Remarks on the Attack of Fouque et al. against the lIC Scheme
In 2007, l -Invertible Cycles (l IC) wasproposed by Ding et al. This is one of the most efficient trapdoorsfor encryption/signature schemes, and of the mixed field type formultivariate quadratic public-key cryptosystems. Such schemes fiton the implementation over low cost smart cards or PDAs. In 2008,Fouque et al. proposed an efficient attack against the l ICsignature scheme by using Grobner basis algorithms. However,they only explicitly dealt with the odd case, i.e. l isodd, but the even case; they only implemented their proposed attackin the odd case. In this paper, we propose an another practicalattack against the l IC encryption/signature scheme. Ourproposed attack does not employ Grobner basis algorithms, andcan be applied to the both even and odd cases. We show theefficiency of the attack by using some experimental results.Furthermore, the attack can be also applied to the l IC-scheme. To the best of our knowledge, we for the first time showsome experimental results of a practical attack against thel IC- scheme for the even case.