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Mat. Vopr. Kriptogr., 2012, Volume 3, Issue 4, Pages 25–53 (Mi mvk66)  

This article is cited in 3 scientific papers (total in 3 papers)

Parameters of Boolean functions generated by the most significant bits of linear recurrent sequences

D. N. Bylkov, O. V. Kamlovskii

LLC "Certification Research Center", Moscow

Abstract: The families of Boolean functions generated by the most significant bits of linear recurrent sequences over the ring $\mathbb Z_{2^n}$ with the marked characteristic polynomial are considered. For these families we investigate their cardinalities, the weights and the degree of nonlinearity of functions, distances between functions. We prove that there exists a rearrangement of arguments (one and the same for all functions in the family) such that the family contains functions which are close to some bent-functions.

Key words: linear recurrent sequences, most significant bit sequences, degree of nonlinearity of Boolean function, distance to the affine functions set.

DOI: https://doi.org/10.4213/mvk66

Full text: PDF file (250 kB)
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Document Type: Article
UDC: 511.336+519.113.6
Received 20.V.2011

Citation: D. N. Bylkov, O. V. Kamlovskii, “Parameters of Boolean functions generated by the most significant bits of linear recurrent sequences”, Mat. Vopr. Kriptogr., 3:4 (2012), 25–53

Citation in format AMSBIB
\Bibitem{BylKam12}
\by D.~N.~Bylkov, O.~V.~Kamlovskii
\paper Parameters of Boolean functions generated by the most significant bits of linear recurrent sequences
\jour Mat. Vopr. Kriptogr.
\yr 2012
\vol 3
\issue 4
\pages 25--53
\mathnet{http://mi.mathnet.ru/mvk66}
\crossref{https://doi.org/10.4213/mvk66}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. N. Bylkov, “Ob odnom klasse bulevykh funktsii, postroennykh s ispolzovaniem starshikh razryadnykh posledovatelnostei lineinykh rekurrent”, PDM. Prilozhenie, 2014, no. 7, 59–60  mathnet
    2. A. D. Bugrov, “Postroenie odnogo klassa funktsii nad konechnymi polyami s ispolzovaniem lineinykh rekurrent nad koltsami Galua”, PDM. Prilozhenie, 2018, no. 11, 34–39  mathnet  crossref
    3. A. D. Bugrov, O. V. Kamlovskii, “Parametry odnogo klassa funktsii, zadannykh na konechnom pole”, Matem. vopr. kriptogr., 9:4 (2018), 31–52  mathnet  crossref
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