| 一类APN幂函数的Walsh谱及其应用 |
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| 引用本文： | 夏永波.一类APN幂函数的Walsh谱及其应用[J].科学技术与工程,2011,11(33):8203-8205,8210. |
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| 作者姓名： | 夏永波 |
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| 作者单位： | 中南民族大学数学与统计学学院,武汉,430074 |
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| 基金项目： | 中央高校基本科研业务费专项资金项目(CZQ11009) |
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| 摘 要： | 设n≥3为一正奇数,令d=(3n+1)/4+(3n-1)/2,则幂函数xd是有限域F3n上的几乎完全非线性函数,即APN(almost perfect nonlinear)函数。到目前为止,该APN函数的Walsh谱还未被确定。计算了APN幂函数xd的Walsh谱,并给出了所得结果的一点应用。
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| 关 键 词： | APN函数 Walsh谱 指数和 有限域 |
| 收稿时间： | 9/5/2011 2:00:21 PM |
| 修稿时间： | 9/5/2011 2:00:21 PM |
The Walsh Spectrum of an APN Power Function and Its Application |
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| xia yongbo.The Walsh Spectrum of an APN Power Function and Its Application[J].Science Technology and Engineering,2011,11(33):8203-8205,8210. |
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| Authors: | xia yongbo |
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| Institution: | (School of Mathematics and Statistics,South-Central University For Nationalities,Wuhan 430074,P.R.China) |
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| Abstract: | Let n be an odd positive integer and d=(3^n 1)/4 (3^n-1)/2. Then, the power function x^d is an APN function over finite field F_{3^n}. The Walsh spectrum of this APN function is not determined up to now. In this paper, the Walsh spectrum of x^d is calculated and an application of this result is given. |
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| Keywords: | APN function Walsh spectrum exponential sum finite fields |
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