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

2026-02-23

AI Summary

This work addresses performance bottlenecks in existing multi-party secure comparison protocols, which suffer from inefficient preprocessing and lack optimization for the online phase or support across algebraic domains (𝔽_p and ℤ_{2^k}). We propose the first multi-party, cross-domain protocol for secure less-than and most significant bit extraction, achieving protocol-level perfect security by leveraging a non-colluding auxiliary party to generate rich correlated randomness. Our design uniquely integrates the auxiliary party’s capabilities into the core protocol architecture, attaining constant-round online complexity over 𝔽_p and O(log_n k)-round complexity over ℤ_{2^k}. The protocol is black-box compatible with diverse MPC backends and adversarial models. Experimental results demonstrate a 1.79× to 19.4× performance improvement over the state-of-the-art, substantially enhancing the practicality of comparison-intensive applications.

Technology Category

• Application Domains: Security
• Machine Learning: Hardware-aware ML
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

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.

Problem

• secure comparison
• multi-party computation
• preprocessing
• dealer-assisted
• domain generality

Innovation

• dealer-assisted MPC
• secure comparison
• LTBits
• MSB extraction
• cross-domain protocols