多方隐私集合交集计算技术综述

高莹; 王玮

doi:10.11999/JEIT220664

多方隐私集合交集计算技术综述

doi: 10.11999/JEIT220664

高莹^{1, 2, 3, ,},
王玮¹

1.
北京航空航天大学网络空间安全学院北京 100191
2.
中关村实验室北京 100094
3.
空天网络安全工业和信息化部重点实验室北京 100191

基金项目: 国家自然科学基金(61932011, 61972017)，北京市自然科学基金(M21033)

详细信息

作者简介:
高莹：女，副教授，研究方向为隐私计算与密码学应用

王玮：女，硕士生，研究方向为多方隐私集合交集计算

通讯作者:
高莹　gaoying@buaa.edu.cn

中图分类号: TN918; TP309.2
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出版历程
- 收稿日期: 2022-05-23
- 修回日期: 2022-11-22
- 网络出版日期: 2022-11-25
- 刊出日期: 2023-05-10

A Survey of Multi-party Private Set Intersection

GAO Ying^{1, 2, 3
, ,},
WANG Wei¹

1.
School of Cyber Science and Technology, Beihang University, Beijing 100191, China
2.
Zhongguancun Laboratory, Beijing 100094, China
3.
Key Laboratory of Aerospace Network Security, Ministry of Industry and Information Technology, Beijing 100191, China

Funds: The National Natural Science Foundation of China (61932011, 61972017), The Natural Science Foundation of Beijing (M21033)

摘要

摘要: 随着互联网、大数据等新技术的快速发展，越来越多的分布式数据需要多方协作处理，隐私保护技术由此面临更大的挑战。安全多方计算是一种重要的隐私保护技术，可为数据的安全高效共享问题提供解决方案。作为安全多方计算的一个重要分支，隐私集合交集(PSI)计算技术可以在保护参与方的数据隐私性前提下计算两个或多个参与者私有数据集的交集，按照参与方数目可分为两方PSI和多方PSI。随着私人数据共享规模的扩大，多于两个参与方的应用场景越来越常见。多方PSI具有与两方PSI相似的技术基础但又有本质的不同。该文首先讨论了两方PSI的研究进展，其次详细梳理多方PSI技术的发展历程，将多方PSI技术依据应用场景的不同分为传统多方PSI技术以及门限多方PSI技术，并在不同场景下按照协议所采用密码技术和功能进行更细致的划分；对典型多方PSI协议进行分析，并对相关密码技术、敌手模型以及计算与通信复杂度进行对比。最后，给出了多方PSI技术的研究热点和未来发展方向。
- 隐私集合交集 /
- 不经意传输 /
- 不经意伪随机函数 /
- 加法同态加密 /
- 零秘密分享
Abstract: With the rapid development of new technologies, such as the Internet and big data, more and more distributed data need to be processed by multiple parties. Therefore, privacy protection technology is facing greater challenges. Secure multi-party computation is an important privacy protection technology, which can provide solutions for the secure and efficient sharing of data. As an important branch of secure multi-party computation, Private Set Intersection (PSI) technology can calculate the intersection of private data sets of two or more participants under the premise of protecting the data privacy of participants. It can be divided into two-party PSI and multi-party PSI according to the number of participants. With the expansion of private data sharing scale, application scenarios with more than two participants are more and more common. Multi party PSI has the same technical basis as the two party PSI, but has essential differences. Firstly, the research progress of the two-party PSI is discussed. Then the development processes of multi-party PSI are analyzed in detail. The multi-party PSI is divided into traditional multi-party PSI and threshold multi-party PSI according to the different scenarios. At the same time, protocols in different scenarios are divided more carefully according to the different basic cryptographic protocols they used and their different functions. The typical protocols are analyzed, and the cryptographic protocols, security model, computation and communication complexity of the protocols are discussed. Finally, the research hotspots and future development directions of multi-party PSI are pointed out.
- Private Set Intersection (PSI) /
- Oblivious Transfer (OT) /
- Oblivious pseudorandom function /
- Additively homomorphic encryption /
- Zero secret sharing

