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Erschienen in:
2011 | OriginalPaper | Buchkapitel
A Variant of the F4 Algorithm
verfasst von : Antoine Joux, Vanessa Vitse
Erschienen in: Topics in Cryptology – CT-RSA 2011
Verlag: Springer Berlin Heidelberg
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Algebraic cryptanalysis usually requires to find solutions of several similar polynomial systems. A standard tool to solve this problem consists of computing the Gröbner bases of the corresponding ideals, and Faugère’s F4 and F5 are two well-known algorithms for this task. In this paper, we adapt the “Gröbner trace” method of Traverso to the context of F4. The resulting variant is a heuristic algorithm, well suited to algebraic attacks of cryptosystems since it is designed to compute with high probability Gröbner bases of a set of polynomial systems having the same shape. It is faster than F4 as it avoids all reductions to zero, but preserves its simplicity and its efficiency, thus competing with F5.