Sigma protocol with Pedersen commitment and Hash function Suppose I construct a Pedersen commitment as $g^m h^r$. I could pick the randomness in a "pseudo-random" fashion, such that $r = H(m)$. My questions are as follows:


Given that $H$ is collision-resistant, does the security properties of the Pedersen commitment still hold? (i.e. is it still hiding and binding?)
Is there a way to construct a Sigma protocol which would prove in Zero-knowledge that a) I know $m$ and b) The commitment randomness is picked such that $r=H(m)$?


Edit: I do not require some specific hash function. Any pseudo-random function would serve my purposes.
This is no longer a secure commitment. Note that there should not be any way to efficiently verify if a given commitment value $c$ is to a message $m$. However, once you derive the randomness in this way, an attacker could try to guess $m$ and verify if this guess is correct by checking if $g^m\cdot h^{H(m)} = c$. Thus, this is not a secure commitment scheme.