Social network motif calculation method based on sparse vector compression method and two rounds of interaction

Abstract

The invention discloses a social network motif calculation method based on a sparse vector compression method and two rounds of interaction, and the method comprises the steps: employing two rounds of interaction between a user and a server, and encrypting transmission data through employing an asymmetric random encryption ARR method and a Laplace technology; the method overcomes the defects that the prior art cannot be applied to general motif calculation and the error in the general motif calculation is high, and can be widely applied to a large-scale user social network. According to the method, the universality of the motif calculation method is expanded, meanwhile, the estimation error of the statistical result is reduced, and the accuracy of social network motif calculation is improved. The sparse vector compression method is designed for topological features of the social network, the defect that in the prior art, a user needs to download a complete social noise graph, and consequently communication overhead is large is overcome, and social network motif calculation efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the field of privacy protection and information security technology, and further relates to a social network motif calculation method based on sparse vector compression method and two-round interaction in the field of network security technology. The present invention adopts the local differential privacy technology of sparse vector compression algorithm to ensure the privacy of information transmission process, and realizes the motif calculation task through two rounds of interaction between users and servers. Background Art

[0002] The dynamic extraction method of social network features is based on the network topology structure features. By dynamically modeling the network and realizing the low-dimensional vector expression of the network, the evolution law of the network is discovered and the social network features are dynamically extracted. Neural network technologies such as matrix decomposition, random walk, and autoencoder are usually used to extract dynamic network features. The captured network features are subsequently input into various practical problems in the context of social networks for solution, including but not limited to social relationship prediction, community division, and recommendation system. Network structure data mining tasks. However, these algorithm models have their own limitations when applied to dynamic feature extraction. The feature vector calculation efficiency based on the matrix decomposition algorithm is complex and it is difficult to capture potential high-order link properties. The algorithm based on random walk is limited by the step size and direction of the random walk, and the feature vector can only extract the second-order network structure characteristics. The network based on autoencoder is a semi-supervised model that can only produce a vector representation of a fixed-length sequence. In social networks, motifs refer to the same subgraphs that appear repeatedly in the network. Counting the frequency of a motif in a social network can help understand the structure, behavior, and interaction patterns of social networks. Mainstream methods can generally be divided into general motif calculation methods and special motif calculation methods. Local differential privacy mechanisms are usually used to achieve data noise-added secure transmission. The server aggregates user information to obtain a complete noise graph and sends response information to the user. The user then reports the number of local motifs, and the server finally aggregates the statistical information. However, these methods have their own limitations when applied to social network motif calculation. The general motif calculation method has high communication overhead because the user needs to download the complete noise graph. In addition, the server and the user use a single round of interaction, and the information noise on the server side is relatively large, resulting in a relatively large final statistical error. Although the special motif calculation method can effectively reduce the estimation error and communication overhead, it is only suitable for counting triangles and lacks versatility.

[0003] Hunan University disclosed a method for local differential privacy protection of decentralized social graph data in its patent document "Local differential privacy protection method and system for decentralized social graph data" (patent application number 202310387867.6, application publication number CN 116401708 A). The implementation steps of this method are: the first step is that the user end implements the Laplace mechanism and the random response mechanism to add noise to the node degree and the adjacent node list respectively and sends them to the server; the second step is that the server counts the upper bound of the node degree and sends the upper bound of the node degree and the noisy social graph to the user end; the third step is that the user end projects its own adjacent node list according to the upper bound of the node degree, and then calculates the number of motifs, and uploads them to the server after adding Laplace noise; the fourth step is that the server accumulates the number of motifs received to obtain the total number of motifs in the social graph; the disadvantage of this method is that the user end needs to download the entire noisy social graph from the server end. In large-scale user social networks, due to the very large communication overhead of this method, it is difficult to be widely used in the engineering field.

[0004] Jacob Imola proposed a communication-efficient triangle counting method based on local differential privacy in his paper "Communication-Efficient Triangle Counting under Local Differential Privacy" (USENIX Security 2022). The implementation steps of this method are: the first step is that the user node locally interferes with the list of adjacent nodes to send it to the server; the second step is that the server adopts a specific edge selection strategy to customize the response information for each user and send the information to the user; the third step is that after the user receives the information, the double clipping technology is used to first clip the number of edges and then the number of noise triangles to reduce global sensitivity; the fourth step is that the user adds Laplace noise to the local statistical results and uploads them to the server; the sixth step is that the server aggregates and corrects the final statistical results. The disadvantage of this method is that it can only be used for triangle number counting tasks in social networks, and cannot be applied to other motif calculation tasks, and lacks versatility. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a social network motif calculation method based on sparse vector compression method and two-round interaction, so as to solve the problem of user privacy leakage in social network motif calculation, as well as the problems of high communication overhead and poor versatility of existing motif calculation methods.

