Introduction

Blockchain technology, with its cryptographic, distributed, and chain-like structure, has enabled data consistency, tamper resistance, and nonrepudiation1. It has facilitated the transformation of the internet of Information to the internet of Value2. After big data, cloud computing, artificial intelligence, and virtual reality, blockchain has become another emerging technology with significant impact3. Blockchain, as a distributed ledger system, can process data from various sources. The system uses a P2P network4 and public key encryption5 to provide a secure solution for high-cost, low-efficiency, and uncertain data storage6. Due to the decentralization, traceability, and immutability features of blockchain, it can be combined well with finance, the Internet of Things, and intelligent manufacturing, among other fields. For example, the combination of blockchain and artificial intelligence can play a significant role7,8. The consensus algorithm is the most important underlying technology of blockchain; this algorithm realizes the communication and interaction functions between any two untrusted nodes, thus achieving consistency among multiple nodes9. All nodes in the blockchain network can store, verify, and compute all submitted copies10. The data in the copies mainly include large amounts of transaction data with specific meanings, which do not require third-party processing and registration11. This consensus algorithm not only enhances the robustness of transactions but also guarantees the reliability of transactions12. As the consensus mechanism is extremely important for the blockchain itself and for security, the consensus mechanism that enables multiple nodes to participate fairly and increases the reliability of accounting nodes is increasingly valued. Among the numerous consensus mechanisms, the DPoS consensus mechanism combines the advantages of the PoW consensus mechanism and the PoS consensus mechanism, does not require mining, and does not require full node verification, which shortens the production time and confirmation time of blocks and improves system efficiency. However, if the DPoS consensus mechanism is to be promoted to public chains and alliance chains, the security, fairness, and efficiency issues mentioned above must be solved. To provide a fair, secure environment and efficient production and verification process for blockchain systems, this paper elaborates on the improvement measures taken. Our contributions are as follows:

To address the challenges posed by the low voting enthusiasm among nodes and the security issues caused by malicious nodes in the DPoS consensus mechanism, a new DL-DPoS (deep link-delegated proof of stake) consensus mechanism is proposed in this paper. This mechanism comprises two key components: (1) The LINK mechanism is introduced to motivate nodes by encouraging inactive nodes to participate in the voting and election process. Nodes must form LINK groups before they can participate in the election of leader nodes. (2) To address the problem of low security of elected nodes, the concept of a comprehensive reputation score is introduced. Nodes are rated based on their wealth level, performance, and stability, and their comprehensive reputation score is calculated as an essential component of the election process.

Section “Related work” of this paper reviews the related work in this field and summarizes the more established consensus algorithms currently available. In Section “The deep link DPoS consensus mechanism”, the DL-DPoS consensus mechanism is proposed, followed by an experimental analysis in Section “Security analysis”. Finally, the paper concludes by summarizing the contributions of the research and suggesting potential directions for further investigation.

Related work

Research on blockchain consensus mechanisms can be divided into two categories: consensus mechanisms based on mainstream blockchains and consensus algorithms based on general distributed systems. The former includes popular methods such as proof of work, proof of stake, delegated proof of stake, and practical Byzantine fault tolerance (BFT), while the latter mainly targets distributed database proof of stake14.

Mainstream blockchain consensus algorithms can be divided into traditional distributed consensus algorithms (such as the PBFT algorithm and Raft algorithm12) and blockchain consensus algorithms (such as proof of work13, proof of stake14, and delegated proof of stake15)16. The main indicators of each algorithm are shown in Table 117.

Table 1 Comparison of common consensus mechanisms.
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One interesting algorithm is the delegated proof of stake (DPoS) algorithm proposed by BitShares in 2013. N nodes are selected as managers through an election process, and they verify and package transactions and generate new blocks according to certain rules. This election is generally open to all nodes, and the number of votes is proportional to the node’s own equity. The DPoS consensus algorithm is similar to an “indirect democracy”, where elected nodes gain power, unlike the proof of stake (PoS) consensus algorithm, which is more like a “direct democracy”. The DPoS algorithm solves the problem of resource waste and the issue of high-equity nodes not wanting to participate in bookkeeping in PoS consensus. It is also faster, more efficient, more centralized, and more flexible18.

Between 2014 and 2018, a large number of consensus algorithms with new ideas emerged. The proof of stake velocity (PoSV) consensus algorithm19 strengthens the security of network transactions and incorporates node transactions into the evaluation, encouraging circulation. The proof of authority (PoA) consensus algorithm20 is based on the basic idea of selecting a group of recognized validators to control the right to create blocks. It is energy efficient, slightly centralized, and mostly used in consortium chains and private chains. The proof of weight (PoWeight) consensus algorithm21 mainly represents the probability that a node will find the next block in the network based on the percentage of the node’s equity in the network. It has highly customized and highly scalable features. The proof of capacity (PoC) consensus algorithm22 uses storage instead of mining, so it consumes less resources and can prevent denial-of-service attacks. The proof of burn (PoBurn) consensus algorithm23 is based on the idea that nodes send a certain amount of equity to a nonexistent address to achieve “burning” behavior and implement the privilege of mining in the entire life cycle of the node through a random selection process. However, this system still has significant resource waste. The 2-hop algorithm24 is based on the PoW and PoS concepts and focuses on solving resource consumption and security issues. The Verifiable Byzantine Fault Tolerance (VBFT) consensus algorithm25 is based on a verifiable random function and greatly enhances the system’s resilience against attacks.

