How do you prove you know a secret without giving away the piece?

A new tool expands ways for users to prove they’ve solved a problem without revealing the solution.

By Pierre Salle edited by Sarah Lewin Frasier

In mathematics, proofs can be written down and shared. In cryptography, when people try to avoid revealing their secretsthe evidence is not always so straightforward, but a new result significantly fills this gap.

Zero-knowledge proofs are the closest cryptography has to magic. They promise to let one person convince another of the truth of a fact (for example, that they know the solution to a Sudoku puzzle) without disclosing any information about it. Such proofs can help people virtually authenticate their identities, conduct online banking, build blockchains, and more.

Cryptographers, however, have long Understood that zero-knowledge proofs cannot be safely written down like a typical mathematical proof. Instead, the prover must interact with the person he or she is convincing. In rare cases, the prover can also persuade someone of something false (for example, that a sudoku puzzle can be completed if it has no solutions).

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Computer scientist Rahul Ilango realized that there was a gap between the definition of zero knowledge and how it is used. Typical zero-knowledge proofs require a demonstration of how to build what is called a simulator, which can recreate the steps of the proof without actually knowing the secret solution. The existence of this simulator shows that the proof process reveals nothing about the solution itself. But Ilango found that it may be enough, in some cases, to simply show that the existence of a simulator cannot be ruled out. He presented the result at the 2025 IEEE Computer Science Foundations Symposium in Sydney.

“You could imagine a really strange scenario where a cryptographic system is not secure. [and reveals something about the information that is locked inside]but it is impossible to prove that it is not secure,” says Ilango, based at the Institute for Advanced Study in Princeton, New Jersey. “This means that it is fundamentally secure for all practical purposes. »

Because this new criterion is just a little easier to satisfy than zero knowledge, Ilango could build protocols that do not require interaction between parties and that prevent the prover from convincing with false answers.

To construct the new proof system, actually called a zero-knowledge proof, Ilango was inspired by the ideas of the mathematician Kurt Gödel’s 1931 incompleteness theoremwhich basically says that many sets of hypotheses contain facts that they can neither prove nor disprove. Ilango showed that he could construct a proof system in which such hypotheses, including a set known as ZFC which underlies much of mathematics, cannot disprove the existence of a simulator even if it does not exist.

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