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Diskr. Mat., 2006, Volume 18, Issue 3, Pages 138–151 (Mi dm66)  

This article is cited in 4 scientific papers (total in 4 papers)

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

V. V. Baev


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.

DOI: https://doi.org/10.4213/dm66

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English version:
Discrete Mathematics and Applications, 2006, 16:5, 439–452

Bibliographic databases:

UDC: 519.7
Received: 15.06.2005

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
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\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://www.ams.org/mathscinet-getitem?mr=2289328}
\zmath{https://zbmath.org/?q=an:1121.94015}
\elib{http://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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846864017}


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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. V. V. Baev, “An enhanced algorithm to search for low-degree annihilators for a Zhegalkin polynomial”, Discrete Math. Appl., 17:5 (2007), 533–538  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. V. V. Bayev, “Some Lower Bounds on the Algebraic Immunity of Functions Given by Their Trace Forms”, Problems Inform. Transmission, 44:3 (2008), 243–265  mathnet  crossref  mathscinet  isi
    3. Leont'ev V. K., “Boolean polynomials and linear transformations”, Dokl. Math., 79:2 (2009), 216–218  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    4. K. N. Koryagin, “Level structure of Zhegalkin polynomials, properties of test sets, and an annihilator search algorithm”, Comput. Math. Math. Phys., 50:7 (2010), 1267–1273  mathnet  crossref  mathscinet  adsnasa  isi
  • Дискретная математика
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