Lightweight consensus protocol PoSF based on mobile block chain scene

Abstract

The invention provides a lightweight consensus protocol PoSF based on a mobile block chain scene, and belongs to the field of computer communication. According to the method, based on a block chain consensus protocol of node stability proof, the SF (Stability Factor) of a node is obtained by combining a reputation value and a communication quality factor of the node, and a complete capability node of which the stability exceeds a threshold value is selected as a representative node to generate a block; and giving an initial reputation value to the node by considering the malicious behavior of the node, rewarding and punishing the reputation value according to the behavior of the node, and kicking the node with the reputation value lower than the initial reputation value out of the block chain. In order to excite the remaining nodes to participate in the block chain verification stage, the stability of the nodes and saved verification delay are used as the income of the verification nodes, and the optimal excitation given to the verification nodes is obtained under constraint conditions such as the income of the verification nodes. The method not only ensures that the block chain mining process is quickly completed during the movement of the equipment, but also ensures the fairness and enthusiasm of all nodes participating in mining.

Description

Technical Field

[0001] The present invention relates to the field of computer communication, and particularly relates to a lightweight consensus protocol PoSF based on a mobile blockchain scenario. Technical Background

[0002] A blockchain is a distributed ledger that participants can share copies of. Each blockchain node maintains a complete copy of the ledger and updates it synchronously through the network. The blockchain ensures that nodes can reach a consensus on the validity of transactions and the order of blocks through a consensus protocol, thereby guaranteeing the security and stability of the blockchain. To ensure the credibility of participating nodes, the consensus protocol imposes some requirements on the participating nodes, thereby increasing the cost for malicious nodes to attack the blockchain. For example, in a blockchain based on PoW (Proof of Work), the node that solves the hash problem first obtains the "right to record accounts", and users who successfully generate a block and pass the verification will receive token rewards. In a blockchain based on PoS (Proof of Stake), users holding more tokens have a greater probability of obtaining the "right to record accounts". In PoA (Proof of Authority), specific nodes are selected by the network administrator to take turns to hold the "right to record accounts". Under the incentive mechanism of PoW, the success probability and income of users are positively correlated with their own computing power. To support some lightweight devices to participate in blockchain mining and improve the user's own computing power, offloading the mining task to the edge cloud and adjacent non-mining devices has been proven to be an effective method. Edge cloud computing can provide a service environment and computing power at the edge of the mobile network. Compared with offloading computing tasks to a remote cloud, it reduces the latency of network operations and service delivery and improves the user experience, and has been widely studied in recent years.

[0003] Currently, most research on mobile blockchains is that mobile blockchains adopt some lightweight and efficient consensus mechanisms. By using lightweight communication protocols and data compression technologies, the communication burden between mobile devices and the blockchain network can be reduced, thereby reducing network latency and traffic consumption, but often sacrificing the fairness and distribution of the blockchain. With the rapid development of edge computing in recent years, a certain amount of computing power has been provided for mobile devices, enabling mobile devices to participate in the blockchain network as blockchain nodes. However, as mobile devices of users, the movement of users may cause some nodes in the network to leave. During the consensus process of the blockchain, this will increase the risk of forks or potential attacks. If the mobile user is one of the key nodes, then the time to broadcast new blocks in the blockchain network may be extended, which will affect the efficiency and performance of the entire network. Summary of the Invention

[0004] To address the above problems, the present invention proposes a lightweight consensus protocol PoSF based on the mobile blockchain scenario. First, the stability of nodes is obtained based on the mobility prediction and historical behavior of blockchain nodes. A candidate list of block representative nodes is generated based on the stability. To incentivize other nodes to participate in verification, the saved verification latency is used as the node income. The optimization function is transformed into a Lagrangian function, and the optimal incentive based on the verification nodes is solved based on the KKT conditions. Finally, the PoSF blockchain system based on the discrete Kalman filtering method is designed and simulated in this paper, demonstrating the performance of the blockchain system based on PoSF and the prediction accuracy of the discrete Kalman filtering method.

[0005] A lightweight consensus protocol PoSF based on the mobile blockchain scenario includes the following steps:

[0006] Step 1: Establish a mobile blockchain communication model based on PoSF, and select representative nodes and verification nodes according to the node stability.

[0007] Step 2: Predict the position of the node at time t+1 based on the discrete Kalman filter.

[0008] Step 3: Calculate the latency saved by the verification nodes, and combine the node reputation value and the communication quality factor to obtain the node stability.

[0009] Step 4: Calculate the incentive of the node according to the node stability and the verification node latency.

[0010] Step 5: With the maximization of the representative node income as the optimization goal, solve the optimal incentive given to the verification nodes.

[0011] Preferably, the specific steps of Step 1 include the following steps:

[0012] Step 1-1: All nodes of the blockchain are divided into two types according to their capabilities: 1) Full-capability nodes, which have the "full" capabilities of generating, verifying, and propagating blocks. 2) Verification-capability nodes, which can only use technologies such as digital signatures and smart contracts to verify the authenticity and validity of the generated block data from the blockchain generation nodes. According to the node stability election, full-capability nodes with a stability exceeding the threshold will be selected as representative nodes, responsible for packing transaction information and generating blocks. While full-capability nodes and verification-capability nodes with insufficient stability become verification nodes to verify the blocks generated by the representative nodes. The communication method between nodes adopts the Gossip protocol. The representative nodes maintain communication with each other, and a batch of verification nodes are recruited within the communication range of each representative node. The propagation of the blocks and verification results of the representative nodes first spreads among the representative nodes, and after receiving the message, the representative nodes broadcast it to the verification nodes within their communication range.

[0013] Step 1-2: The process of the blockchain from generating transaction information to successfully packing the transaction information into a block and adding it to the public ledger is called the system cycle. After each round of the system cycle, the supervisor will give rewards and punishments according to the behavior of the nodes, update their reputation values. Each node has an initial reputation value ρ0. If the representative node behaves maliciously, its reputation value will be reduced, and a new representative node will be re-elected. After each round of the system cycle, the supervisor will update the reputation values of all nodes. However, since the time of the system cycle is relatively short, the movement of nodes will not cause much impact in a short time. Therefore, every (number of representative nodes * 4) rounds of consensus, the positions of each node in the next (number of representative nodes * 4) rounds of consensus cycles will be predicted according to the discrete Kalman filtering method. Based on this prediction result, the communication quality of the nodes will be updated, thereby updating the stability of the nodes. The supervisor will re-elect a batch of new representative nodes according to the stability ranking. Nodes with a stability lower than the initial reputation value ρ0 will be regarded as malicious nodes and kicked out of the blockchain.

