Abhishek S.
Shipping in public. Listening in private.

Abhishek

I lead women’s Indo-Western & Premium at Max Fashion. I also wrote the AI that runs the buying floor.

Rare profile. Category operator who ships production code.

Senior Buying Leader · Max Fashion Women’s Indo-Western & Premium · 530+ India stores NIFT ’12 · Twelve years on the floor

read the CV start a letter
abhishek@bengaluru ~ %
>role: senior buying lead
>dept: women’s indo-western + premium
>floor: 530+ stores india

Zero-Knowledge Proofs

You can prove you know a secret without revealing a single bit of it — and the math says the verifier walks away with literally no more information than they started with. Goldwasser, Micali, and Rackoff worked this out in 1985. It won them the first Gödel Prize in 1993. Forty years later it is the substrate that lets Ethereum compress thousands of transactions into a 200-byte proof and lets a stranger check your age without learning your birthday.

How it works

A zero-knowledge proof must satisfy three properties simultaneously. Completeness: if the statement is true, an honest prover convinces the verifier. Soundness: if false, no cheating prover can convince the verifier except with vanishing probability. Zero-knowledge: the verifier could have simulated the entire interaction alone, given only the statement — so no information transferred beyond the truth value.

The 1986 result by Goldreich, Micali, and Wigderson is the load-bearing theorem of the field: assuming one-way functions exist, every problem in NP has a zero-knowledge proof. They proved it by giving a ZK protocol for graph 3-coloring (NP-complete), then leaning on the Cook-Levin reduction. Anything you can verify in polynomial time given a witness, you can verify in zero-knowledge.

The canonical intuition is Quisquater's 1989 "Cave of Ali Baba": a ring-shaped cave with a magic door in the middle. Prover enters one side, verifier shouts which side to exit from. After 30 honest rounds, a cheater's odds collapse to 1/2³⁰ — about one in a billion. The verifier is convinced. The verifier still doesn't know the magic word.

Where it shows up

Modern ZKPs split into two engineering families with sharply different tradeoffs:

Property ZK-SNARK ZK-STARK
Proof size ~200 bytes ~45–200 KB
Trusted setup Required (ceremony) None
Crypto basis Elliptic-curve pairings Hash functions
Post-quantum No Yes
Deployed in Zcash, Groth16, PLONK StarkNet, zkSync

The trusted-setup problem is the load-bearing weakness of SNARKs: a one-time ceremony produces a Common Reference String, and if a single participant retains their share of the toxic waste, they can forge proofs forever. Zcash's 2017 "Powers of Tau" recruited thousands of participants on the bet that at least one would actually destroy their share. STARKs sidestep the problem by using only public-coin hash commitments — at the cost of proofs 200× larger.

Concrete deployments as of 2025:

The 2025 Gödel Breakthrough

A July 2025 result by Rahul Ilango (MIT CSAIL), winner of the 2025 Machtey Award, overturned a classical impossibility theorem that had stood for decades.

The classical result: you cannot have a zero-knowledge proof that is simultaneously (1) non-interactive (one message, prover to verifier), (2) without trusted setup, and (3) perfectly sound (false statements are never accepted — not even with negligible probability). Any two of these are achievable; all three were believed to be fundamentally incompatible.

Ilango's paper, "Gödel in Cryptography: Effectively Zero-Knowledge Proofs for NP with No Interaction, No Setup, and Perfect Soundness," resolves the impossibility by exploiting logical unprovability — the same move Gödel made in his incompleteness theorems.

The key innovation: instead of requiring that a simulator exists (the traditional zero-knowledge requirement), Ilango requires only that it is logically impossible to prove that no simulator exists — even using all of ZFC (the standard axioms of mathematics). A simulator might or might not exist; what matters is that the verifier can never prove it doesn't. Because the non-existence of a simulator is independent of ZFC, no adversary reasoning within ZFC can establish that information was leaked.

The resulting "effectively zero-knowledge" proofs are not weaker in any practical sense: every falsifiable security property that holds for classical ZKPs also holds for these — without any trusted setup and without interaction. The only sacrifice is in the definition, not in the guarantee.

