Fast RNS Implementation of Elliptic Curve Point Multiplication on FPGAs

作     者：Wu, Tao 

作者机构：Sun Yat Sen Univ Shenzhen Res Inst Yuehai Rd Shenzhen 518057 Guangdong Peoples R China 

出 版 物：《JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY》 (J. Signal Process Syst.)

年 卷 期：2024年第96卷第11期

页      面：673-684页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：2019 Guangzhou Innovation and Entrepreneurship Leader Team Guangzhou Innovation and Entrepreneurship Leader Team 

主　　题：Residue number system Elliptic curve cryptography Montgomery algorithm 

摘      要：Elliptic curve cryptography is the second most important public-key cryptography following RSA cryptography. The fundamental arithmetic of elliptic curve cryptography is a series of modular multiplications and modular additions. Usually, Montgomery algorithm is applied for modular multiplications over large integers to reduce the computational complexity. Targeting at fast elliptic curve point multiplication over prime fields a new approach in residue number system is proposed. Compared with other implementations that apply Montgomery ladder for parallel elliptic curve point multiplication, the proposed method uses a residue number system with a wide dynamic range, which supports continuous multiplications and needs only one RNS Montgomery multiplication to bring down the temporary results to valid range. Hardware implementation results demonstrate that the computation time for elliptic curve point multiplication over Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_p$$\end{document} can be greatly reduced, and it takes about 0.677 ms to compute one time of elliptic curve point multiplication over 384-bit prime curves in Xilinx XC6VSX475t device, costing an area of 41409 slices, 676 DSPs and 138 Brams.