[0014] Preferably, the specific steps of step 2 are as follows:

[0015] Step 2-1: Model the movement patterns of all nodes as a two-dimensional plane model, and the historical trajectory vector dataset of the nodes in two directions is the x-axis coordinate of the node on the two-dimensional plane at time t, is the y-axis coordinate of the node on the two-dimensional plane at time t, and the state vector at time t is

[0016] The state vector is obtained from the state transition equation. The system state equation for predicting the movement trajectory by Kalman filtering is:

[0017] X(k + 1) = A(k)X(k) + T(k)W(k)

[0018] where X(k) is the state vector of the moving object at time k, A(k) is the state transition matrix, T(k) is the interference transition matrix, and W(k) is the system state noise, assumed to be Gaussian white noise.

[0019] Step 2-2: The discrete Kalman filter maps the true system state of the node to the observation space to obtain the observation data. The observation equation of the system state is:

[0020] Z(k) = H(k)X(k) + V(k)

[0021] where Z(k) is the observation vector, H(k) is the observation matrix, and V(k) is the observation noise that appears in the observation estimation process. It is assumed that the system noise and the observation noise are independent of each other, that is

[0022]

[0023] E[W(k)V(k) T ]=0

[0024] Where Q(k) is the covariance of the system noise, R(k) is the covariance of the observation noise, W(i) is the system state noise at time i, W(k) is the system state noise at time k, V(i) is the observation noise at time i, and E[W(i)W(k) T ] represents the expected value of the covariance matrix of the system state noise W(i) and W(k), E[V(i)V(k) T ] represents the expected value of the covariance matrix of observation noise V(i) and V(k).

[0025] Step 2-3: Kalman filtering is a method that uses the linear system state equation to observe the predicted value at time k+1 using the optimal value of the system state at time k. At the same time, it uses the observed value at time k+1 to correct the predicted value at time k+1 to obtain the optimal value at time k+1, and iterates continuously.

[0026] definition (- represents prior, ^ represents estimate) is the prior state estimate at time k when the state before time k is known. X(k)^ is the posterior state estimate at time k when the measured variable is known. This is defined as:

[0027]

[0028] E(k)=X(k)-X(k)^

[0029] is the a priori estimation error and E(k) is the a posteriori estimation error, the a priori estimation error is the difference between the true state and the a priori estimation, and the a posteriori estimation error is the difference between the true state and the posteriori estimation.

[0030]

[0031] The covariance of the prior estimation error is used to measure the statistical characteristics of the prediction error, including the variance of the error and the covariance between different state components.

[0032] P(k)=E[E(k)E(k) T ]

[0033] P(k) is the covariance of the posterior estimation error, which quantifies the accuracy of the posterior estimation, including the variance of each state component and its covariance relationship. The goal of the Kalman filter is to make the estimated value as close to the true state as possible by minimizing P(k).

[0034] Step 2-4: The Kalman filter estimates the process state using a feedback control method: The filter estimates the state at a certain moment in the process and then obtains feedback in the form of a (noisy) measurement variable. Therefore, the Kalman filter can be divided into two parts: the time update equation and the measurement update equation. The time update equation is responsible for timely extrapolating the current state variables and the estimated values of the error covariance forward in time to construct a prior estimate for the next time state. The measurement update equation is responsible for feedback - that is, it combines the prior estimate and the new measurement variable to construct an improved posterior estimate. The time update equation can also be regarded as a prediction equation, and the measurement update equation can be regarded as a correction equation. The final estimation algorithm becomes a prediction-correction algorithm with a numerical solution.

[0035] The time update process of the Kalman filter is as follows:

[0036]

[0037] where, is the prior estimate of the object's motion state at time k+1, is the covariance of the prior estimate error at time k+1.

[0038] The observation update process of the Kalman filter is as follows:

[0039]

[0040] K(k+1) is the gain matrix of the Kalman filter, is the covariance of the prior estimate error at time k+1, Z(k+1) is the observation vector at time k+1, and P(k+1) is the covariance matrix of the posterior estimate error at time k+1. It is obtained from the state noise covariance and the observation noise covariance. The smaller the observation noise covariance R(k), the larger the remaining gain K(k). The prior estimate error covariance is smaller, the smaller the remaining gain K(k).

[0041] Preferably, step 3 specifically includes the following steps:

[0042] Step 3-1: The representative nodes and verification nodes in the blockchain are all mobile devices, and there are several verification nodes within the communication range of the representative nodes. The set of representative nodes is C = {C1, C2,... C i ,.... C I}, the set of verification nodes is V = {V1, V2,.... V J}, and the set of all nodes is N = {C, V}. The representative node i recruits a batch of verification nodes within its own communication range

[0043] Step 3-2: After the representative node i packages a block, it needs to broadcast the block to other verification nodes in the blockchain network for verification. At the representative node layer, the representative node i will communicate with other representative nodes through a wireless link. At the verification node layer, the block received by the consensus node is broadcast to the verification nodes recruited by itself. The representative node i broadcasts the block to the verification nodes recruited by the representative node k The propagation delay of the broadcast block is: where n loop is the number of hops for the block to be transmitted between representative nodes, n loop ≤n loopmax and n loopmax is the maximum number of hops for the message to be broadcast in the blockchain network, s i is the data size of the block, in bits, w i is the transmission rate of the representative node i, B is the wireless channel bandwidth, is the signal-to-noise plus interference ratio at the verification node . When the representative node i that generates the block propagates the block to the verification nodes recruited by itself, n loop =0. Where d ave is the average distance between representative nodes, d i,k is the Euclidean distance between the representative node i and the representative node k, which is where (x' i , y' i ) and (x' k , y' k ) are the predicted values obtained by the discrete Kalman filtering method, which are the positions of the nodes in the next consensus period. The communication signal-to-noise ratio between node i and node j is: where α is the path loss exponent, d i,k is the distance between node i and node k, which can be predicted by the discrete Kalman filtering method, d i,n is the distance between node i and the interference node n, P noise is the noise power.

