Paper 2023/353

Searching for S-boxes with better Diffusion using Evolutionary Algorithm

Abstract

Over the years, a large number of attacks have been proposed against substitution boxes used in symmetric ciphers such as differential attacks, linear attacks, algebraic attacks, etc. In the Advanced Encryption Standard (AES) Block cipher, the substitution box is the only nonlinear component and thus it holds the weight of the cipher. This basically means that if an attacker is able to mount a successful attack on the substitution box of AES, the cipher is compromised. This research work aims to provide a solution for increasing cryptographic immunity of S-boxes against such attacks. A genetic algorithm based approach has been proposed to search for 8 × 8 balanced and bijective S-boxes that exhibit values of differential branch number, non-linearity, differential uniformity, count and length of cycles present and distance from strict avalanche criterion that are similar to or better than the AES S-box. An S-Box evaluation tool is also implemented to evaluate any S-boxes generated. S-box of AES is resistant to the crypt-analytic attacks. S-boxes constructed by the proposed algorithm have better cryptographic properties so they are also resistant to the crypt-analytic attacks. The strict avalanche criterion[11], which is based on completeness[22] and diffusion[5], is an essential property for any 8 × 8 S-box. Good diffusion means that a small change in the plaintext may influence the complete block after a small number of rounds. Therefore, a lower DSAC value is desirable to prevent vulnerabilities to attacks such as differential attacks. The DSAC is therefore used as the primary fitness criterion in this research work to search for S-boxes with better diffusion.