[0006] The technical idea for achieving the purpose of the present invention is that, since the present invention introduces an additional round of interaction on the basis of a single round of interaction between the user and the server, in the first round of interaction, the user uses the asymmetric randomized encryption ARR (Asymmetricrandomized response) method to interfere with the local information and then send it to the server. The server aggregates all user information to obtain the noise graph of the entire social network. Then, the server compresses the noise graph using a sparse vector compression method suitable for social networks and then sends it to the user. In the second round of interaction, the user can download the complete noise social graph from the server, which is convenient for further calculating the number of various motifs, rather than being limited to a single motif calculation task. By adding Laplace noise to the number of motifs and uploading it to the server, the server aggregates the number of local motifs of each user, and then the total number of motifs in the social network can be obtained. After the second round of interaction, the present invention can be applied to diversified motif calculation tasks including triangles, k stars and quadrilaterals. This solves the problem that the prior art has poor versatility and is only suitable for counting single motifs. Because the present invention designs a unique sparse vector compression method for the topological characteristics of social networks. On the server side, the adjacency list of each node is originally a vector list consisting of a string of "0" and "1" bits. The sparse vector compression method only needs to store the number and position information of the bit "1", and does not store the bit "0" information, wherein the number information flag of the bit "1" is fixedly represented by 8 bits, and the position information flag is represented by k bits, and the general k value is 8. According to the characteristics of social networks, the number of friends in a user's adjacency list is generally small. When the number of users of a social network is large, a limited number of k bits are used to store "1" instead of storing a large number of redundant "0" in the adjacency list. Therefore, the social graph compression algorithm of the present invention can greatly reduce the communication overhead of users downloading noise graphs from the server, thereby solving the problem of high communication overhead in existing motif calculation methods.

[0007] The specific steps for achieving the purpose of the present invention include the following:

[0008] Step 1: The user uses asymmetric random encryption to perturb the adjacency list locally and then uploads it to the server;

[0009] Step 2: The server uses a sparse vector compression method to compress the adjacency list of each user to obtain a compressed noisy social graph;

[0010] Step 3, each user downloads the compressed social noise graph from the server, counts the number of local target motifs based on the information provided by the noise graph, and then uploads it to the server;

[0011] Step 4: The server aggregates user statistics and calculates the total number of social network motifs.

[0012] Furthermore, each user in the social network is numbered, and each user has a local obfuscator and an adjacency list. The user uses the local obfuscator to perturb the adjacency list and uploads the obtained noisy adjacency list to the server.

[0013] Furthermore, the adjacency list is a list consisting of a string of bit values, where "1" indicates that two users are friends, and "0" indicates that the two users are not friends; the adjacency list of each user stores the adjacency relationship between the user node and other user nodes.

[0014] Furthermore, the adjacency list is disturbed as follows: the user uses a local obfuscator to randomly flip each bit in the adjacency list through a random response technique, so that the flipped value of "0" is "1" and the flipped value of "1" is "0"; the edge sampling technique is used to randomly sample each edge of the adjacency list flipped using the random response technique; the user generates a noisy adjacency list based on the flipped values ​​in the flipped adjacency list and the randomly sampled edges.

[0015] Furthermore, the server uses a sparse vector compression method to determine the value of the position flag bit number k according to the size of the social network motif to be calculated; uses a vector to represent the number and position of the bit "1" in each user's adjacency list; checks whether the number of bits "1" in each user's adjacency list exceeds the upper limit 2 k If yes, the number flag in the user's adjacency list is represented by all 1s.

[0016] Furthermore, each user downloads a compressed social noise graph from the server, and based on the adjacency list information known by the user, counts the number of times the target motif appears in the noise social graph downloaded from the server.

[0017] Furthermore, the server accumulates the motif statistics of each user after adding Laplace noise. Since the expected value of the Laplace noise term added by the user is 0, the server can eventually obtain an unbiased estimate of the social graph motif statistics.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] First, since the present invention adopts two rounds of interaction between the user and the server, and uses the asymmetric random encryption ARR method and the Laplace technology to encrypt the transmitted data in the first and second rounds of interaction respectively, it can be widely used in large-scale user social networks, overcoming the defects that the prior art cannot be applied to general motif calculation or has high errors in general motif calculation. The present invention reduces the estimation error of the statistical results while expanding the versatility of the motif calculation method, thereby improving the accuracy of social network motif calculation.

[0020] Second, since the present invention designs a sparse vector compression method based on the topological characteristics of social networks, it overcomes the defect of the prior art that users need to download the complete social noise graph, which causes high communication overhead. The present invention can greatly reduce the communication overhead of users downloading the noise graph from the server, and improve the efficiency of social network motif calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flow chart of the present invention;

[0022] Figure 2 It is a schematic diagram of the sparse vector compression method SVC based on the present invention. DETAILED DESCRIPTION

[0023] The specific implementation steps of the present invention are further described below in conjunction with the drawings and embodiments.

