The Zeta-function of an algebraic variety $X$ over $\mathbb{F}_q$ is defined as:
\begin{equation*} Z(X,t) = \exp\left(\sum_{m \geq 1} \frac{N_m}{m}t^m \right) \end{equation*}
where $N_m = |X(\mathbb{F}_{q^m})|$ i.e. the number of $q^m$-points of $X$.
It is often written in works involving calculations about this zeta function that has a lot of applications about the world of cryptography. But in all of these works I can't find any real references to that.
I just want to understand how these zeta function have concrete applications to cryptography (if there are any) and if they arealready used or in development. Or they are theoric concepts.
Thanks for any references.