN cana-1173 58 20 using use VERB cana-1173 58 21 , , PUNCT cana-1173 58 22 qi qi NOUN cana-1173 58 23 = = SYM cana-1173 58 24 fi fi NOUN cana-1173 58 25 + + X cana-1173 58 26 255ri 255ri NOUN cana-1173 58 27 . . PUNCT cana-1173 59 1 hence hence ADV cana-1173 59 2 , , PUNCT cana-1173 59 3 g(s g(s NOUN cana-1173 59 4 ) ) PUNCT cana-1173 59 5 = = SYM cana-1173 59 6 βˆ‘ βˆ‘ PUNCT cana-1173 59 7 qi qi PROPN cana-1173 59 8 s2i+3 s2i+3 PROPN cana-1173 59 9 n n PRON cana-1173 59 10 i=0 i=0 PROPN cana-1173 59 11 . . PUNCT cana-1173 60 1 step step NOUN cana-1173 60 2 2 2 NUM cana-1173 60 3 : : PUNCT cana-1173 60 4 apply apply VERB cana-1173 60 5 inverse inverse ADJ cana-1173 60 6 laplace laplace NOUN cana-1173 60 7 transform transform NOUN cana-1173 60 8 for for ADP cana-1173 60 9 g(s g(s NOUN cana-1173 60 10 ) ) PUNCT cana-1173 60 11 on on ADP cana-1173 60 12 both both DET cana-1173 60 13 sides side NOUN cana-1173 60 14 . . PUNCT cana-1173 61 1 that that PRON cana-1173 61 2 is be AUX cana-1173 61 3 , , PUNCT cana-1173 61 4 lβˆ’1{g(s lβˆ’1{g(s NUM cana-1173 61 5 ) ) PUNCT cana-1173 61 6 } } PUNCT cana-1173 62 1 = = SYM cana-1173 62 2 lβˆ’1 lβˆ’1 PROPN cana-1173 62 3 { { PUNCT cana-1173 62 4 βˆ‘ βˆ‘ PUNCT cana-1173 62 5 qi qi PROPN cana-1173 62 6 si+3 si+3 PROPN cana-1173 62 7 n n PRON cana-1173 62 8 i=0 i=0 PROPN cana-1173 62 9 } } PUNCT cana-1173 62 10 which which PRON cana-1173 62 11 is be AUX cana-1173 62 12 the the DET cana-1173 62 13 first first ADJ cana-1173 62 14 level level NOUN cana-1173 62 15 of of ADP cana-1173 62 16 decryption decryption NOUN cana-1173 62 17 . . PUNCT cana-1173 63 1 hence hence ADV cana-1173 63 2 , , PUNCT cana-1173 63 3 we we PRON cana-1173 63 4 get get VERB cana-1173 63 5 lβˆ’1{g(s lβˆ’1{g(s NUM cana-1173 63 6 ) ) PUNCT cana-1173 63 7 } } PUNCT cana-1173 64 1 = = SYM cana-1173 64 2 f(t f(t NOUN cana-1173 64 3 ) ) PUNCT cana-1173 64 4 . . PUNCT cana-1173 65 1 step step NOUN cana-1173 65 2 3 3 NUM cana-1173 65 3 : : PUNCT cana-1173 65 4 now now ADV cana-1173 65 5 , , PUNCT cana-1173 65 6 write write VERB cana-1173 65 7 the the DET cana-1173 65 8 coefficients coefficient NOUN cana-1173 65 9 of of ADP cana-1173 65 10 f(t f(t NOUN cana-1173 65 11 ) ) PUNCT cana-1173 65 12 in in ADP cana-1173 65 13 matrix matrix NOUN cana-1173 65 14 form form NOUN cana-1173 65 15 say say VERB cana-1173 65 16 e. e. PROPN cana-1173 65 17 step step PROPN cana-1173 65 18 4 4 NUM cana-1173 65 19 : : PUNCT cana-1173 65 20 let let VERB cana-1173 65 21 d d PROPN cana-1173 65 22 ≑ ≑ PROPN cana-1173 65 23 aβˆ’1e(mod aβˆ’1e(mod ADJ cana-1173 65 24 53 53 NUM cana-1173 65 25 ) ) PUNCT cana-1173 65 26 which which PRON cana-1173 65 27 is be AUX cana-1173 65 28 the the DET cana-1173 65 29 second second ADJ cana-1173 65 30 level level NOUN cana-1173 65 31 of of ADP cana-1173 65 32 decryption decryption NOUN cana-1173 65 33 . . PUNCT cana-1173 66 1 step step NOUN cana-1173 66 2 5 5 NUM cana-1173 66 3 : : PUNCT cana-1173 66 4 hence hence ADV cana-1173 66 5 , , PUNCT cana-1173 66 6 we we PRON cana-1173 66 7 get get VERB cana-1173 66 8 d d ADP cana-1173 66 9 which which PRON cana-1173 66 10 is be AUX cana-1173 66 11 same same ADJ cana-1173 66 12 as as ADP cana-1173 66 13 that that PRON cana-1173 66 14 of of ADP cana-1173 66 15 p. p. NOUN cana-1173 66 16 therefore therefore ADV cana-1173 66 17 , , PUNCT cana-1173 66 18 on on ADP cana-1173 66 19 converting convert VERB cana-1173 66 20 the the DET cana-1173 66 21 values value NOUN cana-1173 66 22 of of ADP cana-1173 66 23 the the DET cana-1173 66 24 matrix matrix NOUN cana-1173 66 25 d d NOUN cana-1173 66 26 into into ADP cana-1173 66 27 symbols symbol NOUN cana-1173 66 28 we we PRON cana-1173 66 29 get get VERB cana-1173 66 30 original original ADJ cana-1173 66 31 plain plain ADJ cana-1173 66 32 text text NOUN cana-1173 66 33 . . PUNCT cana-1173 67 1 4 4 X cana-1173 67 2 . . X cana-1173 67 3 results result NOUN cana-1173 67 4 to to PART cana-1173 67 5 see see VERB cana-1173 67 6 how how SCONJ cana-1173 67 7 the the DET cana-1173 67 8 algorithm algorithm NOUN cana-1173 67 9 works work VERB cana-1173 67 10 let let VERB cana-1173 67 11 us we PRON cana-1173 67 12 consider consider VERB cana-1173 67 13 the the DET cana-1173 67 14 following follow VERB cana-1173 67 15 illustrations illustration NOUN cana-1173 67 16 . . PUNCT cana-1173 68 1 example example NOUN cana-1173 68 2 i. i. NOUN cana-1173 68 3 this this DET cana-1173 68 4 illustration illustration NOUN cana-1173 68 5 explains explain VERB cana-1173 68 6 about about ADP cana-1173 68 7 hill hill NOUN cana-1173 68 8 cipher cipher ADJ cana-1173 68 9 using use VERB cana-1173 68 10 laplace laplace NOUN cana-1173 68 11 integral integral ADJ cana-1173 68 12 transform transform NOUN cana-1173 68 13 . . PUNCT cana-1173 69 1 step step NOUN cana-1173 69 2 1 1 NUM cana-1173 69 3 . . PUNCT cana-1173 70 1 let let VERB cana-1173 70 2 the the DET cana-1173 70 3 plain plain ADJ cana-1173 70 4 text text NOUN cana-1173 70 5 to to PART cana-1173 70 6 be be AUX cana-1173 70 7 sent send VERB cana-1173 70 8 is be AUX cana-1173 70 9 environment environment NOUN cana-1173 70 10 day day NOUN cana-1173 70 11 . . PUNCT cana-1173 71 1 now now ADV cana-1173 71 2 convert convert VERB cana-1173 71 3 the the DET cana-1173 71 4 plain plain ADJ cana-1173 71 5 text text NOUN cana-1173 71 6 into into ADP cana-1173 71 7 numbers number NOUN cana-1173 71 8 by by ADP cana-1173 71 9 assigning assign VERB cana-1173 71 10 a=1 a=1 NOUN cana-1173 71 11 , , PUNCT cana-1173 71 12 b=2 b=2 NOUN cana-1173 71 13 … … PUNCT cana-1173 71 14 . . PUNCT cana-1173 72 1 z=26 z=26 NOUN cana-1173 72 2 , , PUNCT cana-1173 72 3 space space NOUN cana-1173 72 4 = = SYM cana-1173 72 5 27 27 NUM cana-1173 72 6 , , PUNCT cana-1173 72 7 a=28 a=28 VERB cana-1173 72 8 , , PUNCT cana-1173 72 9 b=29 b=29 NOUN cana-1173 72 10 … … NUM cana-1173 72 11 . . PUNCT cana-1173 73 1 z=53 z=53 NUM cana-1173 73 2 . . PUNCT cana-1173 74 1 therefore therefore ADV cana-1173 74 2 , , PUNCT cana-1173 74 3 the the DET cana-1173 74 4 plaintext plaintext NOUN cana-1173 74 5 in in ADP cana-1173 74 6 the the DET cana-1173 74 7 form form NOUN cana-1173 74 8 of of ADP cana-1173 74 9 numbers number NOUN cana-1173 74 10 is be AUX cana-1173 74 11 5 5 NUM cana-1173 74 12 41 41 NUM cana-1173 74 13 49 49 NUM cana-1173 74 14 36 36 NUM cana-1173 74 15 45 45 NUM cana-1173 74 16 42 42 NUM cana-1173 74 17 41 41 NUM cana-1173 74 18 40 40 NUM cana-1173 74 19 32 32 NUM cana-1173 74 20 41 41 NUM cana-1173 74 21 47 47 NUM cana-1173 74 22 27 27 NUM cana-1173 74 23 4 4 NUM cana-1173 74 24 28 28 NUM cana-1173 74 25 52 52 NUM cana-1173 74 26 . . PUNCT cana-1173 75 1 step step NOUN cana-1173 75 2 2 2 NUM cana-1173 75 3 : : PUNCT cana-1173 75 4 arrange arrange VERB cana-1173 75 5 the the DET cana-1173 75 6 numbers number NOUN cana-1173 75 7 in in ADP cana-1173 75 8 matrix matrix NOUN cana-1173 75 9 form form NOUN cana-1173 75 10 as as ADP cana-1173 75 11 𝑃 𝑃 NOUN cana-1173 75 12 = = SYM cana-1173 75 13 ( ( PUNCT cana-1173 75 14 5 5 NUM cana-1173 75 15 41 41 NUM cana-1173 75 16 49 49 NUM cana-1173 75 17 42 42 NUM cana-1173 75 18 41 41 NUM cana-1173 75 19 40 40 NUM cana-1173 75 20 47 47 NUM cana-1173 75 21 27 27 NUM cana-1173 75 22 4 4 NUM cana-1173 75 23 36 36 NUM cana-1173 75 24 32 32 NUM cana-1173 75 25 28 28 NUM cana-1173 75 26 45 45 NUM cana-1173 75 27 41 41 NUM cana-1173 75 28 52 52 NUM cana-1173 75 29 ) ) PUNCT cana-1173 75 30 . . PUNCT cana-1173 76 1 communications communication NOUN cana-1173 76 2 on on ADP cana-1173 76 3 applied apply VERB cana-1173 76 4 nonlinear nonlinear ADJ cana-1173 76 5 analysis analysis NOUN cana-1173 76 6 issn issn NOUN cana-1173 76 7 : : PUNCT cana-1173 76 8 1074 1074 NUM cana-1173 76 9 - - PUNCT cana-1173 76 10 133x 133x NUM cana-1173 76 11 vol vol NOUN cana-1173 76 12 31 31 NUM cana-1173 76 13 no no NOUN cana-1173 76 14 . . PUNCT cana-1173 77 1 6s 6s NUM cana-1173 77 2 ( ( PUNCT cana-1173 77 3 2024 2024 NUM cana-1173 77 4 ) ) PUNCT cana-1173 77 5 146 146 NUM cana-1173 77 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 77 7 step step NOUN cana-1173 77 8 3 3 NUM cana-1173 77 9 : : PUNCT cana-1173 77 10 let let VERB cana-1173 77 11 a a PRON cana-1173 77 12 = = X cana-1173 77 13 ( ( PUNCT cana-1173 77 14 3 3 NUM cana-1173 77 15 βˆ’3 βˆ’3 NOUN cana-1173 77 16 4 4 NUM cana-1173 77 17 2 2 NUM cana-1173 77 18 βˆ’3 βˆ’3 NOUN cana-1173 77 19 4 4 NUM cana-1173 77 20 0 0 NUM cana-1173 77 21 βˆ’1 βˆ’1 NOUN cana-1173 77 22 1 1 NUM cana-1173 77 23 ) ) PUNCT cana-1173 77 24 be be AUX cana-1173 77 25 the the DET cana-1173 77 26 encryption encryption NOUN cana-1173 77 27 key key NOUN cana-1173 77 28 and and CCONJ cana-1173 77 29 its its PRON cana-1173 77 30 inverse inverse NOUN cana-1173 77 31 π΄βˆ’1 π΄βˆ’1 NOUN cana-1173 77 32 = = PUNCT cana-1173 77 33 ( ( PUNCT cana-1173 77 34 1 1 NUM cana-1173 77 35 βˆ’1 βˆ’1 NOUN cana-1173 77 36 0 0 NUM cana-1173 77 37 βˆ’2 βˆ’2 NOUN cana-1173 78 1 3 3 NUM cana-1173 78 2 βˆ’4 βˆ’4 NOUN cana-1173 78 3 βˆ’2 βˆ’2 PROPN cana-1173 78 4 3 3 NUM cana-1173 78 5 βˆ’3 βˆ’3 ADV cana-1173 78 6 ) ) PUNCT cana-1173 78 7 be be AUX cana-1173 78 8 the the DET cana-1173 78 9 decryption decryption NOUN cana-1173 78 10 key key NOUN cana-1173 78 11 . . PUNCT cana-1173 79 1 step step NOUN cana-1173 79 2 4 4 NUM cana-1173 79 3 : : PUNCT cana-1173 79 4 i i PRON cana-1173 79 5 stage stage NOUN cana-1173 79 6 of of ADP cana-1173 79 7 encryption encryption NOUN cana-1173 79 8 let let VERB cana-1173 79 9 e e X cana-1173 79 10 ≑ ≑ PROPN cana-1173 79 11 ap(mod ap(mod PROPN cana-1173 79 12 53 53 NUM cana-1173 79 13 ) ) PUNCT cana-1173 79 14 . . PUNCT cana-1173 80 1 ≑ ≑ PROPN cana-1173 80 2 ( ( PUNCT cana-1173 80 3 3 3 NUM cana-1173 80 4 βˆ’3 βˆ’3 NOUN cana-1173 80 5 4 4 NUM cana-1173 80 6 2 2 NUM cana-1173 80 7 βˆ’3 βˆ’3 NOUN cana-1173 80 8 4 4 NUM cana-1173 80 9 0 0 NUM cana-1173 80 10 βˆ’1 βˆ’1 NOUN cana-1173 80 11 1 1 NUM cana-1173 80 12 ) ) PUNCT cana-1173 80 13 ( ( PUNCT cana-1173 80 14 5 5 NUM cana-1173 80 15 41 41 NUM cana-1173 80 16 49 49 NUM cana-1173 80 17 42 42 NUM cana-1173 80 18 41 41 NUM cana-1173 80 19 40 40 NUM cana-1173 80 20 47 47 NUM cana-1173 80 21 27 27 NUM cana-1173 80 22 4 4 NUM cana-1173 80 23 36 36 NUM cana-1173 80 24 32 32 NUM cana-1173 80 25 28 28 NUM cana-1173 80 26 45 45 NUM cana-1173 80 27 41 41 NUM cana-1173 80 28 52 52 NUM cana-1173 80 29 ) ) PUNCT cana-1173 80 30 ( ( PUNCT cana-1173 80 31 mod mod PROPN cana-1173 80 32 53 53 NUM cana-1173 80 33 ) ) PUNCT cana-1173 80 34 . . PUNCT cana-1173 81 1 e e PROPN cana-1173 81 2 ≑ ≑ PROPN cana-1173 81 3 ( ( PUNCT cana-1173 81 4 77 77 NUM cana-1173 81 5 108 108 NUM cana-1173 81 6 43 43 NUM cana-1173 81 7 72 72 NUM cana-1173 81 8 67 67 NUM cana-1173 81 9 βˆ’6 βˆ’6 NOUN cana-1173 81 10 5 5 NUM cana-1173 81 11 βˆ’14 βˆ’14 NUM cana-1173 81 12 βˆ’36 βˆ’36 NOUN cana-1173 81 13 124 124 NUM cana-1173 81 14 88 88 NUM cana-1173 81 15 βˆ’4 βˆ’4 NOUN cana-1173 81 16 220 220 NUM cana-1173 81 17 175 175 NUM cana-1173 81 18 11 11 NUM cana-1173 81 19 ) ) PUNCT cana-1173 81 20 ( ( PUNCT cana-1173 81 21 mod mod PROPN cana-1173 81 22 53 53 NUM cana-1173 81 23 ) ) PUNCT cana-1173 81 24 . . PUNCT cana-1173 82 1 e e X cana-1173 82 2 = = PUNCT cana-1173 83 1 ( ( PUNCT cana-1173 83 2 πŸπŸ’ πŸπŸ’ NUM cana-1173 83 3 𝟐 𝟐 NUM cana-1173 83 4 πŸ’πŸ‘ πŸ’πŸ‘ NUM cana-1173 83 5 πŸπŸ— πŸπŸ— NUM cana-1173 83 6 πŸπŸ’ πŸπŸ’ NUM cana-1173 83 7 πŸ’πŸ• πŸ’πŸ• NUM cana-1173 83 8 πŸ“ πŸ“ NUM cana-1173 83 9 πŸ‘πŸ— πŸ‘πŸ— NUM cana-1173 83 10 πŸπŸ• πŸπŸ• NUM cana-1173 83 11 πŸπŸ– πŸπŸ– NUM cana-1173 83 12 πŸ‘πŸ“ πŸ‘πŸ“ NUM cana-1173 83 13 πŸ’πŸ— πŸ’πŸ— NUM cana-1173 83 14 πŸ– πŸ– NUM cana-1173 83 15 πŸπŸ” πŸπŸ” NUM cana-1173 83 16 𝟏𝟏 𝟏𝟏 NUM cana-1173 83 17 ) ) PUNCT cana-1173 83 18 . . PUNCT cana-1173 84 1 step step NOUN cana-1173 84 2 5 5 NUM cana-1173 84 3 : : PUNCT cana-1173 84 4 ii ii NOUN cana-1173 84 5 stage stage NOUN cana-1173 84 6 of of ADP cana-1173 84 7 encryption encryption NOUN cana-1173 84 8 now now ADV cana-1173 84 9 for for ADP cana-1173 84 10 the the DET cana-1173 84 11 matrix matrix NOUN cana-1173 84 12 e e NOUN cana-1173 84 13 let let VERB cana-1173 84 14 us we PRON cana-1173 84 15 apply apply VERB cana-1173 84 16 laplace laplace NOUN cana-1173 84 17 transform transform NOUN cana-1173 84 18 . . PUNCT cana-1173 85 1 let let VERB cana-1173 85 2 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 85 3 ) ) PUNCT cana-1173 85 4 = = PUNCT cana-1173 85 5 βˆ‘ βˆ‘ PUNCT cana-1173 86 1 𝑑2𝐺𝑖 𝑑2𝐺𝑖 PROPN cana-1173 86 2 14 14 NUM cana-1173 86 3 𝑖=0 𝑖=0 SYM cana-1173 86 4 π‘π‘œπ‘ β„Žπ‘‘ π‘π‘œπ‘ β„Žπ‘‘ NOUN cana-1173 86 5 , , PUNCT cana-1173 86 6 where where SCONJ cana-1173 86 7 π‘π‘œπ‘ β„Žπ‘‘ π‘π‘œπ‘ β„Žπ‘‘ NOUN cana-1173 86 8 = = NOUN cana-1173 86 9 1 1 NUM cana-1173 86 10 + + NUM cana-1173 86 11 𝑑2 𝑑2 PROPN cana-1173 86 12 2 2 NUM cana-1173 86 13 ! ! PUNCT cana-1173 87 1 + + NUM cana-1173 87 2 𝑑4 𝑑4 PROPN cana-1173 87 3 4 4 NUM cana-1173 87 4 ! ! PUNCT cana-1173 88 1 + + PUNCT cana-1173 88 2 𝑑6 𝑑6 PROPN cana-1173 88 3 6 6 NUM cana-1173 88 4 ! ! PUNCT cana-1173 89 1 + + CCONJ cana-1173 89 2 𝑑8 𝑑8 PROPN cana-1173 89 3 