【摘要】 椭圆曲线密码体制是一种基于代数曲线的公开钥密码体制。使用椭圆曲线作为公钥密码体制的基础是由于定义在有限域上的椭圆曲线上的点的集合可构成阿贝尔群，由此可定义其上的离散对数，即椭圆离散对数。而求此离散对数是非常困难的，由此双方可以构造公钥密码体制，但椭圆曲线密码体制上的计算又是很复杂的，在实际实现过程中执行速度往往很慢。从构建快速、安全的密码体制的思想出发，文章分析了影响椭圆曲线密码体制执行速度的相关问题，为了提高椭圆曲线密码体制的运行速度，设计了其上的快速算法。更多还原

【Abstract】 Elliptic curve cryptosystem is a kind of public-key cryptosystem based on algebra curve.The base using elliptic curves as public-key cryptosystem is that because the points set of elliptic curve on finite field can form Abelian group.By this,the discrete logarithm on elliptic curve can be defined.The discrete logarithm on elliptic curve is very difficult to be solved,so both sides can construct public-key croptosystem .But it is very difficult to make operation on the elliptic curve cryptosystem and it always very slow to be implemented. For the purpose that construct the fast and secure cryptosystem, this paper analyzes some correlation problem of the speed of elliptic curve cryptosystem.For improving the speed of elliptic curve cryptosystem,it designes the fast algorithm.更多还原