CN111383005A - Digital currency flow direction tracking method and device - Google Patents
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Abstract
The invention relates to the field of big data information processing, in particular to a digital currency flow direction tracking method, which comprises the steps of obtaining transaction information of a plurality of digital currencies, wherein the transaction information at least comprises transaction addresses; generating an address cluster according to the transaction address; constructing an address cluster transaction graph according to the transaction information, and establishing a directed edge by taking the address cluster as a vertex; calculating the weight of each address cluster in the address cluster transaction graph; acquiring a target address, and determining a target address cluster where the target address is located; and determining the tracking direction, taking the target address cluster as a starting point, acquiring a directed edge consistent with the tracking direction, and sequentially tracking the address cluster with the maximum weight along the direction of the directed edge. The address cluster with the largest weight information in the tracking direction is used as a tracking target, so that key objects can be locked more quickly, problems can be found in time, more important transaction information is tracked preferentially, reliable tracking information of digital currency is provided for financial supervision institutions, and the method has high value.
Description
Technical Field
The invention relates to the field of internet big data processing, in particular to the field of block chains, and specifically relates to a method and a device for tracking the flow direction of digital currency.
Background
The block chain is a chain data structure which combines the data blocks in a sequential connection mode according to the time sequence, and is a distributed account book which is guaranteed in a cryptographic mode and cannot be tampered and forged. Bitcoin is a digital cryptocurrency with a blockchain as the underlying technology. The bitcoin has the characteristics of decentralization and anonymity, wherein decentralization means that point-to-point transaction based on decentralization credit is realized in a distributed system, and anonymity means that a buyer and a seller cannot know the identity of the other party during transaction.
But details of each transaction of the bitcoin are stored in the blockchain, including the transaction hash, the time the transaction occurred, the input address, the output address, the payment amount per input address, the receipt amount per output address, the transaction fee, the blockhash, etc. All can inquire the transaction information and can track the flow of the digital currency.
In order to monitor the circulation of digital currency in a controlled area, a financial regulatory agency needs to track the transaction conditions of the digital currency, so as to effectively monitor the digital currency. However, since the transaction information of the digital money is huge and the transaction address is also dynamically changed, tracking the distribution of the digital money in the huge amount of data is inefficient and has relatively poor reliability.
Disclosure of Invention
In view of this, the embodiment of the present invention provides a method for tracking a flow direction of digital currency, so as to solve the problems of low efficiency and poor reliability of tracking digital currency in the prior art.
According to the first aspect, the embodiment of the invention also provides a digital currency flow direction tracking method, which includes acquiring transaction information of a plurality of digital currencies, wherein the transaction information at least includes a transaction address; generating an address cluster according to the transaction address; constructing an address cluster transaction graph according to the transaction information, and establishing a directed edge by taking the address cluster as a vertex; calculating the weight of each address cluster in the address cluster transaction graph; acquiring a target address, and determining a target address cluster where the target address is located; and determining the tracking direction, taking the target address cluster as a starting point, acquiring a directed edge consistent with the tracking direction, and sequentially tracking the address cluster with the maximum weight along the direction of the directed edge.
In the scheme, after the transaction addresses are combined into the address cluster, the corresponding relation between the address cluster and the transaction information is established, and the transaction addresses are combined into the address cluster, so that the magnitude of the processed transaction address information is greatly reduced; by constructing an address cluster transaction graph, flow information of digital transactions is obtained, important address cluster information can be found by calculating the weight of each address cluster, when the digital currency tracking is carried out, because the transaction information is massive, the most important data can be obtained by tracking the important information, therefore, the address cluster with the maximum weight information in the tracking direction is taken as the tracking target, can lock key objects more quickly, find problems in time, track more important transaction information preferentially, provide reliable tracking information of digital currency for financial supervision authorities, thereby greatly reducing the analysis difficulty of massive bit currency transaction data in the block chain, leading the tracking of the digital currency to be more timely, the tracking information is more efficient and reliable, and the tracking efficiency is improved, so that a faster means is provided for government to monitor digital currency, and the method has a high value.
With reference to the first aspect, optionally, when the tracking direction is forward tracking, a vertex where the target address cluster is located is a starting point of a directed edge; or when the tracking direction is reverse tracking, the vertex where the target address cluster is located is the end point of the directed edge. In the scheme, the tracking direction can be forward tracking, namely tracking according to the sequence of digital currency transactions, and can also be backward tracking, namely acquiring the source information of the digital currency, so that the destination of the digital currency can be tracked and the source of the digital currency can be tracked aiming at the target address, and the tracking of the digital currency is carried out as required, so that the efficiency is higher.
With reference to the first aspect and the optional implementation manner thereof, optionally, the sequentially tracking the address clusters with the largest weights along the directional edge direction includes: and obtaining all transaction information in the tracking direction until the tracked address cluster has no corresponding directed edge in the tracking direction, and thus realizing the whole-network tracking of the transaction data. Or when the tracked address cluster meets the specified conditions, the tracking is finished, such as tracking to a specified exchange, or tracking to a certain number of layers, and reasonably setting according to the needs.
With reference to the first aspect and the optional implementation manner thereof, optionally, the constructing an address cluster transaction graph according to the transaction information, and establishing a directed edge with an address cluster as a vertex includes: acquiring an input address and an output address of a transaction, wherein an address cluster where the input address is located is a first address cluster, and an address cluster where the output address is located is a second address cluster; establishing a directed edge from the first address cluster to the second address cluster; and traversing the input addresses and the output addresses of all transactions, and drawing an address cluster transaction graph. The scheme can construct an address cluster transaction diagram of all transaction information by effectively analyzing the associated information of digital currency such as bit currency transaction, show information of both parties and transaction conditions in the transaction process, and combine real name information, thereby providing real identity of a trader for governments, having high social value, providing simpler and more convenient transaction flow query service for individuals and enterprises, having good economic benefit, and providing information and basis for supervision institutions or related enterprises or individuals.
With reference to the first aspect and optional implementation manners thereof, optionally, the calculating of the weight of each address cluster in the address cluster transaction graph is performed by obtaining the address number, the input transaction number of the address cluster, the output transaction number output by the address cluster, the input transaction amount of the address cluster, and the output transaction amount of the address cluster included in the address cluster, setting the corresponding weight, objectively and accurately reflecting the importance of the address cluster, digitizing information by feature extraction and parameter selection, improving processing efficiency, and ensuring reliability of data.
