How can knowledge of a secret be compared among untrusted entities?

secret-token

3/16/24, 10:52 AM

Lets say entity A sends a secret "token" to anybody that they trust.
The token itself is the proof and its sent equally to everybody and it has or needs to be derived from application specific data.

Entities B, C and D get the same token and want to publish a timestamped event for proof, but they don't trust anybody, each of them separately, salt&hash the secret and publish it to the outer world.

Now everybody that has the secret can verify that B and C and D also have it by taking their salts and the secret to produce the hashes.

However, there is no way for a random entity E to see B, C and Ds hashes & salts and ensure that they have the same secret without having the secret.

Is there any schema that would allow third party entities to ensure both B, C and D had access to the same secret without knowing or revealing the secret?

No need to know A, just take bytes from B and C with metadata and be able to tell if they started from the same unknown secret.

There is no hashing algorithm that I have seen that allows 2 pairs of (hash,salt) to prove they came from the same secret without knowing the secret.

0 + 2

salt

zero-knowledge-proofs

user253751

3/16/24, 12:26 PM

it seems like something Diffie-Hellman-like could maybe work here. like calculating G^secret^blind2^blind3^blind1 and G^blind1^secret^blind3^blind2 and G^blind1^blind2^secret^blind3 and then making sure they are all equal (perhaps by doing the first three steps of each, then publishing the blinds)

knaccc

3/16/24, 12:41 PM

Why not just use HKDF on the secret to derive a private key, and everyone can calculate the corresponding public key. (Note that the secret will need to be high-entropy). Now, people can prove they know the private key for that public key by announcing a signature of a timestamped message. Observers can easily see they are all providing signatures for the same public key. If the secret does not have sufficient entropy, then there is a more complex solution possible using Pedersen commitments

Elon Musk

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EN: How can knowledge of a secret be compared among untrusted entities?

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