A negative answer to Bracken-Tan-Tan?s problem on differentially 4-uniform permutations over

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• 作者：Longjiang Qu ; Hai Xiong ; Chao Li
• 关键词：06E30 ; 11T06 ; 94A60
• 刊名：Finite Fields and Their Applications
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：24
• 期：Complete
• 页码：55-65
• 全文大小：221 K

文摘

Permutations with low differential uniformity are widely used in cipher design. Recently, Bracken, Tan and Tan (2012) presented a method to construct differentially 4-uniform permutations by changing certain conditions of known APN functions. They guessed that only two classes of existing quadratic APN functions have this property. They succeeded in proving one class and left the other one as an open problem. In this paper, with the help of a computer, those polynomials are proved to be differentially 4-uniform but may not be permutation polynomials, which give a negative answer to this problem.