Evolutionary Resilient Substitution Boxes for Secure Cryptography Using Nash equilibrium

Abstract

A substitution box (or S-box) is simply a transformation of an input sequence of bits into another. The input and output sequences do not necessarily have the same number of bits. In cryptography, S-boxes constitute a cornerstone component of symmetric key algorithms. In block ciphers, they are typically used to obscure the relationship between the plaintext and the ciphertext. Non-linear and non-correlated S-boxes are the most secure with respect to linear and differential cryptanalysis. However, such S-boxes are hard to obtain. In this paper, we focus on engineering regular S-boxes, presenting high non-linearity and low auto-correlation properties using evolutionary computation. Hence, there are three properties that need to be optimised: regularity, non-linearity and auto-correlation. We use the Nash equilibrium-based multi-objective evolutionary algorithm to engineer resilient substitution boxes.