1. Construction of Boolean Functions from Hermitian Codes
- Author
-
Guillermo Sosa-Gómez, Octavio Paez-Osuna, Omar Rojas, Pedro Luis del Ángel Rodríguez, Herbert Kanarek, and Evaristo José Madarro-Capó
- Subjects
Boolean function ,Hermitian codes ,nonlinearity ,Hadamard transform ,resilient ,Mathematics ,QA1-939 - 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.
- Published
- 2022
- Full Text
- View/download PDF