Dual-field Modular Multiplication Algorithm and Modular Inversion Algorithm with VLSI Implementation

Hankerson D, Menezes A, and Vanstone S. Guide to Elliptic Curve Cryptography. New York: Springer Verlag New York Inc, 2004: 25-147.[2]Savas E and Koc C K. A scalable and unified multiplier architecture for finite fields GF(P) and GF(2m). Cryptographic Hardware and Embedded Systems(CHES) 2000, Worcester, MA, USA, Augst 17-18, 2000: 277-292.[3]Chiou C W, Lee C Y, and Lin J M. Unified dual-field multiplier in GF(P) and GF(2k)[J].Information Security.2009, 3(2):45-52[4]Wang Jian and Jiang An-ping. A high-speed dual field arithmetic unit and hardware implementation, ASICON'07, Guilin, China, Oct. 22-25, 2007: 213-216.[5]Ma Shi-wei, Hao Yuan-ling, and Pan Zhong-qiao. Fast implementation for modular inversion and scalar multiplication in the elliptic curve cryptography, IITA '08, Beijing, China, Dec. 20-22, 2008: 488-492.[6]Yan Xiao-dong and Li Shu-guo. Modified modular inversion algorithm for VLSI implementation, ASICON'07, Guilin, China, Oct. 22-25, 2007: 90-93.[7]Shieh M D, Chen J H, and Lin W C. A new algorithm for high-speed modular multiplication design[J].Circuits and Systems.2009, 56(9):2009-2019[8]Hussin R, Shakaff A Y M, and Idris N. An efficient modified Booth multiplier architecture electronic design, ICED'08, Beijing, China, Dec. 1-3, 2008: 1-4.[9]Nibouche O, Nibouche M, and Bouridane A. New iterative algorithm for modular multiplication, ICECS 2001, St. Julians. Malta, Sept. 2-5, 2001: 879-882.[10]王健. 椭圆曲线加密体制的双有限域算法及其硬件实现. [博士论文], 北京大学, 2008.[11]Wang Jian. A dual-field algorithm for elliptic curve cryptosystem and its hardware implementation. [Ph.D. dissertation], Peking University, 2008.