密码学报（中英文）2025，Vol.12Issue(6)：1211-1225,15.DOI:10.13868/j.cnki.jcr.000820
BFV全同态加密算法的FPGA快速实现
Fast Implementation of BFV Fully Homomorphic Encryption Algorithm on FPGA
摘要
Abstract
Compared to traditional fully homomorphic encryption(FHE)algorithms,the com-putational efficiency of the BFV algorithm has become relatively favorable.Nevertheless,during the computation process,the BFV encryption system inevitably introduces significant computational overhead.To enhance the computational efficiency of the BFV FHE algorithm on FPGA hardware platforms effectively,the conventional implementation of the BFV algorithm is analyzed,and a novel method based on a 4K-point number theoretic transform(NTT)is proposed to accelerate BFV poly-nomial multiplication.By utilizing the NTT algorithm for fast large number modular multiplication,the computational implementation efficiency on the FPGA platform for the algorithm is improved effectively.Through testing and analysis,it is demonstrated that the conventional BFV algorithm can be correctly implemented under various parameters recommended by the simple encrypted arithmetic library(SEAL).The error accumulation speed under different parameters is consistent with expecta-tions.The FPGA fast implementation scheme of the BFV algorithm based on NTT achieves a 5.01-fold improvement in computational speed over the conventional FPGA implementation and a 29.94-fold improvement compared to the software implementation of the BFV algorithm in the SEAL.The time for a single polynomial modular multiplication in this testing is 17.24 microseconds under a 100 MHz clock,which represents a 56％improvement in computational efficiency compared to the NTT core implemented by Tian et al.through low-latency pipelined arithmetic logic.Furthermore,compared to the optimized hardware implementation by Shakirah et al.that relaxes the strict relationship between NTT parameters,the proposed scheme achieves a 29.8％improvement in computational efficiency.关键词
BFV算法/全同态加密/FPGA实现/SEAL库/NTT算法/硬件加速Key words
BFV algorithm/fully homomorphic encryption/field programmable gate array imple-mentation/SEAL Library/number theoretic transforms algorithm/hardware acceleration分类
信息技术与安全科学引用本文复制引用
杨亚涛,王在舟,曹景沛,陈亮宇..BFV全同态加密算法的FPGA快速实现[J].密码学报（中英文）,2025,12(6):1211-1225,15.基金项目
北京市自然科学基金(4232034) （4232034）
中央高校基本科研业务费(3282025039,3282024058) （3282025039,3282024058）
国家自然科学基金(62476013)Beijing Municipal Natural Science Foundation(4232034) （62476013）
the Fundamental Research Funds for the Central Universities of China(3282025039,3282024058) （3282025039,3282024058）
National Natural Science Foundation of China(62476013) （62476013）
