Nonlinear Transformations Based on Complete Classes of Isomorphic and Automorphic Representations of Field GF(256)

摘要

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.