Decoding Supercodes of Gabidulin Codes and Applications to Cryptanalysis

Error correcting codes are well known to provide possible candidates for building quantum safe cryptographic primitives. Besides the Hamming metric which has a long-standing history, one may consider other metrics such as the rank metric. Gabidulin codes are the rank metric analogue of Reed-Solomon codes and can be efficiently decoded up to half the minimum distance. However, beyond this radius, they are believed to be difficult to decode. Based on this hard problem, in 2005 Faure and Loidreau designed an encryption scheme with small public keys. In 2016 though, this scheme was subject to a very efficient key recovery attack by Gaborit, Otmani and Talé-Kalachi. More recently, two independent repairs of Faure-Loidreau scheme resisting the previous attack appeared. The first one, due to Renner, Puchinger and Wachter-Zeh is called LIGA, and the second one due to Lavauzelle, Loidreau and Pham is called RAMESSES.

In this talk, I will present how to decode any code extending the Gabidulin codes, at the cost of a significant decrease of the decoding radius, and show how this decoder can be used to provide an efficient message recovery attack on LIGA and RAMESSES.

This is joint work with Alain Couvreur.