The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.
Each owner transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next owner and adding these to the end of the coin.
The system is secure as long as honest nodes collectively control more CPU power than any cooperating group of attacker nodes.
In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions.
What is needed is an electronic payment system based on cryptographic proof instead of trust, allowing any two willing parties to transact directly with each other without the need for a trusted third party.
No mechanism exists to make payments over a communications channel without a trusted party.
Merchants must be wary of their customers, hassling them for more information than they would otherwise need.
While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model.
Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments.
A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.
Whoever understands, understands.