几类经典隐私定义间的关系
Relations Between Several Classical Privacy Notions
- 电子学报 2025年53卷第10期 页码：3781-3793
- 作者机构：
1.亚洲大学人工智能系，韩国水原 16499
2.复旦大学计算机科学技术学院，上海 200433
3.兰州理工大学计算机与人工智能学院， 甘肃兰州 730050
4.湘潭大学数学与计算科学学院，湖南湘潭 411105
5.暨南大学信息科学技术学院，广东广州 510632
- 作者简介：
[ "郑智润 男，1995年2月出生于江西省上饶市.现为韩国亚洲大学人工智能系博士后，同时兼任该校软件工程系讲师.主要研究方向为群智系统安全、隐私计算和人工智能安全等. E-mail: zhengzhirun2019@gmail.com" ]
[ "黄橙 男，1991年8月出生于安徽省淮南市.现为复旦大学青年研究员.主要研究方向为人工智能安全. E-mail: chuang@fudan.edu.cn" ]
[ "王萍 女，1994年出生于甘肃省兰州市.现为兰州理工大学讲师.主要研究方向为智能感知、安全计算等. E-mail: wangping51226@gmail.com" ]
[ "李成新 男，1996年出生于湖北省黄冈市.现为湘潭大学博士研究生.主要研究方向为移动群智感知、数据隐私保护等. E-mail: snowwhite@uestc.edu.cn" ]
[ "许雯 女，1997年出生于湖南省邵阳市.现为暨南大学博士研究生.主要研究方向为图数据分析、信息隐私和安全、物联网等. E-mail: wenxu018@gmail.com" ]
[ "李哲涛 男，1980年1月出生于湖南省邵阳市.现为暨南大学教授.主要研究方向为机器学习、深度学习、智能系统安全、云边端资源管理等. E-mail: liztchina@hotmail.com" ]
- 基金信息：国家自然科学基金国际合作重点项目(W2411053)
DOI：10.12263/DZXB.20250078
中图分类号： TP3-05;O211.1收稿：2025-01-22，
录用：2025-09-25，
纸质出版：2025-10-25
- 稿件说明：
移动端阅览
郑智润, 黄橙, 王萍, 等. 几类经典隐私定义间的关系[J]. 电子学报, 2025, 53(10): 3781-3793.
ZHENG Zhi-run, HUANG Cheng, WANG Ping, et al. Relations Between Several Classical Privacy Notions[J]. Acta Electronica Sinica, 2025, 53(10): 3781-3793.
郑智润, 黄橙, 王萍, 等. 几类经典隐私定义间的关系[J]. 电子学报, 2025, 53(10): 3781-3793. DOI：10.12263/DZXB.20250078
ZHENG Zhi-run, HUANG Cheng, WANG Ping, et al. Relations Between Several Classical Privacy Notions[J]. Acta Electronica Sinica, 2025, 53(10): 3781-3793. DOI：10.12263/DZXB.20250078
摘要
针对现有基于不同隐私定义设计的扰动机制在理论上难以比较优劣的问题，本文从理论层面深入分析了中心化场景和本地化场景下可辨识性、差分隐私和互信息隐私这三类经典隐私定义之间的关系，构建了一个完备的隐私定义框架.具体而言，给定由真实数据先验概率分布决定的常数（当先验概率分布为均匀分布时，常数
<math id="M1"><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951070&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951080&type=
8.89000034
3.21733332
），可得以下结论：满足
<math id="M2"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951097&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951071&type=
1.94733346
3.21733332
-可辨识性的隐私保护机制必然也同时满足
<math id="M3"><mfenced separators="|"><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951110&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951098&type=
11.68400002
3.80999994
-差分隐私和
<math id="M4"><mn mathvariant="normal">2</mn><mfenced separators="|"><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951087&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951121&type=
13.80066681
3.80999994
-互信息隐私；满足
<math id="M5"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951113&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951112&type=
2.28600001
3.21733332
-差分隐私的隐私保护机制必然也同时满足
<math id="M6"><mfenced separators="|"><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>+</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951115&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951125&type=
12.10733318
3.89466691
-可辨识性和
<math id="M7"><mn mathvariant="normal">2</mn><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951151&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951150&type=
3.89466691
3.21733332
-互信息隐私；但是，满足
<math id="M8"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951153&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951140&type=
2.70933342
3.21733332
-互信息隐私的隐私保护机制却不一定满足
<math id="M9"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951166&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951142&type=
1.94733346
3.21733332
-可辨识性和
<math id="M10"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951168&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951156&type=
2.28600001
3.21733332
-差分隐私（在
<math id="M11"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951180&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951169&type=
2.70933342
3.21733332
有限的情况下，
<math id="M12"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951172&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951181&type=
1.94733346
3.21733332
和
<math id="M13"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951168&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951156&type=
2.28600001
3.21733332
可能会趋于无穷大）.此外，所提隐私定义框架能一致地推导出隐私定义间的关系，使得对隐私预算上界的估计更加准确.
