Galois Ring GR(2 ³, 8) Dependent 24 × 24 S-Box Design: An RGB Image Encryption Application

An S-box is based on Boolean functions which are essentially the foundation of symmetric cryptographic systems. The Boolean functions are used for S-box designing in block ciphers and exploited as nonlinear components. Boolean functions with optimal nonlinearity and upright cryptographic stuffs play a significant role in the design of block ciphers. Traditionally 8 × 8 S-box is a 16 × 16 look up table over Galois field GF(2 ⁸) and has 112 feasible upper bonds for nonlinearity. A 24 × 24 S-box over Galois field GF(2 ²⁴) is not viable as the computer memory does not support it. In this paper for the construction of 24 × 24 S-box a rout is adopted via maximal cyclic subgroup of the multiplicative group of units of Galois ring GR(2 ³, 8). The newly constructed S-box has much higher confusion capability than any of 8 × 8 S-box. To judge the impact of this new 24 × 24 S-box an RGB color image encryption application is demonstrated. Initially, in the proposed encryption scheme we use 24 × 24 S-box for confusion in RGB channels of plain image, however for diffusion linear permutation P = (i × 32) mod 257 is operated and then by the use of exclusive-or an encrypted image is obtained. Thus, we introduce a novel technique by which 24 binary bits are divided into 3 bytes and each one deals R, G and B channel of the color image separately. A comparison with chaos and DNA based image encryption schemes shows the performance results of this novel RGB image encryption and observed as meeting the standard optimal level. Hence this 24 × 24 S-box dependent encryption method replaces 8 × 8 S-box based RGB color image encryption scheme.