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

Abstract: A 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.