Efficient Multi-Party Secure Comparison over Different Domains with Preprocessing Assistance

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.