With reference to the first aspect and the optional implementation manner thereof, optionally, the method further includes obtaining a number of newly generated blocks; judging whether the number of the newly generated blocks exceeds a preset threshold value or not; when the number of the newly generated blocks exceeds a preset threshold value, regenerating the address cluster, the address cluster transaction graph and the weight of the address cluster; and when the number of the newly generated blocks does not exceed the preset threshold, updating the weight information of the address cluster in the address cluster transaction graph according to the transaction information in the newly generated blocks.
With reference to the first aspect and the optional implementation manner thereof, optionally, in the step of generating the address cluster according to the transaction address, for the bitcoin and the bifurcate coin thereof, merging the transaction addresses of the multiple pieces of transaction information having the same transaction address into one address cluster, including taking all transaction input addresses in each piece of transaction information as a set; judging whether the same transaction address exists in the set or not; if the same transaction address exists, the sets are merged until no identical element exists in any two sets in all sets, and each set is regarded as an address cluster. Because in the transaction information, a plurality of transaction input addresses exist in one transaction, and the transaction input addresses can be generally regarded as one user address or related addresses, if the same transaction input address exists in two transactions, the transaction addresses of the two transactions are associated, for example, the users are the same, and the sets of the same transaction addresses exist and are combined to form an address cluster according to the property. The data volume to be analyzed is greatly reduced through combination, so that the difficulty of mass data analysis is greatly reduced. The address cluster merging mode can also filter wrong labeling information, and the accuracy of the labeling information is improved. And further forming a single address cluster by each output address which is not contained in the input address set, wherein although most output addresses can be contained in the input address set, a small number of output addresses which are not contained in the input addresses may exist, and by forming an address cluster by each output address which is not contained in the input address set, the corresponding relation between all input address clusters and output address clusters in which transactions exist is conveniently established subsequently, so that the real-name transaction flow map is generated.
With reference to the first aspect and the optional implementation manner thereof, optionally, the method further includes labeling identity information for each address cluster, including: acquiring real name information of part or all transaction addresses in each address cluster; and using the real name information with the highest weight as the real name information of the address cluster. Because there are many transaction addresses in each address cluster, each address can obtain real-name information by means of network capture data, real-name information of a transaction place or algorithm labeling or crowdsourcing, and if the real-name information obtained by various methods is different, the real-name information with the highest confidence coefficient is selected as the real-name information of the transaction address; meanwhile, the real name information obtained by the transaction addresses in each address cluster may be different, and the highest weight is used as the transaction information of the address cluster, so that the accuracy of the real name information of the address cluster is improved. The processing of using the real name information with the highest weight as the real name information of the address cluster comprises the following steps: marking the address cluster as real-name information c with the weight of Pc ═ P1/P2 (k/n), wherein n is the number of transaction addresses in the address cluster, k is the number of transaction addresses marked with the real-name information, P1 is the sum of the information source weights of the addresses marked as the real-name information c, and P2 is the sum of the information source weights of the k addresses; and taking the real name information c which maximizes the value of Pc as the real name information of the address cluster. In the scheme, the real-name information is better identified by the information source weight and the proportion of the marked real-name information, so that the real-name information of the address cluster is more accurate.
In combination with the first aspect or other embodiments of the first aspect, according to the second aspect, the present invention further provides a digital currency flow direction tracking device, including: the system comprises an acquisition unit, a processing unit and a display unit, wherein the acquisition unit is used for acquiring a plurality of digital currency transaction information, and the transaction information at least comprises a transaction address; the merging unit is used for merging the transaction addresses of a plurality of transaction messages with the same transaction address into an address cluster; the map generation unit is used for constructing an address cluster transaction map according to the transaction information and establishing directed edges by taking the address cluster as a vertex; the weight calculation unit is used for calculating the weight of each address cluster in the address cluster transaction graph; a target address determining unit, configured to obtain a target address and determine a target address cluster where the target address is located; and the tracking unit is used for determining the tracking direction, taking the target address cluster as a starting point, acquiring a directed edge consistent with the tracking direction, and sequentially tracking the address cluster with the maximum weight along the direction of the directed edge. According to the scheme, an address cluster transaction diagram is constructed to obtain flow direction information of digital transactions, important address cluster information can be found by calculating the weight of each address cluster, when the digital currency is tracked, the transaction information is massive, and the important information can be tracked to obtain the most important data, so that the address cluster with the largest weight information in the tracking direction is used as a tracking target, key objects can be locked more quickly, problems can be found in time, reliable tracking information of the digital currency is provided for a financial supervision institution, the analysis difficulty of massive bit currency transaction data in a block chain is greatly reduced, the digital currency is tracked more timely, and the tracking information is more efficient and reliable.
According to a third aspect, an embodiment of the present invention further provides a server, including: a memory and a processor communicatively coupled to each other, the memory having stored therein computer instructions, the processor executing the computer instructions to perform the digital currency flow tracking method of the first aspect or an alternative embodiment thereof.
According to a fourth aspect, there is also provided in an embodiment of the present invention a computer readable storage medium having stored thereon computer instructions for causing a computer to perform the method of digital currency flow direction tracking of the first aspect or an alternative embodiment thereof.
According to a fifth aspect, embodiments of the present invention provide a computer program product comprising a computer program stored on a computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, cause the computer to perform the digital currency flow direction tracking method of the first aspect and its optional embodiments.
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The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and not to be construed as limiting the invention in any way, and in which:
FIG. 1 is a flowchart showing a digital money flow direction tracking method in embodiment 1;
FIG. 2 shows an address cluster transaction diagram in embodiment 2;
FIG. 3 is a graph showing vertex information of the address cluster transaction graph in FIG. 2 in example 2;
FIG. 4 is a graph showing the weight values of the top points of the address cluster transaction graph in FIG. 2 in example 2;
fig. 5 is a block diagram showing the structure of a digital money flow direction tracking device according to embodiment 3.
