Enhancing the Security of the GPT Cryptosystem Against Attacks

Abstract

The concept of Public key cryptosystems based on error correcting codes was invented by McEliece in 1978. In 1991 Gabidulin, Paramonov and Tretjakov proposed a new mversion of the McEliece cryptosystem (GPT) based on maximum rank distance codes instead of hamming distance codes. Respective structural attacks against dierent variants of the GPT cryptosystem were proposed by Gibson and lately by Overbeck. The Overbeck attack breaks all variants of the GPT cryptosystem and are turned out to be either polynomial or exponential depending on parameters of the cryptosystem. Furthermore, In 2013, Gaborit et al. have presented a decoding attack against the parameters of the simple variant of the GPT cryptosystem which were demonstrated to combat the GPT cryptosystem against Overbeck's attack. In this paper, we introduce two new secure approaches against both the structural (Over-beck's attack) and decoding (brute force) attacks. The rst one is called Distortion Matrix Approach (DMA), and the second is called Advanced Approach for Reducible Rank Codes (ARC). The DMA based on proper choice of a distortion matrix X, while, the ARC based on a proper choice of a scramble matrix P. Furthermore, we evaluate the simple variant of GPT cryptosystem against Gaborit et al. attack and demonstrate a new set of parameters which are secure against all known attacks. Our results show the proposed approaches com- bat the structural and decoding attacks with a large reduction in the key size in comparison to the original McEliece cryptosystem.