剩余类环或有限域上独立随机变量和的极限分布定理

Limit Distribution Theorem for a Sum of Independent Random Variables in a Residue Class Ring or a Finite Field

在密码系统分析和设计中，不引入特征函数仅利用概率性质、分析极限理论以及齐次马尔科夫链有关遍历性理论，给出了剩余类环或有限域上独立随机变量和的极限分布定理。

Abstract With the property of probability and the ergodic theroy of Markov chain, a limit distribution theorem is obtained for a sum of independent random variables in a residue class ring or a finite field. We proved that if a sequence of independent random variables {X n,n≥1} in a residue class ring or a finite field satisfies the sufficient condition which we gave in this article, the limit distribution of the sum of {X n,n≥1} exists and coincides with the uniform distribution.