Our contribution

To address the above privacy and efficiency related challenges, this paper introduces a balanced construction of consortium blockchain with CLAS-CPP scheme. Further we summarize the key contribution as follows:

1. While preserving vehicles privacy in VANETs, realizing unlinkability. Instead of using real identity, we adopt pseudonym identity mechanism. In results, an adversary is unable to track the actual identity of a vehicle.
2. leveraging the semi-decentralized and lightweight nature of consortium blockchain (CBC) where a pre-selected group of nodes from multiple organizations manages the consensus process and much feasible for cross authentication, we couple the RSUs using consortium blockchain technology ensuring higher efficiency and faster transaction speeds while maintaining a degree of decentralization.
3. Traceability is another primary factor to be performed when illegal activities are found in VANET system. For this purpose, we adopted trusted tracing authority (TA) that keeps the record of all registered vehicles and can trace easily in case of abnormal situation.
4. Widespread adoption of certificate based signature scheme affects the system efficiency. Therefore, we use certificateless aggregate signature (CLAS) along with conditional privacy protecting (CPP) approach that increase the system efficiency as well as privacy.
5. Achieved higher privacy and efficiency as compared to existing state of the art schemes. We conduct both theoretical analyses and simulation experiments in real road networks environment using OMNET++ simulation tool.

Organization

Rest of the paper is organized in such way that section II describes the existing privacy and security related challenges for VANETs considered in this paper. Section IV presents the preliminaries for this research. Further, section V demonstrate the proposed scheme comprehensively. Section VI describe a rigorous security analysis of our proposed scheme. Section VIII present an extensive experiments and results. In section IX, we conclude the research with future directions and opportunities.

Query content modification

In VANETs, the query content modification issue arises when the data transmitted between vehicles or between vehicles and infrastructure nodes is altered, either maliciously or unintentionally. For instance, the query passes through multiple relay nodes before reaching the server. An attacker, who has compromised one of these relay nodes, intercepts and modifies the content of the query. Instead of requesting the fastest route, the modified query asks for an alternative, less efficient route. The server, unaware of the modification, processes the query and sends back directions based on the false request. As a result, the user’s vehicle follows a suboptimal route, potentially leading to increased travel time and fuel consumption. This problem can compromise the reliability and integrity of the information shared across the network, such as traffic conditions, safety alerts, and navigation instructions. Malicious nodes might inject false data to create confusion, cause accidents, or manipulate traffic flow for personal gain, while accidental modifications can result from signal interference or transmission errors. To address this, robust security protocols and data validation mechanisms are essential to ensure the authenticity and accuracy of the exchanged information, thereby maintaining the overall safety and efficiency of the VANET system [25].

Content replay

Content replay refers to the malicious retransmission of previously captured valid messages. This form of attack severely disrupts the network’s functionality, as outdated or irrelevant information is injected back into the system, causing confusion and potentially hazardous situations. For example, a replayed emergency braking signal could trigger unnecessary braking actions by other vehicles, leading to accidents or traffic congestion. The effectiveness of the VANET system relies on the timeliness and accuracy of data, so replay attacks undermine these core principles. To mitigate this risk, VANETs must implement strong authentication and time-stamping mechanisms, ensuring that each message is both from a legitimate source and temporally relevant, thereby protecting the network against replay attacks and maintaining its integrity and reliability [26].

Impersonation

Impersonation issue arises when an attacker masquerades as a legitimate vehicle or network node, gaining unauthorized access to the network. This can lead to severe security breaches, as the impersonator can inject false information, manipulate traffic patterns, or even disable critical safety messages. For instance, an attacker might pose as an emergency vehicle to force other cars to yield or change lanes, creating chaos and potentially causing accidents. Impersonation compromises the trust and reliability that VANETs depend on to function effectively. To counteract this, VANETs require robust identity verification protocols and secure cryptographic methods to authenticate the identity of each node, ensuring that all participants in the network are genuine and authorized, thus protecting the system from such malicious exploits [27].

