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

In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space 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.