具有高非线性度和最优代数次数的弹性函数的构造
Construction of Resilient Functions with High Nonlinearity and Optimal Algebraic Degree
作者：刘倩(西安电子科技大学ISN国家重点实验室)；王怀柱(宁夏大学数学计算机学院)；张丽娜(西安科技大学计算机科学与技术学院)
Author：LIU Qian(State Key Laboratory of Integrated Services Networks, Xidian University)；WANG Huai-Zhu(School of Mathematics and Computer Science, Ningxia University)；ZHANG Li-Na(College of Computer Science and Technology, Xi’an University of Science and Technology)
收稿日期：2016-04-26 年卷（期）页码：2017,54(1):61-64
期刊名称：四川大学学报: 自然科学版
Journal Name：Journal of Sichuan University (Natural Science Edition)
关键字：密码学；流密码；布尔函数；非线性度；弹性；代数次数
Key words：cryptography, stream cipher, Boolean function, nonlinearity, resiliency, algebraic degree
基金项目：高等学校博士学科点专项科研基金,国家自然科学基金,国家重点实验室
中文摘要
具有良好的非线性度和最优代数次数的弹性布尔函数在流密码和分组密码设计和分析中起着至关重要的作用。在本文中，通过修改Maiorana-McFarland(M-M)类Bent函数，利用不同的低阶弹性函数，给出构造高非线性度弹性布尔函数的一种新方法,所构造的函数具有严格几乎最优的非线性度和最优的代数次数。
英文摘要
Resilient Boolean functions with good nonlinearity and optimal algebraic degree play an important role in the design and analysis of stream cipher and block ciphers. In this paper, based on different lower resilient functions, a new construction method to obtain high nonlinearity resilient Boolean function is given via modifying Maiorana-McFarland (M-M) class bent functions. It is shown that the constructed functions have the strictly almost optimal nonlinearity and the optimal algebraic degree.
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