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On the (non-)existence of APN (n, n)-functions of algebraic degree n

Lilya Budaghyan, Claude Carlet, Tor Helleseth, Nian Li
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
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