ECC是基于有限域上，椭圆曲线点集E所构成的群上定义的离散对数系统.有限域上椭圆曲线的选择，应避免使用超奇异曲线,以保证足够的安全性.椭圆曲线的运算为给定椭圆曲线E上的一个基点G和一个整数(1 1)nκκ≤≤，求数乘(mod )GQ pκ=，Q也是E上的一点，计算...GGG Gκ=+++ (κ个G相加)相对容易；但若给定椭圆曲线上两点G和Q，求一整数κ，使(mod )GQ pκ=，特别是当G是较高阶的基点时，则非常困难。这就是椭圆曲线离散对数问题。基于椭圆曲线离散对数问题的难解性，形成了ECC体制。-ECC is based on the gal o is field in, elliptic curve set of points Econ statutes on the group defines separate logarithm system In gal o is field elliptic curve choice, Should avoid using the ultra strange curve, guarantees thee no ugh security The elliptic curve operation for assigns on elliptic curve E basic point G and The integer (1 1) n kappa kappa <= <=, asks the number to ride(mod) GQ p kappa =, Q also is on E, computation.. GGG G kappa =+++(kappa G Adds together) is relatively easy　But if assigns in thee l l iptic curve two G and Q, asks an integer kappa, causes (mod) GQ p kappa =, specially when G is compares When Gao Jie basic point, then is extremely difficult This is the elliptic curve separate logarithm question. Based on the elliptic curve separate logarithm question difficult solution, to have formed the ECC system.