How ‘effectively zero-knowledge’ proofs could transform cryptography
A new tool expands the ways people can prove they’ve solved a problem without revealing the solution
In mathematics, proofs can be written and shared. In cryptography, when people try to avoid revealing their secrets, the proofs aren’t always so simple — but a new result closes the gap to a large extent.
Zero-knowledge proofs are the closest cryptography gets to magic. They promise to let one person convince another of the truth of a fact – say, that they know the solution to a Sudoku puzzle – without providing any information about it. Such proof can help people virtually authenticate identity, conduct online banking transactions, create blockchains, and much more.
However, cryptographers have a long understood Zero-knowledge proofs cannot be written safely like ordinary mathematical proofs. Instead, proverbs need to be a conversation with the person they are reassuring. In rare cases, proverbs may even persuade someone of a false belief (such as a Sudoku puzzle being complete when it has no solution).
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Computer scientist Rahul Ilango realized that there is a gap between how zero knowledge is defined and how it is used. Typical zero-knowledge proofs require a demonstration 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 procedure itself does not reveal anything about the solution. But Ilango found that in some cases, this may be enough to show that the existence of the simulator cannot be ruled out. He Presented Results of the 2025 IEEE Symposium on Foundations of Computer Science in Sydney.
“You can imagine some really weird scenario where a cryptographic system is insecure (and reveals something about the information locked inside), but it’s impossible to prove that it’s insecure,” says Ilango, who works at the Institute for Advanced Study in Princeton, N.J. “This means that it’s basically secure for all practical purposes.”
Because this new criterion is slightly easier to satisfy than zero knowledge, Ilango can construct protocols that do not require the parties to interact and that prevent the theorem from being able to be explained by wrong answers.
To create the new proof system, effectively called a zero-knowledge proof, Ilango took the idea from mathematician Kurt Gödel’s 1931 incompleteness theorem, which basically says that many sets of assumptions contain certain facts that they can neither prove nor disprove. Ilango showed that he could construct a proof system consisting of such notions, a set known as ZFC This underlies much of mathematics, which cannot rule out the existence of a simulator, even if it does not exist.
Computer scientist Amit Sahay of the University of California, Los Angeles, who was not involved in the work, says the paradigm is already proving more useful than he expected. “It’s beautiful,” says Sahay. “(Ilango’s) paper is, in my opinion, the most creative and most consequential paper in the field of zero-knowledge proofs in at least the last decade.”
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