A Survey on Local Differential Privacy

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

Abstract

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

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.

Figures/Tables 7

Fig.1

Table 1

Notations"

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

Table 1

Fig.2

Table 2

Comparisons of frequency estimation mechanisms for single-value data in single attribute"

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]	$Ο 1$	$Ο d l o g d ϵ n$	$e ϵ + d - 2 n e ϵ - 1 2$

Table 2

Table 3

Example of set-valued dataset"

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

Table 3

Table 4

Comparisons of frequency estimation mechanisms for set-value data in single attribute"

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

Table 4

Table 5

Comparisons of mean estimation mechanisms for numerical data"

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]	$Ο 1$	$Ο k l o g k ϵ n$	$w 2 e ϵ / 2 3 e ϵ / 2 - 1 2$

Table 5

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