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 recent 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 in contrast to earlier quantum encryption schemes, which solely work for a number of 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 strange “classical” cryptography become simply solvable.
However this putting 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 a press release 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 stated.
Fort within the Sky
You possibly can consider trendy cryptography as a tower with three important elements. The primary half is the bedrock deep beneath the tower, which is manufactured 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, solid secret ballots, and extra.
In between, securing these day-to-day functions to mathematical bedrock, is a basis manufactured from constructing blocks known as one-way capabilities. They’re accountable for the asymmetry inherent in any encryption scheme. “It’s one-way as a result of you may encrypt messages, however you may’t decrypt them,” stated 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 many years later, they nonetheless aren’t sure that the bedrock is powerful sufficient to help it. The difficulty is that the bedrock is manufactured from particular laborious issues—technically referred to as NP issues—whose defining characteristic is that it’s simple to test whether or not any candidate resolution is right. (For instance, breaking a quantity into its prime elements is an NP downside: laborious to do for big numbers, however simple 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 may’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 inconceivable till only a few years in the past, when researchers realized that quantum physics might assist.