CN114500046A - Consensus algorithm based on field area network and IOTA - Google Patents

Consensus algorithm based on field area network and IOTA Download PDF

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CN114500046A
CN114500046A CN202210092079.XA CN202210092079A CN114500046A CN 114500046 A CN114500046 A CN 114500046A CN 202210092079 A CN202210092079 A CN 202210092079A CN 114500046 A CN114500046 A CN 114500046A
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张秀贤
陈勐勐
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Nanjing Xiaozhuang University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00—Network arrangements or protocols for supporting network services or applications
    • H04L67/01—Protocols
    • H04L67/10—Protocols in which an application is distributed across nodes in the network
    • 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
    • H04L63/08—Network architectures or network communication protocols for network security for authentication of entities
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/06—Authentication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/08—Access security
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W74/00—Wireless channel access
    • H04W74/08—Non-scheduled access, e.g. ALOHA
    • H04W74/0808—Non-scheduled access, e.g. ALOHA using carrier sensing, e.g. carrier sense multiple access [CSMA]
    • H04W74/0816—Non-scheduled access, e.g. ALOHA using carrier sensing, e.g. carrier sense multiple access [CSMA] with collision avoidance

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Abstract

The invention discloses a consensus algorithm based on a field area network and an IOTA (internet of things), which comprises the steps of firstly establishing an IOTA consensus time analysis model in the field area network; the IOTA consensus time calculation in the field area network comprises the time for writing the transaction into the tan gle, the time for transmitting the transaction in the network and the consensus time; then establishing a parasitic chain attack success probability analysis model, and analyzing and calculating the ratio of the calculation power required by the malicious node to the total calculation power of the honest nodes in the network if the malicious node wants to attack successfully on the basis of the known honest node event arrival rate; finally, on the basis of the analysis model, a new blockchain consensus algorithm for reducing consensus time by reducing the tan gle writing time is provided, and the IOTA nodes and the adjacent terminals form a cluster; all members of the cluster cooperate to complete the task, the calculation result is returned to the IOTA node, and then the IOTA node writes the data into the angle, so that the consensus time of the network is reduced.

Description

Consensus algorithm based on field area network and IOTA
Technical Field
The invention relates to the technical field of wireless communication, in particular to a consensus algorithm based on a field area network and an IOTA.
Background
With the large-scale development of renewable energy distributed power generation, the next generation of power grid, i.e., smart grid, has been developed by integrating the current information network and information system with the conventional energy network into a new power grid system. However, the current smart grid still faces some challenges, such as lack of effective transaction trust between consumers and renewable energy power generation, difficulty in achieving dynamic balance of energy supply and demand, emergence of network physical security threats, and security of large-scale data sharing. To address these challenges, many researchers are investigating the applicability of blockchain techniques in SGs. For example, the block chain has some important application fields in SG, and can effectively solve the following problems: 1) enabling trusted distributed energy transactions, 2) overcoming privacy and security related challenges, 3) remotely controlling energy flow for a particular area by monitoring usage statistics for the particular area, and 4) assisting in diagnosis and maintenance of SG devices.
However, in SGs with millions of distributed wireless terminals, the selection of block chains is an important issue. It is well known that the consistency algorithm plays a key role in the security and consistency of blockchains. Current popular consensus algorithms include proof of workload (PoW), proof of rights and interests (PoS), and Practical Byzantine Fault Tolerance (PBFT). The core idea of PoW is competition for computing power. Miners continue to hash for the right to generate additional blocks, and this is not the case for poorly computing SGs. PoS determines the probability of the participant gaining accounting rights by evaluating the number and duration of tokens held. In PoS, the higher the probability that a participant with a higher coin age will obtain the right to create a new tile, which may lead to monopoly. In PBFT, there is a primary node in the PBFT consensus mechanism, and the rest of the nodes are generally called replicas. The client sends a request to the master node, and then all honest replica nodes execute the sequence of all transaction requests in the blockchain network by running a protocol consisting of three phases of pre-preparation, preparation and commit. The PBFT consensus algorithm has a high consensus speed, but needs to know the number of all participants in advance, is difficult to expand and is not suitable for SG.
Therefore, due to the inherent characteristics of large SG network size, fast access, limited computing resources, frequent transactions, etc., the conventional consensus algorithm cannot be effectively applied to the network. Therefore, there is a need to develop a consensus algorithm that is resource efficient, low cost, high transaction throughput, and supports concurrency. The IOTA is developed specifically for the internet of things, has a Directed Acyclic Graph (DAG) consensus mechanism, breaks the single chain structure of the consensus mechanism, and allows all nodes to insert new transactions into the distributed ledger immediately after processing and verifying previous transactions. Tangle is a third generation blockchain based on the DAG architecture. The advantage of Tangle is: 1) no transaction fee; 2) reducing resources; 3) reducing the verification delay of the transaction; 4) greater network throughput. The IOTA system is therefore well suited for SG networks.
However, the current research on the problem is mainly focused on a specific consensus algorithm, and a consensus time analysis model aiming at different network scales and different transmission protocols is lacked.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a consensus algorithm based on a field area network and an IOTA, comprehensively considers the number of data wireless transmission hops, a communication protocol and the number of selected tips, establishes a success probability analysis model of field area network consensus time and parasitic chain attack, solves the problem of SG network data and transaction security sharing, and provides a new block chain consensus algorithm on the basis, thereby reducing transaction delay and improving system throughput.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a consensus algorithm based on a field area network and an IOTA comprises the following steps:
step S1, establishing an IOTA consensus time analysis model in the field network; the IOTA consensus time calculation in the field area network comprises the time for writing the transaction into the tan gle, the time for transmitting the transaction in the network and the consensus time; in particular, the amount of the solvent to be used,
step S1.1, trading the time for writing into the angle;
the time that the transaction writes into tandles correlates with the amount of work done to demonstrate the PoW difficulty and the computing power of the device; when a transaction is written into the tangle, firstly selecting unverified transaction tips in the tangle for verification, then performing PoW calculation, finally writing data into the local tangle, and broadcasting the calculation result and the selected tips to the IOTA network; ignoring the verification time of tips, and taking the calculation time of the PoW as the time for writing the transaction into the tan gle;
step S1.2, trading the time of transmission in the network;
selecting a Gossip protocol for transaction transmission, and periodically forwarding the transaction owned by the node but not owned by the adjacent node to the adjacent node; the neighbor node receiving the forwarding message repeats the forwarding step; finally, the transaction information is transmitted to the whole network through forwarding of a plurality of rounds; the transmission time of the transaction, namely the transmission hop number of the transaction in the network is multiplied by the transmission time delay of each hop; neglecting the transmission delay of the wired network, wherein the transmission delay of each hop of the network in the field domain network FAN is the transmission delay in the wireless mesh network mesh; s1.3, consensus achievement time;
the time to reach consensus is the time from when the transaction first exists in all IOTA nodes until each tips can see it, i.e., the time required for the tips to be selected for verification; after the IOTA node writes the transaction into the angle, when the tips number of the transaction is verified to be equal to the prompt number in the network, the consensus is achieved, and the transaction cannot be changed;
step S2, establishing a parasitic chain attack success probability analysis model;
the parasitic chain attack success probability analysis model refers to a closed expression of the probability of the parasitic chain attack success, the honest node event arrival rate and the malicious node event arrival rate; in particular, the amount of the solvent to be used,
as shown in fig. 5, the node first sends a transaction a, and after the transaction is completed consistently, the node receives the material corresponding to the transaction; at the moment, the node sends a double-flower transaction b, when the final accumulated weight of the transaction b is greater than a, the transaction a is abandoned, and the attack is successful at the moment; if the parasitic chain selects transaction d initiated after the consensus completion time for verification, transaction b verifies transaction a; each transaction that verifies transaction b indirectly verifies transaction a, at which point the parasitic chain attack cannot succeed; the transaction selected by the parasitic chain should therefore be a transaction initiated before the agreed upon completion time; after the transaction is selected, attack can be successful only by constructing that the cumulative weight of the parasitic chain is larger than that of the transaction a; calculating the proportion of the calculated amount required by the malicious node when the attack is successful to the calculated amount of the whole network, so as to obtain the probability of successful attack;
step S3, establishing a block chain consensus algorithm based on a field area network and an IOTA;
the IOTA node and the adjacent terminal are combined into a cluster; the terminal sends the transaction to the IOTA node; when the IOTA node receives enough transactions, the IOTA node packs all the transactions and distributes PoW tasks to terminals in the cluster; all members in the cluster collaboratively complete respective tasks, the calculation result is returned to the IOTA node, and the IOTA node writes data into the tandle.
