## Cryptology ePrint Archive: Report 2014/777

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

Koji Nuida and Kaoru Kurosawa

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

Category / Keywords: public-key cryptography / Fully homomorphic encryption, non-binary message