How ‘effectively zero-knowledge’ proofs could transform cryptography

By Peter Hall edited by Sarah Lewin Frasier

In mathematics, proofs can be written down and shared. In cryptography, when people are trying to avoid revealing their secrets, proofs are not always so simple—but a new result significantly closes this gap.

Zero-knowledge proofs are the closest cryptography gets to magic. They promise to let one person convince another of the truth of some fact—say, that they know the solution to a sudoku puzzle—without giving away any information about it. Such proofs can help people authenticate identities virtually, make online banking transactions, build blockchains, and more.

Cryptographers, however, have long understood that zero-knowledge proofs can’t safely be written down like a typical mathematical proof. Instead the prover needs to interact with the person they’re convincing. In rare cases, the prover can also persuade someone of something untrue (such as that a sudoku puzzle is completable when it has no solution).

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Computer scientist Rahul Ilango realized there was a gap between how zero knowledge is defined and how it’s used. Typical zero-knowledge proofs require a demonstration of how to build what’s called a simulator, which can re-create the steps of the proof without actually knowing the secret solution. The existence of this simulator shows that the proof process does not reveal anything about the solution itself. But Ilango found that it can be enough, in some cases, to simply show that a simulator’s existence can’t be ruled out. He presented the result at the 2025 IEEE Symposium on Foundations of Computer Science in Sydney.

“You could imagine some really strange scenario where a cryptographic system is insecure [and reveals something about the information that is locked inside], but it’s impossible to prove it’s insecure,” says Ilango, who is based at the Institute for Advanced Study in Princeton, N.J. “What that means is it’s basically secure for all practical purposes.”

Because this new criterion is just a bit easier to satisfy than zero knowledge, Ilango could build protocols that don’t need the parties to interact and that prevent the prover from being able to convince with false answers.

To construct the new proof system, called an effectively zero-knowledge proof, Ilango took ideas from mathematician Kurt Gödel’s 1931 incompleteness theorem, which basically says many sets of assumptions have some facts they can neither prove nor disprove. Ilango showed that he could construct a proof system in which such assumptions, including a set known as ZFC that underlies much of mathematics, cannot disprove a simulator’s existence even when it doesn’t exist.

University of California, Los Angeles, computer scientist Amit Sahai, who was not involved in the work, says this paradigm is already proving more useful than he initially expected. “It’s just so beautiful,” Sahai says. “[Ilango]’s paper is, in my opinion, the most creative and most consequential paper in the field of zero-knowledge proofs at least in the past decade.”

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