Recent weeks have been exciting for a relatively new kind of currency speculator. In just three weeks, the total value of a unique new digital currency called Bitcoin has jumped four times, to over $40 million.

Bitcoin is underwritten not by a government, but by a clever cryptographic scheme.

For now, little can be bought with bitcoins, and the new currency is still a long way from competing with the dollar. But this explainer lays out what Bitcoin is, why it matters, and what needs to happen for it to succeed.

Where does Bitcoin come from?

In 2008, a programmer known as Satoshi Nakamoto—a name believed to be an alias—posted a paper outlining Bitcoin's design to a cryptography e-mail list. Then, in early 2009, he (or she) released software that can be used to exchange bitcoins using the scheme. That software is now maintained by a volunteer open-source community coordinated by four core developers.

"Satoshi's a bit of a mysterious figure," says Jeff Garzik, a member of that core team and founder of Bitcoin Watch, which tracks the Bitcoin economy. "I and the other core developers have occasionally corresponded with him by e-mail, but it's always a crapshoot as to whether he responds," says Garzik. "That and the forum are the entirety of anyone's experience with him."

How does Bitcoin work?

Nakamoto wanted people to be able to exchange money electronically securely without the need for a third party, such as a bank or a company like PayPal. He based Bitcoin on cryptographic techniques that allow you to be sure the money you receive is genuine, even if you don't trust the sender.

The basics

Once you download and run the Bitcoin client software, it connects over the Internet to the decentralized network of all Bitcoin users and also generates a pair of unique, mathematically linked keys, which you'll need to exchange bitcoins with any other client. One key is private and kept hidden on your computer. The other is public and a version of it dubbed a Bitcoin address is given to other people so they can send you bitcoins. Crucially, it is practically impossible—even with the most powerful supercomputer—to work out someone's private key from their public key. This prevents anyone from impersonating you. Your public and private keys are stored in a file that can be transferred to another computer, for example if you upgrade.

A Bitcoin address looks something like this: 15VjRaDX9zpbA8LVnbrCAFzrVzN7ixHNsC. Stores that accept bitcoins—for example, this one, selling alpaca socks—provide you with their address so you can pay for goods.

Transferring bitcoins

When you perform a transaction, your Bitcoin software performs a mathematical operation to combine the other party's public key and your own private key with the amount of bitcoins that you want to transfer. The result of that operation is then sent out across the distributed Bitcoin network so the transaction can be verified by Bitcoin software clients not involved in the transfer.

Those clients make two checks on a transaction. One uses the public key to confirm that the true owner of the pair sent the money, by exploiting the mathematical relationship between a person's public and private keys; the second refers to a public transaction log stored on the computer of every Bitcoin user to confirm that the person has the bitcoins to spend.

When a client verifies a transaction, it forwards the details to others in the network to check for themselves. In this way a transaction quickly reaches and is verified by every Bitcoin client that is online. Some of those clients - "miners" - also try to add the new transfer to the public transaction log, by racing to solve a cryptographic puzzle. Once one of them wins the updated log is passed throughout the Bitcoin network. When your software receives the updated log it knows your payment was successful.

Security

The nature of the mathematics ensures that it is computationally easy to verify a transaction but practically impossible to generate fake transactions and spend bitcoins you don't own. The existence of a public log of all transactions also provides a deterrent to money laundering, says Garzik. "You're looking at a global public transaction register," he says. "You can trace the history of every single Bitcoin through that log, from its creation through every transaction."