Lattice-Based Universal Designated Verifier Signatures

Universal designated verifier signatures can be used to resolve the conflict between authenticity and privacy in some applications. However, all of existing constructions for this primitive are based on hard problems in number theory, and will be ultimately broken in quantum era. To address this issue, we construct the first lattice-based universal designated verifier signatures as a post-quantum candidate for this primitive. Our construction is obtained by directly extending a ring-based variant of the Gentry-Peikert-Vaikuntanathan signature scheme with some additional algorithms, thus the existing key generation and signing implementation can be used without modification. We also show that our construction is provably secure under the Small Integer Solution problem over rings, in the random oracle model.