Cryptanalysis of the CFVZ cryptosystem

TL;DR

This paper critically analyzes the security of the CFVZ cryptosystem, revealing that its difficulty is comparable to solving a single discrete logarithm problem on an elliptic curve, thus questioning its robustness.

Contribution

It provides a cryptanalysis demonstrating that the CFVZ cryptosystem's security reduces to solving a small number of elliptic curve discrete logarithm problems, challenging its presumed security.

Findings

The problem is as hard as a single elliptic curve discrete logarithm problem.

An adapted Pollard rho algorithm effectively solves the underlying problem.

The cryptosystem's security assumptions are weakened by this analysis.

Abstract

The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system is dominated by the complexity of solving a fixed number of discrete logarithm problems in the group of an elliptic curve. Using an adapted Pollard rho algorithm it is shown that this problem is essentially as hard as solving one discrete logarithm problem in the group of an elliptic curve.