Efficiency

The efficiency issue in Vehicular Ad Hoc Networks (VANETs) pertains to the network’s ability to handle high volumes of data traffic and deliver timely, reliable communication among vehicles and infrastructure nodes. Given the dynamic and highly mobile nature of VANETs, maintaining efficient data transmission is crucial for real-time applications like collision avoidance, traffic management, and navigation assistance. Challenges include managing the rapidly changing network topology, mitigating packet loss and delays, and optimizing bandwidth usage to prevent congestion. Efficient routing protocols, adaptive communication strategies, and robust data dissemination methods are essential to address these challenges. Ensuring high efficiency in VANETs not only enhances the overall user experience but also significantly contributes to road safety and traffic flow optimization, making the network resilient and effective in diverse and demanding conditions [28].

Note that privacy challenges for VANETs are not limited to aforementioned but also include some substantial issues such as data confidentiality, data availability etc. However, these challenges are beyond the scope of this research.

A. Certificateless Aggregate Signature (CLAS)

Certificateless Aggregate Signature (CLAS) significantly enhances privacy protection in Vehicular Ad Hoc Networks (VANETs) by eliminating the need for certificates while enabling efficient and secure communication [40]. In VANETs, vehicles V_i​ communicate by sending signed messages m_i​ to other entities such as Roadside Units (RSUs) and other vehicles V_j​. Using a certificateless approach, each vehicle V_i​ generates a partial private key K_priv​ without relying on a certificate authority. This key is used to produce an individual signature σ_i for the message m_i​. Multiple signatures σ_i ​ from different vehicles are then aggregated into a single compact signature σ_agg represented as , where n is the number of individual signatures. The aggregated signature σ_agg​ is verified using an aggregated public key PK_agg​, ensuring that all n messages m_i​ are authentic and untampered. This method reduces the communication overhead and computational cost associated with handling multiple certificates and signatures, thereby preserving vehicle anonymity and enhancing privacy. The elimination of certificates mitigates the risk of certificate-related attacks and simplifies key management, making CLAS an effective solution for maintaining security and privacy in VANET environments.

B. Conditional privacy-preserving

In VANETs, Conditional Privacy-preserving (CPP) mechanisms are designed to balance privacy and traceability without relying on traditional Public Key Infrastructure (PKI) [41]. Let V = {v₁,v₂,…,v_n} represent the set of vehicles, and P denote the trusted Private Key Generator (PKG). Each vehicle v_i is assigned a partial private key di by P and generates its own secret value x_i and public key P_i = x_i⋅G, where G is a generator of the elliptic curve group. The vehicle’s full private key is S_i = (d_i,x_i). For conditional privacy, each message m sent by vehicle v_i includes a pseudonym P_i,t ​ valid for a time period t, computed as P_i,t = H(t)⋅P_i where H is a hash function. If misbehavior is detected, an authority A can request the PKG to reveal v_i​’s identity by combining di ​ and Pi ​ to trace the pseudonym Pi,t back to the vehicle. The CPP mechanism ensures privacy by keeping x_i secret while enabling accountability through the conditional traceability provided by P and A. This balance maintains security and privacy efficiently without certificates, enhancing trust in VANET communications.

C. Lightweight consortium blockchain

In Vehicular Ad Hoc Networks (VANETs), maintaining the security and trustworthiness of data can be effectively achieved through a lightweight consortium blockchain framework. In blockchain emerging technology, the decentralized nature of the identity management system ensures that no single entity has undue control over the identity information, providing a secure and transparent framework for managing identities in a distributed manner [42–45]. Let D represent the set of participants in the blockchain-based decentralized identity management system, where D = {d₁​,d₂​,…,d_n​}, and n is the total number of participants. Let K denote the set of cryptographic key pairs associated with each participant in the system, where K = {(pk₁​,sk₁​),(pk₂​,sk₂​),…,(pk_n​,sk_n​)}, and pk_i​ and sk_i​ represent the public and private keys of participant di​, respectively. The identity of each participant di​ is represented as ID_i​, where ID_i​ is a unique identifier associated with participant di​ in the blockchain. Transactions in the system are denoted by T, and each transaction t includes relevant information such as the sender’s identity ID_sender​, receiver’s identity ID_receiver​, and the content of the transaction. The blockchain is represented as B, and it consists of a sequence of blocks {B₁​,B₂​,…,B_m​}, where each block B_j​ contains a set of transactions{t₁​,t₂​,…,t_k​} and a reference to the previous block B_j−1. The consensus mechanism used for block validation and addition is denoted by C, and it ensures agreement among participants on the validity of transactions and the order of blocks in the blockchain. The smart contract functionality is denoted by S, and it defines the rules and conditions for executing transactions automatically based on predefined terms within the blockchain.

