Consensus Optimization Algorithm for Distributed Intelligent Medical Diagnostic Collaborative Systems Based on Verifiable Random Functions and Reputation Mechanisms

Abstract

With the deep integration of distributed network technology and intelligent medical care, how to achieve efficient collaboration under the premise of safeguarding data security and system efficiency has become an important challenge for intelligent medical diagnosis systems. The traditional practical Byzantine fault tolerance (PBFT) algorithm has difficulty meeting the demands of large-scale distributed medical scenarios due to high communication overhead and poor scalability. In addition, the existing improvement schemes are still deficient in dynamic node management and complex attack defence. To this end, this paper proposes the VS-PBFT consensus algorithm, which fuses a verifiable random function (VRF) and reputation mechanism, and designs a distributed intelligent medical diagnosis collaboration system based on this algorithm. Firstly, we introduce the VRF technique to achieve random and unpredictable selection of master nodes, which reduces the risk of fixed verification nodes being attacked. Secondly, we construct a dynamic reputation evaluation model to quantitatively score the nodes’ historical behaviors and then adjust their participation priority in the consensus process, thus reducing malicious node interference and redundant communication overhead. In the application of an intelligent medical diagnosis collaboration system, the VS-PBFT algorithm effectively improves the security and efficiency of diagnostic data sharing while safeguarding patient privacy. The experimental results show that in a 40-node network environment, the transaction throughput of VS-PBFT is 21.05% higher than that of PBFT, the delay is reduced by 33.62%, the communication overhead is reduced by 8.63%, and the average number of message copies is reduced by about 7.90%, which demonstrates stronger consensus efficiency and anti-attack capability, providing the smart medical diagnosis collaboration system with the first VS-PBFT algorithm-based technical support.

1. Introduction

Blockchain technology, as a decentralized distributed ledger technology, has become a key technology driver in a number of fields, such as finance, IoT, supply chain, etc., since the introduction of the Bitcoin system [1] in 2008. With the continuous expansion of blockchain application scenarios, traditional consensus algorithms are facing many challenges, especially the balance of efficiency, security, and scalability [2]. Among many blockchain consensus algorithms, the practical Byzantine fault tolerance (PBFT) algorithm has become the consensus mechanism of choice for many federation and permission chains due to its high throughput and deterministic termination properties [3]. However, the standard PBFT algorithm suffers from high communication complexity (O(n²)), rigid node authentication mechanisms, and lack of resilience to malicious node attacks when facing large-scale node networks [4,5], which severely limits its potential application in highly dynamic blockchain systems.

As the scale of distributed systems expands, the balance between security and performance becomes particularly critical. The traditional PBFT algorithm usually adopts a static node configuration, where all authentication nodes have the same weight, and this ‘one-size-fits-all’ design concept cannot adapt to the characteristics of node heterogeneity and dynamic changes in complex network environments [6]. Especially in open network environments, malicious nodes may disrupt the consensus process through witch attacks, eclipse attacks, etc., and the standard PBFT lacks an effective mechanism to identify and respond to these attacks [7]. These limitations have motivated researchers to explore novel consensus algorithm design ideas that combine cryptographic primitives with incentive mechanisms to enhance the security, scalability, and efficiency of PBFT algorithms [8].

Verifiable random functions (VRFs), as an advanced cryptographic tool, are capable of generating publicly verifiable pseudo-random outputs while maintaining the unpredictability of the outputs [9]. This property of VRFs makes them ideal for designing fair and manipulation-resistant leader election mechanisms, which have been successfully applied in blockchain platforms such as Algorand [10] and Dfinity [11]. On the other hand, reputation mechanisms, as a means of dynamically assessing the reliability of node behavior, assign dynamically changing reputation values to nodes by recording and analyzing the nodes’ historical behaviors, thus providing a quantitative basis for system decision making [12]. Reputation systems have been widely used in P2P networks [13], e-commerce [14], and distributed systems [15], providing new ideas for building autonomous and adaptive security mechanisms.

In the design of blockchain consensus algorithms, regulatory compliance constraints for medical data are particularly critical. For example, in the United States, the Health Insurance Portability and Accountability Act (HIPAA) imposes strict limitations on the use and sharing of protected health information (PHI), allowing data exchange only with patient authorization or under legally permissible circumstances [16]. Similarly, the European Union’s General Data Protection Regulation (GDPR) requires adherence to principles such as data minimization, purpose limitation, and informed consent for the processing of personal health data [17]. These regulations mandate the integration of technical safeguards from the outset, including encrypted storage, fine-grained access control, and tamper-proof audit logs, to ensure legal compliance [16,17]. Meanwhile, healthcare data processing must uphold both anonymity and the principle of data minimization. Traditional VRF-based and reputation-based mechanisms, when applied independently, lack inherent support for data anonymization and fine-grained access control, making it difficult to meet the compliance requirements of HIPAA and GDPR [18].

