Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions, even when the size of the Boolean function is large (e.g., more than 20 inputs). While bent Boolean functions represent only a small part of all Boolean functions, there are several subclasses of bent functions providing specific properties and challenges. One of the more interesting subclasses comprises (anti-)self-dual bent Boolean functions.This paper provides a detailed experimentation with evolutionary algorithms with the goal of evolving (anti-)self-dual bent Boolean functions. We experiment with two encodings and two fitness functions to evolve self-dual bent Boolean functions. Our experiments consider Boolean functions with sizes of up to 16 inputs, and we successfully construct self-dual bent functions for each dimension. Moreover, we notice that the difficulty of evolving self-dual bent functions is similar to evolving bent Boolean functions, despite self-dual bent functions being much rarer.

Carlet, C., Durasevic, M., Jakobovic, D., Mariot, L., Picek, S. (2024). Look into the Mirror: Evolving Self-dual Bent Boolean Functions. In Genetic Programming 27th European Conference, EuroGP 2024, Held as Part of EvoStar 2024, Aberystwyth, UK, April 3–5, 2024, Proceedings (pp.161-175). Springer Science and Business Media Deutschland GmbH [10.1007/978-3-031-56957-9_10].

Look into the Mirror: Evolving Self-dual Bent Boolean Functions

Mariot, Luca;
2024

Abstract

Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions, even when the size of the Boolean function is large (e.g., more than 20 inputs). While bent Boolean functions represent only a small part of all Boolean functions, there are several subclasses of bent functions providing specific properties and challenges. One of the more interesting subclasses comprises (anti-)self-dual bent Boolean functions.This paper provides a detailed experimentation with evolutionary algorithms with the goal of evolving (anti-)self-dual bent Boolean functions. We experiment with two encodings and two fitness functions to evolve self-dual bent Boolean functions. Our experiments consider Boolean functions with sizes of up to 16 inputs, and we successfully construct self-dual bent functions for each dimension. Moreover, we notice that the difficulty of evolving self-dual bent functions is similar to evolving bent Boolean functions, despite self-dual bent functions being much rarer.
paper
bent; Boolean functions; evolutionary algorithms; self-dual bent;
English
27th European Conference on Genetic Programming, EuroGP 2024 held as Part of EvoStar 2024 - 3 April 2024 through 5 April 2024
2024
Giacobini, M; Xue, B; Manzoni, L
Genetic Programming 27th European Conference, EuroGP 2024, Held as Part of EvoStar 2024, Aberystwyth, UK, April 3–5, 2024, Proceedings
9783031569562
2024
14631 LNCS
161
175
reserved
Carlet, C., Durasevic, M., Jakobovic, D., Mariot, L., Picek, S. (2024). Look into the Mirror: Evolving Self-dual Bent Boolean Functions. In Genetic Programming 27th European Conference, EuroGP 2024, Held as Part of EvoStar 2024, Aberystwyth, UK, April 3–5, 2024, Proceedings (pp.161-175). Springer Science and Business Media Deutschland GmbH [10.1007/978-3-031-56957-9_10].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/502420
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