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Does the Pedersen commitment scheme allow for checking whether two commitments are made - say by different people - for the same value?

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Committing to a value with a commitment scheme doesn't have something to link it to a certain user (e.g., the committer doesn't have a public key or something like that).

Moreover, the purpose of a commitment scheme is that the committer will interact with the receiver in order to firstly commit to a certain value and then "open" the commitment, i.e., send the "decommitment" information and the original value, so that the receiver can verify that the commitment was correct. Thus, the committer doesn't care of hiding his identity since he interacts either way with the receiver.

Actually, the Pedersen commitment scheme ensures that the commitments are different each time even for the same value. Therefore, one couldn't check even if two commitments have the same or different values, regardless of who created them.

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