An Efficient Strong Designated Verifier Signature Based on <inline-formula> <tex-math notation="LaTeX">$\mathcal{R}-$ </tex-math> </inline-formula>SIS Assumption

Abstract

The designated verifier signature (DVS), introduced by Jakobsson et al. , has the property that only the designated verifier can verify the generated signature. In order to prevent an eavesdropper to get the signature on-line before the designated verifier receives it, they also proposed strong designated verifier signature (SDVS). In this paper, according to an efficient SDVS proposed by Saeednia et al. , we present a post-quantum SDVS in the random oracle model based on lattice assumption. The unforgeability is based on the hardness of the average-case hard problem $\mathcal {R}-$ SIS $_{q,n,m,\beta }$ , which is at least as hard as worst-case SVP $_{\gamma }$ over ideal lattices. In addition, compared with existing lattice-based SDVS schemes, our scheme cuts by more than 50 percent repetitions and the size of signature is shorter with 256 bits security.