A 10-bit S-box generated by Feistel construction from cellular automata

Abstract

We propose a new 10-bit S-box generated from a Feistel construction. The subpermutations are generated by a 5-cell cellular automaton based on a unique well-chosen rule and bijective affine transformations. In particular, the cellular automaton rule is chosen based on empirical tests of its ability to generate good pseudorandom output on a ring cellular automaton. Similarly, Feistel's network layout is based on empirical data regarding the quality of the output S-box. We perform cryptanalysis of the generated 10-bit S-box, and we find security properties comparable to or sometimes even better than those of the standard AES S-box. We believe that our S-box could be used to replace the 5-bit substitution of ciphers like ASCON.