CN112615846B - Block chain system authentication threshold updating method based on DAG - Google Patents

Block chain system authentication threshold updating method based on DAG Download PDF

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CN112615846B
CN112615846B CN202011463675.1A CN202011463675A CN112615846B CN 112615846 B CN112615846 B CN 112615846B CN 202011463675 A CN202011463675 A CN 202011463675A CN 112615846 B CN112615846 B CN 112615846B
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authentication
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block chain
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刘期烈
李孟阳
曹傧
白翔
李云
屈喜龙
胡壹
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/12—Applying verification of the received information
    • G—PHYSICS
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/50—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using hash chains, e.g. blockchains or hash trees

Abstract

The invention belongs to the technical field of block chains, and relates to a method for updating a transaction authentication threshold value in a block chain system; the updating method comprises the steps of constructing a block chain system based on a DAG consensus algorithm; modeling a process from the generation of the transaction to the authentication of the transaction by the node by using a queuing model, minimizing the difference between an authentication threshold given by a block chain system and the cumulative weight of the transaction issued by the node under the arrival condition of the steady-state transaction, obtaining the cumulative weight of the transaction issued by the corresponding node, and calculating the minimum transaction authentication delay; acquiring an updating rule of the authentication threshold by using a random distribution function; if the transaction arrival rate triggers the updating rule, updating the system authentication threshold, otherwise, continuously solving the transaction authentication delay to obtain the updating rule; the invention models according to the authentication process of the transaction in the consensus network, obtains the transaction authentication delay, obtains the updating rule of the authentication threshold of the blockchain system, and establishes the triggering condition of the updating rule to improve the stability of the blockchain system.

Description

Block chain system authentication threshold updating method based on DAG
Technical Field
The invention belongs to the technical field of block chain communication, and relates to a method for updating a transaction authentication threshold value in a block chain system.
Background
Blockchains were originally proposed as a distributed tamper-resistant ledger that records an ordered set of transactions. The blockchain verifies the transactions through a decentralized consensus process between untrusted agents, and finally the transactions are linked into a chain according to a chronological order. The blockchain system can be roughly divided into three categories: public block chains, private block chains, and federation block chains. In the common blockchain, each node may participate in the negotiation process. And only one selected set of nodes is responsible for verifying a tile in the union blockchain. In blockchains, how to achieve consensus among untrusted nodes is the task of the consensus algorithm. Common consensus algorithms include workload certification (Proof of Work), equity certification (Proof of stamp), Byzantine consistency Tolerance (Practical Byzantine factory hierarchy), and directed Acyclic Graph (Direct Acyclic Graph).
In the DAG, validation security for a transaction is measured by accumulated workload proofs for that transaction, each transaction "validating" one or more previous transactions, forming a one-way acyclic data structure. To satisfy the excitation mechanism in the block chain, there are three effective approaches: first, it is rewarding for a node to approve as many previous transactions as possible; second, when many previous transactions are not approved, approval of many previous transactions is encouraged; third, there is no competition between nodes to approve the previous transaction, i.e., no mine is excavated.
Under the demand of massive data networking, a block chain based on DAG tends to become a trend. However, non-uniformity of traffic peaks poses significant challenges to DAG-based block chain performance in future communication networks. In the existing block chain, when the transaction flow is too small, the fixed threshold value which is required to be reached by the transaction authentication can cause the problems of too long authentication delay of the transaction and the like.
Disclosure of Invention
In order to solve the technical problems in the background art, the present invention aims to provide an updating method for a block chain system authentication threshold based on DAG, which is capable of iteratively updating the authentication threshold of the block chain system based on DAG based on a random process analysis value. Specifically, the method is based on DAG as a block chain of the consensus algorithm, a model of transaction authentication under a steady state condition is established, and a closed expression of transaction authentication delay is researched. And then, analyzing the optimized transaction authentication delay according to the queuing model and the random function distribution function to obtain an updating function of the block chain authentication threshold, and finally analyzing the block chain system performance of the DAG structure.
