本地化差分隐私综述

doi:10.11871/jfdc.issn.2096-742X.2023.05.007

数据与计算发展前沿 ›› 2023, Vol. 5 ›› Issue (5): 74-97.

CSTR: 32002.14.jfdc.CN10-1649/TP.2023.05.007

doi: 10.11871/jfdc.issn.2096-742X.2023.05.007

• 专刊:数据要素安全高效流通的关键技术 • 上一篇下一篇

本地化差分隐私综述

孙一帆^1,²(),张锐^1,^2,^*(),陶杨^1,²,高碧柔^1,²,秦诗涵^1,²,安超^1,²

1.中国科学院信息工程研究所，信息安全国家重点实验室，北京 100085
2.中国科学院大学，网络空间安全学院，北京 100049

收稿日期:2023-05-04 出版日期:2023-10-20 发布日期:2023-10-31
通讯作者: *张锐（E-mail: r-zhang@iie.ac.cn）
作者简介:孙一帆，中国科学院信息工程研究所，博士研究生，主要研究方向为数据安全、差分隐私。
本文中负责文献调研、总结归纳、论文写作等。
SUN Yifan is currently a Ph.D. student at the Institute of Information Engineering, Chinese Academy of Sciences. Her research interests include data security and differential privacy.
In this paper, she is responsible for literature research, analyzing and summarizing related work, and paper writing.
E-mail: sunyifan@iie.ac.cn|张锐，中国科学院信息工程研究所，研究员，博士生导师，主要研究方向为密码学与安全协议、后量子密码、数据安全、云计算安全理论与技术和区块链理论与技术。
本文中负责写作思路指导和论文修订等。
ZHANG Rui is a research fellow and Ph.D. supervisor at the Institute of Information Engineering, Chinese Academy of Sciences. His research fields include cryptography and security protocols, post-quantum cryptography, data security, cloud computing security theory and technology, and blockchain theory and technology.
In this paper, he is responsible for guidance of writing ideas and paper revision.
E-mail: r-zhang@iie.ac.cn
基金资助:
国家自然科学基金项目(62172411);国家自然科学基金项目(62172404);国家自然科学基金项目(61972094);国家自然科学基金项目(62202458)

A Survey on Local Differential Privacy

SUN Yifan^1,²(),ZHANG Rui^1,^2,^*(),TAO Yang^1,²,GAO Birou^1,²,QIN Shihan^1,²,AN Chao^1,²

1. SKLOIS, Institute of Information Engineering, Beijing 100085, China
2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2023-05-04 Online:2023-10-20 Published:2023-10-31

摘要/Abstract

摘要：

【目的】 本地化差分隐私是优秀的隐私保护模型，能够在数据共享、发布的场景下对群体进行统计分析，保护个人数据隐私。本文围绕本地化差分隐私进行综述，为未来工作提供参考。【文献范围】 本文调研了来自主流会议、期刊的本地化差分隐私领域的论文，并进行了总结归纳。【方法】 本文以数据统计分析任务类型为线索，从基于本地化差分隐私模型的频率估计、均值估计、多维数据统计分析和机器学习4个方面展开调研。本文对相关研究进行了对比分析，对关键问题进行了总结，对现有工作的不足进行了讨论，对未来的研究方向进行了展望。【结果】 本地化差分隐私模型能够在用户数据被采集、分析时，为用户个人数据隐私提供强有力的隐私保护。【局限】 本文以数据统计分析任务类型为线索，未对图数据相关研究进行总结。【结论】 本地化差分隐私作为一种优秀的隐私保护模型，得到学者们的关注后迅速发展，但是仍然面临着诸多问题和挑战，值得进一步研究和探索。

关键词: 本地化差分隐私, 频率估计, 均值估计, 多维数据统计分析, 机器学习

Abstract:

[Objective] This paper systematically introduces local differential privacy and provides a reference for the protection of personal data privacy under data sharing and publishing. [Coverage] This paper investigates and summarizes papers from mainstream conferences and journals in the field of local differential privacy. [Methods] This paper takes the type of statistical data analysis task as a clue and conducts research based on local differential privacy from four aspects, which concludes frequency estimation, mean estimation, multidimensional data statistical analysis, and machine learning. This paper makes a comparative analysis of relevant studies, summarizes key issues, discusses the shortcomings of existing work, and looks forward to future research directions. [Results] The local differential privacy model can provide strong privacy protection for users' personal data privacy when user data is collected and analyzed. [Limitations] This paper takes the type of statistical data analysis task as a clue and does not summarize the research related to graph data. [Conclusions] Local differential privacy, as an excellent privacy-preserving model, has developed rapidly after gaining the attention of scholars. But it still faces many problems and challenges, which are worthy of further research and exploration.

Key words: local differential privacy, frequency estimation, mean estimation, multidimensional data statistical analysis, machine learning

孙一帆, 张锐, 陶杨, 高碧柔, 秦诗涵, 安超. 本地化差分隐私综述[J]. 数据与计算发展前沿, 2023, 5(5): 74-97.

SUN Yifan, ZHANG Rui, TAO Yang, GAO Birou, QIN Shihan, AN Chao. A Survey on Local Differential Privacy[J]. Frontiers of Data and Computing, 2023, 5(5): 74-97, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2023.05.007.

