Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity

Sihong Su; Xiaohu Tang

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Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity

机译：具有最佳代数免疫力和高非线性度的旋转对称布尔函数的构造

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摘要

Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this paper, based on the knowledge of compositions of an integer, we present two new kinds of construction of rotation symmetric Boolean functions having optimal algebraic immunity on either odd variables or even variables. Our new functions are of much better nonlinearity than all the existing theoretical constructions of rotation symmetric Boolean functions with optimal algebraic immunity. Further, the algebraic degree of our rotation symmetric Boolean functions are also high enough.

机译：最近的研究表明，旋转对称布尔函数类可能具有丰富的密码学意义函数。在本文中，基于对整数组成的了解，我们提出了两种新的旋转对称布尔函数构造，它们对奇数或偶数变量具有最佳代数免疫性。与具有最佳代数免疫力的旋转对称布尔函数的所有现有理论构造相比，我们的新函数具有更好的非线性。此外，我们的旋转对称布尔函数的代数度也足够高。

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来源
《Designs, Codes and Crytography》 |2014年第2期|183-199|共17页
作者
Sihong Su; Xiaohu Tang;
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作者单位

Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu 610031, China,College of Mathematics and Information Science, Henan University, Kaifeng 475004, China;

Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu 610031, China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Boolean function; Algebraic immunity; Walsh spectrum; Nonlinearity; Algebraic degree;

机译：布尔函数;代数免疫沃尔什谱;非线性;代数程度;

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专利

1. A new construction of rotation symmetric Boolean functions with optimal algebraic immunity and higher nonlinearity [J] . Zhang Hui, Su Sihong Discrete Applied Mathematics . 2019,第期

机译：具有最佳代数免疫的旋转对称布尔函数的新构建及更高的非线性
2. Constructions of balanced odd-variable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity [J] . Sun Lei, Fu Fang-Wei Theoretical computer science . 2018,第期

机译：具有最佳代数免疫和高非线性的平衡奇数变旋转对称布尔函数的结构
3. Balanced 2p-variable rotation symmetric Boolean functions with optimal algebraic immunity, good nonlinearity, and good algebraic degree [J] . Li X., Zhou Q., Qian H., Journal of Mathematical Analysis and Applications . 2013,第1期

机译：平衡的2p变量旋转对称布尔函数，具有最佳的代数免疫性，良好的非线性和良好的代数度
4. Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity [C] . Shaojing Fu, Chao Li, Kanta Matsuura, Cryptology and network security . 2009

机译：具有最大代数免疫度的旋转对称布尔函数的构造
5. Rotation Symmetric Boolean Functions [D] . Sanger, Ellyn M. 2018

机译：旋转对称布尔函数
6. On Various Nonlinearity Measures for Boolean Functions [O] . Joan Boyar, Magnus Gausdal Find, René Peralta -1

机译：关于布尔函数的各种非线性测度
7. New Constructions of Balanced Boolean Functions with Maximum Algebraic Immunity, High Nonlinearity and Optimal Algebraic Degree [O] . Dheeraj Kumar SHARMA, Rajoo PANDEY 2020

机译：具有最大代数免疫力，高非线性和最佳代数度的平衡布尔函数的新建筑

Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity

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