Have you looked into VRFs (verifiable random functions)? This is essentially a public key crypto version of HMACs. You have a piece of data and a blinding fact

Have you looked into VRFs (verifiable random functions)? This is essentially a public key crypto version of HMACs. You have a piece of data and a blinding factor, both are committed into a single point on an elliptic curve, and blinding factor is not exposed as-is (as in case with salt for hashed content), but instead committed into a public key (a point). The resulting point preserves the algebraic structure, which allows you to sign proofs about it, but w/o leaking the blinding factor. You can even sign a proof to a "designated verifier", which makes the proof useful only to a specific party, but anyone else wouldn't be able to trust it as it could be forged by that other party.