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Cryptographic transactions

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I remember once studying cryptographic protocols for transactions in which third parties can verify that the transaction has been acknowledged by both main parties yet only the two main parties know the contents of the transaction. I can't remember the names of any such protocols -- can you?

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That would be either simple encryption with no special protocol at all, or a broken protocol.
If you only want to hide a message's content from a non-involved third party, and everything else does not matter, then simple symmetric encryption with any of the available algorithms will do. Compress your data before encrypting to reduce entropy, don't tell anyone else your keys, and you'll be just fine.

On the other hand, most people would want more features, such as perfect forward security and plausable deniability. In other words: what happens when the governmental rogues knock down your door and steal your computer under some premise, will they be able to read the messages you sent a year ago? What happens if you give out your decryption under torture?
There are protocols that give a certain degree of protection against these scenarios, however, it obviously means that a third party cannot verify whether a message has been sent/received/acknowledged, too.

If you explicitely want a third party to know that a message has been received and acknowledged (I can't imagine why, but maybe for logging or whatever?), then you could attach an ID to every message and send that ID (maybe encrypted using the third party's public key, so only the controlling entity can read it) to the third party both when sending out messages, and when sending out ACKs.

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Maybe I didn't fully explain. To verify that two people have read a message isn't hard, they can just sign it, but when that message is a transaction we may need to verify that the transaction, possibly involving several messages, has in fact completed atomically.

Obvious example: I tell one bank to transfer money into another account. The two banks need to be able to make an atomic action. I need to verify that the action was the one I requested. Furthermore to resolve disputes, a court of law ought to be able to verify that the transaction took place without necessarily knowing what the transaction involved. The basic idea would be to have a public hash (signed by me) of the requested action, which hides the transaction request but uniquely identifies it, and the courts can verify that the banks' actomic action pertaining to that hash did complete.

That's the rough idea but the protocol needs to be secure against replay attacks etc etc. It's a bit more subtle than just tagging and signing any old messages. The work has been done academically, I've seen it, I just can't remember who did it.

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