Vehicles (V)

In Vehicular Ad Hoc Networks (VANETs), vehicles equipped with On-Board Units (OBUs) interact to enhance transportation efficiency and safety. OBUs enable vehicles to communicate with each other (Vehicle-to-Vehicle, V2V) and with roadside infrastructure (Vehicle-to-Infrastructure, V2I). This interaction facilitates the exchange of critical information such as traffic conditions, accident alerts, and navigation assistance in real time. By leveraging OBUs, VANET systems improve traffic flow, reduce the likelihood of accidents, and provide drivers with timely information, thereby creating a more connected and intelligent transportation network.

Tracing Authority (TA)

TA plays a pivotal role in maintaining network integrity and security. The TA is responsible for overseeing and managing the network to ensure that the information disseminated is accurate and reliable. If a vehicle disseminates incorrect or malicious information, the TA can trace the source using cryptographic techniques and digital signatures embedded in the messages. By verifying these signatures against a database of registered vehicles, the TA can identify and locate the offending vehicle, thereby maintaining trust and accountability within the network. This capability is essential for preventing misinformation, ensuring the safety of all users, and upholding the effectiveness of VANET systems.

Key Generation Center (KGC)

KGC is responsible for generating and distributing cryptographic keys that vehicles use to authenticate and encrypt their communications. To generate part of a vehicle’s private key, the KGC calls the Partial-Private-Key-Extract (PPKE) function, which involves creating a partial private key using specific cryptographic algorithms and parameters. This partial key is then securely transmitted back to the vehicle. The vehicle combines this partial key with its own unique identifier or other secret information to form its complete private key. This process ensures that even if the partial key is intercepted, it cannot be used alone to compromise the vehicle’s communications, thus enhancing the overall security of the VANET system.

On-Board Units (OBUs)

OBUs play a crucial role in Vehicular Ad-Hoc Networks (VANETs) by enabling communication between vehicles and with roadside infrastructure. OBUs, installed in vehicles, facilitate the exchange of information such as traffic conditions, safety warnings, and navigation assistance. They collect data from various sensors within the vehicle and communicate this information to other vehicles or Roadside Units (RSUs). OBUs forward information to RSUs using Dedicated Short-Range Communications (DSRC) or other wireless communication protocols. This interaction allows for real-time updates on road conditions and enhances overall traffic management and safety by creating a connected network of smart vehicles and infrastructure.

Consortium Blockchain (CBC) based Roadside Unit (RSU)

Suppose that RSUs are extensively deployed on road networks. When a vehicle moves into a different geographic area, it needs to establish trust and secure communication with the local infrastructure and other vehicles. Ensuring continuous access to vital data for vehicles and facilitating the swift recording of new trust information, CBC facilitates this by maintaining a distributed ledger shared among a consortium of trusted entities, such as local authorities and service providers. By integrating RSUs into the vehicular network, a blockchain core network emerges, storing multiple encoded blocks within the RSUs and forming a comprehensive, decentralized database. Even if a vehicle travels out of the initial RSU’s communication range due to high-speed movement, it can still communicate with other RSUs to retrieve query results. RSUs manage query requests from vehicles, creating anonymous cloaking regions and forwarding them to the Location Service Provider. Additionally, RSUs return the query results to the requesting vehicle(s) and are responsible for maintaining the blockchain.

