Accelerating integer based fully homomorphic encryption using frequency domain multiplication

Abstract

In this paper, the hardware implementation of Integer based Fully Homomorphic Encryption (FHE) is investigated. A new methodology is proposed to speed up the encryption process by optimizing the very large asymmetric multiplications required. A frequency domain approach is adopted for the multiplication using the Number Theoretic Transforms (NTTs) where the strict relationship between the NTT parameters is relaxed to allow for more optimized hardware implementations on FPGA. This is achieved specifically by relaxing the traditional requirement for a simple transform kernel in favour of optimal transform lengths and moduli in terms of the number of overall iterations, suitable data path, and FPGA architecture. It is shown both analytically and via implementation results that the proposed approach yields faster FHE over the integers implementations. Based on the methodology, a proposed hardware architecture with optimized NTT parameters synthesized on Xilinx Kintex-7 FPGA shows 55% and 76% speed improvement for Medium and Large key sizes respectively.