CN112866369B - Anonymous P2P network anonymity degree assessment method based on hidden Markov model - Google Patents

Anonymous P2P network anonymity degree assessment method based on hidden Markov model Download PDF

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CN112866369B
CN112866369B CN202110038567.8A CN202110038567A CN112866369B CN 112866369 B CN112866369 B CN 112866369B CN 202110038567 A CN202110038567 A CN 202110038567A CN 112866369 B CN112866369 B CN 112866369B
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杨胜齐
赵鹏远
李然
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Beijing University of Technology
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Abstract

An anonymous P2P network anonymity degree assessment method based on a hidden Markov model relates to the technical field of anonymity degree assessment in anonymous communication. The method simplifies the anonymity degree evaluation process of the complex topological network structure, considers the cross problem among different message paths, and reduces the evaluation complexity while ensuring the precision. The method has the advantages that the network topology structure is obtained through overall tracking attack of the message on the anonymous P2P network, the construction of the anonymity degree assessment method model based on the hidden Markov is realized on the basis of the network topology structure, the accuracy of the relation between the sender and the receiver of the anonymity degree assessment method is calculated, and the effectiveness of anonymity degree assessment is proved.

Description

Anonymous P2P network anonymity degree assessment method based on hidden Markov model
Technical Field
The invention relates to the technical field of anonymity evaluation in anonymous communication, in particular to a method for evaluating anonymity of an anonymous P2P network based on a hidden Markov model.
Background
With the rapid development and wide application of the internet, security of personal privacy information of a network faces a serious challenge. In order to fully protect the speaking freedom and personal privacy of users, an anonymous communication system is an important and effective means for protecting the privacy of users on the Internet, and has urgent needs and great practical significance for research thereof. But anonymous communication technology is to make double sword, various illegal network services to act through the protection of anonymous system, such as selling illegal drugs, smuggling treasures, illegal gun and ammunition transaction, etc.
The combination of P2P technology with anonymous communication networks further improves anonymity, and anonymity assessment has been a hotspot of research. The anonymity degree evaluation of the anonymous communication system is not only beneficial to the improvement and the promotion of the existing anonymity system, but also can further realize a controllable and credible anonymity system, and on the basis of better guaranteeing the privacy security of users, illegal criminal activities are hit, so that the anonymity P2P network is healthier. Most of anonymity evaluation aiming at an anonymous P2P network is concentrated on sender anonymity and receiver anonymity at present, and when the anonymity is evaluated from the aspect of the relation between a sender and a receiver, if the involved nodes are too many and the anonymity network is complex enough, the anonymity evaluation process is complicated, the workload is large and the complexity is high. Therefore, a hidden Markov-based P2P network anonymity assessment method is provided, and the anonymity degree can be quantitatively assessed under the global tracking attack of the message.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: 1. the anonymity mechanism adopted by different anonymity P2P systems is different, and a rerouting mechanism is used at present, but the used path length control strategy and member selection strategy are different. 2. The anonymity evaluation method model of the anonymous P2P network is constructed by using a hidden Markov model, and the network topology structure is converted into the anonymity evaluation method model by using the hidden Markov model.
In order to achieve the purpose, the invention adopts a method for evaluating anonymity degree of an anonymity P2P network based on a hidden Markov model, which comprises the following specific steps:
step 1: and carrying out global tracking on the message of a certain user in the anonymous P2P network, obtaining a data set and constructing a network topology structure.
Step 2: the adaptation model fills in the nodes. The network diagram of message forwarding nodes is not fully adaptable to the hidden markov model. To better adapt the model, it is necessary to add blank nodes in the middle of some message forwarding paths.
Dividing the intermediate forwarding nodes into groups based on the longest path in the network topology structure, wherein a cross-packet connection condition exists among some nodes, so that a blank node needs to be added into the cross-packet to connect two ends, and the forwarding probability of the blank node to the next node is 1. The blank nodes are added only to enable the network topology structure to be better adapted to the hidden Markov model, so that the method has no practical significance and cannot influence the calculation probability result of the model.
Step 3: a probability matrix is calculated. And (3) calculating the forwarding condition among the nodes by the data set obtained by monitoring in the step (1) to obtain the transition probability among the nodes. The forwarding probability between the sender and the intermediate forwarding node forms a state transition matrix A, the forwarding probability between the intermediate forwarding node and the receiver forms a transmitting state matrix B, namely the forwarding probability between the current node and the subsequent node is calculated, and finally a multi-level hidden Markov model is formed.
a) State transition matrix
A＝[a i,j ] N*N (1)
b) Emission state matrix
B＝[b j (k)] N*M (2)
c) Hidden Markov model
λ＝(A,B,π) (3)
In the formula (1), a is a state transition matrix, and N is the number of hidden states, i.e. the number of sender nodes or the number of intermediate forwarding nodes. a, a i,j Representing the probability from hidden states i to j.
