Nonlinear transformations based on complete classes of isomorphic and automorphic representations of field GF(256)

Michael I. Mazurkov; Artem V. Sokolov

doi:10.3103/S0735272713110022

Authors

Michael I. Mazurkov Odessa National Polytechnic University, Ukraine
Artem V. Sokolov Odessa National Polytechnic University, Ukraine

DOI:

https://doi.org/10.3103/S0735272713110022

Keywords:

substitution S-box, automorphism, isomorphism, Galois fields

Abstract

A complete class of maximum-period linear recurrent sequences (MLRS) of volume ψ = 55,296 based on all automorphic and isomorphic representations of the main GF(256) field has been built. Constructions of S-boxes based on MLRS and having length N = 256 with cryptographic properties as good as the Nyberg construction of Rijndael cipher have been proposed. The total number of substitution S-boxes synthesized by the constructive method amounts to |S| = 7.4518×10¹⁶ that makes it possible to use them as a long-term key.

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