AABN: Anonymity Assessment Model Based on Bayesian Network With Application to Blockchain

Tianbo Lu＊,Ru YanMin Lei,Zhimin Lin

1 School of Software Engineering,Beijing University of Posts and Telecommunications,100876 Beijing,China

2 Key Laboratory of Trustworthy Distributed Computing and Service (Beijing University of Posts and Telecommunications),Ministry of Education,100876 Beijing,China

3 Information Security Center,School of Cyberspace Security,Beijing University of Posts and Telecommunications,Beijing 100876,China

Abstract: Blockchain is a technology that uses community validation to keep synchronized the content of ledgers replicated across multiple users,which is the underlying technology of digital currency like bitcoin.The anonymity of blockchain has caused widespread concern.In this paper,we put forward AABN,an Anonymity Assessment model based on Bayesian Network.Firstly,we investigate and analyze the anonymity assessment techniques,and focus on typical anonymity assessment schemes.Then the related concepts involved in the assessment model are introduced and the model construction process is described in detail.Finally,the anonymity in the MIX anonymous network is quantitatively evaluated using the methods of accurate reasoning and approximate reasoning respectively,and the anonymity assessment experiments under different output strategies of the MIX anonymous network are analyzed.

Keywords: blockchain; anonymity assessment; bayesian network; MIX

I.INTRODUCTION

Bitcoin is a decentralized transaction system that combines an append-only data structure,the public known as the “blockchain”,a distributed peer-to-peer network and a probabilistic consensus protocol based on proof-ofwork[1].Bitcoin does not provide true anonymity: transactions involve pseudonymous addresses,meaning a user's transactions can often be easily linked together.Further,if any one of those transactions is linked to the user's identity,all of her transactions may be exposed [2].To preserve user privacy,some Bitcoin users exchange their coins using mixing service,directly analogous to the concept MIX in anonymous communication networks.In the common implementation a mixing address receives coins from multiple clients and forwards them randomly to a fresh address for each client.

In the anonymous communication technology,the MIX anonymous network was originally proposed by Chaum [3].The main idea is to use multiple MIX agents to obfuscate and encrypt messages and then redirect the messages.After many confusions,the message can be reached at receiver.The relation between the sender and the receiver is hidden,so that the two parties communicate with each other anonymously.It can provide users with corresponding anonymous services,enabling users to securely perform network communication,send and receive mails.

In order to better ensure the anonymity and security of users in anonymous networks,it is necessary to effectively assess the anonymity based on the relevant methods of anonymity measures[4].At the same time,anonymity assessment also provide valuable reference for designers of anonymous networks,and it can help to improve factors that have a greater impact on the overall security of anonymous communication systems,such as reliability,performance and availability,which can enhance the overall anonymity.

Our contributions: we put forward an anonymity assessment model based on Bayesian network to quantitatively assess the anonymity in MIX anonymous communication systems,abbreviated as AABN below.We provide two methods of anonymity calculation,accurately reasoning and approximate reasoning.Approximate reasoning method can improve efficiency compared to accurate reasoning.By simulation experiment under different output strategies,we prove that the larger the number of samples,the closer the approximate reasoning results are to the accurate results.

The rest of this paper is organized as follows.First,the Bayesian network theory and related work in the areas of anonymity assessment are introduced in section II.Then,we give the attacker assumptions of the model in Section III.The construction of AABN is described in section IV.In section V,we propose the anonymity assessment process and give a detailed description of the approximate reasoning process.In section VI,we show the simulation experiment results on the different output strategies in the MIX.The application to blockchian of AABN is discussed in section VII.Final,we make a conclusion of this paper in section VIII.

Fig.1.MIX node.

II.RELATED WORK

In this section,we mainly introduce the concept of MIX,anonymity and Bayesian network theory,and conclude the typical anonymity assessment method.