[0044] Step 3-3: To ensure the successful transmission of the message, the signal-to-noise ratio of node i needs to exceed a certain threshold β, which is set to 8 dB in the present invention. The communication quality of node i is According to the historical interaction experience between node i and other nodes j, the evaluation of the credibility of node i by other nodes can be obtained, including b j→i trust, d j→i distrust, and u j→i uncertainty, and b + d + u = 1. The credibility is updated according to the following formula:

[0045]

[0046] Represents the total number of trust evaluations for the node, is the total number of distrust evaluations. The credibility of node i is:

[0047]

[0048] where ρ0 is the initial reputation value of the node.

[0049] The stability SF of node i i is obtained from the communication quality Q i and the combined reputation value ρ i as follows:

[0050]

[0051] Before each round of blockchain mining starts, calculate the stability of each node, and select the nodes with stability higher than the threshold in the candidate node set as representative nodes to generate blocks.

[0052] Preferably, step 4 specifically includes the following steps:

[0053] Step 4-1: To prevent verification nodes from being passive due to lack of incentives and to reduce the adverse effects caused by node movement during the verification phase, use the verification time delay saved by the verification nodes as part of the income of the representative nodes, and take maximizing the income of the representative nodes as the optimization goal to solve the optimal incentive given to the verification nodes. The verification node The verification time delay for verifying that the representative node i generates a block is: where is the verification node the computing resources required for the verification node to verify that the representative node i generates a block, k i is the mapping coefficient from the verification of block bit to CPU cycles for the verification node, s i is the data size of the block, in bits. The verification node The propagation time delay for the verification node to accept the block generated by the representative node i is: where, is the verification node the distance between and the representative node i, is the verification node the communication signal-to-noise ratio between and the representative node i. The time delay saved by the verification node compared to the maximum tolerable verification time delay is:

[0054]

[0055] where, is the maximum tolerable verification time delay, is the verification node recruited by the representative node i from the representative node k the propagation time delay for broadcasting the block, To verify the total time delay of a node in processing a block.

[0056] Step 4-2: The utility U of representative node i i is the stability reward and the saved time delay reward minus the incentive paid to the verification node: where R con is the system reward obtained by the representative node based on stability, is the incentive given by representative node i to the verification node, ξ i is the coefficient of the saved time delay, is the number of successful reports by the verification node, is the number of times the representative node misbehaves. If the verification node makes malicious behavior, such as interfering with the verification process with wrong verification results, the blockchain system will confiscate the deposit of the malicious node and return the verification reward paid by the representative node to the verification node to the representative node. To ensure that the malicious node can be punished, it should be made that where C deposit is the deposit. The utility of the verification node is the obtained incentive minus the verification block cost:

[0057]

[0058] where, is the energy cost coefficient, is the verification node 's switched-capacitor constant. Under the constraint conditions and optimization objectives, the above formula can be simplified to:

[0059]

[0060] Preferably, the optimization objectives and constraint conditions in step 5 are as follows:

[0061]

[0062] The benefits of the representative node must meet the individual rationality (IR, Individual Rationality) and incentive compatibility (IC, incentive compatibility) feasibility constraints of each verification node.

[0063] Compared with the prior art, the present invention has the following technical effects:

[0064] (1) The present invention proposes a lightweight consensus protocol for mobile blockchain scenarios, which not only ensures the rapid completion of the blockchain mining process during device movement, but also ensures the fairness and enthusiasm of all nodes to participate in mining.

[0065] (2) The present invention also considers that the nodes undertaking mining tasks and verifying block tasks in the blockchain are mobile, and the changes in the speed and position of the nodes have an impact on the performance of the blockchain. The Kalman filter prediction results and the historical behavior of the nodes are taken as the consideration factors for node stability, and the representative nodes for generating blocks are selected according to the node stability.

[0066] (3) The lightweight blockchain optimized consensus protocol and incentive mechanism based on Kalman filter prediction suitable for the mobile blockchain scenario of the present invention are designed to encourage nodes to participate in the network according to the rules and maintain honest behavior. Nodes prove their sincerity and commitment to participating in the network by paying a certain amount of deposit to the supervisor. After the end of a round of blockchain mining process, the supervisor will issue rewards to the user nodes that successfully package the blocks, while the deposits of the nodes that perform malicious behaviors will be confiscated as punishment. These malicious behaviors include packaging incorrect transaction information into blocks and giving incorrect verification results for the blocks packaged by the generating nodes during the verification phase. In addition, in order to encourage other nodes to actively participate in the verification process, the present invention takes the saved verification delay as the income of the generating nodes, and solves the best incentive given by the representative nodes to the verification nodes under the constraints of node income, node type, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is the flowchart of the present invention.

[0068] Figure 2 is the system model diagram of the present invention.

[0069] Figure 3 is the blockchain flowchart of the present invention.

[0070] Figure 4 is the comparison of the discrete Kalman filter prediction value, the true value and the measured value.

[0071] Figure 5 is the comparison of node activity under different consensus protocols.

[0072] Figure 6 is the throughput comparison of PoSF, DPoS and DPoS-NCVR. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0073] In order to more clearly illustrate the technical solutions of the present invention, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings:

[0074] As Figure 1What is shown is to establish a lightweight consensus protocol for mobile blockchain scenarios, named PoSF, and use the discrete Kalman filtering method to predict the moving positions of blockchain nodes. By combining the node reputation value and the communication quality factor, the stability of the nodes is obtained. The stability of the nodes and the saved verification delay are used as the benefits of the verification nodes, and the optimal incentive for the verification nodes is obtained under the constraint conditions such as the benefits of the verification nodes. The specific steps are as follows:

[0075] Step 1: Establish a mobile blockchain communication model based on PoSF, and select representative nodes and verification nodes according to the node stability.

[0076] Step 2: Predict the position of the node at the t+1 moment based on the discrete Kalman filtering.

[0077] Step 3: Calculate the saved delay of the verification nodes, and combine the node reputation value and the communication quality factor to obtain the stability of the nodes.

[0078] Step 4: Calculate the incentive of the nodes according to the node stability and the verification node delay.

[0079] Step 5: Take maximizing the benefits of the representative nodes as the optimization goal, and solve the optimal incentive for the verification nodes.

