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。 Elliptic Curve Cryptosystem is a public key cryptosystem based on algebraic curve. The use of elliptic curves as the basis for a public-key cryptosystem is because the set of points defined on an elliptic curve over a finite field can form an Abelian group, from which the discrete logarithm of the elliptic curve can be defined. However, it is very difficult to find the discrete logarithm. Therefore, the public key cryptosystem can be constructed by both parties. However, the calculation of the elliptic curve cryptosystem is very complicated, and the execution speed is often very slow during the actual implementation. Starting from the idea of ​​constructing fast and secure cryptosystem, this paper analyzes the related problems that affect the execution speed of elliptic curve cryptosystem. In order to improve the speed of elliptic curve cryptosystem, a fast algorithm is designed.