Satoshi discussed this 'signature chain' ...
This is a very interesting topic. If a solution was found, a much better, easier, more convenient implementation of Bitcoin would be possible.
Originally, a coin can be just a chain of signatures. With a timestamp service, the old ones could be dropped eventually before there's too much backtrace fan-out, or coins could be kept individually or in denominations. It's the need to check for the absence of double-spends that requires global knowledge of all transactions.
The challenge is, how do you prove that no other spends exist? It seems a node must know about all transactions to be able to verify that. If it only knows the hash of the in/outpoints, it can't check the signatures to see if an outpoint has been spent before. Do you have any ideas on this?
It's hard to think of how to apply zero-knowledge-proofs in this case.
We're trying to prove the absence of something, which seems to require knowing about all and checking that the something isn't included.
... and the result was ...
...
I pursued this line of reasoning in the thread, but it turns out it is a FAIL. It turns out that Satoshi was correct. ...
Satoshi says "The challenge is, how do you prove that no other spends exist?" That means it could work if they found a way to prove it. It could only work with a blockchain. They didn't have a blockchain, they had to create it through running Bitcoin.
But we can use this blockchain for our 'signature transactions' and solve Satoshi's problem.
That's the reason why 'signature chain' works.
