Non-Associative Algebra Redesigning Block Cipher with Color Image Encryption

Abstract

The substitution box (S-box) is a fundamentally important component of symmetric key cryptosystem. An S-box is a primary source of non-linearity in modern block ciphers, and it resists the linear attack. Various approaches have been adopted to construct S-boxes. S-boxes are commonly constructed over commutative and associative algebraic structures including Galois fields, unitary commutative rings and cyclic and non-cyclic finite groups. In this paper, first a non-associative ring of order 512 is obtained by using computational techniques, and then by this ring a triplet of 8 × 8 S-boxes is designed. The motivation behind the designing of these S-boxes is to upsurge the robustness and broaden the key space due to non-associative and non-commutative behavior of the algebraic structure under consideration. A novel color image encryption application is anticipated in which initially these 3 S-boxes are being used to produce confusion in three layers of a standard RGB image. However, for the sake of diffusion 3D Arnold chaotic map is used in the proposed encryption scheme. A comparison with some of existing chaos and S-box dependent color image encryption schemes specs the performance results of the anticipated RGB image encryption and observed as approaching the standard prime level.