A Method for Influence Maximization Based on Homomorphic Encryption

Abstract

The present invention discloses an influence maximization method based on a homomorphic encryption algorithm, belonging to the field of social network mining. The present invention combines the homomorphic encryption algorithm and the degree discount algorithm. Each social client calculates the degree discount value according to the user data it has and encrypts and uploads it to the server; the server decrypts the operation of the degree discount values obtained from each platform and selects the user with the largest degree discount value and sends it to each client. The client repeats the above steps and iteratively selects multiple users to maximize the scope of information dissemination. Based on the degree discount heuristic algorithm, the present invention uses the homomorphic encryption security protocol and relies on a third-party server to perform information encryption and decryption operations and update the seed node set, so as to fuse the user information of each social media platform without revealing user privacy, and has great application value and prospects in scenarios such as advertising placement, product promotion, and information dissemination to find suitable user groups.

Description

Technical Field

[0001] The present invention belongs to the field of social network mining and privacy protection, and specifically relates to an influence maximization method based on homomorphic encryption. Background Art

[0002] With the continuous development of network science, many real-world problems can be modeled as complex network problems and solved. As a typical type of network, a social network refers to a system composed of a group of people or groups connected by a certain relationship, reflecting the interactive information between people. In the field of social networks, the most widely concerned issue is how to find influential node sets to maximize the spread of information, which has important practical significance. For example, how to design an effective advertising strategy on social media platforms (selecting which users to promote) to maximize the number of people who ultimately know about the product; how to find suitable influencers when hiring Weibo celebrities at a high price to promote new products; when a missing person case occurs, how should we find influential users on social media to maximize the spread of information about the missing person, etc.

[0003] In reality, users often have multiple social media accounts, and they can choose several of them to forward and share products. In this case, it is not sufficient to only consider the maximization of the influence of a single social media. Therefore, the problem of maximizing the influence across multiple social media platforms is worthy of attention. Existing methods do not consider the privacy of user data on each social media platform when dealing with the problem of maximizing the influence of multiple social media platforms. From the perspective of users and enterprises, the data recorded by social media platforms often involves personal privacy and has great value. When two or even more companies consider cooperation to obtain greater benefits, they are often unwilling to directly share or exchange their data. Therefore, no platform can collect the complete data of users, and each platform only has a partial structure of the original network. How to integrate the network structure information of each platform without leaking the privacy of users on each social media platform and find a better set of seed users to affect more users has become an important problem currently faced.

[0004] Under the premise of protecting privacy, the present invention uses a homomorphic encryption algorithm to collaboratively fuse user information from different social platforms, find a set of users with greater influence to maximize the diffusion and propagation of information in the social network. At the same time, the influence maximization method based on homomorphic encryption (HE-DD) proposed by the present invention can find a globally better set of seed nodes to maximize the influence propagation range compared to only considering the user information owned by a single platform. Finally, the framework proposed by the present invention can solve the problems of privacy protection and influence maximization simultaneously, that is, without revealing the privacy of users on each platform, fusing the network structure information of multiple platforms, and finding a better set of seed users to make the number of affected users more. Summary of the Invention

[0005] The object of the present invention is to fuse the network structure information of each social media platform under the premise of protecting privacy, with the help of a third-party server (whether trusted or not), and jointly use the homomorphic encryption security protocol to find a better set of seed users to maximize the number of affected users.

[0006] The present invention realizes the above object by the following method steps:

[0007] An influence maximization method based on homomorphic encryption, that is, the HE-DD algorithm, includes the following steps:

[0008] Step 1: Generate a key pair: The key server generates a key pair, publishes the public key to each client, and retains the private key itself;

[0009] Step 2: Encrypt the degree discount value: Each client uses the degree discount heuristic algorithm according to its own private network to calculate the degree discount values of all nodes, and then encrypts and sends the degree discount values of all nodes to the computing server through the public key distributed by the key server;

[0010] Step 3: Fuse the encrypted degree discount values: The computing server fuses and calculates the ciphertexts sent by all clients, and sends the calculation result to the key server;

[0011] Step 4: Decrypt the ciphertext: The key server decrypts the fused ciphertext with the private key, and the decryption function decrypts to obtain the plaintext;

[0012] Step 5: Update the seed node set: Select the node with the largest fused degree discount value that has not been selected as a seed as the seed node for this round, and distribute the result of the updated seed node set to each client, calculate the degree discount values of all nodes in the next iteration, and repeat selecting seeds until a certain number of seeds are selected, and finally the seed set in the original network is obtained.

