CRYPTANALYSIS OF THE PERMUTATION CIPHER OVER COMPOSITION MAPPINGS OF BLOCK CIPHER

CRYPTANALYSIS OF THE PERMUTATION CIPHER OVER COMPOSITION MAPPINGS OF BLOCK

CIPHER

P.Sundarayya

, M.M.Sandeep Kumar

, M.G.Vara Prasad

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

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^-1C 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.

P

= is block of a plain text

C

= 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 P¹ then convert into C¹=P¹0f using co domain of P¹ , we getcipher text C,Now P¹=C¹0f=P¹0f0f^-1 by using co domain ofC¹=P¹0f then we can get plain text P.

This can be observed as follows Encryption

Plain text=P P

C

= P

0f C=cipher text

Decryption

cipher text=C C

= P

0f C

0f

=P plain text

The following algorithms can give complete information of this method.

2.3 Encryption Algorithm

Step2: construct P¹= block of plain text Step3: Key K= permutation (bijection)

Step4: calculate C¹=P¹0K = block of cipher text Step5: write C= cipher text

2.4 Decryption Algorithm

Step2: C¹=P¹0K = block of cipher text Step3: Key K^-1= permutation (bijection) Step4: calculate P¹=C¹0K^-1=block of plain text Step5: write P= plaintext

III. AN EXAMPLES OF ALGORITHM’S WORK 3.1 Example

P= ‘GITAM’ is plain text

P¹= is block of plain text.

KEY K= is permutation

Encryption: C¹=P¹0K C¹=

C¹=

C=’AMGIT’ is cipher text

C¹ = is block of Cipher text

KEY K^-1= is permutation

Decryption: P¹=C¹0K P¹=

P¹=

P= ‘GITAM’ is plain text

3.2 Example

P¹= is block of plain text

KEY K= is permutation

Encryption: C¹=P¹0K C¹=

C¹=

C=’GOGEOL’ is cipher text

C¹= is block of Cipher text

KEY K^-1=

Decryption:: P¹=C¹0K P¹=

P¹=

P= ‘GOOGLE’ is plain text.

3.3 Example

P= ‘MATHEMATICS’ is the plain text

P¹= is block of plain text

KEY K=

Encryption: C¹=P¹0K C¹=

C¹=

C=’ACAIMHTTEMS’ is cipher text

C¹= is block of Cipher text

KEY K^-1=

Decryption:: P¹=C¹0K P¹=

P¹=

P= ‘MATHEMATICS’ is the plain text

IV. CONCLUSION

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,200