Considering the features of above discussed entities, the operational sequence of proposed scheme is summarized more specifically as follows:

1. In first step, overall the system is initialized, and relevant parameters are disseminated among all connected entities which is the requirement for all vehicles to get registration with TA. Vehicle (V_i) requests to TA for registration along with its real identity (RID_i).
2. TA executes the pre-configured pseudonym generation algorithm, and generate a pseudonym identity (PID_i) for the requesting entity V_i. Further V_i preloads the PID_i over OBU.
3. Using secret-value algorithm, V_i generates private key (K_priv) for itself. Further, V_i along with K_priv forward the PID_i to KGC to generate partial private key (Key_ppriv) to be used for further communication.
4. Using partial private key extraction algorithm, KGC generate Key_ppriv using conventional private key extraction algorithm, and return to V_i.
5. Using Key_ppriv and K_priv, V_i generate a new pair of public-private key to be used for subsequent communication among the entities. For this purpose, public-private key generation algorithm is used.
6. Using message (m), PID_i, and K_priv, V_i generates a signature message, and forward to other concerning entities including RSU and vehicles.
7. Before authentication, if reconstruction is proceeded successfully, further communication is carried on; otherwise aborted immediately.
8. On other side, RSU or any other vehicle (V_j) ensure the signature validation based on input parameters such as m, PID_i, and K_pub. V_j accepts the signature if valid otherwise reject and report accordingly.
9. On other hand, V_i may post a request for any point of interest (POI) to location service provider (LSP). In our mechanism, to reduce the communication overhead, we use cache based LSP that responds promptly. Otherwise, LSP post an external route request to online route API, and return the retrieved results back to requesting vehicle.

In this research, we use variety of algorithms including Pseudonym identity generation, Traceability, Partial-Private-Key-Extraction, Signature generation, and implementation of Lightweight Consortium Blockchain for RSUs in VANETs. Further detail of each algorithm is presented in algorithm 1,2,3,4, and 5 as follows.

Algorithm 1. Pseudonym identity generation.

Inputs:

 RID: Real Identity of requesting vehicle Vi

Output:

 PID: Pseudonym Identity for requesting vehicle Vi

Declarations:

 Vi → Requesting vehicle

Process:

 1. if (RID is valid) // Check validity of RID;

 2. then

 3.        generate PID; // Generate a unique pseudonym identity;

 4.        store mapping (RID, PID) in the secure database;

 5. return PID to vehicle Vi;

 6. else

 7.    if (RID is invalid)

 8.    then

 9.        reject request and notify Vi;

Algorithm II. Traceability of malicious vehicle.

Inputs:

 PID_i: Pseudonym Identity of suspected malicious Vi

Output:

 RID_i: Real Identity of requesting vehicle Vi

Declarations:

 TA → tracing authority

 FI→ fake information

 McE→ Misconducting event

 L_msg→ log of vehicles messages

 DB → Secure database

Process:

 1. TA Monitoring the VANET system.

 2. if (L_msg containing (McE or FI)

 3. Then

 4.         Trace PID_i of originating McE or FI

 5.          if (PID_i found in DB)

 6.          Then

 7.                   retrieve corresponding RID_i

 8.                   broadcast RID_i & PID_i over network

 9.                   return PID_i for penalty imposition

 10.else

 11.return indicating unknown PID_i

Algorithm 3. Partial-Private-Key-Extract Algorithm.

Inputs:

 PID_i: Pseudonym Identity for requesting vehicle V_i

 Key_priv: Private key shared by V_i

Output:

 Key_ppriv: partial private key for subsequent V_i

 Key_ppub: partial public key for subsequent V_i

Declarations:

 S_i → random secret key

 P → generator point on the elliptic curve

Process:

 1. Receive PID_i ​and Key_priv from V_i

 2. if (PID_i​ is valid) // Validate the pseudonym identity of subsequent vehicle​;

 3. then

 4.        generate a random secret S_i​;

 5.        calculate the partial private key Key_ppriv ​ = S_i​.

 6. calculate the partial public key Key_ppub ​ = S_i​.P where P is generator point on the elliptic curve.

 7.        store the mapping of Key_ppriv, Key_{ppub, and} PID_i in secure DB

 8.        return Key_ppriv, Key_ppub, to V_i

 9. else

 10.return error message indicating invalid PID_i​;

Algorithm 4. Signature generation mechanism.

Inputs:

 m: message content,

 PID_i: Pseudonym Identity of subsequent V_i

 Key_priv: Private key generated by V_i

Output:

 σ: Signature

Declarations:

 F_q​ → finite field

 P → generator point on the elliptic curve

 q → a large prime number

 R → elliptic curve point

 k → random nonce from 0 to n-1. Where n is total number of vehicles.

