A direct proof of APN-ness of the Kasami functions

Published 31 Jan 2020 in cs.IT, cs.CR, and math.IT | (2002.00050v1)

Abstract: Using recent results on solving the equation $X^{{2^k+1}+X+a=0$} over a finite field $\mathbb{F}{2^n}$, we address an open question raised by the first author in WAIFI 2014 concerning the APN-ness of the Kasami functions $x\mapsto x^{{2^{{2k}-2^k+1}$}} with $gcd(k,n)=1$, $x\in\mathbb{F}{2^n}$.

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