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Succinct non-interactive arguments of knowledge (SNARKs) allow a weak verifier to delegate computation tasks to a powerful prover in a verifiable way. However, most SNARK constructions require the computation tasks to be represented as arithmetic circuits over finite fields, incurring a significant overhead when applied for delegations of modern computer programs, which typically are of \(\mathbb {Z}_{2^{64}}\) or \(\mathbb {Z}_{2^{32}}\) arithmetics. The only exception is Rinocchio (JoC 2023), which builds the first SNARK for rings and features constant proof size. Due to \(\mathbb {Z}_{2^k}\) being lack of large evaluation sets for polynomial interpolations, Rinocchio resorts to Galois ring extensions of \(\mathbb {Z}_{2^k}\) . However, Rinocchio is designated-verifier and the concrete efficiency is unclear at the moment. Towards building publicly verifiable SNARKs for rings \(\mathbb {Z}_{2^k}\) , we follow the well-established framework of polynomial interactive oracle proofs (IOP)-based SNARKs, and obtain the following results:

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Polynomial Commitments for Galois Rings and Applications to SNARKs Over \(\mathbb {Z}_{2^k}\)

  • 会议论文

  • 发表日期：

    2025年

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  • Yuhao Jia,
  • Songsong Li,
  • Chaoping Xing,
  • Yizhou Yao,
  • Chen Yuan

摘要

Succinct non-interactive arguments of knowledge (SNARKs) allow a weak verifier to delegate computation tasks to a powerful prover in a verifiable way. However, most SNARK constructions require the computation tasks to be represented as arithmetic circuits over finite fields, incurring a significant overhead when applied for delegations of modern computer programs, which typically are of \(\mathbb {Z}_{2^{64}}\) or \(\mathbb {Z}_{2^{32}}\) arithmetics. The only exception is Rinocchio (JoC 2023), which builds the first SNARK for rings and features constant proof size. Due to \(\mathbb {Z}_{2^k}\) being lack of large evaluation sets for polynomial interpolations, Rinocchio resorts to Galois ring extensions of \(\mathbb {Z}_{2^k}\) . However, Rinocchio is designated-verifier and the concrete efficiency is unclear at the moment. Towards building publicly verifiable SNARKs for rings \(\mathbb {Z}_{2^k}\) , we follow the well-established framework of polynomial interactive oracle proofs (IOP)-based SNARKs, and obtain the following results: