Why gcd(r,(p-1)/r) needs to be 1 in benaloh cryptosystem I recently discovered the benaloh cryptosystem.
I am working with the system as it is discribed in the following link:
https://en.wikipedia.org/wiki/Benaloh_cryptosystem

However I need some help in order to understand why we need
\begin{equation}
{gcd(r,(p-1)/r)} 
\end{equation}

As far as I understand the condition
\begin{equation}
r \mid (p-1) 
\end{equation}
guarantees the existence of the subgroup of order (p-1)/r which contains the r-residues.

The third condition 

\begin{equation}
{gcd(r,(q-1))} 
\end{equation}

allows us to say that there are 

\begin{equation}
\mid \mathbb{Z}_n^* \mid /r
\end{equation}
r-residues mod n.

what does the other condition add?
$gcd(r,(p-1)/r)$ needs to be $1$ in Benaloh cryptosystem that mean that $(r)$ and $(p-1)$ are preliminary among them.