Construction of Boolean Functions from Hermitian Codes

Guillermo Sosa-Gómez, Octavio Paez-Osuna, Omar Rojas, Pedro Luis del Ángel Rodríguez, Herbert Kanarek and Evaristo José Madarro-Capó
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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
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

Mathematics, 2022, vol. 10, issue 6, 1-16

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.

Keywords: Boolean function; Hermitian codes; nonlinearity; Hadamard transform; resilient (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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