An efficient lattice-based proxy signature with message recovery

Proxy signature scheme is an important cryptographic primitive in which an entity can delegate its signing rights to another entity, the purpose of proxy signature with message recovery is to shorten the length of proxy signatures which can effectively reduce the communication overhead. Although message recovery proxy signature scheme based on conventional number-theoretic problems has been proposed for a long time, the message recovery technique draws no attention to proxy signature scheme from lattice. In this paper, we firstly propose a proxy signature scheme with message recovery from lattice which is more efficient than previous proxy signature schemes in signature size, time and energy cost, and we prove that in the random oracle, our scheme is secure model under the hardness assumption of SIS. Our proxy signature scheme with message recovery would work well in the quantum age based on the underlying lattice problems.