In order to achieve the purpose, the invention provides the technical scheme that:
constructing a block chain system based on a DAG consensus algorithm in a point-to-point mode;
modeling the process from the generation of the transaction to the authentication of the transaction by the nodes by using a queuing model, and calculating the cumulative weight of the transaction issued by each node under the condition of the arrival of the steady-state transaction;
minimizing the difference between the authentication threshold given by the block chain system and the accumulated weight of the node issued transaction to obtain the accumulated weight of the corresponding node issued transaction, thereby calculating the minimum transaction authentication delay;
acquiring an updating rule of the authentication threshold by using a random distribution function according to the minimum transaction authentication time delay;
and if the transaction arrival rate of the current stage triggers the updating rule, updating the system authentication threshold, otherwise, continuously solving the transaction authentication delay to obtain the updating rule.
The invention has the beneficial effects that:
the invention adopts DAG as a consensus mechanism and builds a point-to-point peer-to-peer block chain network which works instantly on the basis of a typical consensus algorithm Tangle. Each node is responsible for broadcasting, authenticating and accounting transactions as a whole node of the network where they are located, and they can actively select which past transactions are approved by a new transaction. According to the rule, a decentralized block chain from a small node to a large distribution can be finally constructed, on one hand, the cost of network management and maintenance can be reduced, and on the other hand, the block chain network structure is simple and can be copied and popularized to various communication systems.
The performance of the DAG consensus network is analyzed from two dimensions, in the first layer, modeling is carried out according to the authentication process of the transaction in the consensus network, and the transaction authentication delay taking the authentication threshold as an independent variable is obtained according to the queuing theory and the Markov chain state transition. In the second aspect, under the condition that the authentication threshold is uncertain, an updating rule of the authentication threshold of the block chain system is obtained according to an optimization theory and random function distribution, and a trigger condition of the updating rule is set to improve the stability of the block chain system.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flowchart of an updating method of block chain system authentication threshold based on DAG according to the present invention;
FIG. 2 is a block chain network model diagram of the algorithm using Tangle as consensus according to the present invention;
FIG. 3 is a graph of cumulative weight increase for a blockchain network with or without update rules using Tangle as a consensus algorithm according to the present invention;
FIG. 4 is a graph illustrating transaction authentication latency under the authentication threshold update rule of the blockchain system according to the present invention;
fig. 5 is a graph of transaction throughput of the blockchain system under the update method of the present invention.
Detailed Description
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 only a part of the embodiments of the present invention, and not all of the embodiments. 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.
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
FIG. 1 is a flowchart of an updating method of a block chain system authentication threshold based on DAG according to the present invention; as shown in fig. 1, the present invention provides an updating method of a block chain system authentication threshold based on DAG to solve the authentication delay and security problems when low transaction traffic arrives in a block chain network, and calculate the transaction authentication delay of the system, including the following steps:
s1, constructing a block chain system based on a DAG consensus algorithm in a point-to-point mode;
in a block chain with DAG as a consensus algorithm, each user is used as a single node to participate in broadcasting transaction information mutually, authenticating the transaction and building a consensus network in a point-to-point mode.
In this embodiment, a block chain network model using tang as a consensus algorithm is shown in fig. 2, where tang is a DAG consensus algorithm, in the DAG-based block chain system in fig. 2, any user may send a generated transaction to a network node for processing through any communication means, and each processing node broadcasts to other networks according to the protocol rules of the current network, for example, an optical user in an optical network follows the protocol rules of the optical network, a cellular user in a cellular network follows the cellular network protocol, and a satellite user in a satellite network follows the satellite network protocol; all nodes in the networks are used as nodes in a blockchain system, the nodes execute a Tangle consensus algorithm to authenticate transactions, and finally, transaction book information shown in a consensus layer in fig. 2 is formed in a storage unit of each node, wherein nodes with different filling shapes represent nodes of different networks.
S2, modeling the process from the node generating transaction to the transaction being authenticated by using a queuing model, and calculating the cumulative weight of each node issuing transaction under the condition of arrival of steady-state transaction;
in the blockchain network described above, the arrival time of each transaction is random and can be abstracted as 0 ≦ t1≤t2.00, then the arrival time interval of the two transactions is Tk＝tk-tk-1In this embodiment, the concept of limit is applied, when the time interval approaches 0, only one transaction is issued for one stage, so T herekAlso denoted the arrival time interval of the arrival time intervals of the kth transaction and the kth-1 transaction, and k ≧ 1.
