> ## 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.

# Halo: Recursive Proof Composition without a Trusted Setup

> The Halo paper introduces a transformative approach to recursive proof composition, addressing one of the most critical challenges in zero-knowledge scalability

# Halo: Recursive Proof Composition without a Trusted Setup

The Halo paper introduces a transformative approach to recursive proof composition, addressing one of the most critical challenges in zero-knowledge scalability

## Abstract

The Halo paper introduces a transformative approach to recursive proof composition, addressing one of the most critical challenges in zero-knowledge scalability: the need for trusted setups. By utilizing an innovative technique involving inner-product arguments and the folding of polynomial commitments, Halo enables the aggregation of proofs without the recursive overhead typically associated with cycle-of-curves constructions. This allows for the verification of an arbitrary number of prior proofs within a single instance, facilitating highly efficient transaction batching and rollups. The research provides a rigorous framework for maintaining proof integrity throughout recursive iterations while mitigating the security risks inherent in structured reference string generation. This advancement is fundamental to modern blockchain scalability research, as it provides a path toward succinct verification of massive transaction histories. The paper demonstrates that cryptographic trust can be decoupled from proof generation, setting a new benchmark for trustless, scalable, and verifiable computation in decentralized networks.

**Authors:** Sean Bowe, Jack Grigg, Daira Hopwood

**Publication:** IACR ePrint Archive

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

## Key findings

* Enables recursive proof composition without requiring a trusted setup.
* Uses a novel polynomial commitment scheme to aggregate proofs efficiently.
* Reduces verification costs for complex state transitions in blockchains.
* Demonstrates robustness against security threats associated with ceremony-based proof systems.

## Citation

Sean Bowe, Jack Grigg, Daira Hopwood (2019). Halo: Recursive Proof Composition without a Trusted Setup. IACR ePrint Archive. [https://eprint.iacr.org/2019/1021](https://eprint.iacr.org/2019/1021)

## 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
* [From Throughput to Reliability: The New Metrics That Matter](/generated/v2/topics/from-throughput-to-reliability-the-new-metrics-that-matter) — article
* [From Throughput to Reliability: The New Metrics That Matter](/generated/v2/topics/from-throughput-to-reliability-the-new-metrics-that-matter) — 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
* [Layer 1](/generated/v2/glossary/layer-1) — glossary
* [Layer 1](/generated/v2/glossary/layer-1) — related-glossary
* [Layer 3 in Blockchain: The Next Big Thing for Crypto Scalability?](/generated/v2/topics/layer-3-in-blockchain-the-next-big-thing-for-crypto-scalability) — article
* [Layer 3 in Blockchain: The Next Big Thing for Crypto Scalability?](/generated/v2/topics/layer-3-in-blockchain-the-next-big-thing-for-crypto-scalability) — related-article
* [Layer 3: The Next Frontier in Blockchain Scalability](/generated/v2/topics/layer-3-the-next-frontier-in-blockchain-scalability) — article
* [Layer 3: The Next Frontier in Blockchain Scalability](/generated/v2/topics/layer-3-the-next-frontier-in-blockchain-scalability) — related-article

***

**Canonical knowledge ID:** `research:halo-recursive-proof-composition-without-a-trusted-setup`