An Efficient Strong Designated Verifier Signature Based on $\mathcal{R}-$ SIS Assumption

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.