高效的多方安全比较在不同域中通过预处理协助
Efficient Multi-Party Secure Comparison over Different Domains with Preprocessing Assistance
AI总结：
本文提出了一种拍卖师辅助的多域安全比较协议，通过预处理优化实现高效且安全的多方计算应用。
摘要：
安全比较是多方计算中的基本原语，支持隐私保护的应用，如机器学习和数据分析。比较协议中的关键性能瓶颈在于其预处理阶段，主要是由于生成必要的相关随机数成本较高。最近的框架引入了一个被动的、不串通的拍卖师来加速预处理。然而，仍然存在两个关键问题。首先，现有的拍卖师辅助方法将拍卖师视为传统预处理的替代品，而没有重新设计比较协议以优化在线阶段。其次，大多数协议专门针对特定的代数域、对手模型或参与方配置，缺乏广泛的通用性。在本工作中，我们提出了第一个拍卖师辅助的n-方LTBits（小于位）和MSB（最显著位）提取协议，适用于$\mathbb{F}_p$和$\mathbb{Z}_{2^k}$，在协议级别实现完美安全。通过充分利用拍卖师生成丰富相关随机数的能力，我们的$\mathbb{F}_p$构造实现了常数轮次的在线复杂度，而我们的$\mathbb{Z}_{2^k}$构造实现了$O(\log_n k)$轮次，具有可调的分支因子。所有协议均通过扩展的ABB模型作为黑盒构造，确保在MPC后端和对手模型之间的可移植性。实验结果表明，与最先进的MPC框架相比，我们的协议在速度上提高了1.79倍到19.4倍，突显了我们的协议在比较密集的MPC应用中的实用性。
英文摘要：
Secure comparison is a fundamental primitive in multi-party computation, supporting privacy-preserving applications such as machine learning and data analytics. A critical performance bottleneck in comparison protocols is their preprocessing phase, primarily due to the high cost of generating the necessary correlated randomness. Recent frameworks introduce a passive, non-colluding dealer to accelerate preprocessing. However, two key issues still remain. First, existing dealer-assisted approaches treat the dealer as a drop-in replacement for conventional preprocessing without redesigning the comparison protocol to optimize the online phase. Second, most protocols are specialized for particular algebraic domains, adversary models, or party configurations, lacking broad generality. In this work, we present the first dealer-assisted $n$-party LTBits (Less-Than-Bits) and MSB (Most Significant Bit) extraction protocols over both $\mathbb{F}_p$ and $\mathbb{Z}_{2^k}$, achieving perfect security at the protocol level. By fully exploiting the dealer's capability to generate rich correlated randomness, our $\mathbb{F}_p$ construction achieves constant-round online complexity and our $\mathbb{Z}_{2^k}$ construction achieves $O(\log_n k)$ rounds with tunable branching factor. All protocols are formulated as black-box constructions via an extended ABB model, ensuring portability across MPC backends and adversary models. Experimental results demonstrate $1.79\times$ to $19.4\times$ speedups over state-of-the-art MPC frameworks, highlighting the practicality of our protocols for comparison-intensive MPC applications.
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