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

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