Hyper-bent Boolean Functions and Evolutionary Algorithms

Luca Mariot, Domagoj Jakobovic, Alberto Leporati, Stjepan Picek

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationGenetic Programming
Subtitle of host publication22nd European Conference, EuroGP 2019, Held as Part of EvoStar 2019, Proceedings
EditorsLukas Sekanina, Ting Hu, Hendrik Richter, Pablo García-Sánchez, Nuno Lourenço
Place of PublicationCham
PublisherSpringer
Pages262-277
Number of pages16
ISBN (Electronic)978-3-030-16670-0
ISBN (Print)978-3-030-16669-4
DOIs
Publication statusPublished - 2019
Event22nd European Conference on Genetic Programming, EuroGP 2019, held as part of EvoStar 2019 - Leipzig, Germany
Duration: 24 Apr 201926 Apr 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11451 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference22nd European Conference on Genetic Programming, EuroGP 2019, held as part of EvoStar 2019
CountryGermany
CityLeipzig
Period24/04/1926/04/19

Keywords

  • Bent functions
  • Evolution strategies
  • Genetic algorithms
  • Genetic programming
  • Hyper-bent functions

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