Hard to be confident of what’s inside (Image: Sipa Press/Rex)

A MATHEMATICAL trick designed by cryptographers could be a key tool in nuclear disarmament.

Current disarmament treaties limit the number of nuclear warheads that a country has deployed and ready to use. Future treaties may also place limits on stored ones, but a country could mock up a fake storage centre and destroy its missiles for show – while keeping its real stockpiles intact.

Radiation scans can verify that a non-deployed warhead is genuine, but would also reveal secret details, making nations unwilling to consent. “An expert can look at the radiation signature and essentially reverse engineer the design,” says Alexander Glaser of Princeton University.


An expert can look at the radiation signature and reverse engineer the warhead’s design

For a way to verify that a warhead marked for destruction is real without spilling a state’s secrets, Glaser and his colleagues turned to a mathematical method that can prove something is true without revealing why it’s true.

Cryptographers dreamed up such “zero-knowledge proofs” in the 1980s. To understand how they work, imagine two cups holding the same number of marbles, x. To prove to someone that both contain x marbles, you first create two buckets, each with 100-minus-x marbles: these are called “inverses” of the cups. A verifier then mixes each original cup with a randomly chosen bucket: if, and only if, the two cups really were the same will the marbles in each of the final, mixed buckets consistently total 100. Yet the verifier never finds out what x was (see below).

How can this be applied to nukes? Firing neutrons through a warhead during a scan produces bubbles in a particular pattern in a liquid-filled detector. This reveals if it is genuine, but also the warhead’s structure. So Glaser’s team has used simulations to show that preloading the detector with an inverse pattern of bubbles and then carrying out the scan would prevent this disclosure. They say that carrying out the same scan on two identical missiles – a deployed one and another from a stockpile marked for destruction – would count as evidence that the stored missile is genuine, since a government is unlikely to deploy fake warheads (Nature, DOI: 10.1038/nature13457).

There is much more work to be done, but David Cliff of VERTIC, which helps to verify international agreements, is optimistic. “It could open a whole new chapter in nuclear arms control treaties.”

This article appeared in print under the headline “Crypto proof paves way for nuke-free world”