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TitleInvolutive method for computing Gr\"obner bases over $mathbb F_2$.
Author(s) Vladimir P. Gerdt, M.V. Zinin
TypeArticle in Journal
AbstractIn this paper, an involutive algorithm for computation of Gröbner bases for polynomial ideals in a ring of polynomials in many variables over the finite field 𝔽2 with the values of variables belonging of 𝔽2 is considered. The algorithm uses Janet division and is specialized for a graded reverse lexicographical order of monomials. We compare efficiency of this algorithm and its implementation in C++ with that of the Buchberger algorithm, as well as with the algorithms of computation of Gröbner bases that are built in the computer algebra systems Singular and CoCoA and in the FGb library for Maple. For the sake of comparison, we took widely used examples of computation of Gröbner bases over ℚ and adapted them for 𝔽2. Polynomial systems over 𝔽2 with the values of variables in 𝔽2 are of interest, in particular, for modeling quantum computation and a number of cryptanalysis problems.
ISSN0361-7688; 1608-3261/e
URL http://link.springer.com/article/10.1134%2FS0361768808040026
JournalProgram. Comput. Softw.
PublisherSpringer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica
Translation No
Refereed No