CRYPTANALYSIS OF THE PERMUTATION CIPHER OVER COMPOSITION MAPPINGS OF BLOCK CIPHER

Transcription

1 CRYPTANALYSIS OF THE PERMUTATION CIPHER OVER COMPOSITION MAPPINGS OF BLOCK CIPHER P.Sundarayya 1, M.M.Sandeep Kumar 2, M.G.Vara Prasad 3 1,2 Department of Mathematics, GITAM, University, (India) 3 Department of Mathematics,VITS College of Engineering, (India) ABSTRACT In this paper using secret key algorithm focus on composition mappings of permutation cipher and block cipher to encrypt and decrypt the plaintext messages without using residue modulo. This paper discuss about block of permutation cipher using plain text and cipher text over composition mapping of permutation. The proposed concept is easy to implement without confusion. Keywords: Permutation Cipher, Blockcipher, Composition Map, Inverse Permutation, Encryption, Decryption. I. INTRODUCTION Cryptography is the science of using mathematics to encrypt and decrypt messages. A cipher is a mathematical function used in the encryption and decryption process. The main problems in cryptography are the development of reliable cryptographic schemes and the search for new effective methods of deciphering existing schemes A cryptographic approach to secure information implies its transformation which enables it to be read only by the owner of the secret key. The reliability of a cryptographic method of securing data depends on cryptanalysis stability of the used scheme. When we talk about cryptanalysis we assume that we know the cryptographic scheme. In other words, a cipher breaking problem is a problem of finding only one true secret key among all possible secret keys, i.e. it is a search problem. The search space is large and the criterion of found solution s "quality" is not usually purely formalized [2]. The security of encrypted data is entirely dependent on two things one is strength of cryptographic algorithm, second one is secrecy of key In this article we focus on the cryptanalysis problem of the block permutation cipher to encrypt and decrypt the plaintext over composition of mappings to avoid residue modulo. An enciphering transformation is a function f from the P of set of all plaintext message units to the set C of all possible cipher text message units.applying function f to the plain text convert as a cipher text. A deciphering transformation f -1 the set C of all possible cipher text message units to the P of set of all plaintext message units. A deciphering transformation f -1 the set C of all possible cipher text message units to the P of set of all plaintext message units Applying function f -1 to the cipher text convert as a plain text[1].it can be represented as 1245 P a g e

2 P C P P is finite set of possible plain text C is is finite set of possible cipher text II. GENERAL METHOD OF PERMUTATION CIPHER Permutation technique is oneinwhich the plaintext remains the same, but the order of characters is shuffled. One simple technique forencryptionis based on the mathematical notation of permutation.the main idea of the permutation cipher is permutation of the position of letters. A permutation is a bijective map from n-element set into itself. Thus every permutation has inverse.in Permutation cipher,k consists set of all possible permutations of N symbols 0,1,2, N-1,For each permutation K, definec=ap and define P=A -1 C where A -1 is the inverse permutation to A. This can be observed as follows P C P P is plain text C is cipher text is permutation 2.1 A Block of Permutation Cipher In this article we consider the particular cryptographic scheme the symmetric block permutation cipher. The main idea of this cipher is that convert into the input text into blocks, i.e. into symbol strings with the length equal to N, and then symbols in every block are rearranged in accordance with the given permutation. is block of a plain text is block of a cipher text 2.2 Composition Map of Permutation Cipher In cryptography, P be a plain text and f be a permutation then construct P 1 then convert into P 1 0f using co domain of P 1, we getcipher text C,Now C 1 0f=P 1 0f0f -1 by using co domain ofp 1 0f then we can get plain text P. This can be observed as follows Encryption Plain text=p P 1 P 1 0f C=cipher text Decryption 1246 P a g e

3 cipher text=c P 1 0f C 1 0f -1 =P plain text The following algorithms can give complete information of this method. 2.3 Encryption Algorithm Step1: given P= plaintext Step2: construct block of plain text Step3: Key K= permutation (bijection) Step4: calculate P 1 0K = block of cipher text Step5: write C= cipher text 2.4 Decryption Algorithm Step1: take C= cipher text Step2: P 1 0K = block of cipher text Step3: Key K -1= permutation (bijection) Step4: calculate C 1 0K -1 =block of plain text Step5: write P= plaintext III. AN EXAMPLES OF ALGORITHM S WORK 3.1 Example P= GITAM is plain text is block of plain text. KEY K= is permutation Encryption: P 1 0K C= AMGIT is cipher text is block of Cipher text KEY K -1 = is permutation Decryption: C 1 0K 3.2 Example P= GITAM is plain text 1247 P a g e

4 P= GOOGLE is plain text is block of plain text KEY K= is permutation Encryption: P 1 0K C= GOGEOL is cipher text is block of Cipher text KEY K -1 = Decryption:: C 1 0K 3.3 Example P= GOOGLE is plain text. P= MATHEMATICS is the plain text is block of plain text KEY K= Encryption: P 1 0K C= ACAIMHTTEMS is cipher text is block of Cipher text KEY K -1 = Decryption:: C 1 0K P= MATHEMATICS is the plain text IV. CONCLUSION 1248 P a g e

5 With the power of computers, permutation encryption can be easily cryptanalyzed, In this paper composition of permutation cipher and block cipher to encrypt and decrypt messages easily without using residue modulo. Since every permutation is bijective,so easily we can find inverse permutation. The composition Of these two basic techniques is a bridge from classic to modern ciphers. With the advanced technologies, things are more complex these days, but the philosophy remains the same. The primary change is that algorithms work on characters. The proposed concept is easy to implement with out confusion. REFERENCES [1]. Neal Koblitz. A Course in Number Theory and Cryptography. Second Edition.Springer-Verlag. New York Berlin Heidelberg London Paris. Tokyo Hong Kong. [2]. Genetic algorithm for finding the key s length and cryptanalysis of the permutation cipher international Journal "Information Theories & Applications" Vol.15 [3]. W. Stallings, Cryptography andnetworksecurity,prenticehall, P a g e