Further, the specific calculation method of the transaction writing time of the tan gle in the step S1.1 is as follows:
setting the number of nodes in the IOTA network as N, when a node i has a transaction written into a tan gle, firstly selecting k tips for verification, then performing PoW calculation, finally writing data into a local tan gle, broadcasting the calculation result and the selected tips to the IOTA network, and writing the transaction of the node i into the time tiComprises the following steps:
Figure BDA0003489573490000031
wherein d isPiFor the number of calculation cycles of PoW, fiIs the computing power of node i; the average time interval h for a transaction to write a local angle is:
Figure BDA0003489573490000032
the specific calculation method of the time of the transaction transmitted in the network in step S1.2 is as follows:
for an IOTA network with N nodes, setting that each node has m +1 neighbors, transmitting to m neighbors each time, setting the average time of transmission of each hop as T, and the probability of successful reception of an event as p, and then the network transmission is equivalent to pm cross tree, and the total transmission hop number is:
L＝logpm(pmN-N+1)-1
the total transmission time is LT;
based on an 802.11MAC broadcast protocol and a Gaussian channel, when data is saturated, calculating the average transmission time T of each hop;
when a node has a data packet to send, the node starts to monitor the channel state, when the idle time of the channel is detected to exceed a distributed frame interval (DIFS), the node enters a backoff stage, otherwise, the node is in the channel monitoring state all the time; after the node enters a backoff stage, randomly selecting a backoff time slot value and starting a backoff counter; when the channel is in an idle state, the backoff counter is decreased by taking a time slot as a unit along with the idle time of the channel, and a data packet is sent until the backoff counter is zero; when the channel is busy in the backoff counter decrementing process, the backoff counting process is frozen, the node monitors the channel again until the channel idle time exceeds DIFS, and returns to the backoff stage again and continues the frozen backoff decrementing process;
setting a back-off time setting range to {1-w0The probability tau of the node transmitting data is 2/(w)0+1), probability p of successful transmission of data in one virtual slots＝nτ(1-τ)n-1The probability of channel being idle is pi＝(1-τ)nProbability of busy channel is pbsy＝1-pi＝1-(1-τ)nWherein n is the number of nodes which are likely to generate collision; within a virtual time slot, the probability of collision is pc＝1-ps-piWhen the channel successfully transmits data or a collision occurs, the transmission delay of the data comprises: data transmission delay LenThe method comprises the following steps of/r, waiting time delay DIFS before distributed frame transmission and propagation time delay delta; wherein L isenThe total length of the frame comprises an MAC data packet header and a physical data packet header, and r is a sending rate; delay T for busy channel due to successful transmissionsAnd a time delay T of channel busy caused by collisioncComprises the following steps:
Figure BDA0003489573490000041
the latency required for each technique of the backoff counter includes: when the channel is idle, the back-off counter is reduced by 1 every time, the time interval is one physical time slot sigma, when the channel successfully transmits data, the back-off counter is frozen, and the waiting time is TsAnd when the channel is collided, the back-off counter is frozen, and the waiting time is Tc(ii) a The backoff counter therefore waits for an interval of time on average:
t0＝(1-pbsy)σ+psTs+pcTc
t0namely a virtual time slot; the initial value D of the back-off timer is set to {1-w0Are evenly distributed, then E [ D ]]＝(w0+ 1)/2; for n nodes which are likely to generate collision, the timer performs 1-down counting after setting the initial value, and the back-off time E [ D ] of each node is averagedn]＝(w0+1)/2n, the average time delay for transmitting a data frame is:
Figure BDA0003489573490000042
setting packet size of IOTA to LpOne data frame of size LenThen, the average time to transmit an IOTA packet is:
Figure BDA0003489573490000051
calculating the probability of successful reception of the IOTA data packet by adopting M-system QAM codes; the bit error rate is expressed as follows:
Figure BDA0003489573490000052
wherein E isb/N0For the purpose of the signal-to-noise ratio,
Figure BDA0003489573490000053
by the probability of data transmission errors being
Figure BDA0003489573490000054
The data transmission failure includes data transmission error or collision, and therefore, the probability of the data transmission failure is: p is a radical ofr＝pc+pe-pc*peThe probability of successfully transmitting an IOTA packet is:
Figure BDA0003489573490000055
the method for calculating the consensus reaching time in the step S1.3 is as follows:
in tangle, the total number of tips R0Maintaining a stable state, and satisfying:
Figure BDA0003489573490000056
at the time t-h, the number of tips is R0At time t, the number of tips is still R0And during the h period, the number of event arrivals is λ h, where
Figure BDA0003489573490000057
Thus, for a tips at time t-h, the probability of a transaction having been verified at time t is
Figure BDA0003489573490000058
Setting the time t-h, and verifying that the tips number of the sitesi is psi (t-h); wherein the verified transaction is called sitesi and the unverified transaction is noted as tipsi; tips at time t-h, and the set that has been verified at time t is: i a i p ψ (t-h) (k-1) ψ (t-h)/k; tips at time t-h and the set of still tips at time t are: i | (1-p) ψ (t-h) ═ ψ (t-h)/k; the tips set without verification of sitesi at time t-h is | C |; at the time of t-h, when a transaction arrives, k tips are required to be selected from all tips for verification, and if the selected tips are in psi (t-h), the newly arrived transaction indirectly verifies sitei; if k tips are all selected from the set B, verifying that the number of tips of sitesi is reduced by k-1; k tips are selected from the set B to be k-1, one of A or C is selected, the number of tips for verifying the sitesi is reduced by k-2, and by analogy, k tips are not selected from B, and at least one selected A is added with 1 when the number of tips for verifying the sitesi at the time t is selected; the following probabilities can be obtained:
+1：
Figure BDA0003489573490000061
Figure BDA0003489573490000062
-1：
Figure BDA0003489573490000063
Figure BDA0003489573490000064
-2：
Figure BDA0003489573490000065
Figure BDA0003489573490000066
……
-(k-1)：
Figure BDA0003489573490000067
ignore
Figure BDA0003489573490000068
