| 引用本文: | 海昕,戴清平,李超.幂函数型完全非线性函数原像分布的特征.[J].国防科技大学学报,2012,34(5):142-145.[点击复制] |
| HAI Xin,DAI Qingping,LI Chao.Property of preimage distribution of perfect nonlinear function with the form of power functions[J].Journal of National University of Defense Technology,2012,34(5):142-145[点击复制] |
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| 幂函数型完全非线性函数原像分布的特征 |
| 海昕, 戴清平, 李超 |
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(国防科技大学 理学院,湖南 长沙 410073)
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| 摘要: |
| 完全非线性函数是特征为奇数的有限域上抗差分密码攻击最优的函数，目前已有的六类完全非线性函数都是2-1的。当Π(x)为Fqm上的Dembowski-Ostrom函数或者Coulter-Matthews函数时，从Fqm到Fq的完全非线性函数tr(aΠ(x))的原像分布恰有两种取值，其中一种取值对应Fqm所有平方剩余元，另一种取值对应Fqm所有非平方剩余元。该结论在文中得到了证明。 |
| 关键词: 完全非线性函数 迹函数 原像分布 |
| DOI： |
| 投稿日期：2012-03-10 |
| 基金项目:国家自然科学基金资助项目(61070215, 61103191) |
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| Property of preimage distribution of perfect nonlinear function with the form of power functions |
| HAI Xin, DAI Qingping, LI Chao |
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(College of Science, National University of Defense Technology, Changsha 410073, China)
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| Abstract: |
| Perfect nonlinear function is the optimal function on finite fields with odd character that can resist differential cryptanalysis. All the six classes of the already known perfect functions currently are 2-1. This study proved that when is Dembowski-Ostrom function or Coulter-Matthews function on , the preimage distribution of the perfect nonlinear function has just two kinds of values, one corresponds to all the elements of quadratic residual on , and the other kind corresponds to all the non quadratic residual on . |
| Keywords: perfect nonlinear function trace function preimage distribution |
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