Original version of This story Appear in Quanta Magazine.
Serious problems are usually not a welcome sight. But cryptographers like them. This is because some hard math problems are the security of modern encryption. Any clever trick to solve them will be spread throughout most forms of encryption.
A few years ago, researchers discovered A thorough encryption method This lacks this potential weakness. This method takes advantage of the features of quantum physics. However, unlike earlier quantum encryption schemes that only work for some special tasks, the new approach can accomplish a wider range of tasks. Even if all the problems at the core of ordinary “classical” cryptography are easy to solve, it works.
However, this compelling finding relies on unrealistic assumptions. The result is “more proof of concept” Fermi Horsea cryptography researcher at the Simmons Institute for Computational Theory in Berkeley, California. “It’s not a statement about the real world.”
Now, New paper Two cryptographers have proposed a path to quantum cryptography without those weird assumptions. “This article says that if some other conjecture is correct, then quantum encryption must exist.”
Castle in the sky
You can think of modern cryptography as a tower with three basic parts. The first part is the bedrock below the tower, which is made of hard mathematical problems. The tower itself is the second part – you can find specific encryption protocols that allow you to send private messages, sign digital documents, cast secret ballots, and more.
In between, ensuring these daily applications into mathematical bedrock is the basis of what is called One-way function. They are responsible for the asymmetry inherent in any encryption scheme. “It’s one-way because you can encrypt messages, but you can’t decrypt them.” Mark Zhandrya cryptographer at NTT Research.
In the 1980s, researchers demonstrated that cryptography built on top of one-way functions would ensure that many different tasks were secure. But decades later, they are still unsure that the bedrock is strong enough to support it. The problem is that the bedrock is made of a special hard problem, which is technically called the NP problem – the definition function is easy to check if any candidate solution is correct. (For example, breaking down a number into a main factor is an NP problem: it’s hard to do for big numbers, but easy to check.)
Many of these problems seem difficult in nature, but computer scientists No proof yet. If someone finds a clever algorithm to quickly solve the most serious NP problem, the bedrock will collapse and the entire tower will collapse.
Unfortunately, you can’t simply move the tower somewhere else. The foundation of the tower (a function) can only sit on the bedrock of the NP problem.
To build towers on more serious issues, cryptologists will need a new foundation, rather than made from one-way functions. Until a few years ago, researchers realized that quantum physics could help, which seemed impossible.
