  A signcryption, which is an integration of a public key encryption and a
digital signature, can provide confidentiality and authenticity simultaneously.
Additionally, a signcryption associated with equality test allows a third party
(e.g., a cloud server) to check whether or not two ciphertexts are encrypted
from the same message without knowing the message. This application plays an
important role especially in computing on encrypted data. In this paper, we
propose the first lattice-based signcryption scheme equipped with a solution to
testing the message equality in the standard model. The proposed signcryption
scheme is proven to be secure against insider attacks under the learning with
errors assumption and the intractability of the short integer solution problem.
As a by-product, we also show that some existing lattice-based signcryptions
either is insecure or does not work correctly.
