Leveled Fully Homomorphic Signcryption From Lattices

With the continuous and rapid development of Cloud Computing, Big Data and Internet of Things, it is extremely critical to protect data with homomorphism, privacy and integrity. For this, Rezaeibagha et al. proposed a new cryptographic primitive, called homomorphic signcryption. However, the current homomorphic signcryption schemes either only support linear computation or are built on non-standard assumption. Therefore, it is interesting to design a leveled fully homomorphic signcryption (FHSC) scheme from the standard assumption. In this work, we present a leveled FHSC scheme from lattices. For this, we exert classical sign-then-encrypt method and surmount the difficulty of homomorphic multiplicative evaluation in the way of encrypting every elements. Moreover, we prove its indistinguishability against chosen plaintext attacks (IND-CPA) and strong unforgeability (SUF) under hard problems of standard lattices.