The New Math of Quantum Cryptography

The unique model of this story appeared in Quanta Journal.Arduous issues are often not a welcome sight. However cryptographers love them. That’s as a result of sure laborious 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 method to encryption that lacks this potential weak spot. The method 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 method can accomplish a a lot wider vary of duties. And it might work even when all the issues on the coronary heart of atypical “classical” cryptography grow to be simply solvable.However this putting discovery relied on unrealistic assumptions. The consequence was “extra of a proof of idea,” mentioned Fermi Ma, a cryptography researcher on the Simons Institute for the Concept of Computing in Berkeley, California. “It’s not a press release about the true world.”Now, a brand 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 mentioned.Citadel within the SkyYou can consider fashionable cryptography as a tower with three important elements. The primary half is the bedrock deep beneath the tower, which is made from laborious 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 capabilities. They’re chargeable for the asymmetry inherent in any encryption scheme. “It’s one-way as a result of you possibly can encrypt messages, however you possibly can’t decrypt them,” mentioned Mark Zhandry, a cryptographer at NTT Analysis.Within the Nineteen Eighties, researchers proved that cryptography constructed atop one-way capabilities would guarantee safety for a lot of completely different duties. However many years later, they nonetheless aren’t sure that the bedrock is robust sufficient to assist it. The difficulty is that the bedrock is made from particular laborious issues—technically generally known as NP issues—whose defining function is that it’s straightforward to test whether or not any candidate answer is appropriate. (For instance, breaking a quantity into its prime elements is an NP downside: laborious to do for big numbers, however straightforward to test.)Many of those issues appear intrinsically troublesome, 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 possibly can’t merely transfer your tower elsewhere. The tower’s basis—one-way capabilities—can solely sit on a bedrock of NP issues.To construct a tower on tougher issues, cryptographers would wish a brand new basis that isn’t made from one-way capabilities. That appeared unattainable till only a few years in the past, when researchers realized that quantum physics might assist.