International Association
for Cryptologic Research

A fully homomorphic encryption (FHE) scheme is envisioned as being a key cryptographic tool in building a secure and reliable cloud computing environment, as it allows arbitrarily evaluation of a ciphertext without revealing the plaintext. However, existing FHE implementations remain impractical due to their very high time and resource costs. Of the proposed schemes that can perform FHE to date, a scheme known as FHE over the integers has the ad-vantage of comparatively simpler theory, as well as the employment of a much shorter public key making its implementation somewhat more practical than other competing schemes.

To the author\'s knowledge, this paper presents the first hardware implemen-tations of encryption primitives for FHE over the integers using FPGA technol-ogy. First of all, a super-size hardware multiplier architecture utilising the Inte-ger-FFT multiplication algorithm is proposed, and a super-size hardware Barrett modular reduction module is designed incorporating the proposed multiplier. Next, two encryption primitives that are used in two schemes of FHE over the integers are designed employing the proposed super-size multiplier and modular reduction modules. Finally, the proposed designs are implemented and verified on the Xilinx Virtex-7 FPGA platform. Experimental results show that the speed improvement factors of up to 44.72 and 54.42 are available for the two FHE encryption schemes implemented in FPGA when compared to the corresponding software implementations. Meanwhile, the performance analysis shows that further improvement is speed of these FHE encryption primitives may still be possible.