An improved Durandal signature scheme

Abstract

Constructing secure and effective code-based signature schemes has been an open problem. In this paper, we efficiently reduce the key size of the Durandal signature scheme introduced by Aragon et al. (EUROCRYPT 2019). We prove that the improved scheme is EUF-CMA secure by reducing its security to the advanced product spaces subspaces indistinguishability ($\rm{PSSI}^+$) problem, the decisional rank syndrome decoding (DRSD) problem, and the affine rank syndrome decoding (ARSD) problem under the random oracle model. Furthermore, our signature scheme is more secure than the Durandal scheme because recovering key attacks are equivalent to solving the rank syndrome decoding (RSD) problem, instead of the rank support learning (RSL) problem in the original Durandal scheme. Our signature scheme takes less time to generate a signature owing to the fact that our signature scheme enjoys smaller security parameters in comparison to the Duradual scheme. We compare the new scheme with existing code-based signature schemes and find that our signature scheme has advantages in terms of the public key size.