Cryptanalysis of some protocols using matrices over group rings

TL;DR

This paper demonstrates that certain cryptographic protocols based on the presumed hardness of the discrete logarithm problem in matrix groups over group rings are vulnerable, allowing complete key recovery and protocol compromise.

Contribution

It provides a cryptanalysis showing the insecurity of protocols relying on matrices over group rings, revealing their vulnerability to key recovery attacks.

Findings

Protocols can be broken by finding secret keys.

Discrete logarithm problem in these groups is not sufficiently hard.

Complete protocol compromise is achievable.

Abstract

We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.