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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Francisco Gonzalez & Ricardo Soto & Broderick Crawford, 2022. "Stochastic Fractal Search Algorithm Improved with Opposition-Based Learning for Solving the Substitution Box Design Problem," Mathematics, MDPI, vol. 10(13), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2172-:d:844889
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    References listed on IDEAS

    as
    1. Tang, Guoping & Liao, Xiaofeng, 2005. "A method for designing dynamical S-boxes based on discretized chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1901-1909.
    2. Lambić, Dragan, 2014. "A novel method of S-box design based on chaotic map and composition method," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 16-21.
    3. Amer Awad Alzaidi & Musheer Ahmad & Hussam S. Ahmed & Eesa Al Solami, 2018. "Sine-Cosine Optimization-Based Bijective Substitution-Boxes Construction Using Enhanced Dynamics of Chaotic Map," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    4. Chen, Guo & Chen, Yong & Liao, Xiaofeng, 2007. "An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 571-579.
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