8 8 NUM cana-1173 89 4 ! ! PUNCT cana-1173 90 1 + + CCONJ cana-1173 90 2 β‹― β‹― NOUN cana-1173 90 3 … … PUNCT cana-1173 90 4 … … PUNCT cana-1173 90 5 here here ADV cana-1173 90 6 , , PUNCT cana-1173 90 7 n=14 n=14 PROPN cana-1173 90 8 . . PUNCT cana-1173 91 1 therefore therefore ADV cana-1173 91 2 , , PUNCT cana-1173 91 3 π‘π‘œπ‘ β„Žπ‘‘ π‘π‘œπ‘ β„Žπ‘‘ NOUN cana-1173 91 4 = = SYM cana-1173 91 5 1 1 NUM cana-1173 91 6 + + NUM cana-1173 91 7 𝑑2 𝑑2 PROPN cana-1173 91 8 2 2 NUM cana-1173 91 9 ! ! PUNCT cana-1173 92 1 + + NUM cana-1173 92 2 𝑑4 𝑑4 PROPN cana-1173 92 3 4 4 NUM cana-1173 92 4 ! ! PUNCT cana-1173 93 1 + + PUNCT cana-1173 93 2 𝑑6 𝑑6 PROPN cana-1173 93 3 6 6 NUM cana-1173 93 4 ! ! PUNCT cana-1173 94 1 + + CCONJ cana-1173 94 2 𝑑8 𝑑8 PROPN cana-1173 94 3 8 8 NUM cana-1173 94 4 ! ! PUNCT cana-1173 95 1 + + CCONJ cana-1173 95 2 𝑑10 𝑑10 PROPN cana-1173 95 3 10 10 NUM cana-1173 95 4 ! ! PUNCT cana-1173 96 1 + + CCONJ cana-1173 96 2 𝑑12 𝑑12 NOUN cana-1173 96 3 12 12 NUM cana-1173 96 4 ! ! PUNCT cana-1173 97 1 + + CCONJ cana-1173 97 2 𝑑14 𝑑14 PROPN cana-1173 97 3 14 14 NUM cana-1173 97 4 ! ! PUNCT cana-1173 98 1 + + CCONJ cana-1173 98 2 𝑑16 𝑑16 ADJ cana-1173 98 3 16 16 NUM cana-1173 98 4 ! ! PUNCT cana-1173 99 1 + + CCONJ cana-1173 99 2 𝑑18 𝑑18 PROPN cana-1173 99 3 18 18 NUM cana-1173 99 4 ! ! PUNCT cana-1173 100 1 + + NUM cana-1173 100 2 𝑑20 𝑑20 NOUN cana-1173 100 3 20 20 NUM cana-1173 100 4 ! ! PUNCT cana-1173 101 1 + + CCONJ cana-1173 101 2 𝑑22 𝑑22 ADV cana-1173 101 3 22 22 NUM cana-1173 101 4 ! ! PUNCT cana-1173 102 1 + + CCONJ cana-1173 102 2 𝑑24 𝑑24 PROPN cana-1173 102 3 24 24 NUM cana-1173 102 4 ! ! PUNCT cana-1173 103 1 + + CCONJ cana-1173 103 2 𝑑26 𝑑26 ADV cana-1173 103 3 26 26 NUM cana-1173 103 4 ! ! PUNCT cana-1173 104 1 + + CCONJ cana-1173 104 2 𝑑28 𝑑28 ADJ cana-1173 104 3 28 28 NUM cana-1173 104 4 ! ! PUNCT cana-1173 104 5 . . PUNCT cana-1173 105 1 𝑓(𝑑 𝑓(𝑑 VERB cana-1173 105 2 ) ) PUNCT cana-1173 105 3 = = SYM cana-1173 106 1 𝐺0 𝐺0 NOUN cana-1173 106 2 + + NUM cana-1173 106 3 𝐺1 𝐺1 NOUN cana-1173 106 4 𝑑2 𝑑2 PROPN cana-1173 106 5 2 2 NUM cana-1173 106 6 ! ! PUNCT cana-1173 107 1 + + CCONJ cana-1173 107 2 𝐺2 𝐺2 ADJ cana-1173 107 3 𝑑4 𝑑4 NOUN cana-1173 107 4 4 4 NUM cana-1173 107 5 ! ! PUNCT cana-1173 108 1 + + CCONJ cana-1173 108 2 𝐺3 𝐺3 PROPN cana-1173 108 3 𝑑6 𝑑6 PROPN cana-1173 108 4 6 6 NUM cana-1173 108 5 ! ! PUNCT cana-1173 109 1 + + NUM cana-1173 109 2 𝐺4 𝐺4 PROPN cana-1173 109 3 𝑑8 𝑑8 PROPN cana-1173 109 4 8 8 NUM cana-1173 109 5 ! ! PUNCT cana-1173 110 1 + + CCONJ cana-1173 110 2 𝐺5 𝐺5 NOUN cana-1173 110 3 𝑑10 𝑑10 PROPN cana-1173 110 4 10 10 NUM cana-1173 110 5 ! ! PUNCT cana-1173 111 1 + + CCONJ cana-1173 111 2 𝐺6 𝐺6 PROPN cana-1173 111 3 𝑑12 𝑑12 NOUN cana-1173 111 4 12 12 NUM cana-1173 111 5 ! ! PUNCT cana-1173 112 1 + + CCONJ cana-1173 112 2 𝐺7 𝐺7 ADJ cana-1173 112 3 𝑑14 𝑑14 NOUN cana-1173 112 4 14 14 NUM cana-1173 112 5 ! ! PUNCT cana-1173 113 1 + + CCONJ cana-1173 113 2 𝐺8 𝐺8 PROPN cana-1173 113 3 𝑑16 𝑑16 VERB cana-1173 113 4 16 16 NUM cana-1173 113 5 ! ! PUNCT cana-1173 114 1 + + CCONJ cana-1173 114 2 𝐺9 𝐺9 PROPN cana-1173 114 3 𝑑18 𝑑18 PROPN cana-1173 114 4 18 18 NUM cana-1173 114 5 ! ! PUNCT cana-1173 115 1 + + CCONJ cana-1173 115 2 𝐺10 𝐺10 PROPN cana-1173 115 3 𝑑20 𝑑20 NOUN cana-1173 115 4 20 20 NUM cana-1173 115 5 ! ! PUNCT cana-1173 116 1 + + CCONJ cana-1173 116 2 𝐺11 𝐺11 NOUN cana-1173 116 3 𝑑22 𝑑22 ADV cana-1173 116 4 22 22 NUM cana-1173 116 5 ! ! PUNCT cana-1173 117 1 + + CCONJ cana-1173 117 2 𝐺12 𝐺12 ADP cana-1173 117 3 𝑑24 𝑑24 NOUN cana-1173 117 4 24 24 NUM cana-1173 117 5 ! ! PUNCT cana-1173 118 1 + + CCONJ cana-1173 118 2 𝐺13 𝐺13 PROPN cana-1173 118 3 𝑑26 𝑑26 ADV cana-1173 118 4 26 26 NUM cana-1173 118 5 ! ! PUNCT cana-1173 119 1 + + CCONJ cana-1173 119 2 𝐺14 𝐺14 PROPN cana-1173 119 3 𝑑28 𝑑28 ADJ cana-1173 119 4 28 28 NUM cana-1173 119 5 ! ! PUNCT cana-1173 120 1 where where SCONJ cana-1173 120 2 𝐺0 𝐺0 NOUN cana-1173 120 3 = = SYM cana-1173 120 4 24 24 NUM cana-1173 120 5 , , PUNCT cana-1173 120 6 𝐺1 𝐺1 NOUN cana-1173 120 7 = = SYM cana-1173 120 8 2 2 NUM cana-1173 120 9 , , PUNCT cana-1173 120 10 𝐺2 𝐺2 NOUN cana-1173 120 11 = = SYM cana-1173 120 12 43 43 NUM cana-1173 120 13 , , PUNCT cana-1173 120 14 𝐺3 𝐺3 NOUN cana-1173 120 15 = = SYM cana-1173 120 16 18 18 NUM cana-1173 120 17 , , PUNCT cana-1173 120 18 𝐺4 𝐺4 NOUN cana-1173 120 19 = = SYM cana-1173 120 20 8 8 NUM cana-1173 120 21 , , PUNCT cana-1173 120 22 𝐺5 𝐺5 NOUN cana-1173 120 23 = = NUM cana-1173 120 24 19 19 NUM cana-1173 120 25 , , PUNCT cana-1173 120 26 𝐺6 𝐺6 NOUN cana-1173 120 27 = = SYM cana-1173 120 28 14 14 NUM cana-1173 120 29 , , PUNCT cana-1173 120 30 𝐺7 𝐺7 ADJ cana-1173 121 1 = = SYM cana-1173 121 2 47 47 NUM cana-1173 121 3 , , PUNCT cana-1173 121 4 𝐺8 𝐺8 PROPN cana-1173 121 5 = = SYM cana-1173 121 6 35 35 NUM cana-1173 121 7 , , PUNCT cana-1173 121 8 𝐺9 𝐺9 PROPN cana-1173 121 9 = = SYM cana-1173 121 10 16 16 NUM cana-1173 121 11 , , PUNCT cana-1173 121 12 𝐺10 𝐺10 PROPN cana-1173 121 13 = = PUNCT cana-1173 121 14 5 5 NUM cana-1173 121 15 , , PUNCT cana-1173 121 16 𝐺11 𝐺11 NOUN cana-1173 121 17 = = SYM cana-1173 121 18 39 39 NUM cana-1173 121 19 , , PUNCT cana-1173 121 20 𝐺12 𝐺12 PROPN cana-1173 121 21 = = SYM cana-1173 121 22 17 17 NUM cana-1173 121 23 , , PUNCT cana-1173 121 24 𝐺13 𝐺13 PROPN cana-1173 121 25 = = PUNCT cana-1173 121 26 49 49 NUM cana-1173 121 27 , , PUNCT cana-1173 121 28 𝐺14 𝐺14 PROPN cana-1173 121 29 = = PUNCT cana-1173 121 30 11 11 NUM cana-1173 121 31 . . PUNCT cana-1173 122 1 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 122 2 ) ) PUNCT cana-1173 123 1 = = SYM cana-1173 123 2 𝑑2 𝑑2 NOUN cana-1173 123 3 [ [ X cana-1173 123 4 24 24 NUM cana-1173 123 5 + + CCONJ cana-1173 123 6 2 2 NUM cana-1173 123 7 𝑑2 𝑑2 NOUN cana-1173 123 8 2 2 NUM cana-1173 123 9 ! ! PUNCT cana-1173 124 1 + + CCONJ cana-1173 124 2 43 43 NUM cana-1173 124 3 𝑑4 𝑑4 NOUN cana-1173 124 4 4 4 NUM cana-1173 124 5 ! ! PUNCT cana-1173 125 1 + + CCONJ cana-1173 125 2 18 18 NUM cana-1173 125 3 𝑑6 𝑑6 NOUN cana-1173 125 4 6 6 NUM cana-1173 125 5 ! ! PUNCT cana-1173 126 1 + + CCONJ cana-1173 126 2 8 8 NUM cana-1173 126 3 𝑑8 𝑑8 PROPN cana-1173 126 4 8 8 NUM cana-1173 126 5 ! ! PUNCT cana-1173 127 1 + + CCONJ cana-1173 127 2 19 19 NUM cana-1173 127 3 𝑑10 𝑑10 NUM cana-1173 127 4 10 10 NUM cana-1173 127 5 ! ! PUNCT cana-1173 128 1 + + CCONJ cana-1173 128 2 14 14 NUM cana-1173 128 3 𝑑12 𝑑12 NOUN cana-1173 128 4 12 12 NUM cana-1173 128 5 ! ! PUNCT cana-1173 129 1 + + CCONJ cana-1173 129 2 47 47 NUM cana-1173 129 3 𝑑14 𝑑14 NOUN cana-1173 129 4 14 14 NUM cana-1173 129 5 ! ! PUNCT cana-1173 130 1 + + CCONJ cana-1173 130 2 35 35 NUM cana-1173 130 3 𝑑16 𝑑16 VERB cana-1173 130 4 16 16 NUM cana-1173 130 5 ! ! PUNCT cana-1173 131 1 + + CCONJ cana-1173 131 2 16 16 NUM cana-1173 131 3 𝑑18 𝑑18 PROPN cana-1173 131 4 18 18 NUM cana-1173 131 5 ! ! PUNCT cana-1173 132 1 + + CCONJ cana-1173 132 2 5 5 NUM cana-1173 132 3 𝑑20 𝑑20 NOUN cana-1173 132 4 20 20 NUM cana-1173 132 5 ! ! PUNCT cana-1173 133 1 + + CCONJ cana-1173 133 2 39 39 NUM cana-1173 133 3 𝑑22 𝑑22 ADJ cana-1173 133 4 22 22 NUM cana-1173 133 5 ! ! PUNCT cana-1173 134 1 + + CCONJ cana-1173 134 2 17 17 NUM cana-1173 134 3 𝑑24 𝑑24 NOUN cana-1173 134 4 24 24 NUM cana-1173 134 5 ! ! PUNCT cana-1173 135 1 + + CCONJ cana-1173 135 2 49 49 NUM cana-1173 135 3 𝑑26 𝑑26 ADV cana-1173 135 4 26 26 NUM cana-1173 135 5 ! ! PUNCT cana-1173 136 1 + + CCONJ cana-1173 136 2 11 11 NUM cana-1173 136 3 𝑑28 𝑑28 NUM cana-1173 136 4 28 28 NUM cana-1173 136 5 ! ! PUNCT cana-1173 136 6 ] ] PUNCT cana-1173 136 7 . . PUNCT cana-1173 137 1 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 137 2 ) ) PUNCT cana-1173 137 3 = = NOUN cana-1173 138 1 [ [ PUNCT cana-1173 138 2 24𝑑2 24𝑑2 NUM cana-1173 138 3 + + CCONJ cana-1173 138 4 2 2 NUM cana-1173 138 5 𝑑4 𝑑4 NOUN cana-1173 138 6 2 2 NUM cana-1173 138 7 ! ! PUNCT cana-1173 139 1 + + CCONJ cana-1173 139 2 43 43 NUM cana-1173 139 3 𝑑6 𝑑6 NOUN cana-1173 139 4 4 4 NUM cana-1173 139 5 ! ! PUNCT cana-1173 140 1 + + CCONJ cana-1173 140 2 18 18 NUM cana-1173 140 3 𝑑8 𝑑8 PROPN cana-1173 140 4 6 6 NUM cana-1173 140 5 ! ! PUNCT cana-1173 141 1 + + CCONJ cana-1173 141 2 8 8 NUM cana-1173 141 3 𝑑10 𝑑10 NUM cana-1173 141 4 8 8 NUM cana-1173 141 5 ! ! PUNCT cana-1173 142 1 + + CCONJ cana-1173 142 2 19 19 NUM cana-1173 142 3 𝑑12 𝑑12 NOUN cana-1173 142 4 10 10 NUM cana-1173 142 5 ! ! PUNCT cana-1173 143 1 + + CCONJ cana-1173 143 2 14 14 NUM cana-1173 143 3 𝑑14 𝑑14 NOUN cana-1173 143 4 12 12 NUM cana-1173 143 5 ! ! PUNCT cana-1173 144 1 + + CCONJ cana-1173 144 2 47 47 NUM cana-1173 144 3 𝑑16 𝑑16 VERB cana-1173 144 4 14 14 NUM cana-1173 144 5 ! ! PUNCT cana-1173 145 1 + + CCONJ cana-1173 145 2 35 35 NUM cana-1173 145 3 𝑑18 𝑑18 NOUN cana-1173 145 4 16 16 NUM cana-1173 145 5 ! ! PUNCT cana-1173 146 1 + + CCONJ cana-1173 146 2 16 16 NUM cana-1173 146 3 𝑑20 𝑑20 NOUN cana-1173 146 4 18 18 NUM cana-1173 146 5 ! ! PUNCT cana-1173 147 1 + + CCONJ cana-1173 147 2 5 5 NUM cana-1173 147 3 𝑑22 𝑑22 ADV cana-1173 147 4 20 20 NUM cana-1173 147 5 ! ! PUNCT cana-1173 148 1 + + CCONJ cana-1173 148 2 39 39 NUM cana-1173 148 3 𝑑24 𝑑24 NOUN cana-1173 148 4 22 22 NUM cana-1173 148 5 ! ! PUNCT cana-1173 149 1 + + CCONJ cana-1173 149 2 17 17 NUM cana-1173 149 3 𝑑26 𝑑26 ADV cana-1173 149 4 24 24 NUM cana-1173 149 5 ! ! PUNCT cana-1173 150 1 + + CCONJ cana-1173 150 2 49 49 NUM cana-1173 150 3 𝑑28 𝑑28 ADJ cana-1173 150 4 26 26 NUM cana-1173 150 5 ! ! PUNCT cana-1173 151 1 + + CCONJ cana-1173 151 2 11 11 NUM cana-1173 151 3 𝑑30 𝑑30 NOUN cana-1173 151 4 28 28 NUM cana-1173 151 5 ! ! PUNCT cana-1173 151 6 ] ] PUNCT cana-1173 151 7 . . PUNCT cana-1173 152 1 apply apply VERB cana-1173 152 2 laplace laplace NOUN cana-1173 152 3 transform transform NOUN cana-1173 152 4 for for ADP cana-1173 152 5 f(t f(t NOUN cana-1173 152 6 ) ) PUNCT cana-1173 152 7 . . PUNCT cana-1173 153 1 𝐿{𝑓(𝑑 𝐿{𝑓(𝑑 PUNCT cana-1173 153 2 ) ) PUNCT cana-1173 153 3 } } PUNCT cana-1173 153 4 = = SYM cana-1173 153 5 𝐿 𝐿 PROPN cana-1173 153 6 { { PUNCT cana-1173 153 7 24𝑑2 24𝑑2 PROPN cana-1173 153 8 + + CCONJ cana-1173 153 9 2 2 NUM cana-1173 153 10 𝑑4 𝑑4 NOUN cana-1173 153 11 2 2 NUM cana-1173 153 12 ! ! PUNCT cana-1173 154 1 + + CCONJ cana-1173 154 2 43 43 NUM cana-1173 154 3 𝑑6 𝑑6 NOUN cana-1173 154 4 4 4 NUM cana-1173 154 5 ! ! PUNCT cana-1173 155 1 + + CCONJ cana-1173 155 2 18 18 NUM cana-1173 155 3 𝑑8 𝑑8 PROPN cana-1173 155 4 6 6 NUM cana-1173 155 5 ! ! PUNCT cana-1173 156 1 + + CCONJ cana-1173 156 2 8 8 NUM cana-1173 156 3 𝑑10 𝑑10 NUM cana-1173 156 4 8 8 NUM cana-1173 156 5 ! ! PUNCT cana-1173 157 1 + + CCONJ cana-1173 157 2 19 19 NUM cana-1173 157 3 𝑑12 𝑑12 NOUN cana-1173 157 4 10 10 NUM cana-1173 157 5 ! ! PUNCT cana-1173 158 1 + + CCONJ cana-1173 158 2 14 14 NUM cana-1173 158 3 𝑑14 𝑑14 NOUN cana-1173 158 4 12 12 NUM cana-1173 158 5 ! ! PUNCT cana-1173 159 1 + + CCONJ cana-1173 159 2 47 47 NUM cana-1173 159 3 𝑑16 𝑑16 VERB cana-1173 159 4 14 14 NUM cana-1173 159 5 ! ! PUNCT cana-1173 160 1 + + CCONJ cana-1173 160 2 35 35 NUM cana-1173 160 3 𝑑18 𝑑18 NOUN cana-1173 160 4 16 16 NUM cana-1173 160 5 ! ! PUNCT cana-1173 161 1 + + CCONJ cana-1173 161 2 16 16 NUM cana-1173 161 3 𝑑20 𝑑20 NOUN cana-1173 161 4 18 18 NUM cana-1173 161 5 ! ! PUNCT cana-1173 162 1 + + CCONJ cana-1173 162 2 5 5 NUM cana-1173 162 3 𝑑22 𝑑22 ADV cana-1173 162 4 20 20 NUM cana-1173 162 5 ! ! PUNCT cana-1173 163 1 + + CCONJ cana-1173 163 2 39 39 NUM cana-1173 163 3 𝑑24 𝑑24 NOUN cana-1173 163 4 22 22 NUM cana-1173 163 5 ! ! PUNCT cana-1173 164 1 + + CCONJ cana-1173 164 2 17 17 NUM cana-1173 164 3 𝑑26 𝑑26 ADV cana-1173 164 4 24 24 NUM cana-1173 164 5 ! ! PUNCT cana-1173 165 1 + + CCONJ cana-1173 165 2 49 49 NUM cana-1173 165 3 𝑑28 𝑑28 ADJ cana-1173 165 4 26 26 NUM cana-1173 165 5 ! ! PUNCT cana-1173 166 1 + + CCONJ cana-1173 166 2 11 11 NUM cana-1173 166 3 𝑑30 𝑑30 NOUN cana-1173 166 4 28 28 NUM cana-1173 166 5 ! ! PUNCT cana-1173 166 6 } } PUNCT cana-1173 166 7 . . PUNCT cana-1173 167 1 communications communication NOUN cana-1173 167 2 on on ADP cana-1173 167 3 applied apply VERB cana-1173 167 4 nonlinear nonlinear ADJ cana-1173 167 5 analysis analysis NOUN cana-1173 167 6 issn issn NOUN cana-1173 167 7 : : PUNCT cana-1173 167 8 1074 1074 NUM cana-1173 167 9 - - PUNCT cana-1173 167 10 133x 133x NUM cana-1173 167 11 vol vol NOUN cana-1173 167 12 31 31 NUM cana-1173 167 13 no no NOUN cana-1173 167 14 . . PUNCT cana-1173 168 1 6s 6s NUM cana-1173 168 2 ( ( PUNCT cana-1173 168 3 2024 2024 NUM cana-1173 168 4 ) ) PUNCT cana-1173 168 5 147 147 NUM cana-1173 168 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 168 7 𝐿{𝑓(𝑑 𝐿{𝑓(𝑑 NUM cana-1173 168 8 ) ) PUNCT cana-1173 168 9 } } PUNCT cana-1173 169 1 = = SYM cana-1173 169 2 24 24 NUM cana-1173 169 3 2 2 NUM cana-1173 169 4 ! ! PUNCT cana-1173 170 1 𝑠3 𝑠3 NOUN cana-1173 170 2 + + NOUN cana-1173 171 1 2 2 NUM cana-1173 171 2 4 4 NUM cana-1173 171 3 ! ! PUNCT cana-1173 172 1 2!𝑠5 2!𝑠5 NUM cana-1173 173 1 + + CCONJ cana-1173 173 2 43 43 NUM cana-1173 173 3 6 6 NUM cana-1173 173 4 ! ! PUNCT cana-1173 174 1 4!𝑠7 4!