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图 1 隐私集合交集计算技术分类图

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图 2 通信结构分类图

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表 1 基于公钥的多方PSI协议比较

协议	安全性	抗勾结	通信复杂度		计算复杂度
协议	安全性	抗勾结	Leader	Client	Leader	Client
文献[37]	半诚实	√	$O\left( {{n^2}{m^2}\lambda } \right)$	$O\left( {{n^2}{m^2}\lambda } \right)$	$O\left( {{n^2}m + n\lambda {m^2}} \right)$	$O\left( {{n^2}m + n\lambda {m^2}} \right)$
文献[38]	半诚实	√	$O\left( {nm\lambda } \right)$	$O\left( {m\lambda } \right)$	$ O\left( {nm{{\log }_2}^{m\kappa }} \right) $	$O\left( {m\kappa } \right)$
文献[38]	恶意	√	$O\left( {\left( {{n^2} + nm{{\log }_2}^m} \right)\kappa } \right)$	$O\left( {\left( {n + m{{\log }_2}^m} \right)\kappa } \right)$	$O\left( {{m^2}} \right)$	$O\left( {{m^2}} \right)$
文献[39]	半诚实	√	$O\left( {dn{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {d{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( d \right)$	$O\left( d \right)$
文献[39]	半诚实	√	$O\left( {d\ell {{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {d{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( d \right)$	$O\left( d \right)$
文献[40]	半诚实	√	$O\left( {m\ell {{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {\lambda m{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( m \right)$	$O\left( {\lambda m} \right)$
文献[41]	半诚实	√	$O\left( {nd} \right)$	$O\left( d \right)$	$O\left( {nd} \right)$	$O\left( d \right)$
文献[41]	半诚实	√	$O\left( {nm} \right)$	$O\left( m \right)$	$O\left( {nmk} \right)$	$O\left( m \right)$
文献[44]	恶意	√	$O\left( {\ell {n^2}{m^2}\kappa } \right)$	$O\left( {\ell {n^2}{m^2}\kappa } \right)$	$O\left( {{\ell ^2}{m^2}{\kappa ^3}} \right)$	$O\left( {{\ell ^2}{m^2}{\kappa ^3}} \right)$
文献[45]	恶意	√	$O\left( {n{m^2}\kappa } \right)$	$O\left( {n{m^2}\kappa } \right)$	$O\left( {n{m^2}\kappa } \right)$	$O\left( {n{m^2}{\kappa ^3}} \right)$
文献[46]	UC	√	$O\left( {n{m^2}\kappa } \right)$	$O\left( {n{m^2}\kappa } \right)$	$O\left( {\ell {m^2}{\kappa ^3}} \right)$	$O\left( {\ell {m^2}{\kappa ^3}} \right)$
文献[47]	恶意	√	$O\left( {\lambda {n^2}m} \right)$	$O\left( {\lambda {n^2}m} \right)$	$O\left( {{n^2}m + nm\lambda } \right)$	$O\left( {{n^2}m + nm\lambda } \right)$
文献[48]	恶意	√	$O\left( {\left( {{n^2} + nm} \right)\kappa } \right)$	$O\left( {\left( {{n^2} + nm} \right)\kappa } \right)$	$O\left( {nm{{\log }_2}^m} \right)$	$O\left( {m{{\left( {{{\log }_2}^m} \right)}^2}} \right)$
文献[49]	恶意	√	$O\left( {{n^2}\kappa + nm\left( {\kappa + \lambda + {{\log }_2}^m} \right)} \right)$	$O\left( {m\left( {\kappa + \lambda + {{\log }_2}^m} \right)} \right)$	$O\left( {nm} \right)$	$O\left( m \right)$
注：在复杂度对比中，$n$为参与方数目，$w$为腐败方数目，$m$为集合大小，$\lambda $和$\kappa $分别为统计和计算安全参数，$k$为哈希函数的个数，$d$为域的大小，$\ell $为同态公钥加密系统的门限值，${\log _2}^{\left\| X \right\|}$为二进制密文$X$的大小。补充说明的是：任意腐败方数目$w$的最大值应小于总参与方数目。

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表 2 基于OT的多方PSI协议比较

协议	安全性	抗勾结	通信复杂度		计算复杂度
协议	安全性	抗勾结	Leader	Client	Leader	Client
文献[51]	半诚实	√	$O\left( {nm\lambda } \right)$	$O\left( {mw\lambda } \right)$	$O\left( {n\kappa } \right)$	$O\left( {w\kappa } \right)$
文献[51]	增强的半诚实	√	$O\left( {nm\lambda } \right)$	$O\left( {m\lambda } \right)$	$O\left( {n\kappa } \right)$	$O\left( \kappa \right)$
文献[52]	半诚实	√	$O\left( {nm\kappa } \right)$	$O\left( {m\kappa k} \right)$	$O\left( {nm\kappa } \right)$	$O\left( {m\kappa k} \right)$
文献[53]	半诚实	√	$O\left( {nm\kappa k} \right)$	$O\left( {nm\kappa k} \right)$	$O\left( {nm\kappa k} \right)$	$O\left( {nm\kappa k} \right)$
文献[53]	增强的半诚实	√	$O\left( {m\kappa k{{\log }_2}^n} \right)$	$O\left( {m\kappa k{{\log }_2}^n} \right)$	$O\left( {nm\kappa k} \right)$	$O\left( {nm\kappa k} \right)$
文献[54]	恶意	√	$ O\left( {nm{\lambda ^2} + nm\lambda {{\log }_2}^{\left( {m\lambda } \right)}} \right) $	$ O\left( {nm{\lambda ^2} + nm\lambda {{\log }_2}^{\left( {m\lambda } \right)}} \right) $	$O\left( {nmk} \right)$	$O\left( {nmk} \right)$
文献[55]	恶意	√	$O\left( {nm{\kappa ^2} + nm\kappa {{\log }_2}^{\left( {m\kappa } \right)}} \right)$	$O\left( {m{\kappa ^2} + m\kappa {{\log }_2}^{\left( {m\kappa } \right)}} \right)$	$O\left( {nm\kappa } \right)$	$O\left( {nm\kappa } \right)$
文献[56]	恶意	×	$O\left( {\left( {m + n} \right)\kappa } \right)$	$O\left( {m\kappa } \right)$	$O\left( {nm\kappa } \right)$	$O\left( {m\kappa } \right)$
文献[56]	恶意	√	$O\left( {m\kappa \cdot \max \left\{ {w,n - w} \right\}} \right)$	$O\left( {m\kappa } \right)$	$O\left( {m\kappa \left( {n - w} \right)} \right)$	$O\left( {mw\kappa } \right)$
文献[57]	恶意	√	$O\left( {nm\kappa + {n^2}\lambda \kappa {{\log }_2}^m} \right)$	$O\left( {m\kappa + n\lambda \kappa {{\log }_2}^m} \right)$	$O\left( {nm\kappa + m{{\left( {{{\log }_2}^m} \right)}^2}} \right)$	$O\left( {m\kappa + m{{\left( {{{\log }_2}^m} \right)}^2}} \right)$
注：在复杂度对比中，$n$为参与方数目，$w$为腐败方数目，$m$为集合大小，$\lambda $和$\kappa $分别为统计和计算安全参数，$k$为哈希函数的个数，$d$为域的大小，$\ell $为同态公钥加密系统的门限值，${\log _2}^{\left\| X \right\|}$为二进制密文$X$的大小。补充说明的是：任意腐败方数目$w$的最大值应小于总参与方数目。