2.1 MIX anonymous communication system

The MIX was proposed by Chaum in 1981[3].The basic idea is to obfuscate and encrypt messages from multiple users through MIX intermediate nodes,making it impossible for an attacker to get the correspondence between input messages and output messages,In the specifictransmission path,and the attacker cannot know “who communicates with whom” and trace out a message during communication.

A MIX node is generally considered to be a computer that can store and forward messages in the system.As shown in figure 1,it can be used to receive fixed-length messages from different sources,and then forward messages to the next node after obfuscating and encrypting,this operation is aim to conceal the correspondence between the input message and the output message.It is difficult for an attacker to trace a message through a separate MIX node.If a message is transmitted by a path consisting of multiple MIX nodes,then as long as any one of the MIX nodes is reliable,it can provide enough anonymous protection[5,6].

2.2 Anonymity

In 2001,Pfitzmann and Hansen et al formally defined anonymity at the Dresden University of Technology in Germany [7].Anonymity refers that an anonymous set consisting of a group of anonymous state entities cannot be identified.The set usually refers to the sender or receiver set corresponding to a specificmessage.Anonymity can be further divided into sender anonymity,recipient anonymity and relationship anonymity.Anonymous communication systems are also designed to provide some kind of disassociation between the sender of a particular message and the real receiver(the recipient is anonymous),and between the message and their real sender (the sender is anonymous) Irrelevant [8].For relationship anonymity,it usually means that the attacker cannot identify the correspondence between the sender and receiver of the message in the network.

The goal of anonymity assessment is to intuitively evaluate the anonymity of system by some systematic standard parameters.The anonymity of the system is measured from different perspectives through the establishment of different theoretical evaluation plans.Anonymity assessment is generally divided into the global perspective and local user perspective.The anonymity of the global perspective is used to evaluate the overall anonymity of the anonymous communication network in the system,and it can be measured by different indicators.The commonly used assessment method is information entropy.The anonymity of the local user perspective is used to evaluate anonymity of a specificuser in an anonymous communication system,and usually comprehensively evaluated based on the average degree of anonymity and the worst degree of anonymity.

2.3 Anonymity assessment method

We research on a variety of quantitative anonymity assessment methods that have been proposed by the academic community.The initial anonymity assessment is based on set theory.

In 1988 Chaum [9]first adopted the concept of anonymous collections to represent all possible senders or receivers in the system,which could hide the actual sender or receiver.The size of the anonymous collection can be used to evaluate the anonymity of the system.The more users in the collection,the higher degree of anonymity of the system.

In 1999,Kesdogan et al.[10]of the Aachen University of Technology in Germany first proposed the concept of probabilistic anonymity,focused on providing anonymity without authentication,and the realization of probabilistic anonymity was based on publicly available security parameters the current assessment methods of probability theory have been extensively studied and verified.

In 2002,Diaz et al.[11]of the Catholic University of Leuven in Belgium proposed a method to evaluate sender anonymity based on information entropy.In 2002,Serjantov et al.[12]of the University of London proposed an information theory model to quantitatively evaluate anonymity,and defined a new anonymous communication model.

In 2007,Edman et al.[13]of Rensselaer Polytechnic Institute proposed a new anonymity assessment method to quantify the anonymity of users in an anonymous communication systems.They use a permafrost-based approach that can effectively assess a large amount of information that is needed for the attacker to reveal the overall communication model.

In 2012,Vankitasubramaniam [14]of Lehigh University in the United States proposed an anonymity guarantee under the zero-sum game model.Itis a zero-sum game between the attacker and the network designer,and anonymity is gained in the process of game.

2.4 Bayesian network

The Bayesian Network abbreviation BN [15],originally proposed by Pearl [16],can be seen as a directed acyclic graph and is also an effective representation of the joint probability distribution of a set of random variables.In the Bayesian network graph model,vertex is used to represent a random variable in the network,and edge is used to represent the correlation between adjacent random variables.It can be seen as a parent-child relationship,and the posterior probability of the evidence node can be provided.Therefore,it can be used as a model for knowledge representation and probabilistic reasoning.The Bayesian network model can be used to mine the potential relationships between data,and can express some causal relationships between different information.