In equation (2), B is a transmission state matrix, and M is the number of observable states, i.e., the number of intermediate forwarding nodes or the number of receiver nodes. b j (k) Representing the probability from the hidden state j to the observable state k.
In the formula (3), λ is a hidden markov model, pi is an initial state probability vector, and the sum of all initial state probabilities is 1, that is, the probability that each sender sends a message first in a unit time.
Step 4: the sender-receiver relationship probability is evaluated. After the evaluation method model is established, an evaluation sender s is calculated i And receiver r j Is a relation probability value P(s) i →r j Lambda).
Step 5: the relative error is calculated. Calculating sender s according to network topology i And receiver r j Theoretical true value y=p(s) i →r j ). And (3) carrying out relative error between the evaluation result obtained by calculation of the evaluation method model and the true value, thereby obtaining the accuracy of the evaluation method model.
Step 6: the anonymity degree is calculated. For any given message, calculating a corresponding relation probability value of a sender and a receiver in the anonymous P2P network according to a previous reasoning process, and measuring anonymity in the anonymous P2P communication system by using an anonymity calculation method in information entropy.
As a preferred technical solution, in order to provide a method for anonymity assessment of an anonymous P2P network based on a hidden markov model, the steps described are implemented as follows:
the preparation working stage: and carrying out global tracking on the message of a certain user in the anonymous P2P network to acquire a data set.
Model construction stage: the network topology will be built from existing datasets, filling in nodes for adapting the hidden markov model. And then calculating a state transition matrix and an emission probability matrix according to the data of the statistical data set, and finally forming a multi-level hidden Markov model. The intermediate forwarding node set L shares an n-layer node set { L } 1 ,...,L n Plus the sender node set S and the receiver node set R, sharing an n+2 layer node set { S, L } 1 ,L 2 ,...,L n R, the number of nodes in the ith layer set is N i . Every two layers of adjacent node sets form a layer of hidden Markov model, so the n+2 layer node sets form an n+1 layer hidden Markov model. The probability recursion between each layer of hidden Markov models is derived as follows:
a) Initializing:
b) Induction calculation:
c) Final summation:
in the formula (4), the amino acid sequence of the compound,representing the probability when the first layer hidden markov model observable sequence is the i-th node, i=1 2 。N 1 The number of nodes in the first layer set, i.e. the number of nodes in S, is represented. N (N) 2 Representing the number of nodes in the second level set, i.e. L 1 The number of nodes in the network. Pi is the initial state probability vector. b j (v i ) Representing the transition from the jth hidden state to the observable state v i Is a function of the transmission probability of (a).
In the formula (5), alpha λk (i) Representing the probability that the k-th layer hidden markov model observable sequence is the i-th node, i=1,.. k+1 。N k Representing the number of nodes in the k-th layer set. N (N) k+1 Representing the number of nodes in the k+1 layer set.Representing the probability that the k-1 layer hidden markov model can observe the j-th node of the sequence. b j (v i ) Representing the transition from the jth hidden state to the observable state v i Is a function of the transmission probability of (a).
In the formula (6), P (osλ) represents a posterior probability of occurrence of the observation sequence, that is, a probability of occurrence of the observation sequence under the condition of the multi-level hidden markov model. N (N) n+1 Representing the number of nodes in the n+1 layer set, i.e. L n The number of nodes in the network.Representing the probability that the n-th layer hidden markov model can observe the j-th node as the sequence. b j (O) represents the probability of transmitting from the jth hidden state to the observable sequence O. O= { r t And r is the observation sequence t E R, R is the set of recipients.
Evaluation phase: and calculating the relative error of the relation probability to obtain the accuracy of the model, and finally evaluating to obtain the anonymity degree of the anonymous P2P network. The specific calculation is as follows:
P(s i →r j =p (O =λ) (7)
Δ= |p (s i -r j Lambda) -Y I (8)
P(s) in formula (7) i -r j #) represents the sender s under the condition of the multi-layer hidden markov model i To receiver r j Is a posterior probability of (c).
In the formula (8), Δ represents the absolute value of the difference between the experimental value and the theoretical true value. Y=p(s) i →r j ) Is a theoretical true value, i.e. sender s i To receiver r j Is a priori probability of (c).
In the expression (9), δ is a relative error of the relation probability.
