Attacking the Niederreiter-type cryptosystem based on rank metric

Abstract

This paper deals with the Niederreiter cryptosystem based on Gabidulin codes which were solidly broken by Overbeck within polynomial time. In this paper, we first review the conditions under Overbeck's attack applications and then adjust corresponding parameters to target a high-security level. Since the permutation matrix and the scrambling matrix are used in Gabidulin codes, then the Frobenius matrices have too much structure to be hidden. By analysing the rank of the system matrix, we can find that choosing the matrix such that the dimension of the kernel of the public parity-check matrix greater than one will achieve a good result. In addition, we also show that bounding the rank of the distortion matrix is to enhance the security of the system. Finally, we give the security analysis of the modified Niederreiter type cryptosystem and demonstrate that it can resist structural and decoding attacks.