On a Class of Quadratic Polynomials with no Zeros and its Application to APN Functions

Carl Bracken, Chik How Tan, Tan Yin

We show that the there exists an infinite family of APN functions of the form $F(x)=x^{2^s+1}+x^{2^{k+s}+2^k}+c{x}^{2^{k+s}+1}+c^{2^k}{x}^{2^k+2^s}+\delta x^{2^k+1}$, over $\gf…