[0080] Step 1: Establish a blockchain model based on PoSF, and select representative nodes and verification nodes according to the node stability.

[0081] The blockchain model based on PoSF is as Figure 2 shown. The communication method between nodes adopts the Gossip protocol. As shown in the figure, the representative nodes maintain communication with each other, and a batch of verification nodes are recruited within the communication range of each representative node. The propagation of the blocks and verification results of the representative nodes first spreads among the representative nodes, and after receiving the message, the representative nodes broadcast it to the verification nodes within their communication range.

[0082] The process of the blockchain from generating transaction information to successfully packing the transaction information into a block and adding it to the public ledger is called the system cycle. After each round of the system cycle ends, the supervisor will give rewards and punishments according to the behavior of the nodes and update their reputation values. If a representative node behaves badly, a new representative node will be re-elected. After each round of the system cycle ends, the supervisor will update the reputation values of all nodes. However, since the time of the system cycle is relatively short, the movement of the nodes will not cause too much impact in a short time. Therefore, after every (number of representative nodes * 4) rounds of consensus, the positions of each node in the next (number of representative nodes * 4) rounds of consensus cycles will be predicted according to the discrete Kalman filtering method. Based on this prediction result, the communication quality of the nodes will be updated, thereby updating the stability of the nodes. The supervisor will re-elect a batch of new representative nodes according to the stability ranking.

[0083] All blockchain nodes are divided into two types based on their capabilities: 1) Fully capable nodes, which have the full capabilities of generating, verifying, and propagating blocks. 2) Verification capable nodes, which can only verify the authenticity and validity of block data generated by blockchain generation nodes using technologies such as digital signatures and smart contracts.

[0084] After calculating the stability of the nodes, the fully capable nodes with stability exceeding the threshold will be selected as representative nodes, responsible for packaging transaction information and generating blocks. The fully capable nodes and verification nodes with insufficient stability will become verification nodes, which will be the basis for the complete process of the PoSF-based blockchain. Figure 3 shown.

[0085] For easier understanding, the following explains the important terms involved in the PoSF-based blockchain consensus protocol:

[0086] Regulator: A trusted third-party entity or organization is responsible for selecting representative nodes to generate blocks based on stability, updating and collecting the stability of nodes after each consensus cycle, and awarding tokens or confiscating deposits based on the performance of the nodes.

[0087] Representative nodes: Fully capable nodes with stability above the threshold are selected as representative nodes, responsible for packaging transaction information into blocks and broadcasting them to other nodes for verification.

[0088] Consensus cycle: The time it takes for all representative nodes in the system to complete the generation and verification of a new block in sequence and successfully upload it to the chain.

[0089] Honest behavior: Nodes within the system participate in system activities according to consensus rules, such as correctly generating transactions, generating blocks, and correctly verifying blocks.

[0090] Malicious behavior: Nodes within the system maliciously disrupt the consensus and verification process, such as tampering with transaction information, sending a large number of invalid requests, submitting incorrect verification results, etc.

[0091] Verification nodes: By paying a deposit to become a blockchain node, they can generate transaction information, including verification capability nodes and fully capable nodes that failed in the representative node election.

[0092] Representative node: A fully capable node that becomes a blockchain node by paying a deposit and has a stability higher than the threshold. It is responsible for packaging new transactions generated within the system and signing new blocks.

[0093] The selected representative nodes take turns to produce blocks within their respective time windows. Since there is no need for a large number of hash calculations like in PoW, the block production time of PoSF is short and the throughput is high. Similar to DPoS, PoSF follows the principle of winning based on the longest chain. This is to prevent some malicious nodes from deliberately delaying block production to generate forked blocks, or a node from generating two duplicate blocks to disrupt the public ledger. During each round of the consensus process, if a consensus node fails to produce a block or takes other malicious actions, it will be reported by other nodes and punished. For malicious nodes, PoSF will confiscate all their deposits and kick them out of the blockchain. When a representative node successfully produces a block, it can only receive the corresponding reward after being confirmed by at least (2 / 3 + 1) other nodes in the blockchain network. The verification nodes can also receive the corresponding verification rewards. Compared with the practice in DPoS where the rights of verification and block production are both in the hands of the shareholders elected by the voters, this approach is more conducive to ensuring the fairness of the blockchain system, preventing the phenomenon of "the rich get richer and the poor get poorer", and motivating nodes to participate in the blockchain actively.

[0094] Figure 5 The following shows the comparison of node activity under three consensus protocols. The three consensus protocols are the PoSF consensus algorithm proposed in the present invention, the DPoS consensus algorithm, and an optimized consensus protocol DPoS-NCVR based on DPoS. DPoS-NCVR introduces the concept of contribution value. The node with the largest contribution value obtains the right to keep accounts. By updating the credibility of global nodes, representative nodes are elected, thus effectively preventing malicious nodes from participating in the consensus. Node activity refers to the percentage of the number of nodes that actively participate in blockchain consensus and verification in the total number of nodes in the blockchain.

[0095] In the traditional DPoS consensus protocol, due to the lack of incentives for voting nodes, voting nodes may exhibit passive voting behavior. In addition, due to the Matthew effect, nodes with fewer tokens will give up participating in blockchain voting due to the phenomenon of the poor getting poorer. To encourage ordinary nodes to vote and prevent malicious nodes from obtaining extra income by bribing ordinary nodes, DPoS-NCVR distributes rewards to the nodes maintaining the system according to their contribution values. The contribution value of a node is related to its own weight, activity, and credibility. The incentive mechanism of DPoS-NCVR greatly improves the enthusiasm of voting nodes to participate in blockchain activities, but still does not fundamentally improve the Matthew effect because more rewards are distributed to representative nodes. As the number of blockchain consensus increases, wealth inevitably accumulates in the hands of a few nodes.

