Paper 2013/624

New Integer-FFT Multiplication Architectures and Implementations for Accelerating Fully Homomorphic Encryption

Xiaolin Cao and Ciara Moore

Abstract

This paper proposes a new hardware architecture of Integer-FFT multiplier for super-size integer multiplications. Firstly, a basic hardware archi-tecture, with the feature of low hardware cost, of the Integer-FFT multiplication algorithm using the serial FFT architecture, is proposed. Next, a modified hardware architecture with a shorter multiplication latency than the basic archi-tecture is presented. Thirdly, both architectures are implemented, verified and compared on the Xilinx Virtex-7 FPGA platform using 256, 512, 1024, 2048 and 8192 point Integer-FFT algorithm respectively with multiplication operands ranging from bits to bits in size. Experimental results show that the hardware cost of the proposed architecture is no more than 1/10 of the prior FPGA solution, and is perfectly within the implementable range of the Xilinx Virtex-7 FPGA platform, and outperforms the software implementations of the same bit-length operand multiplication on the Core-2 Q6600 and Core-i7 870 platforms. Finally, the proposed implementations are employed to evaluate the super-size multiplication in an encryption primitive of fully homomorphic en-cryption (FHE) over the integers. The analysis shows that the speed improve-ment factor is up to 26.2 compared to the corresponding integer-based FHE software implementation on the Core-2 Duo E8400 platform.