Mutual information-based privacy metrics and optimization methods

Abstract

The application relates to a mutual information-based privacy metric and optimization method, belonging to the field of privacy metric, and comprising the following steps: S1, defining social relations according to content importance, user interest similarity and a time model; S2, only considering a simple case of privacy metric between two users, giving a method for privacy metric by using mutual information, and optimizing an objective function; and S3, using mutual information to measure the degree of privacy leakage caused by collusion attack of multiple users. The application can analyze privacy metric and protect certain privacy information, realizes the metric and protection of the privacy information, and has strong privacy metric and protection capability.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of privacy measurement, and relates to a privacy measurement and optimization method based on mutual information. BACKGROUND

[0002] With the development of information technology, more and more users can spread information by means of social network platforms to realize resource sharing. The network brings many conveniences, but also brings hidden risks. The problem of privacy protection has become one of the problems that cannot be ignored in the big data era.

[0003] In real life, privacy is a personal concept, that is, different users have different attitudes towards the same private information. Users are more willing to let their family and friends obtain more accurate personal information, and others can only obtain relatively rough information, and even some sensitive information is not willing to let anyone know, so it is unreasonable for the current most research to provide the same degree of privacy protection for all users on the social network. From another point of view, privacy can be regarded as the desire of a person to control information and interact with others. Sending information related to oneself to other users is usually the cost of establishing a close relationship with other users. In the process of establishing social relationships, the information of each other is gradually known by the other party, and the privacy and privacy will decrease. This is the privacy attenuation of the user's information.

[0004] Nowadays, social relationship combined with privacy measurement has become a research hotspot. The social relationship is introduced into the differential privacy information protection mechanism, and the personalized demand is considered to provide different levels of privacy protection for users based on social relationship. From the perspective of privacy, the existing privacy measurement methods are generally divided into three categories: based on K Anonymity method, differential privacy based method and mutual information based method. There are documents that propose a K-anonymity privacy protection algorithm, but K-anonymity technology cannot resist homogeneity attacks and background knowledge attacks. According to the social distance, the privacy protection level is set, and the differential privacy is applied to model the privacy attack. However, the efficiency of the differential privacy model is defined by the parameter, and at present, the parameter cannot be accurately controlled, so it is not widely used. A multi-level privacy measurement and protection method based on information theory is proposed, but there is no method to measure the privacy leakage caused by diversity attacks. Some documents estimate mutual information as a standard for balancing privacy and utility, but do not include social relationships in the privacy measurement. Some documents use the Jensen-Shannon divergence to measure the degree of privacy information obtained by the adversary node, and use the infectious disease model to model the transmission of privacy information, but do not further analyze how to protect the privacy information leakage. From the perspective of social relationship, the Harkness model can model the social relationship. The micro social relationship strength model can be established based on Brownian motion. In addition, the implicit social relationship is analyzed from the aspects of geographic location popularity, co-occurrence diversity and user mobility. Some documents use spatiotemporal features to propose encounter entropy, and analyze the social background and encounter of users to infer the social relationship of the users. Some documents point out that the social relationship evolves over time, and design an exponential decay social relationship model that accompanies interaction in continuous time. The above documents analyze social relationships from various angles, but do not consider the influence of the content transmitted between users on social relationships. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a mutual information based privacy measurement analysis method.

[0006] To achieve the above purpose, the present application provides the following technical solutions:

[0007] A mutual information based privacy measurement and optimization method, comprising the following steps:

[0008] S1: first, define the social relationship according to the content importance, user interest similarity and time model;

[0009] S2: only consider the simple case of privacy measurement between two users, give the method of privacy measurement by mutual information, and optimize the objective function;

[0010] S3: use mutual information to measure the degree of privacy leakage caused by collusion attack of multiple users.

[0011] Further, the step S1 specifically comprises:

[0012] S11: first, define the content importance by the exponential decay model; the user and the user in the time interval Internal transmission The importance of each piece of information is denoted as: If the importance of content decreases exponentially, then... Therefore, ;

[0013] S12: Combining the number of users interested in the content, calculate the interest similarity using cosine similarity; the evolution of content importance over time satisfies the following ordinary differential equation:

[0014]

[0015] Solving for the given information yields the following results: ,in, It is a step function;

[0016] in, For a moment Information Number of interested users, users and users The interest similarity at that moment is represented as:

[0017]

[0018] in, For users With users exist A collection of information that is always of interest. Indicates user exist The amount of information that is of interest at any given moment;

[0019] S13: Use Markov chains to describe the duration of user communication and the communication time interval model;

[0020]

[0021] in, It is the investigation period. It is the start time. and The value can be estimated using the maximum likelihood method.

