PROCESSOR-ORIENTED NONLINEAR TRANSFORM BASED ON THE FULL CLASSES OF ISOMORPHIC AND AUTOMORPHIC REPRESENTATIONS OF GALOIS FIELDS GF(512) AND GF(1024)

Abstract

The full sets of multilevel linear recurring sequences over all isomorphic and automorphic representations of Galois fields GF(512) and GF(1024) are built. Constructions of cryptographically high quality S-box of processor-oriented lengths N = {512, 1024} are developed. The cardinality of sets of S-boxes are JGF(512) = 1.104×1018 and JGF(1024) = 1.01×1019 which allows to use them as a long-term key to upgrade existing block of symmetric cryptographic algorithms and for development of new ones.

Keywords

• млрп, поле галуа, s-блок подстановки, автоморфизм, изоморфизм
• mlrp, galois field, s-box, automorphism, isomorphism