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表 3 代理多方PSI协议比较表

协议	敌手模型		公平性	可验证	服务器数量
协议	服务器	客户端	公平性	可验证	服务器数量
文献[58]	半诚实、恶意	恶意	√	√	1
文献[59]	诚实	半诚实	√	×	1
文献[60]	诚实	半诚实	√	×	1
文献[61]	半诚实	半诚实	×	×	1
文献[62]	半诚实	半诚实	×	×	1
文献[63]	恶意	半诚实	×	√	1
文献[64]	半诚实	半诚实	×	×	1
文献[65]	半诚实	半诚实	×	×	1
文献[66]	半诚实、社会理性	社会理性	√	×	2
文献[67]	半诚实	半诚实	√	×	2
文献[68]	半诚实	半诚实	√	×	1

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表 4 约束元素出现次数的门限多方PSI协议比较

协议	安全性	抗勾结	通信复杂度		计算复杂度
协议	安全性	抗勾结	Leader	Client	Leader	Client
文献[40]	半诚实	√	$O\left( {mn\ell {{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {\max \left( {\lambda ,n} \right)m{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {mn} \right)$	$O\left( {\max \left( {\lambda ,n} \right)m} \right)$
文献[59]	半诚实	×	$O\left( {\lambda {n^2}m{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {{n^2}m{{\log }_2}^{\left\| X \right\|}} \right)$	$O\left( {\lambda nm{{\log }_2}^{\left\| X \right\|}} \right)$	$ O\left( {\lambda nm} \right) $
文献[78]	半诚实	√	$O\left( {{n^3}m\lambda } \right)$	$O\left( {{n^3}m\lambda } \right)$	$O\left( {{t^4}{n^2}{m^2}} \right)$	$O\left( {{t^4}{n^2}{m^2}} \right)$
文献[79]	半诚实	√	$O\left( {nmtw} \right)$	$O\left( {nmtw} \right)$	$O\left( {m{{\left( {n{{\log }_2}^{{m \mathord{\left/ {\vphantom {m t}} \right. } t}}} \right)}^{2t}}} \right)$	$O\left( {m{{\left( {n{{\log }_2}^{{m \mathord{\left/ {\vphantom {m t}} \right. } t}}} \right)}^{2t}}} \right)$
文献[83]	半诚实	√	$O\left( {nm\left( {\lambda + \kappa + {{\log }_2}^m} \right)} \right)$	$O\left( {m\left( {\lambda + \kappa + {{\log }_2}^m} \right)} \right)$	$O\left( {nm\kappa } \right)$	$O\left( {m\kappa } \right)$
注：在复杂度对比中，$n$为参与方数目，$w$为腐败方数目，$t$为协议门限值，$m$为集合大小，$\lambda $和$\kappa $分别为统计和计算安全参数，$\ell $为同态公钥加密系统的门限值，${\log _2}^{\left\| X \right\|}$为二进制密文$X$的大小。补充说明的是：任意腐败方数目$w$的最大值应小于总参与方数目。

下载: 导出CSV

表 5 约束交集大小的门限多方PSI协议比较

协议	安全性	抗勾结	通信轮数	通信复杂度
文献[86]	半诚实	×	$O\left( n \right)$	$O\left( {{{\left( {nt} \right)}^2}} \right)$
文献[90]	半诚实	√	$O\left( 1 \right)$	$O\left( {nt \cdot {\text{poly}}\left( \lambda \right)} \right)$
文献[91]	半诚实	√	$O\left( 1 \right)$	$O\left( {n{t^2}\kappa \lambda } \right)$
注：在复杂度对比中，$n$为参与方数目，$t$为协议门限值，$\lambda $和$\kappa $分别为统计和计算安全参数。

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