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The designated verifier signature (DVS), introduced by Jakobsson <italic>et al.</italic>, 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 <italic>et al.</italic>, 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 <inline-formula> <tex-math notation="LaTeX">$\mathcal {R}-$ </tex-math></inline-formula>SIS<inline-formula> <tex-math notation="LaTeX">$_{q,n,m,\beta }$ </tex-math></inline-formula>, which is at least as hard as worst-case SVP<inline-formula> <tex-math notation="LaTeX">$_{\gamma }$ </tex-math></inline-formula> 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.