It’s not hard to imagine the advantages of location-based cryptography. The goal is to send a message that can only be read by somebody at a specific location. As long as the perimeter of this location is secure, this message should remain perfectly secret. How governments, the military and banks would like to get their hands on something like that.
For some years now, cryptographers have been working on a such a scheme. Their approach is to verify the position of the receiver by triangulation. So Alice uses a number of transmitters to each send a signal to a Bob who immediately returns these signals at the speed of light. As long as the returns arrive within a certain time window, Alice can use triangulation to be sure that Bob is where he says he is.
A couple of years ago, however, Nishanth Chandran at the University of California, Los Angeles and a few pals proved that this system doesn’t work. The problem is that if Eve uses a large number of attackers to overhear the signals being sent, she can use the information to also triangulate the Bob’s position and break the security.
That was a heavy blow for location-based cryptography
Today, Chandran and pals make amends. They say that while the classical version of this scheme is breakable, a quantum version can be perfectly secure.
To see how, imagine a one dimensional version of the problem in which Alice has two transmitters on a straight line with Bob somewhere in between. Alice’s first transmitter sends Bob a qubit that encodes a certain number. Bob can only extract this number from the qubit if he makes the right type of measurement on it, which he does not know. So Alice’s second transmitter sends him the information he needs to make the measurement.
Bob then makes the measurement and immediately sends the result back to Alice. If it arrives within the correct time window, then Alice can be sure Bob is where he says it is. Chandran and co then go on to show how Alice and Bob can exchange qubits like this to generate a key for encrypting a message.
The result of this position-based key exchange is a one time pad that can then be used to send a perfectly secure message that only Bob can read at his specific location.
Now imagine how Eve might attack this message. She might position her own eavesdroppers on either side of Bob to pick up the information sent by Alice. However, if Eve tries to measure the value of the qubit simply by guessing how to carry out the measurement, she is highly likely to get the wrong answer. On the other hand, if she waits to receive the information from Alice’s second transmitter which reveals how to make the measurement, she cannot then send the answer back in time to fool Alice that she is in Bob’s location.
So Alice can be perfectly sure she is talking only to Bob.
That’s a powerful idea because it makes no assumptions other than that laws of quantum physics are correct. Neither is it technically complex–only the qubit need be sent along a quantum channel, all other communication can be classical. A quantum measurement is necessary but no quantum computation. In short, there is no technological reason why this scheme cannot be implemented now.
But the scheme will need some careful study. While the approach is relatively simple in conception, the proof of its security is complex and involved. And theoretical security is not the same as practical security which looks harder to verify. Chandran and co offer one such scheme at the end of their paper but are unable to nail it. “Unfortunately we do not have a security proof, and we leave it as an open problem to find an attack or prove its security,” they say.
That’s disappointing but it shouldn’t to take away from the substantial achievement of initiating an entirely new line of cryptographic research that could have big implications for how we protect information in future. Expect to hear more about position-based quantum cryptography in the near future
Ref: arxiv.org/abs/1005.1750: Position-Based Quantum Cryptography
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