I'm amazed nobody mentioned Blackbytes in 4 pages.
Blackbytes!
Byteball has two build-in currencies: bytes and blackbytes. Bytes can be traded at Bittrex, blackbytes are untraceable and can't be traded at an exchange (yet). They can only be exchanged after pairing wallets. The Byteball wallet has a chat in which you can do this.
Analogy
Think of Blackbytes as a post-it handed to you by the previous owner. The post-it says: "you are now the new owner". Together with handing you the post-it, the DAG registers that the previous owner is no longer the owner of these Blackbytes. The DAG does not register who received the post-it.
Now, if you lose this post-it, the previous owner can simply give you another post-it that says: "you are now the new owner".
If you want to give your Blackbytes to someone else, your post-it contains all the information you need to create a new valid post-it for the receiving user, and to register the change of ownership in the DAG. Nobody else knows you're the owner, ownership is not registered anywhere.So if I understand correctly, the public block chain is just a "bag of hashes" which cannot be verified or anything by any node or miner. It is just a block chain of "data". These data only have meaning for the people receiving "banknote files", which allows them to check the validity of the whole "banknote". The hashes are in fact nothing else but hashes of "signed transactions", like with bitcoin, except that only the *signature hash* goes on the public block chain, and the actual transaction data remain on the individual banknote file. Is that the gist ? In fact, you need, as you say, TWO signatures (or hashes of signatures): one is the transaction signature (including the new beneficiary) and the other is the "spend" signature of simply the previous output. The first signature (spending signature) makes that you cannot do double spending any more (you have invalidated the file up to the point where you transmit it), and the second signature allows the receiver to have a valid "new address" that he can spend (and only he, because only he has the secret key that goes with it like on bitcoin).
This is indeed a very, very good idea !
Further reading:
Byteball - smart payments made simple
BYTEBALL: Totally new consensus algorithm + private untraceable payments
Byteball: Blackbytes FAQ