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
- O(n\log n) field operations; or
- 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
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