HEPCloud: An FPGA-based Multicore Processor for FV Somewhat Homomorphic Function Evaluation

Abstract

In this paper, we present an FPGA based hardware accelerator ‘ $\mathsf{HEPCloud}$ ’ for homomorphic evaluations of medium depth functions which has applications in cloud computing. Our $\mathsf{HEPCloud}$ architecture supports the polynomial ring based homomorphic encryption scheme FV for a ring-LWE parameter set of dimension $2^{15}$ , modulus size 1,228-bit, and a standard deviation 50. This parameter-set offers a multiplicative depth 36 and at least 85 bit security. The processor of $\mathsf{HEPCloud}$ is composed of multiple parallel cores. To achieve fast computation time for such a large parameter-set, various optimizations in both algorithm and architecture levels are performed. For fast polynomial multiplications, we use CRT with NTT and achieve two dimensional parallelism in $\mathsf{HEPCloud}$ . We optimize the BRAM access, use a fast Barrett like polynomial reduction method, optimize the cost of CRT, and design a fast divide-and-round unit. Beside parallel processing, we apply pipelining strategy in several of the sequential building blocks to reduce the impact of sequential computations. Finally, we implement $\mathsf{HEPCloud}$ on a medium-size Xilinx Virtex 6 FPGA board ML605 board and measure its on-board performance. To store the ciphertexts during a homomorphic function evaluation, we use the large DDR3 memory of the ML605 board. Our FPGA-based implementation of $\mathsf{HEPCloud}$ computes a homomorphic multiplication in 26.67 s, of which the actual computation takes only 3.36 s and the rest is spent for off-chip memory access. It requires about 37,551 s to evaluate the SIMON-64/128 block cipher, but the per-block timing is only about 18 s because $\mathsf{HEPCloud}$ processes 2,048 blocks simultaneously. The results show that FPGA-based acceleration of homomorphic function evaluations is feasible, but fast memory interface is crucial for the performance.