A zero knowledge proof is one in which a person is able to prove something without giving away any unnecessary details. It is an idea present in cryptology and has some important real life applications also. The simplest way I have thought of to explain it is with a magician who, of course, want to demonstrate his magic but doesn’t want to reveal how it works. To do this he asks a member of the audience to stand with his back to the magicians table. The magician will then put a ball under one of two cups on the table and request that the volunteer turns around and selects a cup. If the ball is under there then the two options are the magician was able to move the ball or he got lucky. But if this trick is performed ten times and the amount of cups is increased to five we can see it is incredibly unlikely that the magician could, by chance, have his volunteer pick the right cup so the conclusion must be that he can do magic but we still don’t know how. This fulfils the three rules of zero knowledge problems: Completeness, with enough experiments anyone should be convinced; Soundness, for if the magician is a sham he would statistically be found out; and Zero Knowledge proving his ability gives us no indication of anything but what he attempted to prove.
Now the difficulty is translating the illusion into real life. When two countries wish to negotiate a partial nuclear disarmament it is important that both countries know that the other is not handing over a fake nuclear warhead. But both countries might also not like even an independent third party rifling through the schematics and design of one of their missiles. Currently a computer program is able to analyse key components from the devices but this means at least some sensitive data has to be digitally stored. The solution is to use physical zero knowledge proof. Any nuclear device will react to probing by neutron radiation and so it is possible to use this the confirm the presence of something nuclear. Then the question is whether the recorded counts of neutron radiation fall onto a Poisson distribution. Anything that differs in size, shape or make up would lead to a significantly different results especially over a range of neutron energies. So long as the both sides hold each other to fairness both should receive confirmation of each other’s nuclear devices without revealing details of their own.