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Published in:
2006 | OriginalPaper | Chapter
Cryptanalysis of 2R− Schemes
Authors : Jean-Charles Faugère, Ludovic Perret
Published in: Advances in Cryptology - CRYPTO 2006
Publisher: Springer Berlin Heidelberg
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In this paper, we study the security of 2R
−
schemes [17,18], which are the “minus variant” of two-round schemes. This variant consists in removing some of the
n
polynomials of the public key, and permits to thwart an attack described at Crypto’99 [25] against two-round schemes. Usually, the “minus variant” leads to a real strengthening of the considered schemes. We show here that this is actually not true for 2R
−
schemes. We indeed propose an efficient algorithm for decomposing 2R
−
schemes. For instance, we can remove up to
$\left \lfloor\frac{n}{2} \right \rfloor$
equations and still be able to recover a decomposition in
O
(
n
12
). We provide experimental results illustrating the efficiency of our approach. In practice, we have been able to decompose 2R
−
schemes in less than a handful of hours for most of the challenges proposed by the designers [18]. We believe that this result makes the principle of two-round schemes, including 2R
−
schemes, useless.