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Diskretnaya Matematika, 2006, Volume 18, Issue 3, Pages 138–151
DOI: https://doi.org/10.4213/dm66
(Mi dm66)
 

This article is cited in 7 scientific papers (total in 7 papers)

On some algorithms for constructing low-degree annihilators for Boolean functions

V. V. Baev
References:
Abstract: The algebraic method is widely used in analysis of filter generators of pseudo-random sequences. It is based on obtaining low-degree Boolean equations in bits of the initial states of the generator. The problem to obtain such equations reduces to finding low-degree annihilators for the filtering Boolean function. The presence of nonzero low-degree annihilators decreases the complexity of determining the initial state of the generator by means of its output.
In this research we deal with the problem to find all low-degree annihilators for a Boolean function defined as a polynomial in several variables. We propose two new algorithms which solve this problem. Their complexities are bounded above by polynomials of the number of variables of the function and of the number of monomials in the polynomial which defines the function. We also consider the application of these algorithms to realising the algebraic method by three known scenarios which yield low-degree equations.
Received: 15.06.2005
English version:
Discrete Mathematics and Applications, 2006, Volume 16, Issue 5, Pages 439–452
DOI: https://doi.org/10.1515/156939206779238427
Bibliographic databases:
UDC: 519.7
Language: Russian
Citation: V. V. Baev, “On some algorithms for constructing low-degree annihilators for Boolean functions”, Diskr. Mat., 18:3 (2006), 138–151; Discrete Math. Appl., 16:5 (2006), 439–452
Citation in format AMSBIB
\Bibitem{Bae06}
\by V.~V.~Baev
\paper On some algorithms for constructing low-degree annihilators for Boolean functions
\jour Diskr. Mat.
\yr 2006
\vol 18
\issue 3
\pages 138--151
\mathnet{http://mi.mathnet.ru/dm66}
\crossref{https://doi.org/10.4213/dm66}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2289328}
\zmath{https://zbmath.org/?q=an:1121.94015}
\elib{https://elibrary.ru/item.asp?id=9311215}
\transl
\jour Discrete Math. Appl.
\yr 2006
\vol 16
\issue 5
\pages 439--452
\crossref{https://doi.org/10.1515/156939206779238427}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846864017}
Linking options:
  • https://www.mathnet.ru/eng/dm66
  • https://doi.org/10.4213/dm66
  • https://www.mathnet.ru/eng/dm/v18/i3/p138
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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    Abstract page:971
    Full-text PDF :355
    References:78
    First page:5
     
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