Cryptanalysis of a new version of the MOR scheme

TL;DR

This paper demonstrates an efficient linear decomposition attack on a new version of the MOR cryptographic scheme, revealing vulnerabilities and providing a general method applicable to various matrix groups over fields.

Contribution

It introduces a generalized linear decomposition attack applicable to the new MOR scheme and clarifies inaccuracies in its description.

Findings

The attack can efficiently break the new MOR scheme.

The method applies to different matrix groups over arbitrary fields.

Automorphism exponents can be computed using linear transformations.

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.