Further Generalisations of Twisted Gabidulin Codes

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.Comment: 10 pages, accepted at the International Workshop on Coding and Cryptography (WCC) 201

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

In the present article, we discuss the decoding of Gabidulin and related codes from a cryptographic perspective and we observe that these codes can be decoded with the single knowledge of a generator matrix. Then, we extend and revisit Gibson's and Overbeck's attacks on the generalised GPT encryption scheme (instantiated with Gabidulin codes) for various ranks of the distortion matrix and apply our attack to the case of an instantiation with twisted Gabidulin codes

Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.Comment: 5 pages, accepted at: IEEE International Symposium on Information Theory 201