D(s) in formula (10) i ) For the receiver s i The value of anonymity, n, is the number of recipients.
The beneficial effects of the invention are as follows:
the invention provides a new anonymity evaluation method, which is an anonymity evaluation method of an anonymity P2P network based on a hidden Markov model. The method simplifies the anonymity degree evaluation process of the complex topological network structure, considers the cross problem among different message paths, and reduces the evaluation complexity while ensuring the precision. The method has the advantages that the network topology structure is obtained through overall tracking attack of the message on the anonymous P2P network, the construction of the anonymity degree assessment method model based on the hidden Markov is realized on the basis of the network topology structure, the accuracy of the relation between the sender and the receiver of the anonymity degree assessment method is calculated, and the effectiveness of anonymity degree assessment is proved.
Drawings
FIG. 1 is a general flow chart of the present invention
FIG. 2 is an exemplary network topology
FIG. 3 is a model diagram of an evaluation method after adaptation
Detailed Description
The present invention will be described in detail with reference to the drawings and examples, but the examples are only for explaining the present invention and are not limited thereto.
Referring to fig. 1, fig. 2 and fig. 3, the present embodiment is a hidden markov model-based anonymous P2P network anonymity assessment method.
Step 1: and carrying out global tracking on the message of a certain user in the anonymous P2P network to acquire a data set, thereby obtaining the network topology structure as shown in figure 2. The nodes are divided into three classes in fig. 2: sender set s= { S 1 ,s 2 ,s 3 ,s 4 ,s 5 A set of forwarding nodes M and a set of receivers r= { R } 1 ,r 2 ,r 3 ,r 4 ,r 5 }。
Step 2: filling the network topology adaptation model of fig. 2 into nodes to obtain the model shown in fig. 3. The filling nodes divide the intermediate forwarding nodes into groups based on the longest path in the network topology structure, and a cross-packet connection condition exists among some nodes, so that a blank node needs to be added in the cross-packet to connect two ends, and the forwarding probability of the blank node to the next node is 1.
The longest path in the network topology of fig. 2 is<s 1 ,m 1 ,m 2 ,m 3 ,m 4 ,r 1 >The intermediate forwarding node set M shares the layer 4 node set { L } 1 ,L 2 ,L 3 ,L 4 Plus sender node set S and receiver node set R, there are 6 levels of node sets, where the number of nodes in each level of node set is n= {5,4,3,3,3,5}, so the hidden markov model has 5 levels in total. As in fig. 3, sender s 3 Forward to m 2 Across the first layer L of the intermediate forwarding node set M 1 So at L 1 And padding nodes are added.
Step 3: a probability matrix is calculated. And (3) calculating the forwarding condition among the nodes by the data set obtained by monitoring in the step (1) to obtain the transition probability among the nodes. The forwarding probability between the sender and the intermediate forwarding node forms a state transition matrix A, the forwarding probability between the intermediate forwarding node and the receiver forms a transmitting state matrix B, namely the forwarding probability between the current node and the subsequent node is calculated, and finally a multi-level hidden Markov model is formed. Taking the first layer hidden markov model as an example, the hidden state is sender s= { S 1 ,s 2 ,s 3 ,s 4 ,s 5 Observable state L 1 ＝{m 1 And 3 filling nodes, wherein the emission probability of the observation state corresponding to the filling nodes is 1.
a) First layer state transfer matrix
A＝[a i,j ] 5*5 (1)
b) First layer emission state matrix
B＝[b j (k)] 5*4 (2)
c) First layer hidden Markov model
λ＝(A,B,π) (3)
In the formula (1), A is a state transition matrix, a i,j Representing the probability from hidden states i to j.
In the formula (2), B is an emission state matrix, B j (k) Representing the probability from the hidden state j to the observable state k.
In the formula (3), λ is a hidden markov model, pi is an initial state probability vector, and the sum of all initial state probabilities is 1, that is, the probability that each sender sends a message first in a unit time.
Step 4: the sender-receiver relationship probability is evaluated. After the evaluation method model is established, an evaluation s is calculated i And r j Relation probability value P(s) i →r j Lambda).
To evaluate s 1 To r 1 Relation probability value P(s) 1 →r 1 #) is exemplified, the probability recursion between hidden markov models at each layer is derived as follows:
a) Initializing:
b) Induction calculation:
c) Final summation:
in the formula (4), the amino acid sequence of the compound,representing the probability that the first layer hidden markov model observable sequence is the i-th node, i=1. Pi= (1, 0) is the initial state probability vector, i.e. sender s 1 Is 1.b j (v i ) Representing the transition from the jth hidden state to the observable state v i Is a function of the transmission probability of (a).
