IAS researcher Rahul Ilango has published a major conceptual advance in cryptography that relaxes protocol requirements for zero-knowledge proofs. 

His offering, an “effective” zero-knowledge proof, matches the security guarantees of zero-knowledge proofs in practice while doing away with the need for interaction. 

To remove this necessity of back-and-forth verification, Ilango turned to a surprising source of insight: Gödel’s incompleteness theorem, one of the greatest – and most astonishing – revelations in modern mathematical logic. 

Online verification often involves exposing more information than is necessary. Let’s say you use your email account to log in to other applications. That email platform now knows precisely what other platforms you use, allowing them to gather data on your actions and preferences. Or, say you submit a credit report to a lender to qualify for a loan. They receive detailed financial information spanning years of your life. 

Zero-knowledge proofs allow for online verification without disclosing sensitive information at all. Instead, this form of cryptography allows the sender to verify to the recipient that they have crucial knowledge – or can prove that something is true – without ever needing to reveal the details of that knowledge or truth.

Theoretical overviews often use the example of a Sudoku puzzle to illustrate this. A zero-knowledge proof would allow one party to prove to another that a puzzle has a solution while keeping that solution a secret. The receiving party would get proof that the puzzle was solvable but would never be privy to the actual answers. As a recent Scientific American article on Ilango’s achievement affirms: “Zero-knowledge proofs are the closest cryptography gets to magic.”

Real-world applications hammer home the usefulness of this approach. 

Software can secure the credentials of its users and still never access or store them at all; a zero-knowledge proof is a critical ingredient that allows software to verify that you know your password or PIN without requiring you to transmit it. 

Financial transactions on blockchain technologies maintain privacy and accuracy without a centralized authority or trusted third-party when they use zero-knowledge proofs to confirm valid exchanges without collecting exact transaction data. 

Digital identity verification ensures that users are who they say they are – residents of a certain area or above a certain age – without the need to expose essential personal information like address or birthdate. 

To do this, zero-knowledge proofs rely on an interactive protocol. The sender (or “prover”) communicates to a recipient (or “verifier”) who responds with a challenge. The prover responds in a way that only someone who knows the secret information could. The verifier responds again with another challenge. The prover responds. 

This continues until a sufficient threshold for security has been reached. The verifier never gets the secret information. And yet, the interaction lets the prover demonstrate that their information is authentic – or allows the verifier to realize that the prover is lying.

Until Ilango’s breakthrough, the idea of a non-interactive zero-knowledge proof seemed impossible to mathematicians. Still, it was interesting. 

Could it be feasible to design a version of this security protocol that verifies truth while revealing nothing – without the need for that substantiating dialogue between prover and verifier? 

“It was an intriguing theoretical mystery,” Ilango says. “At the same time, there were convincing results proving this was impossible. It was well established that zero-knowledge proofs always require two essential sacrifices: non-interactivity and perfect soundness. On paper, we all accepted that it was impossible to come up with a secure zero-knowledge proof that didn’t include that challenge-and-response element.”

And yet, to Ilango, this official impossibility was unsatisfying. “It’s very reasonable to use interaction when you’re communicating on the web,” he says. “Servers and clients talk to each other all the time. But the way zero knowledge relies on probability via interaction represents a huge departure from the fundamental concept of mathematical proof that’s been around for thousands of years. I wanted a zero-knowledge proof that didn’t rely on interaction.”

In this publication, Ilango debuts this proof.  His achievement – what Ilango has called a “classically impossible cryptographic dream object” – introduces a version of zero knowledge that eliminates the need for interaction. 

Termed an “effective zero-knowledge proof,” Ilango’s design takes inspiration from longtime IAS faculty member Kurt Gödel, whose 1931 incompleteness theorems juddered positivist ambitions of modern mathematics and introduced uncanny gaps into nearly all the ways we understand the world. 

In short, Gödel’s result showed that there are absolute truths for which we can never produce proof. Any search for a total and completely verifiable mathematical system is hopeless.

Could not being able to prove something be useful? Ilango’s proof creatively applies this principle to cryptography. 

When mathematicians model the interaction protocol in a zero-knowledge proof, they use a simulator, which carries out a hypothetical but completely plausible version of the dialogue between prover and verifier. 

Ilango’s new effective zero-knowledge proof skips the simulator. Instead, he demonstrates, it’s enough to show that it can’t be proved that the simulator doesn’t exist.  

Rather than directly prove that something is possible, this method draws on Gödel’s profound contributions to logic to make absence mathematically meaningful. The simulator doesn't need to exist. If the simulator's nonexistence is unprovable, then that is enough for almost all applications.

This twist in logic bypasses the need for interaction in classical zero-knowledge proofs, creating an elegant loophole in decades of zero-knowledge impossibility results. 

What began as Ilango’s hunch that Gödel’s theorems could be useful in ways never before considered has now become an ambitious series of projects. 

“We’re already thinking about ways to overcome other impossibility results in cryptography,” Ilango says. 

Applications in secure multi-party computation in health care, for example, are one area of Ilango’s current interest. If a machine learning company wants to train its models on patient data without compromising privacy and breaking HIPAA laws, they would need a secure way to sever identity from data. A cryptographic advance in this area could yield private, legally compliant, and trustworthy machine learning models that could lead to lifesaving improvements in research and care.

As Ilango tackles this and other “dream objects” in cryptography, he’s energized by the work of discovering new potential in the past and bringing it into the future.

“It’s inspiring to continue doing this research at IAS. It’s the historical environment where Gödel himself accomplished so much and where today there’s such an exceptional concentration of mathematicians working on these problems,” Ilango says.

 

Goldreich, Oded, Silvio Micali, and Avi Wigderson. “Proofs That Yield Nothing but Their Validity or All Languages in NP Have Zero-Knowledge Proof Systems.” Journal of the ACM, vol. 38, no. 3, 1991, pp. 691–729. https://doi.org/10.1145/116825.116852.

 

Goldreich, Oded, and Yair Oren. “Definitions and Properties of Zero-Knowledge Proof Systems.” Journal of Cryptology, vol. 7, no. 1, 1994, pp. 1–32. https://doi.org/10.1007/BF00195207.

 

Goldwasser, Shafi, Silvio Micali, and Charles Rackoff. “The Knowledge Complexity of Interactive Proof-Systems.” Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing (STOC ’85), ACM, 1985, pp. 291–304. https://doi.org/10.1145/22145.22178.

 

Hall, Peter. “How ‘Effectively Zero-Knowledge’ Proofs Could Transform Cryptography.” Scientific American, 11 Feb. 2026, https://www.scientificamerican.com/article/how-effectively-zero-knowledge-proofs-could-transform-cryptography/.

Ilango, Rahul. Gödel in Cryptography: Effectively Zero-Knowledge Proofs for NP with No Interaction, No Setup, and Perfect Soundness. Cryptology ePrint Archive, Paper 2025/1296, 2025, https://eprint.iacr.org/2025/1296.