The security of the gabidulin public key cryptosystem

Abstract

The Gabidulin Public Key Cryptosystem (PKC), like the well known McEliece PKC, is based on error correcting codes, and was introduced as an alternative to the McEliece system with the claim that much smaller codes could be used, resulting in a more practical system. In this paper an attack on the Gabidulin PKC is given which breaks it for codes of the size envisaged, destroying much of its advantage over the McEliece system. The attack succeeds in polynomial time for Gabidulin’s choice of one of his system parameters, but it does show how to choose this parameter more appropriately. It consists of a reduction of the de- cryption problem for the Gabidulin PKC to consideration of a search problem that is easier to describe, and which with luck should be easier to analyse. It therefore provides a possible starting point for a proof that decryption for the Gabidulin PKC is an N P-complete problem.