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.

• 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。