Paper 2025/457

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

Abstract

In this paper, 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: we test 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 of our S-box, and relate them 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 5-bit substitution of ciphers like ASCON.