Cryptanalysis of 2R- Schemes

Abstract. In this paper, we study the security of 2Rschemes [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 2Rschemes. We indeed propose an efficient algorithm for decomposing 2Rschemes. For instance, we can remove up to n 2 equations and still be able to recover a decomposition in O(n12 ). We provide experimental results illustrating the efficiency of our approach. In practice, we have been able to decompose 2Rschemes 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 2Rschemes, useless.

• Type: Conference
• Year: 2006
• Where: CRYPTO
• Authors: Jean-Charles Faugère, Ludovic Perret
• Keywords: CRYPTO 2006, Cryptology, Minus Variant, Public Key, Two-round Schemes