A Chaos Based Approach for Improving Non Linearity in S Box Design of Symmetric Key Cryptosystems

Abstract

In cryptography, an S-Box (Substitution-box) is a basic component of symmetric key algorithms which performs substitution and is typically used to obscure the relationship between the key and the cipher text. This paper proposes a new method for design of S boxes based on chaos theory. Chaotic equations are popularly known for its randomness, extreme sensitivity to initial conditions and ergodicity. The modified design has been tested with blowfish algorithm which has no effective crypt analysis reported against its design till date because of its salient design features including the key dependant s boxes and complex keys. However every new key requires pre-processing equivalent to encrypting about 4 kilobytes of text, which is very slow compared to other block ciphers and it prevents its usage in memory limited applications and embedded systems. The modified design of S boxes maintains the non linearity[2][4] and key dependency factors of S boxes with a major reduction in time complexity of generation of S boxes and P arrays. The algorithm has been implemented and the proposed design has been analyzed for size of key space, key sensitivity and Avalanche effect. Experimental results on text encryption show that the modified design of key generation continues to offer the same level of security as the original Blowfish cipher with a less computational overhead in key generation.