In schnorr identification protocol, a prover needs to choose a random,let's say $r$ at the beginning, then commit to this randomness as $g^r\bmod p$. When we say "commit", does it really mean we are using a commitment scheme?
if so, a commitment scheme needs to have binding and hiding properties. In this case I can get it is binding. But for hiding, it is not clear for me to see this property. Since the definition of hiding is adversary generate two messages $m_1,m_2$ and the adversary cannot distinguish their commitments.