After 2018, research on the DPoS consensus algorithm has focused mainly on three directions: improving throughput, enhancing decentralization, and maintaining blockchain stability while increasing voting enthusiasm. Fan et al.26 proposed the Roll-DPoS consensus algorithm, which randomly selects block-producing nodes from a scalable pool of candidate nodes during the election process and verifies blocks through PBFT consensus with ECDSA signature key pairs. To prevent centralization and reduce the probability of malicious nodes being elected, Liu et al.27 proposed the DTBM DPoS consensus algorithm, which uses the K-means algorithm to select good nodes in advance for the proxy queue. Wang28 proposed an incentive mechanism based on the Hegselmann–Krause (HK) opinion dynamic clustering algorithm to address the low voting enthusiasm of nodes. Nodes are classified using clustering algorithms, and rewards are distributed to different nodes based on the classification results. He et al.29 introduced the RBF neural network model to limit phenomena in the DPoS consensus mechanism and introduced a reward mechanism based on dynamic games to increase the cost of malicious nodes, thereby enhancing the stability and security of the blockchain. Chen et al.30 proposed a “reward mechanism” based on the DPoS consensus mechanism, which mainly increases voting rewards and adds rewards for reporting malicious nodes, thereby increasing node participation and system security. Cui31 proposed an unlicensed blockchain that uses a DAG structure, where each account is not affected by other unrelated accounts and only reaches consensus when a fork is observed, enhancing the decentralization of the blockchain.

Hu et al.32 proposed a feedback credibility-based partitioning mechanism, and Li et al.4 proposed a dynamic authorization PBFT consensus mechanism based on reputation. The latter builds on a global trust model based on reputation to prevent malicious nodes from engaging in false evaluation and colluding to deceive by proposing a node feedback evaluation mechanism that distinguishes nodes with high global credibility from those with high feedback credibility. This feedback evaluation mechanism takes into account the frequency of transactions between nodes and the similarity of node evaluations as the main reference factors. FCTrust is a trust mechanism that uses mutual evaluation between participating nodes to analyze the number of transactions between nodes, rating comparisons, and node global reputation values to assign a trust value to the node. Then, through iterative operation, a reputation value that is unique and unchanged for all nodes in the global scope is obtained when no transactions are carried out. FCTrust requires that the node evaluations and feedback information on which the final global reputation value depends are recent and effective and that a distributed solution protocol be used to calculate the global reputation value, greatly reducing the complexity of the algorithm.

In summary, consensus algorithms in blockchain networks are based mainly on proof mechanisms, which have led to the development of other algorithms, such as dPoW, PoC, PoB, PoWeight, PoImportance, PoSV, PoA, and 2-hop, which are based on improvements to the PoW and PoS algorithms. The research focus of these consensus algorithms is largely centered on how to take advantage of their strengths while compensating for their weaknesses, with various breakthroughs in efficiency, security, and energy consumption.

The deep link DPoS consensus mechanism

The introduction of the link and reputation evaluation concepts aims to improve the stability and security of the consensus mechanism, decrease the likelihood of malicious nodes joining the consensus, and increase the reliability of the selected consensus nodes.

The link model structure based on joint action

Through the LINK between nodes, all the LINK nodes engage in consistent activities during the operation of the consensus mechanism. The reputation evaluation mechanism evaluates the trustworthiness of nodes based on their historical activity status throughout the entire blockchain. The essence of LINK is to drive inactive nodes to participate in system activities through active nodes. During the stage of selecting leader nodes, nodes are selected through self-recommendation, and the reputation evaluation of candidate nodes and their LINK nodes must be qualified. The top 5 nodes of the total nodes are elected as leader nodes through voting, and the nodes in their LINK status are candidate nodes. In the event that the leader node goes down, the responsibility of the leader node is transferred to the nodes in its LINK through the view-change. The LINK connection algorithm used in this study is shown in Table 2, where LINKm is the linked group and LINKP is the percentage of linked nodes.

Table 2 LINK connection algorithm.
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Node type

This paper presents a classification of nodes in a blockchain system based on their functionalities. The nodes are divided into three categories: leader nodes (LNs), follower nodes (FNs), and general nodes (Ns). The leader nodes (LNs) are responsible for producing blocks and are elected through voting by general nodes. The follower nodes (FNs) are nodes that are linked to leader nodes (LNs) through the LINK mechanism and are responsible for validating blocks. General nodes (N) have the ability to broadcast and disseminate information, participate in elections, and vote. The primary purpose of the LINK mechanism is to act in combination. When nodes are in the LINK, there is a distinction between the master and slave nodes, and there is a limit to the number of nodes in the LINK group (NP = {n1, nf1, nf2 ……,nfn}). As the largest proportion of nodes in the system, general nodes (N) have the right to vote and be elected. In contrast, leader nodes (LNs) and follower nodes (FNs) do not possess this right. This rule reduces the likelihood of a single node dominating the block. When the system needs to change its fundamental settings due to an increase in the number of nodes or transaction volume, a specific number of current leader nodes and candidate nodes need to vote for a reset. Subsequently, general nodes need to vote to confirm this. When both confirmations are successful, the new basic settings are used in the next cycle of the system process. This dual confirmation setting ensures the fairness of the blockchain to a considerable extent. It also ensures that the majority holds the ultimate decision-making power, thereby avoiding the phenomenon of a small number of nodes completely controlling the system.

After the completion of a governance cycle, the blockchain network will conduct a fresh election for the leader and follower nodes. As only general nodes possess the privilege to participate in the election process, the previous consortium of leader and follower nodes will lose their authorization. In the current cycle, they will solely retain broadcasting and receiving permissions for block information, while their corresponding incentives will also decrease. A diagram illustrating the node status can be found in Fig. 1.

