Lattice-based linearly homomorphic signatures in the standard model

At present, there are some linearly homomorphic signatures in the standard model, whose security is based on the RSA assumption and Diffie–Hellman assumption. But there are still no lattice-based linearly homomorphic signature in the standard model. How to construct it? It is proposed as a open problem by Freeman [12]. In this paper, we propose the first lattice-based linearly homomorphic signature in the standard model, which settle this open problem.