The New Math of Quantum Cryptography

The unique model of this story appeared in Quanta Journal.

Onerous issues are normally not a welcome sight. However cryptographers love them. That’s as a result of sure onerous math issues underpin the safety of contemporary encryption. Any intelligent trick for fixing them will doom most types of cryptography.

A number of years in the past, researchers discovered a radically new strategy to encryption that lacks this potential weak spot. The strategy exploits the peculiar options of quantum physics. However not like earlier quantum encryption schemes, which solely work for just a few particular duties, the brand new strategy can accomplish a a lot wider vary of duties. And it may work even when all the issues on the coronary heart of abnormal “classical” cryptography develop into simply solvable.

However this hanging discovery relied on unrealistic assumptions. The end result was “extra of a proof of idea,” stated Fermi Ma, a cryptography researcher on the Simons Institute for the Idea of Computing in Berkeley, California. “It’s not an announcement about the actual world.”

Now, a new paper by two cryptographers has laid out a path to quantum cryptography with out these outlandish assumptions. “This paper is saying that if sure different conjectures are true, then quantum cryptography should exist,” Ma stated.

Fort within the Sky

You possibly can consider trendy cryptography as a tower with three important components. The primary half is the bedrock deep beneath the tower, which is made from onerous mathematical issues. The tower itself is the second half—there you’ll find particular cryptographic protocols that allow you to ship personal messages, signal digital paperwork, forged secret ballots, and extra.

In between, securing these day-to-day functions to mathematical bedrock, is a basis made from constructing blocks referred to as one-way features. They’re chargeable for the asymmetry inherent in any encryption scheme. “It’s one-way as a result of you’ll be able to encrypt messages, however you’ll be able to’t decrypt them,” stated Mark Zhandry, a cryptographer at NTT Analysis.

Within the Nineteen Eighties, researchers proved that cryptography constructed atop one-way features would guarantee safety for a lot of totally different duties. However a long time later, they nonetheless aren’t sure that the bedrock is powerful sufficient to help it. The difficulty is that the bedrock is made from particular onerous issues—technically generally known as NP issues—whose defining characteristic is that it’s simple to test whether or not any candidate answer is appropriate. (For instance, breaking a quantity into its prime components is an NP drawback: onerous to do for big numbers, however simple to test.)

Many of those issues appear intrinsically tough, however pc scientists haven’t been in a position to show it. If somebody discovers an ingenious algorithm for quickly fixing the toughest NP issues, the bedrock will crumble, and the entire tower will collapse.

Sadly, you’ll be able to’t merely transfer your tower elsewhere. The tower’s basis—one-way features—can solely sit on a bedrock of NP issues.

To construct a tower on tougher issues, cryptographers would want a brand new basis that isn’t made from one-way features. That appeared not possible till only a few years in the past, when researchers realized that quantum physics may assist.