A linear decomposition attack

TL;DR

This paper introduces a polynomial-time linear decomposition attack that can recover secret keys from several group-based cryptosystems, challenging the assumed security based on computational hardness.

Contribution

The paper presents a new linear decomposition attack that can break certain cryptosystems efficiently, questioning the reliance on traditional security assumptions.

Findings

The attack is effective on multiple group-based schemes.

Security assumptions may not guarantee scheme security.

The attack's success depends on the platform group.

Abstract

We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in all this schemes under consideration. Furthemore, we show that in this case, contrary to the common opinion, the typical computational security assumptions are not very relevant to the security of the schemes, i.e., one can break the schemes without solving the algorithmic problems on which the assumptions are based. The efficacy of the attack depends on the platform group, so it requires a more thorough analysis in each particular case.