[0096] The PoSF consensus algorithm proposed by the present invention fundamentally solves this problem. The selection of representative nodes no longer depends on voting nodes, but is determined by a trusted third-party supervisor based on the historical performance of the nodes. This mechanism can effectively curb bribery behavior and unfairness within the system, and encourage nodes to be more honest and trustworthy. If ordinary nodes hope to become representative nodes to obtain more benefits, they will strive to maintain honest behavior and improve their communication quality, thus promoting the stability of the blockchain system. As Figure 5 shown, in the blockchains based on DPoS and DPoS-NCVR, the activity of nodes will gradually decline with the number of consensus rounds, while PoSF remains at about 90%. This is because the wealth within the former system will tilt towards a few nodes as the formula rounds are superimposed, resulting in other nodes in the network losing vitality. However, the PoSF representative nodes proposed in this paper will be re-elected after several rounds of consensus cycles, and the election criteria do not rely on the number of tokens held, ensuring the fairness of competition among nodes to the greatest extent.

[0097] Step 2: Predict the position of the node at time t+1 based on the discrete Kalman filter.

[0098] Model the movement patterns of all nodes as a two-dimensional plane model, and the historical trajectory vector dataset of nodes in two directions is the x-axis coordinate of the node on the two-dimensional plane at time t, is the y-axis coordinate of the node on the two-dimensional plane at time t, and the state vector at time t is

[0099] The state vector is obtained from the state transition equation. The system state equation for the Kalman filter to predict the movement trajectory is:

[0100] X(k+1) = A(k)X(k) + T(k)W(k)

[0101] where X(k) is the state vector of the moving object at time k, A(k) is the state transition matrix, T(k) is the interference transition matrix, and Q(k) is the system state noise, assumed to be Gaussian white noise.

[0102] The discrete Kalman filter maps the true system state of the node to the observation space to obtain the observation data. The observation equation for the system state is:

[0103] Z(k) = H(k)X(k) + V(k)

[0104] where Z(k) is the observation vector, H(k) is the observation matrix, and V(k) is the observation noise that appears in the observation estimation process. It is assumed that the system noise and the observation noise are independent of each other, that is

[0105]

[0106]

[0107] E[W(k)V(k) T = 0

[0108] Q(k) is the covariance of the system noise, R(k) is the covariance of the observation noise, W(i) is the system state noise at time i, W(k) is the system state noise at time k, V(i) is the observation noise at time i, and E[W(i)W(k) T represents the expected value of the covariance matrix of the system state noises W(i) and W(k), and E[V(i)V(k) T represents the expected value of the covariance matrix of the observation noises V(i) and V(k).

[0109] Kalman filtering is a method that uses the linear system state equation to utilize the optimal value of the system state at time k to observe the predicted value at time k + 1. At the same time, it uses the observed value at time k + 1 to correct the predicted value at time k + 1 to obtain the optimal value at time k + 1. Kalman filtering is "predict - update the predicted value to the optimal value according to the observed value", and this process is continuously iterated.

[0110] Definition (- represents prior, ^ represents estimation) is the prior state estimate at time k given the state before time k. X(k) ^ is the posterior state estimate at time k given the measured variables. Thus, the definitions are as follows:

[0111]

[0112] E(k) = X(k) - X(k) ^

[0113] is the prior estimation error and E(k) is the posterior estimation error. The prior estimation error is the difference between the true state and the prior estimate, and the posterior estimation error is the difference between the true state and the posterior estimate.

[0114]

[0115] is the covariance of the prior estimation error, which measures the statistical characteristics of the prediction error, including the variance of the error and the covariance between different state components.

[0116] P(k) = E[E(k)E(k) T

[0117] ​P(k) is the covariance of the posterior estimation error, which quantifies the precision of the posterior estimation, including the variances of each state component and their covariance relationships. The goal of the Kalman filter is to make the estimated value as close as possible to the true state by minimizing P(k).

[0118] The Kalman filter estimates the process state using a feedback control method: the filter estimates the state at a certain moment in the process and then obtains feedback in the form of a (noisy) measurement variable. Therefore, the Kalman filter can be divided into two parts: the time update equation and the measurement update equation. The time update equation is responsible for timely extrapolating the values of the current state variables and error covariance estimates forward in time to construct a prior estimate for the next time state. The measurement update equation is responsible for feedback - that is, it combines the prior estimate and the new measurement variable to construct an improved posterior estimate. The time update equation can also be regarded as a prediction equation, and the measurement update equation can be regarded as a correction equation. The final estimation algorithm becomes a prediction - correction algorithm with a numerical solution.

[0119] The time update process of the Kalman filter is as follows:

[0120]

[0121] where, is the prior estimate of the object's motion state at time k + 1, is the covariance of the prior estimation error at time k + 1

[0122] The observation update process of the Kalman filter is as follows:

[0123]

[0124] K(k + 1) is the gain matrix of the Kalman filter, is the covariance of the prior estimation error at time k + 1, Z(k + 1) is the observation vector at time k + 1, and P(k + 1) is the covariance matrix of the posterior estimation error at time k + 1.

[0125] Since the state noise covariance and the observation noise covariance are obtained, the smaller the observation noise covariance R(k), the larger the remaining gain K(k). The prior estimation error covariance is smaller, the smaller the remaining gain K(k).

[0126] Figure 4 Shows the comparison of the predicted values, true values, and measured values obtained based on the discrete Kalman filtering method in a two - dimensional plane. The predicted value is obtained from the optimal value of the system state at the previous moment and the observed value at this moment. The predicted value at this moment is corrected using the observed value at this moment. By continuously iterating and adjusting the Kalman gain, the influence of the observation noise on the predicted value can be reduced, so that the predicted value continuously approaches the true value.

[0127] Step 3: Calculate the time delay saved by the verification node, and combine the node reputation value and the communication quality factor to obtain the stability of the node.

[0128] All nodes can generate transactions and broadcast the transaction information to the entire blockchain network. The representative node packs the transaction information into a block and broadcasts the block to the verification nodes to verify whether the message is correct. To prevent a single representative node from acting maliciously during the consensus process, such as packing incorrect transaction information, etc., within each consensus process, the representative node within the list of representative nodes generated by the supervisor packs the transaction information and broadcasts it to the verification nodes for verification. After the representative node successfully adds the block to the public ledger, it can obtain a system reward, but verification does not bring rewards to the verification nodes. To prevent the lack of rewards from causing the verification nodes to slack off, and at the same time reduce the adverse effects caused by node movement during the verification phase, such as network instability caused by node movement, resulting in nodes being unable to broadcast the verification results to other nodes, or being unable to receive the blocks broadcast by the representative nodes. Therefore, the present invention takes the verification time delay saved by the verification node and the stability as the benefits of the representative node.

