How do you prove you know a secret without spilling the beans?

"Zero-knowledge proofs are the closest cryptography gets to magic. They promise to let one person convince another of the truth of some factsay, that they know the solution to a sudoku puzzlewithout 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."

"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."

Zero-knowledge proofs let a prover convince a verifier of a fact without revealing the secret, supporting identity authentication, online banking, and blockchains. Cryptographers have long known that zero-knowledge proofs cannot safely be written down like typical mathematical proofs, so provers generally must interact with verifiers. In rare cases a prover can falsely convince a verifier, for example by claiming a sudoku puzzle is completable when it has no solution. Typical zero-knowledge proofs require a simulator that reproduces proof steps without the secret, and the simulator's existence demonstrates that no secret information is leaked. Computer scientist Rahul Ilango identified a gap between definition and practice and showed that, in some cases, demonstrating that a simulator's existence cannot be ruled out suffices to establish zero-knowledge; he presented the result at the 2025 IEEE Symposium on Foundations of Computer Science in Sydney.

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