Bayesian reasoning,as a branch of statistical methods,can be used in the field of machine learning and assessment.The method is to compose a full probability formula composed of all the variables in the graph model,which can indicate the conditional relationship and causal relationship between random variables [17].In the reasoning method,this paper mainly considers the posterior probability.The posterior probability of a random event is the conditional probability that is assigned after the relevant evidence or background is taken into account.The Bayesian formula is defined as [18]

P(Bi) represents the probability of event Bi,P(A|Bi) represents the probability of event A under the condition that event Bihas occurred,P(Bi|A) represents the probability of event Biunder the condition that event A has occurred.

Fig.2.MIX system observation model.

In the Bayesian network reasoning,the premise is that each node is conditional independent.It can be seen as a representation of the joint probability distribution of each node.Then the joint probability distribution between each node is calculated as follows [18]:

xipresents a node in a Bayesian network,pa(xi) presents a predecessor node ofxi.

III.ATTACKER ASSUMPTIONS

In the assessment of anonymous for MIX,we consider the relationship anonymity between the sender and receiver.Therefore,we focus on the perspective of attacker,and consider the probability that the attacker obtains the correspondence between the sender and the receiver in a specificattack.The attack method considered in this paper can be viewed as a specificobservation of the attacker in the input and output streams.Through the analysis of the communication flow,the possible message forwarding path can be inferred.

As shown in figure 2,assume the model of the MIX anonymous communication system that the attacker can observe is:

(1) In a MIX system with a threshold value of i,input n messages,after encrypted and obfuscated by m MIX nodes,n messages output in random forwarding path (2) An attacker can observe the input and output communication flow of messages through the MIX anonymous communication network.After a period of observation and analysis,the attacker can obtain the initial sender and the possible receiver of the message.

(3) The forwarding state of the next hop of the MIX node only depends on the state of the previous MIX node.

(4) The message sender and receiver is in a one-to-one correspondence,and it can trace the source information flowing through the MIX node.

(5) Although the routing information of the path in the MIX network can be randomly selected,it may also be limited by some constraint conditions,such as path length,output strategies,and custom configuration.

In the perspective of attacker,we observe the communication flow between messages over a period of time between t0and tn,and finally get the possible relationship between message sender and receiver.The goal of the AABN model is to obtain the probability of corresponding message output after obfuscating and multiple times forwarding through the MIX anonymous network for a given input message,which is equivalent to determining the corresponding relationship between input message and output message in each MIX node.Then the probability of correspondence between the sender and the receiver of a particular message can be obtained.

IV.MODEL CONSTRUCTION

4.1 Mapping

In the MIX observation model in this paper,the forwarding state of the next hop of a MIX node only depends on the state of the previous MIX node,and the probability of transition of each node in the Bayesian network only depends on its precursor node.Therefore,the correspondence between senders and receivers in an MIX anonymous network can be analyzed and evaluated using a Bayesian network structure.First,we describe the correspondence between the MIX anonymous network model and the Bayesian network structure,as shown in TableI.

(1) Bayesian network is causality network,and MIX anonymous network is causal relationship under the attacker's observation mode;

(2) The network nodes in the Bayesian network can correspond to the MIX nodes;

(3) The conditional probability table in the Bayesian network can correspond to the transition probability between MIX nodes (depending on the MIX output strategy);

(4) The directed edges in the Bayesian network can express the relationship between the nodes,and the input and output relations between the MIX nodes can also be represented by directed edges;

(5) The relationships between nodes in Bayesian network are conditionally independent of each other.MIX nodes also have conditionally independent relationships because the relationship between MIX nodes depends only on the output of the previous MIX node(equivalent to the parent-child relationship between the nodes),and the impact of other nonparent-child relationship nodes are negligible.