For a single node, the randomness of the transaction arrival time is geometrically distributed, and then the arrival of the transaction must be continuous from the whole blockchain system level. Then, the arrival time interval T of the transactionkAre distributed exponentially. Suppose the transaction arrival rate of each node is lambdakThen the transaction arrival interval is expected to be E [ T ]k]＝1/λk。
In the layer of the underlying communication network, i.e. the optical network, the cellular network, the satellite network, etc. in fig. 2, considering that the communication protocols of the transaction in different network environments have cross adaptation situations, the transaction is served by using a queue with an infinite service window. The method can be modeled as M/M/n in queuing theory, the first two M represent that the time interval distribution of the arrival time interval distribution and the departure time interval distribution of the transaction are both exponential distribution, and the last n represents the number of queues entering the block chain of each transaction, which are parallel. Then the probability P of success of the service at different queues i can be calculatediComprises the following steps:
Figure BDA0002833137700000051
wherein, here λkNode transaction arrival rate, μ, representing the kth stagekRepresents the node transaction departure rate of the kth stage, and if the queue is infinitely long, lambda must be providedk<nμk；P0Indicating the probability of success of the initial queue service, P0The first function of the piecewise functions is used for solving.
Then, for the node of the kth stage, the arrival rate of the transaction into the Tangle blockchain is:
λ’k＝λkPi (2)
assuming that the hash power of each node to generate a transaction is constant, the expected time of the node at the kth stage to generate a transaction is
Figure BDA0002833137700000061
Denoted by the greek letter alpha. From phase k-1 to phase k, it can be inferred that the average time taken to issue β transactions is:
Figure BDA0002833137700000062
the invention applies the property of exponential distribution, when beta transactions issued in the kth stage are equal to the accumulated transactions in the previous stages, which is equivalent to the task of completing the beta transactions in the kth stage;
Figure BDA0002833137700000063
actually denoted as Tk-β+1To Tk-1And (4) summing.
However, for each phase k ≧ 1, β transactions are issued at the same time, the transaction arrival time interval T in which(k-1)β+kIs a variable lambdakIs exponentially distributed, if λ1'is constant, then k is equal to or more than 1, lambda'kIs also a random variable, and is specifically expressed as follows:
Tk～Exp(λ’1) 1≤k≤β (4)
by analogy, the time interval variable for issuing β transactions is:
T(k-1)β+k～Exp(λ’k) 1≤k≤β (5)
according to the function of the exponential distribution, the probability density function is obtained as:
Figure BDA0002833137700000064
Figure BDA0002833137700000065
equation (6) represents the random variable TkIn the case of unchanged node arrival rate, the node is used for receiving the messageThe time interval probability density distribution function of each node in the kth stage; equation (7) represents the random variable T(k-1)β+kAnd under the condition that the arrival rate of the nodes is not changed, the probability density distribution function of the time interval of the k stage of the single node.
In the blockchain of the Tangle-based consensus algorithm, the work between each node joining the blockchain system is not influenced by each other, and the nodes are independent. Let N denote the number of nodes participating in the consensus process, which corresponds to N parallel queues issuing transactions into the blockchain. Because of TkCan be regarded as the sum of the transactions issued by all nodes in the kth stage, then the transaction of the nth node arrives after entering the Tangle
Figure BDA0002833137700000071
Compliance parameter is λ'kAnd an alvaran distribution of N. Then the following relationship exists:
T1 n～Erlang(λ’1,N) (8)
Figure BDA0002833137700000072
Figure BDA0002833137700000073
Figure BDA0002833137700000074
the above equations (8) and (9) represent the shorthand of the random variable distribution, respectively, and (10) and (11) are the specific probability density function expansions of equations (8) and (9), where the condition is that k is greater than or equal to 1 and n is greater than or equal to 1.
