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A direct proof of APN-ness of the Kasami functions
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2021-01-06 , DOI: 10.1007/s10623-020-00830-y
Claude Carlet , Kwang Ho Kim , Sihem Mesnager

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 $gcd(k,n)=1$, $x\in\mathbb{F}_{2^n}$.

中文翻译:

Kasami 函数的 APN 性的直接证明

使用最近在有限域 $\mathbb{F}_{2^n}$ 上求解方程 $X^{2^k+1}+X+a=0$ 的结果,我们解决了由WAIFI 2014 的第一作者,关于 Kasami 函数 $x\mapsto x^{2^{2k}-2^k+1}$ 的 APN 性,其中 $gcd(k,n)=1$, $x\in \mathbb{F}_{2^n}$。
更新日期:2021-01-06
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