In order to more intuitively demonstrate the advantages of VS-PBFT over existing mainstream consensus mechanisms, in terms of key performance indicators, this paper compares six typical consensus algorithms in terms of throughput, latency, security, scalability, fault-tolerance, resource consumption, and communication overhead, as shown in

Table 1. Comparison of different algorithms under various indicators.

Evaluation Metric	VS-PBFT	PBFT	GR-PBFT	NAC-PBFT	POW	POS
High Transaction Throughput	√	√	×	√	√	×
Low Transaction Latency	√	×	√	×	×	√
Good Scalability	√	×	×	×	√	√
Strong Security	√	×	×	√	×	√
High Fault Tolerance	√	√	×	√	×	×
Low Resource Consumption	√	×	√	√	×	×
Low Communication Overhead	√	×	√	×	×	√

.

Obviously, existing consensus algorithms have their own advantages and disadvantages, and it is difficult to take into account security, efficiency, and scalability at the same time. To this end, this paper proposes an innovative consensus optimization improvement scheme (VS-PBFT) for distributed intelligent medical diagnosis collaborative systems based on a verifiable random function and reputation mechanism, which aims to simultaneously address the limitations of traditional PBFT algorithms in terms of security, efficiency, and scalability.

1.1. Related Work

In the study of consensus mechanisms for distributed systems, the introduction of verifiable random functions (VRFs) and reputation mechanisms provides a new research direction to improve the performance and security of the practical Byzantine fault-tolerant (PBFT) algorithm. In recent years, academics have gradually explored the introduction of reputation mechanisms and verifiable random functions to improve the consensus performance [19,20].

Early improvement efforts mainly focused on quantitatively evaluating nodes through reputation mechanisms so as to dynamically screen out well-performing nodes during the consensus process. In 2010, Barreno et al. [21] proposed a comprehensive security framework for learning systems, analyzing potential threats such as data poisoning and collusion attacks that may affect reputation-based mechanisms. In 2014, Goodfellow et al. [22] introduced an adversarial example generation method, further revealing the vulnerability of learning systems under non-independent and identically distributed (non-i.i.d.) conditions, thereby providing theoretical guidance for the robust design of reputation mechanisms. In 2018, Lei Kai et al. [23] proposed a reputation-based Byzantine fault-tolerant algorithm for the PBFT algorithm in the coalition chain, which reduced the possibility of malicious nodes by obtaining a high voice power during the voting process. In 2020, Chen J. H. et al. [24] proposed an improved PBFT algorithm based on a reputation and voting mechanism. This method reduced the possibility of malicious nodes being elected as master nodes by introducing a reputation model and a voting mechanism to ensure that the master nodes were elected by nodes with higher reputation. In 2021, Tao Wang et al. [25] proposed RBT (distributed reputation system), a distributed reputation system for blockchain-based peer-to-peer energy transactions, which improved the trustworthiness and efficiency of energy trading platforms. In 2022, Rui Gu et al. [26] proposed a PBFT master node election algorithm based on anomaly detection and a reputation model, which reduced the influence of malicious nodes and improved the fault tolerance and security of the system. In 2023, Biggio et al. [27] proposed an evasion attack method targeting machine learning systems, where attackers could bypass model detection during the testing phase, indicating potential risks for reputation mechanisms when facing collusion-based score manipulation. In 2024, Niu Kai et al. [28] proposed an improved method based on reputation value for the PBFT consensus algorithm in IoT environment, which optimized the consensus process and improved the performance and reliability of the system in IoT scenarios.

Meanwhile, in order to solve the centralization and predictability problems in the node election process in the traditional PBFT algorithm, researchers began to focus on the application of VRF in the consensus mechanism. In 2004, Gura et al. [29] evaluated the performance of ECC operations on 8-bit AVR platforms, revealing that a single 160-bit scalar multiplication on an ATmega128 microcontroller took approximately 0.81 s, highlighting the computational burden of VRF on resource-constrained IoT devices. In 2017, Cascudo and David [30] proposed the SCRAPE scheme, which utilized the stochasticity beacon mechanism witnessed by a public entity to provide a more secure stochasticity generation method for distributed systems. Androulaki et al. [31] systematically introduced VRF for the first time in Hyperledger Fabric in 2018, which effectively suppressed witch attacks by selecting consensus nodes through verifiable randomness. In 2020, Kietzmann et al. [32] proposed the integration of lightweight pseudorandom number generation schemes in IoT systems to reduce the performance impact of security mechanisms on resource-constrained devices, offering optimization strategies for deploying VRF on medical edge devices. In 2021, Seo and Azarderakhsh [33] implemented Curve448 computations on the Cortex-M4 platform, showing that core VRF operations required over six million clock cycles. In 2023, Zhang et al. [34] proposed FortunChain, an elliptic curve VRF (EC-VRF)-based scalable blockchain system that implemented state sharding to ensure efficient and secure node selection. In the same year, Jiang et al. [35] proposed the VPBFT algorithm to improve the PBFT consensus mechanism based on VRF and the PageRank algorithm. By introducing VRF for master node election, the unpredictability of master node selection was increased; combined with the PageRank algorithm to evaluate the importance of nodes, the node selection process was optimized. In 2024, Chen et al. [36] proposed the Slicing PBFT (PBFT) consensus algorithm based on VRF, which utilized VRF to group nodes randomly, reducing the communication overhead and improving the consensus efficiency. This improvement effectively solved the performance bottleneck of the traditional PBFT algorithm in large-scale networks.

