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 strategy to encryption that lacks this potential weak spot. The strategy exploits the peculiar options of quantum physics. However in contrast to 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 might work even when all the issues on the coronary heart of atypical “classical” cryptography change into simply solvable.
However this placing discovery relied on unrealistic assumptions. The outcome was “extra of a proof of idea,” stated Fermi Ma, a cryptography researcher on the Simons Institute for the Concept of Computing in Berkeley, California. “It isn’t an announcement about the actual 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 stated.
Fort within the Sky
You possibly can consider fashionable cryptography as a tower with three important components. The primary half is the bedrock deep beneath the tower, which is fabricated from laborious mathematical issues. The tower itself is the second half—there you will discover 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 purposes to mathematical bedrock, is a basis fabricated from constructing blocks referred to as one-way capabilities. They’re answerable 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 capabilities 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 fabricated from particular laborious issues—technically often called 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 drawback: laborious to do for big numbers, however straightforward to test.)
Many of those issues appear intrinsically tough, however pc scientists haven’t been capable of 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 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 fabricated from one-way capabilities. That appeared not possible till only a few years in the past, when researchers realized that quantum physics might assist.
