(Batch) Fully Homomorphic Encryption over Integers for Non-Binary Message Spaces

Abstract

In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space $$\mathbb {Z}_Q$$ for any prime $$Q$$ . Even for the binary case $$Q=2$$ , our decryption circuit has a smaller degree than that of the previous scheme; the multiplicative degree is reduced from $$O(\lambda (\log \lambda )^2)$$ to $$O(\lambda )$$ , where $$\lambda $$ is the security parameter. We also extend our FHE scheme to a batch FHE scheme.