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Transparent SNARKs over Galois Rings

Authors:
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
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Conference: PKC 2025
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 $O(n)$ 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 $O(n)$ prover time, $O(\sqrt{n})$ proof size, and $O(\sqrt{n})$ verifier time. And by combining HyperPlonk in Chen et al. (EUROCRYPT 2023), we present a transparent SNARK for NP circuits over Galois rings, with $O(n\log^2 n)$ prover time, $O(\sqrt{n})$ proof size, and $O(\sqrt{n})$ verifier time.
BibTeX
@inproceedings{pkc-2025-34982,
  title={Transparent SNARKs over Galois Rings},
  publisher={Springer-Verlag},
  author={Yuanju Wei and Xinxuan Zhang and Yi Deng},
  year=2025
}