A novel heuristic method for obtaining S-boxes

An efficient algorithm named chaotic multi-swapping and simulated annealing (CMSSA) for obtaining cryptographically strong 8 × 8 S-boxes is presented. The method is based on chaotic maps and simulated annealing. In addition, cryptographic properties such as bijectivity, strict avalanche criterion, nonlinearity, output bits independence criterion and equiprobable input/output XOR distribution are analyzed in detail for the S-box produced. The results of numerical analysis show that the box has nearly fulfilled the criteria for a cryptographically strong S-box and can effectively resist several attacks.