Cryptanalysis of the Rank Preserving Signature

Abstract

In code-based cryptography, the rank metric usually allows one to have smaller keys and signatures than the traditional Hamming metric. Recently, a new rank-based signature was proposed: Durandal [4]. It relies on the use of proofs of knowledge, namely the Schnorr-Lyubashevsky approach. The authors of the Rank Preserving Signature (RPS) [9] built upon this approach and proposed even smaller keys and signatures than Durandal.

In this paper, we describe attacks against the RPS scheme which break all sets of parameters proposed in [9].

More precisely, our attacks enable us to forge valid signatures in $2^{68}$ and $2^{47}$ operations for sets of parameters whose claimed securities are, respectively, 128 and 192 bits. In addition to this, we give a quantum adaptation of our attack which yields an attack on the last two sets of parameters given in [9].

Overall, our attacks highlight weaknesses of the RPS scheme and give new constraints when designing new parameter sets.

In order to describe the complexities of our attacks, this paper contains theoretical arguments together with experimental results for which we give the source code of our programs.