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

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| = 7.4518×10^16 that makes it possible to use them as a long-term key.