[0013] Further, in the said step 1, it includes the following steps:

[0014] (1.1) Randomly select two large prime numbers and such that where denotes the greatest common divisor;

[0015] (1.2) Calculate a = pq and where denotes the least common multiple;

[0016] (1.3) Randomly select an integer such that where ;

[0017] (1.4) Select the public key k p ={a, g} and the private key k s ={λ} as the generated key pair. The key server makes the public key available to each client and retains the private key for itself.

[0018] Furthermore, step 2 includes the following steps:

[0019] (2.1) Each client, based only on its own private network , uses the degree - discount heuristic algorithm to find the degree - discount values of all nodes. Initially, the degree - discount value of a node is the degree value, denoted as {dd t，1 , dd t，1 , ……, dd t，j , ……, dd t，n}: where represents the th client's private network , j = {1, 2, 3, …, n}, j represents the j - th node among n nodes; n represents the total number of nodes; represents the degree - discount value of the first node of the private network , and the representation of other private networks can be deduced similarly;

[0020] (2.2) Each client encrypts and sends the degree - discount values of all nodes to the computing server through the public key ; where i = {1, 2, 3, ..., n} represents the node in the private network , that is, for the private network , the encrypted degree - discount value, i.e., the ciphertext, is denoted as , where represents the encryption algorithm.

[0021] Furthermore, step 3 includes the following steps:

[0022] (3.1) The computing server fuses all the ciphertexts sent by the clients to obtain the following fused ciphertext vector : ;

[0023] where dd t，j represents the degree discount value of node j in the private network , j = {1, 2, 3, …, n}; represents the encryption algorithm; m represents the number of networks G, and t represents the t-th network G.

[0024] (3.2) The computing server sends the fused ciphertext vector to the key server.

[0025] Furthermore, in step 4, the key server decrypts the ciphertext sent by the computing server using the private key and obtains the plaintext using the homomorphic encryption system : , where represents the decryption scheme, represents the private key.

[0026] Furthermore, in step 5, the following steps are included:

[0027] (5.1) Select the node with the largest fused degree discount value that has not been selected as a seed as the seed node for this round, that is the corresponding seed node as the seed node selected for this round (a node that has already been a seed cannot be repeatedly selected as a new round of seed node), where ,

[0028] (5.2) Distribute the updated seed node set result to each client t, calculate the degree discount values of all nodes in the next iteration, and repeat the selection of seed nodes , , i = {1, 2, 3, ..., k} represents the number of iterations, and k is the number of seed nodes; until seeds are selected, and finally the seed set in the original network is .

[0029] Compared with the prior art, the beneficial effects of the present invention:

[0030] 1. The influence maximization method proposed by the present invention utilizes the homomorphic encryption security protocol and relies on a third-party server for information encryption and decryption operations and the update of the seed node set. Compared with the case of only considering the user information owned by a single platform, a better seed node set can be found to maximize the influence dissemination range;

[0031] 2. The influence maximization method based on homomorphic encryption proposed by the present invention can, without revealing user privacy, integrate the user information of various social media platforms for finding suitable user groups in scenarios such as advertising placement, product promotion, and information dissemination;

[0032] 3. The present invention proposes a framework that can effectively integrate the issues of privacy protection and influence maximization, achieving the maximization of influence in social media while ensuring privacy is not leaked and integrating the user information of multiple platforms. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is the flowchart of the HE-DD algorithm involved in the present invention

[0034] Figure 2 is the schematic diagram of the HE-DD algorithm involved in the present invention

[0035] Figure 3 is the influence range diagram on different data sets

[0036] Figure 4 is the experimental diagram comparing with the influence range of the original network

[0037] Figure 5 is the different propagation probabilities on the Bcspwr10 network of the influence range diagram

[0038] Figure 6 is the different sparsity levels on the Power network and different overlap degrees of the influence range diagram DETAILED DESCRIPTION OF THE INVENTION

[0039] The technical solution of the present invention will be further described below through specific embodiments:

[0040] The experimental data adopted in this example are the publicly available data sets Power data set, Bcspwr10 data set, DD21 data set, and Hep data set.

