A direct proof of APN-ness of the Kasami functions
arXiv:2002.00050v17 citations
Originality Synthesis-oriented
AI Analysis
This resolves a theoretical question in cryptography, but it is incremental as it builds on prior work.
The paper tackles the open problem of proving the APN-ness of Kasami functions over finite fields, achieving a direct proof using recent results on solving specific equations.
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 $gcd(k,n)=1$, $x\in\mathbb{F}_{2^n}$.