An extension of Overbeck’s attack with an application to cryptanalysis of Twisted Gabidulin-based schemes

In this talk, I will discuss the decoding of Gabidulin and related codes from a cryptographic point of view, pointing out that these codes can be decoded solely from the knowledge of a generator matrix. I will also present an extension of Gibson and Overbeck attacks on the generalized GPT encryption scheme (instantiated with the Gabidulin code) for different ranks of the distortion matrix. Finally we will see how we can apply this attack to the case of an instantiation with twisted Gabidulin codes. This is a joint work with Alain Couvreur.