中文摘要：

转换乘法为平方运算,是一种快速计算椭圆曲线密码点乘的代数方法。利用此方法,提出了素域Fp上雅可比坐标系下的3P和3kP算法,其运算量分别为6[M]＋10[S]和（6k）[M]＋（10k）[S],与已有的最好算法相比,算法效率分别提升了11.8%和10.5%。另外,还在文献[1,2]基础上,对素域Fp上仿射坐标系下的2kP和3kP的算法进行了改进,其算法效率比文献[1,2]分别提高了6.3%和3.3%。

英文摘要：

Trading field muhiplications for field squaring is an algebraic method to improve the performance of scalar multiplication in ECC. This paper gave the algorithms of 3P and 3kP over Fp in terms of Jacobian coordinates. And their computational complexity were 6[ M] ＋ 10[ S] and （6k） [ M] ＋ （10k） [ S] respectively,which was improved to 11.8% and 10.5% respectively than the best algorithms at present. In addition, this paper improved the algorithms of 2kP and 3kP over Fp in terms of affine coordinates on the basis of literature [ 1,2]. And their computational complexity was improved to 6.3% and 3.3% respectively than literature [ 1,2 ].