Cryptanalysis of a new version of the MOR scheme

Abstract

We show that an attack based on the linear decomposition method introduced by the author can be efficiently applied to the new version of the MOR scheme proposed in \cite{BMSS}. We draw attention to some inaccuracies in the description of this version. We show how the action of an exponent of a given automorphism (for example, the action of its inverse) can be calculated, and we also show how the unknown exponent of automorphism can be calculated if we go over to the corresponding linear transformation. This method can be applied to different matrix groups over an arbitrary constructive field. It does not depend on the specific properties of the underlined matrix group. The considered problem is reduced in probabilistic polynomial time to the similar problem in small extensions of the underlined field.