The DLP is defined as finding $x$, for:
$$g^x=h\pmod{p}$$
Where $p$ is prime
1) I think that to calculate the multiplicative order you take $g$ and $p$, and find $m$, where $m$ is the minimum positive integer s.t. $g^m=1\pmod{p}$.
2) Another method is that $m=order(Z_p^*)=p-1$
Question: Which method is correct?
I then check if $m$ can be wrote in form $q^e$, where $q$ is prime and $e \ge 1$.
I see that $q$ and $e$ can be used to calculate $x$.
I'm following the algorithm "Proposition 2.34" in Introduction to Mathematical Cryptography by Jones, Silverman et al