Process:

 1. Receive m, PID_i, and Key_priv from V_i.

 2. k = Generate a random nonce k from the finite field F_q​

 3. Calculate R = k. P

 4. If (R is not NULL or Empty)

 5. {

 6.         Calculate r = hash (R) mod q

 7.         Calculate s = (hash (m) + r. Key_priv)^k-1 mod q

 8.  σ = (r,s)

 9. }

 10.Else

 11.{

 12.         Terminate process with message “Invalid input value.”

 13.}

 14.return σ

Algorithm 5. Lightweight Consortium Blockchain for RSUs in VANETs.

Inputs:

 T_i: Transaction from vehicle V_i,

 PID_i: Pseudonym Identity of subsequent V_i

 σ: Signature of the transaction

Output:

 LCBC: lightweight consortium blockchain

Declarations:

 CBC​ → consortium blockchain

 H → Cryptographic hash function

 k → Nonce for proof-of-work

 M → Merkle root of transactions

 H_{prv_block} → hash of previous block.

 RSU_kpub → public key of RSU.

Process:

 1. Receive T_i, PID_i, and σ_i from V_i.

 2. Verify σ_i using PID_i, and RSU_kpub.

 3. if (Verify (σ_i by PID_i, and RSU_kpub) = true)

 4. then

 5.         append verified T_i to the pending transactions list.

 6.         construct a new block:

 7.         gather pending transactions and form a block data structure.

 8.         compute the M of the transactions.

 9.         compute the proof-of-work:

 10.        set k = 0

 11.        for H (H_{prv_block} || M || k) meets the difficulty target

 12.                increment k.

 13.Form the new block with k, M, and the hash of the previous block.

 14.else

 15.Discard T_i, and report.

 16.return σ

A. Query content modification attack resistance

Let S represent the set of legal vehicle-related sensitive information, and let ′S′ represent the set of pseudonym data forwarded by the anonymizer server. Additionally, let C represent the cloaking region generated by the anonymizer server and forwarded to the RSU. Then, the lemma can be expressed as follows:

Lemma. For any adversary A attempting to tamper with the legal vehicle-related sensitive information S, such that S≠S′, in the presence of the anonymizer server and the proposed scheme, the adversary’s ability to modify S is significantly impeded. Mathematically, this can be represented as in Eq 1.

(1)

Where P (A modifies S ∣ S≠ S′, C) denotes the probability of the adversary A successfully modifying the legal vehicle-related sensitive information S when S is different from the pseudonym data ′S′ and the cloaking region C is present. P (A modifies S ∣ S = S′, C) denotes the probability of the adversary A successfully modifying the legal vehicle-related sensitive information S when S matches the pseudonym data ′S′ and the cloaking region C is present.

B. Content replay attack resistance

For any attacker A attempting to perform a replay attack by using a different timestamp ′T′ in place of the original timestamp T, the proposed system effectively detects and rejects the replayed message. Eq 2 presents it mathematical form: (2) Where P (A successfully replays message with T′) denotes the probability of the attacker A successfully replaying a message with a different timestamp ′T′. P (A successfully replays message with T) denotes the probability of the attacker A successfully replaying a message with the original timestamp T. This proof indicates that the proposed system effectively mitigates replay attacks by verifying the freshness of timestamps in traffic-related messages. Since using a different timestamp results in a different value for the inequality check, replayed messages are promptly detected and rejected.

C. Impersonation attack resistance

Let The combination of consortium blockchain, Certificateless Aggregate Signature (CLAS), and conditional privacy-preserving mechanisms provides resistance against impersonation attacks in VANET systems. The lemma against impersonation attack resistance can be formulated as follows:

Lemma. In a VANET system, each vehicle V_i​ communicates securely by generating a pseudonym identity PID_i​ and a private key K_priv, which are used in conjunction with a consortium blockchain and CLAS. When V_i ​sends a message mim_imi​, it generates a signature σ_i using K_priv ​and aggregates it with signatures from other vehicles to form an aggregate signature σ_i​. The aggregated signature σ_iagg = is verified using an aggregated public key PK_agg​, ensuring the authenticity of all n messages m_i​ without relying on individual certificates. The consortium blockchain ensures data integrity and traceability by maintaining a distributed ledger, where each block contains a hashed record of transactions T_i​. Conditional privacy-preserving mechanisms allow trusted authorities to map pseudonym identities PID_i​ back to real identities RID_i​ ​only under specific conditions, preventing unauthorized tracking. If an adversary A attempts an impersonation attack by forging a pseudonym PID_A​ ​and a corresponding signature σ_A​, the absence of a valid private key K_privA linked to PID_A ​ means σ_A ​ will fail verification against PK_agg​. The integrity checks and traceability offered by the consortium blockchain further thwart the attack by detecting inconsistencies. Hence, the integration of consortium blockchain, CLAS, and conditional privacy mechanisms effectively resists impersonation attacks by ensuring only valid, authenticated communications are accepted in the VANET system.

Eq 3 express the formal representation as follows:

(3)

D. Middle-man attack resistance

Let S denote the sender of a message, V denote the verifier, and M represent the message transmitted in the VANET system. The lemma for Resistance to Man-in-the-Middle (MITM) Attack in the described scenario can be formulated as follows:

Lemma. In the VANET system architecture described, incorporating an anonymizer server connected with the On-Board Unit (OBU), tracing Authority (TA) within the core network containing the cache based Location Based Service Provider (LSP) followed by linkage with blockchain and further blockchain network, the system effectively resists Man-in-the-Middle (MITM) attacks. Mathematically, this can be expressed as in Eq 4: (4)

Where P (SV relationship is verified) denotes the probability that the relationship between the sender S and the verifier V is verified, ensuring that the message M is transmitted securely without intervention. M represents the message transmitted in the VANET system. It shows that in the described system architecture, the verification of the relationship between the sender and the verifier is a necessary condition for ensuring message validity and authenticity. By establishing this relationship and ensuring that a genuine message cannot be changed or fabricated, the system effectively mitigates the risk of Man-in-the-Middle (MITM) attacks.

E. Trade-off analysis

Analyzing the proposed consortium Blockchain and certificateless conditional Privacy Protection (CPP) scheme for VANET systems, we must consider the trade-offs between security, privacy, and computational efficiency. Let S, P, and E represent security, privacy, and efficiency, respectively. The proposed scheme leverages the decentralized and immutable properties of blockchain technology to enhance P by ensuring that no single entity has undue control over sensitive information, thus reducing the risk of privacy breaches (P↑). The use of a decentralized identity management system, TA, CLAS, CPP, and consensus mechanisms provides a robust framework for transaction validation and authorization within the VANET, enhancing S by mitigating the risk of malicious attacks (S↑).

However, the introduction of these components can potentially increase the computational overhead (E↓), as blockchain operations inherently involve complex cryptographic processes and consensus mechanisms. The evaluation of the proposed scheme, which demonstrates improved privacy and efficiency, suggests a careful balance between these factors. The performance metrics, including reduced computation time (E↑), communication overhead (E↑), and improved precision, recall, F-measure, and ADP, indicate that the scheme is optimized to enhance E while maintaining high levels of S and P. Thus, the trade-off analysis reveals that the proposed scheme successfully enhances P and S without significantly compromising E, making it a viable solution for the privacy and security challenges in VANET systems.

A. Computation cost

To evaluate our proposed privacy provisioning framework, we evaluate different metrics where computation cost is the first one that refers to the computational resources required to perform various operations such as encryption, decryption, hashing, verification, and other processing tasks. This cost is crucial to consider as it directly impacts the efficiency and performance of the system. Mathematically, the computation cost C is expressed in Eq 5 as the sum of the costs associated with individual operations: (5)

