| 一类4次旋转对称布尔函数的汉明重量和非线性度 |
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| 引用本文： | 王斌,张习勇,陈卫红.一类4次旋转对称布尔函数的汉明重量和非线性度[J].数学学报,2012(4):613-626. |
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| 作者姓名： | 王斌 张习勇 陈卫红 |
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| 作者单位： | 郑州信息工程大学信息工程学院信息研究系;北京国际数学研究中心 |
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| 基金项目： | 国家自然科学基金资助项目(60803154);河南省科技攻关项目(102102210052) |
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| 摘 要： | 旋转对称布尔函数在密码学中具有重要的应用价值.本文研究了一类特殊4次的旋转对称布尔函数的快速求值及其汉明重量的递归关系,通过将该函数分解成数个子函数,并利用这些函数的傅里叶变换值的递归关系,证明了其汉明重量与非线性度相等.本文的结果和处理指数和的方法对于进一步研究Cusick的一个猜想可能有帮助.
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| 关 键 词： | 旋转对称布尔函数 非线性度 傅里叶变换 |
The Hamming Weight and Nonlinearity of a Type of Rotation Symmetric Boolean Function |
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| Bin WANG Xi,Yong ZHANG Wei,Hong CHEN.The Hamming Weight and Nonlinearity of a Type of Rotation Symmetric Boolean Function[J].Acta Mathematica Sinica,2012(4):613-626. |
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| Authors: | Bin WANG Xi Yong ZHANG Wei Hong CHEN |
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| Institution: | Department of Applied Mathematics,Zhengzhou Information Science and Technology Institute,Zhengzhou 450002,P.R.China (Beijing International Center for Mathematical Researc) |
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| Abstract: | Rotation symmetric Boolean functions have important applications in Cryptology. In this paper,we study the fast evaluation of a special type of rotation symmetric Boolean function and the recurrence relation about its Hamming weight.Then,we factor the function into several sub-functions.Finally,we prove that the nonlinearity of the function is the same as its Hamming weight with the recurrence relations about Fourier-transform values of these sub-functions.The conclusions and the methods used to deal with exponential sums in this paper may be applied for the further research on a conjecture of Cusick. |
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| Keywords: | rotation symmetric Boolean functions nonlinearity Fourier transform |
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