Evolutionary Design of Resilient Substitution Boxes: From Coding to Hardware Implementation

Abstract

S-boxes constitute a cornerstone component in symmetric-key cryptographic algorithms, such as DES and AES encryption systems. 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 against linear and differential cryptanalysis. In this paper, we focus on a two-fold objective: first, we evolve regular an S-box with high non-linearity and low auto-correlation properties using evolutionary computation; then automatically generate evolvable hardware for the obtained S-box. Targeting the former, we use the Nash equilibrium-based multi-objective evolutionary algorithm to optimise regularity, non-linearity and auto- correlation, which constitute the three main desired properties in resilient S-boxes. Pursuing the latter, we exploit genetic programming to automatically generate the evolvable hardware designs of substitution boxes that minimise hardware space, encryption/decryption time and dissipated power, which form the three main hardware characteristics. We compare our results against existing and well-known designs, which were produced by using conventional methods as well as through evolution.KeywordsNash EquilibriumCrossover OperatorHardware ImplementationBlock CipherEvolutionary DesignThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.