[0024] Reference Figure 1 , further describes the specific implementation steps of the two-round interaction between the user and the server in the embodiment of the present invention.

[0025] First round of interaction: Users use the asymmetric random encryption ARR method to interfere with local information and then send it to the server. The server aggregates all user information to obtain the noise graph of the entire social network. Then, the server uses a matrix compression algorithm suitable for social networks to compress the noise graph and send it to the user.

[0026] Step 1: The user perturbs the adjacency list locally and uploads it to the server.

[0027] Number the n users in the social network (from 1 to n), v i (i={1,2,...,n}) represents the i-th user in the network. Each user has a local obfuscator and an adjacency list. The user uses the local obfuscator to perturb the adjacency list and send it to the central server to protect the user's privacy during data transmission. The local obfuscator is composed of two technologies, namely, randomized response technology RR (Randomized response) + edge sampling technology (Edge sampling) to enable users to perturb the adjacency list locally.

[0028] The steps for the local obfuscator to perturb the adjacency list are as follows:

[0029] In the first step, the random response technique is used to randomly flip each bit in the adjacency list.

[0030] The adjacency list l is a bit list, where "1" indicates that two users are friends and "0" indicates that two users are not friends. Each user's adjacency list l stores the adjacency relationship between the user node and other user nodes. For example, in the embodiment of the present invention, user v i If the jth bit in the adjacency list l is "1", it means that user v i With user v j is a friend; if it is "0", it means that user v i With v j Not a friend.

[0031] Random response is a common technique for implementing local differential privacy mechanisms. Using random response technology, each bit in the adjacency list l is acted on, the original value is output with a probability of p1, and the flip value is output with a probability of 1-p1. The flip value of "0" is "1", and the flip value of "1" is "0".

[0032] The flipping formula is shown in equation (1) and equation (2):

[0033]

[0034] Where Pr represents probability, b∈{0,1}, and the neighbor list l={b1,b2,...,b n}, bit is the flip of bit b, represents the probability of flipping a bit, and ε1 represents the privacy budget, which controls the strength of privacy protection.

[0035] In the second step, each edge in the adjacency list is randomly sampled using the edge sampling technique. For each edge in the adjacency list flipped using the random response technique, sampling is performed with a probability of p2, that is, the bit "1" in the adjacency list is retained with a probability of p_2, and the bit "1" in the adjacency list is flipped to "0" with a probability of 1-p2. Where p2∈[0,1]. The random response technique and the edge sampling technique constitute the asymmetric random response technique ARR, so the complete ARR perturbation formula is shown in Equation (3) and Equation (4).

[0036]

[0037] in,

[0038] In the third step, the user uploads the perturbed adjacency list to the server.

[0039] After the user uses random response technology and edge sampling technology to perturb the adjacency list, the generated noisy adjacency list is directly uploaded to the server. The noisy adjacency list can effectively prevent user privacy leakage. Even if the attacker obtains the adjacency list information uploaded by the user, he cannot infer the original adjacency list.

[0040] Step 2: The server compresses the noisy social graph.

[0041] After receiving the adjacency list information uploaded by the user, the server aggregates all user information to obtain a complete social network noise graph. The transmission cost of the complete social graph is high, and the present invention proposes a sparse vector compression method SVC (Sparse vector compression) to compress it.

[0042] Reference Figure 2 , the compression steps of the sparse vector compression method SVC of the present invention are further described.

[0043] The first step is to confirm the value of the position flag bit number k.

[0044] Since a byte has 8 bits, the value of k is set to an integer multiple of 8 to facilitate network transmission. The value of k is determined according to the size of the network. If the number of network users n∈[1,2 8 ], k = 8; if n∈(2 8 ,2 16 ], k=16; and so on.

[0045] The second step is to generate a vector representation of the adjacency list.

[0046] Since the noisy social graph represented by the noisy adjacency matrix is ​​a symmetric matrix, we only need to compress the lower triangular matrix. Figure 2 The green boxes in the figure represent the bits that need to be compressed. For each bit in the user's adjacency list that needs to be compressed, a vector is used to represent the number and position of the bit "1". Figure 2 The first 8 bits of the vector represent the number of bits "1". Figure 2 The red box in the figure shows the position of a bit "1" for each subsequent k bits. Figure 2 The positions of the boxes marked in black start from 0.

[0047] The third step is to check whether the quantity flag value exceeds the upper limit

[0048] Set the quantity flag to indicate that the upper limit of the value is 2 k , check the number of bits "1" in the user adjacency list, if it exceeds the upper limit 2 k , the quantity flag is represented by all 1s. For example, in the embodiment of the present invention, when k is 8, the quantity flag is represented by "1111 1111".

