椭圆曲线底层域快速算法的研究

计算机工程与应用 ›› 2014, Vol. 50 ›› Issue (3): 67-70.

椭圆曲线底层域快速算法的研究

赖忠喜，张占军，陶东娅

台州职业技术学院机电工程学院，浙江台州 318000

出版日期:2014-02-01 发布日期:2014-01-26

Study on fast method of field operation in elliptic curves

LAI Zhongxi, ZHANG Zhanjun, TAO Dongya

College of Mechanical and Electrical Engineering, Taizhou Vocational & Technical College, Taizhou, Zhejiang 318000, China

Online:2014-02-01 Published:2014-01-26

摘要/Abstract

摘要： 为了提高椭圆曲线底层域运算的效率，基于将求逆转换为乘法运算的思想，提出了在素数域[FP]上用仿射坐标直接计算4P和5P的快速算法，其运算量分别为I+7M+8S和I+12M+10S，与Duc-Phong和徐凯平等人所提的算法相比，效率分别提升了4.6%和2.6%。同时在仿射坐标下给出了一种直接计算[5kP]的快速算法，其运算量为[I+(15k+1)M+][(10k-1)S]，与徐凯平和Mishra等人所提的算法相比，效率分别提升了5.7%和26.8%。

关键词: 椭圆曲线密码体制, 标量乘法, 底层域运算, 仿射坐标, 求逆

Abstract: To raise the efficiency of field operation on elliptic curve, based on the idea of trading inversions for multiplications, two efficient algorithms are proposed to compute 4P and 5P directly over prime field [FP] in terms of affine coordinates. Their computational complexity are I+7M+8S and I+12M+10S respectively, which are improved to 4.6% and 2.6% respectively than those of Duc-Phong’s and Xu Kaiping’s method. Moreover, a fast method is given to compute [5kP] directly in terms of affine coordinates. Its computational complexity is [I+(15k+1)M+(10k-1)S,] and the efficiency of the new method is improved to 5.7% and 26.8% respectively than those of Xu Kaiping’s and Mishra’s method.

Key words: elliptic curve cryptosystem, scalar multiplication, field operation, affine coordinate, field inversion

赖忠喜，张占军，陶东娅. 椭圆曲线底层域快速算法的研究[J]. 计算机工程与应用, 2014, 50(3): 67-70.

LAI Zhongxi, ZHANG Zhanjun, TAO Dongya. Study on fast method of field operation in elliptic curves[J]. Computer Engineering and Applications, 2014, 50(3): 67-70.

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