Quote from: ymgve2 on February 28, 2024, 01:40:28 AM

As far as I can tell you can't use the fact that key 1 and 2 are a known distance away from each other to discern anything about them. It's a single equation with two unknowns. Example: X + Y = 123, but X and Y could be 0 and 123, or they could be -113258881385746098181140976018376643534 and 113258881385746098181140976018376643657, or any other number.

Another way to think about it: Pick any arbitrary random public key from the blockchain, like say, the genesis block coinbase key, and call it #A1. Calculate #3 - #A1, and call the result #B1. You now have two keys #A1 and #B1 that when added gives #3, the exact same situation in your original question.

If this process would give you any insight into the private key of #A1, elliptic curve cryptography would be fundamentally broken.

This is basically the only possible answer.

While you could get the *public keys* of this sort of operation if you were doing the arithmetic between private keys (and indeed this is what I initially thought the OP was trying to do until I saw the 02 and 03 at the beginning of all the strings), it does not work the other way around.

Public key arithmetic without the private keys is really only interesting to cryptographers.