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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 ,但选择适合的曲线及在其上的计算又是复杂的 .文中分析研究了利用有限域上的椭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椭圆曲线进行了相应的仿射代换和其运算的映射变换 ,对椭圆曲线构建密码体制的椭圆离散对数问题进行了分析研究 .论述了构建有限域上的椭圆曲线密码体制的思想及方法 .
The use of an elliptic curve as the basis of a public-key cryptosystem is based on the definition of the Abelian group of points on an elliptic curve defined on a finite field, from which the discrete logarithm of the elliptic discrete logarithm can be defined Discrete logarithm is very difficult, so both parties can construct the public key cryptosystem, but the choice of appropriate curve and the calculation on it are complex.This paper analyzes and studies the use of elliptic curve over finite fields to construct the correlation of cryptosystem Problem, a kind of elliptic curve suitable for establishing a cryptosystem has been mapped and transformed by corresponding affine substitution and its operation, and the elliptic discrete logarithm problem of elliptic curve constructing cryptosystem has been analyzed and studied. On the elliptic curve cryptosystem ideas and methods.