Research On Differential Privacy Equilibrium Optimization Model And Algorithm

The challenges of privacy and security caused by the rapid development of informatization and in-depth applications,have become a bottleneck restricting data opening,sharing,exchange,and application,and have attracted great attention from the legal and academic communities.From the perspective of technology,the differential privacy(DP)protection algorithm,as an important privacy protection technology,is not mature enough in the research of data privacy protection for multi-dimensional and complex associations.Firstly,due to the mixed data types,sparseness,and large domain value space etc,the multi-dimensional data processing of DP is faced with the challenges such as privacy vulnerability and low computational efficiency.Secondly,the relevance of data fusion,background knowledge attacks and strategic adversary attacks,and the contradiction between data privacy and usability have become prominent issues.For the problems mentioned above,it is a better solution to investigate the trade-off and optimization of privacy and utility from the perspective of the game theory.Thus,this dissertation mainly focuses on the crucial problem of the trade-off between privacy and utility.Based on information entropy,optimization theory and game equilibrium and other related theories and methods,the equilibrium and optimization models are constructed as the main line of this research.A series of results have been achieved in designing of privacy quantification methods,constructing and solving game model between privacy and utility,optimization model establishment and solving,etc.,which provide a reference for solving privacy protection issues from the perspective of combining technology and management.The major contributions can be summarized as follows.1.The information entropy metric models and methods of DP are proposed.For the quantitative problem of privacy,the noisy DP communication model and formalization statement are defined based on the Shannon's fundamental communication model and the randomized perturbation principle of DP.Further,the notions of information entropy,conditional entropy,joint entropy,mutual information and conditional mutual information,etc.,are defined under the differential privacy model,and then,the privacy metric models with information entropy as the core are designed.For the problem of multi-dimensional and correlated attributes,based on the graph and Markov model,etc.,a privacy metric model and method for multi-dimensional and correlated attributes is proposed.Then,the upper and lower bounds of privacy leakage are quantified by using data processing inequality and Fano's inequality.Theoretic analysis and experimental results are demonstrating the proposed metric model and method can effectively achieve the goal of DP quantification,and further provide basic support for privacy leakage risk assessment and privacy protection mechanism design.2.The differential privacy optimization model with background knowledge attacks is proposed.Based on the established fundamental communication model of the DP,lossy compression theory and the proposed privacy metric model,the adversary model which has relevant background knowledge is established,and further the DP communication model with background knowledge attacks is proposed.By using conditional mutual information measures privacy,this dissertation updates the form of the well-known rate distortion function,and proposes the differential privacy optimization model with background knowledge attacks.Further,the alternating minimization iteration algorithm solving the proposed optimization model is designed and implemented based on the Blahut-Arimoto alternating minimization method,and the computation complexity analysis is provided.Theoretic analysis and experimental results are demonstrating the proposed method have significant advantages in data quality and privacy leakage when compared with the existing symmetrical channel mechanism.3.The orderly randomized response perturbation(ORRP)scheme is proposed.For the problem of low efficiency and privacy vulnerability when deal with multi-dimensional data using local differential privacy,and facing the privacy protection requirements of data collection scenarios,this dissertation proposes an orderly randomized response perturbation scheme.The proposed ORRP scheme effectively solves the impact of the existing privacy protection mechanisms ignoring data distribution,and the problem of low computing efficiency caused by the large processing domain value space and sparse data.To be specific,the proposed ORRP scheme is based on the previously proposed privacy metric model.A mutual information optimization model subjects to a given data quality loss constraint that minimize privacy leakage,is proposed by analyzing and quantifying the requirements of privacy and data quality.Further,the probability density function(PDF)of the optimal privacy mechanism is computed by the means above,and it is used to obtain randomized perturbation.Meanwhile,referring to the independent parallel channel model,the above methods are extended to the case of multidimensional data.Finally,theoretical analysis and experimental simulations are given in terms of privacy leakage,data usability quality,and correlation loss.The results demonstrate that the proposed ORRP has more advantages than the existing methods in terms of data semantic integrity,privacy and data availability quality.4.The privacy-preserving attack and defense(PPAD)game model is proposed.For the problem of informed and strategic adversary in the differential privacy system,the selection strategy of differential privacy protection is designed around the data collection scenarios.On the basis of the above,the PPAD game model is proposed,and the trade-off between privacy and utility in the protection of differential privacy is achieved by solving the equilibrium.The proposed scheme is based on the established differential privacy basic communication model.The privacy minimax optimization model is established by analyzing the privacy goals of defender and strategic attacker,and further the formalization statement of PPAD is provided,which includes players' sets,strategic spaces and payoff functions etc.This dissertation cleverly uses the connotation and extension of private mutual information to construct the utility function of privacy protection,and finally realized the construction of a two-person zero-sum(TPZS)game model.Then,this dissertation provides the game analysis by using von Neumann's minimax theorem and concave-convex game,and further designs a strategy optimization selection algorithm to calculate saddle point based on the optimal strategy response.Theoretic analysis and numeric simulation results show that the proposed model and method can effectively solve the problem of comparison between equivalent privacy mechanisms,and also can be used for privacy leakage risk assessment in the worst case of privacy protection.