Every time you buy something online, you put your faith in math – simple math that's easy to do in one direction but difficult to do in reverse. That's what protects your credit card information from would-be thieves. But the system can be hacked.

One popular encryption scheme, for instance, can be undone only by factoring a huge random number, a "key" unlocking encoded information, into two prime numbers. It's a task that today is extraordinarily difficult, but not impossible. With enough computing power, a spying government could break the key. Or some clever mathematician could find an easy way to factor large numbers and do it tomorrow, in theory.

In search of greater security from code breakers, a new generation of code makers has been turning from math to physics. Experts in atoms and other particles, these cryptologists want to exploit the laws of quantum mechanics to send messages that are provably unhackable. They are the architects of a new field called quantum cryptography, which has come of age only in the past few decades.