[0041] As Figure 1 , the technical solution of the present invention includes the following steps:

[0042] Step 1, generate subnet data and key pairs;

[0043] The specific steps are as follows:

[0044] (1) Using the original network, construct three subnets and distribute them to three clients. The process of constructing the three subnets on different datasets is as follows: For each edge in the original network, a random number is generated to determine which subnet an edge in the original network belongs to. If , the edge is not retained in any subnet. If , the edge is retained in only one subnet; if , the edge is retained in two subnets. Otherwise, when , the edge is retained in all subnets. In addition, the parameter is used to control the overall overlap degree of all subnets, that is, the degree of overlap of the three subnets, and the parameter is used to control the overlap degree between two subnets, is a measure of the sparsification level of the subnet. Without special instructions, we set the parameters for generating the three-layer subnet .

[0045] (2) The process of the key server generating the key pair is as follows:

[0046] (2.1) Randomly select two large prime numbers and , satisfying , where represents the greatest common divisor;

[0047] (2.2) Calculate a = pq and , where represents the least common multiple;

[0048] (2.3) Randomly select an integer , satisfying , where ;

[0049] (2.4) Select the public key k p ={a, g} and the private key k s ={λ} as the generated key pair. The key server makes the public key public to each client and retains the private key .

[0050] At this time, the three clients have the subnet structure data and the public key information, and the key server has the private key

[0051] Step two, calculate the degree discount value and encrypt it;

[0052] The specific steps are as follows:

[0053] (1) Each client, based only on its own private network , uses the degree discount heuristic algorithm to calculate the degree discount values of all nodes. Initially, the degree discount value of a node is the degree value, denoted as {dd t，1 , dd t，1 , ……, dd t，j , ……, dd t，n}: where represents the th client having a private network , j = {1, 2, 3, …, n}, j represents the jth node of n nodes; n represents the total number of nodes; represents the degree discount value of the first node of the private network , and the representation of other private networks can be deduced similarly;

[0054] The specific process of the degree discount heuristic algorithm is as follows: Let represent the degree of node , represent the activation probability of each edge, represent the number of seed nodes among the neighbors of node , then the probability that node is not activated by neighbor seed nodes is , and at this time, the expected number of nodes that can be activated by selecting node as a propagation seed is ; the probability that node is activated by neighbor seed nodes is , and at this time, the influence of node is 0. In this way, the expected influence of selecting node as a seed node is:

[0055] ;

[0056] where, represents the degree of node , represents the activation probability of each edge, represents the number of seed nodes among the neighbors of node .

[0057] When node has no neighbor seed nodes, the expected influence of selecting node as a seed node is:

[0058] ;

[0059] Let be the degree discount of each neighbor seed node, then there is , which can be solved to obtain

[0060] ;

[0061] Therefore, when node has neighbor seed nodes, its degree discount is defined as:

[0062] ;

[0063] (2) In the i-th iteration, each client sends the degree discount values of all nodes encrypted by the public key to the computing server, where i = {1, 2, 3,..., n} represents the number of iterations; n represents the total number of nodes; that is, for the private network , the encrypted degree discount value, i.e., the ciphertext, is denoted as , where represents the encryption algorithm.

[0064] Step 3: Fuse the encrypted degree discount values. Specifically, the computing server fuses the ciphertexts sent by all clients to obtain the following fused ciphertext vector : , and sends the fused ciphertext vector to the key server, where dd t，j represents the degree discount value of node j in the private network , j = {1, 2, 3,..., n}; represents the encryption algorithm; m represents the number of networks G, and t represents the t-th network G.

[0065] Step 4: Decrypt the fused ciphertext. Specifically, the key server uses the private key to decrypt the ciphertext sent by the computing server to obtain the plaintext : , where represents the decryption scheme, and represents the private key.