Overall, the improvement of PBFT from 2015 to present has experienced a clear evolutionary trend from the optimization of a single reputation mechanism to the introduction of VRF [37]. Early research focused on how to optimize node election and reduce the impact of malicious behaviors through reputation mechanisms, while the subsequent introduction of VRFs addressed the fairness and unpredictability issues that existed in traditional PBFT election mechanisms [38]. However, previous research has always focused on either a single VRF mechanism or a reputation mechanism. The VS-PBFT algorithm we propose is the first to deeply integrate both, fully leveraging their complementary advantages. Additionally, we have designed a distributed diagnostic collaboration system model to explore its potential applications in the medical field.

1.2. Contribution

Compared with existing research work, this study makes the following contributions to the design and application verification of consensus mechanisms:

(1)

Technical Innovation: In this study, an improved consensus algorithm, VS-PBFT, which incorporates a verifiable random function and dynamic reputation mechanism, is proposed based on the PBFT consensus mechanism. In the leader node selection process, VRF provides cryptographic randomness, avoiding the predictability issues of traditional mechanisms. Meanwhile, the reputation mechanism dynamically adjusts the nodes’ priorities, optimizing efficiency and security in the consensus process. The combination of both effectively reduces the risk of single-point attacks, enhancing the system’s robustness and stability.

(2)

Application Scenario Design: Based on the proposed consensus algorithm, this study designs a distributed diagnosis collaboration system model for intelligent medical scenarios, which serves as a typical application case of the VS-PBFT algorithm, and is used to validate its application potential in medical data security and collaborative processing. The model embodies the applicability of the algorithm in privacy protection, data immutability, and multi-agency collaboration at the system architecture level, which helps to demonstrate the practical value of the proposed algorithm in real complex scenarios.

1.3. Organization

The rest of this paper is organized as follows: Section 2 shows our model design and scenario setting, model evaluation, and system goals. Section 3 describes the research on the optimization of the master node selection mechanism of our proposed enhanced VRF-based VS-PBFT consensus algorithm and the research on the enhanced VS-PBFT consensus algorithm based on the dynamic reputation mechanism. Section 4 discusses the specific setup of the experimental environment and provides experimental results for performance evaluation and comparative analysis. Finally, the paper is summarized in Section 5.

2. System Model Design and Scheme Setup

In this section, we describe our proposed system model and present the model evaluation and system objectives.

2.1. Model Design

The distributed intelligent medical diagnosis collaboration system we propose consists of five core entities working together (as shown in Figure 1). Among them, the trusted authority (TA) serves as the authoritative center of the system, responsible for identity authentication, key distribution, and dynamic reputation assessment of all medical AI agent nodes. To prevent single points of failure or attack risks that the TA may face, we introduce a BLS-based threshold signature mechanism (e.g., in a group of 5 TA nodes, 1 node can fail or be malicious, and at least 3 nodes must jointly sign for it to be valid), thereby constructing a decentralized TA operational structure. During system operation, patients initiate diagnostic requests through smart terminals, and the platform automatically matches the appropriate AI agent nodes based on the provided basic symptoms, medical history, and other information. In the consensus process, the system utilizes the verifiable random function (VRF) mechanism to randomly elect a diagnostic group from the candidate nodes, which is internally weighted based on the latest reputation scores of each node fed back by the diagnostic model to ensure that the high-reputation nodes have a slightly higher probability of winning the VRF, and then reaches a distributed diagnostic result based on the VS-PBFT consensus algorithm that incorporates the dynamic reputation mechanism. Here, there is tight interdependence between the medical diagnostic model and the consensus algorithm: the initial judgment output from the diagnostic model serves as the input for the voting of the consensus nodes, and the voting results of VS-PBFT are in turn used to update the dynamic reputation scores of the agents. This closed-loop feedback mechanism makes it possible that when the diagnostic quality of an agent decreases, its reputation score is automatically cut, resulting in a decrease in its participation ratio in the subsequent VRF lottery election and VS-PBFT voting. On the contrary, high-reputation agents are given more diagnostic and voting opportunities, thus enhancing the system robustness while improving the overall diagnosis accuracy, fully reflecting the synergistic optimization effect of the model and the consensus algorithm. Meanwhile, the medical data center (MDC) is responsible for the security management of the entire data lifecycle. Data are transmitted and processed through TLS 1.3 encrypted channels, and a PKI mechanism is used to achieve mutual authentication between nodes. Critical data are further protected at the application layer using the AES-256 symmetric encryption algorithm, ensuring it cannot be cracked or tampered with. Additionally, we designed a blockchain–EHR interface adaptation mechanism based on middleware. The middleware module can map the structured data on the chain to standard FHIR resources in real time, and at the same time, the diagnostic conclusions confirmed by VS-PBFT consensus will be synchronously pushed to the EHR system and privilege inheritance, so as to realize end-to-end closed-loop synergy from model inference→consensus confirmation→landing of the clinical system, and bi-directional interactions are carried out with the hospital’s EHR system through the RESTful API, supporting data synchronization and privilege inheritance, thus realizing cross-platform data sharing and business synergy. The two-way interaction with the hospital EHR system through the RESTful API supports data synchronization, privilege inheritance and structure conversion, thus realizing cross-platform data sharing and business collaboration. The VS-PBFT algorithm used by the system will be introduced in detail in Section 3.

