Hamming约束集的计数问题（英文）  

The cardinalities of some certain Hamming constraint sets

作　　者：宋佳[1] 陈玉福[1] 

机构地区：[1]中国科学院大学数学科学学院,北京101408

出　　处：《中国科学院大学学报（中英文）》2015年第6期721-727,共7页Journal of University of Chinese Academy of Sciences

基　　金：Supported by the National Natural Science Foundation of China(11271363)

摘　　要：构造一个应用于流密码并且具有良好性质的布尔函数是一个非常困难的问题.最近,Tu和Deng基于一个关于二进制串分布(我们称之为Hamming约束集)的组合猜想的正确性,构造了两类具有良好性质的布尔函数.越来越多的学者致力于Tu-Deng猜想的证明.本文用一种新方法给出某些Hamming约束集的计数公式,从而部分地证明Tu-Deng猜想.It is difficult to find Boolean functions used in stream ciphers that can meet all the necessary performance criteria. Recently,two classes of Boolean functions with many good cryptographic properties have been proposed by Tu and Deng based on correctness of a combinatorial conjecture about binary strings distribution（ we call it Hamming constraint set）. Tu-Deng conjecture has attracted much attention from cryptographers. In this paper we give a new method to obtain the explicit formulas for the cardinalities of some certain Hamming constraint sets,which partially proves Tu-Deng conjecture.

关 键 词：布尔函数 Tu-Deng猜想 Hamming重量 

分 类 号：O157.5[理学—数学]