北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2004, Vol. 27 ›› Issue (3): 113-116.

• 论文 • 上一篇    

(n,m, 1)-弹性函数的构造与计数的一个问题

黄 铮1,3, 丁金扣1, 温巧燕1, 杨义先2   

  1. 1.北京邮电大学 理学院, 北京 100876;
    2.北京邮电大学 信息工程学院, 北京 100876;
    3.中国科学院 信息安全国家重点实验室, 北京100039
  • 收稿日期:2003-02-26 出版日期:2004-03-28
  • 作者简介: 黄 铮(1956—), 女, 副教授. E-mail:huang2003@hotmail.com

A Problem with the Construction and Enumeration of (n,m,1)-Resilient Functions

HUANG Zheng1,3, DING Jin-kou1, WEN Qiao-yan1, YANG Yi-xian2   

  1. 1. Science School, Beijing University of Posts and Telecommunications,Beijing 100876, China;
    2. Information Engineering School, Beijing University of Posts and Telecommunications, Beijing 100876, China;
    3. Stake Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing 100039, China
  • Received:2003-02-26 Online:2004-03-28

摘要: 研究一类重要的多输出布尔函数——弹性函数((n,m,1)-resilient functions)的构造与计数问题。弹性函数的一个重要作用是抵御密码体制中的信息泄露。为保证密码体制的安全性,要求弹性函数的数目必须足够多,因此,研究弹性函数的构造与计数问题是十分必要的。文中研究了弹性性t=1, n-m>t时, (n,m,1)-弹性函数的构造与计数问题。基于已有的n元平衡的1阶相关免疫函数的构造法,并利用弹性函数与0,1上多维空间的正交分划(一个正交矩阵组)之间的等价关系,构造了3类(n,m,1)-弹性函数,给出了(n,m,1)-弹性函数的一个计数下界。

关键词: 弹性函数, 正交矩阵, 计数, 量子密钥分配

Abstract: The resilient function is one of the multiple-output Boolean functions, An important work the resilient function has to do is to prevent the information eavesdropping. The more numbers of the resilient functions have the more safety the cryptographic system will be. On the other hand, construction, as well as enumeration in (n,m,1)-resilient functions, has to be paid more attention to. Construction and enumeration were studied when the order of resiliency was t=1,n-m>t, upon which, three classes of (n,m,1)-resilient functions, based on the construction of n-variables balanced correlation-immune functions of the first-order, and on the equivalence between resilient functions and large sets of orthogonal arrays(a group of orthogonal arrays), are implemented in the case of n-m>t=1. Also, an enumeration lower bound of a (n,m,1)-resilient function was presented.

Key words: resilient functions, orthogonal array, enumeration, quantum crypto-graphic key distribution

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