𝑠7 NUM cana-1173 174 2 + + CCONJ cana-1173 174 3 18 18 NUM cana-1173 174 4 8 8 NUM cana-1173 174 5 ! ! PUNCT cana-1173 175 1 6!𝑠9 6!𝑠9 NUM cana-1173 176 1 + + CCONJ cana-1173 176 2 8 8 NUM cana-1173 176 3 10 10 NUM cana-1173 176 4 ! ! PUNCT cana-1173 177 1 8!𝑠11 8!𝑠11 NUM cana-1173 177 2 + + CCONJ cana-1173 177 3 19 19 NUM cana-1173 177 4 12 12 NUM cana-1173 177 5 ! ! PUNCT cana-1173 178 1 10!𝑠13 10!𝑠13 NOUN cana-1173 179 1 + + CCONJ cana-1173 179 2 14 14 NUM cana-1173 179 3 14 14 NUM cana-1173 179 4 ! ! PUNCT cana-1173 180 1 12!𝑠15 12!𝑠15 NUM cana-1173 180 2 +47 +47 NUM cana-1173 180 3 16 16 NUM cana-1173 180 4 ! ! PUNCT cana-1173 181 1 14!𝑠17 14!𝑠17 NOUN cana-1173 181 2 + + CCONJ cana-1173 181 3 35 35 NUM cana-1173 181 4 18 18 NUM cana-1173 181 5 ! ! PUNCT cana-1173 182 1 16!𝑠19 16!𝑠19 NUM cana-1173 183 1 + + CCONJ cana-1173 183 2 16 16 NUM cana-1173 183 3 20 20 NUM cana-1173 183 4 ! ! PUNCT cana-1173 183 5 18!𝑠21 18!𝑠21 NOUN cana-1173 184 1 + + CCONJ cana-1173 184 2 5 5 NUM cana-1173 184 3 22 22 NUM cana-1173 184 4 ! ! PUNCT cana-1173 185 1 20!𝑠23 20!𝑠23 NUM cana-1173 185 2 + + CCONJ cana-1173 185 3 39 39 NUM cana-1173 185 4 24 24 NUM cana-1173 185 5 ! ! PUNCT cana-1173 185 6 22!𝑠25 22!𝑠25 NUM cana-1173 185 7 + + CCONJ cana-1173 185 8 17 17 NUM cana-1173 185 9 26 26 NUM cana-1173 185 10 ! ! PUNCT cana-1173 185 11 24!𝑠27 24!𝑠27 NUM cana-1173 186 1 + + CCONJ cana-1173 186 2 49 49 NUM cana-1173 186 3 28 28 NUM cana-1173 186 4 ! ! PUNCT cana-1173 187 1 26!𝑠29 26!𝑠29 NUM cana-1173 188 1 + + CCONJ cana-1173 188 2 11 11 NUM cana-1173 188 3 30 30 NUM cana-1173 188 4 ! ! PUNCT cana-1173 188 5 28!𝑠31 28!𝑠31 NUM cana-1173 188 6 . . PUNCT cana-1173 189 1 𝐿{𝑓(𝑑 𝐿{𝑓(𝑑 NUM cana-1173 189 2 ) ) PUNCT cana-1173 189 3 } } PUNCT cana-1173 190 1 = = SYM cana-1173 190 2 48 48 NUM cana-1173 190 3 𝑠3 𝑠3 NOUN cana-1173 190 4 + + CCONJ cana-1173 190 5 24 24 NUM cana-1173 190 6 𝑠5 𝑠5 NOUN cana-1173 190 7 + + CCONJ cana-1173 190 8 1290 1290 NUM cana-1173 190 9 𝑠7 𝑠7 PROPN cana-1173 190 10 + + CCONJ cana-1173 190 11 1008 1008 NUM cana-1173 190 12 𝑠9 𝑠9 NOUN cana-1173 190 13 + + CCONJ cana-1173 190 14 720 720 NUM cana-1173 190 15 𝑠11 𝑠11 ADJ cana-1173 190 16 + + CCONJ cana-1173 190 17 2508 2508 NUM cana-1173 190 18 𝑠13 𝑠13 NOUN cana-1173 190 19 + + CCONJ cana-1173 190 20 2548 2548 NUM cana-1173 190 21 𝑠15 𝑠15 NOUN cana-1173 190 22 + + CCONJ cana-1173 190 23 11280 11280 NUM cana-1173 190 24 𝑠17 𝑠17 NOUN cana-1173 190 25 + + CCONJ cana-1173 190 26 10710 10710 NUM cana-1173 190 27 𝑠19 𝑠19 VERB cana-1173 191 1 + + CCONJ cana-1173 191 2 6080 6080 NUM cana-1173 191 3 𝑠21 𝑠21 NOUN cana-1173 191 4 + + CCONJ cana-1173 191 5 2310 2310 NUM cana-1173 191 6 𝑠23 𝑠23 NUM cana-1173 191 7 + + NUM cana-1173 191 8 21528 21528 NUM cana-1173 191 9 𝑠25 𝑠25 NOUN cana-1173 191 10 + + CCONJ cana-1173 191 11 11050 11050 NUM cana-1173 191 12 𝑠27 𝑠27 NOUN cana-1173 191 13 + + CCONJ cana-1173 191 14 37044 37044 NUM cana-1173 191 15 𝑠29 𝑠29 NOUN cana-1173 191 16 + + CCONJ cana-1173 191 17 9570 9570 NUM cana-1173 191 18 𝑠31 𝑠31 NOUN cana-1173 191 19 . . PUNCT cana-1173 192 1 adjusting adjust VERB cana-1173 192 2 the the DET cana-1173 192 3 values value NOUN cana-1173 192 4 under under ADP cana-1173 192 5 modulo modulo NOUN cana-1173 192 6 255 255 NUM cana-1173 192 7 , , PUNCT cana-1173 192 8 we we PRON cana-1173 192 9 get get VERB cana-1173 192 10 48 48 NUM cana-1173 192 11 ≑ ≑ PROPN cana-1173 192 12 48 48 NUM cana-1173 192 13 mod mod NOUN cana-1173 192 14 255 255 NUM cana-1173 192 15 24 24 NUM cana-1173 192 16 ≑ ≑ PROPN cana-1173 192 17 24 24 NUM cana-1173 192 18 mod mod ADJ cana-1173 192 19 255 255 NUM cana-1173 192 20 1290 1290 NUM cana-1173 192 21 ≑ ≑ PROPN cana-1173 192 22 15 15 NUM cana-1173 192 23 mod mod PROPN cana-1173 192 24 255 255 NUM cana-1173 192 25 1008 1008 NUM cana-1173 192 26 ≑ ≑ PROPN cana-1173 192 27 243 243 NUM cana-1173 193 1 mod mod ADJ cana-1173 193 2 255 255 NUM cana-1173 193 3 720 720 NUM cana-1173 193 4 ≑ ≑ PROPN cana-1173 193 5 210 210 NUM cana-1173 193 6 mod mod ADJ cana-1173 193 7 255 255 NUM cana-1173 193 8 2508 2508 NUM cana-1173 193 9 ≑ ≑ PROPN cana-1173 193 10 213 213 NUM cana-1173 193 11 mod mod ADJ cana-1173 193 12 255 255 NUM cana-1173 193 13 2548 2548 NUM cana-1173 193 14 ≑ ≑ PROPN cana-1173 193 15 253 253 NUM cana-1173 193 16 mod mod ADJ cana-1173 193 17 255 255 NUM cana-1173 193 18 11280 11280 NUM cana-1173 193 19 ≑ ≑ PROPN cana-1173 193 20 60 60 NUM cana-1173 193 21 mod mod PROPN cana-1173 193 22 255 255 NUM cana-1173 193 23 10710 10710 NUM cana-1173 193 24 ≑ ≑ PROPN cana-1173 193 25 0 0 NUM cana-1173 194 1 mod mod ADJ cana-1173 194 2 255 255 NUM cana-1173 194 3 6080 6080 NUM cana-1173 194 4 ≑ ≑ PROPN cana-1173 194 5 215 215 NUM cana-1173 194 6 mod mod ADJ cana-1173 194 7 255 255 NUM cana-1173 194 8 2310 2310 NUM cana-1173 194 9 ≑ ≑ PROPN cana-1173 194 10 15 15 NUM cana-1173 194 11 mod mod ADJ cana-1173 194 12 255 255 NUM cana-1173 194 13 21528 21528 NUM cana-1173 194 14 ≑ ≑ PROPN cana-1173 194 15 108 108 NUM cana-1173 194 16 mod mod NOUN cana-1173 194 17 255 255 NUM cana-1173 194 18 11050 11050 NUM cana-1173 194 19 ≑ ≑ PROPN cana-1173 194 20 85 85 NUM cana-1173 194 21 mod mod NOUN cana-1173 194 22 255 255 NUM cana-1173 194 23 37044 37044 NUM cana-1173 194 24 ≑ ≑ PROPN cana-1173 194 25 69 69 NUM cana-1173 194 26 mod mod ADJ cana-1173 194 27 255 255 NUM cana-1173 194 28 9570 9570 NUM cana-1173 194 29 ≑ ≑ PROPN cana-1173 194 30 135 135 NUM cana-1173 194 31 mod mod NOUN cana-1173 194 32 255 255 NUM cana-1173 194 33 and and CCONJ cana-1173 194 34 the the DET cana-1173 194 35 keys key NOUN cana-1173 194 36 are be AUX cana-1173 194 37 0,0,5,3,2,9,9,44,42,23,9,84,43,145,37 0,0,5,3,2,9,9,44,42,23,9,84,43,145,37 NUM cana-1173 194 38 . . PUNCT cana-1173 195 1 hence hence ADV cana-1173 195 2 , , PUNCT cana-1173 195 3 the the DET cana-1173 195 4 receiver receiver NOUN cana-1173 195 5 receives receive VERB cana-1173 195 6 the the DET cana-1173 195 7 cipher cipher ADJ cana-1173 195 8 text text NOUN cana-1173 195 9 0cansióòáý 0cansióòáý NUM cana-1173 195 10 < < X cana-1173 195 11 nulΓ—lue‑ nulΓ—lue‑ PROPN cana-1173 195 12 along along ADP cana-1173 195 13 with with ADP cana-1173 195 14 key key ADJ cana-1173 195 15 : : PUNCT cana-1173 195 16 0,0,5,3,2,9,9,44,42,23,9,84,43,145,37 0,0,5,3,2,9,9,44,42,23,9,84,43,145,37 NUM cana-1173 195 17 . . PUNCT cana-1173 196 1 step step NOUN cana-1173 196 2 6 6 NUM cana-1173 196 3 : : PUNCT cana-1173 196 4 i i PRON cana-1173 196 5 stage stage NOUN cana-1173 196 6 of of ADP cana-1173 196 7 decryption decryption NOUN cana-1173 196 8 transform transform VERB cana-1173 196 9 the the DET cana-1173 196 10 cipher cipher ADJ cana-1173 196 11 text text NOUN cana-1173 196 12 into into ADP cana-1173 196 13 numbers number NOUN cana-1173 196 14 using use VERB cana-1173 196 15 the the DET cana-1173 196 16 ascii ascii ADJ cana-1173 196 17 values value NOUN cana-1173 196 18 along along ADP cana-1173 196 19 the the DET cana-1173 196 20 key key NOUN cana-1173 196 21 : : PUNCT cana-1173 196 22 0,0,5,3,2,9,9,44,42,23,9,84,43,145,37 0,0,5,3,2,9,9,44,42,23,9,84,43,145,37 NUM cana-1173 196 23 . . PUNCT cana-1173 197 1 since since ADV cana-1173 197 2 , , PUNCT cana-1173 197 3 π‘žπ‘– π‘žπ‘– NOUN cana-1173 197 4 = = SYM cana-1173 197 5 𝐹𝑖 𝐹𝑖 PROPN cana-1173 197 6 + + NUM cana-1173 197 7 255π‘Ÿπ‘– 255π‘Ÿπ‘– NOUN cana-1173 197 8 . . PUNCT cana-1173 198 1 we we PRON cana-1173 198 2 get get VERB cana-1173 198 3 , , PUNCT cana-1173 198 4 𝐺(𝑠 𝐺(𝑠 NUM cana-1173 198 5 ) ) PUNCT cana-1173 198 6 = = SYM cana-1173 199 1 βˆ‘ βˆ‘ PUNCT cana-1173 199 2 π‘žπ‘– π‘žπ‘– PROPN cana-1173 199 3 𝑠2𝑖+3 𝑠2𝑖+3 PROPN cana-1173 199 4 14 14 NUM cana-1173 199 5 𝑖=0 𝑖=0 PROPN cana-1173 199 6 . . PUNCT cana-1173 200 1 communications communication NOUN cana-1173 200 2 on on ADP cana-1173 200 3 applied apply VERB cana-1173 200 4 nonlinear nonlinear ADJ cana-1173 200 5 analysis analysis NOUN cana-1173 200 6 issn issn NOUN cana-1173 200 7 : : PUNCT cana-1173 200 8 1074 1074 NUM cana-1173 200 9 - - PUNCT cana-1173 200 10 133x 133x NUM cana-1173 200 11 vol vol NOUN cana-1173 200 12 31 31 NUM cana-1173 200 13 no no NOUN cana-1173 200 14 . . PUNCT cana-1173 201 1 6s 6s NUM cana-1173 201 2 ( ( PUNCT cana-1173 201 3 2024 2024 NUM cana-1173 201 4 ) ) PUNCT cana-1173 201 5 148 148 NUM cana-1173 201 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 201 7 𝐺(𝑠 𝐺(𝑠 NOUN cana-1173 201 8 ) ) PUNCT cana-1173 201 9 = = VERB cana-1173 201 10 { { PUNCT cana-1173 201 11 48 48 NUM cana-1173 201 12 𝑠3 𝑠3 NOUN cana-1173 201 13 + + CCONJ cana-1173 201 14 24 24 NUM cana-1173 201 15 𝑠5 𝑠5 NOUN cana-1173 201 16 + + CCONJ cana-1173 201 17 1290 1290 NUM cana-1173 201 18 𝑠7 𝑠7 PROPN cana-1173 201 19 + + CCONJ cana-1173 201 20 1008 1008 NUM cana-1173 201 21 𝑠9 𝑠9 NOUN cana-1173 201 22 + + CCONJ cana-1173 201 23 720 720 NUM cana-1173 201 24 𝑠11 𝑠11 ADJ cana-1173 201 25 + + CCONJ cana-1173 201 26 2508 2508 NUM cana-1173 201 27 𝑠13 𝑠13 NOUN cana-1173 201 28 + + CCONJ cana-1173 201 29 2548 2548 NUM cana-1173 201 30 𝑠15 𝑠15 NOUN cana-1173 201 31 + + CCONJ cana-1173 201 32 11280 11280 NUM cana-1173 201 33 𝑠17 𝑠17 NOUN cana-1173 202 1 + + CCONJ cana-1173 203 1 10710 10710 NUM cana-1173 203 2 𝑠19 𝑠19 VERB cana-1173 203 3 + + CCONJ cana-1173 203 4 6080 6080 NUM cana-1173 203 5 𝑠21 𝑠21 NOUN cana-1173 203 6 + + CCONJ cana-1173 203 7 2310 2310 NUM cana-1173 203 8 𝑠23 𝑠23 NUM cana-1173 203 9 + + NUM cana-1173 203 10 21528 21528 NUM cana-1173 203 11 𝑠25 𝑠25 NOUN cana-1173 203 12 + + CCONJ cana-1173 203 13 11050 11050 NUM cana-1173 203 14 𝑠27 𝑠27 NOUN cana-1173 203 15 + + CCONJ cana-1173 203 16 37044 37044 NUM cana-1173 203 17 𝑠29 𝑠29 NOUN cana-1173 203 18 + + CCONJ cana-1173 203 19 9570 9570 NUM cana-1173 203 20 𝑠31 𝑠31 NOUN cana-1173 203 21 } } PUNCT cana-1173 203 22 . . PUNCT cana-1173 204 1 step step NOUN cana-1173 204 2 6 6 NUM cana-1173 204 3 : : PUNCT cana-1173 204 4 apply apply VERB cana-1173 204 5 inverse inverse ADJ cana-1173 204 6 laplace laplace NOUN cana-1173 204 7 transform transform NOUN cana-1173 204 8 for for ADP cana-1173 204 9 𝐺(𝑠 𝐺(𝑠 NOUN cana-1173 204 10 ) ) PUNCT cana-1173 204 11 hence hence ADV cana-1173 204 12 , , PUNCT cana-1173 204 13 πΏβˆ’1{𝐺(𝑠 πΏβˆ’1{𝐺(𝑠 NOUN cana-1173 204 14 ) ) PUNCT cana-1173 204 15 } } PUNCT cana-1173 205 1 = = PUNCT cana-1173 205 2 πΏβˆ’1 πΏβˆ’1 NOUN cana-1173 205 3 { { PUNCT cana-1173 205 4 48 48 NUM cana-1173 205 5 𝑠3 𝑠3 NOUN cana-1173 205 6 + + CCONJ cana-1173 205 7 24 24 NUM cana-1173 205 8 𝑠5 𝑠5 NOUN cana-1173 205 9 + + CCONJ cana-1173 205 10 1290 1290 NUM cana-1173 205 11 𝑠7 𝑠7 PROPN cana-1173 205 12 + + CCONJ cana-1173 205 13 1008 1008 NUM cana-1173 205 14 𝑠9 𝑠9 NOUN cana-1173 205 15 + + CCONJ cana-1173 205 16 720 720 NUM cana-1173 205 17 𝑠11 𝑠11 ADJ cana-1173 205 18 + + CCONJ cana-1173 205 19 2508 2508 NUM cana-1173 205 20 𝑠13 𝑠13 NOUN cana-1173 205 21 + + CCONJ cana-1173 205 22 2548 2548 NUM cana-1173 205 23 𝑠15 𝑠15 NOUN cana-1173 205 24 + + CCONJ cana-1173 205 25 11280 11280 NUM cana-1173 205 26 𝑠17 𝑠17 NOUN cana-1173 205 27 + + CCONJ cana-1173 205 28 10710 10710 NUM cana-1173 205 29 𝑠19 𝑠19 VERB cana-1173 205 30 + + CCONJ cana-1173 205 31 6080 6080 NUM cana-1173 205 32 𝑠21 𝑠21 NOUN cana-1173 205 33 + + CCONJ cana-1173 205 34 2310 2310 NUM cana-1173 205 35 𝑠23 𝑠23 NUM cana-1173 205 36 + + NUM cana-1173 205 37 21528 21528 NUM cana-1173 205 38 𝑠25 𝑠25 NOUN cana-1173 205 39 + + CCONJ cana-1173 205 40 11050 11050 NUM cana-1173 205 41 𝑠27 𝑠27 NOUN cana-1173 205 42 + + CCONJ cana-1173 205 43 37044 37044 NUM cana-1173 205 44 𝑠29 𝑠29 NOUN cana-1173 205 45 + + CCONJ cana-1173 205 46 9570 9570 NUM cana-1173 205 47 𝑠31 𝑠31 NOUN cana-1173 205 48 } } PUNCT cana-1173 205 49 . . PUNCT cana-1173 206 1 = = SYM cana-1173 206 2 48 48 NUM cana-1173 206 3 𝑑2 𝑑2 NOUN cana-1173 206 4 2 2 NUM cana-1173 206 5 ! ! PUNCT cana-1173 207 1 + + CCONJ cana-1173 207 2 24 24 NUM cana-1173 207 3 𝑑4 𝑑4 NOUN cana-1173 207 4 4 4 NUM cana-1173 207 5 ! ! PUNCT cana-1173 208 1 + + CCONJ cana-1173 208 2 1290 1290 NUM cana-1173 208 3 𝑑6 𝑑6 NOUN cana-1173 208 4 6 6 NUM cana-1173 208 5 ! ! PUNCT cana-1173 209 1 + + PUNCT cana-1173 209 2 1008 1008 NUM cana-1173 209 3 𝑑8 𝑑8 PROPN cana-1173 209 4 8 8 NUM cana-1173 209 5 ! ! PUNCT cana-1173 210 1 + + CCONJ cana-1173 210 2 720 720 NUM cana-1173 210 3 𝑑10 𝑑10 NUM cana-1173 210 4 10 10 NUM cana-1173 210 5 ! ! PUNCT cana-1173 211 1 + + CCONJ cana-1173 211 2 2508 2508 NUM cana-1173 211 3 𝑑12 𝑑12 NOUN cana-1173 211 4 12 12 NUM cana-1173 211 5 ! ! PUNCT cana-1173 212 1 + + CCONJ cana-1173 212 2 2548 2548 NUM cana-1173 212 3 𝑑14 𝑑14 NOUN cana-1173 212 4 14 14 NUM cana-1173 212 5 ! ! PUNCT cana-1173 213 1 + + CCONJ cana-1173 213 2 11280 11280 NUM cana-1173 213 3 𝑑16 𝑑16 VERB cana-1173 213 4 16 16 NUM cana-1173 213 5 ! ! PUNCT cana-1173 214 1 + + CCONJ cana-1173 214 2 10710 10710 NUM cana-1173 214 3 𝑑18 𝑑18 PROPN cana-1173 214 4 18 18 NUM cana-1173 214 5 ! ! PUNCT cana-1173 215 1 + + CCONJ cana-1173 215 2 6080 6080 NUM cana-1173 215 3 𝑑20 𝑑20 NOUN cana-1173 215 4 20 20 NUM cana-1173 215 5 ! ! PUNCT cana-1173 216 1 + + CCONJ cana-1173 216 2 2310 2310 NUM cana-1173 216 3 𝑑22 𝑑22 ADV cana-1173 216 4 22 22 NUM cana-1173 216 5 ! ! PUNCT cana-1173 217 1 + + CCONJ cana-1173 217 2 21528 21528 NUM cana-1173 217 3 𝑑24 𝑑24 NOUN cana-1173 217 4 24 24 NUM cana-1173 217 5 ! ! PUNCT cana-1173 218 1 + + CCONJ cana-1173 218 2 11050 11050 NUM cana-1173 218 3 𝑑26 𝑑26 ADV cana-1173 218 4 26 26 NUM cana-1173 218 5 ! ! PUNCT cana-1173 219 1 + + CCONJ cana-1173 219 2 37044 37044 NUM cana-1173 219 3 𝑑28 𝑑28 NUM cana-1173 219 4 28 28 NUM cana-1173 219 5 ! ! PUNCT cana-1173 220 1 + + CCONJ cana-1173 220 2 9570 9570 NUM cana-1173 220 3 𝑑30 𝑑30 NOUN cana-1173 220 4 30 30 NUM cana-1173 220 5 ! ! PUNCT cana-1173 220 6 . . PUNCT cana-1173 221 1 = = PUNCT cana-1173 222 1 24𝑑2 24𝑑2 NUM cana-1173 222 2 + + CCONJ cana-1173 222 3 2 2 NUM cana-1173 222 4 𝑑4 𝑑4 NOUN cana-1173 222 5 2 2 NUM cana-1173 222 6 ! ! PUNCT cana-1173 223 1 + + CCONJ cana-1173 223 2 43 43 NUM cana-1173 223 3 𝑑6 𝑑6 NOUN cana-1173 223 4 4 4 NUM cana-1173 223 5 ! ! PUNCT cana-1173 224 1 + + CCONJ cana-1173 224 2 18 18 NUM cana-1173 224 3 𝑑8 𝑑8 PROPN cana-1173 224 4 6 6 NUM cana-1173 224 5 ! ! PUNCT cana-1173 225 1 + + CCONJ cana-1173 225 2 8 8 NUM cana-1173 225 3 𝑑10 𝑑10 NUM cana-1173 225 4 8 8 NUM cana-1173 225 5 ! ! PUNCT cana-1173 226 1 + + CCONJ cana-1173 226 2 19 19 NUM cana-1173 226 3 𝑑12 𝑑12 NOUN cana-1173 226 4 10 10 NUM cana-1173 226 5 ! ! PUNCT cana-1173 227 1 + + CCONJ cana-1173 227 2 14 14 NUM cana-1173 227 3 𝑑14 𝑑14 NOUN cana-1173 227 4 12 12 NUM cana-1173 227 5 ! ! PUNCT cana-1173 228 1 + + CCONJ cana-1173 228 2 47 47 NUM cana-1173 228 3 𝑑16 𝑑16 VERB cana-1173 228 4 14 14 NUM cana-1173 228 5 ! ! PUNCT cana-1173 229 1 + + CCONJ cana-1173 229 2 35 35 NUM cana-1173 229 3 𝑑18 𝑑18 NOUN cana-1173 229 4 16 16 NUM cana-1173 229 5 ! ! PUNCT cana-1173 230 1 + + CCONJ cana-1173 230 2 16 16 NUM cana-1173 230 3 𝑑20 𝑑20 NOUN cana-1173 230 4 18 18 NUM cana-1173 230 5 ! ! PUNCT cana-1173 231 1 + + CCONJ cana-1173 231 2 5 5 NUM cana-1173 231 3 𝑑22 𝑑22 ADV cana-1173 231 4 20 20 NUM cana-1173 231 5 ! ! PUNCT cana-1173 232 1 + + CCONJ cana-1173 232 2 39 39 NUM cana-1173 232 3 𝑑24 𝑑24 NOUN cana-1173 232 4 22 22 NUM cana-1173 232 5 ! ! PUNCT cana-1173 233 1 + + CCONJ cana-1173 233 2 17 17 NUM cana-1173 233 3 𝑑26 𝑑26 ADV cana-1173 233 4 24 24 NUM cana-1173 233 5 ! ! PUNCT cana-1173 234 1 + + CCONJ cana-1173 234 2 49 49 NUM cana-1173 234 3 𝑑28 𝑑28 ADJ cana-1173 234 4 26 26 NUM cana-1173 234 5 ! ! PUNCT cana-1173 235 1 + + CCONJ cana-1173 235 2 11 11 NUM cana-1173 235 3 𝑑30 𝑑30 NOUN cana-1173 235 4 28 28 NUM cana-1173 235 5 ! ! PUNCT cana-1173 235 6 . . PUNCT cana-1173 236 1 πΏβˆ’1{𝐺(𝑠)}= πΏβˆ’1{𝐺(𝑠)}= PROPN cana-1173 236 2 𝑑2 𝑑2 PROPN cana-1173 237 1 [ [ X cana-1173 237 2 24 24 NUM cana-1173 237 3 + + SYM cana-1173 237 4 2 2 NUM cana-1173 237 5 𝑑2 𝑑2 NOUN cana-1173 237 6 2 2 NUM cana-1173 237 7 ! ! PUNCT cana-1173 238 1 + + CCONJ cana-1173 238 2 43 43 NUM cana-1173 238 3 𝑑4 𝑑4 NOUN cana-1173 238 4 4 4 NUM cana-1173 238 5 ! ! PUNCT cana-1173 239 1 + + CCONJ cana-1173 239 2 18 18 NUM cana-1173 239 3 𝑑6 𝑑6 NOUN cana-1173 239 4 6 6 NUM cana-1173 239 5 ! ! PUNCT cana-1173 240 1 + + CCONJ cana-1173 240 2 8 8 NUM cana-1173 240 3 𝑑8 𝑑8 PROPN cana-1173 240 4 8 8 NUM cana-1173 240 5 ! ! PUNCT cana-1173 241 1 + + CCONJ cana-1173 241 2 19 19 NUM cana-1173 241 3 𝑑10 𝑑10 NUM cana-1173 241 4 10 10 NUM cana-1173 241 5 ! ! PUNCT cana-1173 242 1 + + CCONJ cana-1173 242 2 14 14 NUM cana-1173 242 3 𝑑12 𝑑12 NOUN cana-1173 242 4 12 12 NUM cana-1173 242 5 ! ! PUNCT cana-1173 243 1 + + CCONJ cana-1173 243 2 47 47 NUM cana-1173 243 3 𝑑14 𝑑14 NOUN cana-1173 243 4 14 14 NUM cana-1173 243 5 ! ! PUNCT cana-1173 244 1 + + CCONJ cana-1173 244 2 35 35 NUM cana-1173 244 3 𝑑16 𝑑16 VERB cana-1173 244 4 16 16 NUM cana-1173 244 5 ! ! PUNCT cana-1173 245 1 + + CCONJ cana-1173 245 2 16 16 NUM cana-1173 245 3 𝑑18 𝑑18 PROPN cana-1173 245 4 18 18 NUM cana-1173 245 5 ! ! PUNCT cana-1173 246 1 + + CCONJ cana-1173 246 2 5 5 NUM cana-1173 246 3 𝑑20 𝑑20 NOUN cana-1173 246 4 20 20 NUM cana-1173 246 5 ! ! PUNCT cana-1173 247 1 + + CCONJ cana-1173 247 2 39 39 NUM cana-1173 247 3 𝑑22 𝑑22 ADJ cana-1173 247 4 22 22 NUM cana-1173 247 5 ! ! PUNCT cana-1173 248 1 + + CCONJ cana-1173 248 2 17 17 NUM cana-1173 248 3 𝑑24 𝑑24 NOUN cana-1173 248 4 24 24 NUM cana-1173 248 5 ! ! PUNCT cana-1173 249 1 + + CCONJ cana-1173 249 2 49 49 NUM cana-1173 249 3 𝑑26 𝑑26 ADV cana-1173 249 4 26 26 NUM cana-1173 249 5 ! ! PUNCT cana-1173 250 1 + + CCONJ cana-1173 250 2 11 11 NUM cana-1173 250 3 𝑑28 𝑑28 NUM cana-1173 250 4 28 28 NUM cana-1173 250 5 ! ! PUNCT cana-1173 251 1 ] ] PUNCT cana-1173 251 2 . . PUNCT cana-1173 252 1 therefore therefore ADV cana-1173 252 2 , , PUNCT cana-1173 252 3 πΏβˆ’1{𝐺(𝑠 πΏβˆ’1{𝐺(𝑠 ADJ cana-1173 252 4 ) ) PUNCT cana-1173 252 5 } } PUNCT cana-1173 253 1 = = SYM cana-1173 253 2 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 253 3 ) ) PUNCT cana-1173 253 4 . . PUNCT cana-1173 254 1 step step NOUN cana-1173 254 2 7 7 NUM cana-1173 254 3 : : PUNCT cana-1173 254 4 ii ii NOUN cana-1173 254 5 stage stage NOUN cana-1173 254 6 of of ADP cana-1173 254 7 decryption decryption NOUN cana-1173 254 8 let let VERB cana-1173 254 9 the the DET cana-1173 254 10 coefficients coefficient NOUN cana-1173 254 11 of of ADP cana-1173 254 12 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 254 13 ) ) PUNCT cana-1173 254 14 be be AUX cana-1173 254 15 written write VERB cana-1173 254 16 in in ADP cana-1173 254 17 matrix matrix NOUN cana-1173 254 18 form form NOUN cana-1173 254 19 . . PUNCT cana-1173 255 1 therefore therefore ADV cana-1173 255 2 , , PUNCT cana-1173 255 3 e e X cana-1173 255 4 = = SYM cana-1173 255 5 ( ( PUNCT cana-1173 255 6 24 24 NUM cana-1173 255 7 2 2 NUM cana-1173 255 8 43 43 NUM cana-1173 255 9 19 19 NUM cana-1173 255 10 14 14 NUM cana-1173 255 11 47 47 NUM cana-1173 255 12 5 5 NUM cana-1173 255 13 39 39 NUM cana-1173 255 14 17 17 NUM cana-1173 255 15 18 18 NUM cana-1173 255 16 35 35 NUM cana-1173 255 17 49 49 NUM cana-1173 255 18 8 8 NUM cana-1173 255 19 16 16 NUM cana-1173 255 20 11 11 NUM cana-1173 255 21 ) ) PUNCT cana-1173 255 22 . . PUNCT cana-1173 256 1 step step NOUN cana-1173 256 2 8 8 NUM cana-1173 256 3 : : PUNCT cana-1173 256 4 now now ADV cana-1173 256 5 we we PRON cana-1173 256 6 find find VERB cana-1173 256 7 d d X cana-1173 256 8 ≑ ≑ PROPN cana-1173 256 9 aβˆ’1e(mod aβˆ’1e(mod NOUN cana-1173 256 10 53 53 NUM cana-1173 256 11 ) ) PUNCT cana-1173 256 12 . . PUNCT cana-1173 257 1 d d X cana-1173 257 2 ≑ ≑ PROPN cana-1173 257 3 ( ( PUNCT cana-1173 257 4 1 1 NUM cana-1173 257 5 βˆ’1 βˆ’1 NOUN cana-1173 257 6 0 0 NUM cana-1173 257 7 βˆ’2 βˆ’2 NOUN cana-1173 257 8 3 3 NUM cana-1173 257 9 βˆ’4 βˆ’4 NOUN cana-1173 257 10 βˆ’2 βˆ’2 PROPN cana-1173 257 11 3 3 NUM cana-1173 257 12 βˆ’3 βˆ’3 NOUN cana-1173 257 13 ) ) PUNCT cana-1173 257 14 ( ( PUNCT cana-1173 257 15 24 24 NUM cana-1173 257 16 2 2 NUM cana-1173 257 17 43 43 NUM cana-1173 257 18 19 19 NUM cana-1173 257 19 14 14 NUM cana-1173 257 20 47 47 NUM cana-1173 257 21 5 5 NUM cana-1173 257 22 39 39 NUM cana-1173 257 23 17 17 NUM cana-1173 257 24 18 18 NUM cana-1173 257 25 35 35 NUM cana-1173 257 26 49 49 NUM cana-1173 257 27 8 8 NUM cana-1173 257 28 16 16 NUM cana-1173 257 29 11 11 NUM cana-1173 257 30 ) ) PUNCT cana-1173 257 31 ( ( PUNCT cana-1173 257 32 mod mod PROPN cana-1173 257 33 53 53 NUM cana-1173 257 34 ) ) PUNCT cana-1173 257 35 . . PUNCT cana-1173 258 1 ≑ ≑ PROPN cana-1173 258 2 ( ( PUNCT cana-1173 258 3 5 5 NUM cana-1173 258 4 βˆ’12 βˆ’12 NUM cana-1173 258 5 βˆ’4 βˆ’4 NOUN cana-1173 258 6 βˆ’11 βˆ’11 X cana-1173 258 7 βˆ’118 βˆ’118 NOUN cana-1173 258 8 βˆ’13 βˆ’13 NOUN cana-1173 258 9 βˆ’6 βˆ’6 PRON cana-1173 258 10 βˆ’79 βˆ’79 NOUN cana-1173 258 11 4 4 NUM cana-1173 258 12 βˆ’17 βˆ’17 NOUN cana-1173 258 13 βˆ’127 βˆ’127 NOUN cana-1173 258 14 βˆ’78 βˆ’78 NOUN cana-1173 258 15 βˆ’8 βˆ’8 X cana-1173 258 16 βˆ’12 βˆ’12 NOUN cana-1173 258 17 βˆ’1 βˆ’1 NOUN cana-1173 258 18 ) ) PUNCT cana-1173 258 19 ( ( PUNCT cana-1173 258 20 mod mod PROPN cana-1173 258 21 53 53 NUM cana-1173 258 22 ) ) PUNCT cana-1173 258 23 . . PUNCT cana-1173 259 1 d d NOUN cana-1173 259 2 = = PRON cana-1173 259 3 ( ( PUNCT cana-1173 259 4 5 5 NUM cana-1173 259 5 41 41 NUM cana-1173 259 6 49 49 NUM cana-1173 259 7 42 42 NUM cana-1173 259 8 41 41 NUM cana-1173 259 9 40 40 NUM cana-1173 259 10 47 47 NUM cana-1173 259 11 27 27 NUM cana-1173 259 12 4 4 NUM cana-1173 259 13 36 36 NUM cana-1173 259 14 32 32 NUM cana-1173 259 15 28 28 NUM cana-1173 259 16 45 45 NUM cana-1173 259 17 41 41 NUM cana-1173 259 18 52 52 NUM cana-1173 259 19 ) ) PUNCT cana-1173 259 20 . . PUNCT cana-1173 260 1 the the DET cana-1173 260 2 matrix matrix NOUN cana-1173 260 3 d d NOUN cana-1173 260 4 is be AUX cana-1173 260 5 same same ADJ cana-1173 260 6 as as ADP cana-1173 260 7 matrix matrix NOUN cana-1173 260 8 p. p. NOUN cana-1173 260 9 hence hence ADV cana-1173 260 10 , , PUNCT cana-1173 260 11 on on ADP cana-1173 260 12 arranging arrange VERB cana-1173 260 13 the the DET cana-1173 260 14 numbers number NOUN cana-1173 260 15 in in ADP cana-1173 260 16 order order NOUN cana-1173 260 17 we we PRON cana-1173 260 18 get get VERB cana-1173 260 19 5 5 NUM cana-1173 260 20 41 41 NUM cana-1173 260 21 49 49 NUM cana-1173 260 22 36 36 NUM cana-1173 260 23 45 45 NUM cana-1173 260 24 42 42 NUM cana-1173 260 25 41 41 NUM cana-1173 260 26 40 40 NUM cana-1173 260 27 32 32 NUM cana-1173 260 28 41 41 NUM cana-1173 260 29 47 47 NUM cana-1173 260 30 27 27 NUM cana-1173 260 31 4 4 NUM cana-1173 260 32 28 28 NUM cana-1173 260 33 52 52 NUM cana-1173 260 34 and and CCONJ cana-1173 260 35 on on ADP cana-1173 260 36 transforming transform VERB cana-1173 260 37 into into ADP cana-1173 260 38 alphabets alphabet NOUN cana-1173 260 39 we we PRON cana-1173 260 40 get get VERB cana-1173 260 41 the the DET cana-1173 260 42 plain plain ADJ cana-1173 260 43 text text NOUN cana-1173 260 44 as as ADP cana-1173 260 45 environment environment NOUN cana-1173 260 46 day day PROPN cana-1173 260 47 . . PUNCT cana-1173 261 1 example example PROPN cana-1173 261 2 ii ii PROPN cana-1173 261 3 . . PUNCT cana-1173 262 1 this this DET cana-1173 262 2 illustration illustration NOUN cana-1173 262 3 explains explain VERB cana-1173 262 4 about about ADP cana-1173 262 5 hill hill NOUN cana-1173 262 6 cipher cipher ADJ cana-1173 262 7 using use VERB cana-1173 262 8 kamal kamal ADJ cana-1173 262 9 integral integral ADJ cana-1173 262 10 transform transform NOUN cana-1173 262 11 . . PUNCT cana-1173 263 1 step step NOUN cana-1173 263 2 1 1 NUM cana-1173 263 3 : : PUNCT cana-1173 263 4 let let VERB cana-1173 263 5 the the DET cana-1173 263 6 plain plain ADJ cana-1173 263 7 text text NOUN cana-1173 263 8 to to PART cana-1173 263 9 be be AUX cana-1173 263 10 sent send VERB cana-1173 263 11 is be AUX cana-1173 263 12 pseudo pseudo NOUN cana-1173 263 13 prime prime NOUN cana-1173 263 14 . . PUNCT cana-1173 264 1 communications communication NOUN cana-1173 264 2 on on ADP cana-1173 264 3 applied apply VERB cana-1173 264 4 nonlinear nonlinear ADJ cana-1173 264 5 analysis analysis NOUN cana-1173 264 6 issn issn NOUN cana-1173 264 7 : : PUNCT cana-1173 264 8 1074 1074 NUM cana-1173 264 9 - - PUNCT cana-1173 264 10 133x 133x NUM cana-1173 264 11 vol vol NOUN cana-1173 264 12 31 31 NUM cana-1173 264 13 no no NOUN cana-1173 264 14 . . PUNCT cana-1173 265 1 6s 6s NUM cana-1173 265 2 ( ( PUNCT cana-1173 265 3 2024 2024 NUM cana-1173 265 4 ) ) PUNCT cana-1173 265 5 149 149 NUM cana-1173 265 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 265 7 step step NOUN cana-1173 265 8 2 2 NUM cana-1173 265 9 : : PUNCT cana-1173 265 10 transform transform VERB cana-1173 265 11 the the DET cana-1173 265 12 plain plain ADJ cana-1173 265 13 text text NOUN cana-1173 265 14 into into ADP cana-1173 265 15 numbers number NOUN cana-1173 265 16 using use VERB cana-1173 265 17 ascii ascii NOUN cana-1173 265 18 values value NOUN cana-1173 265 19 . . PUNCT cana-1173 266 1 let let VERB cana-1173 266 2 𝑃 𝑃 VERB cana-1173 266 3 = = SYM cana-1173 266 4 ( ( PUNCT cana-1173 266 5 80 80 NUM cana-1173 266 6 115 115 NUM cana-1173 266 7 101 101 NUM cana-1173 266 8 117 117 NUM cana-1173 266 9 100 100 NUM cana-1173 266 10 111 111 NUM cana-1173 266 11 32 32 NUM cana-1173 266 12 80 80 NUM cana-1173 266 13 114 114 NUM cana-1173 266 14 105 105 NUM cana-1173 266 15 109 109 NUM cana-1173 266 16 101 101 NUM cana-1173 266 17 ) ) PUNCT cana-1173 266 18 . . PUNCT cana-1173 267 1 arrange arrange NOUN cana-1173 267 2 p p NOUN cana-1173 267 3 in in ADP cana-1173 267 4 the the DET cana-1173 267 5 matrix matrix NOUN cana-1173 267 6 form form NOUN cana-1173 267 7 hence hence ADV cana-1173 267 8 𝑃 𝑃 VERB cana-1173 267 9 = = SYM cana-1173 267 10 [ [ PUNCT cana-1173 267 11 80 80 NUM cana-1173 267 12 117 117 NUM cana-1173 267 13 32 32 NUM cana-1173 267 14 105 105 NUM cana-1173 267 15 115 115 NUM cana-1173 267 16 100 100 NUM cana-1173 267 17 80 80 NUM cana-1173 267 18 109 109 NUM cana-1173 267 19 101 101 NUM cana-1173 267 20 111 111 NUM cana-1173 267 21 114 114 NUM cana-1173 267 22 101 101 NUM cana-1173 267 23 ] ] PUNCT cana-1173 267 24 . . PUNCT cana-1173 268 1 step step NOUN cana-1173 268 2 3 3 NUM cana-1173 