环Z_(pq)上逻辑函数的分解及其应用  

Decomposition of Logical Functions over Ring Z_(pq) and its Application

作　　者：赵亚群[1] 金栋梁[1] 

机构地区：[1]信息工程大学信息工程学院,郑州450002

出　　处：《工程数学学报》2010年第3期521-526,共6页Chinese Journal of Engineering Mathematics

基　　金：信息安全国家重点实验室开放基金(01-02)~~

摘　　要：为克服一般剩余类环上合数值逻辑函数无统一多项式表示给函数研究工作带来的困难,本文利用中国剩余定理对环Z_(pq)(p<q且均为素数)上的pq值随机变量进行了分解;并由此对pq值逻辑函数及其变元进行了CRT-分解,给出了pq值逻辑函数的分解函数的代数标准型,据此可得pq值逻辑函数在CRT-分解意义下的代数标准型;又讨论了pq值相关免疫逻辑函数在CRT-分解意义下的等价判别条件,给出了利用分解函数的代数标准型构造pq值相关免疫逻辑函数的一种方法。To overcome the difficulty that the composite-valued logical functions over the residual class ring can not be represented by canonical polynomials, the decompositions for pq-valued random variables are presented by the Chinese remainder theorem （CRT）, and the CRT-decompositions of the pq-valued logical functions and their variables are shown, and the algebraic normal form of decomposable functions for pq-valued logical functions is obtained. The algebraic normal form for pq-valued logical functions is presented under the according CRT-decomposition. Then the criteria of correlation immune pq-valued logical functions are discussed under the CRT-decomposition, so a construction method for correlation immune pq-valued logical functions is derived by the algebraic normal form of the decomposable function.

关 键 词：pq值逻辑函数 CRT-分解 代数标准型 相关免疫 分解谱 

分 类 号：TN918.1[电子电信—通信与信息系统]