I have a question regarding the Fiat–Shamir identification protocol. In this source (pdf) for example it says on pages 9 and 10 that the random commitment $r$ and the private key $s$ have to be smaller than $n$ (the RSA-like Modulus). I am wondering why this has to be.
The verification works even if $r$ and $s$ are greater than $n$. Also, if $r$ is smaller than $n$, an observer could calculate $r$, using the equation $y=r*s^e$ mod $n$. If $e=0$, this is equal to $y=r$ mod $n$, and since $r<n$, this is the same as $y=r$, so if somebody gets to know $y$, he would also know $r$. I thought that somebody was not supposed to be able to get information out of the knowledge of $y$ or $x$.
Is there something I am getting wrong here?