Jacobian坐标系下椭圆曲线底层域算法的研究  

Study on the Methods of Field Operations in Jacobian Coordinates on Elliptic Curves

作　　者：赖忠喜[1] 张占军[1] 

机构地区：[1]台州职业技术学院机电工程学院,浙江台州318000

出　　处：《科技通报》2015年第10期244-248,共5页Bulletin of Science and Technology

基　　金：台州职业技术学院重点课题(2014ZD03)

摘　　要：为提高椭圆曲线底层域运算的效率,利用除法多项式和将乘法运算转换为平方运算的思想,提出了素数域GFP雅克比坐标系下一种计算7P和7kP的算法,其运算量分别为16M+15S和(16k-1)M+(14k+3)S,当S/M=0.6时,新算法的效率比传统算法和Longa算法分别提高了29.8%、31.5%、1.6%和3.9%。另外,利用相同的思想,给出了素数域GFP上用雅克比坐标系计算5P和5kP的改进算法,其运算量分别为9M+15S和(9k-1)M+(14k+3)S,当S/M=0.6时,新算法的效率比MISHRA算法和Longa算法分别提高了14.3%、14.7%、6.3%和9.4%。To raise the efficiency of field operations on elliptic curve , based on the division polynomials and the idea of trading multiplications for squares, two algorithms are proposed to compute 7P and 7kP directly over GFP in terms of jacobian coordinates, their computational complexity are 16M+15S and (16k-1)M+(14k+3)S respectively, when S/M=0.6, the new algorithm's efficiency are increased by 29.8%、31.5%、1.6%and 3.9%respectively compared with traditional and Longa 's algorithms. Moreover, using the same idea, two improved methods are given to compute 5P and 5kP over GFP in terms of jacobian coordinates, their computational complexity are 9M+15S and (9k-1)M+(14k+3)S, when S/M=0.6, the efficiency of the new methods are improved by 14.3%、14.7%、6.3%and 9.4%respectively compared with MISHRA 's and Longa 's methods.

关 键 词：椭圆曲线密码体制 标量乘法 平方 底层域运算 雅克比坐标 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]