On the Evolution of Boomerang Uniformity in Cryptographic S-boxes

Marko Durasevic; Domagoj Jakobovic; Luca Mariot; Sihem Mesnager; Stjepan Picek

doi:10.1007/978-3-031-30229-9_16

On the Evolution of Boomerang Uniformity in Cryptographic S-boxes

Marko Durasevic, Domagoj Jakobovic, Luca Mariot, Sihem Mesnager, Stjepan Picek^*

^*Corresponding author for this work

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

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Abstract

S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value, the more secure the algorithm. One example of such a property is called boomerang uniformity, which helps to be resilient against boomerang attacks. How to construct S-boxes with good boomerang uniformity is not always clear. There are algebraic techniques that can result in good boomerang uniformity, but the results are still rare. In this work, we explore the evolution of S-boxes with good values of boomerang uniformity. We consider three different encodings and five S-box sizes. For sizes 4 × 4 and 5 × 5, we manage to obtain optimal solutions. For 6 × 6, we obtain optimal boomerang uniformity for the non-APN function. For larger sizes, the results indicate the problem to be very difficult (even more difficult than evolving differential uniformity, which can be considered a well-researched problem).

Original language	English
Title of host publication	Applications of Evolutionary Computation - 26th European Conference, EvoApplications 2023, Held as Part of EvoStar 2023, Proceedings
Editors	João Correia, Stephen Smith, Raneem Qaddoura
Publisher	Springer
Pages	237-252
Number of pages	16
ISBN (Print)	9783031302282
DOIs	https://doi.org/10.1007/978-3-031-30229-9_16
Publication status	Published - 9 Apr 2023
Event	26th International Conference on Applications of Evolutionary Computation, EvoApplications 2023 - Brno, Czech Republic Duration: 12 Apr 2023 → 14 Apr 2023 Conference number: 26

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13989 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	26th International Conference on Applications of Evolutionary Computation, EvoApplications 2023
Abbreviated title	EvoApplications
Country/Territory	Czech Republic
City	Brno
Period	12/04/23 → 14/04/23
Other	held as part of EvoStar 2023

Keywords

2024 OA procedure
Evolutionary Algorithms
Permutations
S-boxes
Boomerang Uniformity

Access to Document

10.1007/978-3-031-30229-9_16

978-3-031-30229-9_16Final published version, 430 KBLicence: Taverne

Cite this

Durasevic, M., Jakobovic, D., Mariot, L., Mesnager, S., & Picek, S. (2023). On the Evolution of Boomerang Uniformity in Cryptographic S-boxes. In J. Correia, S. Smith, & R. Qaddoura (Eds.), Applications of Evolutionary Computation - 26th European Conference, EvoApplications 2023, Held as Part of EvoStar 2023, Proceedings (pp. 237-252). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13989 LNCS). Springer. https://doi.org/10.1007/978-3-031-30229-9_16

Durasevic, Marko ; Jakobovic, Domagoj ; Mariot, Luca et al. / On the Evolution of Boomerang Uniformity in Cryptographic S-boxes. Applications of Evolutionary Computation - 26th European Conference, EvoApplications 2023, Held as Part of EvoStar 2023, Proceedings. editor / João Correia ; Stephen Smith ; Raneem Qaddoura. Springer, 2023. pp. 237-252 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value, the more secure the algorithm. One example of such a property is called boomerang uniformity, which helps to be resilient against boomerang attacks. How to construct S-boxes with good boomerang uniformity is not always clear. There are algebraic techniques that can result in good boomerang uniformity, but the results are still rare. In this work, we explore the evolution of S-boxes with good values of boomerang uniformity. We consider three different encodings and five S-box sizes. For sizes 4 × 4 and 5 × 5, we manage to obtain optimal solutions. For 6 × 6, we obtain optimal boomerang uniformity for the non-APN function. For larger sizes, the results indicate the problem to be very difficult (even more difficult than evolving differential uniformity, which can be considered a well-researched problem).",

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Durasevic, M, Jakobovic, D, Mariot, L, Mesnager, S & Picek, S 2023, On the Evolution of Boomerang Uniformity in Cryptographic S-boxes. in J Correia, S Smith & R Qaddoura (eds), Applications of Evolutionary Computation - 26th European Conference, EvoApplications 2023, Held as Part of EvoStar 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13989 LNCS, Springer, pp. 237-252, 26th International Conference on Applications of Evolutionary Computation, EvoApplications 2023, Brno, Czech Republic, 12/04/23. https://doi.org/10.1007/978-3-031-30229-9_16

On the Evolution of Boomerang Uniformity in Cryptographic S-boxes. / Durasevic, Marko; Jakobovic, Domagoj; Mariot, Luca et al.
Applications of Evolutionary Computation - 26th European Conference, EvoApplications 2023, Held as Part of EvoStar 2023, Proceedings. ed. / João Correia; Stephen Smith; Raneem Qaddoura. Springer, 2023. p. 237-252 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13989 LNCS).

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

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T1 - On the Evolution of Boomerang Uniformity in Cryptographic S-boxes

AU - Durasevic, Marko

AU - Jakobovic, Domagoj

AU - Mariot, Luca

AU - Mesnager, Sihem

AU - Picek, Stjepan

N1 - Conference code: 26

PY - 2023/4/9

Y1 - 2023/4/9

N2 - S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value, the more secure the algorithm. One example of such a property is called boomerang uniformity, which helps to be resilient against boomerang attacks. How to construct S-boxes with good boomerang uniformity is not always clear. There are algebraic techniques that can result in good boomerang uniformity, but the results are still rare. In this work, we explore the evolution of S-boxes with good values of boomerang uniformity. We consider three different encodings and five S-box sizes. For sizes 4 × 4 and 5 × 5, we manage to obtain optimal solutions. For 6 × 6, we obtain optimal boomerang uniformity for the non-APN function. For larger sizes, the results indicate the problem to be very difficult (even more difficult than evolving differential uniformity, which can be considered a well-researched problem).

AB - S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value, the more secure the algorithm. One example of such a property is called boomerang uniformity, which helps to be resilient against boomerang attacks. How to construct S-boxes with good boomerang uniformity is not always clear. There are algebraic techniques that can result in good boomerang uniformity, but the results are still rare. In this work, we explore the evolution of S-boxes with good values of boomerang uniformity. We consider three different encodings and five S-box sizes. For sizes 4 × 4 and 5 × 5, we manage to obtain optimal solutions. For 6 × 6, we obtain optimal boomerang uniformity for the non-APN function. For larger sizes, the results indicate the problem to be very difficult (even more difficult than evolving differential uniformity, which can be considered a well-researched problem).

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KW - Permutations

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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PB - Springer

T2 - 26th International Conference on Applications of Evolutionary Computation, EvoApplications 2023

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Durasevic M, Jakobovic D, Mariot L, Mesnager S, Picek S. On the Evolution of Boomerang Uniformity in Cryptographic S-boxes. In Correia J, Smith S, Qaddoura R, editors, Applications of Evolutionary Computation - 26th European Conference, EvoApplications 2023, Held as Part of EvoStar 2023, Proceedings. Springer. 2023. p. 237-252. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-30229-9_16

On the Evolution of Boomerang Uniformity in Cryptographic S-boxes

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