[0066] Step 5: Select the node with the largest degree discount value and update the seed set. Specifically, it includes the following steps:

[0067] (1) Select the node with the largest fused degree discount value as the first-round seed node, that is, the corresponding seed node as the first-round selected seed node, and add it to the seed set S, where ;

[0068] (2) Distribute the updated seed node set S results to each client t, calculate the degree discount values of all nodes in the next iteration, repeat steps two, three, and four, and select the node with the largest degree discount value after fusion that has not been selected as a seed as the seed node for this round , , i = {1, 2, 3,..., k} represents the number of iterations, k is the number of seed nodes, and add it to , until seeds are selected, and finally the seed set in the original network is .

[0069] The following combines the attached drawings to conduct a performance analysis of the example:

[0070] For the comparative experiment, in this experiment, the independent cascade (IC) model of is used to characterize the propagation influence range of the seed node set selected by the algorithm, so as to measure the advantages and disadvantages of different algorithms.

[0071] 1. Influence range on different data sets

[0072] In this experiment, the parameters for generating a three-layer subnet are set , the propagation probability , the seed set sizes of the Power network, Bcspor10 network, and DD21 network that include generating three sub-networks , the seed set size of the Hep network that includes generating three sub-networks . The experimental results of the influence range of the three-layer subnet changing with the seed set size are as Figure 3 shown.

[0073] It can be seen from Figure 3 that: under different networks, compared with only using the structural information of a single subnet, the HE-DD algorithm can find a seed node set that makes the influence range of the original network wider, and the result is significantly better than that of a single subnet, that is, only using the structural information of a single subnet is not sufficient.

[0074] 2. Comparison of the influence ranges of a single subnet, fusion, and the original network

[0075] The propagation rate of the network in this experiment , for the Hep network, take , and for the rest of the networks, take .

[0076] Define the relative ratio (RR) to describe how many times the influence of other algorithms needs to be multiplied to reach the influence of the algorithm that fully knows the network structure The same influence range. Therefore, if the RR value of an algorithm is closer to 1 than that of other algorithms, it indicates that the algorithm has the best performance in maximizing the influence range.

[0077] Figure 4 Shows the comparison of the propagation ranges under the full network, three private networks, and the HE-DD algorithm when selecting the number of seed nodes. It can be seen that the influence range of the seed nodes found by the HE-DD algorithm is closer to that of the full network compared to the three private networks, highlighting the effectiveness of the HE-DD algorithm once again.

[0078] 3. Influence range under different propagation probabilities Values

[0079] In this experiment, the dataset is the Bcspwr10 network. When the seed set is , the comparison results of the final influence ranges of the three parties and the fusion under different propagation rates are as Figure 5 shown.

[0080] From Figure 5 it can be seen that no matter what propagation rate is taken, the final propagation range of the HE-DD algorithm is significantly better than that of using only any one subnet.

[0081] 4. Influence range under different values of generated network parameters

[0082] In this experiment, the propagation probability is selected, including the Power network that generates three subnets, and the number of seeds

[0083] Figure 6 (a) in shows the comparison of the influence ranges of the three-party subnets and the HE-DD algorithm under the condition of fixed overlap degree and when the sparsity of the network varies.

[0084] Figure 6 From (a) in it can be seen that as

[0085] Figure 6 increases, the three-party subnets obtain more structural information about the original network, which is more conducive to finding the seed node set of the original network, and the propagation ranges under all algorithms show an increasing trend. (b) in shows the comparison of the influence ranges of the three-party subnets and the HE-DD algorithm under the condition of fixed sparsity Comparison of the influence ranges of the lower three-party subnet and the HE-DD algorithm.

[0086] From Figure 6 (b) in it, it can be seen that as the overlap degree increases, the structural differences between subnets become smaller and smaller, the differences in the propagation ranges are not significant, and at the same time, the information that the HE-DD algorithm uses the structure of each subnet to find the set of seed nodes is very limited. Therefore, the propagation range also shows a downward trend.

[0087] In this application, in order to solve the problem of "how to fuse the network structure information of each social media platform under the premise of protecting privacy and find a better set of seed users to maximize the number of affected users", a method for maximizing influence based on homomorphic encryption is proposed. Under the premise of protecting privacy, the user information of different social platforms is synergistically fused to find a set of users with greater influence to maximize the diffusion and propagation of information in the social network; and through examples, it is shown that the HE-DD algorithm proposed by the present invention can find a better set of seed nodes to maximize the influence propagation range compared to only considering the structural information of a single network.