Figure 1
figure 1

Node status diagram.

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Election method

The election method adopts the node self-nomination mode. If a node wants to participate in an election, it must form a node group with one master and three slaves. One master node group and three slave node groups are inferred based on experience in this paper; these groups can balance efficiency and security and are suitable for other project collaborations. The successfully elected node joins the leader node set, and its slave nodes enter the follower node set. Considering the network situation, the maximum threshold for producing a block is set to 1 s. If the block fails to be successfully generated within the specified time, it is regarded as a disconnected state, and its reputation score is deducted. The node is skipped, and in severe cases, a view transformation is performed, switching from the master node to the slave node and inheriting its leader's rights in the next round of block generation. Although the nodes that become leaders are high-reputation nodes, they still have the possibility of misconduct. If a node engages in misconduct, its activity will be immediately stopped, its comprehensive reputation score will be lowered, it will be disqualified from participating in the next election, and its equity will be reduced by 30%. The election process is shown in Fig. 2.

Figure 2
figure 2

The election process.

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Incentives and penalties

To balance the rewards between leader nodes and ordinary nodes and prevent a large income gap, two incentive/penalty methods will be employed. First, as the number of network nodes and transaction volume increase, more active nodes with significant stakes emerge. After a prolonged period of running the blockchain, there will inevitably be significant class distinctions, and ordinary nodes will not be able to win in the election without special circumstances. To address this issue, this paper proposes that rewards be reduced for nodes with stakes exceeding a certain threshold, with the reduction rate increasing linearly until it reaches zero. Second, in the event that a leader or follower node violates the consensus process, such as by producing a block out of order or being unresponsive for an extended period, penalties will be imposed. The violation handling process is illustrated in Fig. 3.

Figure 3
figure 3

Violation handling process.

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Comprehensive reputation evaluation and election mechanism based on historical transactions

This paper reveals that the core of the DPoS consensus mechanism is the election process. If a blockchain is to run stably for a long time, it is essential to consider a reasonable election method. This paper proposes a comprehensive reputation evaluation election mechanism based on historical records. The mechanism considers the performance indicators of nodes in three dimensions: production rate, tokens, and validity. Additionally, their historical records are considered, particularly whether or not the nodes have engaged in malicious behavior. For example, nodes that have ever been malicious will receive low scores during the election process unless their overall quality is exceptionally high and they have considerable support from other nodes. Only in this case can such a node be eligible for election or become a leader node. The comprehensive reputation score is the node’s self-evaluation score, and the committee size does not affect the computational complexity.

Moreover, the comprehensive reputation evaluation proposed in this paper not only is a threshold required for node election but also converts the evaluation into corresponding votes based on the number of voters. Therefore, the election is related not only to the benefits obtained by the node but also to its comprehensive evaluation and the number of voters. If two nodes receive the same vote, the node with a higher comprehensive reputation is given priority in the ranking. For example, in an election where node A and node B each receive 1000 votes, node A’s number of stake votes is 800, its comprehensive reputation score is 50, and only four nodes vote for it. Node B’s number of stake votes is 600, its comprehensive reputation score is 80, and it receives votes from five nodes. In this situation, if only one leader node position remains, B will be selected as the leader node. Displayed in descending order of priority as comprehensive credit rating, number of voters, and stake votes, this approach aims to solve the problem of node misconduct at its root by democratizing the process and subjecting leader nodes to constraints, thereby safeguarding the fundamental interests of the vast majority of nodes.

Comprehensive reputation evaluation

This paper argues that the election process of the DPoS consensus mechanism is too simplistic, as it considers only the number of election votes that a node receives. This approach fails to comprehensively reflect the node's actual capabilities and does not consider the voters' election preferences. As a result, nodes with a significant stake often win and become leader nodes. To address this issue, the comprehensive reputation evaluation score is normalized considering various attributes of the nodes. The scoring results are shown in Table 3.

Table 3 Comprehensive reputation evaluation.
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Since some of the evaluation indicators in Table 3 are continuous while others are discrete, different normalization methods need to be employed to obtain corresponding scores for different indicators. The continuous indicators include the number of transactions/people, wealth balance, network latency, network jitter, and network bandwidth, while the discrete indicators include the number of violations, the number of successful elections, and the number of votes. The value range of the indicator “number of transactions/people” is (0,1), and the value range of the other indicators is (0, + ∞). The equation for calculating the “number of transactions/people” is set as shown in Eq. (1).

$$A_{1} = \left\{ {\begin{array}{*{20}l} {0,} \hfill & {{\text{G}} = 0} \hfill \\ {\frac{{\text{N}}}{{\text{G}}}*10,} \hfill & {{\text{G}} > 0} \hfill \\ \end{array} } \right.$$
(1)

where N represents the number of transactional nodes and G represents the number of transactions. It reflects the degree of connection between the node and other nodes. Generally, nodes that transact with many others are safer than those with a large number of transactions with only a few nodes. The limit value of each item, denoted by x, is determined based on the situation and falls within the specified range, as shown in Eq. (2). The wealth balance and network bandwidth indicators use the same function to set their respective values.

$${A}_{i}=20*\left(\frac{1}{1+{e}^{-{a}_{i}x}}-0.5\right)$$
(2)

where x indicates the value of this item and expresses the limit value.

In Eq. (3), x represents the limited value of this indicator. The lower the network latency and network jitter are, the higher the score will be.

