基于率失真的差分隐私效用优化模型  

Utility Optimal Model for Differential Privacy Based on the Rate Distortion

作　　者：吴宁博 彭长根[1,2] 田有亮 牛坤[1] 丁红发 WU Ning-Bo;PENG Chang-Gen;TIAN You-Liang;NIU Kun;DING Hong-Fa(State Key Laboratory of Public Big Data,College of Computer Science and Technology,Guizhou University,Guiyang 550025;Institute of Cryptography and Data Security,Guizhou University,Guiyang 550025;College of Information,Guizhou University of Finance and Economics,Guiyang 550025)

机构地区：[1]贵州大学计算机科学与技术学院公共大数据国家重点实验室,贵阳550025 [2]贵州大学密码学与数据安全研究所,贵阳550025 [3]贵州财经大学信息学院,贵阳550025

出　　处：《计算机学报》2020年第8期1463-1478,共16页Chinese Journal of Computers

基　　金：国家自然科学基金(U1836205,61662009,61772008);“十三五”国家密码发展基金(MMJJ20170129);贵州省科技计划项目(黔科合重大专项字[2018]3001、[2018]3007、[2017]3002);黔科合平台人才([2020]5017);黔科合基础([2017]1045);贵州省高等学校创新人才团队(黔教合人才团队([2013]09));贵州省研究生科研基金立项课题(KYJJ2017005)资助。

摘　　要：隐私保护与数据效用矛盾问题的解决方案是隐私保护领域中的一个研究热点.针对差分隐私离线数据发布场景中的隐私与效用平衡问题,利用率失真理论研究了平衡隐私与数据效用的最优化差分隐私机制.首先,基于Shannon通信理论抽象差分隐私的噪声信道模型,以互信息量与失真函数度量数据发布的隐私与效用,构建基于率失真理论的最优化模型.其次,考虑关联辅助背景知识对互信息隐私泄露的影响,提出基于联合事件的互信息隐私度量,并进一步修改率失真函数提出最小化隐私泄露模型.最后,针对Lagrange求解过程中计算困难性问题,基于Blahut-Arimoto交替最小化算法提出了互信息隐私最优化信道机制的近似求解算法.通过实验仿真,验证了所提出的迭代近似计算方法的有效性.同时,实验结果表明所提出的方法比对称离散信道机制在限失真条件下互信息隐私泄露量平均降低了21.7%,在相同的隐私容忍度条件下,数据效用提升了38.3%.Privacy leakage has become a widely concerned issue and a major restricting factor for data releasing and sharing in the era of big data.This issue urgently needs effective privacy preserving mechanism to protect individual’s private information while preserving the accuracy of released data.Commonly,the privacy-preserving data release is achieved by data distortion disturbance.Indeed,this will raise a problem of tradeoff between privacy protection intensity and the degree of data distortion,that is known as the problem of privacy-utility tradeoff.Recently years,the issue of privacy-utility tradeoff has become a hot topic in the field of privacy.Additionally,differential privacy(DP)as a strict privacy protection technology has been widely studied by researchers.The basic idea of DP is randomized perturbation for the purpose to release noisy data.Thus,the privacy-utility tradeoff is still the key research of differential privacy.In this paper,we mainly focus on the scenario of differential privacy offline data release.Based on Shannon’s communication theory,we adopt privacy spread communication model to simulate data releasing and model the randomized perturbation of differential privacy as a noisy channel model,i.e.,a randomized probability mapping.Further,we adopt mutual information and expected distortion measure function to quantify privacy leakage and data usability.Thus,the problem of tradeoff between privacy and utility can be formalized as mutual information privacy optimization problem,which can be solved by celebrated rate-distortion theory.In this regard,Wang et al presented the mutual information privacy(PD-MIP),and utilized Karush-Kuhn-Tucker(KKT)condition to illustrate optimality criterion of mutual information privacy.And then,they proved that the optimal mutual information privacy also is close to the optimal differential privacy level when given a distortion constraint.Besides,Kalantari also pointed out that differential privacy leakage is the upper bound of mutual information privacy leakage.

关 键 词：率失真函数 隐私与效用平衡 差分隐私 互信息隐私泄露 数据效用优化 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]