To obtain the growth rate of ψ (t):
Figure BDA0003489573490000069
since ψ (0) is 1, set
Figure BDA00034895734900000610
Can obtain the product
Figure BDA00034895734900000611
Wherein the content of the first and second substances,
Figure BDA00034895734900000612
is a lambobo function;
namely:
Figure BDA00034895734900000613
Figure BDA00034895734900000614
order:
Figure BDA00034895734900000615
Figure BDA00034895734900000616
when psi (t) ═ R0Then, sitei agrees, and the agreement agrees in time:
Figure BDA00034895734900000617
when network transmission delay is ignored, the consensus time is as follows:
Figure BDA00034895734900000618
when the network transmission is added, delaying, writing a transaction into the angle by a node i in the network at a certain moment, wherein the tipsi is only visible in the local angle of the node i before the tipsi is transmitted to other nodes, and when other new transactions arrive, only the transactions arriving in the node i can select the tipsi as a father node; when data is put in a local angle but is not transmitted to a neighbor node, namely T < T, the number of tips for verifying the tipsi is psi (T) ═ 1/N exp (at/h), when T <2T, the tipsi is transmitted to pm neighbor nodes, at the moment, the number of tips for verifying the tipsi is psi (T) ═ 1/N exp (at/h) + (pm/N) exp (a (T-T)/h), and the same can be obtained, and in the period from the time when the transaction is written into the angle for the first time to the time when the broadcast in the network is completed, the number of tips for verifying the tipsi is:
Figure BDA0003489573490000071
order to
Figure BDA0003489573490000072
Figure BDA0003489573490000073
After the broadcast is completed: the value of ψ (t) at time LT is the initial value of t ≧ LT,
Figure BDA0003489573490000074
Figure BDA0003489573490000075
wherein, t0For the time from the data writing into the angle to the completion of the consensus, when ψ (t) ═ R0Then, sitei agrees, so agreement is reached for time tcComprises the following steps:
Figure BDA0003489573490000076
under the condition that the network transmission delay is not negligible, the consensus time is as follows:
Figure BDA0003489573490000077
further, the specific method for establishing the parasitic chain attack success probability analysis model in the step S2 is as follows:
setting the event arrival rate of honest nodes as lambda and the event arrival rate of malicious nodes as mu, the cumulative weight when transaction a reaches consensus is phi (t)0) Wherein t is0The time it takes for the transaction to write a match to a consensus;
for honest nodes, after consensus is achieved, as things issued by each honest node verify tips which are already known, the growth rate of the cumulative weight is lambda and the growth rate of the cumulative weight of transaction b is mu after consensus is achieved for transaction a; setting the time of transaction a release as T1Parasitic chain start time is T2(ii) a If T2After the consensus completion time t of the transaction a, the transaction b verifies the transaction a, namely, each transaction of the verification transaction b indirectly verifies the transaction a, the parasitic chain attack cannot be successful, and therefore, the parasitic chain starting time is smaller than the consensus completion time t0(ii) a When the transaction a consensus is reached, the cumulative weight of the parasitic chain is μ (t)0-T2) The cumulative weight of honest nodes is phi (t)0-T1) (ii) a Thus, if the attack is successful, after consensus is achieved, the parasitic chain cumulative weight should be greater than the honest node cumulative weight, i.e., (t)0-T1)-μ(t0-T2)<0; setting T1＝T20, i.e. the parasitic chain starts to prepare when transaction a writes a, then (t)0)-μ(t0)<0; next, the cumulative weight phi (t) at the time of completion of consensus is calculated separately0) And the probability that the parasitic chain transaction a starts to prepare and attack successfully at the moment of writing into the tan gle;
cumulative weight at transaction consensus completion: when a new transaction arrives, at least one of the k tips verifies sitei, the new transaction can indirectly verify the sitei, and the cumulative weight of the sitei is added with 1; the probability of at least one tips verification site i is 1- (1-psi (t-h)/R0)k
Figure BDA0003489573490000081
Where φ (t) is the cumulative weight;
Figure BDA0003489573490000082
Figure BDA0003489573490000083
the following can be obtained:
Figure BDA0003489573490000084
wherein the content of the first and second substances,
Figure BDA0003489573490000085
Figure BDA0003489573490000086
by the nature of the omega function
Figure BDA0003489573490000087
The following can be obtained:
Figure BDA0003489573490000088
thus, the cumulative weight φ (t) can be calculated as:
Figure BDA0003489573490000089
since the weight accumulation time is mainly in the data transmission stage and the consensus achievement stage, t in the above formula is the sum of the data transmission time and the accumulated weight time0The cumulative weight is expressed as follows:
Figure BDA0003489573490000091
probability of success of parasitic chain attack: as the honest nodes conform to Poisson distribution with the event arrival rate of lambda, the time intervals of the adjacent things of the honest nodes are independent and equally distributed exponential variables, and the 1/lambda exponential distribution is obeyed; in the same way, the time interval of the adjacent things of the malicious node is 1/mu of independent and identically distributed index variable; the following can be obtained:
Figure BDA0003489573490000092
Figure BDA0003489573490000093
when mu is>When the value is more than or equal to lambda, the cumulative weight of transaction b is more than that of transaction a, and the attack success is possible, namely phi (t)0)-μ(t0)>0; when the attack is successful, the malicious node should catch up the difference phi (t) of the parasitic chain and the cumulative weight of the verification transaction a0)-μ(t0) Thus, the probability of success of a parasitic chain attack is:
Figure BDA0003489573490000094
further, the establishing of the blockchain consensus algorithm based on the field area network and the IOTA in the step S3 specifically includes: an IOTA node and adjacent terminals form a cluster. The terminal sends a transaction to the IOTA node. When the IOTA node receives enough transactions, it will bundle all transactions and distribute the PoW tasks to the terminals in the cluster. All members of the cluster cooperate with each other to complete respective tasks, a calculation result is returned to the IOTA node, and then the IOTA node writes data into a chaotic node. Thus, the workload of the IOTA node, and the time required to write data to the chaotic data, can be significantly reduced.