The last indicators, which are the number of violations, the number of elections, and the number of votes, are discrete values and are assigned different scores according to their respective ranges. The scores corresponding to each count are shown in Table 4.

$$A_{3} = \left\{ {\begin{array}{*{20}l} {10*\cos \frac{\pi }{200}x,} \hfill & {0 \le x \le 100} \hfill \\ {0,} \hfill & {x > 100} \hfill \\ \end{array} } \right.$$
(3)
Table 4 Score conversion.
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The reputation evaluation mechanism proposed in this paper comprehensively considers three aspects of nodes, wealth level, node performance, and stability, to calculate their scores. Moreover, the scores obtain the present data based on historical records. Each node is set as an M × N dimensional matrix, where M represents M times the reputation evaluation score and N represents N dimensions of reputation evaluation (M < = N), as shown in Eq. (4).

$${\text{N}} = \left( {\begin{array}{*{20}c} {a_{11} } & \cdots & {a_{1n} } \\ \vdots & \ddots & \vdots \\ {a_{m1} } & \cdots & {a_{mn} } \\ \end{array} } \right)$$
(4)

The comprehensive reputation rating is a combined concept related to three dimensions. The rating is set after rating each aspect of the node. The weight w and the matrix l are not fixed. They are also transformed into matrix states as the position of the node in the system changes. The result of the rating is set as the output using Eq. (5).

$$\text{T}=\text{lN}{w}^{T}=\left({l}_{1}\dots {\text{l}}_{\text{m}}\right)\left(\begin{array}{ccc}{a}_{11}& \cdots & {a}_{1n}\\ \vdots & \ddots & \vdots \\ {a}_{m1}& \cdots & {a}_{mn}\end{array}\right){\left({w}_{1}\dots {w}_{n}\right)}^{T}$$
(5)

Here, T represents the comprehensive reputation score, and l and w represent the correlation coefficient. Because l is a matrix of order 1*M, M is the number of times in historical records, and M <  = N is set, the number of dimensions of l is uncertain. Set the term l above to add up to 1, which is l1 + l2 + …… + ln = 1; w is also a one-dimensional matrix whose dimension is N*1, and its purpose is to act as a weight; within a certain period of time, w is a fixed matrix, and w will not change until the system changes the basic settings.

Assume that a node conducts its first comprehensive reputation rating, with no previous transaction volume, violations, elections or vote. The initial wealth of the node is 10, the latency is 50 ms, the jitter is 100 ms, and the network bandwidth is 100 M. According to the equation, the node's comprehensive reputation rating is 41.55. This score is relatively good at the beginning and gradually increases as the patient participates in system activities continuously.

Voting calculation method

To ensure the security and stability of the blockchain system, this paper combines the comprehensive reputation score with voting and randomly sorts the blocks, as shown in Eqs. (3–6).

$$Z=\sum_{i=1}^{n}{X}_{i}+nT$$
(6)

where Z represents the final election score, Xi represents the voting rights earned by the node, n is the number of nodes that vote for this node, and T is the comprehensive reputation score.

The voting process is divided into stake votes and reputation votes. The more reputation scores and voters there are, the more total votes that are obtained. In the early stages of blockchain operation, nodes have relatively few stakes, so the impact of reputation votes is greater than that of equity votes. This is aimed at selecting the most suitable node as the leader node in the early stage. As an operation progresses, the role of equity votes becomes increasingly important, and corresponding mechanisms need to be established to regulate it. The election vote algorithm used in this paper is shown in Table 5.

Table 5 Election vote counting algorithm.
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This paper argues that the election process utilized by the original DPoS consensus mechanism is overly simplistic, as it relies solely on the vote count to select the node that will oversee the entire blockchain. This approach cannot ensure the security and stability of the voting process, and if a malicious node behaves improperly during an election, it can pose a significant threat to the stability and security of the system as well as the safety of other nodes’ assets. Therefore, this paper proposes a different approach to the election process of the DPoS consensus mechanism by increasing the complexity of the process. We set up a threshold and optimized the vote-counting process to enhance the security and stability of the election. The specific performance of the proposed method was verified through experiments.

The election cycle in this paper can be customized, but it requires the agreement of the blockchain committee and general nodes. The election cycle includes four steps: node self-recommendation, calculating the comprehensive reputation score, voting, and replacing the new leader. Election is conducted only among general nodes without affecting the production or verification processes of leader nodes or follower nodes. Nodes start voting for preferred nodes. If they have no preference, they can use the LINK mechanism to collaborate with other nodes and gain additional rewards.

View changes

During the consensus process, conducting a large number of updates is not in line with the system’s interests, as the leader node (LN) and follower node (FN) on each node have already been established. Therefore, it is crucial to handle problematic nodes accurately when issues arise with either the LN or FN. For instance, when a node fails to perform its duties for an extended period or frequently fails to produce or verify blocks within the specified time range due to latency, the system will precisely handle them. For leader nodes, if they engage in malicious behavior such as producing blocks out of order, the behavior is recorded, and their identity as a leader node is downgraded to a follower node. The follower node inherits the leader node’s position, and the nature of their work is transformed as they swap their responsibilities of producing and verifying blocks with their original work. This type of behavior will not significantly affect the operation of the blockchain system. Instead of waiting until the end of the current committee round to punish malicious nodes, dynamic punishment is imposed on the nodes that affect the operation of the blockchain system to maintain system security. The view change operation is illustrated in Fig. 4.

Figure 4
figure 4

View changes.

