- author = "Claude Carlet and Marko Durasevic and Domagoj Jakobovic and Stjepan Picek and Luca Mariot",
- title = "A systematic study on the design of odd-sized highly nonlinear boolean functions via evolutionary algorithms",
- journal = "Genetic Programming and Evolvable Machines",
- year = "2026",
- volume = "27",
- pages = "Article no 1",
- note = "Online first",
- keywords = "genetic algorithms, genetic programming, Boolean functions, Nonlinearity, Evolutionary algorithms, Odd dimension, Primary construction, Secondary construction",
- ISSN = "1389-2576",
-
DOI = "
10.1007/s10710-025-09526-5",
- abstract = "We evolve Boolean functions of odd sizes with high nonlinearity, a property of cryptographic relevance. Despite its simple formulation, this problem turns out to be remarkably difficult. We conduct a systematic evaluation by considering three solution encodings and four problem instances, analyzing how well different types of evolutionary algorithms behave in finding a maximally nonlinear Boolean function. Our results show that genetic programming generally outperforms other evolutionary algorithms, although it falls short of the best-known results achieved by ad-hoc heuristics. Interestingly, by adding local search and restricting the space to rotation symmetric Boolean functions, we show that a genetic algorithm with the bitstring encoding manages to evolve a 9-variable Boolean function with nonlinearity 241",
-
notes = "Highlights of Genetic Programming 2024 & 2025
Events
Published 18 Dec 2025
Department of Mathematics, University Paris 8, 2 Rue de la Liberte, 93526, Saint-Denis Cedex, France",