After clustering, data can be written into the tandle only after the transaction reaches the maximum value of the IOTA data packet, and then the data collection time is as follows:
Figure BDA0003489573490000095
wherein n istIs the average number of transactions in a data packet, NgIs the number of nodes in a cluster, λiEvent arrival rate for node i; the time for writing data into the tandle is mainly PoW calculation time, and the PoW after clustering is completed cooperatively by members in the cluster, so the time for writing data into the tandle is as follows:
Figure BDA0003489573490000101
wherein d isPiNumber of calculation cycles for PoW calculation, FiTotal computing power for cluster i
Figure BDA0003489573490000102
The average time interval for the event to write to the local tangle is:
Figure BDA0003489573490000103
because data only needs to be transmitted to the IOTANode node in the network, the time for transmitting the data in the network is less than or equal to the transmission time when the data are not clustered, and the maximum transmission time LT is taken;
the consensus time is:
Figure BDA0003489573490000104
wherein
Figure BDA0003489573490000105
Consensus time is expressed as follows:
Figure BDA0003489573490000106
has the advantages that:
the consensus algorithm based on the field area network and the IOTA provided by the invention is aimed at a large-scale distributed wireless network of SG, an IOTA analysis model is established under the condition of considering network transmission delay, a basis is provided for block chain application analysis of the distributed wireless network, a closed expression of consensus time of parasitic chain attack success probability is further deduced, a basis is provided for calculation of the block chain consensus time of the distributed wireless network and probability analysis of parasitic chain attack, a novel consensus algorithm for node clustering and coordinated completion of PoW among nodes is finally provided, the IOTA consensus time is reduced, and the transaction efficiency is improved.
Drawings
FIG. 1 is a schematic view of the Tangle structure;
FIG. 2 is a system model diagram of the consensus algorithm provided by the present invention;
FIG. 3 is a schematic diagram of a tips selection algorithm in an embodiment of the present invention;
FIG. 4 is a schematic diagram of tips locations selected for a parasitic chain attack in an embodiment of the present invention;
fig. 5 is a schematic diagram of a parasitic chain attack time point in an embodiment of the invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all 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 invention comprehensively considers the number of data wireless transmission hops, the communication protocol and the number of selected tips, establishes a field area network consensus time and a success probability analysis model of parasitic chain attack, and provides a new block chain consensus algorithm on the basis, as shown in figure 2. The method specifically comprises the following steps:
and step S1, establishing an IOTA consensus time analysis model in the field area network. The IOTA consensus time calculation in the LAN includes the time when the transaction is written into the tan gle, the time when the transaction is transmitted in the network and the consensus time. In particular, the amount of the solvent to be used,
step S1.1, transact the time for writing the tan gle.
The time a transaction writes a tan gle is related to the amount of work done to justify the difficulty of the PoW and the computing power of the device. When a node has a transaction written into the angle, tips are selected to be verified, then PoW calculation is carried out, finally data are written into the local angle, and the calculation result and the selected tips are broadcasted to the IOTA network. Since the tips verification time is negligible compared with the PoW calculation time, the time required from the selection of tips by the node i to the successful writing of the event into the local angle is mainly the PoW calculation time, and the PoW calculation time is used as the time for writing the transaction into the angle.
Setting the number of nodes in the IOTA network as N, when a node i has a transaction written in the tandle, firstly selecting k tips for verification, then performing PoW calculation, finally writing data in the local tandle, broadcasting the calculation result and the selected tips to the IOTA network, and writing the transaction of the node i into the time tiComprises the following steps:
Figure BDA0003489573490000111
wherein d isPiNumber of cycles for calculation of PoW, fiIs the computational power of node i. The average time interval h for a transaction to write a local angle is:
Figure BDA0003489573490000112
step S1.2, time of transmission in the network is traded.
And selecting a Gossip protocol for transaction transmission, and periodically forwarding the transaction owned by the node but not owned by the adjacent node to the adjacent node. The neighbor node that receives the forwarding message repeats the forwarding step. The transaction information is ultimately communicated throughout the network by forwarding through multiple rounds. The transmission time of the transaction, i.e. the number of transmission hops of the transaction in the network, is multiplied by the transmission delay per hop. Neglecting the transmission delay of the wired network, the transmission delay of each hop of the network in the FAN is the transmission delay in the mesh.
For an IOTA network with N nodes, setting that each node has m +1 neighbors, transmitting to m neighbors each time, setting the average time of transmission of each hop as T, and the probability of successful reception of an event as p, and then the network transmission is equivalent to pm cross tree, and the total transmission hop number is:
L＝logpm(pmN-N+1)-1
the total transmission time is LT.
Based on the 802.11MAC broadcast protocol, gaussian channel, when the data is saturated, the average transmission time per hop T is calculated.
When a node has a data packet to send, the node starts to monitor the channel state, when the idle time of the channel is detected to exceed a distributed frame interval DIFS, the node enters a backoff stage, otherwise, the node is in the channel monitoring state all the time. And after the node enters a backoff stage, randomly selecting a backoff time slot value and starting a backoff counter. When the channel is in an idle state, the backoff counter is decreased by taking a time slot as a unit along with the idle time of the channel, and the data packet is transmitted until the backoff counter is zero. And when the channel is busy in the backoff counter decrementing process, freezing the backoff counting process, and monitoring the channel again by the node until the channel idle time exceeds DIFS, returning to the backoff stage again and continuing the frozen backoff decrementing process.
Setting a back-off time setting range to {1-w0The probability tau of the node transmitting data is 2/(w)0+1), probability p of successful transmission of data in one virtual slots＝nτ(1-τ)n-1The probability of channel being idle is pi＝(1-τ)nProbability of busy channel is pbsy＝1-pi＝1-(1-τ)nAnd n is the number of nodes which can generate collision. Within a virtual time slot, the probability of collision is pc＝1-ps-piWhen the channel successfully transmits data or a collision occurs, the transmission delay of the data comprises: data transmission delay Len/r, latency DIFS before transmission of the distributed frame and propagation delay δ. Wherein L isenThe total length of the frame includes a MAC data packet header and a physical data packet header, and r is the transmission rate. Delay T for busy channel due to successful transmissionsAnd a time delay T of channel busy caused by collisioncComprises the following steps:
Figure BDA0003489573490000121
the latency required by the backoff counter per technique includes: when the channel is idle, the back-off counter is reduced by 1 every time, the time interval is one physical time slot sigma, when the channel successfully transmits data, the back-off counter is frozen, and the waiting time is TsAnd when the channel is collided, the back-off counter is frozen, and the waiting time is Tc. The backoff counter therefore waits for an interval of time on average:
t0＝(1-pbsy)σ+psTs+pcTc
t0i.e. a virtual time slot. The initial value D of the back-off timer is set to {1-w0Are evenly distributed, then E [ D ]]＝(w0+1)/2. For n nodes which are likely to generate collision, the timer performs 1-down counting after setting the initial value, and the back-off time E [ D ] of each node is averagedn]＝(w0+1)/2n, the average time delay for transmitting a data frame is:
Figure BDA0003489573490000131
setting packet size of IOTA to LpOne data frame of size LenThen, the average time to transmit an IOTA packet is:
Figure BDA0003489573490000132
and calculating the probability of successful reception of the IOTA data packet by adopting M-ary QAM codes. The bit error rate is expressed as follows:
Figure BDA0003489573490000133
wherein E isb/N0For the purpose of the signal-to-noise ratio,
Figure BDA0003489573490000134
by the probability of data transmission errors being
Figure BDA0003489573490000135
The data transmission failure includes data transmission error or collision, and therefore, the probability of the data transmission failure is: p is a radical of formular＝pc+pe-pc*peThe probability of successfully transmitting an IOTA packet is:
Figure BDA0003489573490000136
and S1.3, consensus achievement time.
