> ## Documentation Index
> Fetch the complete documentation index at: https://docs.theblockchainlibrary.com/llms.txt
> Use this file to discover all available pages before exploring further.

# PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge

> This paper introduces PLONK (Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge), a new type of universal and updatable zero

# PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge

This paper introduces PLONK (Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge), a new type of universal and updatable zero

## Abstract

This paper introduces PLONK (Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge), a new type of universal and updatable zero-knowledge proof system. Unlike previous SNARKs that often required custom circuits for each computation, PLONK introduces a generic circuit structure based on arithmetic circuits and permutation arguments. The core innovation lies in its ability to use a single trusted setup for all computations, significantly reducing the overhead for developers who no longer need to generate new setups for each new smart contract. The system leverages Lagrange polynomial bases and a permutation argument to efficiently prove the correct execution of arbitrary computations. PLONK achieves quadratic scaling in the size of the statement and logarithmic scaling in the size of the witness, making it a practical choice for various blockchain applications requiring efficient and verifiable computation. Its universality and updatability make it a foundational contribution to the field of zero-knowledge proofs, paving the way for more flexible and scalable privacy-preserving technologies in Web3.

**Authors:** Ariel Gabizon, Zachary J. Williamson, Oana Ciobotaru

**Publication:** IACR ePrint Archive

**Publication date:** 2019-01-01

## Key findings

* PLONK presents a universal and updatable zero-knowledge proof system that supports arbitrary computations with a single trusted setup.
* The system utilizes arithmetic circuits and a permutation argument over Lagrange polynomial bases for efficient proof generation and verification.
* It significantly reduces the setup overhead for developers compared to previous SNARKs requiring custom circuits.
* PLONK's performance characteristics enable practical applications in privacy-preserving blockchain solutions.

## Citation

Ariel Gabizon, Zachary J. Williamson, Oana Ciobotaru (2019). PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge. IACR ePrint Archive. [https://eprint.iacr.org/2019/953.pdf](https://eprint.iacr.org/2019/953.pdf)

## Related knowledge

* [Cryptography](/categories/cryptography) — glossary
* [Cryptography](/categories/cryptography) — related-glossary
* [From Hype to Reality: The Rise of Quantum-Resistant Cryptography](/generated/v2/topics/from-hype-to-reality-the-rise-of-quantum-resistant-cryptography) — article
* [From Hype to Reality: The Rise of Quantum-Resistant Cryptography](/generated/v2/topics/from-hype-to-reality-the-rise-of-quantum-resistant-cryptography) — related-article
* [Hash Function](/generated/v2/glossary/hash-function) — glossary
* [Hash Function](/generated/v2/glossary/hash-function) — related-glossary
* [Immutability](/generated/v2/glossary/immutability) — glossary
* [Immutability](/generated/v2/glossary/immutability) — related-glossary
* [Multi-Party Computation](/generated/v2/glossary/multi-party-computation) — glossary
* [Multi-Party Computation](/generated/v2/glossary/multi-party-computation) — related-glossary
* [Privacy on the Blockchain: How Zero-Knowledge Proofs Are Changing the Game](/generated/v2/topics/privacy-on-the-blockchain-how-zero-knowledge-proofs-are-changing-the-game) — article
* [Privacy on the Blockchain: How Zero-Knowledge Proofs Are Changing the Game](/generated/v2/topics/privacy-on-the-blockchain-how-zero-knowledge-proofs-are-changing-the-game) — related-article
* [Quantum Computing in 2030: Predictions and Challenges Ahead](/generated/v2/topics/quantum-computing-in-2030-predictions-and-challenges-ahead) — article
* [Quantum Computing in 2030: Predictions and Challenges Ahead](/generated/v2/topics/quantum-computing-in-2030-predictions-and-challenges-ahead) — related-article
* [RSA](/generated/v2/glossary/rsa) — glossary
* [RSA](/generated/v2/glossary/rsa) — related-glossary

***

**Canonical knowledge ID:** `research:plonk-permutations-over-lagrange-bases-for-oecumenical-noninteractive-arguments-of-knowledge`