4.2 Representation

As shown in figure 3,according to the corresponding relationship between the MIX anonymous network model and the Bayesian network structure,the attacker observation model in the MIX anonymous network communication can be converted to the MIX system model based on the Bayesian network.The Bayesian network model can be described formally with the binary group ＜G,P＞: G denotes the Bayesian network structure diagram,described with G=＜M,E＞,and P denotes the conditional probability transfer table of the node.The AABN can be described as BGM＜M,E,P＞.

M represents node sets in the MIX anonymous network,E represents directed edge sets in the message possible forwarding path,and P represents the forwarding probability table of messages.Any MIX node can be represented by mx,it's precursor node set is MIN(mx),and it's successor node set is MOUT(mx).

In BGM＜M,E,P＞,the following conditional constraints are given:

(1) ∀ E ∈ M × M ,∀e∈E,

e=EIN(e)→EOUT(e).

EIN(e) represents the status before the message is forwarded,EOUT(e) represents the statusafter the message is forwarded,and → represents the process of forwarding a message.

TableI.Mapping between MIX system and Bayesian network.

Fig.3.Structured representation of the AABN model.

(2) Conditional independence: the MIX node is independent of its non-children node.We let the MIN(mx) represents precursor node of the node mxandrepresents the non-child node (ie,non-successor node),that is:

(3) In the MIX node,there are two states:mx=0 represents that the current message has not been forwarded by mx; otherwise,mx=1 represents that the message is forwarded by mx.

Based on the above model structure definition and constraints,the construction of the model focus on two aspects: on the one hand,the topology of the MIX anonymous network structure that the attacker can observe (can be seen as a snapshot of the communication flow),on the other hand,the message forwarding probability table between the MIX nodes.In a given Bayesian network conditional independence assumption,we use the joint probability of the MIX node forwarding path to express the possibility of the sender-receiver correspondence.Therefore,for each message that enters the MIX network,we can get the probability formula P(Sx→Rx) for calculating the correspondence between the receiver and the sender:

Sxrepresents the sender of the message,Rxrepresents the receiver of the message,P(Sx→Rx) represents the probability that receiver is Sxand the corresponding sender is Rx,Iirepresents the reachable path of the current message,and mxrepresents the MIX node in the path Ii.We will further analyze and calculate anonymity under specific examples in the following sections.

V.ASSESSMENT

5.1 Assessment process

The AABN anonymity assessment process is shown in figure 4.The steps in this assessment process are elaborated as follows:

(1) Initialize the MIX anonymous network,determine the sender and receiver sets,and specify the message output strategy in the MIX.

(2) According to the observation of the attacker,obtain the MIX anonymous network communication flow for a certain period,that is,obtain the correspondence relation of the externally observed communication flow between the MIX nodes;

(3) Convert the observed MIX anonymous network model to the corresponding Bayesian network structure diagrams,and accurately reasoning the probability of the receiver node corresponding to given sender node;

(4) According to the known Bayesian network structure,approximate reasoning possible relationships between nodes,use Monte Carlo algorithm for approximate reasoning simulation,and statistical and analysis samples;

(5) Perform error analysis between the probability obtained by approximate reasoning and the probability calculated by accurate reasoning to evaluate the availability of the algorithm;

(6) Based on the anonymity calculation formula,the anonymity of the system is calculated and evaluated.

For arbitrary given message ix,the probability of the correspondence between the sender and the receiver in the MIX can be calculated according to the previous reasoning process,and then the anonymity in the MIX is measured using the anonymity calculation method in the information entropy measure.Therefor in the attacker observation mode,the anonymity in the entire MIX anonymous network is reasonably quantified.

