复乘法构建椭圆曲线的一种改进

Improving of Construct Elliptic Curve by Complex Multiplication

在使用椭圆曲线密码学中,有一种根据有限域上的点阶数来构建椭圆曲线的方法,关于这一算法,Atkin和Morain建议使用复乘理论构建这些曲线.这种算法仅对低阶多项式有效,对高度数多项式的分解是非常费时的,尤其是对多精度浮点多项式和复杂算术运算更是不实用.我们的方法是根据,预先计算类多项式,然后再在预存的集合中查找相应的素数,实践证明我们的算法具有较高的效率.

In using elliptic curves for cryptography,one often needs to construct elliptic curves with a given or known number of points over a given finite field.Atkin and Morain suggested the use of the theory of complex multiplication to construct such curves. But this method is efficient only when the degree of the class polynomial is small, in general, factoring a high degree polynomial is time consuming,Furthermore,the construction of the class polynomial requires multi-precision floating-point and complex number arithmetic. our method precalculates class polynomial as a separate of off-line process, We choose a discriminant and then search for an appropriate primes,In practice ,Our algorithm is quick and can be compactly code.