[Resource Topic] 2016/143: On upper bounds for algebraic degrees of APN functions

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On upper bounds for algebraic degrees of APN functions

Authors: Lilya Budaghyan, Claude Carlet, Tor Helleseth, Nian Li, Bo Sun


We study the problem of existence of APN functions of algebraic degree n over \ftwon. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions F over \ftwon the function x^{2^n-1}+F(x) is not APN, and changing a value of F in a single point results in non-APN functions.

ePrint: https://eprint.iacr.org/2016/143

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