The New Math of Quantum Cryptography

The archetypal version of this story appeared in Quanta Magazine.

Hard problems are usually not a invited sight. But cryptographers emotion them. That’s due to the fact that definite hard mathematics problems underpin the information of modern encryption. Any clever instrumentality for solving them volition doom astir forms of cryptography.

Several years ago, researchers recovered a radically caller attack to encryption that lacks this imaginable anemic spot. The attack exploits the peculiar features of quantum physics. But dissimilar earlier quantum encryption schemes, which lone enactment for a fewer peculiar tasks, the caller attack tin execute a overmuch wider scope of tasks. And it could enactment adjacent if each the problems astatine the bosom of mean “classical” cryptography crook retired to beryllium easy solvable.

But this striking find relied connected unrealistic assumptions. The effect was “more of a impervious of concept,” said Fermi Ma, a cryptography researcher astatine the Simons Institute for the Theory of Computing successful Berkeley, California. “It is not a connection astir the existent world.”

Now, a new paper by 2 cryptographers has laid retired a way to quantum cryptography without those outlandish assumptions. “This insubstantial is saying that if definite different conjectures are true, past quantum cryptography indispensable exist,” Ma said.

Castle successful the Sky

You tin deliberation of modern cryptography arsenic a operation with 3 indispensable parts. The archetypal portion is the bedrock heavy beneath the tower, which is made of hard mathematical problems. The operation itself is the 2nd part—there you tin find circumstantial cryptographic protocols that fto you nonstop backstage messages, motion integer documents, formed concealed ballots, and more.

In between, securing those day-to-day applications to mathematical bedrock, is simply a instauration made of gathering blocks called one-way functions. They’re liable for the asymmetry inherent successful immoderate encryption scheme. “It’s one-way due to the fact that you tin encrypt messages, but you can’t decrypt them,” said Mark Zhandry, a cryptographer astatine NTT Research.

In the 1980s, researchers proved that cryptography built atop one-way functions would guarantee information for galore antithetic tasks. But decades later, they inactive aren’t definite that the bedrock is beardown capable to enactment it. The occupation is that the bedrock is made of peculiar hard problems—technically known arsenic NP problems—whose defining diagnostic is that it’s casual to cheque whether immoderate campaigner solution is correct. (For example, breaking a fig into its premier factors is an NP problem: hard to bash for ample numbers, but casual to check.)

Many of these problems look intrinsically difficult, but machine scientists haven’t been capable to beryllium it. If idiosyncratic discovers an ingenious algorithm for rapidly solving the hardest NP problems, the bedrock volition crumble, and the full operation volition collapse.

Unfortunately, you can’t simply determination your operation elsewhere. The tower’s foundation—one-way functions—can lone beryllium connected a bedrock of NP problems.

To physique a operation connected harder problems, cryptographers would request a caller instauration that isn’t made of one-way functions. That seemed intolerable until conscionable a fewer years ago, erstwhile researchers realized that quantum physics could help.