2.2. System Objectives

This study proposes and implements an improved VS-PBFT consensus algorithm based on the deep integration of a verifiable random function (VRF) and a node reputation mechanism. By introducing randomized leader election and dynamic reputation evaluation, the system’s security and fault tolerance are significantly enhanced. Building upon this foundation, a distributed medical diagnosis system is designed, utilizing a blockchain ledger to record the entire diagnostic process and results, thereby ensuring data integrity, traceability, and tamper resistance.

3. VS-PBFT Algorithm Based on the Combination of Reputation Mechanism and Verifiable Random Function (VRF)

The VS-PBFT algorithm proposed in this paper combines a verifiable random function and reputation mechanism to optimize the master node election and node trust management of the traditional PBFT, thereby enhancing the fairness, robustness, and security of the consensus process. It is particularly suitable for distributed intelligent medical systems requiring high performance and security. The specific flow of the algorithm is shown in Figure 2 below.

3.1. Optimization of Master Node Selection Mechanism of Enhanced VS-PBFT Consensus Algorithm Based on VRF

In distributed system consensus algorithms, the master node selection mechanism is a critical component for ensuring system security, performance, and fairness. The verifiable random function (VRF) needs to satisfy the following properties:

• Verifiability: For all key pairs $(pk,sk)\in \mathrm{KeyGen}(1^{\lambda })$ and strings $\mathrm{m}\in {\{0,1\}}^{in(\lambda )}$, if $(\delta ,\rho )=Prove(sk,\mathrm{m})$, then there exists a negligible polynomial $\mu$, such that:

  $$\mathrm{Pr}[\mathrm{Verify}(pk,\mathrm{m},\delta ,\rho )=1]=1-\mu (\lambda )$$

  (1)
• Uniqueness: For all key pairs $(pk,sk)\in \mathrm{Keypair}(1^{\lambda })$ and prime strings $\mathrm{m}\in {\{0,1\}}^{in(\lambda )}$, there exists no $\left({\delta }_1,{\delta }_2,{\rho }_1,{\rho }_2\right)$ such that $\mathrm{Verify}\left(pk,\mathrm{m},{\delta }_1,{\rho }_1\right)=1$ and $\mathrm{Verify}\left(pk,\mathrm{m},{\delta }_2,{\rho }_2\right)=1$ hold simultaneously, i.e.,:

  $$\mathrm{Pr}[{\delta }_1\ne {\delta }_2{|}_{\mathrm{Verify}(pk,\mathrm{m},{\delta }_2,{\rho }_2)=1}^{\mathrm{Verify}(pk,\mathrm{m},{\delta }_1,{\rho }_1)=1,}]\le \mu (\lambda )$$

  (2)
• For all functions where $\mathrm{D}$ obeys the PPT distribution, there exists a negligible polynomial $\mu$, such that:

  $$\mathrm{Pr}[D(1^{\lambda },F(sk,\mathrm{m}))=1]-\mathrm{Pr}[D(1^{\lambda },{\{0,1\}}^{\mathrm{out}(\lambda )})=1]\le \mu (\lambda )$$

  (3)

Figure 3 shows a sketch of the security proofing of the VRF module in the VS-PBFT protocol based on the universally composable (UC) security framework. The model portrays the contrasting relationship between the real protocol and the ideal functionality by formally modeling the participating entities in the system and their interaction behaviors. Environment A acts as an external driver, receiving inputs r, x, and j and coordinating the protocol flow. Adversary A intercepts inputs r and x and intervenes in the execution behavior of participant P_i by calling the interface in x. System participant P_i receives inputs r, x, and j from Environment A and coordinates the protocol flow. System participant P_i receives commands from the ambient body and the input module, executes the corresponding protocol logic, and feeds the output back to the ambient body. The dashed box on the right shows the ideal functional area containing the generator module Γ_VRF for the verifiable random function and its functional abstraction F_VRF, where Γ_VRF receives the seed values and outputs pseudo-random pairs (y,π) through the secure VRF generator component G, and F_VRF subsequently provides interfaces for protocol calls to ensure that the outputs are unpredictable and verifiable. The security model uniformly schedules the VRF behavior through abstract functionalities F to limit the intervention of adversaries in the randomness and output process, thus ensuring the robustness and composable security of the protocol in the face of malicious environments.

