# #StackBounty: #reference-request #commitments Computationally binding commitment

### Bounty: 100

A Computationally Binding commitment scheme is defined as a tuple of protocols $$(mathsf{Keygen}, mathsf{Com}, mathsf{Open})$$, that along with correctness guarantees that for all PPT algorithms the probability that, given a correctly generated commitment key $$k$$, it outputs a commitment and two different openings is negligible.

Now, if the receiver sends a message $$R$$ between the committing phase and the opening phase, called $$m$$ the message revealed, then it’s almost never the case that $$m$$ and $$R$$ are independent (with negligible probability the adversary could open to a function of $$R$$). Can we at least say that $$m$$ and $$R$$ are "almost independent" (in this question I proposed a way to have relaxed independence)?

In case the answer is negative, what are computationally binding commitments used for?

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