Lattice-Based Signcryption Without Random Oracles

Signcryption is a scheme that achieves both functionalities of public key encryption and digital signatures, and hence it is an important and fundamental protocol in cryptography. On the other hand, it is interesting to efficiently construct a signcryption scheme based on lattice-based problems, since lattice-based construction is expected to have resistance against quantum computing. The contribution of this paper is to construct an efficient lattice-based signcryption satisfying strong security without random oracles. We propose such a construction based on the problems of the learning with errors (LWE) and small integer solution (SIS). The public-key size and ciphertext size in our construction are shorter than any other schemes, and there is no disadvantage for ours in other parameters compared to other ones in terms of public/secret-key and ciphertext sizes.