A negative answer to Bracken-Tan-Tan's problem on differentially 4-uniform permutations over F-2n

作者：Qu, Longjiang^*; Xiong, Hai; Li, Chao

来源：Finite Fields and Their Applications, 2013, 24: 55-65.

DOI：10.1016/j.ffa.2013.05.007

• APN function
• Differentially 4-uniform function
• Permutation polynomial

Permutations with low differential uniformity are widely used in cipher design. Recently, Bracken, Tan and Tan (2012) [5] 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.

• 出版日期2013-11
• 单位中国人民解放军国防科学技术大学