期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 52, 期 9, 页码 4160-4170出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2006.880036
关键词
almost bent function; almost perfect nonlinear (APN) function; power function; permutation polynomial
We investigate some open problems on almost perfect nonlinear (APN) functions over a finite, field of characteristic 2. We provide new characterizations of APN functions and of APN permutations by means of their component functions. We generalize some results of Nyberg (1994) and strengthen a conjecture on the upper bound of nonlinearity of APN functions. We also focus on the case of quadratic functions. We contribute to the current works on APN quadratic functions by proving that a large class of quadratic functions cannot be APN.
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