[0049] Second round of interaction: Users download the complete noisy social graph from the server to further calculate the number of various motifs. The number of motifs is uploaded to the server after adding Laplace noise.

[0050] Step 3: The user counts the number of motifs locally and uploads them to the server.

[0051] In the first step, each user downloads the compressed social noise graph from the server and counts the number of local target motifs based on the information provided by the noise graph.

[0052] In the embodiment of the present invention, the target motif is a triangle. Assume that the adjacency list of user v0 is [0, 1, 1], that is, user v0 is in a friend relationship with users v1 and v2. If the noisy social graph received by v0 shows that v1 and v2 are also in a friend relationship, then users v0, v1, and v2 form a triangle, and the number of triangle motif statistics of user v0 is increased by 1.

[0053] In the second step, the user adds Laplace noise to the local statistical result t according to the method shown in formula (5) to prevent the result from being leaked, and then uploads it to the server.

[0054] τ=t+Lap(ε2) (5)

[0055] Among them, Lap represents the Laplace mechanism, and ε2 represents the privacy budget of the second round.

[0056] Step 4: The server aggregates user statistics and calculates the total number of social network motifs.

[0057] After the server aggregates the number of local motifs of each user in the manner shown in formula (6), the total number of motifs in the social network can be obtained.

[0058]

[0059] Among them, i={0,1,…,n}, τ i Indicates user v with ID i i Statistics of uploaded models.

[0060] The server accumulates the motif statistics of each user after adding Laplace noise. Since the expected value of the Laplace noise term added by the user is 0, the server can eventually obtain an unbiased estimate of the social graph motif statistics.

Claims

1. A social network motif calculation method based on sparse vector compression method and two-round interaction, characterized in that: Two rounds of interaction are used between the user and the server to encrypt the transmitted data, and the server uses sparse vector compression to compress the adjacency list of each user; The social network motif calculation method comprises the following steps: Step 1: The user uses asymmetric random encryption to perturb the adjacency list locally and then uploads it to the server; Step 2: The server uses sparse vector compression to compress the adjacency list of each user to obtain a compressed noisy social graph. Step 3, each user downloads the compressed social noise graph from the server, counts the number of local target motifs based on the information provided by the noise graph, and then uploads it to the server; Step 4: The server aggregates user statistics and calculates the total number of social network motifs.

2. The social network motif calculation method based on sparse vector compression method and two-round interaction according to claim 1 is characterized in that: The asymmetric random encryption method described in step 1 refers to numbering each user in the social network, each user has a local obfuscator and an adjacency list, the user uses the local obfuscator to perturb the adjacency list, and uploads the obtained noise adjacency list to the server.

3. The social network motif calculation method based on sparse vector compression method and two-round interaction according to claim 1 is characterized in that: The adjacency list in step 1 refers to a list consisting of a string of bit values, where "1" indicates that two users are friends, and "0" indicates that the two users are not friends; the adjacency list of each user stores the adjacency relationship between the user node and other user nodes.

4. The social network motif calculation method based on sparse vector compression method and two-round interaction according to claim 2, characterized in that: The steps of perturbing the adjacency list are as follows: In the first step, the user uses a local obfuscator to randomly flip each bit in the adjacency list through random response technology. The flip value of "0" is "1", and the flip value of "1" is "0"; In the second step, the edge sampling technique is used to randomly sample each edge of the adjacency list flipped using the random response technique; In the third step, the user generates a noisy adjacency list based on the flipped values ​​in the flipped adjacency list and the randomly sampled edges.

5. The social network motif calculation method based on sparse vector compression and two-round interaction according to claim 1, characterized in that: The steps of the sparse vector compression method described in step 3 are as follows: The first step is to determine the value of the position flag bit number k according to the size of the social network motif to be calculated; The second step is to use a vector to represent the number and position of the bit "1" in each user's adjacency list; The third step is to check whether the number of bits "1" in each user's adjacency list exceeds the upper limit 2. k If yes, the number flag in the user's adjacency list is represented by all 1s.

6. The social network motif calculation method based on sparse vector compression method and two-round interaction according to claim 1, characterized in that: The counting of the number of local target motifs described in step 3 means that each user downloads a compressed social noise graph from the server, and based on the adjacency list information known by the user, counts the number of times the target motif appears in the noisy social graph downloaded from the server.

7. The social network motif calculation method based on sparse vector compression and two-round interaction according to claim 1, characterized in that: The calculation of the total number of social network motifs in step 4 means that the server accumulates the motif statistics of each user after adding Laplace noise. Since the expected value of the Laplace noise term added by the user is 0, the server can finally obtain an unbiased estimate of the social graph motif statistics.

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