Fig. 6 shows a block diagram of the server in embodiment 4.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
The present embodiment provides a method for tracking a flow direction of digital currency, which is used to analyze Transaction information of the digital currency, and the method is suitable for digital encrypted currency adopting an UTXO (un-consumed Transaction Output), including various kinds of bifurcate currency including a bitcoin and a bitcoin.
The digital currency flow direction tracking method in this embodiment is described by taking a bitcoin as an example, and includes the following steps:
and S11, acquiring a plurality of digital currency transaction information, wherein the transaction information at least comprises a transaction input address. In other alternative embodiments, the output address of the transaction may also be selected as the transaction address for subsequent processing.
The transaction information of the bitcoin is stored in the block chain, and all transaction information can be obtained through the global account book. First, the blockchain data is analyzed to obtain all transactions. All blocks B ═ B on the chain are obtained by parsing1,B2,…,BnIn which B isiFor one of the blocks, n is the total number of blocks. For each block BiObtaining all transactions T in the blocki＝{ti1,ti2,…,timWhere t isijM is the total number of transactions in the block. Each transaction includes the time, amount, input address, output address, etc. at which the transaction occurred. By aggregating all transactions to obtain T ═ UTiWhere i is 1,2, …, n.
The Coin mixing (Coin Shuffle) is a transaction mode in the bitcoin transaction, and can enable a user to be quickly and efficiently mixed with the funds of other users, and a random mapping relation is created between the existing user account and a new account after the Coin mixing, so that complete anonymity is realized. In a further preferred embodiment of this embodiment, in order to avoid inaccuracy of subsequent analysis caused by mixed currency transactions, only the transaction information except for mixed currency transactions is considered in the embodiment of the present invention, so that the mixed currency transactions may be deleted in all the transaction information.
One way to delete a mixed currency transaction is to: and defining an input address number threshold hi and an output address number threshold ho, and judging that the mixed currency transaction is carried out when the input address number of one transaction is greater than or equal to hi and/or the output address number is greater than or equal to ho. In an alternative embodiment, the input address number threshold hi may be selected to be 100, and the output address number threshold ho may be selected to be 100, and may also be set appropriately according to the current data.
Another way to delete a mixed currency transaction is: training a classifier, such as an SVM classifier, using mixed-currency transaction and non-mixed-currency transaction data, wherein the adopted characteristics comprise the number of input addresses of transactions, the number of output addresses of transactions, the difference value of the number of input and output addresses of transactions and the like; the mixed currency transaction is then determined using the classifier.
By the method, the mixed currency transaction can be effectively deleted, and the accuracy of subsequent transaction analysis is ensured.
And S12, generating an address cluster according to the transaction address.
The embodiment is directed to bitcoin, and transaction addresses of a plurality of transaction messages with the same transaction address are combined into one address cluster. In this embodiment, the transaction address is selected as the transaction input address. In other alternative embodiments, the transaction address may also be selected as the output address, or a set of input and output addresses.
For bitcoin, bifurcate bitcoin, and currency with a mechanism similar to bitcoin using UTXO mode, transaction addresses may be used for merging to obtain address clusters. For other currencies, when generating the address cluster, the transaction addresses may not be merged, and each transaction address is taken as an address cluster.
The process of synthesizing address clusters for bitcoins in this embodiment is as follows:
in the first step, all input addresses in each transaction message are used as a set. Since each transaction message generally includes a plurality of addresses, these addresses are regarded as a set of addresses.
For each transaction tij∈ T, the input address set A of the transaction is obtainedij＝{aij1,aij2,…,aijsIn which a isijkIs a transaction tijS is the total number of input addresses (A) in the transactionijThe addresses in (1) may or may not be deduplicated according to the address hash). All input address sets a ═ UAijWhere i is 1,2, …, n, j is 1,2, …, m.
And secondly, judging whether the same input address exists in the set or not.
In establishing the address cluster, it is considered that there is similarity of users of the same input address, and thus any two A' sijIf the addresses in (1) intersect, then the two A' sijAll addresses in (1) belong to the same address cluster; and obtaining the address cluster by judging whether the same input address exists or not.
And thirdly, if the same input address exists, merging the sets until any two sets in all the sets do not have the same element, and taking each remaining set as an address cluster.
The specific calculation method of the address cluster can be two, and the first method is as follows: each A isijAnd as an initial address cluster, checking whether the two address clusters have an intersection, if so, merging the two address clusters into one address cluster, and continuously circulating until the two address clusters cannot be merged.
The second way is: when the same element exists in the sets, setting the distance d between the two sets to be 0; when no identical element is present in the set, set d to 1. Then, the sets with the distance of 0 are continuously clustered into address clusters through a clustering algorithm.
In the above manner, the address cluster CA is formed from the transaction T ═ { CA ═ CA1,CA2,…,CAgIn which CAiG is the number of address clusters for one of the address clusters. Any two address clusters CAiAddress disjointness in (1); any two of AijIf the addresses in (1) intersect, then the two A' sijAll addresses in (1) belong to the same address cluster; the address in the CA contains all the input addresses in the transaction T.
Because in the transaction information, a plurality of input addresses exist in one transaction, the plurality of input addresses can be generally regarded as one user address or related addresses, if the same input address exists in two transactions, the input addresses of the two transactions are associated, for example, the users are the same, the sets with the same input address exist are combined according to the property to form an address cluster, and each address cluster can be verified through a plurality of transaction addresses by combining the address clusters, so that wrong labeling information can be filtered, and the accuracy of real name labeling is improved. The data volume to be analyzed is greatly reduced through combination, so that the difficulty of mass data analysis is greatly reduced.
After the address clusters are merged, identity information may be further tagged to each of the address clusters, and at this time, identity information may be tagged to all the address clusters. Of course, in other embodiments, the step of labeling the identity information of the address cluster may also be performed after the end of the tracking, and only the identity information of the tracked address cluster may be labeled at this time, so as to reduce the data processing amount. The method for labeling the identity information for each address cluster is the same, and comprises the following steps:
firstly, acquiring real name information of part or all input addresses in each address cluster;
each address cluster is provided with a plurality of input address information, and the real-name labeling is carried out on the address clusters through the input address information. The real-name labeling information of the address can be acquired from the link or the labeling can be continuously carried out through an algorithm on the basis of the existing real-name labeling information. The real-name information of the input address can be obtained by capturing data from the internet through a crawler and then cleaning the data; real name information corresponding to the bitcoin address can be obtained from the exchange and the mine pool; people can also provide real name information of addresses in a crowdsourcing mode; or the classifier can be constructed and labeled by a classification algorithm, or labeled by a heuristic algorithm or an expert system, and the like.