[0022] S14: Combining content importance, interest similarity, and contact time models, social relationships are defined as:

[0023]

[0024] in, , This is a weighting factor and can be adjusted according to the actual situation.

[0025] Further, step S2 specifically comprises:

[0026] Let denote the real detailed information of a user, denote its possible values; denote the coarse information released to the user whose social relation strength is , denote its possible values; when the target user sends the coarse information to other users, the privacy leakage caused by the coarse information is defined as ; is the mutual information between the detailed information and the coarse information of the information sending user:

[0027]

[0028] The availability measure of the coarse information is as follows

[0029]

[0030] where is the prior probability distribution of the real detailed information, is the conditional probability, is the distortion function between the detailed information and the coarse information;

[0031] Given the information of a user at a certain time, the coarse information sent to the user and the availability constraint , the optimization objective is to make the conditional probability achieve the minimum leakage of privacy under the availability constraint and the validity of the probability distribution, then the optimization objective function is to minimize the leakage of the privacy information, denoted as

[0032]

[0033] where the equations and are used to ensure the validity of the probability distribution, and the inequality is the availability objective to ensure the utility of the network system.

[0034] Further, the steps of solving the optimization objective function are as follows:

[0035] Define the Lagrange function as:

[0036]

[0037] The KKT conditions of the optimal solution are as follows:

[0038]

[0039] wherein, represents the optimal solution, is a coefficient of a constraint condition satisfying system utility, and is a constraint coefficient ensuring the validity of the conditional probability distribution;

[0040] The minimum distance between two probability distribution convex sets is calculated by using an alternating minimization algorithm to solve the optimization objective function, and the conditional probability is obtained:

[0041]

[0042] wherein, ;

[0043] The mutual information privacy leakage amount is

[0044] .

[0045] Further, in step S3, considering the collusion attack in the network, the target user is given the information at a certain moment, the rough information sent to the user and the availability constraint , so that the conditional probability reaches the minimum leakage of privacy under the condition of the availability constraint, that is:

[0046]

[0047] The availability measure is:

[0048]

[0049] The joint mutual information is obtained by using the improved Blahut-Arimoto algorithm to solve the objective function:

[0050] .

[0051] The beneficial effects of the present application are:

[0052] 1) The definition of social relationship is given by using the content importance, interest similarity and time contact model, which can more accurately measure the social relationship of the user, so as to further study;

[0053] 2) The mutual information is used to solve the compromise problem between user privacy information privacy and utility, and the privacy measure of two users is given, which lays a foundation for analyzing the privacy leakage caused by collusion attack, improves the measurement accuracy of privacy leakage, and thus improves the privacy awareness of the user and facilitates the protection of the privacy of the user;

[0054] 3) The joint mutual information is used to measure the privacy leakage caused by collusion attack of users, and the optimal solution of the optimization algorithm is given, which can better solve the compromise problem between the privacy and usability of users.

[0055] Other advantages, objects, and features of the application will be set forth in part by the description that follows, and in part will become apparent to those skilled in the art upon examination of the following specification or can be learned by practice of the application. The objects and other advantages of the application can be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to make the objects, technical solutions and advantages of the present application clearer, the preferred embodiments of the present application will be described in detail below with reference to the drawings, in which:

[0057] Fig. 1 The flow chart of the mutual information-based privacy measurement method of the present application is shown in Figure 1.

[0058] Fig. 2 The privacy propagation example of D2D users in a social network is shown in Figure 2.

[0059] Fig. 3 The privacy propagation model based on user movement is shown in Figure 3. DETAILED DESCRIPTION

[0060] The embodiments of the present application are described below through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the disclosure of the present specification. The present application can also be implemented or applied through other different embodiments, and the details in the present specification can be modified or changed in various ways based on different views and applications without departing from the spirit of the present application. It should be noted that the diagrams provided in the following examples only illustrate the basic concept of the present application in a schematic manner, and the following examples and features in the examples can be combined with each other without conflict.

[0061] The drawings are only used for illustrative explanation, and the representation is only a schematic diagram, not a physical diagram, and should not be understood as a limitation on the present application; in order to better illustrate the embodiments of the present application, some components in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product; it is understandable to those skilled in the art that some known structures and their descriptions in the drawings may be omitted.

