Paper 2025/385
MERCURY: A multilinear Polynomial Commitment Scheme with constant proof size and no prover FFTs
Abstract
We construct a pairing-based polynomial commitment scheme for multilinear polynomials of size $n$ where constructing an opening proof requires $O(n)$ field operations, and $2n+O(\sqrt n)$ scalar multiplications. Moreover, the opening proof consists of a constant number of field elements. This is a significant improvement over previous works which would require either 1. $O(n\log n)$ field operations; or 2. $O(\log n)$ size opening proof. The main technical component is a new method of verifiably folding a witness via univariate polynomial division. As opposed to previous methods, the proof size and prover time remain constant *regardless of the folding factor*.
Note: sumcheck refs
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- SNARKsPolynomial Commitment Schemes
- Contact author(s)
-
liameagen @ protonmail com
ariel @ aztec-labs com - History
- 2025-03-08: last of 6 revisions
- 2025-02-28: received
- See all versions
- Short URL
- https://ia.cr/2025/385
- License
-
CC0
BibTeX
@misc{cryptoeprint:2025/385,
author = {Liam Eagen and Ariel Gabizon},
title = {{MERCURY}: A multilinear Polynomial Commitment Scheme with constant proof size and no prover {FFTs}},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/385},
year = {2025},
url = {https://eprint.iacr.org/2025/385}
}