268 3 : : PUNCT cana-1173 268 4 let let VERB cana-1173 268 5 𝐴 𝐴 PROPN cana-1173 268 6 = = PUNCT cana-1173 268 7 [ [ PUNCT cana-1173 268 8 βˆ’1 βˆ’1 NOUN cana-1173 268 9 1 1 NUM cana-1173 268 10 2 2 NUM cana-1173 268 11 βˆ’1 βˆ’1 NOUN cana-1173 268 12 βˆ’3 βˆ’3 NOUN cana-1173 268 13 1 1 NUM cana-1173 268 14 βˆ’5 βˆ’5 NOUN cana-1173 268 15 1 1 NUM cana-1173 268 16 3 3 NUM cana-1173 268 17 βˆ’1 βˆ’1 NOUN cana-1173 268 18 2 2 NUM cana-1173 268 19 0 0 NUM cana-1173 268 20 βˆ’1 βˆ’1 NOUN cana-1173 268 21 0 0 PUNCT cana-1173 269 1 βˆ’3 βˆ’3 NOUN cana-1173 269 2 1 1 NUM cana-1173 269 3 ] ] PUNCT cana-1173 269 4 be be AUX cana-1173 269 5 the the DET cana-1173 269 6 matrix matrix NOUN cana-1173 269 7 which which PRON cana-1173 269 8 acts act VERB cana-1173 269 9 as as ADP cana-1173 269 10 an an DET cana-1173 269 11 encryption encryption NOUN cana-1173 269 12 key key NOUN cana-1173 269 13 whose whose DET cana-1173 269 14 inverse inverse NOUN cana-1173 269 15 exists exist VERB cana-1173 269 16 . . PUNCT cana-1173 270 1 therefore therefore ADV cana-1173 270 2 , , PUNCT cana-1173 270 3 π΄βˆ’1 π΄βˆ’1 PROPN cana-1173 270 4 = = PUNCT cana-1173 270 5 [ [ PUNCT cana-1173 270 6 0 0 NUM cana-1173 270 7 1 1 NUM cana-1173 270 8 1 1 NUM cana-1173 270 9 βˆ’1 βˆ’1 NOUN cana-1173 270 10 2 2 NUM cana-1173 270 11 1 1 NUM cana-1173 270 12 2 2 NUM cana-1173 270 13 1 1 NUM cana-1173 270 14 1 1 NUM cana-1173 270 15 βˆ’1 βˆ’1 NOUN cana-1173 270 16 0 0 NUM cana-1173 270 17 2 2 NUM cana-1173 270 18 3 3 NUM cana-1173 270 19 βˆ’2 βˆ’2 NOUN cana-1173 270 20 1 1 NUM cana-1173 270 21 6 6 NUM cana-1173 270 22 ] ] PUNCT cana-1173 270 23 is be AUX cana-1173 270 24 the the DET cana-1173 270 25 matrix matrix NOUN cana-1173 270 26 which which PRON cana-1173 270 27 acts act VERB cana-1173 270 28 as as ADP cana-1173 270 29 a a DET cana-1173 270 30 decryption decryption NOUN cana-1173 270 31 key key NOUN cana-1173 270 32 . . PUNCT cana-1173 271 1 step step NOUN cana-1173 271 2 4 4 NUM cana-1173 271 3 : : PUNCT cana-1173 271 4 i i PRON cana-1173 271 5 stage stage NOUN cana-1173 271 6 of of ADP cana-1173 271 7 encryption encryption NOUN cana-1173 271 8 let let VERB cana-1173 271 9 e e PROPN cana-1173 271 10 ≑ ≑ PROPN cana-1173 271 11 ap ap PROPN cana-1173 271 12 ( ( PUNCT cana-1173 271 13 mod mod PROPN cana-1173 271 14 255 255 NUM cana-1173 271 15 ) ) PUNCT cana-1173 271 16 . . PUNCT cana-1173 272 1 e e X cana-1173 272 2 ≑ ≑ PROPN cana-1173 272 3 [ [ PUNCT cana-1173 272 4 βˆ’1 βˆ’1 NOUN cana-1173 272 5 1 1 NUM cana-1173 272 6 2 2 NUM cana-1173 272 7 βˆ’1 βˆ’1 NOUN cana-1173 272 8 βˆ’3 βˆ’3 NOUN cana-1173 272 9 1 1 NUM cana-1173 272 10 βˆ’5 βˆ’5 NOUN cana-1173 272 11 1 1 NUM cana-1173 272 12 3 3 NUM cana-1173 272 13 βˆ’1 βˆ’1 NOUN cana-1173 272 14 2 2 NUM cana-1173 272 15 0 0 NUM cana-1173 272 16 βˆ’1 βˆ’1 NOUN cana-1173 272 17 0 0 PUNCT cana-1173 273 1 βˆ’3 βˆ’3 NOUN cana-1173 273 2 1 1 NUM cana-1173 273 3 ] ] PUNCT cana-1173 273 4 [ [ PUNCT cana-1173 273 5 80 80 NUM cana-1173 273 6 117 117 NUM cana-1173 273 7 32 32 NUM cana-1173 273 8 105 105 NUM cana-1173 273 9 115 115 NUM cana-1173 273 10 100 100 NUM cana-1173 273 11 80 80 NUM cana-1173 273 12 109 109 NUM cana-1173 273 13 101 101 NUM cana-1173 273 14 111 111 NUM cana-1173 273 15 114 114 NUM cana-1173 273 16 101 101 NUM cana-1173 273 17 ] ] PUNCT cana-1173 273 18 ( ( PUNCT cana-1173 273 19 mod mod PROPN cana-1173 273 20 255 255 NUM cana-1173 273 21 ) ) PUNCT cana-1173 273 22 . . PUNCT cana-1173 274 1 ≑ ≑ PROPN cana-1173 274 2 [ [ PUNCT cana-1173 274 3 βˆ’440 βˆ’440 NOUN cana-1173 274 4 165 165 NUM cana-1173 274 5 βˆ’676 βˆ’676 NOUN cana-1173 274 6 142 142 NUM cana-1173 274 7 βˆ’284 βˆ’284 NOUN cana-1173 274 8 135 135 NUM cana-1173 274 9 βˆ’437 βˆ’437 NOUN cana-1173 274 10 94 94 NUM cana-1173 274 11 62 62 NUM cana-1173 274 12 98 98 NUM cana-1173 274 13 βˆ’428 βˆ’428 NOUN cana-1173 274 14 111 111 NUM cana-1173 274 15 ] ] PUNCT cana-1173 274 16 ( ( PUNCT cana-1173 274 17 mod mod PROPN cana-1173 274 18 255 255 NUM cana-1173 274 19 ) ) PUNCT cana-1173 274 20 . . PUNCT cana-1173 275 1 e e X cana-1173 276 1 = = PUNCT cana-1173 277 1 [ [ PUNCT cana-1173 277 2 70 70 NUM cana-1173 277 3 165 165 NUM cana-1173 277 4 89 89 NUM cana-1173 277 5 142 142 NUM cana-1173 277 6 226 226 NUM cana-1173 277 7 135 135 NUM cana-1173 277 8 73 73 NUM cana-1173 277 9 94 94 NUM cana-1173 277 10 62 62 NUM cana-1173 277 11 98 98 NUM cana-1173 277 12 82 82 NUM cana-1173 277 13 111 111 NUM cana-1173 277 14 ] ] PUNCT cana-1173 277 15 . . PUNCT cana-1173 278 1 step step NOUN cana-1173 278 2 5 5 NUM cana-1173 278 3 : : PUNCT cana-1173 278 4 ii ii NOUN cana-1173 278 5 stage stage NOUN cana-1173 278 6 of of ADP cana-1173 278 7 encryption encryption NOUN cana-1173 278 8 for for ADP cana-1173 278 9 further further ADJ cana-1173 278 10 security security NOUN cana-1173 278 11 purpose purpose NOUN cana-1173 278 12 let let VERB cana-1173 278 13 us we PRON cana-1173 278 14 encode encode VERB cana-1173 278 15 the the DET cana-1173 278 16 above above ADJ cana-1173 278 17 e e NOUN cana-1173 278 18 matrix matrix NOUN cana-1173 278 19 using use VERB cana-1173 278 20 kamal kamal ADJ cana-1173 278 21 integral integral ADJ cana-1173 278 22 transform transform NOUN cana-1173 278 23 let let VERB cana-1173 278 24 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 278 25 ) ) PUNCT cana-1173 279 1 = = PUNCT cana-1173 279 2 βˆ‘ βˆ‘ PUNCT cana-1173 279 3 𝐺𝑖𝑑 𝐺𝑖𝑑 PROPN cana-1173 279 4 2𝑒2𝑑11 2𝑒2𝑑11 NUM cana-1173 279 5 𝑖=0 𝑖=0 PROPN cana-1173 279 6 . . PUNCT cana-1173 280 1 here here ADV cana-1173 280 2 , , PUNCT cana-1173 280 3 𝐺𝑖 𝐺𝑖 VERB cana-1173 280 4 are be AUX cana-1173 280 5 the the DET cana-1173 280 6 coefficients coefficient NOUN cana-1173 280 7 which which PRON cana-1173 280 8 takes take VERB cana-1173 280 9 the the DET cana-1173 280 10 values value NOUN cana-1173 280 11 of of ADP cana-1173 280 12 matrix matrix NOUN cana-1173 280 13 e. e. PROPN cana-1173 280 14 𝐺0 𝐺0 PROPN cana-1173 280 15 = = SYM cana-1173 280 16 70 70 NUM cana-1173 280 17 , , PUNCT cana-1173 280 18 𝐺1 𝐺1 X cana-1173 280 19 = = NOUN cana-1173 280 20 226,𝐺2 226,𝐺2 NUM cana-1173 280 21 = = SYM cana-1173 280 22 62 62 NUM cana-1173 280 23 , , PUNCT cana-1173 280 24 𝐺3 𝐺3 PRON cana-1173 280 25 = = SYM cana-1173 280 26 165,𝐺4 165,𝐺4 NUM cana-1173 280 27 = = SYM cana-1173 280 28 135 135 NUM cana-1173 280 29 , , PUNCT cana-1173 280 30 𝐺5 𝐺5 NOUN cana-1173 280 31 = = SYM cana-1173 280 32 98,𝐺6 98,𝐺6 PROPN cana-1173 280 33 = = SYM cana-1173 280 34 89 89 NUM cana-1173 280 35 , , PUNCT cana-1173 280 36 𝐺7 𝐺7 ADJ cana-1173 280 37 = = SYM cana-1173 280 38 73,𝐺8 73,𝐺8 NOUN cana-1173 280 39 = = SYM cana-1173 280 40 82 82 NUM cana-1173 280 41 , , PUNCT cana-1173 280 42 𝐺9 𝐺9 VERB cana-1173 280 43 = = NOUN cana-1173 280 44 142 142 NUM cana-1173 280 45 , , PUNCT cana-1173 280 46 𝐺10 𝐺10 PROPN cana-1173 280 47 = = PUNCT cana-1173 280 48 94 94 NUM cana-1173 280 49 , , PUNCT cana-1173 280 50 𝐺11 𝐺11 NOUN cana-1173 280 51 = = SYM cana-1173 280 52 111 111 NUM cana-1173 280 53 . . PUNCT cana-1173 281 1 we we PRON cana-1173 281 2 know know VERB cana-1173 281 3 𝑒𝑑 𝑒𝑑 NOUN cana-1173 281 4 = = NOUN cana-1173 281 5 1 1 NUM cana-1173 281 6 + + NUM cana-1173 281 7 𝑑 𝑑 PROPN cana-1173 281 8 + + NOUN cana-1173 281 9 𝑑2 𝑑2 ADJ cana-1173 281 10 2 2 NUM cana-1173 281 11 ! ! PUNCT cana-1173 282 1 + + CCONJ cana-1173 282 2 𝑑3 𝑑3 PROPN cana-1173 282 3 3 3 NUM cana-1173 282 4 ! ! PUNCT cana-1173 283 1 + + NUM cana-1173 283 2 𝑑4 𝑑4 PROPN cana-1173 283 3 4 4 NUM cana-1173 283 4 ! ! PUNCT cana-1173 284 1 + + CCONJ cana-1173 284 2 β‹― β‹― PROPN cana-1173 284 3 .. .. PUNCT cana-1173 284 4 therefore therefore ADV cana-1173 284 5 , , PUNCT cana-1173 284 6 𝑒2𝑑 𝑒2𝑑 NOUN cana-1173 284 7 = = SYM cana-1173 284 8 1 1 NUM cana-1173 284 9 + + NUM cana-1173 284 10 2𝑑 2𝑑 NOUN cana-1173 284 11 + + CCONJ cana-1173 284 12 ( ( PUNCT cana-1173 284 13 2𝑑)2 2𝑑)2 NUM cana-1173 284 14 2 2 NUM cana-1173 284 15 ! ! PUNCT cana-1173 285 1 + + CCONJ cana-1173 285 2 ( ( PUNCT cana-1173 285 3 2𝑑)3 2𝑑)3 NUM cana-1173 285 4 3 3 NUM cana-1173 285 5 ! ! PUNCT cana-1173 286 1 + + CCONJ cana-1173 286 2 ( ( PUNCT cana-1173 286 3 2𝑑)4 2𝑑)4 NUM cana-1173 286 4 4 4 NUM cana-1173 286 5 ! ! PUNCT cana-1173 287 1 + + CCONJ cana-1173 287 2 β‹― β‹― NOUN cana-1173 287 3 .. .. PUNCT cana-1173 287 4 communications communication NOUN cana-1173 287 5 on on ADP cana-1173 287 6 applied apply VERB cana-1173 287 7 nonlinear nonlinear ADJ cana-1173 287 8 analysis analysis NOUN cana-1173 287 9 issn issn NOUN cana-1173 287 10 : : PUNCT cana-1173 287 11 1074 1074 NUM cana-1173 287 12 - - PUNCT cana-1173 287 13 133x 133x NUM cana-1173 287 14 vol vol NOUN cana-1173 287 15 31 31 NUM cana-1173 287 16 no no NOUN cana-1173 287 17 . . PUNCT cana-1173 288 1 6s 6s NUM cana-1173 288 2 ( ( PUNCT cana-1173 288 3 2024 2024 NUM cana-1173 288 4 ) ) PUNCT cana-1173 288 5 150 150 NUM cana-1173 288 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 288 7 𝑓(𝑑 𝑓(𝑑 PROPN cana-1173 288 8 ) ) PUNCT cana-1173 288 9 = = SYM cana-1173 289 1 𝑑2 𝑑2 NOUN cana-1173 290 1 [ [ X cana-1173 290 2 𝐺0 𝐺0 X cana-1173 290 3 + + PUNCT cana-1173 290 4 𝐺1(2𝑑 𝐺1(2𝑑 ADJ cana-1173 290 5 ) ) PUNCT cana-1173 290 6 + + CCONJ cana-1173 290 7 𝐺2 𝐺2 ADJ cana-1173 290 8 ( ( PUNCT cana-1173 290 9 2𝑑)2 2𝑑)2 NUM cana-1173 290 10 2 2 NUM cana-1173 290 11 ! ! PUNCT cana-1173 291 1 + + CCONJ cana-1173 291 2 𝐺3 𝐺3 PROPN cana-1173 291 3 ( ( PUNCT cana-1173 291 4 2𝑑)3 2𝑑)3 NUM cana-1173 291 5 3 3 NUM cana-1173 291 6 ! ! PUNCT cana-1173 291 7 + + NUM cana-1173 291 8 𝐺4 𝐺4 NOUN cana-1173 291 9 ( ( PUNCT cana-1173 291 10 2𝑑)4 2𝑑)4 NUM cana-1173 291 11 4 4 NUM cana-1173 291 12 ! ! PUNCT cana-1173 292 1 + + CCONJ cana-1173 292 2 𝐺5 𝐺5 NOUN cana-1173 292 3 ( ( PUNCT cana-1173 292 4 2𝑑)5 2𝑑)5 NUM cana-1173 292 5 5 5 NUM cana-1173 292 6 ! ! PUNCT cana-1173 293 1 + + CCONJ cana-1173 293 2 𝐺6 𝐺6 NOUN cana-1173 293 3 ( ( PUNCT cana-1173 293 4 2𝑑)6 2𝑑)6 NUM cana-1173 293 5 6 6 NUM cana-1173 293 6 ! ! PUNCT cana-1173 294 1 + + CCONJ cana-1173 294 2 𝐺7 𝐺7 ADJ cana-1173 294 3 ( ( PUNCT cana-1173 294 4 2𝑑)7 2𝑑)7 NUM cana-1173 294 5 7 7 NUM cana-1173 294 6 ! ! PUNCT cana-1173 295 1 + + CCONJ cana-1173 295 2 𝐺8 𝐺8 NOUN cana-1173 295 3 ( ( PUNCT cana-1173 295 4 2𝑑)8 2𝑑)8 NUM cana-1173 295 5 8 8 NUM cana-1173 295 6 ! ! PUNCT cana-1173 296 1 + + CCONJ cana-1173 296 2 𝐺9 𝐺9 ADJ cana-1173 296 3 ( ( PUNCT cana-1173 296 4 2𝑑)9 2𝑑)9 NUM cana-1173 296 5 9 9 NUM cana-1173 296 6 ! ! PUNCT cana-1173 297 1 + + CCONJ cana-1173 297 2 𝐺10 𝐺10 PROPN cana-1173 297 3 ( ( PUNCT cana-1173 297 4 2𝑑)10 2𝑑)10 NUM cana-1173 297 5 10 10 NUM cana-1173 297 6 ! ! PUNCT cana-1173 298 1 + + CCONJ cana-1173 298 2 𝐺11 𝐺11 NOUN cana-1173 298 3 ( ( PUNCT cana-1173 298 4 2𝑑)11 2𝑑)11 NUM cana-1173 298 5 11 11 NUM cana-1173 298 6 ! ! PUNCT cana-1173 299 1 ] ] PUNCT cana-1173 299 2 . . PUNCT cana-1173 300 1 where,𝐺0 where,𝐺0 NOUN cana-1173 300 2 = = NOUN cana-1173 300 3 70 70 NUM cana-1173 300 4 , , PUNCT cana-1173 300 5 𝐺1 𝐺1 X cana-1173 301 1 = = NOUN cana-1173 301 2 226,𝐺2 226,𝐺2 NUM cana-1173 301 3 = = SYM cana-1173 301 4 62 62 NUM cana-1173 301 5 , , PUNCT cana-1173 301 6 𝐺3 𝐺3 PRON cana-1173 301 7 = = SYM cana-1173 301 8 165,𝐺4 165,𝐺4 NUM cana-1173 301 9 = = SYM cana-1173 301 10 135 135 NUM cana-1173 301 11 , , PUNCT cana-1173 301 12 𝐺5 𝐺5 NOUN cana-1173 301 13 = = SYM cana-1173 301 14 98,𝐺6 98,𝐺6 PROPN cana-1173 301 15 = = SYM cana-1173 301 16 89 89 NUM cana-1173 301 17 , , PUNCT cana-1173 301 18 𝐺7 𝐺7 ADJ cana-1173 301 19 = = SYM cana-1173 301 20 73,𝐺8 73,𝐺8 NOUN cana-1173 301 21 = = SYM cana-1173 301 22 82 82 NUM cana-1173 301 23 , , PUNCT cana-1173 301 24 𝐺9 𝐺9 VERB cana-1173 301 25 = = NOUN cana-1173 301 26 142,𝐺10 142,𝐺10 NUM cana-1173 301 27 = = SYM cana-1173 301 28 94 94 NUM cana-1173 301 29 , , PUNCT cana-1173 301 30 𝐺11 𝐺11 NOUN cana-1173 301 31 = = SYM cana-1173 301 32 111 111 NUM cana-1173 301 33 . . PUNCT cana-1173 302 1 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 302 2 ) ) PUNCT cana-1173 303 1 = = SYM cana-1173 303 2 𝑑2 𝑑2 NOUN cana-1173 304 1 [ [ X cana-1173 304 2 70 70 NUM cana-1173 304 3 + + CCONJ cana-1173 304 4 226(2𝑑 226(2𝑑 NUM cana-1173 304 5 ) ) PUNCT cana-1173 305 1 + + CCONJ cana-1173 305 2 62 62 NUM cana-1173 305 3 ( ( PUNCT cana-1173 305 4 2𝑑)2 2𝑑)2 NUM cana-1173 305 5 2 2 NUM cana-1173 305 6 ! ! PUNCT cana-1173 306 1 + + CCONJ cana-1173 306 2 165 165 NUM cana-1173 306 3 ( ( PUNCT cana-1173 306 4 2𝑑)3 2𝑑)3 NUM cana-1173 306 5 3 3 NUM cana-1173 306 6 ! ! PUNCT cana-1173 307 1 + + CCONJ cana-1173 307 2 135 135 NUM cana-1173 307 3 ( ( PUNCT cana-1173 307 4 2𝑑)4 2𝑑)4 NUM cana-1173 307 5 4 4 NUM cana-1173 307 6 ! ! PUNCT cana-1173 308 1 + + CCONJ cana-1173 308 2 98 98 NUM cana-1173 308 3 ( ( PUNCT cana-1173 308 4 2𝑑)5 2𝑑)5 NUM cana-1173 308 5 5 5 NUM cana-1173 308 6 ! ! PUNCT cana-1173 309 1 + + CCONJ cana-1173 309 2 89 89 NUM cana-1173 309 3 ( ( PUNCT cana-1173 309 4 2𝑑)6 2𝑑)6 NUM cana-1173 309 5 6 6 NUM cana-1173 309 6 ! ! PUNCT cana-1173 310 1 + + CCONJ cana-1173 310 2 73 73 NUM cana-1173 310 3 ( ( PUNCT cana-1173 310 4 2𝑑)7 2𝑑)7 NUM cana-1173 310 5 7 7 NUM cana-1173 310 6 ! ! PUNCT cana-1173 