It is said that for the group $\mathbb{Z}_p^*$, the factorization of $p-1$, is critical.
If $p-1$ has some small factors $q_1, q_2, q_3, q_4$, then when we transmit $g^x \bmod p$ where $g$ is a generator of this group, the attacker can derive $x \bmod q_1q_2q_3q_4$
How does it happen?
Can someone please provide a practical example, say for $p = 29$, where $p$ is prime but $p-1$ has a bunch of small factors?