The agreed-upon time is the time it takes for each tips to see it from the first time the transaction exists in all IOTA nodes, i.e., the time it takes for the tips to be selected for verification. After the IOTA node writes the transaction into the angle, when the tips number of the transaction is verified to be equal to the prompt number in the network, the consensus is achieved, and the transaction cannot be changed.
In tangle, the total number of tips R0Is maintained in a stable state and satisfies the following conditions:
Figure BDA0003489573490000137
at the time t-h, the number of tips is R0At time t, the number of tips remains R0And in hWithin the time period, the number of event arrivals is λ h, where
Figure BDA0003489573490000138
Thus, for a tips at time t-h, the probability of a transaction having been verified at time t is
Figure BDA0003489573490000139
As shown in FIG. 3, the number of tips of the verified sitesi is set to ψ (t-h) at time t-h. Where the transaction that has been validated is called sitesi and the unverified transaction is noted as tipsi. Tips at time t-h, and the set that has been verified at time t is: i a | ═ p ψ (t-h) ═ k-1 ψ (t-h)/k. Tips at time t-h and the set of still tips at time t are: i B | (1-p) ψ (t-h) | ψ (t-h)/k. At the time of t-h, the tips set of sitesi is not verified to be | C |; at time t-h, when a transaction arrives, k tips from all tips need to be selected for verification, and if the selected tips are in ψ (t-h), the newly arrived transaction will indirectly verify sitei. If all k tips are selected from set B, the number of tips verifying sitesi is reduced by k-1. And selecting k-1 tips from the set B by k tips, selecting one from A or C, reducing the number of the tips for verifying sitesi by k-2, and repeating the steps until k tips are not selected from B, and if at least one tip is selected from A, adding 1 to the number of the tips for verifying the sitesi at the time t. The following probabilities can be obtained:
+1：
Figure BDA0003489573490000141
Figure BDA0003489573490000142
-1：
Figure BDA0003489573490000143
Figure BDA0003489573490000144
-2：
Figure BDA0003489573490000145
Figure BDA0003489573490000146
……
-(k-1)：
Figure BDA0003489573490000147
ignore
Figure BDA0003489573490000148
To obtain the growth rate of ψ (t):
Figure BDA0003489573490000149
since psi (0) is equal to 1, setting
Figure BDA00034895734900001410
Can obtain the product
Figure BDA00034895734900001411
Wherein the content of the first and second substances,
Figure BDA00034895734900001412
is a lambert omega function.
Namely:
Figure BDA00034895734900001413
Figure BDA00034895734900001414
order:
Figure BDA00034895734900001415
Figure BDA0003489573490000151
when psi (t) ═ R0Then, sitei achieves consensus, the consensus time is:
Figure BDA0003489573490000152
when network transmission delay is ignored, the consensus time is as follows:
Figure BDA0003489573490000153
when the network transmission is added, delay is delayed, at a certain moment, a node i in the network writes a transaction into the angle, at the moment, before the tipsi is transmitted to other nodes, the tipsi is only visible in the local angle of the node i, and when other new transactions arrive, only the transactions arriving in the node i can select the tipsi as a father node. When data is put in a local angle but is not transmitted to a neighbor node, namely T < T, the number of tips for verifying the tipsi is psi (T) ═ 1/N exp (at/h), when T <2T, the tipsi is transmitted to pm neighbor nodes, at the moment, the number of tips for verifying the tipsi is psi (T) ═ 1/N exp (at/h) + (pm/N) exp (a (T-T)/h), and the same can be obtained, and in the period from the time when the transaction is written into the angle for the first time to the time when the broadcast in the network is completed, the number of tips for verifying the tipsi is:
Figure BDA0003489573490000154
order to
Figure BDA0003489573490000155
Figure BDA0003489573490000156
After the broadcast is completed: the value of ψ (t) at time LT is the initial value of t ≧ LT,
Figure BDA0003489573490000157
Figure BDA0003489573490000158
wherein, t0For the time from the data writing into the angle to the completion of the consensus, when ψ (t) ═ R0Then, sitei agrees, so agreement is reached for time tcComprises the following steps:
Figure BDA0003489573490000159
under the condition that the network transmission delay is not negligible, the consensus time is as follows:
Figure BDA0003489573490000161
and step S2, establishing a parasitic chain attack success probability analysis model.
The parasitic chain attack success probability analysis model refers to a closed expression of the probability of the parasitic chain attack success, the honest node event arrival rate and the malicious node event arrival rate. In particular, the amount of the solvent to be used,
as shown in fig. 5, the node first sends a transaction a, and after the transaction is completed, the node receives the material corresponding to the transaction. At the moment, the node sends a double-flower transaction b, when the final accumulated weight of the transaction b is greater than a, the transaction a is abandoned, and the attack is successful. Transaction b validates transaction a if the parasitic chain chooses to validate transaction d initiated after the consensus completion time. Each transaction that verifies transaction b indirectly verifies transaction a, when a parasitic chain attack is unlikely to succeed. The transaction selected by the parasitic chain should be a transaction initiated before the agreed upon completion time is negotiated. After the transaction is selected, the attack can be successful only by constructing that the cumulative weight of the parasitic chain is larger than that of the transaction a. And calculating the proportion of the calculated amount required by the malicious node when the attack is successful to the calculated amount of the whole network, so as to obtain the probability of successful attack.
Setting the event arrival rate of honest nodes as lambda and the event arrival rate of malicious nodes as mu, the cumulative weight when transaction a reaches consensus is phi (t)0) Wherein t is0The time it takes for the transaction to write a match to reach consensus.
For honest nodes, after consensus is achieved, since things issued by each honest node will verify tips that are already in consensus, the cumulative weight growth rate for transaction a after consensus is achieved is λ, and the cumulative weight growth rate for transaction b is μ. As shown in FIG. 4, the time for transaction a to be issued is set to T1Parasitic chain start time is T2. If T2After the consensus completion time t of the transaction a, the transaction b verifies the transaction a, namely, each transaction of the verification transaction b indirectly verifies the transaction a, the parasitic chain attack cannot be successful, and therefore, the parasitic chain starting time is smaller than the consensus completion time t0. When the transaction a consensus is reached, the cumulative weight of the parasitic chain is μ (t)0-T2) The cumulative weight of honest nodes is phi (t)0-T1). Thus, if the attack is successful, after consensus is achieved, the parasitic chain cumulative weight should be greater than the honest node cumulative weight, i.e., (t)0-T1)-μ(t0-T2)<0. Setting T1＝T 20, i.e. the parasitic chain starts to prepare when transaction a writes a, then (t)0)-μ(t0)<0. Next, the cumulative weight phi (t) at the time of completion of consensus is calculated separately0) And the probability of success of the attack when the parasitic chain transaction a is written into the tangle.
