KentuckyFC writes: "Public key cryptography allows anybody to encrypt a message using a public key but only those with another private key can decrypt the message. That's possible because of certain mathematical functions that are easy to perform in one direction but hard to do in reverse. The most famous example is multiplication. It's easy to multiply two numbers together to get a third but hard to start with the third number and work out its factors. Now Japanese researchers have discovered a quantum problem that is hard to solve in one direction but easy to do in reverse. This asymmetry, they say, could form the basis of a new kind of quantum public key cryptography. Their system is based on the problem of distinguishing between two ensembles of quantum states. This is similar to the problem of determining whether two graphs are identical, ie whether they correspond vertex-for-vertex and edge-for-edge. Increasing the complexity of the graph can always make this problem practically impossible for a quantum computer to solve in a reasonable time. But knowing the structure of a subset of the graph makes this problem easy, so this acts as a kind of private key for decrypting messages."