p^r值逻辑函数相关免疫的等价判别条件

New Criterion of Correlation Immunity for pr-Valued Logic Functions

本文首先基于环Zpr中的元的padic分解并结合概率论的思想,给出了pr值随机变量的分解性质及pr值随机变量独立性的等价描述,然后在对pr值逻辑函数及其变元都进行padic分解的基础上,直接通过p值逻辑函数的Chrestenson谱给出了padic分解意义下pr值逻辑函数k阶相关免疫的线性组合引理和谱判别定理.

Combining the p-adic decomposition of the variables in Zp^r and the thought of probability theory, this paper firstly presents the decompose properties and equivalent description of p^r-valued r. v. Then the p-adic decomposition of both the p^r- valued logic functions and the variables is shown. Based on this,a linear combining lemma and spectrum criterion of k order correlation-immunity of p^r- valued logic functions is given in the sense of p- adic decomposition by using Chrestenson transformation of p- valued logic functions directly.