基于plateaued函数的平衡布尔函数构造

doi:10.11772/j.issn.1001-9081.2016.06.1563

计算机应用 ›› 2016, Vol. 36 ›› Issue (6): 1563-1566.DOI: 10.11772/j.issn.1001-9081.2016.06.1563

基于plateaued函数的平衡布尔函数构造

张轶毅¹, 孟凡荣¹, 张凤荣¹, 石记红^1,2

1. 中国矿业大学计算机科学与技术学院, 江苏徐州 221116;
2. 郑州煤炭工业(集团)有限责任公司通风管理部, 郑州 450042

收稿日期:2015-11-12 修回日期:2016-01-06 出版日期:2016-06-10 发布日期:2016-06-08
通讯作者: 张轶毅
作者简介:张轶毅(1978-),男,河北保定人,硕士研究生,主要研究方向:信息安全、密码算法;孟凡荣(1962-),女,辽宁沈阳人,教授,博士,主要研究方向:数据库、智能信息数据处理;张凤荣(1982-),男,河北邯郸人,副教授,博士,主要研究方向:密码函数、对称密码;石记红(1985-),女,山西太谷人,工程师,硕士研究生,主要研究方向:数据挖掘、信息处理、数据结构。
基金资助:
国家自然科学基金资助项目(61303263);中国博士后基金资助项目(2014M562494,2015T80600);江苏省博士后基金资助项目(1401056B);国家自然科学基金煤炭联合基金重点项目(U1261201)。

Construction of balanced Boolean functions using plateaued functions

ZHANG Yiyi¹, MENG Fanrong¹, ZHANG Fengrong¹, SHI Jihong^1,2

1. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou Jiangsu 221116, China;
2. Department of Ventilation Magement, Zhengzhou Coal Industry(Group) Company Limited, Zhengzhou Henan 450042, China

Received:2015-11-12 Revised:2016-01-06 Online:2016-06-10 Published:2016-06-08
Supported by:
This work is partially supported by the National Science Foundation of China (61303263), the China Postdoctoral Science Foundation (2015T80600, 2014M562494), the Jiangsu Postdoctoral Science Foundation (1401056B), the National Natural Science Foundation of China Coal Joint Fund Project (U1261201).

摘要/Abstract

摘要： 布尔函数在对称密码的设计和分析中起着重要的作用。通过对谱不相交函数集中子函数平衡性的问题的研究给出了包含4个plateaued函数的函数集中有3个为平衡函数的充分条件。在此基础上,基于3个平衡的谱不相交plateaued函数,一类特殊的布尔置换以及一个高非线性度平衡函数,提出了一个构造高非线性度平衡布尔函数的方法。通过分析可知,利用该方法可以构造代数次数达到最优、非线性度不小于2^2k-1-2^k-1-2^k/2-2^{⌈(k-1)/2⌉}的2k元平衡函数。

关键词: 布尔函数, 平衡函数, bent函数, plateaued函数, 非线性度

Abstract: Boolean function plays an important role in the design and analysis of symmetric cryptography. Firstly, by studying the balanced property of subfunctions of the disjoint spectra function set, some sufficient conditions were provided that there were three balanced Boolean functions in the set of four plateaued functions. Then, based on three balanced disjoint spectra plateaued functions, a special Boolean permutation and a balanced Boolean function with high nonlinearity, a method of constructing balanced Boolean functions with high nonlinearity was proposed on a small number of variables. The analysis results show that the proposed method can construct the 2k-variable balanced Boolean functions with the optimal algebraic number and the nonlinearity is not less than 2^2k-1-2^k-1-2^k/2-2^{⌈(k-1)/2⌉}.

Key words: Boolean function, balanced function, bent function, plateaued function, nonlinearity

中图分类号:

TN918.1

张轶毅, 孟凡荣, 张凤荣, 石记红. 基于plateaued函数的平衡布尔函数构造[J]. 计算机应用, 2016, 36(6): 1563-1566.

ZHANG Yiyi, MENG Fanrong, ZHANG Fengrong, SHI Jihong. Construction of balanced Boolean functions using plateaued functions[J]. Journal of Computer Applications, 2016, 36(6): 1563-1566.

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基于plateaued函数的平衡布尔函数构造

Construction of balanced Boolean functions using plateaued functions

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