A Secure and Low-Overhead Authentication Protocol for Vehicle Ad Hoc Networks with Batch and Transfer Authentication

Summary

In a vehicular ad hoc network (VANET), vehicles communicate with each other, and every message must be verified to prevent malicious interference. Traditional authentication methods verify each vehicle individually, creating significant delays. To address this issue, the proposed research introduces an authentication mechanism that combines batch and transfer authentication.

Abstract

Vehicular Ad Hoc Networks (VANETs) require secure, efficient, and scalable authentication mechanisms to ensure trust among vehicles and roadside units (RSUs). Traditional one-to-one authentication approaches often lead to high communication and computational overheads, making them unsuitable for large-scale vehicular environments. This leads to a security traffic jam, rendering the process inefficient and unsuitable for real-time safety applications. To address this, study proposes a lightweight authentication protocol that supports both batch and transfer authentication, enabling multiple vehicles to be authenticated simultaneously and allowing authentication validity to be transferred between RSUs without re-executing the full protocol. In batch authentication, a roadside unit verifies a group of vehicles simultaneously instead of one at a time, much like a guard approving an entire busload of pre-verified passengers, which greatly reduces delays at intersections or toll booths. In transfer authentication, when a vehicle moves from one roadside unit’s area to another, the verification data are securely transferred, allowing seamless continuity without restarting the process, similar to a concert wristband that lets attendees move between stages without repeated checks. This scheme leverages the mathematical properties of Chebyshev polynomials to provide strong security with reduced overhead. Performance analysis shows that the proposed method achieves a communication cost of only 42n bytes and a significantly lower computational complexity than existing schemes. This approach enhances scalability, reduces message exchange, and maintains robust resistance against common attacks, making it well-suited for real-time vehicular communications. Overall, this new protocol enhances the practicality of VANETs by reducing data overhead, accelerating authentication, and efficiently managing high traffic volumes, making it a secure and scalable solution for the future of intelligent transportation systems.

Introduction

Vehicular ad-hoc networks (VANETs) enable vehicles to communicate with each other (vehicle-to-vehicle (V2V)) and with vehicles to roadside infrastructure (vehicle-to-infrastructure (V2I)) to improve the safety and efficiency of transportation. In this open wireless environment, any vehicle can broadcast safety messages (e.g., accident warnings or traffic updates); therefore, robust authentication is critical to ensure that the messages originate from legitimate sources. Simultaneously, VANETs impose strict performance requirements, and vehicles exchange messages at high frequencies (often 10 messages per second), leaving only a few milliseconds to verify each message before the next message arrives. Traditional public-key authentication methods, such as elliptic curve digital signature algorithm (ECDSA) digital signatures, as in the WAVE/IEEE 1609.2 standard, incur significant computation and communication overheads. Verifying a single ECDSA signature or managing a public key certificate for every message can overwhelm a resource-constrained onboard unit (OBU) and cause unacceptable delays when multiple messages arrive concurrently. Moreover, vehicles frequently change their point of attachment (moving from one roadside unit (RSU) to another), requiring repeated authentication or handshakes, which can further increase latency.

Channel	Frequency Range (GHz)	Priority	Primary Functions
CCH-178	5.885 – 5.895	High	Authentication control, service advertisements, initial message dissemination from RSUs, batch authentication initiation.
SCH-172	5.855 – 5.865	High	Time-critical messages (batch authentication acknowledgments, urgent safety notifications).
SCH-174	5.865 – 5.875	Medium to High	Navigation-based validation, traffic-aware batch coordination (urban mobility scenarios).
SCH-176	5.875 – 5.885	Low to Medium	Broadcasting revocation lists, group credential updates, periodic re-authentication alerts.
SCH-180	5.895 – 5.905	Medium	Secure post-authentication message exchanges (updates/notifications for authenticated batches).
SCH-182	5.905 – 5.915	Low	Non-critical services (cloud-assisted verification, internet-based checks, background messages).
SCH-184	5.915 – 5.925	Medium to High	High-throughput applications (video streaming, map distribution, OTA updates for authenticated groups).

Table 1: DSRC channel specifications for secure vehicular networks. It explains the control channel (CCH) and different service channels (SCHs) used in VANETs. All these channels operate within the 5.855–5.925 GHz frequency range, and each has a 10 MHz bandwidth. This setup supports smooth and organized communication, especially for batch authentication and important safety messages. CCH-178 (5.885–5.895 GHz) was the main control channel. It is used to initiate the authentication process and send safety-related messages, high-priority SCHs, such as SCH-172, SCH-174, and SCH-184, are used for time-sensitive tasks, such as emergency alerts and large data transfers, medium and low-priority SCHs, such as SCH-176, SCH-180, and SCH-182, handle less urgent tasks, such as updating revocation lists, reauthenticating vehicles, or managing general services. Abbreviations; DSRC = Dedicated Short-Range Communications; VANET = Vehicular Ad Hoc Network; CCH = Control Channel; SCH = Service Channel; GHz = Gigahertz; MHz = Megahertz.

The dedicated short-range communication (DSRC) spectrum, as shown in Table 1, illustrates its use in vehicular networks. This table outlines channel allocation in the dedicated short-range communications (DSRC) 5.9 GHz band (5.855–5.925 GHz), with each channel having a 10 MHz bandwidth. It highlights the control channel (CCH) and various service channels (SCHs) used in Vehicular Ad Hoc Networks (VANETs) to ensure organized, prioritized communication. Channel 178 serves as the primary CCH for initiating the authentication processes and broadcasting safety-related messages. High-priority SCHs (such as 172, 174, and 184) support time-critical applications like emergency alerts and large data transfers, while medium- and low-priority SCHs (such as 176, 180, and 182) handle less urgent tasks, including revocation list updates, vehicle re-authentication, and general services.

