Startseite Boolean functions constructed using digital sequences of linear recurrences
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Boolean functions constructed using digital sequences of linear recurrences

  • Andrey A. Gruba EMAIL logo
Veröffentlicht/Copyright: 6. September 2025
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

A class of Boolean functions constructed from digital sequences of linear recurrences over the ring Z2n is considered. We investigate distances between functions, the cardinality of the class, nonlinearity and weights of functions. It is shown that this class consists of functions that are rather distant from the class of all affine functions.


Originally published in Diskretnaya Matematika (2023) 35, №1, 54–61 (in Russian).


References

[1] Lidl R., Niederreiter H., Finite Fields, Addison-Wesley Publ. Inc., 1983, 755 pp.Suche in Google Scholar

[2] Nechaev A. A., “Cycle types of linear substitutions over finite commutative rings”, Russian Acad. Sci. Sb. Math., 782 (1994), 283–311.10.1070/SM1994v078n02ABEH003470Suche in Google Scholar

[3] Bylkov D. N., Kamlovskii O. V., “Parameters of Boolean functions generated by the most significant bits of linear recurrent sequences”, Matematicheskie voprosy kriptografii, 34 (2012), 25–53 (in Russian).10.4213/mvk66Suche in Google Scholar

[4] Bylkov D. N., “Boolean functions generated by the most significant bits of linear recurrent sequences”, PDM. Prilozhenie, 2014, № 7, 59–60 (in Russian).Suche in Google Scholar

[5] Bugrov A. D., Kamlovskii O. V., “Parameters of a class of functions over a finite field”, Matematicheskie voprosy kriptografii, 94 (2018), 35–52 (in Russian).Suche in Google Scholar

[6] Solodovnikov V. I., “Bent functions from a finite abelian group into a finite abelian group”, Discrete Math. Appl., 122 (2002), 111–126.10.1515/dma-2002-0203Suche in Google Scholar

[7] Kamlovskiy O. V., “Estimating the number of solutions of systems of nonlinear equations with linear recurring arguments by the spectral method”, Discrete Math. Appl., 274 (2017), 199–211.10.1515/dma-2017-0022Suche in Google Scholar

[8] Kamlovskii O. V., “Exponential sums method for frequencies of most significant bit r-patterns in linear recurrent sequences over ℤ2n”, Matematicheskie voprosy kriptografii, 14 (2010), 33–62 (in Russian).Suche in Google Scholar

[9] Kamlovsky O. V., Kuzmin A. S., “Bounds for the number of occurrences of elements in a linear recurring sequence over a Galois ring”, Fundamentalnaya i prikladnaya matematika, 64 (2000), 1083–1094.Suche in Google Scholar

[10] Dictionary of cryptographic terms, eds. Pogorelov B. A., Sachkov V. N., M.: MCCME, 2006 (in Russian), 92 pp.Suche in Google Scholar

[11] Bylkov D. N., “A class of injective compressing maps on linear recurring sequences over a Galois ring”, Problems Inform. Transmission, 463 (2010), 245–252.10.1134/S003294601003004XSuche in Google Scholar

[12] Kamlovskii O. V., “Frequency characteristics of linear recurrence sequences over Galois rings”, Sb. Math., 2004 (2009), 499–519.10.1070/SM2009v200n04ABEH004006Suche in Google Scholar

[13] Logachev O. A., Salnikov A. A., Yashchenko V. V., Boolean functions in coding theory and cryptology, M.: MCCME, 2004 (in Russian), 470 pp.Suche in Google Scholar

Received: 2022-11-16
Published Online: 2025-09-06
Published in Print: 2025-08-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 27.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2025-0016/html
Button zum nach oben scrollen