[0062] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it is understood that if the orientations or positional relationships indicated by the terms "upper", "lower", "left", "right", "front", "back", etc. are based on the orientations or positional relationships shown in the drawings, they are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationships in the drawings are only used for exemplary illustration, and cannot be understood as a limitation on the present application, for those skilled in the art, the specific meanings of the above terms can be understood according to the specific circumstances.

[0063] Please refer to Figs. 1-3 A mutual information-based privacy metric analysis method, comprising the following steps:

[0064] Step 1: First, define the social relationship according to the content importance, user interest similarity and time model, and propose the definition of content importance to measure the social relationship; define the social relationship according to the content importance transmitted between users. The importance of information content will decay with time. Generally speaking, the more immediate the content is, the more important it is, and the more urgent it is. A weight is used to describe the strength of content importance, considering a group of users in communication And In order to construct the model of content importance transmitted between users with continuous time, the following assumptions are made for the evolution of content importance:

[0065] a) Each piece of information has its own value and influence. User Transmits the th information to user in the time interval , and the content importance of the information is denoted as , which decays exponentially, so , and ;

[0066] b) If two users transmit information at time , then the content importance degree decreases from that time. The evolution of content importance with time satisfies the following ordinary differential equation:

[0067]

[0068] The solution is , where is a step function.

[0069] where is the information at time The number of users of interest, that is, the user and the user The interest similarity at the moment can be expressed as

[0070]

[0071] wherein is the user and the user The information set that both users are interested in at moment, then the number of information that the user is interested in at moment is expressed. Combining the content importance, interest similarity and contact time model, the social relationship is defined as

[0072]

[0073] wherein , is a weight factor, which can be adjusted according to actual situation.

[0074] Step two: only considering the simple case of privacy measurement between two users, a method of privacy measurement by mutual information is given, and the objective function is optimized;

[0075] The random variables and respectively represent the real detailed information of the user and the rough information published to the user with social relationship strength , and respectively represent the possible values of the two random variables. When the target user sends the rough information to other users, the privacy leakage caused by the rough information is defined as . is the mutual information between the detailed information and the rough information of the information sending user

[0076]

[0077] The availability measure of the rough information is as follows

[0078]

[0079] wherein is the prior probability distribution of the real detailed information, is the conditional probability, is the distortion function between the detailed information and the rough information.

[0080] Given the information of the user at a moment, the rough information sent to the user and availability constraints The optimization objective is to minimize the privacy leakage of the conditional probability under the availability constraints and the validity of the probability distribution, i.e.

[0081]

[0082] The above equation is the optimization objective function, i.e., minimizing the privacy information leakage, the equality and ensures the validity of the probability distribution, and the inequality is the availability objective to guarantee the utility of the network system. Since the mutual information of the conditional probability is a convex function, the above optimization problem is a convex optimization problem.

[0083] The Lagrange multiplier method is a typical solution to the optimization problem with equality and inequality constraints, and the Lagrange function is defined as:

[0084]

[0085] For the optimization problem with equality and inequality constraints, the KKT conditions need to be satisfied to obtain the optimal solution. The KKT conditions of the optimal solution are as follows:

[0086]

[0087] where represents the optimal solution, is the coefficient of the constraint condition that satisfies the system utility, and are the constraint coefficients that ensure the validity of the conditional probability distribution.

[0088] The minimum distance between the two probability distribution convex sets is calculated using the alternating minimization algorithm, and the conditional probability

[0089]

[0090] where .

[0091] Therefore, the mutual information privacy leakage is

[0092]

[0093] Step three: use mutual information to measure the degree of privacy leakage when multiple users cause collusion attacks.

[0094] Because of the complex social relationship among users in real social network, in addition to the target user, other users will also establish social relationship, these users will combine the private information of the target user they have, that is, collude, and then infer more detailed private information of the target user. This situation will further leak the private information of the target user, in order to measure the degree of this private information leakage, it is assumed that the user is the target user, the user is the attack user, and the user is the mastermind user, at this time, the private information leakage caused only by the social relationship between the target user and the mastermind user is When the user establishes social relationship with other users in the network and analyzes the private information of the target user in combination, the private information leakage at this time is defined as Wherein represents the union set of two user neighbors, represents the private information obtained by the attack user who establishes social relationship with the target user. Because the mutual information quantity of joint attack is not less than the mutual information quantity , the collusion attack will cause more and deeper private information leakage of the target user.

