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Modern block ciphers can be used for designing security schemes to meet the security requirements in underwater acoustic sensor networks. The substitution boxes (S-boxes) used in block ciphers must have good cryptographic properties to resist various attacks. The difficulty in the design of S-boxes is that the cryptographic properties of S-boxes have no obvious distribution. In this paper, we investigate the certain subgraph of the Cayley graph of the symmetric group to get some information about the distribution of the cryptographic properties of S-boxes. Based on the information obtained, an algorithm for designing S-boxes with good cryptographic properties is proposed. The security analysis shows that the preferred S-box constructed by the proposed algorithm has good cryptographic properties.

S-Boxes Construction Based on the Cayley Graph of the Symmetric Group for UASNs