3.1.1. Key Generation for VRF

In this study, we used the Ed25519 algorithm of elliptic curve cryptography to implement the verifiable random function. The general form of the elliptic curve equation is:

$$\mathrm{f}(\mathrm{u})=v^2\mathrm{mod}p=u^3+au+b(\mathrm{mod}p)$$

(4)

where a, b, and p are constants defining a particular elliptic curve and (u, v) are points on the curve. During the key generation phase, each node generates a unique public–private key pair, and the Ed25519 system ensures key security and unforgeability:

$$pk={\mathrm{G}}^{\mathrm{sk}}\mathrm{mod}p$$

(5)

where the private key (sk) is a random number that is the base of the Ed25519 elliptic curve and p is the modulus of the prime field. pk is the 32-byte public key; sk is the 64-byte private key.

3.1.2. Generation and Output of Random Numbers

Each node i generates r based on sk and m. We used a hash-based pseudo-random number generation method, where m first undergoes a SHA-512 hash computation to produce a 512-bit hash value. Then, we intercepted the first 64 bytes to form an intermediate result and introduced exponential and logarithmic operations to increase the complexity:

$$M=\left({\displaystyle \sum _{i=1}^{64}{H}_{64}}[i]\times 2^i\right)\mathrm{mod}\mathrm{p}$$

(6)

$$N={\log }_2\left(1+{\displaystyle \prod _{i=1}^{64}(H_{64}[i]+1)}\right)\mathrm{mod}\mathrm{p}$$

(7)

where $H_{64}[i]$ denotes the ith byte of the intercept, $M$ is an intermediate random number generated by weighted exponentiation, and $N$ is a nonlinear random number generated by combining logarithm and product. Finally, we further introduced bitwise operations and nonlinear mapping $\mathrm{f}\left(\mathrm{x}\right)$ to enhance the complexity of the output, i.e., the final random number output, which can be expressed by the following equation:

$$r=(M\oplus N)+\left(H_{256}(H_{64})\times \left(e^{M\mathrm{mod}\mathrm{p}}+{\log }_2(N+1)\right)\right)\mathrm{mod}$$

(8)

where $e^{M\mathrm{mod}\mathrm{p}}$ introduces an exponential operation to amplify the nonlinear effect and ${\log }_2(N+1)$ balances the numerical growth to avoid overflow.

3.1.3. Proof Generation

During the master node election process, each node i generates the corresponding proof simultaneously based on private key sk and message m (the implementation is shown in Algorithm 1). The VRF proof generation process can be represented as follows:

$$\pi =(H_{256}(r\cdot G),H_{256}((r+H_{512}(\mathrm{r}+\mathrm{H}\cdot \mathrm{s})\mathrm{mod}\mathrm{p}))$$

(9)

where $H_{256}(m)$ denotes the SHA-256 hash performed, $\mathrm{R}=\mathrm{r}\cdot G$ is the curve point corresponding to $r$, and s is the sk-derived scalar. After completing the construction, the legitimacy of the proof is also verified by checking whether the curve point computation is $R^{\prime }=\mathrm{R}$. If consistent, the node identity is confirmed. The specific verification formula can be expressed as follows:

$$R^{\prime }=s^{-1}\cdot (S\cdot G-H_{512}(R\parallel \mathrm{pk}\parallel m)\cdot \mathrm{pk})$$

(10)

Algorithm 1 VRF Proof Generation Algorithm

Input: Secret key sk, Message m

Output: Proof π

1: CP(sk, m):

2:  SD ← sk[0…31]

3:  HS ← Init_SHA512()

4:  HS ← Up(HS, SD)

5:  HS ← Up(HS, m)

6:  H ← R(HS)

7:  π ← S(h, sk)

8:  return −1

9:  if VS(H, π, DP(sk)) = F then

10:   return CP(sk, m)

11:  else

12:   return π

13:  End if

Where CP denotes the ComputeProof function, SD is the private key seed, HS denotes the current hash state, Init_SHA512 denotes initializing the hash state, Up denotes updating the hash state, H denotes the hash value, R denotes the final result, S denotes the use of the signature algorithm for signing, VS denotes the use of the public key for verifying the signature, D denotes the public key exported from the private key, F is the false, and T is true. The algorithm notations in subsequent sections will not be repeated if already introduced.

