The cryptographic security of the syndrome decoding problem for rank distance codes

Abstract

We present an algorithm that achieves general syndrome decoding of a (n, k, r) linear rank distance code over GF((q m) in O(nr + m) 3 q (m−r)(r−1)) elementary operations. As a consequence, the cryptographical schemes [Che94, Che96] which rely on this problem are not secure with the proposed parameters. We also derive from our algorithm a bound on the minimal rank distance of a linear code which shows that the parameters from [Che94] are inconsistent.