Cumulative weight at transaction consensus completion: when a new transaction arrives, at least one of the k tips selected verifies sitei, the new transaction will indirectly verify sitei, and the cumulative weight of sitei is increased by 1. The probability of at least one tips validating sitei is 1- (1-psi (t-h)/R0)k
Figure BDA0003489573490000171
Where phi (t) is the cumulative weight.
Figure BDA0003489573490000172
Figure BDA0003489573490000173
The following can be obtained:
Figure BDA0003489573490000174
wherein the content of the first and second substances,
Figure BDA0003489573490000175
Figure BDA0003489573490000176
from the properties of the omega function
Figure BDA0003489573490000177
The following can be obtained:
Figure BDA0003489573490000178
thus, the cumulative weight φ (t) can be calculated as:
Figure BDA0003489573490000179
since the weight accumulation time is mainly in the data transmission stage and the consensus achievement stage, t in the above formula is the sum of the data transmission time and the accumulated weight time0The cumulative weight is expressed as follows:
Figure BDA00034895734900001710
probability of success of parasitic chain attack: since honest nodes conform to a Poisson distribution with an event arrival rate of lambda, the 1/lambda exponential distribution is obeyed to exponential variables with time intervals of honest node neighbors being independent and the same distribution. Similarly, the time interval of the malicious node neighbors is 1/mu of independent and equally distributed exponential variable. The following can be obtained:
Figure BDA00034895734900001711
Figure BDA00034895734900001712
when mu is>When the value is more than or equal to lambda, the cumulative weight of transaction b is more than that of transaction a, and the attack success is possible, namely phi (t)0)-μ(t0)>0. When the attack is successful, the malicious node should catch up the difference phi (t) of the parasitic chain and the cumulative weight of the verification transaction a0)-μ(t0) Thus, the probability of success of a parasitic chain attack is:
Figure BDA0003489573490000181
and step S3, establishing a block chain consensus algorithm based on the field area network and the IOTA.
The IOTA nodes and adjacent terminals are grouped into clusters. The terminal sends the transaction to the IOTA node. When the IOTA node receives enough transactions, it packages all transactions and distributes PoW tasks to the terminals in the cluster. All members in the cluster collaboratively complete respective tasks, the calculation result is returned to the IOTA node, and the IOTA node writes data into the tandle.
The algorithm mainly reduces the consensus time by reducing the tan gle writing time, and specifically comprises the following steps: the consensus time is reduced by reducing the tandle write time. The method comprises the steps of clustering nodes in a network, wherein each cluster comprises an IOTA node and a plurality of terminals, the terminals in the cluster send data to the IOTA node, when the IOTA node receives enough data, all the data are packaged, PoW tasks are distributed to the terminals in the cluster, all members in the cluster cooperatively complete the PoW tasks, the calculation result is returned to the IOTA node, and the IOTA node completes the work of writing the data into the symbol. Therefore, the workload of the IOTA node can be greatly reduced, and the time for writing data into the tan gle is reduced.
After clustering, data can be written into the tandle only after the transaction reaches the maximum value of the IOTA data packet, and then the data collection time is as follows:
Figure BDA0003489573490000182
wherein n istIs the average number of transactions in a data packet, NgIs the number of nodes in a cluster, lambdaiIs the event arrival rate of node i. The time for writing data into the tandle is mainly PoW calculation time, and the PoW after clustering is completed cooperatively by members in the cluster, so the time for writing data into the tandle is as follows:
Figure BDA0003489573490000183
wherein d isPiNumber of calculation cycles for PoW calculation, FiTotal computing power for cluster i
Figure BDA0003489573490000184
The average time interval for the event to write to the local tangle is:
Figure BDA0003489573490000185
since data only needs to be transmitted to the IOTA node in the network, the time for data transmission in the network is less than or equal to the transmission time when the data is not clustered, and here, the maximum transmission time LT is taken.
The consensus time is:
Figure BDA0003489573490000191
wherein
Figure BDA0003489573490000192
Consensus time is expressed as follows:
Figure BDA0003489573490000193
the above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (4)

1. A consensus algorithm based on a field area network and an IOTA, characterized by comprising the following steps:
step S1, establishing an IOTA consensus time analysis model in the field network; the IOTA consensus time calculation in the field area network comprises the time of writing a transaction into an IOTA database (the schematic structure diagram of the tan is shown in FIG. 1), the time of transmitting the transaction in the network and the consensus achievement time; in particular, the amount of the solvent to be used,
step S1.1, trading the time for writing into the angle;
the time that the transaction writes into tandles correlates with the amount of work done to demonstrate the PoW difficulty and the computing power of the device; when a transaction is written into the tangle, firstly selecting unverified transaction tips in the tangle for verification, then performing PoW calculation, finally writing data into the local tangle, and broadcasting the calculation result and the selected tips to the IOTA network; ignoring the verification time of tips, and taking the calculation time of the PoW as the time for writing the transaction into the tan gle;
step S1.2, trading the time of transmission in the network;
selecting a Gossip protocol for transaction transmission, and periodically forwarding the transaction owned by the node but not owned by the adjacent node to the adjacent node; the neighbor node receiving the forwarding message repeats the forwarding step; finally, the transaction information is transmitted to the whole network through forwarding of a plurality of rounds; the transmission time of the transaction, namely the transmission hop number of the transaction in the network is multiplied by the transmission time delay of each hop; neglecting the transmission delay of the wired network, wherein the transmission delay of each hop of the network in the field domain network FAN is the transmission delay in the wireless mesh network mesh;
s1.3, consensus achievement time;
the time to reach consensus is the time from when the transaction first exists in all IOTA nodes until each tips can see it, i.e., the time required for the tips to be selected for verification; after the IOTA node writes the transaction into the angle, when the tips number of the transaction is verified to be equal to the prompt number in the network, the consensus is achieved, and the transaction cannot be changed;
step S2, establishing a parasitic chain attack success probability analysis model;
the parasitic chain attack success probability analysis model refers to a closed expression of the probability of the parasitic chain attack success, the honest node event arrival rate and the malicious node event arrival rate; in particular, the amount of the solvent to be used,
as shown in fig. 5, the node first sends a transaction a, and after the transaction is completed consistently, the node receives the material corresponding to the transaction; at the moment, the node sends a double-flower transaction b, when the final accumulated weight of the transaction b is greater than a, the transaction a is abandoned, and the attack is successful at the moment; if the parasitic chain selects transaction d initiated after the consensus completion time for verification, transaction b verifies transaction a; each transaction that verifies transaction b indirectly verifies transaction a, at which point the parasitic chain attack cannot succeed; the transaction selected by the parasitic chain should therefore be a transaction initiated before the agreed upon completion time; after the transaction is selected, attack can be successful only by constructing that the cumulative weight of the parasitic chain is larger than that of the transaction a; calculating the proportion of the calculated amount required by the malicious node when the attack is successful to the calculated amount of the whole network, so as to obtain the probability of successful attack;
step S3, establishing a block chain consensus algorithm based on a field area network and an IOTA;
the IOTA node and the adjacent terminal are combined into a cluster; the terminal sends the transaction to the IOTA node; when the IOTA node receives enough transactions, the IOTA node packs all the transactions and distributes PoW tasks to terminals in the cluster; all members in the cluster collaboratively complete respective tasks, the calculation result is returned to the IOTA node, and the IOTA node writes data into the tandle.
