Bent Boolean functions play an important role in the design of secure symmetric ciphers, since they achieve the maximum distance from affine functions allowed by Parseval’s relation. Hyper-bent functions, in turn, are those bent functions which additionally reach maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being characterized by a stricter definition, hyper-bent functions are rarer than bent functions, and much more difficult to construct. In this paper, we employ several evolutionary algorithms in order to evolve hyper-bent Boolean functions of various sizes. Our results show that hyper-bent functions are extremely difficult to evolve, since we manage to find such functions only for the smallest investigated size. Interestingly, we are able to identify this difficulty as not lying in the evolution of hyper-bent functions itself, but rather in evolving some of their components, i.e. bent functions. Finally, we present an additional parameter to evaluate the performance of evolutionary algorithms when evolving Boolean functions: the diversity of the obtained solutions.

Mariot, L., Jakobovic, D., Leporati, A., Picek, S. (2019). Hyper-bent Boolean Functions and Evolutionary Algorithms. Intervento presentato a: European Conference on Genetic Programming, EuroGP 2019, held as part of EvoStar 2019, Leipzig, Germany [10.1007/978-3-030-16670-0_17].

Hyper-bent Boolean Functions and Evolutionary Algorithms

Mariot, L
;
Leporati, A;
2019

Abstract

Bent Boolean functions play an important role in the design of secure symmetric ciphers, since they achieve the maximum distance from affine functions allowed by Parseval’s relation. Hyper-bent functions, in turn, are those bent functions which additionally reach maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being characterized by a stricter definition, hyper-bent functions are rarer than bent functions, and much more difficult to construct. In this paper, we employ several evolutionary algorithms in order to evolve hyper-bent Boolean functions of various sizes. Our results show that hyper-bent functions are extremely difficult to evolve, since we manage to find such functions only for the smallest investigated size. Interestingly, we are able to identify this difficulty as not lying in the evolution of hyper-bent functions itself, but rather in evolving some of their components, i.e. bent functions. Finally, we present an additional parameter to evaluate the performance of evolutionary algorithms when evolving Boolean functions: the diversity of the obtained solutions.
paper
Bent functions; Evolution strategies; Genetic algorithms; Genetic programming; Hyper-bent functions
English
European Conference on Genetic Programming, EuroGP 2019, held as part of EvoStar 2019
2019
9783030166694
2019
11451
262
277
none
Mariot, L., Jakobovic, D., Leporati, A., Picek, S. (2019). Hyper-bent Boolean Functions and Evolutionary Algorithms. Intervento presentato a: European Conference on Genetic Programming, EuroGP 2019, held as part of EvoStar 2019, Leipzig, Germany [10.1007/978-3-030-16670-0_17].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/255394
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