A lattice-based signcryption scheme without random oracles

In order to achieve secure signcryption schemes in the quantum era, Li Fagen et al. [Concurrency and Computation: Practice and Experience, 2012, 25(4): 2112–2122] and Wang Fenghe et al. [Applied Mathematics & Information Sciences, 2012, 6(1): 23–28] have independently extended the concept of signcryption to lattice-based cryptography. However, their schemes are only secure under the random oracle model. In this paper, we present a lattice-based signcryption scheme which is secure under the standard model. We prove that our scheme achieves indistinguishability against adaptive chosen-ciphertext attacks (IND-CCA2) under the learning with errors (LWE) assumption and existential unforgeability against adaptive chosen-message attacks (EUFCMA) under the small integer solution (SIS) assumption.