Algebraic methods for generating optimal s-blocks

Abstract

The paper presents a review of algebraic methods for generating cryptographic S-boxes. In this paper, we consider methods for generating S-boxes based on the use of polynomial transformations (linear, quadratic, cubic), fractional linear transformations, and other special types of algebraic transformations. A number of examples of generating S-boxes using quasigroups and other algebraic structures are also given. The considered methods for generating S-boxes make it possible to obtain new S-boxes that have the necessary cryptographic properties that are the same or even better than those of the S-box built for the Rijndael algorithm.