Bitcoin is a very interesting virtual currency that uses advanced cryptography to create and maintain the value of the currency.

Benjamin Wallace at Wired Magazine has an excellent report on "The Rise and Fall of Bitcoin."

One of the core challenges of designing a digital currency involves something called the double-spending problem. If a digital dollar is just information, free from the corporeal strictures of paper and metal, what’s to prevent people from copying and pasting it as easily as a chunk of text, “spending” it as many times as they want?

The conventional answer involved using a central clearinghouse to keep a real-time ledger of all transactions—ensuring that, if someone spends his last digital dollar, he can’t then spend it again. The ledger prevents fraud, but it also requires a trusted third party to administer it.

Bitcoin did away with the third party by publicly distributing the ledger, what Nakamoto called the “block chain.” Users willing to devote CPU power to running a special piece of software would be called miners and would form a network to maintain the block chain collectively. In the process, they would also generate new currency.

Bitcoin is an excellent example of what cryptography can achieve but also an example showing that even advanced cryptography has weaknesses and limits. It'll be fascinating to see the next generation of Bitcoin technologies.