Polynomial multipliers for fully homomorphic encryption on FPGA

Fully Homomorphic Encryption (FHE) becomes an important encryption scheme in the frame of Cloud computing. Current software implementations are however very slow and require a huge computing power. This work investigates the possibility to accelerate FHE by implementing it in off-the-shelf FPGAs. The focus is on one critical function in the FHE scheme: the polynomial multiplication. In this paper, three algorithms are considered and an optimized architecture is proposed for each of them. The major contribution of this paper is the comparison of the different multiplication algorithms on a programmable device: results show that the simplest algorithm is the most efficient for a hardware implementation, in the case of polynomials of order 511 with 32-bit coefficients. The acceleration is about one order of magnitude compared with a software reference implementation.