The unique model of this story appeared in Quanta Journal.
Exhausting issues are often 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 in contrast to earlier quantum encryption schemes, which solely work for a number of 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 peculiar “classical” cryptography turn into simply solvable.
However this placing discovery relied on unrealistic assumptions. The outcome 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 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 mentioned.
Fort within the Sky
You may consider fashionable cryptography as a tower with three important elements. The primary half is the bedrock deep beneath the tower, which is product of onerous mathematical issues. The tower itself is the second half—there yow 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 product of 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 possibly can encrypt messages, however you possibly can’t decrypt them,” mentioned Mark Zhandry, a cryptographer at NTT Analysis.
Within the Eighties, researchers proved that cryptography constructed atop one-way features would guarantee safety for a lot of completely different duties. However a long time later, they nonetheless aren’t sure that the bedrock is robust sufficient to assist it. The difficulty is that the bedrock is product of particular onerous issues—technically often known as NP issues—whose defining function is that it’s straightforward to test whether or not any candidate resolution is right. (For instance, breaking a quantity into its prime elements is an NP drawback: onerous to do for giant 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 possibly can’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 more durable issues, cryptographers would wish a brand new basis that isn’t product of one-way features. That appeared not possible till only a few years in the past, when researchers realized that quantum physics might assist.