We calculate anonymity according to the calculation formula as follows in the literature[11]:

5.2 Approximate reasoning process

Bayesian network reasoning is used to analysis and probability calculation of uncertain information.In the process of reasoning in Bayesian network,reasoning algorithms can be divided into accurate reasoning and approximate reasoning.Accurate reasoning is based on the given network structure and conditional probability tables known by the nodes.The related mathematical formulas are used to derive the joint probability distribution.Accurate reasoning can obtain the accurate probability results.However,when considering the complex network structure reasoning,this method with high time and space complexity,makes the processing process relatively inefficient[19].In this section,we focus on the approach of approximate reasoning and apply to the observation model of the MIX network system proposed in Section 3.3.The stochastic simulation method is also called the Monte Carlo algorithm.Its specific implementation is mainly to use a random number sampling method to generate user-desired samples,and then perform statistical processing on them to count the number of events occurring in the experiment,and finally get an approximation of the expected probability [19].

In order to make the reasoning model in this section more versatile,we have designed an AABN approximate reasoning anonymity assessment method based on the stochastic simulation and combined with the random number iterative sampling algorithm used in literature [20].According to the MIX network structure diagram and the path forwarding probability table,the status of each node is filtered by comparing the generated random number with the forwarding probability in the MIX node,and then after continuous iterative sampling,we can finally generate the samples we need to obtain the reasoning process for the correspondence between the sender and the receiver,and further measure and analyze the anonymity of the MIX network.The approximate reasoning steps are described as figure 5.The steps in are elaborated as follows:

Fig.4.AABN anonymity assessment process.

(1) Determine the Bayesian network structure diagram according to the given topology structure of the MIX network structure; describe the data structure of the network diagram,set the MIX node number and determine the relationship between the MIX nodes,and create output probability table of.

(2) For a given message sender Sx,the output status of each MIX node is sampled to obtain the final receiver identity corresponding to the message.In the sampling process,according to the random number generated by the random number generator (set in the range of [0,1]),compare with the path forwarding probability of the MIX node: let the path output probability of the node is p,if random number generated is smaller than p,the state of this MIX node is marked as 1 to indicate the current message is forwarded by this node; otherwise,the state of the MIX node is marked as 0,that is,the current message is not forwarded by this node.

Fig.5.Approximate reasoning assessment process.

(3) Through the loop traversal of all nodes,the state of the node in the MIX anonymous network is sampled,and the state set of the receiver will be finally obtained; the subsequent sample sequence will be sampled using iterative assignment,and each round uses the current MIX node's status as the sampling basis for the MIX child nodes.

(4) After sampling,collect all sampled values,obtain the number of times each candidate receiver receives,and perform subsequent statistical analysis and calculation for sample data.

(5) Calculate the distribution of conditional probability of the sender and receiver.According to the sample set of MIX nodes obtained by the approximate reasoning algorithm,we need to statistically analyze the sample set of receiver node.Under the condition of initial input (the sender node),the approximate conditional probability distribution of the receiver node can be obtained,and finally the information entropy of the MIX network can be calculated.In order to calculate P(Sx→Rx) between the sender and the receiver,it can be converted into the calculating the conditional probability P(Sx→Rx|E),when the given evidence E is the MIX node that is known to be forwarded through the message path,the P(Sx→Rx) can directly reflect the correspondence between the message sender and the receiver.Further,the sample set S corresponding to the known evidence node E can be analyzed and the number of samples is represented by S(sum).The set of possible receiver node samples is represented by S(Rx),and the approximate probability distribution of the receiver node corresponding to the message can be obtained:

(6) Sample statistics and error analysis.In order to objectively evaluate the feasibility and reliability of the sample,the error analysisis performed to compare the probability obtained from the approximate reasoning and the accurate reasoning.We use the relative error calculation method based on the calculation method in literature [20],PARrepresents the probability by approximate reasoning and PEIrepresents the probability by accurate reasoning,the calculation formula is as follows:

VI.EXPERIMENT

6.1 Experiment Design

In the AABN anonymity assessment,in addition to considering the MIX node network topology observed by the attacker,it is necessary to consider the path forwarding probability of each node,which mainly depends on the output strategy in the communication process.The anonymity of MIX based on different output strategies is analyzed in this section.Through the research on the different output strategies in the MIX anonymous network,the AABN can be more versatile.