2. The consensus algorithm based on FIELD and IOTA as claimed in claim 1, wherein the specific calculation method of the transaction writing time of the tan gle in step S1.1 is as follows:
setting the number of nodes in the IOTA network as N, when a node i has a transaction written into a tan gle, firstly selecting k tips for verification, then performing PoW calculation, finally writing data into a local tan gle, broadcasting the calculation result and the selected tips to the IOTA network, and writing the transaction of the node i into the time tiComprises the following steps:
Figure FDA0003489573480000021
wherein d isPiFor the number of calculation cycles of PoW, fiIs the computational power of node i; the average time interval h for a transaction to write a local angle is:
Figure FDA0003489573480000022
the specific calculation method of the time of the transaction transmitted in the network in step S1.2 is as follows:
for an IOTA network with N nodes, setting that each node has m +1 neighbors, transmitting to m neighbors each time, setting the average time of transmission of each hop as T, and the probability of successful reception of an event as p, and then the network transmission is equivalent to pm cross tree, and the total transmission hop number is:
L＝logpm(pmN-N+1)-1
the total transmission time is LT;
based on an 802.11MAC broadcast protocol and a Gaussian channel, when data is saturated, calculating the average transmission time T of each hop;
when a node has a data packet to send, the node starts to monitor the channel state, when the idle time of the channel is detected to exceed a distributed frame interval (DIFS), the node enters a backoff stage, otherwise, the node is in the channel monitoring state all the time; after the node enters a backoff stage, randomly selecting a backoff time slot value and starting a backoff counter; when the channel is in an idle state, the backoff counter is decreased by taking a time slot as a unit along with the idle time of the channel, and a data packet is sent until the backoff counter is zero; when the channel is busy in the backoff counter decrementing process, the backoff counting process is frozen, the node monitors the channel again until the channel idle time exceeds DIFS, and returns to the backoff stage again and continues the frozen backoff decrementing process;
setting a back-off time setting range to {1-w0The probability tau of the node transmitting data is 2/(w)0+1), probability p of successful transmission of data in one virtual slots＝nτ(1-τ)n-1The probability of channel being idle is pi＝(1-τ)nProbability of busy channel is pbsy＝1-pi＝1-(1-τ)nWherein n is the number of nodes which are likely to generate collision; within a virtual time slot, the probability of collision is pc＝1-ps-piWhen the channel successfully transmits data or a collision occurs, the transmission delay of the data comprises: data transmission delay LenThe method comprises the following steps of/r, waiting time delay DIFS before distributed frame transmission and propagation time delay delta; wherein L isenThe total length of the frame comprises an MAC data packet header and a physical data packet header, and r is a sending rate; delay T for busy channel due to successful transmissionsAnd a time delay T of channel busy caused by collisioncComprises the following steps:
Figure FDA0003489573480000031
the latency required by the backoff counter per technique includes: when the channel is idle, the time interval is one physical time slot every time the back-off counter is reduced by 1σ, when the channel successfully transmits data, the backoff counter is frozen, with a waiting time TsAnd when the channel is collided, the back-off counter is frozen, and the waiting time is Tc(ii) a The backoff counter therefore waits for an interval of time on average:
t0＝(1-pbsy)σ+psTs+pcTc
t0namely a virtual time slot; the initial value D of the back-off timer is set to {1-w0Are evenly distributed, then E [ D ]]＝(w0+ 1)/2; for n nodes which are likely to generate collision, the timer performs 1-down counting after setting the initial value, and the back-off time E [ D ] of each node is averagedn]＝(w0+1)/2n, the average time delay for transmitting a data frame is:
Figure FDA0003489573480000032
setting packet size of IOTA to LpOne data frame of size LenThen, the average time to transmit an IOTA packet is:
Figure FDA0003489573480000033
calculating the probability of successful reception of the IOTA data packet by adopting M-system QAM codes; the bit error rate is expressed as follows:
Figure FDA0003489573480000034
wherein, Eb/N0For the purpose of the signal-to-noise ratio,
Figure FDA0003489573480000041
by the probability of data transmission errors being
Figure FDA00034895734800000411
The data transmission failure includes data transmission error or collision, and therefore, the probability of the data transmission failure is: p is a radical of formular＝pc+pe-pc*peThe probability of successfully transmitting an IOTA packet is:
Figure FDA0003489573480000042
the method for calculating the consensus reaching time in the step S1.3 is as follows:
in tangle, the total number of tips R0Is maintained in a stable state and satisfies the following conditions:
Figure FDA0003489573480000043
at the time t-h, the number of tips is R0At time t, the number of tips is still R0And during the h period, the number of event arrivals is λ h, where
Figure FDA0003489573480000044
Thus, for a tips at time t-h, the probability of a transaction having been verified at time t is
Figure FDA0003489573480000045
As shown in FIG. 3, the number of tips of sites i is verified to be ψ (t-h) at time t-h; the verified transaction is called sites i, and the unverified transaction is marked as tips i; tips at time t-h, and the set that has been verified at time t is: i a i p ψ (t-h) (k-1) ψ (t-h)/k; tips at time t-h, and the set of still tips at time t is: i | (1-p) ψ (t-h) ═ ψ (t-h)/k; tips of sites i were not verified to be | C |; at the time of t-h, when a transaction arrives, k tips are required to be selected from all tips for verification, and if the selected tips are in psi (t-h), the newly arrived transaction indirectly verifies site i; if all the k tips are selected from the set B, the number of tips of the verification sites i is reduced by k-1; k tips are selected from the set B to be k-1, one of A or C is selected, the number of tips for verifying the sites i is reduced by k-2, and by analogy, k tips are not selected from B, and at least one selected A is added with 1 when the number of tips for verifying the sites i at the time t is selected; the following probabilities can be obtained:
+1：
Figure FDA0003489573480000046
Figure FDA0003489573480000047
-1：
Figure FDA0003489573480000048
Figure FDA0003489573480000049
-2：
Figure FDA00034895734800000410
Figure FDA0003489573480000051
……
-(k-1)：
Figure FDA0003489573480000052
ignore
Figure FDA0003489573480000053
To obtain the growth rate of ψ (t):
Figure FDA0003489573480000054
due to the fact thatPsi (0) is set to 1
Figure FDA0003489573480000055
Can obtain the product
Figure FDA0003489573480000056
Wherein the content of the first and second substances,
Figure FDA0003489573480000057
is a lambobo function;
namely:
Figure FDA0003489573480000058
order:
Figure FDA0003489573480000059
Figure FDA00034895734800000510
when psi (t) is equal to R0Then, site i agrees, and the agreement achieving time is as follows:
Figure FDA00034895734800000511
when network transmission delay is ignored, the consensus time is as follows:
Figure FDA00034895734800000512