311 1 + + CCONJ cana-1173 311 2 82 82 NUM cana-1173 311 3 ( ( PUNCT cana-1173 311 4 2𝑑)8 2𝑑)8 NUM cana-1173 311 5 8 8 NUM cana-1173 311 6 ! ! PUNCT cana-1173 312 1 + + CCONJ cana-1173 312 2 142 142 NUM cana-1173 312 3 ( ( PUNCT cana-1173 312 4 2𝑑)9 2𝑑)9 NUM cana-1173 312 5 9 9 NUM cana-1173 312 6 ! ! PUNCT cana-1173 313 1 + + CCONJ cana-1173 313 2 94 94 NUM cana-1173 313 3 ( ( PUNCT cana-1173 313 4 2𝑑)10 2𝑑)10 NUM cana-1173 313 5 10 10 NUM cana-1173 313 6 ! ! PUNCT cana-1173 314 1 + + CCONJ cana-1173 314 2 111 111 NUM cana-1173 314 3 ( ( PUNCT cana-1173 314 4 2𝑑)11 2𝑑)11 NUM cana-1173 314 5 11 11 NUM cana-1173 314 6 ! ! PUNCT cana-1173 314 7 ] ] PUNCT cana-1173 314 8 . . PUNCT cana-1173 315 1 = = PUNCT cana-1173 316 1 [ [ X cana-1173 316 2 70𝑑2 70𝑑2 NUM cana-1173 316 3 + + NUM cana-1173 316 4 226(2𝑑)𝑑2 226(2𝑑)𝑑2 NUM cana-1173 316 5 + + CCONJ cana-1173 316 6 62 62 NUM cana-1173 316 7 ( ( PUNCT cana-1173 316 8 2𝑑)2 2𝑑)2 NUM cana-1173 316 9 2 2 NUM cana-1173 316 10 ! ! PUNCT cana-1173 316 11 𝑑2 𝑑2 NOUN cana-1173 316 12 + + CCONJ cana-1173 316 13 165 165 NUM cana-1173 316 14 ( ( PUNCT cana-1173 316 15 2𝑑)3 2𝑑)3 NUM cana-1173 316 16 3 3 NUM cana-1173 316 17 ! ! PUNCT cana-1173 316 18 𝑑2 𝑑2 NOUN cana-1173 316 19 + + CCONJ cana-1173 316 20 135 135 NUM cana-1173 316 21 ( ( PUNCT cana-1173 316 22 2𝑑)4 2𝑑)4 NUM cana-1173 316 23 4 4 NUM cana-1173 316 24 ! ! PUNCT cana-1173 316 25 𝑑2 𝑑2 NOUN cana-1173 316 26 + + CCONJ cana-1173 316 27 98 98 NUM cana-1173 316 28 ( ( PUNCT cana-1173 316 29 2𝑑)5 2𝑑)5 NUM cana-1173 316 30 5 5 NUM cana-1173 316 31 ! ! PUNCT cana-1173 317 1 𝑑2 𝑑2 PROPN cana-1173 317 2 + + CCONJ cana-1173 317 3 89 89 NUM cana-1173 317 4 ( ( PUNCT cana-1173 317 5 2𝑑)6 2𝑑)6 NUM cana-1173 317 6 6 6 NUM cana-1173 317 7 ! ! PUNCT cana-1173 318 1 𝑑2 𝑑2 NOUN cana-1173 318 2 + + CCONJ cana-1173 318 3 73 73 NUM cana-1173 318 4 ( ( PUNCT cana-1173 318 5 2𝑑)7 2𝑑)7 NUM cana-1173 318 6 7 7 NUM cana-1173 318 7 ! ! PUNCT cana-1173 318 8 𝑑2 𝑑2 NOUN cana-1173 319 1 + + CCONJ cana-1173 319 2 82 82 NUM cana-1173 319 3 ( ( PUNCT cana-1173 320 1 2𝑑)8 2𝑑)8 NUM cana-1173 320 2 8 8 NUM cana-1173 320 3 ! ! PUNCT cana-1173 321 1 𝑑2 𝑑2 NOUN cana-1173 321 2 + + CCONJ cana-1173 321 3 142 142 NUM cana-1173 321 4 ( ( PUNCT cana-1173 321 5 2𝑑)9 2𝑑)9 NUM cana-1173 321 6 9 9 NUM cana-1173 321 7 ! ! PUNCT cana-1173 322 1 𝑑2 𝑑2 NOUN cana-1173 322 2 + + CCONJ cana-1173 322 3 94 94 NUM cana-1173 322 4 ( ( PUNCT cana-1173 322 5 2𝑑)10 2𝑑)10 NUM cana-1173 322 6 10 10 NUM cana-1173 322 7 ! ! PUNCT cana-1173 323 1 𝑑2 𝑑2 NOUN cana-1173 323 2 + + CCONJ cana-1173 323 3 111 111 NUM cana-1173 323 4 ( ( PUNCT cana-1173 323 5 2𝑑)11 2𝑑)11 NUM cana-1173 323 6 11 11 NUM cana-1173 323 7 ! ! PUNCT cana-1173 324 1 𝑑2 𝑑2 NOUN cana-1173 324 2 ] ] PUNCT cana-1173 324 3 . . PUNCT cana-1173 325 1 apply apply VERB cana-1173 325 2 kamal kamal PROPN cana-1173 325 3 transform transform NOUN cana-1173 325 4 on on ADP cana-1173 325 5 both both DET cana-1173 325 6 sides side NOUN cana-1173 325 7 𝐾[𝑓(𝑑 𝐾[𝑓(𝑑 ADJ cana-1173 325 8 ) ) PUNCT cana-1173 325 9 ] ] PUNCT cana-1173 326 1 = = X cana-1173 326 2 k[70𝑑2 k[70𝑑2 X cana-1173 326 3 + + CCONJ cana-1173 326 4 226(2𝑑)𝑑2 226(2𝑑)𝑑2 NUM cana-1173 326 5 + + SYM cana-1173 326 6 62 62 NUM cana-1173 326 7 ( ( PUNCT cana-1173 326 8 2𝑑)2 2𝑑)2 NUM cana-1173 326 9 2 2 NUM cana-1173 326 10 ! ! PUNCT cana-1173 326 11 𝑑2 𝑑2 NOUN cana-1173 326 12 + + CCONJ cana-1173 326 13 165 165 NUM cana-1173 326 14 ( ( PUNCT cana-1173 326 15 2𝑑)3 2𝑑)3 NUM cana-1173 326 16 3 3 NUM cana-1173 326 17 ! ! PUNCT cana-1173 326 18 𝑑2 𝑑2 NOUN cana-1173 326 19 + + CCONJ cana-1173 326 20 135 135 NUM cana-1173 326 21 ( ( PUNCT cana-1173 326 22 2𝑑)4 2𝑑)4 NUM cana-1173 326 23 4 4 NUM cana-1173 326 24 ! ! PUNCT cana-1173 326 25 𝑑2 𝑑2 NOUN cana-1173 326 26 + + CCONJ cana-1173 326 27 98 98 NUM cana-1173 326 28 ( ( PUNCT cana-1173 326 29 2𝑑)5 2𝑑)5 NUM cana-1173 326 30 5 5 NUM cana-1173 326 31 ! ! PUNCT cana-1173 327 1 𝑑2 𝑑2 PROPN cana-1173 327 2 + + CCONJ cana-1173 327 3 89 89 NUM cana-1173 327 4 ( ( PUNCT cana-1173 327 5 2𝑑)6 2𝑑)6 NUM cana-1173 327 6 6 6 NUM cana-1173 327 7 ! ! PUNCT cana-1173 328 1 𝑑2 𝑑2 NOUN cana-1173 328 2 + + CCONJ cana-1173 328 3 73 73 NUM cana-1173 328 4 ( ( PUNCT cana-1173 328 5 2𝑑)7 2𝑑)7 NUM cana-1173 328 6 7 7 NUM cana-1173 328 7 ! ! PUNCT cana-1173 328 8 𝑑2 𝑑2 NOUN cana-1173 329 1 + + CCONJ cana-1173 329 2 82 82 NUM cana-1173 329 3 ( ( PUNCT cana-1173 330 1 2𝑑)8 2𝑑)8 NUM cana-1173 330 2 8 8 NUM cana-1173 330 3 ! ! PUNCT cana-1173 331 1 𝑑2 𝑑2 NOUN cana-1173 331 2 + + CCONJ cana-1173 331 3 142 142 NUM cana-1173 331 4 ( ( PUNCT cana-1173 331 5 2𝑑)9 2𝑑)9 NUM cana-1173 331 6 9 9 NUM cana-1173 331 7 ! ! PUNCT cana-1173 332 1 𝑑2 𝑑2 NOUN cana-1173 332 2 + + CCONJ cana-1173 332 3 94 94 NUM cana-1173 332 4 ( ( PUNCT cana-1173 332 5 2𝑑)10 2𝑑)10 NUM cana-1173 332 6 10 10 NUM cana-1173 332 7 ! ! PUNCT cana-1173 333 1 𝑑2 𝑑2 NOUN cana-1173 333 2 + + CCONJ cana-1173 333 3 111 111 NUM cana-1173 333 4 ( ( PUNCT cana-1173 333 5 2𝑑)11 2𝑑)11 NUM cana-1173 333 6 11 11 NUM cana-1173 333 7 ! ! PUNCT cana-1173 334 1 𝑑2 𝑑2 NOUN cana-1173 334 2 ] ] PUNCT cana-1173 334 3 . . PUNCT cana-1173 335 1 = = PUNCT cana-1173 335 2 70(2!)𝑣3 70(2!)𝑣3 NUM cana-1173 335 3 + + NOUN cana-1173 335 4 226(2)(3!)𝑣4 226(2)(3!)𝑣4 NUM cana-1173 335 5 + + CCONJ cana-1173 335 6 62(4 62(4 NUM cana-1173 335 7 ) ) PUNCT cana-1173 335 8 22 22 NUM cana-1173 335 9 2 2 NUM cana-1173 335 10 ! ! PUNCT cana-1173 336 1 𝑣5 𝑣5 NOUN cana-1173 336 2 + + CCONJ cana-1173 336 3 165(23)5 165(23)5 NUM cana-1173 336 4 ! ! PUNCT cana-1173 336 5 𝑣6 𝑣6 PROPN cana-1173 336 6 3 3 X cana-1173 336 7 ! ! PUNCT cana-1173 337 1 + + X cana-1173 337 2 135(24)6 135(24)6 NUM cana-1173 337 3 ! ! PUNCT cana-1173 337 4 𝑣7 𝑣7 ADJ cana-1173 337 5 4 4 NUM cana-1173 337 6 ! ! PUNCT cana-1173 338 1 + + X cana-1173 338 2 98(24)7 98(24)7 X cana-1173 338 3 ! ! PUNCT cana-1173 339 1 𝑣8 𝑣8 NOUN cana-1173 339 2 5 5 NUM cana-1173 339 3 ! ! PUNCT cana-1173 340 1 + + CCONJ cana-1173 340 2 89(26)8 89(26)8 NUM cana-1173 340 3 ! ! PUNCT cana-1173 341 1 𝑣9 𝑣9 ADP cana-1173 341 2 6 6 NUM cana-1173 341 3 ! ! PUNCT cana-1173 342 1 + + CCONJ cana-1173 342 2 73(27)9 73(27)9 X cana-1173 342 3 ! ! PUNCT cana-1173 342 4 𝑣10 𝑣10 NOUN cana-1173 342 5 7 7 NUM cana-1173 342 6 ! ! PUNCT cana-1173 343 1 + + CCONJ cana-1173 343 2 82(28)10 82(28)10 PROPN cana-1173 343 3 ! ! PUNCT cana-1173 343 4 𝑣11 𝑣11 VERB cana-1173 343 5 8 8 NUM cana-1173 343 6 ! ! PUNCT cana-1173 344 1 + + CCONJ cana-1173 344 2 142(29)11 142(29)11 NUM cana-1173 344 3 ! ! PUNCT cana-1173 345 1 𝑣12 𝑣12 PROPN cana-1173 345 2 9 9 NUM cana-1173 345 3 ! ! PUNCT cana-1173 346 1 + + NOUN cana-1173 346 2 94(210)12 94(210)12 X cana-1173 346 3 ! ! PUNCT cana-1173 346 4 𝑣13 𝑣13 PROPN cana-1173 346 5 10 10 NUM cana-1173 346 6 ! ! PUNCT cana-1173 347 1 + + CCONJ cana-1173 348 1 111(211)13 111(211)13 NUM cana-1173 348 2 ! ! PUNCT cana-1173 349 1 𝑣14 𝑣14 NUM cana-1173 349 2 11 11 NUM cana-1173 349 3 ! ! PUNCT cana-1173 350 1 = = NOUN cana-1173 351 1 140𝑣3 140𝑣3 NUM cana-1173 351 2 + + CCONJ cana-1173 351 3 2712𝑣4 2712𝑣4 NUM cana-1173 352 1 + + CCONJ cana-1173 352 2 2976𝑣5 2976𝑣5 NUM cana-1173 352 3 + + CCONJ cana-1173 352 4 26400𝑣6 26400𝑣6 NUM cana-1173 352 5 + + CCONJ cana-1173 352 6 64800𝑣7 64800𝑣7 NUM cana-1173 353 1 + + CCONJ cana-1173 353 2 131712𝑣8 131712𝑣8 NUM cana-1173 353 3 + + NUM cana-1173 353 4 318976𝑣9 318976𝑣9 NUM cana-1173 353 5 + + CCONJ cana-1173 353 6 672768𝑣10 672768𝑣10 NOUN cana-1173 353 7 + + CCONJ cana-1173 353 8 1889280𝑣11 1889280𝑣11 NUM cana-1173 353 9 + + CCONJ cana-1173 353 10 7997440𝑣12 7997440𝑣12 NUM cana-1173 353 11 + + SYM cana-1173 353 12 12705792𝑣13 12705792𝑣13 NUM cana-1173 353 13 + + CCONJ cana-1173 353 14 35463168𝑣14 35463168𝑣14 NUM cana-1173 353 15 . . PUNCT cana-1173 354 1 adjusting adjust VERB cana-1173 354 2 the the DET cana-1173 354 3 above above ADJ cana-1173 354 4 coefficients coefficient NOUN cana-1173 354 5 under under ADP cana-1173 354 6 modulo modulo NOUN cana-1173 354 7 255 255 NUM cana-1173 354 8 by by ADP cana-1173 354 9 taking take VERB cana-1173 354 10 qi qi PROPN cana-1173 354 11 ≑ ≑ PROPN cana-1173 354 12 pi pi NOUN cana-1173 354 13 ( ( PUNCT cana-1173 354 14 mod mod PROPN cana-1173 354 15 255 255 NUM cana-1173 354 16 ) ) PUNCT cana-1173 354 17 . . PUNCT cana-1173 355 1 here here ADV cana-1173 355 2 , , PUNCT cana-1173 355 3 qiβ€²s qiβ€²s PROPN cana-1173 355 4 are be AUX cana-1173 355 5 140 140 NUM cana-1173 355 6 ≑ ≑ PROPN cana-1173 355 7 140(mod 140(mod NUM cana-1173 355 8 255 255 NUM cana-1173 355 9 ) ) PUNCT cana-1173 355 10 . . PUNCT cana-1173 356 1 2712 2712 NUM cana-1173 356 2 ≑ ≑ PROPN cana-1173 356 3 162(mod 162(mod NUM cana-1173 356 4 255 255 NUM cana-1173 356 5 ) ) PUNCT cana-1173 356 6 . . PUNCT cana-1173 357 1 2976 2976 NUM cana-1173 357 2 ≑ ≑ PROPN cana-1173 357 3 171(mod 171(mod NUM cana-1173 357 4 255 255 NUM cana-1173 357 5 ) ) PUNCT cana-1173 357 6 . . PUNCT cana-1173 358 1 26400 26400 NUM cana-1173 358 2 ≑ ≑ PROPN cana-1173 358 3 135(mod 135(mod NUM cana-1173 358 4 255 255 NUM cana-1173 358 5 ) ) PUNCT cana-1173 358 6 . . PUNCT cana-1173 359 1 64800 64800 NUM cana-1173 359 2 ≑ ≑ PROPN cana-1173 359 3 30(mod 30(mod PROPN cana-1173 359 4 255 255 NUM cana-1173 359 5 ) ) PUNCT cana-1173 359 6 . . PUNCT cana-1173 360 1 131712 131712 NUM cana-1173 360 2 ≑ ≑ PROPN cana-1173 360 3 132(mod 132(mod PROPN cana-1173 360 4 255 255 NUM cana-1173 360 5 ) ) PUNCT cana-1173 360 6 . . PUNCT cana-1173 361 1 318976 318976 NUM cana-1173 361 2 ≑ ≑ PROPN cana-1173 361 3 226(mod 226(mod NUM cana-1173 361 4 255 255 NUM cana-1173 361 5 ) ) PUNCT cana-1173 361 6 . . PUNCT cana-1173 362 1 672768 672768 NUM cana-1173 362 2 ≑ ≑ PROPN cana-1173 362 3 78(mod 78(mod NOUN cana-1173 362 4 255 255 NUM cana-1173 362 5 ) ) PUNCT cana-1173 362 6 . . PUNCT cana-1173 363 1 1889280 1889280 NUM cana-1173 363 2 ≑ ≑ PROPN cana-1173 363 3 240(mod 240(mod PROPN cana-1173 363 4 255 255 NUM cana-1173 363 5 ) ) PUNCT cana-1173 363 6 . . PUNCT cana-1173 364 1 7997440 7997440 NUM cana-1173 364 2 ≑ ≑ PROPN cana-1173 364 3 130(mod 130(mod PROPN cana-1173 364 4 255 255 NUM cana-1173 364 5 ) ) PUNCT cana-1173 364 6 . . PUNCT cana-1173 365 1 12705792 12705792 NUM cana-1173 365 2 ≑ ≑ PROPN cana-1173 365 3 162(mod 162(mod NUM cana-1173 365 4 255 255 NUM cana-1173 365 5 ) ) PUNCT cana-1173 365 6 . . PUNCT cana-1173 366 1 communications communication NOUN cana-1173 366 2 on on ADP cana-1173 366 3 applied apply VERB cana-1173 366 4 nonlinear nonlinear ADJ cana-1173 366 5 analysis analysis NOUN cana-1173 366 6 issn issn NOUN cana-1173 366 7 : : PUNCT cana-1173 366 8 1074 1074 NUM cana-1173 366 9 - - PUNCT cana-1173 366 10 133x 133x NUM cana-1173 366 11 vol vol NOUN cana-1173 366 12 31 31 NUM cana-1173 366 13 no no NOUN cana-1173 366 14 . . PUNCT cana-1173 367 1 6s 6s NUM cana-1173 367 2 ( ( PUNCT cana-1173 367 3 2024 2024 NUM cana-1173 367 4 ) ) PUNCT cana-1173 367 5 151 151 NUM cana-1173 367 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 367 7 354631618 354631618 NUM cana-1173 367 8 ≑ ≑ PROPN cana-1173 367 9 58(mod 58(mod PROPN cana-1173 367 10 255 255 NUM cana-1173 367 11 ) ) PUNCT cana-1173 367 12 . . PUNCT cana-1173 368 1 here here ADV cana-1173 368 2 piβ€²s piβ€² NOUN cana-1173 368 3 are be AUX cana-1173 368 4 140,162,171,135,30,132,226,78,240,130,162,58 140,162,171,135,30,132,226,78,240,130,162,58 NUM cana-1173 368 5 which which PRON cana-1173 368 6 are be AUX cana-1173 368 7 converted convert VERB cana-1173 368 8 to to ADP cana-1173 368 9 ascii ascii NOUN cana-1173 368 10 codes code NOUN cana-1173 368 11 hence hence ADV cana-1173 368 12 , , PUNCT cana-1173 368 13 the the DET cana-1173 368 14 receiver receiver NOUN cana-1173 368 15 receives receive VERB cana-1173 368 16 the the DET cana-1173 368 17 cipher cipher ADJ cana-1173 368 18 text text NOUN cana-1173 368 19 along along ADP cana-1173 368 20 with with ADP cana-1173 368 21 the the DET cana-1173 368 22 key key NOUN cana-1173 368 23 , , PUNCT cana-1173 368 24 π‘˜π‘– π‘˜π‘– ADP cana-1173 368 25 = = PUNCT cana-1173 368 26 π‘žπ‘–βˆ’π‘π‘– π‘žπ‘–βˆ’π‘π‘– NOUN cana-1173 368 27 255 255 NUM cana-1173 368 28 where where SCONJ cana-1173 368 29 kiβ€²s kiβ€²s PROPN cana-1173 368 30 are be AUX cana-1173 368 31 0,10,11,103,254,516,1250,2638,7408,31362,49826,1390712 0,10,11,103,254,516,1250,2638,7408,31362,49826,1390712 NOUN cana-1173 368 32 . . PUNCT cana-1173 369 1 step step NOUN cana-1173 369 2 6 6 NUM cana-1173 369 3 : : PUNCT cana-1173 369 4 i i PRON cana-1173 369 5 stage stage NOUN cana-1173 369 6 of of ADP cana-1173 369 7 decryption decryption NOUN cana-1173 369 8 to to PART cana-1173 369 9 decrypt decrypt VERB cana-1173 369 10 the the DET cana-1173 369 11 message message NOUN cana-1173 369 12 , , PUNCT cana-1173 369 13 let let VERB cana-1173 369 14 π‘žπ‘– π‘žπ‘– PRON cana-1173 369 15 = = PUNCT cana-1173 369 16 𝑝𝑖 𝑝𝑖 NOUN cana-1173 369 17 + + NOUN cana-1173 369 18 255π‘˜π‘–. 