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J. Hefei Univ. Tech. (Nat. Sci.)

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

Competent Authorities: Ministry of Education of the People's Republic of China

Sponsor by: Hefei University of Technology

ISSN 1000-1646, CN 34-1001/N

Efficient FPGA implementation of Curve25519 point multiplication algorithm

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Curve25519 点乘算法的高效 FPGA 实现

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Nov.2024, Vol.47 No.11: 1493-1497, 1504

DOI: 10.3969/j.issn.1003-5060.2024.11.009

Authors

HU Yue, XIAO Hao, ZHAO Yanrui, LIU Xiaofan

(School of Microelectronics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: 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 125 $ \mu $s 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.

Keywords: field programmable gate array (FPGA); elliptic curve; Curve25519; point multiplication; modular multiplication

作者信息

胡越，肖昊，赵延睿，刘笑帆

（合肥工业大学微电子学院，安徽合肥230601）

摘要和关键词

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 $ 125 \mu s $。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。

关键词: 现场可编程门阵列(FPGA)；椭圆曲线；曲线 Curve25519；点乘；模乘

Funding

国家自然科学基金资助项目（61974039）

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