Discrete Logarithm in a specific group
Discrete logarithm can be hard in Paillier group. One case for example is when $p$ and $q$ are safe primes, i.e. $p=2p'+1$ and $q=2q'+1$ where $p',q'$ are themselves prime.

You can find more information about the critieria in this paper (and from its references): On the Portability of Generalized Schnorr Proofs, by Camenisch et al, Eurocrypt 2009