255π‘˜π‘–. NUM cana-1173 369 19 we we PRON cana-1173 369 20 define define VERB cana-1173 369 21 𝐺(𝑠 𝐺(𝑠 NUM cana-1173 369 22 ) ) PUNCT cana-1173 369 23 = = SYM cana-1173 370 1 βˆ‘ βˆ‘ PUNCT cana-1173 370 2 π‘žπ‘›π‘£π‘–+311 π‘žπ‘›π‘£π‘–+311 NOUN cana-1173 370 3 𝑖=0 𝑖=0 NOUN cana-1173 370 4 𝐺(𝑠 𝐺(𝑠 NUM cana-1173 370 5 ) ) PUNCT cana-1173 370 6 = = PUNCT cana-1173 371 1 140𝑣3 140𝑣3 NUM cana-1173 371 2 + + CCONJ cana-1173 371 3 2712𝑣4 2712𝑣4 NUM cana-1173 372 1 + + CCONJ cana-1173 372 2 2976𝑣5 2976𝑣5 NUM cana-1173 372 3 + + CCONJ cana-1173 372 4 26400𝑣6 26400𝑣6 NUM cana-1173 372 5 + + CCONJ cana-1173 372 6 64800𝑣7 64800𝑣7 NUM cana-1173 373 1 + + CCONJ cana-1173 373 2 131712𝑣8 131712𝑣8 NUM cana-1173 373 3 + + NUM cana-1173 373 4 318976𝑣9 318976𝑣9 NUM cana-1173 373 5 + + CCONJ cana-1173 373 6 672768𝑣10 672768𝑣10 NOUN cana-1173 373 7 + + CCONJ cana-1173 373 8 1889280𝑣11 1889280𝑣11 NUM cana-1173 373 9 + + CCONJ cana-1173 373 10 7997440𝑣12 7997440𝑣12 NUM cana-1173 373 11 + + SYM cana-1173 373 12 12705792𝑣13 12705792𝑣13 NUM cana-1173 373 13 + + SYM cana-1173 373 14 35463168𝑣14 35463168𝑣14 NUM cana-1173 373 15 . . X cana-1173 373 16 apply apply VERB cana-1173 373 17 inverse inverse NOUN cana-1173 373 18 kamal kamal PROPN cana-1173 373 19 transform transform PROPN cana-1173 373 20 πΎβˆ’1[𝐺(𝑠 πΎβˆ’1[𝐺(𝑠 PROPN cana-1173 373 21 ) ) PUNCT cana-1173 373 22 ] ] PUNCT cana-1173 374 1 = = SYM cana-1173 374 2 πΎβˆ’1[140𝑣3 πΎβˆ’1[140𝑣3 NUM cana-1173 374 3 + + NUM cana-1173 374 4 2712𝑣4 2712𝑣4 NUM cana-1173 374 5 + + CCONJ cana-1173 374 6 2976𝑣5 2976𝑣5 NUM cana-1173 374 7 + + CCONJ cana-1173 374 8 26400𝑣6 26400𝑣6 NUM cana-1173 374 9 + + CCONJ cana-1173 374 10 64800𝑣7 64800𝑣7 NUM cana-1173 374 11 + + CCONJ cana-1173 374 12 131712𝑣8 131712𝑣8 NUM cana-1173 374 13 + + NUM cana-1173 374 14 318976𝑣9 318976𝑣9 NUM cana-1173 374 15 + + CCONJ cana-1173 374 16 672768𝑣10 672768𝑣10 NOUN cana-1173 374 17 + + CCONJ cana-1173 374 18 1889280𝑣11 1889280𝑣11 NUM cana-1173 374 19 + + CCONJ cana-1173 374 20 7997440𝑣12 7997440𝑣12 NUM cana-1173 374 21 + + SYM cana-1173 374 22 12705792𝑣13 12705792𝑣13 NUM cana-1173 374 23 + + CCONJ cana-1173 374 24 35463168𝑣14 35463168𝑣14 NUM cana-1173 374 25 ] ] PUNCT cana-1173 374 26 . . PUNCT cana-1173 375 1 = = SYM cana-1173 375 2 140 140 NUM cana-1173 375 3 𝑑2 𝑑2 NOUN cana-1173 375 4 2 2 NUM cana-1173 375 5 ! ! PUNCT cana-1173 376 1 + + CCONJ cana-1173 376 2 2712 2712 NUM cana-1173 376 3 𝑑3 𝑑3 PROPN cana-1173 376 4 3 3 NUM cana-1173 376 5 ! ! PUNCT cana-1173 377 1 + + CCONJ cana-1173 377 2 2976 2976 NUM cana-1173 377 3 𝑑4 𝑑4 NOUN cana-1173 377 4 4 4 NUM cana-1173 377 5 ! ! PUNCT cana-1173 378 1 + + CCONJ cana-1173 378 2 26400 26400 NUM cana-1173 378 3 𝑑5 𝑑5 VERB cana-1173 378 4 5 5 NUM cana-1173 378 5 ! ! PUNCT cana-1173 379 1 + + CCONJ cana-1173 379 2 64800 64800 NUM cana-1173 379 3 𝑑6 𝑑6 NOUN cana-1173 379 4 6 6 NUM cana-1173 379 5 ! ! PUNCT cana-1173 380 1 + + CCONJ cana-1173 380 2 131712 131712 NUM cana-1173 380 3 𝑑7 𝑑7 NOUN cana-1173 380 4 7 7 NUM cana-1173 380 5 ! ! PUNCT cana-1173 381 1 + + CCONJ cana-1173 381 2 318976 318976 NUM cana-1173 381 3 𝑑8 𝑑8 PROPN cana-1173 381 4 8 8 NUM cana-1173 381 5 ! ! PUNCT cana-1173 382 1 + + CCONJ cana-1173 382 2 672768 672768 NUM cana-1173 382 3 𝑑9 𝑑9 NOUN cana-1173 382 4 9 9 NUM cana-1173 382 5 ! ! PUNCT cana-1173 383 1 + + CCONJ cana-1173 383 2 1889280 1889280 NUM cana-1173 383 3 𝑑10 𝑑10 NOUN cana-1173 383 4 10 10 NUM cana-1173 383 5 ! ! PUNCT cana-1173 384 1 + + CCONJ cana-1173 384 2 7997440 7997440 NUM cana-1173 384 3 𝑑11 𝑑11 ADP cana-1173 384 4 11 11 NUM cana-1173 384 5 ! ! PUNCT cana-1173 385 1 + + CCONJ cana-1173 385 2 12705792 12705792 NUM cana-1173 385 3 𝑑12 𝑑12 NOUN cana-1173 385 4 12 12 NUM cana-1173 385 5 ! ! PUNCT cana-1173 386 1 + + CCONJ cana-1173 386 2 35463168 35463168 NUM cana-1173 386 3 𝑑13 𝑑13 NOUN cana-1173 386 4 13 13 NUM cana-1173 386 5 ! ! PUNCT cana-1173 386 6 . . PUNCT cana-1173 387 1 =[ =[ NOUN cana-1173 387 2 70𝑑2 70𝑑2 NUM cana-1173 387 3 + + NUM cana-1173 387 4 226(2𝑑)𝑑2 226(2𝑑)𝑑2 NUM cana-1173 387 5 + + CCONJ cana-1173 387 6 62 62 NUM cana-1173 387 7 ( ( PUNCT cana-1173 387 8 2𝑑)2 2𝑑)2 NUM cana-1173 387 9 2 2 NUM cana-1173 387 10 ! ! PUNCT cana-1173 387 11 𝑑2 𝑑2 NOUN cana-1173 388 1 + + CCONJ cana-1173 388 2 165 165 NUM cana-1173 388 3 ( ( PUNCT cana-1173 388 4 2𝑑)3 2𝑑)3 NUM cana-1173 388 5 3 3 NUM cana-1173 388 6 ! ! PUNCT cana-1173 388 7 𝑑2 𝑑2 NOUN cana-1173 388 8 + + CCONJ cana-1173 388 9 135 135 NUM cana-1173 388 10 ( ( PUNCT cana-1173 388 11 2𝑑)4 2𝑑)4 NUM cana-1173 388 12 4 4 NUM cana-1173 388 13 ! ! PUNCT cana-1173 389 1 𝑑2 𝑑2 NOUN cana-1173 389 2 + + CCONJ cana-1173 389 3 98 98 NUM cana-1173 389 4 ( ( PUNCT cana-1173 389 5 2𝑑)5 2𝑑)5 NUM cana-1173 389 6 5 5 NUM cana-1173 389 7 ! ! PUNCT cana-1173 390 1 𝑑2 𝑑2 PROPN cana-1173 390 2 + + CCONJ cana-1173 390 3 89 89 NUM cana-1173 390 4 ( ( PUNCT cana-1173 390 5 2𝑑)6 2𝑑)6 NUM cana-1173 390 6 6 6 NUM cana-1173 390 7 ! ! PUNCT cana-1173 391 1 𝑑2 𝑑2 NOUN cana-1173 391 2 + + CCONJ cana-1173 391 3 73 73 NUM cana-1173 391 4 ( ( PUNCT cana-1173 391 5 2𝑑)7 2𝑑)7 NUM cana-1173 391 6 7 7 NUM cana-1173 391 7 ! ! PUNCT cana-1173 391 8 𝑑2 𝑑2 NOUN cana-1173 392 1 + + CCONJ cana-1173 392 2 82 82 NUM cana-1173 392 3 ( ( PUNCT cana-1173 393 1 2𝑑)8 2𝑑)8 NUM cana-1173 393 2 8 8 NUM cana-1173 393 3 ! ! PUNCT cana-1173 394 1 𝑑2 𝑑2 NOUN cana-1173 394 2 + + CCONJ cana-1173 394 3 142 142 NUM cana-1173 394 4 ( ( PUNCT cana-1173 394 5 2𝑑)9 2𝑑)9 NUM cana-1173 394 6 9 9 NUM cana-1173 394 7 ! ! PUNCT cana-1173 395 1 𝑑2 𝑑2 NOUN cana-1173 395 2 + + CCONJ cana-1173 395 3 94 94 NUM cana-1173 395 4 ( ( PUNCT cana-1173 395 5 2𝑑)10 2𝑑)10 NUM cana-1173 395 6 10 10 NUM cana-1173 395 7 ! ! PUNCT cana-1173 396 1 𝑑2 𝑑2 NOUN cana-1173 396 2 + + CCONJ cana-1173 396 3 111 111 NUM cana-1173 396 4 ( ( PUNCT cana-1173 396 5 2𝑑)11 2𝑑)11 NUM cana-1173 396 6 11 11 NUM cana-1173 396 7 ! ! PUNCT cana-1173 397 1 𝑑2 𝑑2 NOUN cana-1173 397 2 ] ] PUNCT cana-1173 397 3 . . PUNCT cana-1173 398 1 = = NOUN cana-1173 398 2 𝑑2 𝑑2 PROPN cana-1173 399 1 [ [ X cana-1173 399 2 70 70 NUM cana-1173 399 3 + + CCONJ cana-1173 399 4 226(2𝑑 226(2𝑑 NUM cana-1173 399 5 ) ) PUNCT cana-1173 400 1 + + CCONJ cana-1173 400 2 62 62 NUM cana-1173 400 3 ( ( PUNCT cana-1173 400 4 2𝑑)2 2𝑑)2 NUM cana-1173 400 5 2 2 NUM cana-1173 400 6 ! ! PUNCT cana-1173 401 1 + + CCONJ cana-1173 401 2 165 165 NUM cana-1173 401 3 ( ( PUNCT cana-1173 401 4 2𝑑)3 2𝑑)3 NUM cana-1173 401 5 3 3 NUM cana-1173 401 6 ! ! PUNCT cana-1173 402 1 + + CCONJ cana-1173 402 2 135 135 NUM cana-1173 402 3 ( ( PUNCT cana-1173 402 4 2𝑑)4 2𝑑)4 NUM cana-1173 402 5 4 4 NUM cana-1173 402 6 ! ! PUNCT cana-1173 403 1 + + CCONJ cana-1173 403 2 98 98 NUM cana-1173 403 3 ( ( PUNCT cana-1173 403 4 2𝑑)5 2𝑑)5 NUM cana-1173 403 5 5 5 NUM cana-1173 403 6 ! ! PUNCT cana-1173 404 1 + + CCONJ cana-1173 404 2 89 89 NUM cana-1173 404 3 ( ( PUNCT cana-1173 404 4 2𝑑)6 2𝑑)6 NUM cana-1173 404 5 6 6 NUM cana-1173 404 6 ! ! PUNCT cana-1173 405 1 + + CCONJ cana-1173 405 2 73 73 NUM cana-1173 405 3 ( ( PUNCT cana-1173 405 4 2𝑑)7 2𝑑)7 NUM cana-1173 405 5 7 7 NUM cana-1173 405 6 ! ! PUNCT cana-1173 406 1 + + CCONJ cana-1173 406 2 82 82 NUM cana-1173 406 3 ( ( PUNCT cana-1173 406 4 2𝑑)8 2𝑑)8 NUM cana-1173 406 5 8 8 NUM cana-1173 406 6 ! ! PUNCT cana-1173 407 1 + + CCONJ cana-1173 407 2 142 142 NUM cana-1173 407 3 ( ( PUNCT cana-1173 407 4 2𝑑)9 2𝑑)9 NUM cana-1173 407 5 9 9 NUM cana-1173 407 6 ! ! PUNCT cana-1173 408 1 + + CCONJ cana-1173 408 2 94 94 NUM cana-1173 408 3 ( ( PUNCT cana-1173 408 4 2𝑑)10 2𝑑)10 NUM cana-1173 408 5 10 10 NUM cana-1173 408 6 ! ! PUNCT cana-1173 409 1 + + CCONJ cana-1173 409 2 111 111 NUM cana-1173 409 3 ( ( PUNCT cana-1173 409 4 2𝑑)11 2𝑑)11 NUM cana-1173 409 5 11 11 NUM cana-1173 409 6 ! ! PUNCT cana-1173 409 7 ] ] PUNCT cana-1173 409 8 . . PUNCT cana-1173 410 1 = = PUNCT cana-1173 410 2 𝑓(𝑑 𝑓(𝑑 NOUN cana-1173 410 3 ) ) PUNCT cana-1173 410 4 . . PUNCT cana-1173 411 1 step step NOUN cana-1173 411 2 7 7 NUM cana-1173 411 3 : : PUNCT cana-1173 411 4 ii ii NOUN cana-1173 411 5 stage stage NOUN cana-1173 411 6 of of ADP cana-1173 411 7 decryption decryption NOUN cana-1173 411 8 now now ADV cana-1173 411 9 , , PUNCT cana-1173 411 10 the the DET cana-1173 411 11 coefficients coefficient NOUN cana-1173 411 12 in in ADP cana-1173 411 13 f(t f(t NOUN cana-1173 411 14 ) ) PUNCT cana-1173 411 15 are be AUX cana-1173 411 16 written write VERB cana-1173 411 17 in in ADP cana-1173 411 18 matrix matrix NOUN cana-1173 411 19 form form NOUN cana-1173 411 20 . . PUNCT cana-1173 412 1 let let VERB cana-1173 412 2 e= e= NOUN cana-1173 412 3 [ [ PUNCT cana-1173 412 4 70 70 NUM cana-1173 412 5 165 165 NUM cana-1173 412 6 89 89 NUM cana-1173 412 7 142 142 NUM cana-1173 412 8 226 226 NUM cana-1173 412 9 135 135 NUM cana-1173 412 10 73 73 NUM cana-1173 412 11 94 94 NUM cana-1173 412 12 62 62 NUM cana-1173 412 13 98 98 NUM cana-1173 412 14 82 82 NUM cana-1173 412 15 111 111 NUM cana-1173 412 16 ] ] PUNCT cana-1173 412 17 . . PUNCT cana-1173 413 1 let let VERB cana-1173 413 2 d d X cana-1173 413 3 ≑ ≑ PROPN cana-1173 413 4 aβˆ’1e(mod aβˆ’1e(mod ADJ cana-1173 413 5 255 255 NUM cana-1173 413 6 ) ) PUNCT cana-1173 413 7 . . PUNCT cana-1173 414 1 d d X cana-1173 414 2 ≑ ≑ PROPN cana-1173 414 3 [ [ PUNCT cana-1173 414 4 0 0 NUM cana-1173 414 5 1 1 NUM cana-1173 414 6 1 1 NUM cana-1173 414 7 βˆ’1 βˆ’1 NOUN cana-1173 414 8 2 2 NUM cana-1173 414 9 1 1 NUM cana-1173 414 10 2 2 NUM cana-1173 414 11 1 1 NUM cana-1173 414 12 1 1 NUM cana-1173 414 13 βˆ’1 βˆ’1 NOUN cana-1173 414 14 0 0 NUM cana-1173 414 15 2 2 NUM cana-1173 414 16 3 3 NUM cana-1173 414 17 βˆ’2 βˆ’2 NOUN cana-1173 414 18 1 1 NUM cana-1173 414 19 6 6 NUM cana-1173 414 20 ] ] PUNCT cana-1173 414 21 [ [ PUNCT cana-1173 414 22 70 70 NUM cana-1173 414 23 165 165 NUM cana-1173 414 24 89 89 NUM cana-1173 414 25 142 142 NUM cana-1173 414 26 226 226 NUM cana-1173 414 27 135 135 NUM cana-1173 414 28 73 73 NUM cana-1173 414 29 94 94 NUM cana-1173 414 30 62 62 NUM cana-1173 414 31 98 98 NUM cana-1173 414 32 82 82 NUM cana-1173 414 33 111 111 NUM cana-1173 414 34 ] ] PUNCT cana-1173 414 35 ( ( PUNCT cana-1173 414 36 mod mod PROPN cana-1173 414 37 255 255 NUM cana-1173 414 38 ) ) PUNCT cana-1173 414 39 . . PUNCT cana-1173 415 1 communications communication NOUN cana-1173 415 2 on on ADP cana-1173 415 3 applied apply VERB cana-1173 415 4 nonlinear nonlinear ADJ cana-1173 415 5 analysis analysis NOUN cana-1173 415 6 issn issn NOUN cana-1173 415 7 : : PUNCT cana-1173 415 8 1074 1074 NUM cana-1173 415 9 - - PUNCT cana-1173 415 10 133x 133x NUM cana-1173 415 11 vol vol NOUN cana-1173 415 12 31 31 NUM cana-1173 415 13 no no NOUN cana-1173 415 14 . . PUNCT cana-1173 416 1 6s 6s NUM cana-1173 416 2 ( ( PUNCT cana-1173 416 3 2024 2024 NUM cana-1173 416 4 ) ) PUNCT cana-1173 416 5 152 152 NUM cana-1173 416 6 https://internationalpubls.com https://internationalpubls.com X cana-1173 416 7 d d X cana-1173 416 8 ≑ ≑ PROPN cana-1173 416 9 [ [ PUNCT cana-1173 416 10 845 845 NUM cana-1173 416 11 βˆ’138 βˆ’138 NOUN cana-1173 416 12 542 542 NUM cana-1173 416 13 1125 1125 NUM cana-1173 416 14 625 625 NUM cana-1173 416 15 100 100 NUM cana-1173 416 16 590 590 NUM cana-1173 416 17 619 619 NUM cana-1173 416 18 611 611 NUM cana-1173 416 19 βˆ’144 βˆ’144 NOUN cana-1173 416 20 369 369 NUM cana-1173 416 21 866 866 NUM cana-1173 416 22 ] ] PUNCT cana-1173 416 23 ( ( PUNCT cana-1173 416 24 mod mod PROPN cana-1173 416 25 255 255 NUM cana-1173 416 26 ) ) PUNCT cana-1173 416 27 . . PUNCT cana-1173 417 1 d d NOUN cana-1173 417 2 = = PUNCT cana-1173 418 1 [ [ PUNCT cana-1173 418 2 80 80 NUM cana-1173 418 3 117 117 NUM cana-1173 418 4 32 32 NUM cana-1173 418 5 105 105 NUM cana-1173 418 6 115 115 NUM cana-1173 418 7 100 100 NUM cana-1173 418 8 80 80 NUM cana-1173 418 9 109 109 NUM cana-1173 418 10 101 101 NUM cana-1173 418 11 111 111 NUM cana-1173 418 12 114 114 NUM cana-1173 418 13 101 101 NUM cana-1173 418 14 ] ] PUNCT cana-1173 418 15 which which PRON cana-1173 418 16 is be AUX cana-1173 418 17 same same ADJ cana-1173 418 18 as as ADP cana-1173 418 19 p. p. NOUN cana-1173 418 20 hence hence ADV cana-1173 418 21 , , PUNCT cana-1173 418 22 the the DET cana-1173 418 23 original original ADJ cana-1173 418 24 message message NOUN cana-1173 418 25 is be AUX cana-1173 418 26 retrieved retrieve VERB cana-1173 418 27 as as ADP cana-1173 418 28 pseudo pseudo NOUN cana-1173 418 29 prime prime NOUN cana-1173 418 30 . . PUNCT cana-1173 419 1 5 5 X cana-1173 419 2 . . X cana-1173 419 3 conclusion conclusion NOUN cana-1173 419 4 in in ADP cana-1173 419 5 most most ADJ cana-1173 419 6 of of ADP cana-1173 419 7 the the DET cana-1173 419 8 cases case NOUN cana-1173 419 9 , , PUNCT cana-1173 419 10 hill hill NOUN cana-1173 419 11 cipher cipher ADJ cana-1173 419 12 encryption encryption NOUN cana-1173 419 13 and and CCONJ cana-1173 419 14 decryption decryption NOUN cana-1173 419 15 can can AUX cana-1173 419 16 be be AUX cana-1173 419 17 easily easily ADV cana-1173 419 18 hacked hack VERB cana-1173 419 19 as as SCONJ cana-1173 419 20 it it PRON cana-1173 419 21 involves involve VERB cana-1173 419 22 only only ADV cana-1173 419 23 one one NUM cana-1173 419 24 key key NOUN cana-1173 419 25 . . PUNCT cana-1173 420 1 hence hence ADV cana-1173 420 2 , , PUNCT cana-1173 420 3 in in ADP cana-1173 420 4 this