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There is a paper available here: http://www.bitcoin.org/sites/default/files/bitcoin.pdf

It's using digital signatures to transfer coins. The prior owner will sign a coin and the new owner's public key. The new owner will verify the prior signature before accepting the coin. This is a longstanding idea going back to the 80's.

The rest of the details are to prevent double-spending without having a centrally trusted authority. I haven't spent time looking at this and can't say whether it works as advertised.




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