[0129] After the representative node i packs a block, it needs to broadcast the block to other verification nodes in the blockchain network for verification. At the representative node layer, the representative node i communicates with other representative nodes through a wireless link. At the verification node layer, the block received by the consensus node is broadcast to the verification nodes recruited by itself. The representative node i broadcasts the block to the verification nodes recruited by the representative node k The propagation time delay of the broadcast block is:

[0130]

[0131] where n loop is the number of hops for the block to be transmitted among the representative nodes, n loop ≤n loopmax and n loopmax is the maximum number of hops for the message to be broadcast in the blockchain network, s i is the data size of the block, in bits, w i is the transmission rate of the representative node i, B is the wireless channel bandwidth, is the signal-to-noise plus interference ratio at the verification node When the representative node i that generates the block propagates the block to the verification nodes recruited by itself, n loop = 0. Where d ave is the average distance between the representative nodes, d i,k is the Euclidean distance between the representative node i and the representative node k, which is where (x' i , y' i ) and (x' k, y' k ) is the predicted value obtained by the discrete Kalman filtering method and is the position of the node in the next consensus period. The communication signal-to-noise ratio between node i and node j is: where α is the path loss exponent, d i,k is the distance between node i and node k, which can be predicted by the discrete Kalman filtering method, d i,n is the distance between node i and interfering node n, P noise is the noise power.

[0132] To ensure the successful transmission of messages, the signal-to-noise ratio of node i needs to exceed a certain threshold β, which is set to 8 dB in the present invention. The communication quality of node i is:

[0133]

[0134] Based on the historical interaction experience between node i and other nodes j, the evaluation of the credibility of node i by other nodes can be obtained, including b j→i trust, d j→i distrust, and u j→i uncertainty, and b + d + u = 1. The credibility is updated according to the following formula:

[0135]

[0136] represents the total number of trust evaluations for this node, is the total number of distrust evaluations. The credibility of node i is:

[0137]

[0138] where ρ0 is the initial reputation value of the node.

[0139] In summary, the stability SF of node i i is obtained by combining the communication quality Q i and the reputation value ρ i as follows:

[0140]

[0141] Before the start of each round of blockchain mining, calculate the stability of each node, and select the nodes with stability higher than the threshold in the candidate node set as representative nodes to generate blocks.

[0142] Step 4: Calculate the incentive of the node according to the node stability and the verification node delay.

[0143] To prevent verification nodes from being inactive due to lack of incentives and to mitigate the adverse effects caused by node movement during the verification phase, the verification delay saved by verification nodes is used as part of the representative node's revenue, and maximizing the revenue of representative nodes is taken as the optimization goal to solve for the optimal incentive given to verification nodes. Verification nodes The verification delay for verification representative node i to generate a block is: Where is the verification node The computing resources required for verification representative node i to generate a block, k i is the mapping coefficient from the verification of a block bit to CPU cycles for the verification node, s i is the data size of the block, in bits. Verification nodes The propagation delay for verification nodes to receive the block generated by representative node i is:

[0144] Where, is the verification node the distance between and representative node i, is the verification node the communication signal-to-noise ratio between and representative node i. The delay saved by verification nodes compared to the maximum tolerable verification delay is:

[0145]

[0146] Where, is the maximum tolerable verification delay, is the verification node recruited by representative node i from representative node k the propagation delay of the broadcast block, and is the total delay for the verification node to process the block.

[0147] The utility U of representative node i i is the stability reward and the saved delay reward minus the incentive paid to the verification node:

[0148]

[0149] Where, R con is the system reward obtained by the representative node based on stability, is the incentive given by representative node i to the verification node, ξ i is the coefficient of the saved delay. If a verification node behaves maliciously, such as interfering with the verification process with incorrect verification results, the blockchain system will confiscate the deposit of the malicious node and return the verification reward paid by the representative node to the verification node to the representative node. To ensure that malicious nodes can be punished, it should be such that Where C deposit is the deposit. Verification nodes The utility is the obtained incentive minus the cost of verifying the block:

[0150]

[0151] Among them, is the energy cost coefficient, is the verification node 's switched-capacitor constant.

[0152] Figure 6 Shows the throughput comparison of PoSF, DPoS, and DPoS-NCVR proposed by the present invention. The blockchain throughput TPS (Transaction Per Second) refers to the number of transactions that the blockchain network can process per unit time, which is an important indicator to measure the performance of the blockchain and reflects the speed and scalability of the blockchain network. The calculation method of blockchain TPS is: TPS = (block size / average transaction size) / block time, and TPS increases with the increase of the block size. A high-TPS network can support more transaction volumes, which is very beneficial for the commercial applications of the blockchain, while a low-TPS network may lead to transaction delays and reduce the user experience and competitiveness of the blockchain itself. The PoSF algorithm proposed by the present invention does not require voting nodes to elect representative nodes, so the consensus cycle is shorter and the throughput is higher compared to DPoS and DPoS-NCVR. The throughput in DPoS-NCVR is higher than that in DPoS. On the one hand, it is because nodes maintain active communication with other nodes to improve their own contribution values, shortening the block propagation delay; on the other hand, it is because the system timely clears malicious nodes, reducing the probability of forks where malicious nodes refuse to produce blocks or produce blocks multiple times. The throughput of PoSF is increased by 26.433% and 12.147% respectively compared to DPoS and DPoS-NCVR.

[0153] Step 5: Taking maximizing the revenue of representative nodes as the optimization goal, solve for the optimal incentive given to verification nodes.

[0154] The optimization goal is the total revenue obtained after a round of block production by representative nodes. The optimization goal and constraints are as follows:

[0155]

[0156] The benefits of representative nodes must meet the individual rationality (IR, Individual Rationality) and incentive compatibility (IC, incentive compatibility) feasibility constraints of each verification node.

[0157] Classify verification node j according to the value into different types. The type set of verification node is Sort Θ i in ascending order

[0158]

[0159] Based on Equation (10), Equation (8) can be simplified to:

[0160]

[0161] The optimization problem (9) with complex IR constraints and IC constraints is non-convex. To obtain the optimal solution of the optimization problem (9), the following corollary is introduced to simplify the IR and IC constraints.

