International Journal of Engineering Science Invention Research & Development; Vol. II Issue VIII February e-issn:

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1 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: 236 MULTIPLE ENCRYPTIONS OF VARIOUS CIPHERS A. ChadraSekhar*,1, B.Ravi Kumar 2, Ch.Pragathi 3 ad Ashok Kumar 1 Professor, 2 Assistat Professor, 3 Associate Professor, Research Scholar, Egieerig Mathematics, GITAM Uiversity, Visakhapatam, Idia 1 acs@gitam.edu, 2 ravikumarbrk6@gmail.com, 3 ch.prgathi1@gmail.com, saiashok.8@gmail.com ABSTRACT The multiple ecryptios of symmetric cryptosystems provide additioal security rather tha ormal ecryptio. Desigiig of idepedet ciphers usig mathematical models is vital i this process. I this paper we proposed two idepedet ciphers Keywords Fiboacci marix, Affie, Vigere trasformatios. I. INTRODUCTION If the th is expressed i terms of its precedig umbers (ot ecessarily all) is the recurrece relatio. Geeratig matrices out of these recurrece relatios refers to the recurrece relatio. Further such matrices order ca be exteded cosequetly. A. FIBONACCI MATRIX The Fiboacci Qmatrix [7] [8][] is the 2 1 matrix defied by Q Where Q F F 1 F F 1 1 F F 1 1 F is a Fiboacci umber. The F F 1 Iverse of 2 2, Fiboacci matrix is N Q Q B. EXTENSION OF FIBONACCI MATRIX The Q1 matrix is so formed such that its determiat is ivariat without loss of geerality to the Cassii formula which is oe of the most importat theorems of the Fiboacci umbers theory[7]. 2 Q F 1 F 1 F ( 1). Also similarly it ca be exteded to a matrix matrix ad ay order square matrix. The extesio of 3 3 Fiboacci matrix is as follows Q Q a. Affie Cipher A affie ecipherig trasformatiois C ap b mod N where the pair (a, b) is the ecryptig key ad gcd(a,n)1. If y E(x) (axb)mod26,[1]the we ca solve for x i terms of y ad so E 1 ( y) that is, if y ax b mod26 the y b axmod26 ax y b or equivaletly mod26. b. Vigere ciphere The Vigeere cipher was geerated by Giova Batista Belaso i 13[1]. This cipher uses a secret keyword to ecrypt the plaitext. First, each letter i the plaitext is coverted ito a umber.the this umerical value for each letter of the plaitext is added to theumerical value of each letter of a secret keyword to get the ciphertext.the Vigeereciphers are more powerful tha substitutio ciphers. C. PROPOSED WORK A Algorithm for multi ecryptio usig Fiboacci matrix as the first layer of ecryptio A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/82

2 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: 236 ad the affie trasformatio for super ecryptio [1][8][1] II. MULTIPLE ENCRYPTION A. ENCRYPTION ALGORITHM: Step1: Alice creates plaitexts P p 1 p 2, p 3 p m Step2: Alice computes C 1 P Q ad get 1 sr ciphertext Step3:Alice computes C 2 C 1 F i for i1,2,3, m where C 2 is the compute first cipher text. Step: Alice perform super ecryptio with the Affie trasformatio E(x) (axb) mod 26, Gcd(a,N)1 ad take a ad b are secrete, from the first level ecryptio message. Step: Alice seds super ecrypted message to Bob. B. DECRYPTION ALGORITHM: Step1: Bob receives the super ecrypted message. Step2: Bob decrypts the super ecrypted 1 E y a 1 y b mod26 message by usig (P 1 ) Step3: Bob computes PP 1 1 origial plaitext message. Q to get the III. SUPER ENCYPTION OF VIGENERE CIPHER A. ENCRYPTION ALGORITHM: Step1: Alice creates plaitexts P p 1 p 2, p 3 p m Step2: Alice computes C 1 P Q ad get 1 sr ciphertext ad get 1 sr ciphertext Step3:Alice computes C 2 C 1 F i for i1,2,3, m where C 2 is the compute first cipher text. Step: Alice apply super ecryptio of vigeere trasformatio use off set rule with to the umerical value of each letter of a secret keyword to first level ecryptio message. Step: Alice seds super ecryptio message to Bob. B. DECRYPTION ALGORITHM: Step1: Bob receives the super ecryptio message. Step2: Bob decrypts with the iverse vigeere trasformatio to super ecrypted message. It is the first decryptio message P 1 Step3: Bob computes PP 1 1 origial plaitext message. Q to get the A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Fiboacci 3 3 matix Case1: For 1 F2 F1 1 we get Q F1 F Ecryptio algorithm: P R O 1 1 Step1: Let the Plai text be P S O R 1 Step2: Alice computes C 1 P Q 1 A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/83

3 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: Step3: applyig affie trasformatio E(x)(axb) mod 26 for a & b X 1 1 x (x) mod Secod Ecrypted message is Y V J L K D J V Y Step: Ecrypted message C 2 is YVJLKDJVY Decryptio algorithm: Step1: First Decrypted Message is YVJLKDJVY Step2: Compute Iverse of Affie trasformatio P 1 1 E y a 1 y b mod26 Message Y V J L K D J V Y Y y (y) (y)mod First Decrypted text R G O E J S O G R R G O 6 1 First decrypted text P 1 E J S O G R 1 6 Step3: Compute PP 1 (Q 1 ) 1 to get origial message Mod Secod Decrypted message is P R O S O R Case2: For 2 F3 F we get Q F2 F Ecryptio algorithm: P R O 1 1 Step1: Let the Plai text be P S O R 1 A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/8

