Construction of 24-by-24 nonlinear layer for symmetric algorithm and its application to data encryption in parallel with DNA transform

Abstract

The principal constituent of a block cipher in symmetric-key cryptography is the Boolean function, determining the substitution box (S-box). Block ciphers rely totally on S-boxes with excellent nonlinearity and upright cryptographic structures. In AES, an 8 × 8 S-box is a 16 × 16 lookup table over the Galois field $\mathrm{GF}\left({2}^{8}\right),$ that occupies 8 × 2⁸ bytes storage of computer memory. By using traditional method to construct a 24 × 24 S-box over Galois field $\mathrm{GF}\left({2}^{24}\right),$ which lodges a storage memory of 24 × 2²⁴ bytes in traditional sense. Thus, the memory storage does not support a 24 × 24 S-box over a very larger order Galois field like $\mathrm{GF}\left({2}^{24}\right)$. A resolute of this difficulty is possibly coming out from the algebraic structure of the commutative finite chain ring $\frac{{F}_{q}[{\varvec{x}}]}{<{{\varvec{x}}}^{{\varvec{k}}}>}={\sum }_{i=0}^{k-1}{x}^{i}{F}_{q}.$ In this study, a subgroup of the multiplicative group of units of the chain ring $\frac{{F}_{2}[x]}{<{x}^{24}>}={\sum }_{i=0}^{23}{x}^{i}{F}_{2}$ is considered to construct a 24 × 24 S-box that occupy just 24 × 2⁸ bits storage memory of computer. The proposed S-box has a substantial potential to create confusion during substitution phase of the color image enciphering algorithm. While for the permutation component of the algorithm, DNA transform is applied for creating diffusion in the pixels of the color image. The proposed RGB image encryption attains the standard optimum level when compared it to the DNA and chaos-based image encryption techniques.