For address cluster CAiThe input address may be labeled with different real name information by different information sources. Weights are set for different information sources, if the weight of the information source which is officially authenticated or verified by multiple users is higher, the weight of the individual information source is lower, and the weights can be obtained by quantifying reasonable analysis of the information source by a person skilled in the art. For the same input address, if the real name information obtained from different information sources is inconsistent, the real name information obtained from the information source with the highest weight can be used as the real name information of the input address.
Then, the real name information with the highest weight is used as the real name information of the address cluster.
Let CAiTotally containing n addresses, wherein k addresses are marked with real name information, k is less than or equal to n, and determining an address cluster CAiThe weight of the real name information can be the highest in two ways, one is as follows: the real name information of the input address marked by the information source with the highest weight in the k addresses is used as the real name information of the address cluster CAi;
the second method is as follows: defining the probability of marking the address cluster as real-name information c as Pc ═ (P1/P2) × (k/n), wherein P1 is the sum of the weights of the information sources of which the addresses are marked as real-name information c, namely when a plurality of information sources mark the address of P1 as c, the weights of the information sources are added; p2 is the sum of information source weights of k addresses, Pc is used as the weight of the real name information c, and c with the largest value of Pc is used as the address cluster CAiThe real name information of (1).
By the method, all input addresses of transaction information in the bit currency transaction can be subjected to real-name labeling in an address cluster mode, the number of required labels can be greatly reduced by constructing the address cluster, for example, 413695310 addresses can be combined into about 198424095 address clusters in the current bit currency transaction, so that the difficulty of mass data analysis is greatly reduced, and conditions are created for analyzing data by a user. In addition, the address clusters are labeled according to the mixed labeling information of the addresses in the address clusters, so that each address cluster can be verified through a plurality of transaction addresses, wrong labeling information can be filtered, and the accuracy of real-name labeling is improved. The real-name labeling data can also be used as a reference basis for a supervision department or related enterprises, and provide real-name basic information for analyzing the transaction information of the user.
And S13, constructing an address cluster transaction graph according to the transaction information, and establishing a directed edge by taking the address cluster as a vertex.
Generating address cluster transaction information according to the address cluster and the transaction information, constructing an address cluster transaction graph, wherein each vertex in the address cluster transaction graph is an address cluster, and establishing a directed edge according to the transaction information, wherein the method comprises the following steps:
the method comprises the steps of firstly, obtaining an input address and an output address of existing transaction, wherein an address cluster where the input address is located is a first address cluster, and an address cluster where the output address is located is a second address cluster.
Since the address cluster in this embodiment is constructed according to the input address, the address cluster includes all the input addresses in the transaction, and each output address not included in the input addresses constitutes an address cluster separately, so that all the input addresses and output addresses can be allocated to the address cluster, and the real name information of the address clusters can be obtained by the real name tagging method in the above embodiment.
The address cluster formed by the input address and the address cluster of the output address which is not contained in the input address are merged, and then real name information labeling can be carried out.
For a transaction t, a is the input address of t, b is the output address of t, address a ∈ CAiAnd address b ∈ CAjI.e. two address clusters CAiAnd CAjThere is a transaction T ∈ T in between.
And secondly, establishing a directed edge from the first address cluster to the second address cluster.
If a transaction T ∈ T exists between the address a ∈ CAi and the address b ∈ CAj of the two address clusters CAi and CAj, wherein a is an input address of T and b is an output address of T, a directed edge from CAi to CAj is added to the real-name address cluster transaction graph.
And thirdly, traversing all input addresses and output addresses of existing transactions, and drawing an address cluster transaction graph.
And aiming at all transactions in the global account book, establishing directed graphs of all transactions after traversing to form an address cluster transaction graph. The scheme can construct an address cluster transaction diagram of all transaction information by effectively analyzing the associated information of digital currency such as bit currency transaction, show information of both parties and transaction conditions in the transaction process, and combine real name information, thereby providing real identity of a trader for governments, having high social value, providing simpler and more convenient transaction flow query service for individuals and enterprises, having good economic benefit, and providing information and basis for supervision institutions or related enterprises or individuals.
And S14, calculating the weight of each address cluster in the address cluster transaction graph.
Firstly, acquiring relevant information of address clusters serving as vertexes in an address cluster transaction graph, and indicating transaction relations among the address clusters by directed edges.
A cluster of addresses at a graph vertex comprising the following variables:
address num, the number of addresses in the address cluster, that is, the number of transaction addresses contained in the address cluster;
inputTxNum, the input transaction number of the address cluster, that is, the transaction number of the address cluster as the transaction output address in the digital currency transaction;
outputTxNum, the output transaction number of the address cluster, i.e. the transaction number of the address cluster as the transaction input address in the digital currency transaction;
inputTxValue, the input transaction amount of the address cluster, and the total transaction amount of each address in the address cluster;
output txvalue, the output transaction amount for the address cluster, the total transaction amount that flows from each address in the address cluster.
Each directed edge is provided with a variable: weight, the weight of the directed edge; txNum, the transaction number corresponding to the directed edge, i.e., the transaction number after deduplication is performed for all transactions from each address in the source address cluster of the directed edge to each address in the destination address cluster of the directed edge.
The specific construction process is as follows:
firstly, each address cluster in the address cluster set AC obtained in the second step is taken as a vertex, added into an address cluster trading graph, and variables inputTxNum, outputTxNum, inputTxValue and outputTxValue corresponding to the vertex are set to be 0; address num is set to the number of addresses in the address cluster.
Secondly, traversing each transaction T in the T, obtaining all input addresses and output addresses of the T, setting a temporary address cluster set ACT for the T, wherein all input addresses of the T necessarily belong to the same address cluster which is set to be ACi, and adding ACi into the ACT; for each output address b of t, its corresponding address cluster ACj is obtained, and if there is no directed edge Eij from ACi to ACj in the address cluster transaction graph, the directed edge Eij is added. The receiving amount of b added to the outputTxValue of the vertex corresponding to ACi and the receiving amount of b added to the inputTxValue of the vertex corresponding to ACj are added. If ACj does not belong to ACT, add 1 to the outputTxNum of the vertex corresponding to ACi, add 1 to the inputTxNum of the vertex corresponding to ACj, and add 1 to the transaction number txNum of Eij. ACj is then added to the ACT.
