While reading some papers, I found that sometimes $Z_p$ was used but sometimes $F_p$ was used ($p$ is prime). Usually, the author will only use their subgroups like this: choose a big prime factor of $p-1$ , denote $q$, and set $G=\langle g \rangle$.
My questions are :
- Why do we only use the subgroup while $Z_p$ OR $F_p$? Or maybe we can choose a $p$ such that $p-1$ is prime and now if $Z_p^*$ or $F_p^*$ can be directly used?
- What's the difference of using $Z_p$ and $F_p$?