Lattice-based Strong Designate Verifier Signature and Its Applications

Abstract

Motivated by the need to have secure strong designate verifier signatures (SDVS) even in the presence of quantum computers, a post-quantum lattice-based SDVS scheme is proposed based on the hardness of the short integer solution problem (SIS) and the learning with errors problem (LWE). The proposed SDVS scheme utilizes the Bonsai trees and pre-image sample-able function primitives to generate the designate verifier signature (DVS). In this construction, the un- forge-ability is based on the hardness of the SIS problem which is proven in the random oracle model and the non-transferability is based on the hardness of the LWE problem. As an application of the proposed SDVS scheme, we design a strong designate verifier ring signature scheme (SDVRS) which satisfies non-transferability. It is proven that the identity of the signer is unconditionally protected not only for any third-party but also for the designate verifier. Under the hardness of the SIS problem, the proposed SDVRS scheme is proven to be existentially un-forgeable in the random oracle model.