一种计算旋转对称布尔函数的汉明重量和非线性度的新方法

张习勇; 祁应红; 高光普; 李玉娟

doi:10.11999/JEIT 150164

一种计算旋转对称布尔函数的汉明重量和非线性度的新方法

doi: 10.11999/JEIT 150164

2.
(信息工程大学郑州 450002) ②(数学工程与先进计算国家重点实验室无锡 214215) ③(洛阳外国语学校洛阳 471003) ④(信息保障技术重点实验室北京 100072)

基金项目:

国家自然科学基金(61402522, 60803154, 61572027)；数学工程与先进计算国家重点实验室课题；信息保障技术重点实验室开放基金(KJ-13-108)

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出版历程
- 收稿日期: 2015-01-29
- 修回日期: 2015-06-11
- 刊出日期: 2015-11-19

A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions

Funds:

The National Natural Science Foundation of China (61402522, 60803154, 61572027)

摘要

摘要: 旋转对称布尔函数是一类重要的密码学函数，研究其重量和非线性度等密码学性质具有很好的理论价值。区别于已有的计算方法，该文利用特定的正规基把这些布尔函数的问题转化为有限域上的指数和问题，得到了4 ?? n和n=2s 时一些二次旋转对称布尔函数的重量和非线性度的新结果。使用所提的方法，可以计算几乎全部的二次旋转对称布尔函数的重量和非线性度。所提的新方法对于研究一般的旋转对称布尔函数具有一定的参考意义。
- 密码学 /
- 旋转对称布尔函数 /
- 非线性度 /
- 汉明重量 /
- 正规基
Abstract: Rotation-symmetric Boolean function is a class of Boolean functions with good cryptographic properties, and researches on its weight and nonlinearity cryptographic properties have good theoretical value. Different from the conventional calculation method, in this paper, these problems are converted to the evaluation of exponential sum on finite fields with a specific normal basis. Some new results about the weight and nonlinearity of some rotation-symmetric Boolean functions of degree 2 with4 ?? n and n=2s are obtained. Using the proposed method, the weight and nonlinearity of almost all Rotation-symmetric Boolean functions of degree 2 can be evaluated. This new method is also interesting for studies on the other Boolean functions.
- Cryptography /
- Rotation-symmetric Boolean functions /
- Nonlinearity /
- Hamming weight /
- Normal bases

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参考文献(16)

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