Abstract
We address the challenge of theoretically evaluating various perturbation-based privacy-preserving mechanisms designed under different privacy notions. By analyzing the relationships among three classical privacy notions
namely identifiability
differential privacy
and mutual-information privacy
in both centralized and local settings
we propose a complete privacy notion framework that establishes theoretical relations among them. Specifically
given a constant
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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951196&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951173&type=
4.48733330
3.21733332
determined by the prior probability distribution of the real data (the constant
<math id="M15"><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0</mn></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951186&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951176&type=
8.89000034
3.21733332
when the prior distribution is uniform)
the following theorems are formally proved in both central and local settings. First
the mechanism satisfying
<math id="M16"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951202&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951213&type=
1.94733346
3.21733332
-identifiability must also satisfy
<math id="M17"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951204&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951203&type=
2.28600001
3.21733332
-differential privacy with
<math id="M18"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951218&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951205&type=
14.22399998
3.21733332
. Second
the mechanism satisfying
<math id="M19"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951241&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951240&type=
2.28600001
3.21733332
-differential privacy must also satisfy
<math id="M20"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951202&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951213&type=
1.94733346
3.21733332
-identifiability with
<math id="M21"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>+</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951255&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951254&type=
14.22399998
3.21733332
. Third
the mechanism satisfying
<math id="M22"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951245&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951233&type=
1.94733346
3.21733332
-identifiability must also satisfy
<math id="M23"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951247&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951235&type=
2.70933342
3.21733332
-mutual-information privacy with
<math id="M24"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><mo stretchy="false">(</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951261&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951260&type=
18.54199982
3.89466691
. Fourth
the mechanism satisfying
<math id="M25"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951263&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951262&type=
2.70933342
3.21733332
-mutual-information privacy does not guarantee
<math id="M26"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951265&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951276&type=
2.28600001
3.21733332
-differential privacy. Fifth
the mechanism satisfying
<math id="M27"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951298&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951286&type=
2.28600001
3.21733332
-differential privacy must also satisfy
<math id="M28"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951288&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951279&type=
2.70933342
3.21733332
-mutual-information privacy with
<math id="M29"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">2</mn><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951301&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951289&type=
9.39799976
3.21733332
. Sixth
the mechanism satisfying
<math id="M30"><msub><mrow><mi>ε</mi></mrow><mrow><mi>m</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951291&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951314&type=
2.70933342
3.21733332
-mutual-information privacy does not guarantee
<math id="M31"><msub><mrow><mi>ε</mi></mrow><mrow><mi>d</mi></mrow></msub></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951304&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=99951292&type=
2.28600001
3.21733332
-differential privacy. The proposed framework systematically derives the theoretical relationships among identifiability
differential privacy
and mutual-information privacy
enabling a more precise estimation of privacy budget bounds. Furthermore
the framework provides a theoretical foundation for achieving privacy preservation in data-driven applications such as crowdsensing systems
location-based services
and large language models.
关键词
Keywords
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