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In traditional PBFT, view changes are performed according to the view change protocol by changing the view number V to the next view number V + 1. During this process, nodes only receive view change messages and no other messages from other nodes. In this paper, the leader node group (LN) and follower node group (FN) are selected through an election of the LINK group. The node with LINKi[0] is added to the LN leader node group, while the other three LINK groups’ follower nodes join the FN follower node group since it is a configuration pattern of one master and three slaves. The view change in this paper requires only rearranging the node order within the LINK group to easily remove malicious nodes. Afterward, the change is broadcast to other committee nodes, and during the view transition, the LINK group does not receive block production or verification commands from the committee for stability reasons until the transition is completed.

Security analysis

Decentralization analysis of DL-PoS

Before introducing security, let us first analyze how decentralized the DL-DPoS consensus mechanism is. As an improved consensus algorithm of the DPoS consensus mechanism, its degree of decentralization is closer to that of DPoS, but due to the introduction of comprehensive reputation value as an important part of the election process, its degree of decentralization is lower than that of the traditional DPoS consensus mechanism because the number of votes provided by comprehensive reputation value in the election process is proportional to the number of voters. In this way, nodes with high comprehensive reputation values and majority votes have a better chance to obtain block rights and become leader nodes, which is in line with the interests of most nodes, to avoid the phenomenon of individual nodes controlling elections. In the voting stage, if there is a node whose comprehensive trust value is 75, the number of votes is 800, the number of votes is 1, and the other node has a comprehensive credit value of 90, the number of votes is 9, and the number of votes is 10; in this case, the second node is successfully elected and receives the block power. The degree of decentralization of the popular consensus machine is shown in Table 6.

Table 6 Comparison of the security performance of the consensus mechanism.
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As shown in the above table, the PoW consensus mechanism has the highest security and can protect the privacy of nodes. Its mechanism based on computational power competition for block rights causes it to have the characteristic of high consumption, and it is easy to fork due to its high degree of decentralization and protection of node privacy. The PoS consensus mechanism is based on the rights of nodes to compete for block rights; its consumption is low, it is difficult to fork, and it has high security; however, due to the concept of the PoS coin age, it will lead to the existence of a node with a high interest for a long time, resulting in “the poorer the poorer, and the richer get richer”. The DPoS consensus mechanism introduces the committee mechanism: block rights are controlled by the committee, consumption is very low, and there is basically no fork; however, because the mechanism focuses only on the committee nodes selected according to the voting rights results, the rights are concentrated, decreasing the degree of decentralization. As an improved version of DPoS, the DL-DPoS proposed in this paper inherits the committee.

Therefore, the system inherits the advantages of low consumption and no forks of the DPoS consensus mechanism, draws lessons from the selection of committee nodes not only by relying on the results of equity voting but also by introducing the mechanism of comprehensive credit value and selecting committee nodes that are more secure in the system based on the common action of the number of voters and voting rights, which is more democratic than DPoS is.

Suppose that the probability of node A being selected as a leader is p, the probability of the node's comprehensive reputation exceeding the threshold value is q, the leader node is n, the number of following nodes is m, and the probability of its node doing evil is k. The probability A of a specific node elected at one time not doing evil is shown in Eq. (7).

$$A_{1} = C_{n}^{n} (P*q^{m} *(1 - K))^{n} *(1 - p*q^{m} *(1 - k))^{0}$$
(7)

By introducing the probability of successful view conversion as b, the probability that the node does evil but the system can run normally is shown in Eq. (8), where i > 2n/3.

$$A_{2} = \sum\limits_{n}^{i} {C_{n}^{i} (1 - p*q^{m} *k*C_{m}^{0} *b^{0} *(1 - b)^{m} )^{i} *(p*q^{m} *k*C_{m}^{0} *b^{0} *(1 - b)^{m} )^{n - i} }$$
(8)

The normal operation probability of the node of the traditional DPoS consensus mechanism is shown in Eq. (9), where i < n/2.

$$A = p*\sum\limits_{n}^{i} {C_{n}^{i} k^{i} *(1 - k)^{n - i} }$$
(9)

As seen from the above equation, the difficulty of the DL-DPoS consensus mechanism is much greater than that of the DPoS consensus mechanism in electing specific nodes to the committee. In terms of the normal operation of the system, the DL-DPoS consensus mechanism also has a greater probability of normal operation. Assuming that the probability of the node doing evil is 10%, the number of leader nodes is 3, the number of follower nodes of a leader is 3, and the probability of view conversion success is 90%, we can see from the above equation that the probability of the traditional DPsS consensus mechanism working normally is 97.2%, while the probability of the DL-DPoS consensus mechanism working normally is 99.9%. When the number of leader nodes and follower nodes increases, the probability of normal operation will continue to increase.

DL-DPoS consensus mechanism classic attack defense analysis

Security analysis of fork attack

A fork attack is a classic attack method that threatens the security of a blockchain. By creating a large number of blockchains in a short period of time, branch chains of the same height or different heights appear on the blockchain. However, the possibility of forking attacks in the DL-DPoS consensus mechanism is very small. Because the block out right of the node is in the hands of the leader node of the committee, because the verification node needs to verify the identity of the block creator, the node executing the attack cannot forge its own identity; if the nonleader node is an unauthorized block, then it will be severely punished, such as by directly removing the system.

If it is an internal node of the committee, then it also needs to generate legitimate information and cannot generate malicious information. For example, if the block height is wrong, the transaction information is wrong. If the node produces a block that contains malicious information, then it will also be penalized, deduct equity and cause a comprehensive credit value. In addition, the DL-DPoS consensus mechanism limits the order in which nodes produce blocks. If nodes do not produce blocks in order without permission, they will be severely punished.

