The unique model of this story appeared in Quanta Journal.
Exhausting issues are normally not a welcome sight. However cryptographers love them. That’s as a result of sure arduous 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 might work even when all the issues on the coronary heart of atypical “classical” cryptography turn into 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 Principle of Computing in Berkeley, California. “It isn’t an announcement about the true 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.
Fortress within the Sky
You may consider trendy cryptography as a tower with three important elements. The primary half is the bedrock deep beneath the tower, which is manufactured from arduous mathematical issues. The tower itself is the second half—there you’ll find particular cryptographic protocols that allow you to ship non-public messages, signal digital paperwork, solid secret ballots, and extra.
In between, securing these day-to-day purposes to mathematical bedrock, is a basis manufactured from constructing blocks known as one-way capabilities. They’re answerable 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 capabilities 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 manufactured from particular arduous issues—technically often called NP issues—whose defining function is that it’s straightforward to examine whether or not any candidate answer is right. (For instance, breaking a quantity into its prime elements is an NP downside: arduous to do for big numbers, however straightforward to examine.)
Many of those issues appear intrinsically tough, however laptop 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 more durable issues, cryptographers would want a brand new basis that isn’t manufactured from one-way capabilities. That appeared unattainable till only a few years in the past, when researchers realized that quantum physics might assist.
