(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 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(λ(log λ) 2) to O(λ), where λ is the security parameter. We also extend our FHE scheme to a batch FHE scheme.