4 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: 236 Step2: Alice computes C 1 P Q Step3: applyig affie trasformatio E(x)(axb) mod 26 for a & b 16 X x (x16) mod Secod Ecrypted message is U B I J D C U M X Step: Ecrypted message C 2 is UBIJDCUMX Decryptio algorithm: Step1: First Decrypted Message is UBIJDCUMX Step2: Compute Iverse of Affie trasformatio P 1 1 E y a 1 y b mod26 Message Y y16 21(y16) 21(y16) mod26 First Decrypted text U B I J D C U M X G W O J N S G U R G W O First decrypted text P 1 J N S 13 G U R 6 2 Step3: Compute PP 1 (Q 2 ) 1 to get origial message Mod Secod Decrypted message is P R O S O R IV. A. FIBONACCI 3 3 MATIX Case1: For 1 F2 F1 1 1 we get Q F1 F VIGENERE CIPHER B. ENCRYPTION ALGORITHM: A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/8

5 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: 236 P R O 1 1 Step1: Let the Plai text be P S O R 1 Step2: Alice computes C 1 P Q Usig vigeere ciphers take key F A L S E Step3: Offset rule with the first decrypted message 1 1 Offset rule with key Mod Secod Ecryptio message is W H Z W N X O R J Step: Ecrypted message C 2 is WHZWNXORJ C. DECRYPTION ALGORITHM: Step1: First Decrypted Message is WHZWNXORJ Step2: Decrypts with the iverse of vigeere trasformatio is P Offset rule with key Mod First Decrypted text R G O E J S O G R R G O 6 1 First decrypted text P 1 E J S O V Z Step3: Compute PP 1 (Q 1 ) 1 to get origial message Mod Secod Decrypted message is P R O S O R A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/86

6 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: 236 Case2: For 2 F3 F2 1 we get Q F2 F D. ENCRYPTION ALGORITHM: P R O 1 1 Step1: Let the Plai text be P S O R 1 Step2: Compute C 1 P Q Usig vigeere ciphers take key Step3: Offset rule with the first decrypted message Offset rule with key Step: Ecrypted message C 2 is LXZBRXGFJ F A L S E E. DECRYPTION ALGORITHM: Step1: First Decrypted Message is LXZBRXGFJ Step2: Decrypts with the iverse of vigeere trasformatio is P Reverse offset rule with key Mod First Decrypted text G X O J N S G U R G X O First decrypted text P 1 J N S 13 G U R 6 2 Step3: Compute P 1 (Q 2 ) 1 to get origial message P Mod Secod Ecryptio message is L X Z B R X G F J A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/87

7 Iteratioal Joural of Egieerig Sciece Ivetio Research & Developmet; Vol. II Issue VIII February eissn: Mod Secod Decrypted message is P R O S O R V. RESULT ANALYSIS S.No First ecryptio Time for first ecryptio Super ecryptio Time for super ecryptio 1 Fiboacci matrix MILLI SEC Affie or vigeere 12 MILLI SEC VI. CONCLUSIONS The Fiboacci matrixes stads more secure, i terms of the time ad difficulty i ecodig ad decodig the message compared to the usual umber systems such as Fiboacci Lucas ad PellLucas. All the Fiboacci, Lucas ad Pell umber systems are desiged with characters i the order of additios. Whereas the Fiboacci matrix is developed with 3 multiplicatios ad additios by the order of. I view of all these reasos, this particular system is applied i this paper. REFERENCES [8] Fiboacci ad lucas umbers with applicatios thomas Khoshy ISBN: [] K.R.Sudha, A. Chadra Sekhar, P.V.G.D, Prasad Reddy, "Cryptographic Protectio Of Digital Sigal Usig some Recurrece Relatios" IJCNS, May 27, PP27. [1] Liear idepedet spaig sets ad liear trasformatios for multilevel ecryptio, A.ChadraSekhar, V.Ausha, B.Ravi Kumar, S.Ashok Kumar Vol36(21), No., PP;38. [1] A. ChadraSekhar, D. Chaya Kumari, S. Ashok Kumar "Symmetric Key Cryptosystem for Multiple Ecryptios",Iteratioal Joural of Mathematics Treds ad Techology (IJMTT). V2 (2):11 Jauary 216. ISSN: [1] A. Chadra Sekhar, Prasad Reddy. P.V.G.D, A.S.N.Murty, B.Krisha Gadhi "SelfEcryptig Data Streams Usig Graph Structures" IETECH Iteratioal Joural Of Advaced Computatios PP 7, 28, vol 2. [2] A.P.Stakhov The Golde matrices ad a ew kid of cryptography chaos, solutios ad Fractals (27) pp386. [3] A.P.Stakhov The Golde sectio ad moder harmoy mathematics. Applicatios of Fiboacci umbers,kluwer Academic publishers (18). pp333 [] A. Chadra Sekhar, K.R. Sudha ad Prasad Reddy. P.V.G.D "Data Ecryptio Techique Usig Radom Geerator" IEEE Iteratioal Coferece o Graular Computig GrC7, Nov 2, 27, Silico Valley, USA, PP 767. [] B.Krisha Gadhi, A. Chadra Sekhar ad Prasad Reddy P.V.G.D: Cryptographic Scheme for Digital sigals" INTECH Iteratioal Joural Of Advaced Computatios", Vol:2 No:, PP12,28. [6] E.H.Lock Wood, A siglelight o pascal's triagle, Math, Gazette 1(167), PP 2. [7] Fiboacci, Lucas ad Pell umbers adpascal's triagle, Thomas Khoshy, Applied Probability Trust, PP 121. A. ChadraSekhar, B.Ravi Kumar, Ch.Pragathi ad Ashok Kumar ijesird, Vol. II Issue VIII February 216/88