If a malicious node wants to carry out a fork attack, it must be a committee node that is currently out of the block. There are many restrictions in the election process in this paper. First of all, it is necessary to calculate the comprehensive credibility value. If the node has been evil in the period of becoming a committee node, then its comprehensive credit value will be greatly reduced, and it will not be eligible to participate in the election for a long time. If the current block leader node produces several legitimate blocks in a short period of time and broadcasts them, because in a block verification process, the verification node records the block header information of the verification block after the verification block. If a second type of header information appears, the verification node will know that there is a malicious node that does not issue a block as needed. The current block producing node is punished. This paper introduces the PBFT algorithm for verification, which has the advantages of fast confirmation speed and high concurrent processing performance. When a certain block is verified by two-thirds of the verification nodes, the block becomes irreversible.

Security analysis of other attacks

  1. (1)

    Most producers cheat. If most of the committee nodes become corrupt, then they will produce an infinite number of forks; in this case, it is necessary to return to the longest chain algorithm, and the chain with the most leader node approval will become the main chain because in the chain with the most approval, the honest node has the most decision and influence. A diagram of majority producer fraud is shown in Fig. 5.

    Assuming nodes 2 and 3 can cause most node fraud to cause infinite bifurcation; in this case, returning to the longest chain can maximize the benefit of node 1. This situation will not last because the behavior will harm the interests of the largest number of general nodes, and the general nodes will not vote for these nodes.

  2. (2)

    Insufficient committee nodes. If the committee node is insufficient, the system will select the appropriate node to become the leader node according to the comprehensive reputation value.

  3. (3)

    Witch attacks. Due to the introduction of the LINK mechanism and the concept of comprehensive creditworthiness, conditions need to be met if participation in the election is required. Since the general node does not affect the ability of block production, the operation of the blockchain can be affected only by entering the committee, and simply forging identities and conducting which attacks has no effect.

  4. (4)

    Eclipse attack. If the leader node or the follower node cannot receive the block from the normal network because of the eclipse attack, it will be sent to the next node in order after a certain time, and after a certain number of times, the system will degrade this node, and its follower node will get its right to issue the block on behalf of it.

  5. (5)

    51% computing power attack. Because of the existence of the committee mechanism, if you want to carry out 51% computing power attack, you must buy a large number of nodes, more than two-thirds of the elected committee nodes into their own nodes, which is not worth the cost of resources.

  6. (6)

    Mining Trojan Horse. The DL-DPoS consensus mechanism is not a mining consensus mechanism; it does not need to consume much computing power, and the block power is concentrated within the committee. Thus, the system of the DL-DPoS consensus mechanism will not be affected by the mining Trojan, or the impact will be very limited.

  7. (7)

    DDoS attacks. Generally, DDoS attacks require a large amount of resources, while the resources in nodes are limited. Since the block-out power and verification power are concentrated in the committee node, general nodes cannot affect system functions other than elections during operation, so general nodes will not affect system operation when they are attacked by DDoS. When the committee node is attacked by DDoS, due to the advantages of the blockchain system using the P2P network, as long as more than half of the committee nodes are in normal operation, the system will not be affected.

Figure 5
figure 5

Schematic of the most producer fraud.

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For the above attacks that threaten the stability of blockchain, the DL-DPoS consensus algorithm proposed in this paper can effectively avoid or protect against them. This paper proposes that the most threatening attacks to the blockchain system are the majority of producer fraud and 51% of computing power attacks, both of which are costly and highly threatening. The consumption generated by controlling the committee node is not proportional to the benefit; it can only succeed in theory in small blockchain systems; it will be abandoned by the shareholder node due to the impact on the node's interests; and it will not last for a long time.

Experimental analysis

This section compares DL-DPoS with the DPoS algorithm in terms of block generation throughput, comprehensive block verification latency, block producer node distribution, and node equity distribution to verify the performance of the DL-DPoS consensus mechanism.

Experimental environment

To verify the performance of the DL-DPoS consensus algorithm proposed in this paper, we used an Intel(R) Core(TM) i5-10500 CPU @ 3.10 GHz processor, 8.00 GB of memory, and Windows 10 as the operating system. We used Golang as the programming language. The experimental configuration is shown in Table 7.

Table 7 Experimental configuration.
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Experimental design

To ensure scalability, we design an experimental setup consisting of 50 nodes forming a blockchain system, with 3 nodes selected as leader nodes and 9 nodes as follower nodes. Since block election voting is involved, we initialize the stakes of all nodes to 100 points. To ensure a balanced distribution of node performance, we initialize the attributes of each node to achieve diversity in performance. We managed to achieve a P2P decentralized network structure for the blockchain. For the three functional modules of the blockchain cycle, we provide a detailed explanation below.

  1. (1)

    Election Module: The election module includes the functions of selecting nodes, computing the comprehensive credibility value of nodes, and recording the results of node election. The node selection function is used to record the selected node election candidates in the LINK group. The consensus mechanism requires self-recommended nodes to become election candidates, which are not automatically selected for election under normal circumstances. The computation of comprehensive reputation scores for nodes calculates the reputation values for nodes that volunteered to be part of the LINK group based on the operations described in the previous section. Only when the comprehensive reputation scores of all nodes in the LINK group exceed the system-set threshold will they be added to the list of election candidates. The function of recording election results is to record the vote count received by the elected node candidates. At the end of the voting, the LINK group with the highest number of votes is selected as the leader and follower nodes, and their voting order is shuffled to determine their block production order.

