Security of the GPT-Type Cryptosystems

The Gabidulin-Paramonov-Tretjakov (GPT) public-key cryptosystem and the GPT system with column scrambler, both based on Gabidulin codes, seem to have some advantages over McEliece´s public-key cryptosystems using Goppa codes. Since the parameters of the GPT-type systems affect the work factors of attacks in different fashions and determine the effectiveness of these attacks in some cases, we evaluate the security and study the choice of parameters of the GPT-type cryptosystems with respect to some well-known structural and decoding attacks jointly. The performances of the GPT system with column scrambler and the GPT system are compared with that of McEliece´s system