Column scrambler for the GPT cryptosystem Original Research Article

In 1991, Gabidulin, Paramonov and Tretjakov presented a public key cryptosystem of the McEliece type based on rank codes correcting array errors, the GPT system. Making use of rank codes in cryptographic applications is advantageous since it is practically impossible to utilize combinatoric decoding. This enabled using public keys of a smaller size. Subsequently, in a series of works Gibson developed attacks that break the GPT system for public keys of about 5 Kbits. In this paper, we present a new PKC based on the idea of a column scrambler—a non-singular matrix by which the public key is multiplied to the right. The column scrambler ‘mixes’ columns of the public key. It makes system more resistant to structural attacks at a little extra cost of a few additional columns. Possible attacks are carefully studied. The system is found to be secure against known attacks for public keys greater than 10 Kbits.