when the node I is added into the network for transmission, delaying, writing one transaction into the angle by the node I in the network at a certain moment, wherein the tips i is only visible in the local angle of the node I before the tips i is transmitted to other nodes, and when other new transactions arrive, only the transactions coming in the node I can select the tips i as a father node; when data is put in a local angle but is not transmitted to a neighbor node, namely T is less than T, the number of tips of the verified tips i is psi (T) ═ 1/N exp (at/h), when T is less than 2T, the tips i is transmitted to pm neighbor nodes, at the moment, the number of tips of the verified tips i is psi (T) ═ 1/N exp (at/h) + (pm/N) exp (a (T-T)/h), and the same can be obtained in the same way, during the period from the initial writing of angle in a transaction to the completion of the broadcast in the network, the number of tips of the verified tips i is:
Figure FDA00034895734800000513
Figure FDA0003489573480000061
order to
Figure FDA0003489573480000062
Figure FDA0003489573480000063
After the broadcast is completed: the value of ψ (t) at time LT is the initial value of t ≧ LT,
Figure FDA0003489573480000064
Figure FDA0003489573480000065
wherein, t0For the time from the data writing into the angle to the completion of the consensus, when ψ (t) ═ R0At time, site i agrees, and thus agreement is achieved for time tcComprises the following steps:
Figure FDA0003489573480000066
under the condition that the network transmission delay is not negligible, the consensus time is as follows:
Figure FDA0003489573480000067
3. the consensus algorithm based on a field area network and an IOTA according to claim 1, wherein the specific method for establishing the parasitic chain attack success probability analysis model in the step S2 is as follows:
setting the event arrival rate of honest nodes as lambda and the event arrival rate of malicious nodes as mu, the cumulative weight when transaction a reaches consensus is phi (t)0) Wherein t is0The time it takes for the transaction to write a match to a consensus;
for honest nodes, after consensus is achieved, as things issued by each honest node verify tips which are already known, the growth rate of the cumulative weight is lambda and the growth rate of the cumulative weight of transaction b is mu after consensus is achieved for transaction a; setting the time of transaction a release as T1Parasitic chain start time is T2(ii) a If T2After the consensus completion time t of the transaction a, the transaction b verifies the transaction a, namely, each transaction of the verification transaction b indirectly verifies the transaction a, the parasitic chain attack cannot be successful, and therefore, the parasitic chain starting time is smaller than the consensus completion time t0(ii) a When the transaction a consensus is reached, the cumulative weight of the parasitic chain is μ (t)0-T2) The cumulative weight of honest nodes is phi (t)0-T1) (ii) a Thus, if the attack is successful, after consensus is achieved, the parasitic chain cumulative weight should be greater than the honest node cumulative weight, i.e., (t)0-T1)-μ(t0-T2) Less than 0; setting T1＝T20, i.e. the parasitic chain starts to prepare when transaction a writes a, then (t)0)-μ(t0) Less than 0; next, the cumulative weight phi (t) at the time of completion of consensus is calculated separately0) Andpreparing the parasitic chain transaction a at the moment of writing the tan gle, and determining the probability of successful attack;
cumulative weight at transaction consensus completion: when a new transaction arrives, at least one verification site i is selected from the k tips, the new transaction can indirectly verify the site i, and the cumulative weight of the site i is added with 1; the probability of at least one tips verification site i is 1- (1-psi (t-h)/R0)k
Figure FDA0003489573480000071
Where φ (t) is the cumulative weight;
Figure FDA0003489573480000072
Figure FDA0003489573480000073
the following can be obtained:
Figure FDA0003489573480000074
wherein the content of the first and second substances,
Figure FDA0003489573480000075
Figure FDA0003489573480000076
by the nature of the omega function
Figure FDA0003489573480000077
The following can be obtained:
Figure FDA0003489573480000078
thus, the cumulative weight φ (t) can be calculated as:
Figure FDA0003489573480000079
since the weight accumulation time is mainly in the data transmission stage and the consensus achievement stage, t in the above formula is the sum of the data transmission time and the accumulated weight time0The cumulative weight is expressed as follows:
Figure FDA00034895734800000710
probability of success of parasitic chain attack: as the honest nodes conform to Poisson distribution with the event arrival rate of lambda, the time intervals of the adjacent things of the honest nodes are independent and equally distributed exponential variables, and the 1/lambda exponential distribution is obeyed; in the same way, the time interval of the adjacent things of the malicious node is 1/mu of independent and identically distributed index variable; the following can be obtained:
Figure FDA0003489573480000081
Figure FDA0003489573480000082
when mu is more than lambda, the parasitic chain attack will always succeed, when mu is less than lambda, the attack will be possible to succeed only if the cumulative weight of transaction b is greater than that of transaction a when transaction a agrees, i.e., (t)0)-μ(t0) Is greater than 0; when the attack is successful, the malicious node should catch up the difference phi (t) of the parasitic chain and the cumulative weight of the verification transaction a0)-μ(t0) Thus, the probability of success of a parasitic chain attack is:
Figure FDA0003489573480000083
4. the consensus algorithm based on a field area network and an IOTA of claim 1, wherein the establishing of the block chain consensus algorithm based on a field area network and an IOTA in step S3 specifically comprises: an IOTA node and adjacent terminals form a cluster. The terminal sends a transaction to the IOTA node. When the IOTA node receives enough transactions, it will bundle all transactions and distribute the PoW tasks to the terminals in the cluster. All members of the cluster cooperate with each other to complete respective tasks, a calculation result is returned to the IOTA node, and then the IOTA node writes data into a chaotic node. Thus, the workload of the IOTA node, and the time required to write data to the chaotic data, can be significantly reduced.
After clustering, the data can be written into the tandle only after the transaction reaches the maximum value of the IOTA data packet, and then the data collection time is as follows:
Figure FDA0003489573480000084
wherein n istIs the average number of transactions in a data packet, NgIs the number of nodes in a cluster, lambdaiEvent arrival rate for node i; the time for writing data into the tandle is mainly PoW calculation time, and the PoW after clustering is completed cooperatively by members in the cluster, so the time for writing data into the tandle is as follows:
Figure FDA0003489573480000085
wherein d isPiNumber of calculation cycles for PoW calculation, FiTotal computing power for cluster i
Figure FDA0003489573480000086
The average time interval for the event to write to the local tangle is:
Figure FDA0003489573480000087
because data only needs to be transmitted to the IOTA node in the network, the time for transmitting the data in the network is less than or equal to the transmission time when the data are not clustered, and the maximum transmission time LT is taken;
the consensus time is:
Figure FDA0003489573480000091
wherein
Figure FDA0003489573480000092
Consensus time is expressed as follows:
Figure FDA0003489573480000093
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