有限域GF（q）上安全椭圆曲线的选取

椭圆曲线密码体制是安全性最高的公钥密码体制，它的安全性是基于椭圆曲线上的离散对数问题，同时椭圆曲线参数的选择对系统的安全性也至关重要。本文首先介绍了椭圆曲线密码体制的基本概念和相关数论知识，其次阐述了选择安全椭圆曲线的原则，最后详细介绍了如何通过选取合适的椭圆曲线参数来产生安全椭圆曲线，并对这些参数的合理性进行了验证。结果表明，按照这种方式所选取的椭圆曲线，抵御现有算法攻击能力大大增强。

Selection of security elliptic curve in finite field GF(q)

Elliptic Curve Cryptography（ECC） is the most secure public key cryptosystem, whose security is based on the discrete logarithm problem in finite fields. The choice of elliptic curve is also crucial to system security. This article first introduces the basic concepts of elliptic curve and related number theory knowledge, then describes the selection principle of security elliptic curve, and introduces how to generate security elliptic curve by choosing appropriate parameters and verifies the rationality of these parameters at last. The results show that the ability of the elliptic curve, selected by this way, against the attack of existing algorithms, has been enhanced greatly.