Geodesic
Hybrid approach to the search for Boolean functions with high algebraic immunity based on heuristics
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 37-40.

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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 $n\leq8$ variables demonstrate the effectiveness of the proposed approach.
Keywords: genetic algorithm, Hill Climbing algorithm, algebraic immunity, nonlinearity, heuristics. 
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     author = {N. D. Atutova},
     title = {Hybrid approach to the search for {Boolean} functions with high algebraic immunity based on heuristics},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
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     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a4/}
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N. D. Atutova. Hybrid approach to the search for Boolean functions with high algebraic immunity based on heuristics. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 37-40. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a4/

[1] Courtois N., Meier W., “Algebraic attacks on stream ciphers with linear feedback”, LNCS, 2656, 2003, 345–359 | MR | Zbl

[2] Millan W., Clark A., Dawson E., “An effective genetic algorithm for finding highly nonlinear Boolean functions”, LNCS, 1334, 1997, 149–158 | Zbl

[3] Clark J., Jacob J., Stepney S., et al., “Evolving Boolean functions satisfying multiple criteria”, LNCS, 2551, 2002, 246–259 | Zbl

[4] Picek S., Jakobovic D., Miller J., et al., “Cryptographic Boolean functions: one output, many design criteria”, Appl. Soft Computing, 40 (2016), 635–653 | DOI

[5] Behera P., Gangopadhyay S., “An improved hybrid genetic algorithm to construct balanced Boolean function with optimal cryptographic properties”, Evolutionary Intelligence, 2021, no. 1, 1–15

[6] Matsui M., “Linear cryptanalysis method for DES cipher”, LNCS, 765, 1994, 386–397 | Zbl

[7] Lobanov M. S., “Tochnye sootnosheniya mezhdu nelineinostyu i algebraicheskoi immunnostyu”, Diskretnyi analiz i issledovanie operatsii, 15:6 (2008), 34–47 | MR | Zbl