A 10-Bit S-box Generated by Feistel Construction from Cellular Automata.

We propose a new 10-bit S-box generated from a Feistel construction. The subpermutations are generated by a five-cell cellular automaton (CA) based on a unique, well-chosen, local transition rule and bijective affine transformations. In particular, the CA rule is chosen based on empirical tests of its ability to generate good pseudorandom output on a ring CA. Similarly, the Feistel 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: testing the properties of algebraic degree, algebraic complexity, nonlinearity, strict avalanche criterion, bit independence criterion, linear approximation probability, differential approximation probability, differential uniformity and boomerang uniformity. We relate the properties to those of the AES S-box. 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 five-bit substitution of ciphers like ASCON.