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Modern efficient secure multi-party computation (MPC) protocols typically follow an offline-online design, where offline protocols produce a sufficient amount of correlated randomness that would be consumed during the online phases. The past decades have witnessed maturing of efficient online protocols, for computing circuits over either arbitrary finite fields or rings \(\mathbb {Z}_{p^k}\) . In particular, protocols tailored for \(\mathbb {Z}_{2^k}\) arithmetic have achieved better concrete efficiency in most real-life applications, as it naturally captures modern CPU architectures. On the other hand, a recent paradigm of pseudorandom correlation generator (PCG) initiated by Boyle et al. (CCS’18, Crypto’19) opens a door to efficient preprocessing with sublinear communication. Since then, PCGs have been extensively studied and developed to produce various types of correlations required from online protocols. Although Li et al. (EuroCrypt’25) recently put a significant step forward and propose efficient PCGs for arbitrary finite fields, the current state of PCGs for rings is not satisfying at all. Towards the great demand for efficiently generating correlations over rings, we investigate PCGs for general Galois rings, which simultaneously unify finite fields and integer rings modulo \(p^k\) . In summary, we establish the following results:

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Efficient Pseudorandom Correlation Generators over  \(\mathbb {Z}/p^k\mathbb {Z}\)

  • 会议论文

  • 发表日期：

    2025年

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  • Zhe Li,
  • Chaoping Xing,
  • Yizhou Yao,
  • Chen Yuan

摘要

Modern efficient secure multi-party computation (MPC) protocols typically follow an offline-online design, where offline protocols produce a sufficient amount of correlated randomness that would be consumed during the online phases. The past decades have witnessed maturing of efficient online protocols, for computing circuits over either arbitrary finite fields or rings \(\mathbb {Z}_{p^k}\) . In particular, protocols tailored for \(\mathbb {Z}_{2^k}\) arithmetic have achieved better concrete efficiency in most real-life applications, as it naturally captures modern CPU architectures. On the other hand, a recent paradigm of pseudorandom correlation generator (PCG) initiated by Boyle et al. (CCS’18, Crypto’19) opens a door to efficient preprocessing with sublinear communication. Since then, PCGs have been extensively studied and developed to produce various types of correlations required from online protocols. Although Li et al. (EuroCrypt’25) recently put a significant step forward and propose efficient PCGs for arbitrary finite fields, the current state of PCGs for rings is not satisfying at all. Towards the great demand for efficiently generating correlations over rings, we investigate PCGs for general Galois rings, which simultaneously unify finite fields and integer rings modulo \(p^k\) . In summary, we establish the following results: