适于建立密码体制的椭圆曲线研究

Research on Constructing Elliptic Curves Suitable for Cryptosystem

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。使用随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，所以双方可以构造公钥密码体制，但选择适合的曲线及在其上的计算又是复杂的。从构建快速、安全的密码体制的思想出发分析了利用随圆曲线构建密码体制的相关问题。对于适于建立密码体制的一类随圆曲线进行了相应的仿射代换和其运算的映射变换，对其性质进行了阐述和分析。

Elliptic curve cryptosystem is a kind of public-key cryptosystem based on algebra curve. The base that using elliptic curves as public-key cryptosystem is 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 the both sides can construct publickey cryptosystem, but select the suited elliptic curve and make operation on it is very difficult For the purpose that construct the fast and secure cryptosystem, analyzed some correlation problem of using elliptic curve construct cryptosystem. Make the correlation counterchange on the elliptic curve that suitable for constructiong the cryptosystem and the operation on it. At last, it expatiated and analyzed the character of this kind of elliptic curves.