Hybrid approach to the search for boolean functions with high algebraic immunity based on heuristics | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/4

Hybrid approach to the search for boolean functions with high algebraic immunity based on heuristics

Currently, one of the most promising and developing methods for analyzing ciphers is algebraic cryptanalysis. In order to provide resilience to such type of attack, it is necessary to use Boolean functions with high algebraic immunity in constructing components of block and stream ciphers. The paper proposes a combined approach to the search for Boolean functions with high algebraic immunity based on heuristic methods, in particular, the genetic algorithm and the Hill Climbing algorithm. Computational experiments for Boolean functions in n < 8 variables demonstrate the effectiveness of the proposed approach.

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Keywords

heuristics, algebraic immunity, nonlinearity, Hil l Climbing algorithm, genetic algorithm

Authors

Name	Organization	E-mail
Atutova N. D.	Novosibirsk State University; JetBrains Research Crypto Lab	atutova.n@yandex.ru

Всего: 1

References

Лобанов М. С. Точные соотношения между нелинейностью и алгебраической иммунностью // Дискретный анализ и исследование операций. 2008. Т. 15. № 6. С. 34-47.

Behera P. and Gangopadhyay S. An improved hybrid genetic algorithm to construct balanced Boolean function with optimal cryptographic properties // Evolutionary Intelligence. 2021. No. 1. P. 1-15.

Matsui M. Linear cryptanalysis method for DES cipher // LNCS. 1994. V. 765. P. 386-397.

Clark J., Jacob J., Stepney S., et al. Evolving Boolean functions satisfying multiple criteria // LNCS. 2002. V. 2551. P. 246-259.

Picek S., Jakobovic D., Miller J., et al. Cryptographic Boolean functions: one output, many design criteria // Appl. Soft Computing. 2016. No. 40. P. 635-653.

Millan W., Clark A., and Dawson E. An effective genetic algorithm for finding highly nonlinear Boolean functions // LNCS. 1997. V. 1334. P. 149-158.

Courtois N. and Meier W. Algebraic attacks on stream ciphers with linear feedback // LNCS. 2003. V. 2656. P. 345-359.