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中国科学院大学学报 ›› 2015, Vol. 32 ›› Issue (6): 721-727.DOI: 10.7523/j.issn.2095-6134.2015.06.001

• 数学 •    下一篇

Hamming约束集的计数问题

宋佳, 陈玉福   

  1. 中国科学院大学数学科学学院, 北京 101408
  • 收稿日期:2015-01-05 修回日期:2015-04-10 发布日期:2015-11-15
  • 通讯作者: 宋佳
  • 基金资助:

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

The cardinalities of some certain Hamming constraint sets

SONG Jia, CHEN Yufu   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China
  • Received:2015-01-05 Revised:2015-04-10 Published:2015-11-15
  • Supported by:

    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.

关键词: 布尔函数, Tu-Deng猜想, Hamming重量

Abstract:

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.

Key words: Boolean function, Tu-Deng conjecture, Hamming weight

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