  2. (2)

    Consensus Validation Module: The consensus validation module includes the functions of block generation by leader nodes, block validation by follower nodes, broadcasting validation results, and replacement of malicious nodes. The function of leader node block production is to produce blocks in order for leader nodes, and a node will be skipped if it fails to produce a block after a specified time delay. The function of follower node validation is to validate the blocks produced by the leader node according to the rules described above. The purpose of validation result broadcasting is to upload the validated blocks and broadcast the results from the leader and follower nodes to the general nodes. The function of malicious node replacement is to demote, dismiss, replace, and punish the malicious leader and follower nodes according to the rules described above.

  3. (3)

    Reward Module: The reward module includes the functions of recording node behavior and distributing rewards based on the behavior. The function of recording node behavior is used to record behaviors such as node voting and malfeasance, which serve as the basis for rewards distributed at the end of a cycle. The function of distributing rewards based on behavior is used to distribute rewards to nodes based on previous behavior and calculate the node limit value λ.

First, the main function is executed to create 50 node accounts on the chain and initialize balance and basic information for election voting and computing comprehensive reputation scores. Then, the election module is executed, nodes vote and elect committee leader and follower nodes based on their preset basic states and operating modes, with the leader node's block generation order randomized. After that, the block validation phase begins (during which the next committee election is also held), during which the transaction information is packaged into blocks according to the generation and validation algorithm described above. These blocks are validated by follower nodes and then broadcast to the general nodes after being successfully validated. If a node acts maliciously during the consensus, it is resolved according to the previous process.

Performance verification

In this paper, the performance of the blockchain system is mainly verified in terms of system block production efficiency, block generation rights distribution, and block equity distribution. We analyze and verify the various aspects of the proposed consensus mechanism, such as efficiency, effectiveness, and integrity, by extracting the same data at the same time using two different consensus algorithms.

Block production efficiency and stability

TPS stands for “transactions per second” and is a measurement unit in blockchain which refers to the number of blocks produced within a certain time. The TPS is an important metric for measuring the performance of a blockchain system. In this section, we validate the improvement in block production by introducing the improved PBFT consensus algorithm. We compare the number of blocks produced during different time intervals, namely, 10 min, 20 min, 30 min, 40 min, 50 min, and 60 min, based on the block heights. Six sets of data are selected for comparison, as shown in Fig. 6.

Figure 6
figure 6

Number of generated blocks.

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As seen from the data in the figure, the DL-DPoS consensus mechanism slightly improves block production compared to that of the DPoS. Multiple runs of blockchain operation data show that the block production stability of both the DL-DPoS and DPoS consensus mechanisms is very stable, which should be due to the existence of the committee mechanism that concentrates block production rights and improves block production efficiency. Approximately 90 blocks are produced by DPoS in approximately 10 min, while approximately 110 blocks are produced by DL-DPoS. The ratio of the number of blocks produced by the DL-DPoS consensus mechanism to that produced by the DPoS consensus mechanism is shown in Fig. 7.

Figure 7
figure 7

Production block ratio.

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The figure shows that the DL-DPoS consensus mechanism improves block production by up to 23% compared to that of the DPoS. In terms of block production, the DL-DPoS is superior to the traditional DPoS. The voting stage of DL-DPoS is similar to that of DPoS, as it also relies on the number of votes obtained by nodes to determine the leader nodes. However, the DL-DPoS consensus mechanism adds steps to calculate the overall reputation value of nodes, and LINK nodes can self-recommend to form teams during the preparation stage before voting, resulting in a slightly increased block production speed compared to that of the DPoS. Although the increase is limited, it is essential for system stability and security.

In Fig. 8, the production efficiency and stability of DL-DPoS are evaluated by utilizing the real number of blocks produced by the consensus mechanism as the numerator and the expected number of blocks produced as the denominator.

Figure 8
figure 8

Block production efficiency.

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Figure 6 clearly shows the block efficiency of the nodes during the six time periods of 10 min, 20 min, 30 min, 40 min, 50 min, and 60 min in the experimental run. Although the efficiency appears steep, the majority of the efficiency rates range from 90 to 95%, ensuring stability. This 5% difference is likely caused by block or validation delays due to latency issues. Both the DL-DPoS and DPoS consensus mechanisms have fixed orders of leader nodes for block production; thus, if a node that should produce a block has delay and does not respond after waiting for a period of time, the block production right will be given to the next node.

In summary, the DL-DPoS consensus mechanism is superior to the traditional DPoS consensus mechanism in terms of both block production efficiency and stability. In the next section, we will conduct experiments to illustrate the impact of the DL-DPoS on the nodes in the blockchain system after it has been in operation for a while.

Evaluation of the mechanism of LINK validation

Before studying the distribution of node rights, it is necessary to test node participation, which refers to the quantity and quality of nodes participating in transactions. The greater the node participation in a blockchain network is, the more active the network becomes, as more nodes participate in the network.

In this paper, nodes that participated in the voting and election process are marked, and the node participation rate is the ratio of the number of marked nodes to the total number of nodes. This section verifies the performance improvement achieved by the LINK mechanism. We still compare the six runs of the DPoS consensus mechanism and the DL-DPoS consensus mechanism at six time periods of 10 min, 20 min, 30 min, 40 min, 50 min, and 60 min. The results are shown in Fig. 9.

Figure 9
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Node participation.

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As shown in the graph, in most cases, the node participation rate in the DL-DPoS consensus mechanism is much greater than that in the traditional DPoS consensus mechanism. In particular, the node participation rate in the DL-DPoS consensus mechanism can reach more than 80% even after running for 60 min, while the node participation rate in the DPoS consensus mechanism ranges from 40 to 50%. This indicates that the DL-DPoS consensus mechanism can achieve its maximum activity level faster and maintain its vitality for a longer time than can the DPoS consensus mechanism.