3.1.4. VRF Proof Verification

The goal of the VRF verification algorithm is to verify the validity of proof $\pi$ generated from a private key by means of public key pk and input message m. First, for input message m and public key pk, a hash value hash is computed. Mathematically, this can be expressed as follows:

$$\mathrm{Hash}=H_{512}(pk\parallel M)=H_{512}(p{k}_1,p{k}_2,\dots ,p{k}_n,m_1,m_2,\dots ,m_k)$$

(11)

where $\mathrm{pk}=(p{k}_1,p{k}_2,\dots ,p{k}_n)$ denotes the byte sequence of the public key and $message=(m_1,m_2,\dots ,m_k)$ denotes the byte sequence of the message. Then, in the Ed25519 algorithm, the signature verification process makes the following equation hold by checking for the existence of private key sk:

$$H(pk,m)=R(pk,m)+sk\cdot Q(pk,m)$$

(12)

where $R(pk,m)$ and $Q(pk,m)$ are elliptic curve points associated with message m and public key pk, and $H(pk,m)$ is the hash value generated from the message and the public key. Finally, if the signature is successfully verified, the proof is valid and 0 is returned; otherwise, an error code −1 is returned, indicating that the proof is invalid.

3.1.5. Master Node Election Process

With the introduction of VRF, the master node election process becomes more dynamic and unpredictable. First, the master node election is based on the random number generated by VRF. Each node i generates a random number $r_i^{\prime }$ based on its own private key and shared message m. A new master node can be elected by the following formula:

$$X=r_i^{\prime }[0]\mathrm{mod}$$

(13)

where $r_i^{\prime }[0]$ is the first byte of the random number generated by node i and N is the total number of nodes in the network. To avoid selecting a node already acting as a master, the system recalculates the master node ID through a simple mechanism:

$$\mathrm{X}=\left(\mathrm{X}+1\right)modN$$

(14)

This adjustment mechanism effectively avoids the same node becoming the master node consecutively and ensures the fairness and decentralization of the consensus process. The specific implementation is shown in Algorithm 2:

Algorithm 2 VRF-based View Change Algorithm

INPUT: Current view v, Number of nodes N, Current leader LC

OUTPUT: New leader LN, New view v’

1: CV(v, N, L):

2:  v’ ← v + 1

3: NI ← r[0] mod N

4:  SD ← “leader-election” || v’

5:  (pk, sk) ← G(λ)

6:  π ← CP(sk, SD)

7:  r ← CO(π)

8:  CL ← r[0] mod N

9:  if CL = L then

10:   LN ← (CL + 1) mod N

11:   else

12:   LN ← CL

13:   End i

14:   BV(v’, LN, π, r)

15:   return (LN, v’)

Where CV denotes the attempt conversion, v denotes the current attempt number, v’ denotes the new attempt number, L denotes the current leader, NI denotes the new leader ID, G is a key pair generating function, CL denotes the candidate leader, LN is the new leader, and BV denotes the broadcasting of the new leader information.

3.2. Research on Enhanced VS-PBFT Consensus Algorithm Based on Dynamic Reputation Mechanism

In this section, we introduce how the reputation mechanism can dynamically adjust node participation authority and improve the security and fault tolerance of the algorithm.

3.2.1. Credibility Constraints on the Consensus Process

Each node maintains a reputation $R_i$, whose reputation ${\mathrm{R}}_i$ is affected by successful or failed execution. Specifically, when a node successfully completes a vote in consensus, its reputation increases; and vice versa decreases. The update rule of reputation degree is shown in Equation (15):

$$R_i=R_i+k\cdot \mathrm{T}-m\cdot \mathrm{F}(0<R_i<100)$$

(15)

where $k$ is the percentage of credibility increase in case of success, $m$ is the percentage of decrease in case of failure, $\mathrm{T}$ stands for completion of voting, and $\mathrm{F}$ stands for verification failure. When the reputation of a node falls below a predefined threshold, the node will be excluded from participating in the consensus process. The reputation of all nodes at startup is initialized to 50.0; it is automatically trimmed to the range of 0–100 after each update to avoid overshooting or underflow. As shown below, where $ϵ$ is the credibility threshold.

$$\mathrm{Y}=\left\{\begin{array}{lll}1,\hfill & R_i>ϵ\hfill & \hfill \\ 0,\hfill & R_i\le ϵ\hfill & \hfill \end{array}\right.$$

(16)

