1988年国外提出基于Internet上的远程医疗会诊的思想,由于网络的开放性及信息系统的安全性,信息的安全保密变得愈来愈重要.本文论述了网络的数据安全问题及公钥密码体制的原理,提出了一种利用椭圆曲线实现数据保密通信的方法,即通过构造一个单向置换群,椭圆曲线可以应用在基于离散对数问题的公钥密码体制中.并完整给出一种简单形式椭圆曲线密码体制的设计与实现. Due to the openness of the network and the security of the information system, the security and confidentiality of information becomes more and more important in 1988 when it comes to foreign countries based on the idea of ​​remote medical consultations. This article discusses the data security of the network and public key cryptosystem , A method of using Elliptic Curve for data secure communication is proposed. By constructing a unidirectional permutation group, the elliptic curve can be applied to public key cryptosystem based on discrete logarithm problem, and a simple Design and Implementation of Elliptic Curve Cryptosystem.