Where, C(comp) is the total computation cost, n is the total number of operations, and C_i​ represents the cost of each individual operation. The computation cost for different operations can vary depending on factors such as algorithm complexity, key length, message size, and processing power of the devices involved. To calculate the computation cost in VANET systems, one must consider the specific operations involved in tasks such as encryption for securing communications, hashing for data integrity verification, signature generation and verification for authentication, and any other cryptographic operations necessary for privacy protection and security. Additionally, factors such as the number of vehicles, the frequency of message exchanges, and the computational capabilities of the network nodes need to be taken into account for accurate computation cost estimation. The computation cost analysis is illustrated in Fig 3 as outlined below. In terms of V2V communication, our scheme demonstrates a significantly lower computational cost compared to the referenced schemes, with a value of 0.23972. This indicates a substantial reduction in computational overhead, enhancing efficiency. Similarly, for V2RSU communication, our scheme exhibits a substantially lower computational cost of 0.13166 compared to the referenced schemes, further emphasizing the efficiency gains achieved. These results suggest that our proposed scheme effectively minimizes computational costs, making it a promising solution for VANET systems.

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Fig 3. Computation cost for V2V and V2RSU.

https://doi.org/10.1371/journal.pone.0310267.g003

B. Communication cost

In our experiments, the second evaluation metric is communication cost that refers to the resources expended in transmitting data between vehicles, roadside units (RSUs), and other network components. It encompasses factors such as bandwidth usage, message overhead, and transmission delays. Mathematically, the communication cost C(com)​ is expressed in Eq 6 as follows: (6)

Where, Bi​ represents the bandwidth consumption of the i^th communication link, Ti​ denotes the transmission time for data over the i^th link, and n is the total number of communication links in the network. In our experiments, analysis of communication cost evaluation across various schemes, including references [37–39], compared to our proposed scheme, reveals significant differences in resource utilization. According to Fig 4, in the case of V2V communication, our scheme demonstrates notably lower communication costs, with 534 and 530 bits compared to 1664, 2912, and 2560 bits for references [37–39], respectively. Similarly, for V2RSU communication, our scheme exhibits reduced communication costs, registering values of 530 compared to 1920, 4416, and 2880 in references [37–39], respectively. These findings underscore the efficiency and optimization achieved in communication resource utilization through our proposed scheme, suggesting its superiority in minimizing communication overhead in VANET systems.

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Fig 4. Communication cost.

https://doi.org/10.1371/journal.pone.0310267.g004

C. Cache hit ratio

We evaluate the effective usage of cache while receiving queries from the vehicles. In a VANET system employing a cache-based anonymizer server situated between OBUs and RSUs, the cache hit ratio R_hit​ represents the proportion of queries successfully resolved from the cache compared to the total number of queries made. It can be expressed as in Eq 7: (7) Where, N_hit​ is the number of queries successfully resolved from the cache, and N_query​ ​is the total number of queries made by OBUs to the anonymizer server. Fig 5 presents the impact of cache usage that significantly improve the overall system. We observe that at initial level, cache hit ratio is almost in all methods, but a significant difference once the number of queries increased.

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Fig 5. Cache hit ratio.

https://doi.org/10.1371/journal.pone.0310267.g005

D. Location Leakage Probability (LLP)

To calculate the location leakage probability in VANET systems, we define it as the probability that an adversary can accurately infer the location of a vehicle based on the information available to them. LLP can express as in Eq 8 as follows. (8) Where P (Location Leakage) is the location leakage probability, "Number of Successful Location Inferences" represents the instances where the adversary correctly identifies the location of the vehicle, and "Total Number of Location Queries" denotes the total number of times the adversary attempts to infer the location of the vehicle. This evaluation can be performed over a given period or set of scenarios to assess the effectiveness of privacy protection mechanisms in the VANET system. As depicted in Fig 6, the probability LLP stands at 0.15 with centralized architecture, ranging between 0.1 and 0.12 with distributed architecture, and between 0.1 and 0.13 with cache-based centralized architecture. In contrast, our proposed architecture lowers the probability to approximately 0.05%. Consequently, the effectiveness of LLP protection is significantly enhanced with our proposed architecture.

