一种安全可扩展的变体阈值多方隐私集合求交协议

doi:10.3969/j.issn.1671-1122.2026.04.003

摘要/Abstract

摘要：

多方隐私集合求交（MPSI）协议的核心能力在于安全地找出多方集合的交集并输出结果，同时不泄露任何信息。然而，某些特殊且实用的场景无法直接通过传统 MPSI 协议解决，其中一种场景是为第三方获取仅出现在部分集合中（至少出现k次）的元素集合。但现有方法（如Quorum PSI）仅能处理已知元素的特殊交集问题。超阈值隐私集合求交虽能解决此问题，但需执行多次操作，当参与者数量庞大时效率低下。文章提出一种安全可扩展的变体阈值多方隐私集合求交协议，仅需执行n− k + 1次操作，在高阈值 k 场景下更具效率优势。

关键词: 隐私集合求交, 私有集合成员测试, 隐私信息检索, 等值测试

Abstract:

The ability of multi-party private intersection (MPSI) protocols is to securely find the intersection of multi-party sets and output it without disclosing any other information. However, there are some special and useful scenarios that cannot be solved directly using traditional MPSI protocols. One of such scenarios is to compute the set of elements that appear in some but not all sets (at least k times) for only a third party. However, the previous method(Quorum PSI) can only addresse the problem of getting special intersections of known elements. The over-threshold PSI can address the issue, but needs to perform times, which is inefficient when the number of participants is large. This paper proposed a secure and scalable variant-threshold multiparty private set intersection protocol. It only executes n − k + 1 times, which is more efficient in cases with a high threshold k.

Key words: private set intersection, private set membership test, private information retrieval, equal test

中图分类号:

TP309

郑东, 刘雁荣, 秦宝东. 一种安全可扩展的变体阈值多方隐私集合求交协议[J]. 信息网络安全, 2026, 26(4): 542-551.

ZHENG Dong, LIU Yanrong, QIN Baodong. A Secure and Scalable Variant-Threshold Multiparty Private Set Intersection Protocol[J]. Netinfo Security, 2026, 26(4): 542-551.

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符号	说明
X_i	参与方集合
$n$	参与方数量
$u$	集合大小
$\kappa $	安全参数
$\lambda $	计算安全参数
$k$	阈值
$\left[ n \right]~$	从1到$~n~$的整数集合
$\left[ x \right]$	$x$的秘密共享
$x$	$x$的加法秘密共享
$m$	$n$−k+1 个参与方
$Tabl{{e}_{\left[ i \right]~}}\left[ j \right]$	哈希表的第$i$个参与方的第j个箱子
$s~\leftarrow ~S$	s是 S里随机选取的元素

协议	通信复杂度	计算复杂度
Kissner Song^[27]协议	$O~\left(u~\cdot~n~\right)$	$O~\left( {{u}^{2}}\cdot ~{{n}^{2}} \right)$
t-PSI^[39]协议	$O~\left( u~\cdot ~n~\cdot ~t \right)$	$O~\left( u\cdot ~n~\cdot ~t \right)$
本文协议	$O~\left( mu\left( n~-~1 \right) \right)$	$O~\left( mu~\left( n-1 \right)+n\cdot m\text{lg}n \right)$