In Schoenmakers' PVSS scheme, the secret distributor selects a random number $s \in \mathbb{Z}_q$, and the secret is defined as $S=h^s\bmod p$.
What restricts the PVSS scheme to sharing the secret $h^s$ instead of $s$ itself?
Additionally, $S=h^s$ does not allow arbitrary setting of the secret value, how can I configure the secret to ensure that any desired secret value can be used? Is there a simple method to achieve this?
