In this sense, the same miner could process both transactions.
Mmm... you can't have the same miner process both transactions if they're on different networks.
The two parties would set up transactions on both sides such that when they both sign the transactions, the second signer's signature triggers the release of both
It's this part that strikes me as as a generic description of a cross-chain atomic swap. Granted, I think the implementations that were made later actually work with scripts containing hashes and pre-images, but the idea is basically the same: we craft 2 contracts built in such a way that when you claim your part, you end up releasing the information I need to claim mine. It's atomic in the sense that you either have the 2 things happening or nothing happens.
And I'm no cryptography wizzard, but I believe there is a way to do this with signatures.
Do you know about merged-mining?
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Yes, but he's talking about "trades" there, that's why I don't think merged mining applies.
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but specifically about a trade between merged mined chains: Bitcoin and BitDNS. You would have to know already that Satoshi suggested BitDNS as a use case for merged mining. Therefore he does actually mean a trade between merged mined chains.
Maybe he had a more general meaning, but that's my understanding from the context of the BitDNS discussion.
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