北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2007, Vol. 30 ›› Issue (1): 49-52.doi: 10.13190/jbupt.200701.49.128

• 论文 • 上一篇    下一篇

对称相关免疫函数的构造与计数

莫 骄, 温巧燕   

  1. 北京邮电大学 理学院, 北京 100876
  • 收稿日期:2006-03-15 修回日期:1900-01-01 出版日期:2007-03-30 发布日期:2007-03-30
  • 通讯作者: 莫 骄

The Construction and Enumeration of Symmetric Correlation Immune Functions

MO Jiao, WEN Qiao-yan   

  1. 1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China
  • Received:2006-03-15 Revised:1900-01-01 Online:2007-03-30 Published:2007-03-30
  • Contact: MO Jiao

摘要:

指明n元一阶相关免疫对称函数的构造与计数等价于某个方程在二元域上的求解与解的计数,同时指明n元m(m>1)阶相关免疫对称函数的构造也取决于该方程的求解.得到了这个方程的等价方程.通过求解等价方程,提供了高阶相关免疫对称函数的构造方法和一阶相关免疫对称函数的计数方法,并在2种情形下给出了n元一阶相关免疫对称函数的计数下界.

关键词: 对称函数, 一阶相关免疫函数, 高阶相关免疫函数, 等价方程.

Abstract:

It was claimed that the construction and enumeration of symmetric correlation immune functions with order one was equivalent to the solutions in the binary field and their enumeration for a certain equation. It was also shown that the construction of symmetric correlation immune functions with order m was also related to the solutions in the binary field of the above equation. The equivalent equation was obtained. By solving the equivalent equation, the methods to construct symmetric correlation immune functions with higher order and to enumerate symmetric correlation immune functions with order one were presented. The lower bound of enumeration of symmetric correlation immune functions with order one was also given in two cases.

Key words: symmetric functions, symmetric correlation immune functions with order one, symmetric correlation immune functions with higher order;equivalent equation

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