This simulation experiment specificexecution flow is shown in figure 6.First,the Bayesian network model is constructed based on the known MIX network topology and the path forwarding probability table.Then,perform the approximate reasoning process,generate the receiver samples by iterative sampling of each MIX node status in the MIX anonymous network.The probability of the correspondence relationship between the sender and the receiver is calculated.Finally,the anonymity and relative error can be calculated and analyzed.

6.2 Anonymity assessment on different output strategies

The output strategy of the MIX node mainly considers two points.On the one hand,it output message when what condition is reached;on the other hand,what targeted messages it output.According to these two points,there are a variety of output strategies.We mainly considers two typical MIX node output strategies in this section [21].

6.2.1 Assessment on Threshold Output Policies

In the threshold output strategy,the MIX node stores the input message,when the number of messages reaches the threshold n,all the stored messages are forwarded together to the destination of the next hop (forwarded to MIX node or receiver node).According to the message forwarding rule based on the threshold output policy,it is assumed that after a period of observation,an attacker obtain the MIX network topology as shown in figure 7: the MIX network includes 5 MIX nodes,and each MIX node's threshold is 2.

Fig.6.AABN anonymity assessment experiment design.

Fig.7.MIX network topology based on threshold policy.

According to the AABN described in figure 4 in the attacker observation mode,for each message that enters the MIX network,the probability calculation formula of the correspondence between sender and receiver can be calculated by using accurate reasoning and approximate reasoning respectively

(1) Accurate reasoning calculation process

Taking the sender S1as an example,we calculate the probability of all the receivers it may correspond to.Using the probability formula for calculating the correspondence between the sender and the receiver proposed in Section 4,the corresponding probability P(Sx→Rx) can be calculated as follows:

Fig.8.Sample results based on threshold policies.

Fig.9.Comparison of error analysis between accurate reasoning and approximate reasoning.

Similarly,you can calculate the probability of the corresponding relationship between the senderS1and other receivers:

Then,according to the anonymity calculation formula introduced in Section 5,the anonymity entropy of the system at this time can be calculated as 1.93.

(2) Approximate reasoning calculation process

By running the approximate reasoning algorithm through simulation,the sample values of the sender and the receiver that the MIX node may correspond to can be obtained based on the threshold strategy.The obtained simulation result (taking the number of samples as 10000 as example) is shown in figure 8.

(3)Error analysis

For further error analysis of the sample,we obtain the probability of correspondence between the sender S1and receiver R1in different sampling times,and compare it with the probability obtained by the accurate reasoning,and the AABN assessment model can be accurately inferred.The error analysis result is shown in figure 9.

Further,based on the obtained statistical data,the relative error between the accurate reasoning and the approximate reasoning is calculated according to the formula 8.With the number of samples increasing,the relative error rate is shown in figure 10.

According to the comparison of the relative error of the probability calculated by the accurate reasoning and approximate reasoning shown in figure 9 and figure 10,the following conclusions can be analyzed:

(1) When the number of samples is less than 1000,the relative error probability is relatively large.The simulation sample can't indicate the probability of the correspondence between the sender and the receiver well.

(2) With the number of samples increasing,this relative error gradually decreases.The larger the number of samples,the closer the simulated results are to the true results.

(3) With the number of samples increasing,this relative error gradually decreases.The larger the number of samples,the closer the simulated results are to the true results.When the number of samples reaches 10,000 or more,the relative error between approximate reasoning and accurate reasoning is reduced to 0.25%,the AABN approximate reasoning is feasible.

6.2.2 Assessment Based on Message Pool Policies

In the message pool output strategy,the MIX node has a message buffer pool,which stores n false messages in advance.When a MIX node collects N new messages,the node randomly selects N messages from N + n messages forwarding to next hop [35].At the same time,the remaining n messages will still be stored in the MIX node's message pool and continue to wait for the next round of confusion.After multiple rounds of confusion,the anonymous set in the MIX system will continue to expand,making the current output message may be confused by many rounds,the analysis is more complicated.