3.2.2. Combination of Credibility Update and Consensus Process

In the PREPARED phase of the VS-PBFT protocol, whenever a node votes on a “ready” message, the reputation-weighted message validation algorithm is shown in Algorithm 3, the system will first check its reputation. It can only participate if $R_i>30$. If the validation is successful, the reputation will be increased; if the validation is unsuccessful, the reputation will be deducted. If voting is prohibited due to a reputation lower than 30, the reputation will also be deducted again for failure to participate in the consensus, accelerating the elimination of unreliable nodes. The node reputation update formula in the reputation mechanism can be expressed as follows:

$$R_i(t)=\left\{\begin{array}{ll}{R}_i(t-1)+{\eta }_1\cdot \left(100-R_i(t-1)\right)\cdot {\gamma }_s,\hfill & s(t)\in \Omega \hfill \\ R_i(t-1)-\left(1-{\eta }_2\cdot {\gamma }_f\right),\hfill & f(t)\in \Phi \hfill \end{array}\right.$$

(17)

where $R_i(t)$ denotes the reputation of node i at moment t; $R_i(t-1)$ denotes the reputation of node i at the previous moment t − 1; ${\eta }_1$ and ${\eta }_2$ are the adjustment factors for successful and failed participation in the consensus, respectively; and ${\gamma }_s$ and ${\gamma }_f$ are the influence factors for successful and failed participation in the consensus, respectively. $\mathrm{s}(t)$ and $f(t)$ are the schematic functions denoting the success and failure events, respectively. $\Omega$ and $\Phi$ denote the success and failure of the set of events indicating whether the node is successful in the current round of message propagation or not, respectively, and the node controls whether it participates in the subsequent consensus phase through these dynamically changing reputation. Specifically, $R_i(t)$ can be denoted as follows:

$$\Delta R_t(t)=\left\{\begin{array}{lll}{R}_i+0.09,\hfill & s(t)\in \Omega \hfill & \hfill \\ R_i-0.5,\hfill & f(t)\in \Phi \hfill & \hfill \end{array}\right.$$

(18)

Algorithm 3 Reputation-Weighted Message Verification Algorithm

INPUT: Message m, Sender ID s, Recipient ID r, Current reputations {Rep_i}_{i = 1}^N

OUTPUT: Boolean result, Updated reputation R’

1: VM(m, s, r, {R}_{i = 1}^N):

2:  θ ← 30.0

3:  if CanP(s, R, θ) = F then

4:   return (F, R)

5:  End if

6:  SV ← (m[6] = ‘1’)

7:  CM ← (CCT(m[3]) = CI)

8:  VIM ← (CCT(m[4]) = VIN)

9:  if SV ∧ CM ∧ VIM then

10:    R’ ← UR(s, R, T)

11:    return (T, R’)

12:   else

13:    R’ ← UR(s, R, F)

14:    return (F, R’)

15:   End if

Where VM denotes the verification of message accuracy, θ is to set the threshold of credibility, Canp checks the credibility of the node comparing with the threshold, SV verifies whether the signature is legal or not, CM verifies whether the client matches or not, CCT denotes the conversion of characters to integer, and VIM verifies the numbering of the attempts.

4. Experimental Results and Analysis

This section describes the experimental environment setup of this paper and evaluates and analyzes the performance of the VS-PBFT algorithm.

4.1. Experimental Environment Setup

The experiment was conducted in a virtual machine environment with a Ryzen 7 7840H processor (AMD Inc., Santa Clara, CA, USA) and Ubuntu 20.04.3 operating system, configured with 8 GB RAM and a 40 GB SCSI hard disk. The experiment was based on the NS3.40 framework in C++ and the development tool was Visual Studio Code 1.98.1. The experiment used IPv4 as the network layer protocol, the link type was P2P, the link propagation delay was 2 ms, the transport layer protocol was UDP, the initial reputation value was set to 50.0, the network topology was a fully-connected (mesh) structure, the link bandwidth was 5 Mbps, the IP address was assigned in the 10.1.1.0/24 network segment, and the communication port was 7071. Tests of different environments in the NS3 framework with 10–40 nodes and 10–30 consensus rounds were performed. The experimental data were averaged over 50 independent runs with the outliers removed.

Messages delivered by the node consensus process used the lightweight UCI Heart Disease Data Set (https://github.com/Ruohan-Yang/Heart-Disease-Data-Set, accessed on 25 April 2025), a healthcare dataset that was primarily used to validate the system’s protocol stability in handling business loads with data transfer capability. The Github address for this experimental code is: https://github.com/ZDQCDB/VS-PBFT-main/tree/master (accessed on 25 April 2025).

4.2. Experimental Results

In this section, we show and analyze the performance of our proposed consensus optimization algorithm VS-PBFT for distributed intelligent medical diagnostic collaborative systems based on a verifiable random function and reputation mechanism versus the traditional PBFT algorithm in terms of transaction throughput TPS, average transaction latency, average number of message replicas, communication overhead, reputation variations, DOS attacks under different number of nodes (10 to 40), and performance comparison in a consensus rounds (10 to 30) environment.

