Modified Niederreiter type of GPT cryptosystem based on reducible rank codes

Abstract

GPT public key cryptosystem was proposed by Gabidulin, Paramonov and Tretjakov in 1991. This cryptosystem is based on rank error correcting codes. The main advantage of using rank codes in cryptography is that, it has smaller key size as compared to other code based public key cryptosystems. Several attacks against this system were published and some modifications were also proposed withstanding these attacks. In this paper, we have proposed a modified Niederreiter type GPT cryptosystem based on reducible rank codes by properly choosing the column scrambler matrix to withstand these attacks. Although, the idea of choosing column scrambler matrix from extension field is not new but the approach proposed in this paper, provides more elements of column scrambler matrix from extension field as compared to any previous modifications which makes system more secure against attacks.