Extending Coggia-Couvreur Attack on Loidreau's Rank-metric Cryptosystem

TL;DR

This paper extends a known polynomial-time attack on Loidreau's rank-metric cryptosystem to cases where the defining subspace has higher dimension, revealing vulnerabilities for a broader set of parameters.

Contribution

It generalizes the Coggia-Couvreur attack to subspaces of dimension greater than 2, broadening the scope of cryptanalysis on Loidreau's scheme.

Findings

Extended attack successfully targets larger subspace dimensions

Identified vulnerabilities in Loidreau's cryptosystem for new parameter ranges

Demonstrated the attack's effectiveness through theoretical analysis

Abstract

A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau's encryption scheme, based on rank-metric codes, for some parameters. The secret matrix component of Loidreau's scheme is chosen over a defining subspace of the field associated with the rank-metric code. We partially extend the Coggia-Couvreur attack to deal with the case when the defining subspace has dimension greater than 2.