On the Equivalence of Polynomial Commitments for an Identical Polynomial under Different Bases

Dengji Ma; Jingyu Ke; Sinka Gao; Guoqiang Li

Paper 2025/2258

On the Equivalence of Polynomial Commitments for an Identical Polynomial under Different Bases

Dengji Ma, Delphinus Lab

Jingyu Ke

, Shanghai Jiao Tong University

Sinka Gao, Delphinus Lab

Guoqiang Li

, Shanghai Jiao Tong University

Abstract

We propose a Pairing-based Polynomial Consistency Protocol (PPCP) that verifies the equivalence of polynomial commitments generated under different basis representations, such as the coefficient and Lagrange bases. By leveraging pairing relations, PPCP proves that two commitments correspond to an identical underlying polynomial vector without revealing the polynomial itself. This enables efficient proof aggregation and recursive composition across heterogeneous SNARK systems that adopt distinct polynomial encodings.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Zero-knowledge proofs Polynomial commitment schemes Proof aggregation Cross-system interoperability
Contact author(s): ponymdj @ gmail com
Windocotber @ sjtu edu cn
xgao @ zoyoe com
li g @ sjtu edu cn
History: 2025-12-18: approved; 2025-12-16: received; See all versions
Short URL: https://ia.cr/2025/2258
License: CC BY

BibTeX

@misc{cryptoeprint:2025/2258,
      author = {Dengji Ma and Jingyu Ke and Sinka Gao and Guoqiang Li},
      title = {On the Equivalence of Polynomial Commitments for an Identical Polynomial under Different Bases},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/2258},
      year = {2025},
      url = {https://eprint.iacr.org/2025/2258}
}