According to the basic criteria of the Tangle consensus algorithm, the cumulative weight value of a transaction is the sum of the self-weight of the transaction plus the cumulative weight of transactions that have been approved directly or indirectly. However, the deadweight of each transaction is proportional to its hash power, by rnRepresents the nth nodeThe transaction self-weight issued at this node is rn N，0<rn<1. Thus, at the kth stage, the transaction cumulative weight issued from the nth node is represented as:
Figure BDA0002833137700000075
in the Tangle network, new transactions in steady state are in full coverage to approve old transactions between them, and the weight increase of transactions is linear. Transaction cumulative weight
Figure BDA0002833137700000076
And can be represented as:
Figure BDA0002833137700000077
s3, minimizing the difference between the authentication threshold given by the blockchain system and the accumulated weight of the transaction issued by the node to obtain the accumulated weight of the transaction issued by the corresponding node, thereby calculating the corresponding transaction authentication delay;
after the steady-state transaction arrival is analyzed, in order to solve the problem of excessively large transaction authentication delay under a low transaction arrival rate, the transaction authentication delay needs to be made as small as possible under the condition of a given system authentication threshold. In order to obtain a conversion equation of the transaction arrival rate, a random variable lambda 'of a state transition density function of the node transaction conversion rate needs to be derived from k stages to (k +1) th stage'1(k+1)|λ’1(k) And (5) expressing. It can be known as λ'1(k +1) must be a follower TkMonotonically increasing, then from λ'1(k +1) to TkAnd from λ'1(k +1) to λ'1(k) Is equivalent, then there is the formula:
Figure BDA0002833137700000081
the alrong distribution is substituted to give the expression:
Figure BDA0002833137700000082
in the above formula, δk+1And N represents a parameter of the Alron distribution, and δk+1Independent of the transaction arrival rate. Deltak+1Can be expressed as:
Figure BDA0002833137700000083
except for the initial stage of TkRandom variable T of all other stageskAre all the same. It should be noted that the random variable T for the time of issuing beta transactions(k-1)β+kIs the result of the superposition of a plurality of exponential distributions, and the probability density function of the result is integrated to obtain:
Figure BDA0002833137700000091
thus, each node gets a random variable T that issues β transactions(k-1)β+kThe same is true of the distribution function that proves that different nodes are issuing transactions in different phases.
Under the support of the above analysis, the present invention only needs to optimize the authentication delay of any node in any stage of the transaction, and this embodiment minimizes the difference between the authentication threshold given by the blockchain system and the accumulated weight of the transaction issued by the node, so as to obtain the accumulated weight of the transaction issued by the corresponding node, thereby calculating the corresponding transaction authentication delay; by WtDenotes the authentication threshold, W, given by the Tangle blockchain systemtRepresenting an attribute weight value given by the Tangle block chain system to the authentication delay; for any one of the transactions, making the value of the parameter θ as small as possible, otherwise equal to 0, results in the smallest authentication delay.
Figure BDA0002833137700000092
Determined by the formula (18)
Figure BDA0002833137700000093
In combination (12) and (13), the corresponding transaction authentication time delay can be found as:
Figure BDA0002833137700000094
s4, obtaining the updating rule of the authentication threshold by using a random distribution function according to the transaction authentication delay;
the probability distribution of the transaction arrival rate at each stage of each node has been given above, and the transaction authentication delay T is obtained by letting θ equal to 0dI.e. an optimal result. In the case where the computation value of each node is constant, at different stages, the following relationships exist:
rk＝r(k-1)N+1＝r(k-1)N+2＝...＝rkN (20)
the above formula shows that the computing power of a node at different stages is finally multiplied by the ratio of the computing power in the network where the node is located. And the probability of service P for each n-th node queuenIs invariant, the expression is:
Figure BDA0002833137700000101
in conjunction with equation (2), the updated expression of the arrival of the transaction can be obtained as:
λ’k＝λ’(k-1)N+1＝λ’(k-1)N+2＝...＝λ’kN (22)
equations (20), (21) and (22) show that the relationship between computing power and transaction arrival rate is directly proportional. Since the authentication threshold of the initial Tangle blockchain system is constant, it is multiplied by a constant to obtain the following relation:
Figure BDA0002833137700000102
however, the time it takes to issue β exchanges in a total of k phases must be the starting time representing the next phase, then β can be expressed as:
Figure BDA0002833137700000103
from equations (3) and (24), it can be found that:
Figure BDA0002833137700000104
then, the optimal transaction authentication delay at each stage can be obtained according to the update rule of the weight threshold of the blockchain system. From the independence of the parameters of the alvaran distribution of equation (17), equation (25) can be further abbreviated as:
Figure BDA0002833137700000105
the above formula shows that when other conditions are constant, when the number of nodes in the Tangle block chain increases, the authentication threshold updated in the next stage of the system increases, and in order to ensure security, it must be ensured that the nodes issue more transactions to reach the target task. Similarly, when the number of nodes is small, the arrival rate of the transaction entering the Tangle blockchain is also reduced, and δ is calculated according to the relation of equation (17)kIf the time increases, the target time α spent for issuing β transactions also increases, and the weight value of the next stage to be updated decreases, thereby reducing the authentication delay when a low transaction arrives.