In the formula (5), the amino acid sequence of the compound,representing the probability that the k-th layer hidden markov model observable sequence is the i-th node, i=1,.. k+1 Wherein N is k+1 Representing the number of nodes in the k+1 layer set. N (N) k Representing the number of nodes in the k-th layer set.Representing the probability that the k-1 layer hidden markov model can observe the j-th node of the sequence. b j (v i ) Representing the transition from the jth hidden state to the observable state v i Is a function of the transmission probability of (a).
In the formula (6), P (osλ) represents a posterior probability of occurrence of the observation sequence, that is, a probability of occurrence of the observation sequence under the condition of the multi-level hidden markov model.Representing the probability of the layer 5 hidden markov model observable sequence being the j-th node. b j (O) represents the probability of transmitting from the jth hidden state to the observable sequence O. O= { r 1 And r is the observation sequence 1 E R, R is the set of recipients.
In an anonymous P2P network, the selection of intermediate forwarding nodes is independent, namely, the selection of the next hop node of a forwarding path is only selectedDepending on the current intermediate node. The relationship between hidden Markov models is also conditional, s 1 To the current observation node r 1 The probability calculation result of (2) is only related to the emission probability of the prior layer hidden Markov model. From which s is derived 1 To r 1 The relational probability formula is:
step 5: the relative error is calculated. Calculating s according to the network topology structure of the simulation experiment 1 And r 1 Theoretical true value y=p(s) 1 →r 1 ). And (3) carrying out relative error between the evaluation result obtained by calculation of the evaluation method model and the true value, thereby obtaining the accuracy of the evaluation method model.
The probability of the relationship between the sender and the receiver can be calculated theoretically through the topological structure of the anonymous P2P network and the node next hop random forwarding strategy. As shown in fig. 3, slave sender s 1 To receiver r 1 There are two paths, so s is calculated 1 And r 1 Is a theoretical true value of the relation probability:
P(s 1 →r 1 )＝P(s 1 m 1 m 4 r 1 )+P(s 1 m 1 m 2 m 3 m 4 r 1 ) (8)
obtaining a relation probability, namely:
calculating the relative error of the relation probability to obtain the accuracy of the model, wherein the accuracy is calculated as follows:
Δ= |p (s 1 -r 1 Lambda) -Y I (10)
In the formula (10), Δ represents an absolute value of a difference between the experimental value and the theoretical true value, and Y represents the theoretical true value.
In the expression (11), δ is a relative error of the relation probability.
Step 6: the anonymity degree is calculated. Calculating sender s in anonymous P2P network according to previous reasoning process 1 And receiver r 1 And similarly can calculate the sender s 1 The probability of relation to other elements of the receiver set R, i.e. P (s 1 →r 2 )、P(s 1 →r 3 )、P(s 1 →r 4 )、P(s 1 →r 5 )。
Anonymity in an anonymous P2P communication system is measured using an anonymity calculation method in information entropy. Calculation s 1 The anonymity of (2) is:

Claims (2)

1. a method for evaluating anonymity degree of an anonymous P2P network based on a hidden Markov model is characterized by comprising the following specific steps:
step 1: in the preparation working stage, global tracking is carried out on a message of a certain user in an anonymous P2P network, a data set is obtained, and a network topology structure is constructed;
step 2: model construction stage, adapting model filling nodes; the network diagram formed by the message forwarding nodes cannot be completely adapted to the hidden Markov model; to adapt the model, blank nodes need to be added in the middle of some message forwarding paths;
dividing the intermediate forwarding nodes into groups based on the longest path in the network topology structure, wherein a cross-packet connection condition exists among some nodes, so that a blank node needs to be added in the cross-packet to connect two ends, and the forwarding probability of the blank node to the next node is 1;
step 3: the model construction stage, calculating a probability matrix; the transition probability among the nodes is obtained by counting the forwarding conditions among the nodes by the data set obtained by monitoring in the step 1; the forwarding probability between the sender and the intermediate forwarding node forms a state transition matrix A, the forwarding probability between the intermediate forwarding node and the receiver forms a transmitting state matrix B, and the B is used for calculating the forwarding probability between the current node and the subsequent node, and finally a multi-level hidden Markov model is formed;
a) State transition matrix
A＝[a i,j ] N*N (1)
b) Emission state matrix
B＝[b j (k)] N*M (2)
c) Hidden Markov model
λ＝(A,B,π) (3)
In the formula (1), A is a state transition matrix, N is the number of hidden states, and N is used for representing the number of sender nodes or the number of intermediate forwarding nodes; a, a i,j Representing the probability from hidden state i to j;
in the formula (2), B is a transmitting state matrix, M is the number of observable states, and M is used for representing the number of intermediate forwarding nodes or the number of receiver nodes; b j (k) Representing the probability from the hidden state j to the observable state k;
in the formula (3), lambda is a hidden Markov model, pi is an initial state probability vector, the sum of all initial state probabilities is 1, and pi is used for representing the probability that each sender sends a message first in unit time;
step 4: the model construction stage is used for evaluating the relation probability of the sender and the receiver; after the evaluation method model is established, an evaluation sender s is calculated i And receiver r j Is a relation probability value P(s) i →r j Lambda);
step 5: an evaluation stage, calculating a relative error; calculating sender s according to network topology i And receiver r j Theoretical true value y=p(s) i →r j ) The method comprises the steps of carrying out a first treatment on the surface of the The evaluation result obtained by calculation of the evaluation method model and the true value are subjected to relative error, so that the accuracy of the evaluation method model is obtained;
step 6: an evaluation stage, namely calculating anonymity degree; for any given message, calculating according to step 5 to obtain the sender in anonymous P2P networkRelationship probability values between sender and receiver using shannon information theory based information entropy measurementCalculating anonymity of an anonymous P2P communication system;
n is the node set layer number of the intermediate forwarding node set L.
