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.

翻译：安全比较是多方计算中的基础原语，支撑着机器学习与数据分析等隐私保护应用。比较协议的关键性能瓶颈在于其预处理阶段，主要源于生成必要关联随机性的高昂开销。近期研究框架引入被动非共谋的第三方来加速预处理，但仍存在两个关键问题：首先，现有第三方辅助方案仅将其作为传统预处理的直接替代，未重新设计比较协议以优化在线阶段性能；其次，多数协议专用于特定代数域、敌手模型或参与方配置，缺乏广泛通用性。本文首次提出在$\mathbb{F}_p$和$\mathbb{Z}_{2^k}$域上支持第三方辅助的$n$方LTBits（低位比较）与MSB（最高有效位提取）协议，在协议层面实现完美安全性。通过充分利用第三方生成丰富关联随机性的能力，我们的$\mathbb{F}_p$构造实现恒定轮在线复杂度，$\mathbb{Z}_{2^k}$构造实现$O(\log_n k)$轮次且具有可调分支因子。所有协议均通过扩展ABB模型构建为黑盒方案，确保跨MPC后端与敌手模型的移植性。实验结果表明，相较于最先进的MPC框架，本协议实现了1.79倍至19.4倍的加速，彰显了其在比较密集型MPC应用中的实用性。