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In this paper, we study the problem of existence of almost perfect nonlinear (APN) functions of algebraic degree n over F2n . We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which imply, in particular, that for most of the known APN functions F over F2n the function x 2 n −1 + F (x) is not APN.doi:10.1109/isit.2016.7541345 dblp:conf/isit/BudaghyanCHL16 fatcat:y7hu2ytc6jardbkbsd2p3la2ia