A new almost perfect nonlinear function which is not quadratic
Yves Edel Alexander Pott
Advances in Mathematics of Communications 2009, 3(1): 59-81 doi: 10.3934/amc.2009.3.59
Following an example in [12], we show how to change one coordinate function of an almost perfect nonlinear (APN) function in order to obtain new examples. It turns out that this is a very powerful method to construct new APN functions. In particular, we show that our approach can be used to construct a ''non-quadratic'' APN function. This new example is in remarkable contrast to all recently constructed functions which have all been quadratic. An equivalent function has been found independently by Brinkmann and Leander [8]. However, they claimed that their function is CCZ equivalent to a quadratic one. In this paper we give several reasons why this new function is not equivalent to a quadratic one.
keywords: equivalence of functions almost bent. Walsh spectrum Almost perfect nonlinear

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