Curve25519点乘算法的高效FPGA实现  

Efficient FPGA implementation of Curve25519 point multiplication algorithm

作　　者：胡越 肖昊 赵延睿 刘笑帆 HU Yue;XIAO Hao;ZHAO Yanrui;LIU Xiaofan(School of Microelectronics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学微电子学院,安徽合肥230601

出　　处：《合肥工业大学学报（自然科学版）》2024年第11期1493-1497,1504,共6页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(61974039)。

摘　　要：为了提高X25519密钥交换算法的运算效率,文章基于现场可编程门阵列(field programmable gate array,FPGA)提出一种高效的曲线Curve25519的点乘设计方案。首先在底层的有限域计算上,针对模约减计算次数多的问题,提出一种基于冗余数的模运算单元,减少了约减次数;同时,所提出的结构可以减少点乘中常系数乘法的运算周期,从而优化了点乘运算通路,提高了并行度,最终减少了运算时间。该文在Xilinx XC7Z020 FPGA上实现了该点乘设计方案,完成一次点乘需要125μs。研究结果表明,与现有的设计相比,所提出的方案具有较低的面积时间积,达到了面积和性能的平衡。In order to improve the computational efficiency of X25519 key exchange algorithm,this paper proposes an efficient point multiplication design scheme of Curve25519 based on field programmable gate array(FPGA).Firstly,on the bottom level of the finite field calculation,a modular arithmetic unit based on redundant numbers is proposed to reduce the number of reduction calculation.At the same time,the proposed structure can reduce the operation cycle of constant coefficient multiplication in point multiplication,thus optimize the path of point multiplication,improve the parallelism,and finally reduce the operation time.The design scheme of point multiplication is implemented on Xilinx XC7Z020 FPGA,it takes 125μs to complete a point multiplication.The results show that the proposed scheme has a lower area-time product than existing implementations,achieving a balance between area and performance.

关 键 词：现场可编程门阵列(FPGA) 椭圆曲线 曲线Curve25519 点乘 模乘 

分 类 号：TN918.1[电子电信—通信与信息系统]