Security of the GPT cryptosystem and its applications to cryptography

Abstract

Abstract The public key cryptosystem (PKC) based on rank error correcting codes (the GPT cryptosystem) was proposed in 1991. 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. Several attacks against this system were published, including Gibson's attacks and more recently Overbeck's attacks. A few modifications were proposed withstanding Gibson's attack but at least one of them was broken by the stronger attacks by Overbeck. A tool to prevent Overbeck's attack is presented by Gabidulin, which makes the cryptographer define a proper column scrambler matrix over the extension field without violating the standard mode of GPT cryptosystem. In this paper, we apply this tool to another variant of the GPT cryptosystem. Furthermore we increase the security of the proposed system against all known attacks and reduce the public key size to 4 Kbits instead of 10 Kbits. Copyright © 2010 John Wiley & Sons, Ltd.