Design of a strong S-box based on a matrix approach

Abstract

In this paper, we present a matrix approach based on the rule 90 cellular automata, and a fractional linear transformation over Galois field $$GF(2^8)$$ , to implement a strong substitution box (S-box). To make the assessment of this proposal, some standard tests are performed, and the obtained numerical results show that this proposed S-box is comparable or superior to some S-boxes used as benchmarks in this work. Also, to measure the strength of the S-box in image encryption, some statistical tests are carried out, which prove that our proposal exhibits appealing security properties.