Stochastic Fractal Search Algorithm Improved with Opposition-Based Learning for Solving the Substitution Box Design Problem

Francisco Gonzalez, Ricardo Soto and Broderick Crawford
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Francisco Gonzalez: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Ricardo Soto: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Broderick Crawford: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile

Mathematics, 2022, vol. 10, issue 13, 1-25

Abstract: The main component of a cryptographic system that allows us to ensure its strength against attacks, is the substitution box. The strength of this component can be validated by various metrics, one of them being the nonlinearity. To this end, it is essential to develop a design for substitution boxes that allows us to guarantee compliance with this metric. In this work, we implemented a hybrid between the stochastic fractal search algorithm in conjunction with opposition-based learning. This design is supported by sequential model algorithm configuration for the proper parameters configuration. We obtained substitution boxes of high nonlinearity in comparison with other works based on metaheuristics and chaotic schemes. The proposed substitution box is evaluated using bijectivity, the strict avalanche criterion, nonlinearity, linear probability, differential probability and bit-independence criterion, which demonstrate the excellent performance of the proposed approach.

Keywords: cryptography; substitution box; opposition-based learning; metaheuristics; stochastic fractal search (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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