Further results on differentially 4-uniform permutations over \(\mathbb{F}_{2^{2m} } \)

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• 作者：ZhengBang Zha ; Lei Hu ; SiWei Sun ; JinYong Shan
• 关键词：permutation ; differentially 4 ; uniform function ; nonlinearity ; algebraic degree ; 94A60 ; 11T71 ; 14G50
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：58
• 期：7
• 页码：1577-1588
• 全文大小：238 KB
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• 作者单位：ZhengBang Zha (1) (2)
  Lei Hu (2) (3)
  SiWei Sun (2)
  JinYong Shan (2)
  
  1. School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471022, China
  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China
  3. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

We present several new constructions of differentially 4-uniform permutations over \(\mathbb{F}_{2^{2m} } \) by modifying the values of the inverse function on some subsets of \(\mathbb{F}_{2^{2m} } \). The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of crytographic substitution boxes.