# Compute a hash function given commitment to some secret element

Given a secret key x and a commitment to it comm(x) where comm(x) is both binding and hiding (it can be for example $$g^x$$ or some homomorphic encryption). Given public parameters $$P_1,...,P_k$$, comm(x), and an index i, is there a scheme, other than fully homomorphic encryption, to to compute $$H(P_1,...,P_{i-1},x,P_{i+1},...,P_k)$$ (where H is some collision resistant hash function that act as a random oracle both on x and over public parameters $$P_i$$'s)?

• The whole point of using a blinding factor is to ensure that the bytes of 𝑥 for the commitment 𝑐𝑜𝑚𝑚(𝑥) cannot be known by an observer, and therefore cannot be concatenated into the hash input. Perhaps you are referring to a more elaborate scheme that would involve blind interaction with the owner of the secret key $x$? Jun 30, 2022 at 18:28
• Actually, if you could do that (without interacting with the committer), you could use that to test potential values of $x$, hence showing that your commitment scheme wasn't hiding... Jun 30, 2022 at 18:52
• @knaccc You are right. And If there was another way to compute this hash without concatenating x, then this hash would not be collision resistant. Thanks! Jun 30, 2022 at 20:48
• @poncho perhaps you could argue that this hash is a random oracle and therefore you could not gain any significant information on x. But basically you are right. Jun 30, 2022 at 20:50