椭圆曲线底层域快速算法的优化  

Optimizing fast field operation in 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：《计算机工程与应用》2015年第22期115-118,共4页Computer Engineering and Applications

基　　金：浙江省教育厅科研项目资助(No.Y201533946)

摘　　要：为了提高椭圆曲线底层域运算的效率,基于将乘法转换为平方运算的思想,提出在素数域FP上用雅克比坐标直接计算2kP和3kP的改进算法,其运算量分别为(3k-1)M+(5k+3)S和(6k-1)M+(9k+3)S,与DIMITROY和周梦等人所提的算法相比,算法效率分别提升了6.25%和5%。另外,利用相同的原理,给出了素数域FP上用在仿射坐标系直接计算3kP的改进算法,其运算量为I+(6k+1)M+(9k+1)S,与周梦和殷新春等人所提的算法相比,效率分别提升了3.4%和24%。To raise the efficiency of field operation on elliptic curve, based on the idea of trading multiplications for squares, two modified algorithms are proposed to compute 4P and 5P directly over prime field FPin terms of affine coordinates, their computational complexity are（3k- 1）M ＋（5k ＋ 3）S and（6k- 1）M ＋（9k ＋ 3）S respectively, which are improved to 6.25% and 5% respectively than those of Dimitroy’s and Zhou meng’s method. Moreover, using the same idea, an improved method is given to compute 3kP directly in terms of affine coordinates, its computational complexity is I ＋（6k ＋ 1）M ＋（9k ＋ 1）S, and the efficiency of the new method is improved to 3.4% and 24% respectively than those of Zhong meng’s and Yin xin-chun’s method.

关 键 词：椭圆曲线密码体制 标量乘法 底层域运算 仿射坐标 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]