图/表 7

图1

表1

符号"

符号	描述
$n$	用户总数
$k$	数据维度
$d$	属性域空间大小
$v / v *$	原始数据/扰动数据
$R$	随机算法
$ϵ$	隐私预算
$p / q$	扰动概率
$H / H$	哈希函数集合/哈希函数
$n v i / n ? v i / n^v i$	数据 $v i$ 的真实/统计/估计频数
$f v i / f^v i$	数据 $v i$ 的真实/估计频率

表1

图2

表2

单属性单值数据的频率估计机制对比"

编码扰动方式		典型机制	通信代价	渐近误差边界	方差
直接扰动		BRR^[17]	$Ο 1$	$Ο 1 ϵ n$	$e ϵ n e ϵ - 1 2$
直接扰动		GRR^[24]	$Ο l o g d$	$Ο d l o g d ϵ n$	$e ϵ + d - 2 n e ϵ - 1 2$
先编码后扰动	独热编码	SUE^[25]	$Ο d$	$Ο l o g k ϵ n$	$e ϵ / 2 n e ϵ / 2 - 1 2$
	独热编码	OUE^[25]	$Ο d$	$Ο l o g d ϵ n$	$4 e ϵ n e ϵ - 1 2$
	基于哈希函数	RAPPOR^[26]	$Θ d$	$Ο d ϵ n$	$e ϵ / 2 n e ϵ / 2 - 1 2$
		BLH^[25]	$Ο l o g d$	$Ο l o g d ϵ n$	$e ϵ + 1 2 n e ϵ - 1 2$
		OLH^[25,33]	$Ο l o g d$	$Ο l o g d ϵ n$	$4 e ϵ n e ϵ - 1 2$
	基于矩阵变换	S-Hist^[27]	$Ο l o g m$	$Ο l o g d ϵ n$	$e ϵ n e ϵ - 1 2$
	基于矩阵变换	HRR^[34,35]	$Ο l o g d$	$Ο l o g d ϵ n$	$4 e ϵ n e ϵ - 1 2$
	子集选择	$k$ -subset^[29?-31]	$Ο 1$	$Ο d l o g d ϵ n$	$e ϵ + d - 2 n e ϵ - 1 2$

表2

表3

集值数据集示例"

用户	集值数据
$u 1$	$1,3, 4$
$u 2$	$2,5$
$u 3$	$1,3, 4,5$
$u 4$	$3$
$u 5$	$?$
$u 6$	$1,2, 3,4, 5$

表3

表4

单属性集值数据的频率估计机制对比"

分析任务	典型机制	关键技术	优点	缺点
频繁项挖掘	LDPMiner^[36]	填充采样；修正候选集合	采样避免隐私预算的分割频率统计和频繁项集合的确定二者分离	不适用 $d$ 很大的情况
	PEM^[37]	构建前缀树；用户分组	计算开销小	隐私预算划分降低数据可用性
	PrivSet^[38]	填充采样；子集选择	估计结果误差小	子集大小的确定不高效
	Calibrate^[22]	利用先验知识	根据先验知识建模减小误差	增大了计算开销
	GFIM^[39]	候选集合去冗余；用户分组	减小候选集，降低时间复杂度	增大了计算开销
	IC^[40]	子域分割；交互的FRR	通信成本低	采样方法降低数据可用性
频繁项集挖掘	SVSM^[37]	GRR；OLH；猜测概率	可以选择频率估计机制减小候选集	猜测概率引入额外的误差
	Ma’s^[41]	HRR；FP-tree	通信开销小	增大了计算开销
	Priv_OA^[42]	两级随机化技术	考虑了数据项之间的关联性	不适用 $d$ 很大的情况
	LDP-FPMiner^[43]	GRR；OLH；FP-tree	考虑了数据项集之间的关联性	没有讨论用户分组大小

表4

表5

数值型数据的均值估计机制对比"

编码扰动方式	典型机制	通信代价	渐近误差边界	方差（ $k = 1$ 时）
无界扰动	Laplace^[9]	$Ο k$	$Ο k l o g k ϵ n$	$8 ϵ 2$
有界扰动	Duchi’s^[46]	$Ο k$	$Ο k l o g k ϵ n$	$e ϵ + 1 e ϵ - 1 2$
	Harmony^[47]	$Ο 1$	$Ο k l o g k ϵ n$	$e ϵ + 1 e ϵ - 1 2$
	PM^[48]	$Ο m$	$Ο k l o g k ϵ n$	$4 e ϵ / 2 3 e ϵ / 2 - 1 2$
	HM^[48]	$Ο m$	$Ο k l o g k ϵ n$	$e ϵ / 2 + 3 3 e ϵ / 2 e ϵ / 2 - 1 + e ϵ + 1 2 e ϵ / 2 e ϵ - 1 2, i f ϵ > 0.61, e ϵ + 1 2 e ϵ - 1 2, i f ϵ ≤ 0.61 .$
	PWP^[49]	$Ο 1$	$Ο k l o g k ϵ n$	$w 2 e ϵ / 2 3 e ϵ / 2 - 1 2$

表5

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本地化差分隐私综述

A Survey on Local Differential Privacy

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