Transparent SNARKs over Galois Rings

Yuanju Wei; Xinxuan Zhang; Yi Deng

Paper 2025/263

Transparent SNARKs over Galois Rings

Yuanju Wei

, Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS; School of Cyber Security, University of Chinese Academy of Sciences

Xinxuan Zhang

, Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS; School of Cyber Security, University of Chinese Academy of Sciences

Yi Deng

, Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS; School of Cyber Security, University of Chinese Academy of Sciences

Abstract

Recently, there is a growing need for SNARKs to operate over a broader range of algebraic structures, and one important structure is Galois ring. We present transparent SNARK schemes over arbitrary Galois rings. Compared with Rinocchio scheme in Ganesh et al. (J Cryptol 2023), our SNARK schemes do not require a trusted third party to establish a structured reference string (SRS). In this paper, we present the expander code over arbitrary Galois rings, which can be encoded in time. Using this expander code, we then extend the Brakedown commitment scheme in Golovnev et al. (CRYPTO 2023) to Galois rings. By combining the Libra framework in Xie et al. (CRYPTO 2019), we present a transparent SNARK for log-space uniform circuits over Galois rings, achieving prover time, proof size, and verifier time. And by combining HyperPlonk in Chen et al. (EUROCRYPT 2023), we present a transparent SNARK for NP circuits over Galois rings, with prover time, proof size, and verifier time.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: A major revision of an IACR publication in PKC 2025
Keywords: SNARKs Galois rings polynomial commitment
Contact author(s): weiyuanju @ iie ac cn
zhangxinxuan @ iie ac cn
deng @ iie ac cn
History: 2025-02-19: revised; 2025-02-18: received; See all versions
Short URL: https://ia.cr/2025/263
License: CC BY

BibTeX

@misc{cryptoeprint:2025/263,
      author = {Yuanju Wei and Xinxuan Zhang and Yi Deng},
      title = {Transparent {SNARKs} over Galois Rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/263},
      year = {2025},
      url = {https://eprint.iacr.org/2025/263}
}