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Construction of Boolean Functions from Hermitian Codes

Author

Listed:
  • Guillermo Sosa-Gómez

    (Facultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan 45010, Mexico)

  • Octavio Paez-Osuna

    (Ronin Institute, Montclair, NJ 07043, USA)

  • Omar Rojas

    (Facultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan 45010, Mexico
    Faculty of Economics and Business, Universitas Airlangga, Surabaya 60286, Indonesia)

  • Pedro Luis del Ángel Rodríguez

    (Centro de Investigación en Matemáticas, Guanajuato 36023, Mexico)

  • Herbert Kanarek

    (Departamento de Matemáticas, Universidad de Guanajuato, Guanajuato 36240, Mexico)

  • Evaristo José Madarro-Capó

    (Institute of Cryptography, University of Havana, Havana 10400, Cuba)

Abstract

In 2005, Guillot published a method for the construction of Boolean functions using linear codes through the Maiorana–McFarland construction of Boolean functions. In this work, we present a construction using Hermitian codes, starting from the classic Maiorana–McFarland construction. This new construction describes how the set of variables is divided into two complementary subspaces, one of these subspaces being a Hermitian Code. The ideal theoretical parameters of the Hermitian code are proposed to reach desirable values of the cryptographic properties of the constructed Boolean functions such as nonlinearity, resiliency order, and order of propagation. An extension of Guillot’s work is also made regarding parameters selection using algebraic geometric tools, including explicit examples.

Suggested Citation

  • Guillermo Sosa-Gómez & Octavio Paez-Osuna & Omar Rojas & Pedro Luis del Ángel Rodríguez & Herbert Kanarek & Evaristo José Madarro-Capó, 2022. "Construction of Boolean Functions from Hermitian Codes," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:899-:d:769043
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    Cited by:

    1. Luyang Li & Linhui Wang & Qinglan Zhao & Dong Zheng, 2022. "On Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity," Mathematics, MDPI, vol. 10(24), pages 1-15, December.

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