Semi-classical Encryption

There’s been a bit in the news lately about Kish’s classical encryption scheme, which is really quite clever. The idea is that in any circuit with resistance there is thermal noise–called Johnson noise–that depends on the total resistance of the circuit. If Alice and Bob have a wire running between them Alice can put one of two resistors in the circuit to ground, corresponding to 1 and 0. Bob attaches similar resistors randomly. Since Bob knows what his resistor is he can work out which resistor Alice is using by looking at the noise spectrum. But since no one but Bob knows what Bob’s resistance is at any given time, no one else can work out which resistor Alice has on the wire at any given time.

Like all these things it is subject to extreme person-in-the-middle attacks: if Malfoy cuts the wire and replaces Bob (from Alice’s perspective) and Alic (from Bob’s perspective) he can both decode Alice’s message and send anything he likes to Bob. But apart from that it’s deeply secure. Cracking it would be a violation of the 2nd Law of Thermodynamics.

This got me thinking that there is a comparable semi-classical, or partially quantum, technique that is similar: connect Alice and Bob by a fibre-optic loop. Alice sends photons down the fibre that are randomly polarized in some linear basis, but such that she knows which photon has what polarization. This could be done with an EPR-type parametric down-conversion source where Alice just measures the polarization of one member of the pair in some linear basis, or it could be done with a rapid optical switch between output arms of a polarizing beam-splitter for a perfectly ordinary single-photon emission source.

In this set-up, Bob is sending a message to Alice. When a photon reaches Bob he either sends it through a quarter-wave plate, or not. The overall polarization of the beam is still zero, but it now consists of circularly rather than linearly polarized photons if it passed through the quarter-wave plate.

The photons then travel down the other half of the loop, back to Alice. Alice sends them through a polarizing beam splitter that has the same basis as her original measurement. When Bob is not interfering with the beam, the arriving photons will still have the polarization they left with, and she can correlate her measurements on the arriving photons with the value she measured them into on the way out. When Bob is interfering with the beam Alice will see no correlation between the incoming measurement and her outgoing one.

Since only Alice knows her basis states and which state was being fed into the fibre optic for a given photon, only Alice can see the correlation. So there is something quantum going on here even if there isn’t any use of an EPR source (such a source would make things a good deal simpler in the implementation, however.)

There are likely many schemes of this nature. The question is: are any of them susceptible to practical implementation? I would say it is likely that the one described here is, and I will assert without proof (because really, it’s obvious… although that doesn’t mean it’s true) that this scheme is perfectly secure against all attacks that do not break the fibre.