Optimal distortion parameter for the GPT public-key cryptosystem

The Gabidulin-Paramonov-Trejtakov (GPT) public-key cryptosystems, based on Gabidulin codes, seem to have some advantages over McEliece´s public-key cryptosystems using Goppa codes. In this paper we define the optimal distortion parameter for the GPT cryptosystem to be the distortion parameter that maximizes the workload of the best (structural or decoding) attack. The work factors achieved by the GPT cryptosystem using the optimal distortion parameter thus give the guaranteed level of security against any attack. We also show that under reasonable assumptions, the optimal distortion parameter always exists and is unique. Furthermore, we propose an algorithm that computes the optimal distortion parameter with low complexity