Given a commitment scheme which is computationally binding (based on some conjectured hard problem, say), does it also imply that the scheme is unconditionally hiding?
My idea was: Since the scheme is computationally binding, it can be broken by an unbounded adversary, who can produce two openings to the same commitment. But this would make the scheme perfectly hiding, because even an unrestricted attacker cannot distinguish between the two (or more) openings of the same commitment by any means.
Is this correct? If not, are there any schemes that prove otherwise?