Secondly, after the information is obtained, calculating the weight of each address cluster in the address cluster transaction graph, wherein the weight can be calculated by adopting a formula, and the walletWeight represents the weight of the address cluster, and the calculation method is as follows:
walletWeight＝w1*inputTxNum/maxInputTxNum
+w2*inputTxValue/maxInputTxValue
+w3*outputTxNum/maxOutputTxNum
+w4*outputTxValue/maxOutputTxValue
+w5*addressNum/maxAddressNum
wherein, walletWeight represents the weight of an address cluster, addressNum represents the address number contained in the address cluster, inputTxNum represents the input transaction number of the address cluster, outputTxNum represents the output transaction number output by the address cluster, inputTxValue represents the input transaction amount of the address cluster, and outputTxValue represents the output transaction amount of the address cluster;
maxInputTxNum is the maximum value of inputTxNum in all address clusters,
maxInputTxValue is the maximum value of inputTxValue in all address clusters,
maxouttxnum is the maximum value of outputTxNum in all address clusters,
maxOutputTxValue is the maximum value for outputTxValue in all address clusters,
maxAddresNum is the maximum value of the addressNum in all the address clusters;
w1, w2, w3, w4 and w5 are corresponding weights, and w1+ w2+ w3+ w4+ w5 is 1. The larger the weight, the more important the representation of the feature term. In specific embodiments, w1 and w3 are generally selected to be larger, and w2, w4 and w5 are selected to be smaller.
In the method, the weight of each address cluster in the address cluster transaction graph is calculated through the address number contained in the address cluster, the input transaction number of the address cluster, the output transaction number output by the address cluster, the input transaction amount of the address cluster and the output transaction amount of the address cluster, the corresponding weight is set corresponding to the transaction information, the importance degree of the address cluster can be objectively and accurately reflected, the information is digitized through feature extraction and parameter selection, the processing efficiency is improved, and the reliability of the data is ensured.
As another method for calculating the weight of each address cluster, a PageRank algorithm, which is a technique of calculating based on mutual hyperlinks between web pages, may be used, and the weight of an address cluster may also be calculated by the PageRank algorithm. When the PageRank algorithm is adopted, the weight edgeWeight of the directed edge needs to be set. For the directed edges Eij of ACi through ACj, edgeWeight is set to txNum/txNum, which is the sum of directed edges txNum starting at ACi.
S15, acquiring the target address, and determining the target address cluster where the target address is located.
And regarding the digital currency address needing to be tracked as a target address, confirming the address cluster where the address is located in the address cluster transaction graph. Since the target address is from one address in the whole network transaction address, the target address is necessarily included in a certain address cluster, and the address cluster where the target address is located is found as the target address cluster.
And S16, determining the tracking direction, taking the target address cluster as a starting point, acquiring a directed edge consistent with the tracking direction, and sequentially tracking the address cluster with the maximum weight along the direction of the directed edge.
When tracking the target address, the tracking direction may be forward tracking or backward tracking. The forward tracking is to track according to the transaction flow direction of the digital currency, and the tracking direction is consistent with the trend of the digital currency; the reverse tracking is based on tracking the source of the digital currency and is directed to the reverse tracking of transactions in the digital currency.
In the forward tracing, the vertex where the target address cluster is located is the starting point of the directed edge, tracing is performed along the direction of the directed edge in the address cluster transaction graph (the direction from the starting point to the end point), and when a plurality of directed edges exist by taking the vertex as the starting point at a certain vertex, the address cluster corresponding to the end point with the large walletWeight is preferentially selected as the next vertex, and the tracing is performed sequentially.
When the tracking direction is reverse tracking, the vertex where the target address cluster is located is an end point of a directed edge, tracking is performed along the reverse direction of the directed edge in the address cluster transaction graph (the direction from the end point to a starting point), and when a plurality of directed edges exist by taking the vertex as the end point at a certain vertex, the address cluster corresponding to the starting point with the large walletWeight is preferentially selected as the next vertex, and tracking is performed sequentially.
Whether the address is tracked in the forward direction or the backward direction, when the tracked address cluster has no corresponding directed edge in the tracking direction, the tracking is finished. Or when the tracked address cluster meets the specified conditions, ending the tracking, if the address cluster is marked as a digital currency exchange, ending the tracking; or the end condition is that the tracing reaches the specified limit of the layer number, and the tracing is ended. The condition of the tracking end is reasonably set according to needs, the data processing amount is saved, the tracking needs are met, and the tracking reliability is guaranteed.
In the scheme, the tracking direction can be forward tracking, namely tracking according to the sequence of digital currency transactions, and can also be backward tracking, namely acquiring the source information of the digital currency, so that the destination of the digital currency can be tracked and the source of the digital currency can be tracked aiming at the target address, and the tracking of the digital currency is carried out as required, so that the efficiency is higher.
In the method for tracking the flow direction of the digital currency, after transaction addresses are combined into address clusters, an address cluster transaction graph is constructed, important address cluster information can be found by calculating the weight of each address cluster, when the digital currency is tracked, as the transaction information is massive, the important transaction information can be tracked to obtain the most important data, the address cluster with the largest weight information in the tracking direction is taken as a tracking target, a key object can be locked more quickly, problems can be found in time, the more important transaction information is tracked preferentially, reliable tracking information of the digital currency is provided for a financial supervision institution, the analysis difficulty of massive bit currency transaction data in a block chain is greatly reduced, the digital currency is tracked more timely, the tracking information is more efficient and reliable, the tracking efficiency is improved, and a faster means is provided for government to supervise the digital currency, has high value.
As a further embodiment, new blocks are continuously generated on the block chain, and when one or more new blocks are generated, the method further includes the following steps:
in the first step, the number of newly generated blocks is obtained. The number of blocks is continuously increased, new blocks are continuously generated, and in order to avoid frequent processing of global data, the scheme is set according to the number of the newly generated blocks.
