This post makes me think (keep thinking) if we can use a solution that I used for another project in another context: using a Cryptographic Feistel Network to compute UUIDS so they are reversible if you need to know the original order. Each entity uses another key for the generation but if they know the keys they can know the order of the other party. Basically is using an existing cryptographic function if the block size is the same and if not adaping it to a specific block size via a Feistel Network.