The Gödel connection is not metaphorical. The proof technique imports Gödel's machinery directly: it encodes the question "does this simulator exist?" as a statement of the type Gödel showed can be true but unprovable. The unprovability of the statement becomes the security guarantee. Mathematics' most famous limit (there are true statements with no proof) becomes a resource that can be harvested for cryptographic security.

One strange implication: a cryptographic system built on Gödel unprovability could be insecure — and it would be impossible to prove that it is insecure. The system is not proven safe; it is safe because proving it unsafe requires ZFC to settle a question ZFC cannot settle.

What's contested

The interesting argument is not whether ZKPs work — they do. It is what they cost and who they serve.

Provers are expensive. Generating a SNARK for a non-trivial computation can take seconds to minutes on consumer hardware and burns substantial energy at scale. The asymmetry — cheap verification, expensive proving — pushes proving into centralized clusters, which reintroduces the trust problem ZK was meant to eliminate. "Decentralized prover networks" are an open research area, not a solved one.

There is also no consensus on what "zero-knowledge" guarantees in practice. The formal definition assumes ideal hash functions, ideal random oracles, ideal setup ceremonies, and a verifier following the protocol. Real implementations leak side-channel information (timing, memory access patterns), and ZK circuit bugs have produced silent soundness failures in deployed systems — at least three high-profile incidents in 2022-2024 in major rollup verifiers. The math is solid; the engineering is fragile.

The regulatory question is open: privacy-preserving compliance sounds elegant, but ZK proofs are equally good at proving "this transaction is legal" and at making illegal transactions unauditable. Tornado Cash and its 2022 OFAC sanction sit on exactly this knife edge.

Why this has to do with other realms

ZKPs are the limiting case of concept information theory. Shannon measures how much information a channel can carry; a ZK proof carries maximum conviction at zero Shannon bits about the witness. Read as physics, this is a strange object: a transmission that changes the receiver's beliefs without transmitting the thing the belief is about.

They also sit at a sharp angle to concept godel incompleteness. Gödel separated truth from provability — true statements can lack proofs. ZKPs separate the proof from the knowledge — proofs can be transmitted without their content. Three levels, not two: what is true, what is provable, and what can be conveyed about a proof. The third level was invisible until 1985.

The Judicial Edge Case

Courts, peer review, journalism, teaching: all rest on the assumption that conviction requires sharing your reasoning. ZKPs prove that assumption is mathematical convention, not necessity.

The most immediate institutional collision is criminal alibi defense. A defendant was somewhere private at the time of the crime — but proving it exposes information (a relationship, a medical condition, an illegal-but-victimless activity) they are entitled to keep private. Standard alibi evidence (cell records, witnesses, receipts) proves location and exposes the secret simultaneously. A ZKP alibi would prove "I was not in City A" without revealing where they were.

A 2022 paper by Bitan, Canetti, Goldwasser, and Wexler proposed ZKPs to reconcile law enforcement secrecy with fair trial rights in the opposite direction: police proving forensic software produced a specific output without disclosing the source code. A 2025 Springer chapter ("Privacy Paradigm Shift: Zero Knowledge Proofs in Criminal e-Evidence Collection") addressed the alibi direction directly.

The Ilango 2025 result is critical here: SNARKs require a trusted setup ceremony — unsuitable for judicial evidence without a neutral third party. STARKs and Bulletproofs require no trusted setup but produce large proofs. Ilango's single-message, no-interaction, no-setup construction could in principle allow a defendant to generate their own proof without any trusted party.

The deep tension: courts require explainable truth. Due process includes the right to confront evidence. A mathematically valid ZKP proof is opaque to a lay jury. This is the Chinese Room concept chinese room at institutional scale: verification without understanding.

For the full analysis of ZKPs in judicial contexts — range proofs, due process, the institutional chain required to make location ZKPs trustworthy — see concept zkp judicial.

An open question

If a sufficiently powerful prover can convince any verifier of any true NP statement without revealing why — what happens to the social institution of explanation? Courts, peer review, journalism, teaching: all rest on the assumption that conviction requires sharing your reasoning. ZKPs prove that assumption is mathematical convention, not necessity. Which of those institutions survive when the convention dissolves?

Key sources

Further reading

See Also