快速得到大周期多项式的方法

Fast method to getting high order polynomials

在密码学和编码学中,经常需要构造周期很大的多项式,然而多项式周期的计算是亚指数级别的算法,因此确定一个多项式的周期是非常复杂的事情,在实践中一般只是估计多项式的周期。利用分析根的方法,给出了一类特殊多项式因子的周期估计定理的一种新的证明方法,该方法简单直观,可以用来解决其它类似问题,最后对定理进行了推广,得出了一个一般性的结论,并根据结论给出一个得到大周期多项式的算法。

It＇s necessary to constructing polynomials with large period in the cipher and coding, but the computation of the period of polynomials is sub-exponential, it＇s very difficult to confirm the period of polynomial. In practice, we just estimate the period of the polynomials. A new prove of a famous theorem is given, about estimating the order of polynomials, throuth analysing the roots ofthe polynomials. The method is very simply to understand, and can be used in other problems. At last, the famous theo.rem is extended, and fast method to get high order polynomials is gotten,