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Hyper-bent Boolean Functions and Evolutionary Algorithms

Mariot, Luca; Jakobovic, Domagoj; Leporati, Alberto; Picek, Stjepan
Hyper-bent Boolean Functions and Evolutionary Algorithms // European Conference on Genetic Programming EuroGP 2019
Leipzig, Njemačka, 2019. str. 262-277 doi:10.1007/978-3-030-16670-0_17 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)

Hyper-bent Boolean Functions and Evolutionary Algorithms

Mariot, Luca ; Jakobovic, Domagoj ; Leporati, Alberto ; Picek, Stjepan

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

European Conference on Genetic Programming EuroGP 2019 / - , 2019, 262-277


Genetic Programming. EuroGP 2019.

Mjesto i datum
Leipzig, Njemačka, 24-26.04.2019.

Vrsta sudjelovanja

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Bent functions ; Hyper-bent functions ; Genetic programming ; Genetic algorithms ; Evolution strategies

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.

Izvorni jezik

Znanstvena područja


Projekt / tema
HRZZ-IP-2014-09-4882 - Heuristička optimizacija u kriptologiji (Domagoj Jakobović, )

Fakultet elektrotehnike i računarstva, Zagreb