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

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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.

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Acknowledgements

J. A. Aboytes-González is a doctoral fellow of CONACyT (México) in the Graduate Program on “Ciencias Aplicadas” at IICO-UASLP.

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Authors and Affiliations

  1. Instituto de Investigación en Comunicación Óptica, Universidad Autónoma de San Luis Potosí (UASLP), Álvaro Obregón 64, 78000, San Luis Potosí, S.L.P., Mexico

    J. A. Aboytes-González & M. Mejía-Carlos

  2. Laboratorio Nacional CI3M, Facultad de Ciencias, Universidad Autónoma de San Luis Potosí (UASLP), Álvaro Obregón 64, 78000, San Luis Potosí, S.L.P., Mexico

    J. S. Murguía & H. González-Aguilar

  3. Coordinación Académica Región Altiplano Oeste, Universidad Autónoma de San Luis Potosí (UASLP), Carretera Salinas-Santo Domingo # 200 Salinas, San Luis Potosi, Mexico

    M. T. Ramírez-Torres

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  1. J. A. Aboytes-González
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  2. J. S. Murguía
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  3. M. Mejía-Carlos
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  4. H. González-Aguilar
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  5. M. T. Ramírez-Torres
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Correspondence to J. S. Murguía.

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Aboytes-González, J.A., Murguía, J.S., Mejía-Carlos, M. et al. Design of a strong S-box based on a matrix approach. Nonlinear Dyn 94, 2003–2012 (2018). https://doi.org/10.1007/s11071-018-4471-z

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  • DOI: https://doi.org/10.1007/s11071-018-4471-z

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