On cryptographic properties of S-boxes

Abstract

The article is devoted to the study of cryptographic properties of S-boxes. S-box is a function that accepts n bits at the input, converts them according to a certain algorithm and returns m bits at the output. n and m are not necessarily equal. S-boxes are one of the main components of modern cryptographic algorithms that determine their nonlinearity. To protect cryptographic algorithms from various types of attacks, S-boxes must meet a number of criteria. The purpose of this work is to study the existing cryptographic properties of S-boxes, which will allow us to further analyze the existing criteria that S-boxes must meet and make a reasonable choice of a set of criteria for optimal S-boxes. This article provides an overview of the main properties of S-boxes that are important in the formation of optimality criteria. Differential uniformity, difference distribution table, nonlinearity, linear distribution table, algebraic degree, algebraic immunity, algebraic complexity, avalanche effect, strict avalanche effect, distance to strictly avalanche effect, completeness, linear structures, balancedness, correlation immunity, bit independence criterion, propagation criterion, period, number of fixed points and opposite fixed points, cycles, inversions, increases, boomerang connection table, boomerang difference table are considered. The existing methods of generating S-boxes with the necessary optimal characteristics are also considered.