ZHOU Chang-ying1, Kwok-Yan-Lam1, ZHOU Zheng-ou2. An efficient method to generate elliptic curves[J]. 2001, (12): 94-98.DOI：
产生安全椭圆曲线的一种有效方法
摘要
本文在寻找安全椭圆曲线的CM方法的基础上
实现了一种更具适用性的产生安全椭圆曲线的有效方法。通常
为了抵抗诸如MOV等算法可能的攻击
以域GF（q）上的椭圆曲线为基础的公钥密码系统
对该椭圆曲线必须要求满足以下条件:m阶曲线具有一个形式为2p+1的大素数因子
这里p是一个素数且q21 mod m。这个条件在不损害安全性的情况下对形式为2p+1的大素因子可以放宽到包括形式为2ip+1的素数（i是一个小整数）。因此
适用于公钥密码系统的安全椭圆曲线的数目显著增加。本文对这一方法进行了实现
它表明用该方法来产生适用于公钥密码系统的椭圆曲线比原来的方案快得多。
Abstract
In this paper
an efficient method to generate elliptic curves for public key cryptosystems based on discrete logarithm problem is presented. Usually
to resist possible attacks
such as MOV reduction
public key cryptosystems based on elliptic curve E over field GF（q） must satify the following condition: the order m of the curve has a large prime factor of the form 2p+1 where p is a prime and q21 mod m. This condition can be relaxed to include primes of the form 2ip+1 （i is a small integer） without compromising security. Hence
the number of elliptic curves suitable for use by public key cryptosystems is increased greatly. We design a method to implement such a scheme
showing that
it is much faster to generate a suitable elliptic curve with this new scheme than with the original scheme.
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