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arXiv:2602.19604

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

Kaiwen Wang, Xiaolin Chang, Yuehan Dong, Ruichen Zhang

Published Feb 23, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2602.19604

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Secure multi-party computation (MPC) is a cryptographic tool that enables a set of parties to compute a function jointly while keeping each input secret. Since MPC based on secret sharing (SS) achieves high throughput and works fast, many applications have been developed. However, SS-based MPC requires many communication rounds in general, and this becomes a performance bottleneck in real-world applications under high-latency networks. In this paper, we propose SS-based secure three-party computation with almost no preprocessing based on our new (small-)constant-round fundamental gates, by revisiting a framework in a few previous works where a number of parties are assisted by another party who may partially learn secret information. Instead of ordinary logical gates, our fundamental gate is an efficient Equality, for which the result leaks to the third party, and we develop novel two-round constructions of secure building-block protocols (LessThan Comparison, RightShift, Table LookUp, etc.) from the insecure Equality. To show the practicality of our protocols, we implement a secure exact edit distance protocol for two genome strings. Our experiments show that in some network setting our protocol is about 2 times faster (14 times faster taking preprocessing into consideration) than the state-of-the-art SS-based protocol (Ohata and Nuida, FC 2020).
We put forth a new paradigm for secure multi-party computation (MPC) in the preprocessing model, where a feasible one-time setup can enable a lifetime of efficient online secure computations. Our protocols match the security guarantees and low costs of the cheapest category of MPC solutions, namely 3-party protocols (3PC) secure against a single malicious party, with the qualitative advantages that one party communicates data sublinear in the circuit size, and can go offline after its initial messages. This “2+ 1“-party structure can alternatively be instantiated between 2 parties with the aid of an (untrusted) dealer. Within such existing protocols, we provide comparable online performance while improving the storage and offline dealer-to-party communication requirements by more than 3 orders of magnitude. At the technical level, we build on the Fully Linear Interactive Oracle Proof (FLIOP)-based protocol design of Boyle et al. (CRYPTO 2021). We provide an extensive assortment of algorithmic and implementation-level optimizations, design efficient distributed proofs of well-formedness of complex FLIOP correlations, and make them circuit-independent. We implement and benchmark our end-to-end system against the state of the art in the 2+1 regime, a dealer-aided variant of SPDZ for Boolean circuits. We additionally extend our techniques to the(n+1)(n+1)(n+1)party setting, where a dealer aids general dishonest-majority MPC, and provide a variant of the protocol which further achieves security with “identifiable abort.”
We construct the first efficient, unconditionally secure MPC protocol that only requires black-box access to a non-commutative ring R. Previous results in the same setting were efficient only either for a constant number of corruptions or when computing branching programs and formulas. Our techniques are based on a generalization of Shamir’s secret sharing to non-commutative rings, which we derive from the work on Reed Solomon codes by Quintin, Barbier and Chabot (IEEE Transactions on Information Theory, 2013). When the center of the ring contains a set A={α0,…,αn}A = \{\alpha _0, \ldots , \alpha _n\}A={α0​,…,αn​} such that ∀i≠j,αi − αj∈R∗\forall i \ne j, \alpha _i \,-\, \alpha _j \in R^*∀i=j,αi​−αj​∈R∗ , the resulting secret sharing scheme is strongly multiplicative and we can generalize existing constructions over finite fields without much trouble. Most of our work is devoted to the case where the elements of A do not commute with all of R, but they just commute with each other. For such rings, the secret sharing scheme cannot be linear “on both sides” and furthermore it is not multiplicative. Nevertheless, we are still able to build MPC protocols with a concretely efficient online phase and black-box access to R. As an example we consider the ring Mm×m(Z/2kZ)\mathcal {M}_{m\times m}(\mathbb {Z}/2^k\mathbb {Z})Mm×m​(Z/2kZ) , for which when m>log⁡(n+1)m > \log (n+1)m>log(n+1) , we obtain protocols that require around ⌈log⁡(n+1)⌉/2\lceil \log (n+1)\rceil /2⌈log(n+1)⌉/2 less communication and 2⌈log⁡(n+1)⌉2\lceil \log (n+1)\rceil 2⌈log(n+1)⌉ less computation than the state of the art protocol based on Circuit Amortization Friendly Encodings (Dalskov, Lee and Soria-Vazquez, ASIACRYPT 2020). In this setting with a “less commutative” A, our black-box preprocessing phase has a less practical complexity of poly(n)\mathsf {poly}(n)poly(n) . We fix this by additionally providing specialized, concretely efficient preprocessing protocols for Mm×m(Z/2kZ)\mathcal {M}_{m\times m}(\mathbb {Z}/2^k\mathbb {Z})Mm×m​(Z/2kZ) that exploit the structure of the matrix ring.
Secure multi-party computation (MPC) allows multiple parties to jointly compute a task while preserving the privacy of their individual inputs. In recent years, researchers have extensively studied various security protocols to improve the efficiency of MPC and reduce communication overhead. However, the efficiency of MPC in annnn-party setting still remains a challenge. In this paper, we introduce WINK, a MPC framework designed for the semi-honest security model that accommodates an arbitrary number of participants. We design annnn-party multiplication protocol in thennn-out-of-nnnarithmetic secret sharing setting and, based on this, construct independent multiplication triples. We leverage a RLWE-based oblivious linear evaluation (OLE) technique to batch generate multiplication triples between any two parties, significantly reducing communication overhead. Furthermore, we design a constant-round n-party comparison protocol based on the properties of odd-sized rings and garbled circuits. This protocol completes in only three rounds of communication with the help of additional non-colluding semi-honest servers, marking a significant improvement over previousnnn-party comparison protocols. We prove that our framework achieves universally composable security. Moreover, experimental results demonstrate that our proposed comparison protocol outperforms existing comparison protocols in terms of efficiency.
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In this paper, we propose memory- and round-efficient protocols for securely evaluating arithmetic primitives. We focus on secure two-party computation over the ring ℤ2k that achieves security against semi-honest adversaries and works in the pre-processing model. Our protocols rely on the unit vectorization technique introduced by Boyle et al. (TCC 2019). The unit vectorization technique provides online-optimal protocols for several fundamental operations in the pre-processing model. However, a relatively large memory cost for correlated randomness is required, which might become an obstacle in a large-scale application. In order to achieve both memory and communication efficiency, we propose a size reduction method that uses unit vectorization only for short-length inputs, and based on this, construct two-round protocols for equality test, detecting the most significant non-zero bit, detecting wrap-around, and less-than comparison. In addition, as applications of these results, we provide practically efficient protocols for integer division, integer square root, integer logarithm, and modular exponentiation.