According to the forwarding rule of the message pool output strategy,it is assumed that after the attacker observes for a period,the attacker can obtain the MIX network topology as shown in figure 11: the MIX network includes five nodes.

In the MIX anonymous network based on the message pool output strategy,set threshold for it,First,we need to set relevant parameters for the MIX message pool,n represents the size of the message pool,x is an adjustable parameters,Nmis the total amount of messages that each MIX node can store,N is the threshold size and uniformly distributed in the interval [n+x,Nm],and the output probability of the message ixin the current node can be expressed as [21]:

Fig.10.Relative error rate change.

Fig.11.MIX network topology based on message pool policy.

In the actual communication process of the MIX system based on the message pool output strategy,the message output probability changes with threshold N continuously after multiple rounds of confusion.Therefore,we take the first round of obfuscation as example.Suppose the attacker obtains Nmis 10,n is 3,and x is 0 in the MIX anonymous network,and assumes that the MIX node is not refreshed.Then the simulation results can be obtained by approximate reasoning algorithm simulation corresponding to the sender and the receiver.The result is shown in figure 12.

According to the formula 8,the anonymity entropy of the current MIX network can be obtained as 1.54.After the MIX anonymity communication system has undergone r-round confusion,the probability that the message input in the i-round can output is [21]:

Fig.12.Relationship between input and output messages based on the message pool policy.

Actually,in the MIX anonymous communication system based on the buffer pool strategy,if an attacker observes an MIX anonymous communication system after multiple rounds of encrypted obfuscation,it is difficult to establish correspondence between the input message and the output message,and thus it is impossible to calculate possible probability between the sender and receiver.If the message pool of the MIX anonymous communication system is not refreshed,the attacker can't to obtain the complete path of messages.At this time,the attacker's observation mode can basically be considered invalid,the anonymity of the MIX anonymous network is high,and the system is considered to be secure.

VII.APPLICATION TO BLOCKCHAIN

Bitcoin does not provide true anonymity.Bitcoin address can be potentially mapped to physical entity by examining its related history of transactions that are stored on the publicly accessible blockchain.This has prompted researchers to introduce various techniques for achieving anonymity in blockchian.One such prominent approach is mixing service analogous to the concept MIX in anonymous communication networks.Current,there are lots of anonymous service based on MIX,like Mixcoin,Bitcoin Laundry,BitMix,and so on.Such mixing service provide the ability to exchange user's bitcoins for different ones which cannot be associated with the original owner,thereby breaking the link between old and new wallets and giving user the freedom to transact anonymously on the blockchain.

The AABN can be applied to evaluate the anonymity of mixing service in blockchian.Transaction information is public in the blockchain.First,collect blockchain transaction records in a period of time.With mixing service as node and a transaction as side,built conditional probability transfer table according to the mixing rules,and construct a Bayesian-based transaction network graph BGM＜M,E,P＞.Then,the anonymity provided by mixing service can be quantitatively analyzed and evaluated using AABN approximate reasoning method.

On the one hand,quantitative anonymity assessment model AABN can give users confidence to blockchain technology,on the other hand,it provide guiding significance for developers in the research process.It can help to find a widely accepted anonymity technique that compatible blockchain structure.Strengthening anonymity can make blockchain technology apply in more scenarios and promote the development of blockchain.

VIII.CONCLUSION

Anonymity of the Bitcoin block chain is a problem that has attracted much attention.Many different designs of Bitcoin mixing services have been proposed,but we found that there is a lack of standards to measure these services.In order to evaluate anonymity provided by these services,we propose an anonymity assessment model based on Bayesian network reasoning AABN in Mix.It can be applied to blockchain and other anonymous network,and provides a quantitative assessment model.

According to the attacker's observation conditions,we design the overall model and anonymity assessment process of the AABN.The AABN approximate reasoning scheme is put forward,and the sampling process description and sample error analysis of the approximate reasoning algorithm were carried out.Experiments show that AABN is effective under different output strategies in MIX.