Publication detail

Semantic Mutation Operator for Fast and Efficient Design of Bent Boolean Functions

HUSA, J. SEKANINA, L.

Original Title

Semantic Mutation Operator for Fast and Efficient Design of Bent Boolean Functions

Type

journal article in Web of Science

Language

English

Original Abstract

Boolean functions are important cryptographic primitives with extensive use in symmetric cryptography. These functions need to possess various properties, such as nonlinearity to be useful. The main limiting factor of the quality of a Boolean function is the number of its input variables, which has to be sufficiently large. The contemporary design methods either scale poorly or are able to create only a small subset of all functions with the desired properties. This necessitates the development of new and more efficient ways of Boolean function design. In this paper, we propose a new semantic mutation operator for the design of bent Boolean functions via genetic programming. The principle of the proposed operator lies in evaluating the function's nonlinearity in detail to purposely avoid mutations that could be disruptive and taking advantage of the fact that the nonlinearity of a Boolean function is invariant under all affine transformations. To assess the efficiency of this operator, we experiment with three distinct variants of genetic programming and compare its performance to three other commonly used non-semantic mutation operators. The detailed experimental evaluation proved that the proposed semantic mutation operator is not only significantly more efficient in terms of evaluations required by genetic programming but also nearly three times faster than the second-best operator when designing bent functions with 12 inputs and almost six times faster for functions with 20 inputs.

Keywords

Nonlinearity, Bent Boolean Functions, Heuristic Optimization, Genetic Programming, Semantic Mutation

Authors

HUSA, J.; SEKANINA, L.

Released

1. 1. 2024

ISBN

1389-2576

Periodical

Genetic Programming and Evolvable Machines

Year of study

25

Number

3

State

United States of America

Pages from

1

Pages to

32

Pages count

32

URL

BibTex

@article{BUT186770,
  author="Jakub {Husa} and Lukáš {Sekanina}",
  title="Semantic Mutation Operator for Fast and Efficient Design of Bent Boolean Functions",
  journal="Genetic Programming and Evolvable Machines",
  year="2024",
  volume="25",
  number="3",
  pages="1--32",
  doi="10.1007/s10710-023-09476-w",
  issn="1389-2576",
  url="https://rdcu.be/ds8Zc"
}