I am looking into the security of Diffie-Hellman and the discrete log in general.
To make sure an attacker can not use Pohlig-Hellman to solve the discrete log quickly we need to make sure that the order of the group, $n$, has a large prime factor.
For Diffie-Hellman in $F_p$ this would mean that we should factorize $p-1$. Since we should take $p$ to be at least $1024$ bits, how are we supposed to factor $p-1$? is this not just as hard as the RSA problem?