this PRON cana-1173 420 5 we we PRON cana-1173 420 6 discuss discuss VERB cana-1173 420 7 the the DET cana-1173 420 8 results result NOUN cana-1173 420 9 which which PRON cana-1173 420 10 includes include VERB cana-1173 420 11 dual dual ADJ cana-1173 420 12 encryption encryption NOUN cana-1173 420 13 and and CCONJ cana-1173 420 14 decryption decryption NOUN cana-1173 420 15 of of ADP cana-1173 420 16 data datum NOUN cana-1173 420 17 using use VERB cana-1173 420 18 hill hill NOUN cana-1173 420 19 cipher cipher ADJ cana-1173 420 20 with with ADP cana-1173 420 21 integral integral ADJ cana-1173 420 22 transforms transform NOUN cana-1173 420 23 like like ADP cana-1173 420 24 laplace laplace NOUN cana-1173 420 25 transforms transform VERB cana-1173 420 26 and and CCONJ cana-1173 420 27 kamal kamal PROPN cana-1173 420 28 transforms transform VERB cana-1173 420 29 where where SCONJ cana-1173 420 30 the the DET cana-1173 420 31 receiver receiver NOUN cana-1173 420 32 receives receive VERB cana-1173 420 33 the the DET cana-1173 420 34 cipher cipher ADJ cana-1173 420 35 text text NOUN cana-1173 420 36 along along ADP cana-1173 420 37 the the DET cana-1173 420 38 key key NOUN cana-1173 420 39 which which PRON cana-1173 420 40 acts act VERB cana-1173 420 41 as as ADP cana-1173 420 42 private private ADJ cana-1173 420 43 key key NOUN cana-1173 420 44 throughout throughout ADP cana-1173 420 45 cryptoanalysis cryptoanalysis NOUN cana-1173 420 46 process process NOUN cana-1173 420 47 . . PUNCT cana-1173 421 1 further far ADV cana-1173 421 2 , , PUNCT cana-1173 421 3 we we PRON cana-1173 421 4 can can AUX cana-1173 421 5 extend extend VERB cana-1173 421 6 the the DET cana-1173 421 7 results result NOUN cana-1173 421 8 using use VERB cana-1173 421 9 other other ADJ cana-1173 421 10 integral integral ADJ cana-1173 421 11 transforms transform NOUN cana-1173 421 12 like like ADP cana-1173 421 13 ezaki ezaki NOUN cana-1173 421 14 , , PUNCT cana-1173 421 15 aboodh aboodh PROPN cana-1173 421 16 , , PUNCT cana-1173 421 17 mahgoub mahgoub NOUN cana-1173 421 18 and and CCONJ cana-1173 421 19 many many ADJ cana-1173 421 20 more more ADJ cana-1173 421 21 . . PUNCT cana-1173 422 1 references reference NOUN cana-1173 422 2 [ [ X cana-1173 422 3 1 1 X cana-1173 422 4 ] ] PUNCT cana-1173 422 5 jadhav jadhav PROPN cana-1173 422 6 shaila shaila PROPN cana-1173 422 7 shivaji shivaji PROPN cana-1173 422 8 . . PROPN cana-1173 423 1 and and CCONJ cana-1173 423 2 hiwarekar hiwarekar PROPN cana-1173 423 3 a.p a.p PROPN cana-1173 423 4 . . PROPN cana-1173 423 5 , , PUNCT cana-1173 423 6 cryptographic cryptographic ADJ cana-1173 423 7 method method NOUN cana-1173 423 8 based base VERB cana-1173 423 9 on on ADP cana-1173 423 10 laplace laplace NOUN cana-1173 423 11 -elzaki -elzaki NOUN cana-1173 423 12 transform transform NOUN cana-1173 423 13 , , PUNCT cana-1173 423 14 journal journal NOUN cana-1173 423 15 of of ADP cana-1173 423 16 the the DET cana-1173 423 17 maharaja maharaja PROPN cana-1173 423 18 sayajirao sayajirao PROPN cana-1173 423 19 university university PROPN cana-1173 423 20 of of ADP cana-1173 423 21 baroda baroda PROPN cana-1173 423 22 , , PUNCT cana-1173 423 23 issn:0025 issn:0025 NOUN cana-1173 423 24 - - PUNCT cana-1173 423 25 0422 0422 NUM cana-1173 423 26 , , PUNCT cana-1173 423 27 vol-55 vol-55 NUM cana-1173 423 28 , , PUNCT cana-1173 423 29 no no INTJ cana-1173 423 30 . . PUNCT cana-1173 424 1 i i PRON cana-1173 424 2 ( ( PUNCT cana-1173 424 3 viii viii PROPN cana-1173 424 4 ) ) PUNCT cana-1173 424 5 , , PUNCT cana-1173 424 6 pp187191 pp187191 NOUN cana-1173 424 7 , , PUNCT cana-1173 424 8 ( ( PUNCT cana-1173 424 9 2021 2021 NUM cana-1173 424 10 ) ) PUNCT cana-1173 424 11 . . PUNCT cana-1173 425 1 [ [ X cana-1173 425 2 2 2 X cana-1173 425 3 ] ] PUNCT cana-1173 425 4 akinola akinola PROPN cana-1173 425 5 emmanuel emmanuel PROPN cana-1173 425 6 idowu idowu PROPN cana-1173 425 7 , , PUNCT cana-1173 425 8 alao alao PROPN cana-1173 425 9 saheed sahee VERB cana-1173 425 10 , , PUNCT cana-1173 425 11 oderinu oderinu PROPN cana-1173 425 12 rasaq rasaq NOUN cana-1173 425 13 adekola adekola PROPN cana-1173 425 14 and and CCONJ cana-1173 425 15 folorunsa folorunsa VERB cana-1173 425 16 esther esther PROPN cana-1173 425 17 omofa omofa PROPN cana-1173 425 18 . . PUNCT cana-1173 426 1 an an DET cana-1173 426 2 application application NOUN cana-1173 426 3 of of ADP cana-1173 426 4 integral integral ADJ cana-1173 426 5 transform transform NOUN cana-1173 426 6 based base VERB cana-1173 426 7 method method NOUN cana-1173 426 8 in in ADP cana-1173 426 9 cryptograph cryptograph PROPN cana-1173 426 10 , , PUNCT cana-1173 426 11 asian asian ADJ cana-1173 426 12 journal journal NOUN cana-1173 426 13 of of ADP cana-1173 426 14 pure pure ADJ cana-1173 426 15 and and CCONJ cana-1173 426 16 applied applied ADJ cana-1173 426 17 mathematics mathematic NOUN cana-1173 426 18 , , PUNCT cana-1173 426 19 3(1):13 3(1):13 NUM cana-1173 426 20 - - SYM cana-1173 426 21 18 18 NUM cana-1173 426 22 , , PUNCT cana-1173 426 23 2021 2021 NUM cana-1173 426 24 ; ; PUNCT cana-1173 426 25 article article NOUN cana-1173 426 26 no no PROPN cana-1173 426 27 . . PUNCT cana-1173 426 28 ajpam.518 ajpam.518 NOUN cana-1173 426 29 . . PUNCT cana-1173 427 1 [ [ X cana-1173 427 2 3 3 X cana-1173 427 3 ] ] X cana-1173 427 4 bhuvaneswari bhuvaneswari PROPN cana-1173 427 5 k. k. PROPN cana-1173 427 6 and and CCONJ cana-1173 427 7 bhuvaneswari bhuvaneswari PROPN cana-1173 427 8 r. r. PROPN cana-1173 427 9 , , PUNCT cana-1173 427 10 application application NOUN cana-1173 427 11 of of ADP cana-1173 427 12 tarig tarig NOUN cana-1173 427 13 transform transform NOUN cana-1173 427 14 in in ADP cana-1173 427 15 cryptography cryptography NOUN cana-1173 427 16 , , PUNCT cana-1173 427 17 international international ADJ cana-1173 427 18 journal journal NOUN cana-1173 427 19 of of ADP cana-1173 427 20 creative creative ADJ cana-1173 427 21 research research NOUN cana-1173 427 22 thoughts thought NOUN cana-1173 427 23 , , PUNCT cana-1173 427 24 vol vol NOUN cana-1173 427 25 . . NOUN cana-1173 427 26 8 8 NUM cana-1173 427 27 , , PUNCT cana-1173 427 28 issue issue NOUN cana-1173 427 29 6 6 NUM cana-1173 427 30 pp1878 pp1878 NOUN cana-1173 427 31 - - PUNCT cana-1173 427 32 1880 1880 NUM cana-1173 427 33 , , PUNCT cana-1173 427 34 ( ( PUNCT cana-1173 427 35 june2020 june2020 PROPN cana-1173 427 36 ) ) PUNCT cana-1173 427 37 . . PUNCT cana-1173 428 1 [ [ X cana-1173 428 2 4 4 NUM cana-1173 428 3 ] ] X cana-1173 428 4 ch ch PROPN cana-1173 428 5 jayanthi jayanthi PROPN cana-1173 428 6 , , PUNCT cana-1173 428 7 v v PROPN cana-1173 428 8 srinivas srinivas PROPN cana-1173 428 9 . . PUNCT cana-1173 429 1 mathematical mathematical ADJ cana-1173 429 2 modelling modelling NOUN cana-1173 429 3 for for ADP cana-1173 429 4 cryptography cryptography NOUN cana-1173 429 5 using use VERB cana-1173 429 6 laplace laplace NOUN cana-1173 429 7 transform transform NOUN cana-1173 429 8 , , PUNCT cana-1173 429 9 international international ADJ cana-1173 429 10 journal journal NOUN cana-1173 429 11 of of ADP cana-1173 429 12 mathematics mathematics NOUN cana-1173 429 13 trends trend NOUN cana-1173 429 14 and and CCONJ cana-1173 429 15 technology technology NOUN cana-1173 429 16 vol vol NOUN cana-1173 429 17 65 65 NUM cana-1173 429 18 , , PUNCT cana-1173 429 19 pp pp ADP cana-1173 429 20 10 10 NUM cana-1173 429 21 - - PUNCT cana-1173 429 22 15,2019 15,2019 NUM cana-1173 429 23 . . PUNCT cana-1173 430 1 [ [ X cana-1173 430 2 5 5 NUM cana-1173 430 3 ] ] PUNCT cana-1173 430 4 hiwarekar hiwarekar PROPN cana-1173 430 5 a.p a.p PROPN cana-1173 430 6 . . PROPN cana-1173 430 7 , , PUNCT cana-1173 430 8 application application NOUN cana-1173 430 9 of of ADP cana-1173 430 10 laplace laplace NOUN cana-1173 430 11 transform transform NOUN cana-1173 430 12 for for ADP cana-1173 430 13 cryptography cryptography NOUN cana-1173 430 14 , , PUNCT cana-1173 430 15 international international ADJ cana-1173 430 16 journal journal NOUN cana-1173 430 17 of of ADP cana-1173 430 18 engineering engineering PROPN cana-1173 430 19 & & CCONJ cana-1173 430 20 science science PROPN cana-1173 430 21 research research PROPN cana-1173 430 22 , , PUNCT cana-1173 430 23 vol-5 vol-5 X cana-1173 430 24 , , PUNCT cana-1173 430 25 issue-4 issue-4 PROPN cana-1173 430 26 , , PUNCT cana-1173 430 27 pp pp ADJ cana-1173 430 28 129 129 NUM cana-1173 430 29 - - SYM cana-1173 430 30 135 135 NUM cana-1173 430 31 , , PUNCT cana-1173 430 32 ( ( PUNCT cana-1173 430 33 april april PROPN cana-1173 430 34 2015 2015 NUM cana-1173 430 35 ) ) PUNCT cana-1173 430 36 . . PUNCT cana-1173 431 1 [ [ X cana-1173 431 2 6 6 NUM cana-1173 431 3 ] ] PUNCT cana-1173 431 4 hiwarekar hiwarekar PROPN cana-1173 431 5 a.p a.p PROPN cana-1173 431 6 . . PROPN cana-1173 431 7 , , PUNCT cana-1173 431 8 a a DET cana-1173 431 9 new new ADJ cana-1173 431 10 method method NOUN cana-1173 431 11 of of ADP cana-1173 431 12 cryptography cryptography NOUN cana-1173 431 13 using use VERB cana-1173 431 14 laplace laplace NOUN cana-1173 431 15 transform transform NOUN cana-1173 431 16 , , PUNCT cana-1173 431 17 international international ADJ cana-1173 431 18 journal journal NOUN cana-1173 431 19 of of ADP cana-1173 431 20 mathematical mathematical ADJ cana-1173 431 21 archive archive NOUN cana-1173 431 22 , , PUNCT cana-1173 431 23 3(3 3(3 NUM cana-1173 431 24 ) ) PUNCT cana-1173 431 25 , , PUNCT cana-1173 431 26 pp pp ADP cana-1173 431 27 1193 1193 NUM cana-1173 431 28 - - SYM cana-1173 431 29 1197 1197 NUM cana-1173 431 30 , , PUNCT cana-1173 431 31 ( ( PUNCT cana-1173 431 32 2012 2012 NUM cana-1173 431 33 ) ) PUNCT cana-1173 431 34 . . PUNCT cana-1173 432 1 [ [ X cana-1173 432 2 7 7 X cana-1173 432 3 ] ] X cana-1173 432 4 tarig tarig PROPN cana-1173 432 5 m m NOUN cana-1173 432 6 elzaki elzaki PROPN cana-1173 432 7 , , PUNCT cana-1173 432 8 salil salil PROPN cana-1173 432 9 m m PROPN cana-1173 432 10 elzaki elzaki PROPN cana-1173 432 11 , , PUNCT cana-1173 432 12 elnour elnour PROPN cana-1173 432 13 ea ea NOUN cana-1173 432 14 . . PUNCT cana-1173 433 1 on on ADP cana-1173 433 2 the the DET cana-1173 433 3 new new ADJ cana-1173 433 4 integral integral ADJ cana-1173 433 5 transform transform NOUN cana-1173 433 6 elzaki elzaki NOUN cana-1173 433 7 transform transform VERB cana-1173 433 8 fundamental fundamental ADJ cana-1173 433 9 properties property NOUN cana-1173 433 10 investigations investigation NOUN cana-1173 433 11 and and CCONJ cana-1173 433 12 applications application NOUN cana-1173 433 13 , , PUNCT cana-1173 433 14 global global ADJ cana-1173 433 15 journal journal NOUN cana-1173 433 16 of of ADP cana-1173 433 17 mathematical mathematical ADJ cana-1173 433 18 sciences science NOUN cana-1173 433 19 : : PUNCT cana-1173 433 20 theory theory NOUN cana-1173 433 21 and and CCONJ cana-1173 433 22 practical practical ADJ cana-1173 433 23 . . PUNCT cana-1173 434 1 2012;4(1):1 2012;4(1):1 NOUN cana-1173 434 2 - - PUNCT cana-1173 434 3 13 13 NUM cana-1173 434 4 . . PUNCT cana-1173 435 1 [ [ X cana-1173 435 2 8 8 NUM cana-1173 435 3 ] ] X cana-1173 435 4 naga naga NOUN cana-1173 435 5 lakshmi lakshmi PROPN cana-1173 435 6 g g PROPN cana-1173 435 7 , , PUNCT cana-1173 435 8 ravi ravi PROPN cana-1173 435 9 kumar kumar PROPN cana-1173 435 10 b b PROPN cana-1173 435 11 , , PUNCT cana-1173 435 12 chandra chandra PROPN cana-1173 435 13 sekhar sekhar PROPN cana-1173 435 14 a. a. PROPN cana-1173 435 15 a a DET cana-1173 435 16 cryptographic cryptographic ADJ cana-1173 435 17 scheme scheme NOUN cana-1173 435 18 of of ADP cana-1173 435 19 laplace laplace NOUN cana-1173 435 20 transforms transform VERB cana-1173 435 21 , , PUNCT cana-1173 435 22 intr.j intr.j PROPN cana-1173 435 23 . . PUNCT cana-1173 435 24 math math PROPN cana-1173 435 25 . . PUNCT cana-1173 436 1 arch.2011;2(12):2515 arch.2011;2(12):2515 NOUN cana-1173 436 2 - - PUNCT cana-1173 436 3 2519 2519 NUM cana-1173 436 4 . . PUNCT cana-1173 437 1 [ [ X cana-1173 437 2 9 9 NUM cana-1173 437 3 ] ] PUNCT cana-1173 437 4 tarig tarig NOUN cana-1173 437 5 . . PUNCT cana-1173 437 6 m. m. NOUN cana-1173 437 7 elzaki elzaki PROPN cana-1173 437 8 . . PROPN cana-1173 437 9 , , PUNCT cana-1173 437 10 2011 2011 NUM cana-1173 437 11 , , PUNCT cana-1173 437 12 β€œ " PUNCT cana-1173 437 13 the the DET cana-1173 437 14 new new ADJ cana-1173 437 15 integral integral ADJ cana-1173 437 16 transform transform NOUN cana-1173 437 17 elzaki elzaki NOUN cana-1173 437 18 transform transform NOUN cana-1173 437 19 β€œ " PUNCT cana-1173 437 20 , , PUNCT cana-1173 437 21 global global ADJ cana-1173 437 22 journal journal NOUN cana-1173 437 23 of of ADP cana-1173 437 24 pure pure ADJ cana-1173 437 25 and and CCONJ cana-1173 437 26 applied applied ADJ cana-1173 437 27 mathematics mathematic NOUN cana-1173 437 28 , , PUNCT cana-1173 437 29 7(1 7(1 NUM cana-1173 437 30 ) ) PUNCT cana-1173 437 31 , , PUNCT cana-1173 437 32 pp pp ADP cana-1173 437 33 57 57 NUM cana-1173 437 34 - - SYM cana-1173 437 35 64 64 NUM cana-1173 437 36 . . PUNCT