A Publicly Verifiable Leveled Fully Homomorphic Signcryption Scheme

With the deepening of research, how to construct a fully homomorphic signcryption scheme based on standard assumptions is a problem that we need to solve. For this question, recently, Jin et al. proposed a leveled fully homomorphic signcryption scheme from standard lattices. However, when verifying, it is supposed to unsigncrypt first as they utilize sign-then-encrypt method. This leads to users being unable to verify the authenticity of the data first, which resulting in the waste of resources. This raises another question of how to construct an fully homomorphic signcryption (FHSC) scheme with public verifiability. To solve this problem, we propose a leveled fully homomorphic signcryption scheme that can be publicly verified and show its completeness, IND-CPA security, and strong unforgeability.