Design of Dynamic S-boxes Based on Simulated Annealing Algorithm and Its Application in Chaotic Masking Protection

In recent years, the security of chaotic block ciphers has been evaluated through conventional security tests and has been widely applied in encryption algorithms. However, chaotic block ciphers are vulnerable to side-channel attacks during hardware implementation. Attackers can exploit physical information leaked from the algorithm hardware encryption process and the median value of the attack point location to crack the algorithm key, seriously threatening the hardware security of the algorithm. To address this issue, this paper proposes a chaotic masking scheme based on dynamic S-boxes for the algorithmic protection of chaotic block ciphers, achieving resistance to side-channel attacks without affecting the results of hardware encryption. In terms of dynamic S-boxes, this paper proposes a design scheme for dynamic S-boxes based on hash functions. The chaotic sequences generated by a three-dimensional discrete chaotic system are mapped to fixed-length hash values. These hash values are then divided into bytes and the remaining chaotic sequences are used as indices to extract a portion of those bytes as internal elements of the S-box. Additionally, a parallel generation method is employed to improve the efficiency of S-box generation. In the case of the generated initial S-box, the nonlinearity can also be calculated using the position exchange method for optimization. The optimized dynamic S-box nonlinearity can reach 111, and the strict avalanche criteria calculation result differs from the ideal value of 0.5 by only 0.0002, which is a relatively obvious effect. At the same time, in terms of chaos masking design, double-layer protection is applied to the S-box to reduce the correlation between energy traces and intermediate values. Masking is added from both the plaintext and key perspectives to ensure that each operation output contains masking differences. The experimental results demonstrate that the masking scheme designed in this paper successfully resists template attacks and nonprofiled attacks, thereby effectively improving the security of chaotic block ciphers in the hardware encryption process.