2. The method according to claim 1, characterized in that:
the preparation working stage: globally tracking a message of a certain user in an anonymous P2P network to acquire a data set;
model construction stage: constructing a network topology structure according to the existing data set, and filling nodes for adapting to the hidden Markov model; calculating a state transition matrix and a transmitting state matrix according to the data of the statistical data set, and finally forming a multi-level hidden Markov model; the intermediate forwarding node set L shares an n-layer node set { L } 1 ,...,L n Plus the sender node set S and the receiver node set R, sharing an n+2 layer node set { S, L } 1 ,L 2 ,...,L n R, the number of nodes in the ith layer set is N i The method comprises the steps of carrying out a first treatment on the surface of the Every two layers of adjacent node sets form a layer of hidden Markov model, so that an n+2 layer of node sets form an n+1 layer of hidden Markov model; the probability recursion between each layer of hidden Markov models is derived as follows:
a) Initializing:
b) Induction calculation:
c) Final summation:
in the formula (4), the amino acid sequence of the compound,representing the probability when the first layer hidden markov model observable sequence is the i-th node, i=1 2 ；N 1 Representing the number of nodes in the first layer set, namely the number of nodes in S; n (N) 2 Representing the number of nodes in the second level set, i.e. L 1 The number of nodes in (a); pi j An initial state probability vector for the j-th hidden state; b j (v i ) Representing the transition from the jth hidden state to the observable state v i Is a transmission probability of (1);
in the formula (5), the amino acid sequence of the compound,representing the probability that the k-th layer hidden markov model observable sequence is the i-th node, i=1,.. k+1 ；N k Representing the number of nodes in the k-th layer set; n (N) k+1 Representing the number of nodes in the k+1 layer set; />Representing the probability of the k-1 layer hidden Markov model observable sequence being the j node; b j (v i ) Representing the transition from the jth hidden state to the observable state v i Is a transmission probability of (1);
in the formula (6), P (O I lambda) represents the posterior probability of the occurrence of the observation sequence, namely the probability of the occurrence of the observation sequence under the condition of a multi-level hidden Markov model; n (N) n+1 Representing the number of nodes in the n+1 layer set, i.e. L n The number of nodes in (a);representing the probability of the observable sequence of the n-th layer hidden Markov model being the j-th node; b j (o) represents the transition from the jth hidden state to the observable sequenceO emission probability; wherein the observable sequence o= { r t }，r t E, R is a receiver node set;
evaluation phase: calculating the relative error of the relation probability to obtain the accuracy of the model, and finally evaluating to obtain the anonymity degree of the anonymous P2P network; the specific calculation is as follows:
P(s i →r j =p (O =λ) (7)
Δ= |p (s i -r j Lambda) -Y I (8)
P(s) in formula (7) i -r j #) represents the sender s under the condition of the multi-layer hidden markov model i To receiver r j Posterior probability of (2);
in the formula (8), delta represents the absolute value of the difference between the experimental value and the theoretical true value; y=p(s) i →r j ) Is a theoretical true value, i.e. sender s i To receiver r j Is a priori probability of (2);
delta in the formula (9) is a relative error of relation probability;
d(s) in formula (10) i ) For sender s i The value of anonymity, n is the node set layer number of the intermediate forwarding node set L.
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