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Multi-Party Private Set Operations from Predicative Zero-Sharing

Minglang Dong, Yu Chen, Cong Zhang, Yujie Bai, Yang Cao

TL;DR

This work introduces a unified framework for multi-party private set operations (MPSO) that supports arbitrary set formulas across $m>2$ parties, with a leader learning the final result while clients learn nothing. It hinges on a canonical predicate formula (CPF) representation of set formulas and a predicative zero-sharing (PZS) primitive, including a tailored membership-zero-sharing instantiation, built from lightweight OT-based primitives (ROT, OPPRF) and batch secret-sharing tests. The framework realizes MPSO, MPSO-card, and circuit-MPSO, and efficiently instantiates well-known functionalities such as MPSI, MPSI-card, MPSI-card-sum, MPSU, and circuit-MPSU, achieving near-optimal complexity in the standard semi-honest model and strong security against arbitrary collusion. It also provides comprehensive complexity analyses and experimental evaluations demonstrating practical online performance on large-scale settings, with implications for real-world privacy-preserving data collaboration tasks. Overall, the approach unifies disparate MPSO protocols under CPF and PZS constructs, delivering scalable, secure, and flexible private set operations without relying on generic MPC, thus broadening the applicability of private set computations in practice.

Abstract

Typical protocols in the multi-party private set operations (MPSO) setting enable m > 2 parties to perform certain secure computation on the intersection or union of their private sets, realizing a very limited range of MPSO functionalities. Most works in this field focus on just one or two specific functionalities, resulting in a large variety of isolated schemes and a lack of a unified framework in MPSO research. In this work, we present an MPSO framework, which allows m parties, each holding a set, to securely compute any set formulas (arbitrary compositions of a finite number of binary set operations, including intersection, union and difference) on their private sets. Our framework is highly versatile and can be instantiated to accommodate a broad spectrum of MPSO functionalities. To the best of our knowledge, this is the first framework to achieve such a level of flexibility and generality in MPSO, without relying on generic secure multi-party computation (MPC) techniques. Our framework exhibits favorable theoretical and practical performance. The computation and communication complexity scale linearly with the set size n, and it achieves optimal complexity that is on par with the naive solution for widely used functionalities, such as multi-party private set intersection (MPSI), MPSI with cardinality output (MPSI-card), and MPSI with cardinality and sum (MPSI-card-sum), in the standard semi-honest model. Furthermore, the instantiations of our framework mainly from symmetric-key techniques yield efficient protocols for MPSI, MPSI-card, MPSI-card-sum, and multi-party private set union (MPSU), with online performance surpassing or matching the state of the art.

Multi-Party Private Set Operations from Predicative Zero-Sharing

TL;DR

This work introduces a unified framework for multi-party private set operations (MPSO) that supports arbitrary set formulas across parties, with a leader learning the final result while clients learn nothing. It hinges on a canonical predicate formula (CPF) representation of set formulas and a predicative zero-sharing (PZS) primitive, including a tailored membership-zero-sharing instantiation, built from lightweight OT-based primitives (ROT, OPPRF) and batch secret-sharing tests. The framework realizes MPSO, MPSO-card, and circuit-MPSO, and efficiently instantiates well-known functionalities such as MPSI, MPSI-card, MPSI-card-sum, MPSU, and circuit-MPSU, achieving near-optimal complexity in the standard semi-honest model and strong security against arbitrary collusion. It also provides comprehensive complexity analyses and experimental evaluations demonstrating practical online performance on large-scale settings, with implications for real-world privacy-preserving data collaboration tasks. Overall, the approach unifies disparate MPSO protocols under CPF and PZS constructs, delivering scalable, secure, and flexible private set operations without relying on generic MPC, thus broadening the applicability of private set computations in practice.

Abstract

Typical protocols in the multi-party private set operations (MPSO) setting enable m > 2 parties to perform certain secure computation on the intersection or union of their private sets, realizing a very limited range of MPSO functionalities. Most works in this field focus on just one or two specific functionalities, resulting in a large variety of isolated schemes and a lack of a unified framework in MPSO research. In this work, we present an MPSO framework, which allows m parties, each holding a set, to securely compute any set formulas (arbitrary compositions of a finite number of binary set operations, including intersection, union and difference) on their private sets. Our framework is highly versatile and can be instantiated to accommodate a broad spectrum of MPSO functionalities. To the best of our knowledge, this is the first framework to achieve such a level of flexibility and generality in MPSO, without relying on generic secure multi-party computation (MPC) techniques. Our framework exhibits favorable theoretical and practical performance. The computation and communication complexity scale linearly with the set size n, and it achieves optimal complexity that is on par with the naive solution for widely used functionalities, such as multi-party private set intersection (MPSI), MPSI with cardinality output (MPSI-card), and MPSI with cardinality and sum (MPSI-card-sum), in the standard semi-honest model. Furthermore, the instantiations of our framework mainly from symmetric-key techniques yield efficient protocols for MPSI, MPSI-card, MPSI-card-sum, and multi-party private set union (MPSU), with online performance surpassing or matching the state of the art.
Paper Structure (48 sections, 7 theorems, 23 equations, 21 figures, 7 tables)

This paper contains 48 sections, 7 theorems, 23 equations, 21 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Preliminaries
  5. Notation
  6. Security Model
  7. Multi-party Private Set Operations
  8. Random Oblivious Transfer
  9. Batch Oblivious Programmable Pseudorandom Function
  10. Batch Secret-Shared Private Membership Test
  11. Multi-Party Secret-Shared Shuffle
  12. Hashing to Bins
  13. Predicate Formula Representation of Set Formulas
  14. Constructible Set
  15. Canonical Predicate Formula Representation
  16. ...and 33 more sections

Key Result

theorem thmcountertheorem

Let $X_1,\cdots,X_m$ be $m$ sets and $Y$ is a constructible set. There exists a set predicate formula $\varphi(x,X_1,\cdots,X_m)$, s.t. for any urelement $x$,

Figures (21)

  • Figure 1: Typical Functionalities in MPSO
  • Figure 2: 1-out-of-2 Random OT Functionality $\mathcal{F}_\mathsf{ROT}$
  • Figure 3: Batch OPPRF Functionality $\mathcal{F}_\mathsf{bOPPRF}$
  • Figure 4: Batch ssPMT Functionality $\mathcal{F}_\mathsf{bssPMT}$
  • Figure 5: Multi-Party Secret-Shared Shuffle Functionality $\mathcal{F}_\mathsf{shuffle}$
  • ...and 16 more figures

Theorems & Definitions (15)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • theorem thmcountertheorem
  • definition thmcounterdefinition
  • corollary thmcountercorollary
  • definition thmcounterdefinition
  • theorem thmcountertheorem
  • theorem thmcountertheorem
  • theorem thmcountertheorem
  • ...and 5 more