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Fig 6. Location leakage probability.

https://doi.org/10.1371/journal.pone.0310267.g006

E. Precision

In VANET (Vehicular Ad-Hoc Network) systems, precision is a metric used to evaluate the accuracy of a system in correctly identifying relevant instances among the total instances that it has identified as positive. Precision is particularly relevant in the context of security and trust models, where it measures the proportion of correctly identified positive instances among the instances identified as positive. The precision is calculated using Eq (9) as follows: (9)

In the context of VANET systems, precision can be applied to various aspects, such as the accuracy of identifying trustworthy vehicles or the precision of detecting security-related events. A higher precision value indicates a lower rate of false positives, signifying a more accurate positive identification by the system. The precision of the privacy provisioning models is depicted in Fig 7. It indicates that in defined scenarios with a limited number of malicious vehicles, all four trust models achieve a precision surpassing 90%. This highlights the proficiency of the trust models in accurately identifying malicious messages transmitted by these vehicles with malicious intent.

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Fig 7. Influence of different proportions of malicious vehicles on precision.

https://doi.org/10.1371/journal.pone.0310267.g007

F. Recall

Recall, also known as sensitivity or true positive rate, in VANET systems measures the ability of a trust model to correctly identify all relevant instances of malicious behavior, indicating the proportion of actual positive instances that were correctly detected. Eq 10 presents the mathematical form to calculate recall.

(10)

True Positive represents instances where the trust model correctly identifies malicious behavior, and False Negative represents instances where malicious behavior is present but the trust model fails to detect it. Our suggested scheme demonstrates superior performance compared to all existing methods in terms of recall, as illustrated in Fig 8. In situations where the network includes 50% malicious vehicles, our scheme achieves recall values that exceed the existing methods by 12%, 19%, and 22% respectively.

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Fig 8. Recall impact while malicious attacks at different levels.

https://doi.org/10.1371/journal.pone.0310267.g008

G. F-measure (F1 score)

In VANET systems, the F-measure or F1 score is a metric that combines both precision and recall to provide a balanced evaluation of a system’s performance. It considers both the false positives and false negatives and is particularly useful when the classes are imbalanced. The F-measure is calculated using the following Eq 11 as follows: (11)

Fig 9 illustrate that our scheme outperformed the existing method, and achieved 18%, 22%, and 26% higher F-measures when the number of malicious attacks is at maximum range.

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Fig 9. Impact of different malicious attacks on F-measure.

https://doi.org/10.1371/journal.pone.0310267.g009

H. False positive rate (FPR)

The false positive rate in VANET systems is a metric that quantifies the proportion of legitimate messages or events wrongly identified as malicious or unauthorized. In the context of VANET security, a false positive occurs when the system mistakenly flags a valid communication or activity as a security threat. The false positive rate is a crucial measure as it helps evaluate the accuracy of intrusion detection systems and other security mechanisms in distinguishing between normal and potentially harmful behavior. The formula to calculate the false positive rate is given as follows in Eq 12.

(12)

This rate provides insights into the efficiency of the system in avoiding unnecessary alarms or alerts for non-malicious activities, contributing to the overall reliability of the security infrastructure in VANETs. Fig 10 shows the impact of different malicious attacks on false positive rate (FPR).

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Fig 10. Impact of different malicious attacks on false positive rate (FPR).

https://doi.org/10.1371/journal.pone.0310267.g010

I. Attack detection probability (ADP)

Attack detection probability in VANET systems is a metric that quantifies the likelihood of correctly identifying and detecting malicious activities or attacks within the network. It measures the effectiveness of the security mechanisms in place to recognize and respond to potential threats as shown in Fig 11. The attack detection probability is calculated using the following formula in Eq 13 as follows: (13)

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Fig 11. Probability of attack detection at different number of malicious attacks.

https://doi.org/10.1371/journal.pone.0310267.g011

We conducted a comprehensive assessment and comparison to gauge the effectiveness of the proposed authentication scheme and trust model in relation to other pertinent authentication schemes and trust models. The evaluation of the authentication scheme takes into account factors such as computation and communication overhead, along with accuracy. The performance of existing privacy provisioning models, including our proposed solution, is scrutinized based on metrics such as precision, recall, F-measure, False Positive Rate (FPR), and Attack Detection Precision (ADP). The results unequivocally demonstrate the superior performance of our proposed scheme, showcasing reduced computation time and communication overhead compared to alternative schemes. Furthermore, our scheme outperforms the compared models by achieving elevated precision, recall, F-measure, and ADP.