And secondly, judging whether the number of the newly generated blocks exceeds a preset threshold value, executing the third step when the number of the newly generated blocks exceeds the preset threshold value, and otherwise executing the fourth step. The preset threshold is reasonably selected according to the number of blocks in the global network.
And thirdly, when the number of the newly generated blocks exceeds a preset threshold value, regenerating the address cluster, the address cluster transaction graph and the weight of the address cluster. That is, with the digital currency flow tracking method described above in this embodiment, steps S11-S14 are re-executed to re-generate the address clusters, the address cluster transaction map, and the weights of the address clusters.
And fourthly, when the number of the newly generated blocks does not exceed the preset threshold, updating the weight information of the address clusters in the address cluster transaction graph according to the transaction information in the newly generated blocks, for example, generating a new block Bn +1, acquiring a new transaction set Tn +1 from the new block, updating variables in the address cluster transaction graph according to the method in S14 for the t ∈ Tn +1, and calculating the weight of the address clusters.
In other further embodiments, since new transaction information is continuously generated, the method may be configured to perform a timing update, and in the timing update, in order to reduce the data processing amount, the data update may be performed only on the transaction information between the last time the method is executed and the current time point. The method can also be set to carry out global updating once when the new transaction quantity reaches a certain degree, so as to ensure the timeliness of data updating.
Example 2
In this embodiment, a method for tracking a flow direction of digital currency is provided in combination with specific transaction information of a bitcoin, and includes the following steps:
first, the block is analyzed to obtain transaction data. All blocks B on the chain are obtained by analysis, where Bi is one block and n is the total number of blocks { B1, B2, …, Bn }. For each block Bi, all transactions Ti in the block are obtained { Ti1, Ti2, …, tim }, where tij is one transaction in the block and m is the total number of transactions in the block. Each transaction includes a transaction hash, the time the transaction occurred, the input address, the output address, the payment amount for each input address, the receipt amount for each output address, a transaction fee, a block hash, and the like. T ═ UTi is obtained by aggregating all transactions, where i ═ 1,2, …, n.
Three of the transactions are taken as an example and are marked as transaction a, transaction b and transaction c.
Part of the information for transaction a is as follows,
transaction hashing:
423f0ff62d34ba62b55dc9ea44f69516b2bbde12d46b16948145c8383f3cf189
time:
2017-12-2011: 38:16(GMT +8 time zone)
Transaction fee:
0.00228669BTC
block hashing:
000000000000000000268411603ce97362d2236db5673854361614fad41548de
the total input amount:
0.04344293BTC
the total output amount:
0.04115624BTC
inputting:
17ZYtkA8KMLV8ujJApyKHu7bdWxASXJ136 0.04344293BTC
and (3) outputting:
3EikD7mfPtvpaEUazqmaoARzg414E2K3wn 0.03957607BTC
1KdqybxckoubnKh7yzPedrPZxgxRvYY37z 0.00158017BTC
part of the information for transaction b is as follows,
transaction hashing:
5e56ec1b427e7a60ee7d1d0c4d2838235c461acb41558b46d02de9e1a01e8279
time:
2017-12-2013: 53:01(GMT +8 time zone)
Transaction fee:
0.00172521BTC
block hashing:
000000000000000000357acc11e6e75a2a131622b447ec78eba3b7aff0c3f13e
the total input amount:
0.04107646BTC
the total output amount:
0.03935125BTC
inputting:
3EikD7mfPtvpaEUazqmaoARzg414E2K3wn 0.03957607BTC
3DizWK4d4wTdZV11UcJBTbHpJi3qtPTF9Y 0.00150039BTC
and (3) outputting:
1GFW8Q16v7MSkgXgUiuPuqAKqjFtQvc8RE 0.00828788BTC
1FkKaVz5ZhfK8P3D7rP87ibo7r1QC9yL3y 0.03106337BTC
part of the information for transaction c is as follows,
transaction hashing:
97d6089252c09004e18e3d019a5e5f48edf8f769fe8f9e4fdb6dfcd619cb9028
time:
2018-01-2308: 02:28(GMT +8 time zone)
Transaction fee:
0.00300671BTC
block hashing:
0000000000000000004647e97e20a19f3135228e453fa9a882b6b71c4deb1b78
the total input amount:
0.23140281BTC
the total output amount:
0.2283961BTC
inputting:
and (3) outputting:
13Bmqxx6NXDqaa8JyGEFhhj23KxaxGYqb7 0.22814476BTC
17KWzXhpAXTMhHDcCHVEtniCpMkisNDhdG 0.00025134BTC
and secondly, merging the transaction addresses of a plurality of transaction messages with the same transaction address into an address cluster. The method comprises the following steps:
for transaction a, its input address set is:
{17ZYtkA8KMLV8ujJApyKHu7bdWxASXJ136}
the set of output addresses is:
{3EikD7mfPtvpaEUazqmaoARzg414E2K3wn,
1KdqybxckoubnKh7yzPedrPZxgxRvYY37z}
for transaction b, its set of input addresses is:
{3EikD7mfPtvpaEUazqmaoARzg414E2K3wn,
3DizWK4d4wTdZV11UcJBTbHpJi3qtPTF9Y}
the set of output addresses is:
{1GFW8Q16v7MSkgXgUiuPuqAKqjFtQvc8RE,
1FkKaVz5ZhfK8P3D7rP87ibo7r1QC9yL3y}
for transaction c, its set of input addresses is:
{1Ppfdpu6pZNB556bc4QVdyWyU3qRd9b2Vh,
17ZYtkA8KMLV8ujJApyKHu7bdWxASXJ136,
17bLy2i46ihqppL5GS2GfXZLGM9kPwQygK,
1JLwVhYB8yWvzLBXF2BpjFnL3uVatgKfzU,
1KdqybxckoubnKh7yzPedrPZxgxRvYY37z,
1LoCQThyMmhXuG72zMiKArjz4Drs7whCNC}
the set of output addresses is:
{13Bmqxx6NXDqaa8JyGEFhhj23KxaxGYqb7,
17KWzXhpAXTMhHDcCHVEtniCpMkisNDhdG}
six address clusters AC1, AC2, AC3, AC4, AC5, AC6 are formed
Where the AC1 contains 6 addresses:
{17ZYtkA8KMLV8ujJApyKHu7bdWxASXJ136,
17bLy2i46ihqppL5GS2GfXZLGM9kPwQygK,
1JLwVhYB8yWvzLBXF2BpjFnL3uVatgKfzU,
1KdqybxckoubnKh7yzPedrPZxgxRvYY37z,
1LoCQThyMmhXuG72zMiKArjz4Drs7whCNC,
1Ppfdpu6pZNB556bc4QVdyWyU3qRd9b2Vh}
the AC2 contains 2 addresses:
{3EikD7mfPtvpaEUazqmaoARzg414E2K3wn,
3DizWK4d4wTdZV11UcJBTbHpJi3qtPTF9Y}
AC3 contains 1 address:
{1GFW8Q16v7MSkgXgUiuPuqAKqjFtQvc8RE}
AC4 contains 1 address:
{1FkKaVz5ZhfK8P3D7rP87ibo7r1QC9yL3y}
AC5 contains 1 address:
{13Bmqxx6NXDqaa8JyGEFhhj23KxaxGYqb7}
AC6 contains 1 address:
{17KWzXhpAXTMhHDcCHVEtniCpMkisNDhdG}
and thirdly, constructing an address cluster transaction graph, constructing the address cluster transaction graph according to the transaction information, and establishing a directed edge by taking the address cluster as a vertex.
