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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 public key cryptosystem based on algebraic curve. The use of a circular curve as the basis of a public-key cryptosystem is based on the definition of an Abelian group of points on an elliptic curve over a finite field, from which the discrete logarithm of the elliptic curve can be defined. It is very difficult to find this discrete logarithm, so both parties can construct a public-key cryptosystem, but choosing a suitable curve and the computations on it is complex. Starting from the idea of constructing fast and secure cryptosystem, this paper analyzes the related problems of using the cryptosystem with circular curve. For a class of cryptosystem that is suitable for establishing a cryptosystem, the corresponding affine substitution and its mapping operation are carried out, and its properties are described and analyzed.