A direct proof of APN-ness of the Kasami functions

摘要

Using recent results on solving the equation X2k+1 + X + a = 0 over a finite field F-2n provided by the second and the third authors, we address an open question raised by the first author in WAIFI 2014 concerning the APN-ness of the Kasami functions x bar right arrow x(22k-)2(k)+ 1 with gcd(k, n) = 1, x is an element of F-2n