Of course, Eve is all the while trying to listen in on the communication. Her best bet is to splice off some photons and, like Bob, measure them in a random coordinate system. About half of the time, she'll get the coordinate system right and measure the correct bit (0 or 1). The other half of the time, though, she gets it wrong. To hide her meddling, she needs to send photons on to Bob (or else he'd see that they're missing).  But she has no way of knowing what basis the photons were sent in, and so she must randomly guess in which coordinate system to resend the photon. She will get this wrong half of the time.

 Alice and Bob can then check if Eve tried to eavesdrop. They can publicly compare some subset of their distilled set. If they find discrepancies, they know that someone was listening in. Depending on the rate of the discrepancy, they can correct against the eavesdropper, or just break off their communication for the time being.

When the BB84 protocol was proposed in 1984,  people got a first proof of the power that quantum mechanics holds for information processing (Feynman had suggested but not proved the power of a quantum computer in 1981).  Since its introduction, many other types of quantum cryptography have been discovered, and we'll discuss the more important ones later in this series. BB84 is probably one of the easiest to understand, and is still one of the most powerful. 

In the next part of this series, we will consider some physical implementations of BB84.  It's come a long way in the last few years, and we'll consider the experiments that have brought it thus far.
 

[1] PKCS #1: RSA Cryptography Standard (RSA Laboratories website)

[2] Image from radio.weblogs.com/0105910/2004/05/03.html

[3] RSA Laboratories - http://www.rsa.com/rsalabs/node.asp?id=2094

[4] R. Feynman, “Simulating Physics with Computers, ”International Journal of Theoretical Physics 21 (6&7), pp. 467– 488,1981.