| 几种低差分一致的二项式函数 |
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| 引用本文： | 郭腓望,张习勇,韩文报.几种低差分一致的二项式函数[J].北京大学学报(自然科学版),2011,47(6):973-977. |
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| 作者姓名： | 郭腓望 张习勇 韩文报 |
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| 作者单位： | 信息工程大学信息工程学院应用数学系，郑州 450002; |
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| 基金项目： | 国家自然科学基金(60803154)资助 |
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| 摘 要： | 通过选取两个单项式的组合，给出几种低差分一致的函数的构造, 得到一些二次差分4一致性和三次差分6一致性的二项式函数, 并利用二阶非线性度等给出了三次函数的非线性度的一个下界。新构造的函数具有低差分一致性和较高的非线性度。
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| 关 键 词： | 差分一致性 几乎完全非线性函数 完全非线性函数 Walsh谱 二阶非线性度 |
| 收稿时间： | 2010-11-30 |
Several Binomial Functions with Low Differential Uniformity |
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| GUO Feiwang,ZHANG Xiyong,HAN Wenbao.Several Binomial Functions with Low Differential Uniformity[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2011,47(6):973-977. |
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| Authors: | GUO Feiwang ZHANG Xiyong HAN Wenbao |
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| Institution: | Department of Applied Mathematics, School of Institute of Information Engineering, Information Engineering University, Zhengzhou 450002; |
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| Abstract: | Selecting the combinations of two appropriate monomial functions,the authors construct several functions with low differential uniformity,find some quadratic highly nonlinear differentially 4-uniform and cubic differentially 6-uniform binomial functions,and give a bound of nonlinearity of cubic functions by second order nonlinearity.These new functions have higher nonlinearity and lower uniformity. |
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| Keywords: | differential uniformity almost perfect nonlinear functions perfect nonlinear functions Walsh spectrum second order nonlinearity |
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