The significantly greater activity in the graph compared to that in the DPoS consensus mechanism is due to the existence of the LINK mechanism in the DL-DPoS consensus mechanism. The LINK mechanism connects multiple nodes into groups, with the idea of active nodes driving inactive nodes to participate in the system consensus. The LINK mechanism connects multiple nodes into groups, with the idea of active nodes driving inactive nodes to participate in the consensus process. If some nodes are not interested in participating in voting and election activities, they can participate in the activity by following active nodes through the LINK mechanism. After the election, they can receive corresponding rewards based on their own contributions. This mechanism can fully mobilize node participation and ensure the vitality of the blockchain system.

In summary, the LINK mechanism in the DL-DPoS consensus mechanism significantly enhances node participation, ensuring the vitality of the blockchain system.

After analyzing node activity, the node power distribution is analyzed. The node power distribution is an important indicator that reflects the stability and fairness of the system. The more dispersed the distribution is, the more opportunities each node has to control the right to produce blocks. Correspondingly, the distribution of power will also improve, and the system stability and fairness will increase. Conversely, the more concentrated the distribution is, the more the Matthew effect in the system is strengthened, which affects the stability of the system and the fairness between nodes.

To analyze the node power distribution, the system was run for 60 rounds, and the winning nodes were marked. After the run, the number of times each node gained the right to produce a block was recorded, and the nodes were divided into five categories: 0, 1–5, 6–15, 16–25, and above 25. The distribution of these five categories is shown in Fig. 10.

Figure 10
figure 10

The distribution of these five categories.

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Based on the data in Fig. 10, it can be observed that in the traditional DPoS consensus mechanism, more than 60% of nodes have never obtained production rights, whereas in the DL-DPoS consensus mechanism, the proportion of nodes that have obtained production rights is approximately 30%. In the segment where the number of block production rights obtained is between 1 and 5, there are significantly more nodes in the DL-DPoS than in the DPoS. After that, both sides have relatively few nodes. With DPoS, a small number of nodes may monopolize block production rights, leaving a majority of nodes unable to obtain them. Under the DL-DPoS consensus mechanism, the distribution of node rights is much better, with only a small number of nodes failing to obtain block production rights, while most nodes obtain block production rights a limited number of times, thus alleviating the concentration of block production rights.

Verification of malicious node handling efficiency

In this section, we assume that a malicious node will appear during one round of block production by committee nodes in the consensus process, and this malicious node may be a committee node or a general node. We run the consensus process for 60 rounds with the same number of nodes as in the previous section and record the time it takes for the malicious node to be flagged and punished. The results are presented in Fig. 11.

Figure 11
figure 11

Malicious node handling efficiency.

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As shown in Fig. 11, the processing speed of malicious nodes generally falls within 5 s, with most cases occurring within 1.5 s. This is because malicious nodes are quickly detected since they cannot produce blocks. Similarly, a follower node has the right to validate only blocks and has no block production rights. If these two types of nodes become malicious, they are quickly detected and punished. If a committee node becomes malicious, it cannot be determined quickly, and whether it violates the rules during the validation process needs to be determined quickly. Due to latency, the processing time may be slightly greater than that of other methods, but once latency is determined, the processing time will increase immediately.

Future work

The present study proposes improvements to the DPoS consensus mechanism. However, there are still shortcomings in the current research to improve its practical implementation. Further improvements are required in the following areas. First, algorithm design is emphasized in this paper, but if the mechanism is to be used formally, more nodes may cause more delays. Second, computing and verification capabilities need to be further enhanced to accommodate faster-paced transaction activities. Third, the use of block rights is too simple, only for voting and trading, and more extensions are needed to adapt to real scenarios. Finally, to ensure higher security and stability of nodes, a more flexible and deeper selection system is needed, which could involve deep learning technology.

As the core component of blockchain technology, consensus mechanisms should receive more attention in future research. The development trend for future blockchain consensus mechanisms should focus on the following areas:

Designing a provably secure consensus mechanism, such as combining the security of the PoW consensus mechanism with the scalability of the PoS to create a new generation of provable blockchain consensus mechanisms.

New technologies such as big data and cloud computing can be used to assist in blockchain data computation and verification. The advantages of blockchain P2P networks include solving fork issues and allowing blockchain to handle multiple transactions at the same time.

Conclusion

This paper introduces a new consensus mechanism called DL-DPoS, which improves upon the DPoS consensus mechanism by introducing the concepts of LINK and reputation. The performance of DL-DPoS was demonstrated to surpass that of DPoS in terms of block generation speed, stability, fairness, and security. The contributions of this paper are summarized as follows: First, in the consensus initiation stage, the LINK mechanism is introduced, allowing nodes to automatically form teams based on their own needs in preparation for the election phase. The LINK mechanism aims to transform individual actions into team actions, and nodes that form LINK groups vote for their main node during the election process. The rewards are then distributed among the group members based on their contributions, and additional rewards are given to increase their activity levels. Like fund management, the manager is responsible for the team's investment strategy. To become a leader node, a node also needs to form a LINK group to become an election team. Second, during the election stage, comprehensive reputation scores are calculated for LINK group members who want to become leader nodes. All team members must exceed a certain threshold to qualify for the position. Once elected, the main node in the LINK group becomes the leader, responsible for block production, while the other nodes become followers, responsible for block verification. Third, in the consensus stage, the leader node produces blocks, while the follower nodes verify them.

Improvements were made to all three stages, resulting in an overall increase in the security, scalability, and tamper resistance of the blockchain system, surpassing the traditional DPoS consensus mechanism in all aspects.