The transaction graph is a directed graph, address clusters are used as vertexes, and directed edges represent the relation of the address clusters. Wherein the vertices W1, W2, W3, W4, W5, and W6 correspond to the address clusters AC1, AC2, AC3, AC4, AC5, and AC6, respectively. The directed edges E15, E16, E12, E23, and E24 represent the relationship between address clusters, as shown in FIG. 2.
The values of the variables corresponding to the vertices are shown in fig. 3.
The variables txNum for the directed edges E15, E16, E12, E23, and E24 are all 1.
And fourthly, calculating the weight walletWeight of each address cluster according to the address cluster transaction graph.
The method comprises the following steps: walletWeight ═ w1 inputTxNum/maxInputTxNum
+w2*inputTxValue/maxInputTxValue
+w3*outputTxNum/maxOutputTxNum
+w4*outputTxValue/maxOutputTxValue
+w5*addressNum/maxAddressNum
Wherein, w1 is 0.3, w2 is 0.1, w3 is 0.3, w4 is 0.1, and w5 is 0.2, and the weights of the vertices are shown in fig. 4.
And fifthly, tracking the flow direction of the digital currency.
When the flow direction of the address cluster currency of the address 17ZYtkA8KMLV8ujJApyKHu7 bdWxASJ 136 needs to be tracked, the address is confirmed to be in the address cluster W1 in the address cluster transaction map, when forward tracking is carried out, three directed edges with the W1 as the starting point are respectively E12, E15 and E16, and the corresponding end points are respectively W2, W5 and W6. Since W2 is weighted more heavily than W5 and W6, tracking is prioritized along the direction of W2. Since the data size is very large in the block chain, tracking the digital currency flow in a huge amount of data is inefficient. By the method, more important address clusters can be tracked preferentially, and the tracking efficiency is effectively improved, so that a faster means is provided for government to monitor digital currency.
Example 3
In one embodiment, a digital currency flow direction tracking device is provided, including:
the acquisition unit 01 is used for acquiring a plurality of digital currency transaction information, and the transaction information at least comprises a transaction address; see step S11 in example 1 for details.
A merging unit 02 for generating an address cluster according to the transaction address; see step S12 in example 1 for details.
The map generation unit 03 is used for constructing an address cluster transaction map according to the transaction information and establishing directed edges by taking the address clusters as vertexes; see step S13 in example 1 for details.
The weight calculation unit 04 is used for calculating the weight of each address cluster in the address cluster transaction graph; see step S14 in example 1 for details.
A target address determining unit 05, configured to obtain a target address and determine a target address cluster where the target address is located; see step S15 in example 1 for details.
And the tracking unit 06 is configured to determine a tracking direction, obtain a directed edge consistent with the tracking direction with the target address cluster as a starting point, and sequentially track the address cluster with the largest weight along the direction of the directed edge. See step S16 in example 1 for details.
According to the scheme, an address cluster transaction diagram is constructed to obtain flow direction information of digital transactions, important address cluster information can be found by calculating the weight of each address cluster, when the digital currency is tracked, the transaction information is massive, and the important information can be tracked to obtain the most important data, so that the address cluster with the largest weight information in the tracking direction is used as a tracking target, key objects can be locked more quickly, problems can be found in time, reliable tracking information of the digital currency is provided for a financial supervision institution, the analysis difficulty of massive bit currency transaction data in a block chain is greatly reduced, the digital currency is tracked more timely, and the tracking information is more efficient and reliable.
Example 4
A server for data mining of digital currency transaction information for tracking digital currency flow, comprising: a memory 51 and a processor 52, the memory 51 and the processor 52 are communicatively connected to each other, wherein the processor 52 and the memory 51 may be connected by a bus or other means, and fig. 5 illustrates an example of a connection by a bus. The memory has stored therein computer instructions that, when executed by the processor, perform the digital currency flow direction tracking method of embodiment 1 or 2.
The memory 51, which is a non-transitory computer readable storage medium, may be used to store non-transitory software programs, non-transitory computer executable programs, and modules. The processor 52 executes various functional applications and data processing of the processor by executing the non-transitory software programs, instructions and modules stored in the memory 51, that is, implements the digital currency flow direction tracking method described in embodiment 1 or embodiment 2 above.
The memory 51 may include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the storage data area may store data created by the processor 52, and the like. Further, the memory 51 may include high speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, memory 51 optionally includes memory located remotely from processor 52, and these remote memories may be connected to processor 52 via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The one or more modules are stored in the memory 51 and when executed by the processor 52, perform the digital currency flow direction tracking method of embodiment 1 or embodiment 2.
Example 5
There is provided in this embodiment a computer readable storage medium having stored thereon computer instructions for performing the digital currency flow direction tracking as described in embodiment 1 or embodiment 2. It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic Disk, an optical Disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a Flash Memory (Flash Memory), a Hard Disk (Hard Disk Drive, abbreviated as HDD), a Solid State Drive (SSD), or the like; the storage medium may also comprise a combination of memories of the kind described above.
Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations fall within the scope defined by the appended claims.
Claims (11)
1. A method for tracking a flow of digital currency, comprising:
acquiring transaction information of a plurality of digital currencies, wherein the transaction information at least comprises transaction addresses;
generating an address cluster according to the transaction address;
constructing an address cluster transaction graph according to the transaction information, and establishing a directed edge by taking the address cluster as a vertex;
calculating the weight of each address cluster in the address cluster transaction graph;
acquiring a target address, and determining a target address cluster where the target address is located;
and determining the tracking direction, taking the target address cluster as a starting point, acquiring a directed edge consistent with the tracking direction, and sequentially tracking the address cluster with the maximum weight along the direction of the directed edge.
2. The method according to claim 1, wherein when the tracing direction is forward tracing, the vertex where the target address cluster is located is a starting point of a directed edge; or
And when the tracking direction is reverse tracking, the vertex where the target address cluster is located is the end point of the directed edge.
3. The method according to claim 1 or 2, wherein tracking the address cluster with the largest weight in the direction of the directed edge comprises:
until the tracked address cluster has no corresponding directed edge in the tracking direction, ending the tracking; or
The tracked address cluster satisfies a specified condition.
4. The method of claim 1, wherein constructing an address cluster transaction graph according to the transaction information, and establishing a directed edge with an address cluster as a vertex comprises:
acquiring an input address and an output address of a transaction, wherein an address cluster where the input address is located is a first address cluster, and an address cluster where the output address is located is a second address cluster;
establishing a directed edge from the first address cluster to the second address cluster;
and traversing all input addresses and output addresses of existing transactions, and drawing an address cluster transaction graph.
5. The method of claim 1 or 2, wherein the calculating the weight of each address cluster in the address cluster transaction graph comprises
walletWeight＝w1*inputTxNum/maxInputTxNum
+w2*inputTxValue/maxInputTxValue
+w3*outputTxNum/maxOutputTxNum
+w4*outputTxValue/maxOutputTxValue
+w5*addressNum/maxAddressNum
Wherein, walletWeight represents the weight of an address cluster, addressNum represents the address number contained in the address cluster, inputTxNum represents the input transaction number of the address cluster, outputTxNum represents the output transaction number output by the address cluster, inputTxValue represents the input transaction amount of the address cluster, and outputTxValue represents the output transaction amount of the address cluster;
maxInputTxNum is the maximum value of inputTxNum in all address clusters,
maxInputTxValue is the maximum value of inputTxValue in all address clusters,
maxouttxnum is the maximum value of outputTxNum in all address clusters,
maxOutputTxValue is the maximum value of outputTxValue in all address clusters,
maxAddresNum is the maximum value of the addressNum in all the address clusters;
w1, w2, w3, w4 and w5 are corresponding weights, and w1+ w2+ w3+ w4+ w5 is 1.
6. The method of claim 1, further comprising:
acquiring the number of newly generated blocks;
judging whether the number of the newly generated blocks exceeds a preset threshold value or not;
when the number of the newly generated blocks exceeds a preset threshold value, regenerating the address cluster, the address cluster transaction graph and the weight of the address cluster;
and when the number of the newly generated blocks does not exceed the preset threshold, updating the weight information of the address cluster in the address cluster transaction graph according to the transaction information in the newly generated blocks.
7. The method of claim 1, wherein the step of generating an address cluster according to the transaction address comprises, for bitcoin and its bifurcate, combining the transaction addresses of a plurality of transaction messages having the same transaction address into an address cluster by:
all transaction input addresses in each transaction message are used as a set;
judging whether the same transaction address exists in the set or not;
if the same transaction address exists, merging the sets until any two sets in all sets do not have the same element, and taking each remaining set as an address cluster; each output address that is not included in the set of input addresses forms a separate cluster of addresses.
8. The method of claim 1, further comprising labeling the address cluster with identity information, comprising:
acquiring real name information of part or all transaction addresses in each address cluster;
the real name information with the highest weight is used as the real name information of the address cluster, and the method comprises the following steps:
weight for marking address clusters as real name information c: pc ═ P1/P2 (k/n), where n is the number of transaction addresses in the address cluster, k is the number of transaction addresses to which real-name information has been tagged, P1 is the sum of information source weights for addresses tagged as real-name information c, and P2 is the sum of information source weights for k addresses;
and taking the real name information c which maximizes the value of Pc as the real name information of the address cluster.
9. A digital currency flow direction tracking device, comprising:
the system comprises an acquisition unit, a processing unit and a display unit, wherein the acquisition unit is used for acquiring a plurality of digital currency transaction information, and the transaction information at least comprises a transaction address;
the merging unit generates an address cluster according to the transaction address;
the map generation unit is used for constructing an address cluster transaction map according to the transaction information and establishing directed edges by taking the address cluster as a vertex;
the weight calculation unit is used for calculating the weight of each address cluster in the address cluster transaction graph;
a target address determining unit, configured to obtain a target address and determine a target address cluster where the target address is located;
and the tracking unit is used for determining the tracking direction, taking the target address cluster as a starting point, acquiring a directed edge consistent with the tracking direction, and sequentially tracking the address cluster with the maximum weight along the direction of the directed edge.
10. A server apparatus, comprising: a memory and a processor communicatively coupled to each other, the memory having stored therein computer instructions, the processor executing the computer instructions to perform the digital currency flow direction tracking method of claims 1-8.
11. A computer-readable storage medium having stored thereon computer instructions for causing a computer to perform the digital currency flow direction tracking method of claims 1-8.
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| CN112700332A (en) * | 2021-01-11 | 2021-04-23 | 北京金色大数据有限公司 | Bit currency account clustering method based on graph calculation |
| CN113627919A (en) * | 2021-08-11 | 2021-11-09 | 杭州橙鹰数据技术有限公司 | Resource tracking method and device |
| CN114266603A (en) * | 2021-12-28 | 2022-04-01 | 山东浪潮工业互联网产业股份有限公司 | Block chain UTXO transaction-based point management method, equipment and medium |
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