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We consider an infinite family of exponents $e(l,k)$ with two parameters, $l$and $k$, and derive sufficient conditions for $e(l,k)$ to be 0-APN over$\mathbb{F}_{2^n}$. These conditions allow us to generate, for each choice of$l$ and $k$, an infinite list of dimensions $n$ where $x^{e(l,k)}$ is 0-APNmuch more efficiently than in general. We observe that the Gold and Inverseexponents, as well as the inverses of the Gold exponents can be expressed inthe form $e(l,k)$ for suitable $l$ and $k$. We characterize all cases in which$e(l,k)$ can be cyclotomic equivalent to a representative from the Gold,Kasami, Welch, Niho, and Inverse families of exponents. We characterize when$e(l,k)$ can lie in the same cyclotomic coset as the Dobbertin exponent(without considering inverses) and provide computational data showing that theDobbertin inverse is never equivalent to $e(l,k)$. We computationally test theAPN-ness of $e(l,k)$ for small values of $l$ and $k$ over $\mathbb{F}_{2^n}$for $n \le 100$, and sketch the limits to which such tests can be performedusing currently available technology. We conclude that there are no APNmonomials among the tested functions, outside of known classes.

An infinite family of 0-APN monomials with two parameters