S5, if the transaction arrival rate of the current stage triggers the updating rule, updating the system authentication threshold, otherwise, returning to the step S2 to continuously solve the transaction authentication delay to obtain the updating rule;
the updating rule of the authentication threshold of the Tangle blockchain system is obtained, but the updating rule of the system is quite sensitive and is updated and iterated at any time. Therefore, to improve stability, a trigger condition needs to be added to a given update rule. Firstly, solving T for random variable(k-1)β+kIts expected value:
Figure BDA0002833137700000111
its variance can also be found as:
Figure BDA0002833137700000112
from the above two formulas, it is found that the reason why the transaction arrival time interval changes unstably when the number of nodes is constant is due to the rapid increase of the transaction arrival rate in the Tangle block chain. Therefore, the invention can well improve the stability of the blockchain system by taking the change of the transaction arrival rate as the trigger condition.
For the number of transactions into the blockchain at the kth stage, it may be denoted as λ'kAnd N, when the difference between the expected value and the expected value is larger than the variance, the rule updating of the authentication threshold is considered to be necessary at the moment, and the expression is as follows:
Figure BDA0002833137700000113
and then, when the triggering condition is met, updating the authentication threshold of the block chain system, otherwise, directly calculating the authentication delay of the current transaction.
On the basis of the above embodiment, it can be found that the method for updating the block chain system authentication threshold based on the DAG improves the authentication efficiency when the low transaction arrives to a certain extent. Unlike the conventional Tangle Block chain, the present invention contemplates a communication networkStability of (1-P), filtering transactions using nodes of infinite queue length, indicating outside of service windowiThe queue cannot enter the blockchain. In addition, in the conventional Tangle blockchain, transactions often go through an adaptation period, and the number of new transactions in the network fluctuates. However, what is considered in the present invention is that the transaction arrives in a steady state situation, there is no substantial change in the number of new transactions to perform the approval task, and the above embodiments are directed to the secondary random variable TkTo T(k-1)β+kThe analysis of (a) demonstrates the rationality of this approach.
In a preferred embodiment, in order to verify the validity of the method for updating the authentication threshold, the invention first uses a mathematical tool to find the authentication delay of the blockchain transaction and the throughput of the network under the condition of the existence of the authentication threshold updating rule.
The following lists an expression for transaction authentication latency without a threshold update rule:
Figure BDA0002833137700000121
note that λ ═ λ 'here'k，
Figure BDA0002833137700000122
When the updating rule exists, the transaction authentication delay without the trigger condition is also represented by a formula (30), and the expression of the transaction authentication delay of the trigger condition is as follows:
Figure BDA0002833137700000123
accordingly, the transaction throughput of the blockchain system can be given:
Figure BDA0002833137700000131
the application effect of the present invention will be described in detail with reference to the simulation.
1) Simulation conditions
The trade arrival time intervals are exponentially distributed according to the assumption in the actual model, and are simulated in MATLAB. The blockchain system parameters are set as follows: the number N of the nodes participating in the consensus verification is 100, and the probability P of successful communication network service i1 is ═ 1; in the Tangle block chain, the normalized calculation force r of each noden0.01, then the unit of weight of each transaction is 1, and the lower constant system authentication threshold W without update rulest1000, there is an initial value W of the system authentication threshold under the update rule0＝100。
2) Simulation result
Figure 3 is a graph comparing the weight change for transactions without a system authentication threshold to the weight change for transactions with a system authentication threshold. It has been found that transactions can gain faster weight gain even in the initial phase after introducing updated rules for system authentication thresholds, which is caused by transactions that go through a centralized process to approve a transaction.
Fig. 4 shows a curve under the authentication threshold updating rule of the blockchain system proposed by the present invention, which can find that the authentication delay of the transaction is significantly reduced in the very initial stage, that is, when the transaction arrival rate is low, and the transaction authentication efficiency under the optimal condition is improved by 67%. However, the optimization effect of the method gradually becomes saturated due to the gradual increase of the transaction arrival rate of the random, and the fact that the Tangle consensus algorithm is designed for the block chain scene of the Internet of things under the condition of large flow is indirectly verified. The transaction throughput of the block chain system authenticated to be transacted in unit time is shown in the authentication time delay of the transaction according to fig. 5, and in the initial low transaction arrival stage, the transaction throughput is greatly improved by the method adopted by the invention, and then the throughput of the two approaches to be smooth and the difference is gradually reduced.