As shown in Figure 4, the TPS and latency variations of six PBFT variants (VS-PBFT, PBFT, GR-PBFT, POS_PBFT, POW_PBFT, and NAC_PBFT) under the same number of consensus rounds are compared to validate the advantages of VS-PBFT. The transaction latency of all algorithms increases with the number of nodes, but VS-PBFT always maintains the lowest latency. At 40 nodes, its latency is only 66.48% of PBFT and the growth curve is flat, indicating that it effectively reduces the latency by optimizing the communication mechanism, while the latency of PBFT, POW, and NAC_PBFT increases significantly when the number of nodes exceeds 30. Figure 5 shows that the throughput of each algorithm decreases with node expansion, but VS-PBFT not only maintains the highest throughput, which is significantly better than POS and GR-PBFT at 10–20 nodes, but also maintains more than 2000 tps at more than 25 nodes, which is significantly better than the other algorithms (which are all lower than 1500 tps).

In the distributed network experiments containing 25 nodes and 30 rounds (Figure 6 and Figure 7), VS-PBFT keeps the average message replica count lower than PBFT, GR-PBFT, and NAC_PBFT through dynamic reputation evaluation with randomized role assignment. The experiments show that the replica count of VS-PBFT grows more moderately with increases in the number of nodes and the number of consensus rounds, which proves that its reputation strategy is able to effectively suppress the communication overhead.

The experimental results in Figure 8 and Figure 9 show that the communication overhead of each algorithm rises significantly as the number of nodes increases from 10 to 40; however, at 40 nodes, the communication data size of VS-PBFT is 4860 KB, which is about 10.4% and 7.7% lower than that of PBFT and NAC_PBFT, respectively, and in the range of 30–40 nodes, its overhead rate (77.1%) is lower than that of PBFT (85.2%) and GR-PBFT (81.2%). The advantage of VS-PBFT in overhead is also gradually revealed when the number of consensus rounds increases.

In terms of reputation management, Figure 10 and Figure 11 show that VS-PBFT maintains high reputation stability as the node size increases from 10 to 40. The average reputation of the nodes increases steadily, and the difference between the maximum and minimum reputation is about 1 percentage point, which exhibits a better fair regulation mechanism. Finally, the DoS attack defense experimental results presented in Figure 12 show that VS-PBFT, by integrating the reputation mechanism with the verifiable random function (VRF), its attack success rate is always controlled at 0.15–0.25% (only 0.18% at 10 nodes), and the number of attacks grows extremely slowly, thus significantly improving the system’s attack resistance.

Figure 13 shows the comparison of five key metrics between VS-PBFT and FHIRChain under 10 to 25 nodes, including the audit trail generation time, maximum/minimum response time, average node audit time, and generation rate. The results show that VS-PBFT outperforms FHIRChain overall in all metrics, and the performance maintains higher stability with the increase in the number of nodes, while FHIRChain fluctuates significantly. Specifically, in the case of 25 nodes, the audit trail generation rate of VS-PBFT is 42.14% higher than that of FHIRChain, and the generation time is 29.60% lower.

5. Conclusions

5.1. Research Summary

In this paper, we propose the consensus optimization algorithm VS-PBFT based on a verifiable random function and reputation mechanism for distributed intelligent medical diagnosis collaboration systems. The algorithm breaks through the performance bottleneck of the traditional PBFT in large-scale networks by combining reputation evaluation and VRF random node selection. The experimental results show that VS-PBFT significantly outperforms traditional algorithms in terms of transaction throughput, latency, network security, communication efficiency, and reputation management. Its dynamic update of node weights can effectively curb malicious behaviors, and the optimized message propagation and view switching strategy reduces redundant communication while realizing a balanced distribution of node reputation to ensure stable operation of the system, thus providing efficient and reliable consensus support for intelligent medical diagnosis collaboration systems.

5.2. Limitations and Future Work

Although the VS-PBFT algorithm showed excellent performance in this study, large-scale scaling in a multi-hospital network still faces certain challenges, such as coordination overhead due to heterogeneity among nodes and cross-institutional data privacy protection. In addition, the current system has not yet been deployed and validated in a real clinical environment, and in-depth research in conjunction with the regulatory approval process is needed in the future. We also fully recognize the importance of collaborating with medical professionals to conduct case studies, and our future work will focus on conducting joint research with clinical partners to promote a pilot application and field validation of the system in real medical scenarios. On the other hand, the reputation mechanism has a cold start problem, and the lack of effective historical data support for new nodes at the initial stage may affect the system’s decision-making efficiency. To address this limitation, subsequent work can introduce a reputation cross-validation extension mechanism based on federated learning, in which each institution locally scores the behavior of nodes and shares the parameters of encrypted models to achieve collaborative cross-organizational reputation updating, which will enhance the accurate assessment of node reputation while protecting privacy, and thus further improve the system’s scalability and adaptability in complex and heterogeneous healthcare environments.