On Patarin's Attack against the <i>l</i>IC Scheme

Abstract

In 2007, Ding et al. proposed an attractive scheme, which is called the l-Invertible Cycles (lIC) scheme. lIC is one of the most efficient multivariate public-key cryptosystems (MPKC); these schemes would be suitable for using under limited computational resources. In 2008, an efficient attack against lIC using Grobner basis algorithms was proposed by Fouque et al. However, they only estimated the complexity of their attack based on their experimental results. On the other hand, Patarin had proposed an efficient attack against some multivariate public-key cryptosystems. We call this attack Patarin's attack. The complexity of Patarin's attack can be estimated by finding relations corresponding to each scheme. In this paper, we propose an another practical attack against the lIC encryption/signature scheme. We estimate the complexity of our attack (not experimentally) by adapting Patarin's attack. The attack can be also applied to the lIC- scheme. Moreover, we show some experimental results of a practical attack against the lIC/lIC- schemes. This is the first implementation of both our proposed attack and an attack based on Grobner basis algorithm for the even case, that is, a parameter l is even.