Designing secure substitution boxes based on permutation of symmetric group

Abstract

The strength of cryptosystems heavily relies on the substitution boxes. Cryptosystems with weak substitution boxes cannot resist algebraic attacks, linear and differential cryptanalysis. In this paper, first, we propose a strong algebraic structure for the construction of substitution boxes. The proposed substitution boxes have good algebraic properties and are able to resist against algebraic attacks. Second, we propose a new method for creating multiple substitution boxes with the same algebraic properties using permutation of symmetric group on a set of size 8 and bitwise XOR operation. Third, the proposed substitution boxes with the same algebraic properties are then applied to images and it is observed that the statistical properties of substituted images are different from each other. The simulation results and statistical and security analysis for the proposed substitution boxes are very competitive. Also, it is shown in this work that the proposed substitution boxes can resist differential and linear cryptanalysis and sustain algebraic attacks.