An analysis of Coggia-Couvreur attack on Loidreau's rank-metric public key encryption scheme in the general case

TL;DR

This paper extends the Coggia-Couvreur attack to Loidreau's rank-metric encryption scheme, demonstrating that the attack can recover secret keys in polynomial time when the masking vector space has dimension 3, under certain distinguishability conditions.

Contribution

It generalizes the Coggia-Couvreur attack to broader cases of Loidreau's scheme and links distinguishability of the public key to successful key recovery.

Findings

Attack can recover secret key in polynomial time for dimension 3

Distinguishability of public key implies vulnerability

Extends previous attack results to more general cases

Abstract

In this paper we show that in the case where the public-key can be distinguished from a random code in Loidreau's encryption scheme, then Coggia-Couvreur attack can be extended to recover an equivalent secret key. This attack can be conducted in polynomial-time if the masking vector space has dimension 3, thus recovering the results of Ghatak.