Welcome to the resource topic for 2024/827
Title:
Multivariate Multi-Polynomial Commitment and its Applications
Authors: Xiao Yang, Chengru Zhang, Mark Ryan, Gao Meng
Abstract:We introduce and formally define Multivariate Multi-Polynomial (MMP) commitment, a commitment scheme on multiple multivariate polynomials, and illustrate the concept with an efficient construction, which enjoys constant commitment size and logarithmic proof size. We further enhance our MMP scheme to achieve the zero-knowledge property.
Additionally, combined with a novel zero-knowledge range proof for Pedersen subvector commitment, we present a Zero-Knowledge Range Proof (ZKRP) for MMP commitment.
We present two sample applications. Firstly, our MMP commitment can be used for efficient aggregation of SNARK based on multivariate polynomial commitments. As a showcase, we apply MMP commitment to HyperPlonk and refer to this variant of HyperPlonk as aHyperPlonk. For k instances, each with circuit size n, the communication and verification complexity is reduced from O(k \cdot \log n) to O(\log k + \log n), while the prover complexity remains the same. Secondly, we propose a novel zero-knowledge proof for vehicle GPS traces based on ZKRP for MMP, which allows vehicle owners to prove if a vehicle has/hasn’t passed through some location during a specific time interval.
ePrint: https://eprint.iacr.org/2024/827
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