Structural cryptanalysis of McEliece schemes with compact keys

A very popular trend in code-based cryptography is to decrease the public-key size by focusing on subclasses of alternant/Goppa codes which admit a very compact public matrix, typically quasi-cyclic (QC), quasi-dyadic (QD), or quasi-monoidic (QM) matrices. We show that the very same reason which allows to construct a compact public-key makes the key-recovery problem intrinsically much easier. The gain on the public-key size induces an important security drop, which is as large as the compression factor p on the public-key. The fundamental remark is that from the k × n public generator matrix of a compact McEliece, one can construct a k/p × n/p generator matrix which is – from an attacker point of view – as good as the initial public-key. We call this new smaller code the folded code. Any key-recovery attack can be deployed equivalently on this smaller generator matrix. To mount the key-recovery in practice, we also improve the algebraic technique of Faug`ere, Otmani, Perret and T...

• Type: Journal
• Year: 2016
• Where: DCC
• Authors: Jean-Charles Faugère, Ayoub Otmani, Ludovic Perret, Frédéric de Portzamparc, Jean-Pierre Tillich
• Keywords: Computer Graphics, DCC 2016