[0162] The following can be obtained through iterative constraints

[0163]

[0164] Substituting Equation (11) into the optimization objective function (9) gives:

[0165]

[0166] where The optimization function (12) is a concave function on, and the constraint set is a convex set. Therefore, the Karush-Kuhn-Tucker (KKT) conditions are used to solve the optimization problem (12). The Lagrangian function of the optimization problem (12) can be constructed as

[0167]

[0168] where δ and λ are the Lagrangian coefficients of the constraint (9) respectively.

[0169] Based on the Lagrangian function, the dual problem of the original optimization problem is defined as

[0170]

[0171] The solution of the optimization problem (14) is equivalent to the solution of the original optimization problem (12). In the optimization problem (12), the objective function is convex, and each constraint is a closed convex function. Therefore, there is a unique optimal solution (f * , λ * , δ * ) in the optimization problem (14). The KKT conditions satisfied by the optimal solution of the optimization problem (14) are:

[0172]

[0173] Case 1: When and f ij When it is greater than 0, let δ j = 0, That is, the optimal solution is obtained as follows:

[0174]

[0175] Case 2: When and at the same time, let δ j > 0, That is, the Lagrangian function is obtained as shown below:

[0176]

[0177] Eliminating the denominator in the above formula gives:

[0178]

[0179] Let Equation (18) is transformed into:

[0180]

[0181] By solving (19), we can obtain three optimal solutions If satisfies the constraints, then

[0182] Case 3: When and at the same time, let δ j = 0, We get This solution contradicts the constraint (12), so the solution in this case is discarded.

[0183] Case 4: When and at the same time, let δ j > 0, We get The result is the same as that in Case 3, so the solution in this case is discarded.

[0184] In the four cases, the Lagrange multiplier λ is always equal to 0. When δ j > 0, the solution in Case 2 is the optimal solution; otherwise, the solution in Case 1 is the optimal solution. The obtained optimal solution needs to be verified whether it satisfies the monotonicity constraint (9). When the optimal solution set is a non-decreasing sequence, the solution is feasible.

[0185] According to the finally obtained feasible solution and Equation (11), the optimal incentive can be obtained

[0186] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A lightweight consensus protocol PoSF based on mobile blockchain scenarios, characterized in that, It includes the following steps: Step 1: Establish a mobile blockchain communication model based on the PoSF protocol, and select representative nodes and verification nodes according to node stability; Step 2: Use the discrete Kalman filter method to predict the position of the node at time t+l; Step 3: Calculate the latency saved by the verification nodes, and combine the node reputation value and the communication quality factor to obtain the node stability; Step 4: Calculate the incentives of the nodes according to the node stability and the latency of the verification nodes; Step 5: Take maximizing the revenue of the representative nodes as the optimization goal, and solve the optimal incentives given to the verification nodes.

2. The lightweight consensus protocol PoSF based on the mobile blockchain scenario according to claim 1, wherein The specific steps of Step 1 include the following: Step 1-1: All nodes of the blockchain are divided into two types according to their capabilities: 1) Full-capability nodes, which have the "complete" capabilities of generating, verifying, and propagating blocks; 2) Verification-capability nodes, which can only use technologies such as digital signatures and smart contracts to verify the authenticity and validity of the block generation data from the blockchain generation nodes; According to the node stability, the full-capability nodes with stability exceeding the threshold will be selected as representative nodes, responsible for packing transaction information and generating blocks; while the full-capability nodes with insufficient stability and the verification-capability nodes will become verification nodes to verify the blocks generated by the representative nodes; The communication method between nodes adopts the Gossip protocol. The representative nodes maintain communication with each other, and a batch of verification nodes are recruited within their respective communication ranges. The propagation of the blocks and verification results of the representative nodes first spreads among the representative nodes, and after receiving the message, the representative nodes broadcast it to the verification nodes within their communication ranges; Step 1-2: The process of the blockchain from generating transaction information to successfully packing the transaction information into a block and adding it to the public ledger is called the system cycle; After each round of the system cycle ends, the supervisor will make rewards and punishments according to the behavior of the nodes, update their reputation values, and re-elect new representative nodes; After each round of the system cycle ends, the supervisor will update the reputation values of all nodes. However, since the time of the system cycle is relatively short, the movement of the nodes will not have a great impact in a short time. Therefore, every (number of representative nodes *4) rounds of consensus, the position of each node will be predicted according to the discrete Kalman filter method within the next (number of representative nodes *4) rounds of consensus cycles. Based on this prediction result, the communication quality of the nodes will be updated, thereby updating the node stability, and the supervisor will re-elect a batch of new representative nodes according to the stability ranking.