[0095] In order to obtain the optimal solution of the joint mutual information private information leakage quantity, the joint mutual information is simplified and analyzed first. According to the relationship between joint mutual information and information entropy, there is

[0096]

[0097] Further, according to the definition of information entropy and conditional entropy, it can be obtained that

[0098]

[0099] According to the independence of random variables , the marginal distribution of user joint information is

[0100]

[0101] And

[0102]

[0103] Therefore

[0104]

[0105] According to the Bayes formula

[0106]

[0107] Therefore

[0108]

[0109] Thus

[0110]

[0111] According to the above derivation, knowing the information probability distribution of the target user , the conditional probability distribution , the mutual information can be calculated .

[0112] Considering the case of collusion attacks in the network, given the information of the target user at a certain moment, the coarse information sent to the user and the availability constraint , the conditional probability reaches the minimum leakage of privacy under the condition of availability constraint, that is

[0113]

[0114] The availability metric at this time is

[0115]

[0116] The Lagrange function is constructed

[0117]

[0118] where is the coefficient that satisfies the constraint condition of system utility, and are constraint coefficients to ensure the validity of the conditional probability distribution. Taking the partial derivative of the above equation, the conditional probability

[0119]

[0120] Thus the joint mutual information is

[0121]

[0122] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should be covered in the scope of the claims of the present application.​

Claims

1. A privacy measurement and optimization method based on mutual information, characterized in that: Includes the following steps: S1: First, define social relationships based on content importance, user interest similarity, and a time model; step S1 specifically includes: S11: First, content importance is defined using an exponential decay model; users With users In time interval Internal transmission The importance of each piece of information is denoted as: If the importance of content decreases exponentially, then... Therefore, ; S12: Combining the number of users interested in the content, calculate the interest similarity using cosine similarity; the evolution of content importance over time satisfies the following ordinary differential equation: Solving for the given information yields the following results: ,in, It is a step function; in, For a moment Information Number of interested users, users and users The interest similarity at that moment is represented as: in, For users With users exist A collection of information that is always of interest. Indicates user exist The amount of information that is of interest at any given moment; S13: Use Markov chains to describe the duration of user communication and the communication time interval model; in, It is the investigation period. It is the start time; and The value is estimated using the maximum likelihood method; S14: Combining content importance, interest similarity, and contact time models, social relationships are defined as: in, , This is a weighting factor and can be adjusted according to the actual situation; S2: Considering only the simple case of privacy measurement between two users, provide a method for privacy measurement using mutual information and optimize the objective function; Step S2 specifically includes: Use random variables Represents the user's true and detailed information. Indicates its possible values; Indicates the strength of social relationships. The user's rough information, This indicates its possible values; when the target user provides rough information... When sent to other users, it contains coarse information. Privacy breaches resulting from this are defined as follows: ; It is mutual information between the detailed and rough information of the information sending user: The availability of coarse information is measured as follows: in It is the prior probability distribution of real detailed information. It is conditional probability. It is a distortion function between detailed and coarse information; Given information about a user at a certain moment, and sending a rough estimate to the user. and availability constraints The optimization objective is to minimize privacy leakage under the conditions of availability constraints and an effective probability distribution. Therefore, the optimization objective function is to minimize the leakage of privacy information, expressed as: Where the equation and Inequalities are used to ensure the validity of probability distributions. It is an availability goal to ensure the effectiveness of the network system; S3: Use mutual information to measure the extent of privacy breaches in a collusive attack caused by multiple users.

2. The privacy measurement and optimization method based on mutual information as described in claim 1, characterized in that: The steps to solve the optimization objective function are as follows: Define the Lagrange function as: The KKT conditions for the optimal solution are as follows: in, This represents the optimal solution. These are the coefficients that satisfy the constraints on system utility. and These are constraint coefficients that ensure the validity of the conditional probability distribution; The minimum distance between two convex sets of probability distributions is calculated using the alternating minimization algorithm. The objective function is then solved to obtain the conditional probability. in, ; The amount of information privacy leaks is 。 3. The privacy measurement and optimization method based on mutual information as described in claim 1, characterized in that: In step S3, considering the possibility of collusive attacks in the network, given the target user... Information sent to the user at a certain moment. rough information and availability constraints This ensures that the conditional probability achieves minimal privacy leakage under availability constraints, i.e.: Availability metrics are: The joint mutual information obtained by solving the objective function using the improved Blahut-Arimoto algorithm is as follows: 。

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