## Cryptology ePrint Archive: Report 2020/100

A direct proof of APN-ness of the Kasami functions

Claude Carlet and Kwang Ho Kim and Sihem Mesnager

Abstract: Using recent results on solving the equation $X^{2^k+1}+X+a=0$ over a finite field $\GF{2^n}$, 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 $gcd(k,n)=1$, $x\in\GF{2^n}$

Category / Keywords: secret-key cryptography / APN function, Equation , Muller-Cohen-Matthews (MCM) polynomial, Dickson polynomial, Zeros of a polynomial, Irreducible polynomial.