[Resource Topic] 2025/385: MERCURY: A multilinear Polynomial Commitment Scheme with constant proof size and no prover FFTs

Welcome to the resource topic for 2025/385

Title:
MERCURY: A multilinear Polynomial Commitment Scheme with constant proof size and no prover FFTs

Authors: Liam Eagen, Ariel Gabizon

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.

ePrint: https://eprint.iacr.org/2025/385

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .