I was reading an introduction on elliptic curves, when the symbol $$\mathbb{F}_p^{\ast}$$ showed up. I understand that $\mathbb{F}_p = \mathbb{Z}/p\mathbb{Z}$ is the Galois field of the integers modulo the prime number $p$, but I cannot make my mind about the asterisk $\ast$.
In case it can be useful, it was used to provide an example of field for which the discrete logarithm problem is considered hard—namely $(\mathbb{F}_p^{\ast},\cdot)$.
In a ring $A$, the asterisk usually means the set of "regular elements" of $A=:A^*$ (elements $a\in A$ such that for every $b\in A$ if $ab=0$ then $b=0$).
On the other hand $A^{\times}$ denotes the set of "inversible elements" (elements $a\in A$ such that one can find $b\in A$ such that $ab=1=ba$).
So in your case $\mathbb{F}_p^*$ denotes the set of regular elements of the ring $\mathbb{Z}/p\mathbb{Z}$ but because you are on a finite ring $A$, you always have $A^*=A^{\times}$ (it is actually an easy and interesting exercise to show this), so that $\mathbb{F}_p^*$ also denotes the group of inversible elements of the ring $\mathbb{Z}/p\mathbb{Z}$.