3. A lightweight consensus protocol PoSF based on the mobile blockchain scenario according to claim 1, characterized in that The specific steps of Step 2 include the following: Step 2-1: Model the movement patterns of all nodes as a two-dimensional plane model, and the historical trajectory vector datasets of the nodes in two directions is the x-axis coordinate of the node on the two-dimensional plane at time t, is the y-axis coordinate of the node on the two-dimensional plane at time t, and the state vector at time t is The state vector is obtained from the state transition equation. The system state equation for the Kalman filter to predict the moving trajectory is: X(k+1) = A(k)X(k) + T(k)W(k) where X(k) is the state vector of the moving object at time k, A(k) is the state transition matrix, T(k) is the interference transition matrix, and W(k) is the system state noise, assumed to be Gaussian white noise; Step 2-2: The discrete Kalman filter maps the true system state of the node to the observation space to obtain the observation data. The observation equation of the system state is: Z(k) = H(k)X(k) + V(k) Among them, Z(k) is the observation vector, H(k) is the observation matrix, and V(k) is the observation noise that occurs in the observation estimation process. Assuming that the system noise and the observation noise are independent of each other, that is, E[W(k)V(k) T = 0 Among them, Q(k) is the covariance of the system noise, R(k) is the covariance of the observation noise, W(i) is the system state noise at time i, W(k) is the system state noise at time k, V(i) is the observation noise at time i, and E[W(i)W(k) T represents the expected value of the covariance matrix of the system state noises W(i) and W(k), and E[V(i)V(k) T represents the expected value of the covariance matrix of the observation noises V(i) and V(k); Step 2-3: Kalman filtering is a method that uses the linear system state equation to observe the predicted value at time k+1 using the optimal value of the system state at time k. At the same time, the predicted value at time k+1 is corrected using the observed value at time k+1 to obtain the optimal value at time k+1, and the process continues in an iterative cycle. Definition (- represents the prior, ^ represents the estimate) is the prior state estimate at the k-th moment given the state before the k-th moment. X(k)^ is the posterior state estimate at the k-th moment given the known measurement variable. Thus, the prior estimation error is defined as and the posterior estimation error E(k). The prior estimation error is the difference between the true state and the prior estimate, and the posterior estimation error is the difference between the true state and the posterior estimate: E(k)=X(k)-X(k)^ Covariance of the prior estimation error is as follows: The covariance of the posterior estimation error is: P(k) = E[E(j)E(j) T ​ Steps 2-4: The Kalman filter estimates the process state using feedback control: the filter estimates the state of the process at a certain moment and then obtains feedback in the form of (noisy) measurement variables. Therefore, the Kalman filter can be divided into two parts: the time update equation and the measurement update equation. The time update equation is responsible for extrapolating the values of the current state variables and error covariance estimates forward in time to construct a priori estimates for the state at the next time. The measurement update equation is responsible for feedback - that is, it combines the prior estimates with the new measurement variables to construct an improved a posteriori estimate. The time update equation can also be regarded as an estimation equation, and the measurement update equation can be regarded as a correction equation. The final estimation algorithm becomes a prediction-correction algorithm with a numerical solution. The time update process of the Kalman filter is as follows: Among them, is the prior estimate of the object's motion state at time k + 1, is the covariance of the prior estimate error at time k + 1; The observation update process of the Kalman filter is as follows: K(k + 1) is the gain matrix of the Kalman filter, is the covariance of the prior estimation error at time k + 1, Z(k + 1) is the observation vector at time k + 1, P(k + 1) is the covariance matrix of the posterior estimation error at time k + 1, which is obtained from the state noise covariance and the observation noise covariance. The smaller the observation noise covariance R(k), the larger the remaining gain and the larger K(k). The prior estimation error covariance is smaller, and the remaining gain K(k) is smaller.

4. A lightweight consensus protocol PoSF based on a mobile blockchain scenario according to claim 1, characterized in that The step 3 specifically includes the following steps: Step 3-1: The representative nodes and verification nodes in the blockchain are all mobile devices. There are several verification nodes within the communication range of the representative nodes. The set of representative nodes is C = {C1, C2,...C i ,....C I}, the set of verification nodes is V = {V1, V2,....V J}, and the set of all nodes is N = {C, V}. Representative node i recruits a batch of verification nodes within its own communication range Step 3-2: After representative node i packs a block, it needs to broadcast the block to other verification nodes in the blockchain network for verification. At the representative node layer, representative node i communicates with other representative nodes through a wireless link. At the verification node layer, the block received by the consensus node is broadcast to the verification nodes it recruits. Representative node i broadcasts the block to the verification nodes recruited by representative node k The propagation delay of the broadcast block is: where n loop is the number of hops for the block to be transmitted between representative nodes, n loop ≤n loopmax , n loopmax is the maximum number of hops for the message to be broadcast in the blockchain network, s i is the data size of the block in bits, w i is the transmission rate of representative node i, B is the wireless channel bandwidth, is the signal-to-noise plus interference ratio at the verification node ; when the representative node i that generates the block propagates the block to the verification nodes it recruits, n loop = 0, where d ave is the average distance between representative nodes, d i,k is the Euclidean distance between representative node i and representative node k as where (x′ i , y′ i ) and (x′ k , y′ k ) are the predicted values obtained by the discrete Kalman filtering method, which are the positions of the nodes in the next consensus period. The communication signal-to-noise ratio between node i and node j is: where α is the path loss exponent, d i,k is the distance between node i and node k, which can be predicted by the discrete Kalman filtering method, d i,n is the distance between node i and interfering node n, and P noise is the noise power; Step 3-3: To ensure successful message transmission, the signal-to-noise ratio of node i needs to exceed a certain threshold β, which is set to 8 dB in the present invention, and the communication quality of node i is Based on the historical interaction experience between node i and other node j, an evaluation of the credibility of node i by other nodes can be obtained, including b j→i trust, d j→i distrust, and u j→i uncertainty. The three evaluations satisfy b + d + u = 1, and the credibility is updated according to the following formula: Indicates the total number of trust evaluations for this node, is the total number of distrust evaluations, and the credibility of node i is: Among them, ρ0 is the initial reputation value of the node; Stability factor SF of node i i From communication quality Q i Combined reputation value ρ i Obtained as follows: Before each round of blockchain mining begins, the stability of each node is calculated, and the node with a stability higher than the threshold is selected from the candidate node set and called the representative node to generate the block.

5. A lightweight consensus protocol PoSF based on a mobile blockchain scenario according to claim 1, characterized in that, The step 4 specifically includes the following steps: Step 4-1: Verify the node The verification delay for verifying that the representative node i generates a block is: Where is the verification node is the computing resource required for the verification representative node i to generate a block, k i is the mapping coefficient from the verification block bit to the CPU cycle number, s i is the data size of the block, in bits, for the verification node The propagation delay for the verification node to accept the block generated by the representative node i is: Among them, is the verification node and the distance between the representative node i, is the verification node and the communication signal-to-noise ratio between the representative node i. The time delay saved by the verification node compared to the maximum tolerable verification time delay is: Among them, is the maximum tolerable verification delay, represents the verification node recruited by representative node i from representative node k is the propagation delay of the broadcast block, is the total delay for the verification node to process the block; Step 4-2: The utility U of representative node i i is the stability reward and the saved latency reward minus the incentive paid to the verification node: where R con is the system reward obtained by the representative node based on stability, is the incentive given by representative node i to the verification node, ξ i is the coefficient of the saved latency, is the number of successful reports by the verification node, is the number of times the representative node behaves maliciously; Verification node The utility is the obtained incentive minus the verification block cost: Among them, is the energy cost coefficient, is the verification node 's switched capacitor constant.

6. A lightweight consensus protocol PoSF based on mobile blockchain scenarios according to claim 1, characterized in that, The optimization objectives and constraints in step 5 are as follows: The benefits of representative nodes must comply with the feasibility constraints of individual rationality (IR) and incentive compatibility (IC) of each verification node.

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