Quantum-inspired design of resilient substitution boxes: From coding to hardware implementation

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 twofold objective: first, we evolve regular S-boxes with high non-linearity and low auto-correlation properties; then automatically generate evolvable hardware for the obtained S-box. Targeting the former, we use a quantum-inspired evolutionary algorithm to optimize regularity, non-linearity and auto-correlation, which constitute the three main desired properties in resilient S-boxes. Pursuing the latter, we exploit the same algorithm to automatically generate the evolvable hardware designs of substitution boxes that minimize hardware space and encryption/decryption time, which form the two main hardware characteristics. We compare our results against existing and well-known designs, which were produced by using conventional methods as well as through genetic algorithm. We will show that our approach provides higher quality S-boxes coding as well as circuits.