A New Angle: On Evolving Rotation Symmetric Boolean Functions

Claude Carlet; Marko Durasevic; Bruno Gasperov; Domagoj Jakobovic; Luca Mariot; Stjepan Picek

doi:10.1007/978-3-031-56852-7_19

A New Angle: On Evolving Rotation Symmetric Boolean Functions

Claude Carlet, Marko Durasevic, Bruno Gasperov, Domagoj Jakobovic^*, Luca Mariot, Stjepan Picek

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

4 Citations (Scopus)

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Abstract

Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent cryptographic properties, making them interesting for various practical applications. The usage of metaheuristics to construct rotation symmetric Boolean functions is a direction that has been explored for almost twenty years. Despite that, there are very few results considering evolutionary computation methods. This paper uses several evolutionary algorithms to evolve rotation symmetric Boolean functions with different properties. Despite using generic metaheuristics, we obtain results that are competitive with prior work relying on customized heuristics. Surprisingly, we find that bitstring and floating point encodings work better than the tree encoding. Moreover, evolving highly nonlinear general Boolean functions is easier than rotation symmetric ones.

Original language	English
Title of host publication	Applications of Evolutionary Computation - 27th European Conference, EvoApplications 2024, Held as Part of EvoStar 2024, Proceedings
Editors	Stephen Smith, João Correia, Christian Cintrano
Publisher	Springer
Pages	287-302
Number of pages	16
ISBN (Electronic)	978-3-031-56852-7
ISBN (Print)	978-3-031-56851-0
DOIs	https://doi.org/10.1007/978-3-031-56852-7_19
Publication status	Published - 21 Mar 2024
Event	27th International Conference on Applications of Evolutionary Computation, EvoApplications 2024 - Aberystwyth, United Kingdom Duration: 3 Apr 2024 → 5 Apr 2024 Conference number: 27

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	14634
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Conference on Applications of Evolutionary Computation, EvoApplications 2024
Abbreviated title	EvoApplications 2024
Country/Territory	United Kingdom
City	Aberystwyth
Period	3/04/24 → 5/04/24

Keywords

2024 OA procedure
Metaheuristics
Nonlinearity
Rotation symmetry
Boolean functions

Access to Document

10.1007/978-3-031-56852-7_19

978-3-031-56852-7_19Final published version, 394 KBLicence: Taverne

Cite this

Carlet, C., Durasevic, M., Gasperov, B., Jakobovic, D., Mariot, L., & Picek, S. (2024). A New Angle: On Evolving Rotation Symmetric Boolean Functions. In S. Smith, J. Correia, & C. Cintrano (Eds.), Applications of Evolutionary Computation - 27th European Conference, EvoApplications 2024, Held as Part of EvoStar 2024, Proceedings (pp. 287-302). (Lecture Notes in Computer Science; Vol. 14634). Springer. https://doi.org/10.1007/978-3-031-56852-7_19

Carlet, Claude ; Durasevic, Marko ; Gasperov, Bruno et al. / A New Angle : On Evolving Rotation Symmetric Boolean Functions. Applications of Evolutionary Computation - 27th European Conference, EvoApplications 2024, Held as Part of EvoStar 2024, Proceedings. editor / Stephen Smith ; João Correia ; Christian Cintrano. Springer, 2024. pp. 287-302 (Lecture Notes in Computer Science).

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abstract = "Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent cryptographic properties, making them interesting for various practical applications. The usage of metaheuristics to construct rotation symmetric Boolean functions is a direction that has been explored for almost twenty years. Despite that, there are very few results considering evolutionary computation methods. This paper uses several evolutionary algorithms to evolve rotation symmetric Boolean functions with different properties. Despite using generic metaheuristics, we obtain results that are competitive with prior work relying on customized heuristics. Surprisingly, we find that bitstring and floating point encodings work better than the tree encoding. Moreover, evolving highly nonlinear general Boolean functions is easier than rotation symmetric ones.",

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note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 27th International Conference on Applications of Evolutionary Computation, EvoApplications 2024, EvoApplications 2024 ; Conference date: 03-04-2024 Through 05-04-2024",

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Carlet, C, Durasevic, M, Gasperov, B, Jakobovic, D, Mariot, L & Picek, S 2024, A New Angle: On Evolving Rotation Symmetric Boolean Functions. in S Smith, J Correia & C Cintrano (eds), Applications of Evolutionary Computation - 27th European Conference, EvoApplications 2024, Held as Part of EvoStar 2024, Proceedings. Lecture Notes in Computer Science, vol. 14634, Springer, pp. 287-302, 27th International Conference on Applications of Evolutionary Computation, EvoApplications 2024, Aberystwyth, United Kingdom, 3/04/24. https://doi.org/10.1007/978-3-031-56852-7_19

A New Angle: On Evolving Rotation Symmetric Boolean Functions. / Carlet, Claude; Durasevic, Marko; Gasperov, Bruno et al.
Applications of Evolutionary Computation - 27th European Conference, EvoApplications 2024, Held as Part of EvoStar 2024, Proceedings. ed. / Stephen Smith; João Correia; Christian Cintrano. Springer, 2024. p. 287-302 (Lecture Notes in Computer Science; Vol. 14634).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Carlet, Claude

AU - Durasevic, Marko

AU - Gasperov, Bruno

AU - Jakobovic, Domagoj

AU - Mariot, Luca

AU - Picek, Stjepan

N1 - Conference code: 27

PY - 2024/3/21

Y1 - 2024/3/21

N2 - Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent cryptographic properties, making them interesting for various practical applications. The usage of metaheuristics to construct rotation symmetric Boolean functions is a direction that has been explored for almost twenty years. Despite that, there are very few results considering evolutionary computation methods. This paper uses several evolutionary algorithms to evolve rotation symmetric Boolean functions with different properties. Despite using generic metaheuristics, we obtain results that are competitive with prior work relying on customized heuristics. Surprisingly, we find that bitstring and floating point encodings work better than the tree encoding. Moreover, evolving highly nonlinear general Boolean functions is easier than rotation symmetric ones.

AB - Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent cryptographic properties, making them interesting for various practical applications. The usage of metaheuristics to construct rotation symmetric Boolean functions is a direction that has been explored for almost twenty years. Despite that, there are very few results considering evolutionary computation methods. This paper uses several evolutionary algorithms to evolve rotation symmetric Boolean functions with different properties. Despite using generic metaheuristics, we obtain results that are competitive with prior work relying on customized heuristics. Surprisingly, we find that bitstring and floating point encodings work better than the tree encoding. Moreover, evolving highly nonlinear general Boolean functions is easier than rotation symmetric ones.

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Carlet C, Durasevic M, Gasperov B, Jakobovic D, Mariot L, Picek S. A New Angle: On Evolving Rotation Symmetric Boolean Functions. In Smith S, Correia J, Cintrano C, editors, Applications of Evolutionary Computation - 27th European Conference, EvoApplications 2024, Held as Part of EvoStar 2024, Proceedings. Springer. 2024. p. 287-302. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-56852-7_19

A New Angle: On Evolving Rotation Symmetric Boolean Functions

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