基于密钥交换中离散对数生成元的研究

Researching of Discrete Logarithm's Primitive Root in Key Exchange

从离散对数的生成元的选择问题出发 ,根据欧拉定理和拉格朗日定理提出加快寻找生成元的简便算法 ,该算法的重要思想是 :如果我们选择安全素 P=2 * Q+1,则判断集合 ZP 中的元素是否是生成元的次数达到最少。该算法加快了生成元的寻找速度 。

This paper sets to research from the problem of selecting primitive root of discrete logarithm, and according to Euler theory and Lagrance theory, presents an algorithm of searching the primitive root, accelerates the speed of searching the primitive root. The importance of this algorithm is if a large safe prime P=2*Q+1 (P,Q are large primes) is selected, the number of the primitive root generated in set Zp can be decided in least times. The algorithm will save the computing time and the computation space.