On Counts and Densities of Homogeneous Bent Functions: An Evolutionary Approach
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909905748754432 |
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| author | Carlet, Claude Ðurasevic, Marko Jakobovic, Domagoj Mariot, Luca Picek, Stjepan Polujan, Alexandr |
| author_facet | Carlet, Claude Ðurasevic, Marko Jakobovic, Domagoj Mariot, Luca Picek, Stjepan Polujan, Alexandr |
| contents | Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or metaheuristics. This paper examines the use of Evolutionary Algorithms (EAs) to evolve homogeneous bent Boolean functions, that is, functions whose algebraic normal form contains only monomials of the same degree and that are maximally nonlinear. We introduce the notion of density of homogeneous bent functions, facilitating the algorithmic design that results in finding quadratic and cubic bent functions in different numbers of variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Counts and Densities of Homogeneous Bent Functions: An Evolutionary Approach Carlet, Claude Ðurasevic, Marko Jakobovic, Domagoj Mariot, Luca Picek, Stjepan Polujan, Alexandr Neural and Evolutionary Computing Cryptography and Security Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or metaheuristics. This paper examines the use of Evolutionary Algorithms (EAs) to evolve homogeneous bent Boolean functions, that is, functions whose algebraic normal form contains only monomials of the same degree and that are maximally nonlinear. We introduce the notion of density of homogeneous bent functions, facilitating the algorithmic design that results in finding quadratic and cubic bent functions in different numbers of variables. |
| title | On Counts and Densities of Homogeneous Bent Functions: An Evolutionary Approach |
| topic | Neural and Evolutionary Computing Cryptography and Security |
| url | https://arxiv.org/abs/2511.12652 |