[0088] The content described in this embodiment is only an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms stated in the embodiment. The protection scope of the present invention also extends to equivalent technical means that those skilled in the art can think of according to the inventive concept of the present invention.

Claims

1. A method for maximizing influence based on homomorphic encryption, characterized in that , The method includes the following steps: Step 1: Generate a key pair: The key server generates a key pair, makes the public key public to each client, and retains the private key itself; The said Step 1 includes the following steps: (1.1) Randomly select two large prime numbers and , satisfying , where represents the greatest common divisor; (1.2) Calculate a = pq and , where represents the least common multiple; (1.3) Randomly select an integer , satisfying , where ; (1.4) Select the public key k p = {a, g} and the private key k s = {λ} as the generated key pair. The key server makes the public key available to each client and retains the private key for itself; Step 2: Calculate the degree discount value: Each client, according to its own private network, uses the degree discount heuristic algorithm to calculate the degree discount values of all nodes, and then encrypts and sends the degree discount values of all nodes to the computing server through the public key distributed by the key server; Step 3: Fuse the encrypted degree discount values: The computing server fuses and calculates the ciphertexts sent by all clients, and sends the calculation result to the key server; Step 4: Decrypt the ciphertext: The key server decrypts the fused ciphertext with the private key, and the decryption function decrypts to obtain the plaintext; Step 5: Update the seed node set: Select the node with the largest degree discount value after fusion that has not been selected as a seed as the seed node for this round, and distribute the result of the updated seed node set to each client. Calculate the degree discount values of all nodes in the next iteration, and repeat the selection of seeds until a certain number of seeds are selected, and finally obtain the seed set in the original network.

2. The influence maximization method based on homomorphic encryption according to claim 1, wherein: The said Step 2 includes the following steps: (2.1) Each client only depends on its own private network , and uses the degree discount heuristic algorithm to calculate the degree discount values of all nodes. Initially, the degree discount value of a node is the degree value, denoted as {dd t，1 , dd t，1 , ……, dd t，j , ……, dd t，n}: where represents the th client having a private network , j = {1, 2, 3, …, n}, j represents the jth node of n nodes; n represents the total number of nodes; represents the degree discount value of the first node of the private network , and the representations of other private networks can be deduced similarly; (2.2) At the i-th iteration, each client encrypts and sends the degree discount values of all nodes to the computing server through the public key, where i = {1, 2, 3, …, n} represents the number of iterations; n represents the total number of nodes; that is, for the private network denote the encrypted degree discount value, i.e., the ciphertext, as where represents the encryption algorithm. ​ 3. The method for maximizing influence based on homomorphic encryption according to claim 1, wherein: The said Step 3 includes the following steps: (3.1) The computing server fuses all the ciphertexts sent by the clients to obtain the following fused ciphertext vector : ； Among them, dd t，j represents the degree discount value of node j in the private network , where j = {1, 2, 3, …, n}; represents the encryption algorithm; m represents the number of networks G, and t represents the t-th network G; (3.2) The computing server sends the fused ciphertext vector to the key server.

4. The method for maximizing influence based on homomorphic encryption according to claim 1, characterized in that: In the said step 4, the key server uses the private key to decrypt the ciphertext sent by the computing server and obtains the plaintext by using the homomorphic encryption system as follows: ； Among them represents the decryption scheme, represents the private key.

5. The method for maximizing influence based on homomorphic encryption according to claim 1, characterized in that: The said Step 5 includes the following steps: (5.1) Select the node with the largest degree discount value after fusion and not selected as a seed as the seed node for this round, that is The corresponding seed node As the seed node selected in this round, the nodes that have been used as seeds cannot be repeatedly selected as new round seed nodes, where ; (5.2) Distribute the updated seed node set result to each client t, calculate the degree discount values of all nodes in the next iteration, and repeatedly select seed nodes , , where i = {1, 2, 3,..., k} represents the number of iterations, and k is the number of seed nodes; until seeds are selected, and finally the seed set in the original network is .

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