In the description of the present invention, it is to be understood that the terms "coaxial", "bottom", "one end", "top", "middle", "other end", "upper", "one side", "top", "inner", "outer", "front", "center", "both ends", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "disposed," "connected," "fixed," "rotated," and the like are to be construed broadly, e.g., as meaning fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; the terms may be directly connected or indirectly connected through an intermediate, and may be communication between two elements or interaction relationship between two elements, unless otherwise specifically limited, and the specific meaning of the terms in the present invention will be understood by those skilled in the art according to specific situations.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. A DAG-based method for updating a block chain system authentication threshold, the method comprising:
constructing a block chain system based on a DAG consensus algorithm in a point-to-point mode;
modeling a process from the generation of the transaction to the authentication of the transaction by the node by using a queuing model, and establishing a process from the generation of the transaction to the authentication of the transaction by using an M/M/n model, wherein two M sequentially represent time interval distribution of transaction arrival time interval distribution and time interval distribution of transaction departure time interval distribution; n represents the number of queues into the blockchain for each transaction; calculating the node transaction arrival rate of the current stage and the transaction arrival rate of the node entering the blockchain system through the M/M/n model to obtain the successful service of the transaction in the queue iProbability PiExpressed as:
Figure FDA0003500644570000011
wherein λ iskAnd mukRespectively representing the arrival rate and the departure rate of the transaction in the kth stage; p0Representing the probability of success of the initial queue service;
under the arrival condition of steady-state transaction, calculating the cumulative weight of the transaction issued by each node;
minimizing the difference between the authentication threshold given by the block chain system and the accumulated weight of the node issued transaction to obtain the accumulated weight of the corresponding node issued transaction, thereby calculating the corresponding transaction authentication delay;
acquiring an updating rule of the authentication threshold by using a random distribution function according to the transaction authentication delay;
and if the transaction arrival rate of the current stage triggers the updating rule, updating the system authentication threshold, otherwise, continuously solving the transaction authentication delay to obtain the updating rule.
2. The method of claim 1, wherein the node issues a calculation formula of transaction accumulation weight, the calculation formula comprising:
Figure FDA0003500644570000021
wherein the content of the first and second substances,
Figure FDA0003500644570000022
indicating that in the kth stage, the nth node issues transaction accumulated weight; r isnRepresenting the computational power of the nth node; n represents the number of nodes participating in the consensus process; lambda [ alpha ]1' an exponential distribution variable representing the transaction arrival time interval of the first node.
3. The method for updating the authentication threshold of the DAG-based blockchain system according to claim 1, wherein the calculation formula of the transaction authentication delay comprises:
Figure FDA0003500644570000023
wherein, TdIndicating a transaction authentication time delay;
Figure FDA0003500644570000024
indicating that in the kth stage, transaction cumulative weights are issued from the nth node; lambda'kAn exponential distribution variable representing the transaction arrival time interval at the kth stage; r isnRepresenting the computational power of the nth node; n represents the number of nodes participating in the consensus process.
4. The method as claimed in claim 1, wherein the update rule for obtaining the authentication threshold using the random distribution function is represented as:
Figure FDA0003500644570000025
wherein, W(k+1)tRepresents the authentication threshold at the k +1 th phase, i.e. the next phase; n represents the number of nodes participating in the consensus process; beta represents the total number of transactions issued by the node in the kth stage, namely the current stage; deltakAn alrong distribution parameter representing a kth stage; alpha represents the target time spent by the node in issuing beta transactions; wktRepresenting the authentication threshold at the kth stage.
5. The method of claim 4, wherein the total number of transactions issued by the node at the kth stage comprises:
Figure FDA0003500644570000026
wherein λ iskRepresenting the node transaction arrival rate at the kth stage.
6. The method as recited in claim 1, wherein triggering the update rule by the arrival rate of the transactions at the current stage comprises triggering the update rule when the difference between the number of transactions entering the blockchain system and their expected value is greater than their variance at the kth stage.
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