1

For example imagine the situation where i have one unspent output valued at 0.5 XMR

In another wallet i also have another unspent output valued at 0.5 XMR

even thought these outputs share the same values they have different history's

when i construct a range proof for these outputs separately will the range proof be the same? or does the range proof generate uniquely based on the output you are using?

By same i mean that the data the range proof is constructed from is an exact match in the two cases with no data differing.

3

First of all, each Pedersen Commitment hides the committed amount by adding a random "blinding factor", so two commitments committing to the same amount will look completely differently.

Second, the range proof generation algorithm internally uses a lot of random numbers, so even for the same Pedersen Commitment, two or more range proofs will look completely differently. This property is true for all cryptographic signature schemes in general for security reasons: when the algorithm is run for a certain public key, the resulting signature data is always random and unique.

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