Another challenge is privacy. Vehicles should be authenticated without revealing their permanent identity in every message (to prevent tracking). Solutions such as pseudonymous certificates provide anonymity by using temporary identities; however, they introduce overheads for distributing and revoking large numbers of certificates. A vehicle can use group signature schemes to sign messages for a group. This authenticates the message while keeping the specific vehicles anonymous. However, these group signatures, along with other public-key methods, rely on complex mathematics, such as bilinear pairings and large exponentiations. These operations are not practical for a VANET environment, which is always moving fast and requires low latency. Packet loss worsens this situation. Therefore, a lightweight cryptography method is required. Therefore, a technique that can quickly check multiple messages simultaneously without compromising privacy or security needs to be developed. In this context, researchers have investigated the application of Chebyshev polynomials, which possess two significant characteristics appropriate for cryptography: the semigroup property and chaotic behavior. The main advantage of using Chebyshev polynomial operations is that they consume less computational complexity than elliptic curves. This special property has been used to build new authentication systems that combine ideas from symmetrical and public-key cryptography. For instance, they use one-way functions built from these polynomials to create shared secrets or digital signatures, which provide efficiency and non-repudiation. Studies have already shown that when these Chebyshev protocols are used for authentication, the amount of work that the onboard units of vehicles must perform is much lower. This study provides formal definitions and mathematical details of the Chebyshev polynomial-based operations used in the proposed scheme. Specifically, this study bases security on two assumptions analogous to classical cryptographic hard problems: the Chebyshev polynomial discrete logarithm problem (CPDLP) and the Chebyshev Polynomial Diffie–Hellman Problem (CPDHP). These problems are known to be computationally intractable, which proves that forging a vehicle’s authentication or impersonating a valid node is computationally infeasible. Moreover, it is explicitly stated that, when Chebyshev polynomials are defined over large finite fields with practical bit-lengths (e.g., 160–256 bits), retrieving the polynomial degree or secret parameter from a public polynomial is computationally infeasible with current classical algorithms¹.

In recent years, the schemas CDAS (centralized data authentication scheme) and DDAS (distributed data authentication scheme) were proposed² to handle electricity data in Vehicle-to-Grid (V2G) systems. Both methods showed better speed, security, and efficiency than earlier approaches and effectively protected user privacy. However, this work lacks real-world deployment, ignores dynamic pricing scenarios. A smart and efficient batch authentication scheme for V2G networks that uses bilinear pairings and aggregate signatures to verify multiple electric vehicle (EV) signatures simultaneously was proposed³ for saving time and minimizing the computing power, but this work doesn’t address how blockchain affects long-term storage. A smart batch authentication approach for V2G networks using edge computing to check dense EVs at the same time, was proposed⁴ using short group signatures and certificateless cryptography to reduce delay and to avoid certificate problems. The batch authentication method for V2G networks using edge computing and short group signatures to check group EVs at once was created⁵ but, However, it does not fully check the performance in largely crowded EV areas, they did not specify the revocation policy of EV’s.

A framework for privacy-focused data sharing in V2G networks using blockchain was proposed⁶ a framework for attribute-based encryption (ABE), but in this work they fail to address batch authentication. A privacy-preserving authentication method for V2G networks using blockchain and batch processing was created⁷ to address elliptic curve cryptography (ECC) based to check group of EVs simultaneously. However, they fail to address scalability challenges for dense was networks. A blockchain-based key management for V2G that also uses batch processing proposed⁸ a few smart contracts for secure key distribution, renewal, and revocation, thereby ensuring EV privacy; However, it does not check real-time work and is not clear about revoking EVs in a batch. A lightweight batch authentication method for VANETs was proposed⁹ that uses Chebyshev polynomials to check many vehicles simultaneously with low computation. The mathematical features of Chebyshev polynomials help avoid heavy cryptographic steps, so the system works faster and is more suitable for real-time vehicle communication. It also maintains privacy and provides strong security. However, it does not fully explain how it will manage very large traffic, moving vehicles, revoked users, and the key update process. The VANETs batch authentication scheme by using Chebyshev polynomials was presented¹⁰ to verify many vehicle IDs together with less delay. The chaotic parts of Chebyshev polynomials support anonymous IDs, key generation, and privacy. However, this study did not explain much about heavy traffic, high-speed cars, removing bad vehicles in batches, transfer authentication, and full key handling. A light batch authentication system for VANETs was created¹¹, a safe system using Chebyshev polynomials to check large groups of vehicles at once with low cost. It provides privacy and allows for tracing if necessary. However, it does not discuss large-scale networks. It also fails to address the work with VANET rules and full key handling. A Chebyshev chaotic map-based batch authentication scheme for VANETs was proposed¹² to authenticate multiple vehicles simultaneously with reduced computational cost. It maintains user privacy by providing anonymous IDs, tracing ability, and skipping heavy cryptographic operations, so it is suitable for live communication. However, it does not explain the revocation of malicious vehicles or compliance with VANET rules. A lightweight batch authentication for VANET networks by using authentication and key agreement (AKA) schemes combined with Chebyshev chaotic maps to check multiple vehicle messages at once was proposed¹³ for saving time and work. The scheme maintains privacy, message safety, and makes it suitable for real traffic. However, it does not explain how it works for large groups of vehicles, the adoption of fast RSU changes, or removing malicious vehicles in batches. A light batch authentication method for VANETs using Chebyshev chaotic maps was created¹⁴ to check many vehicle messages quickly with less delay and less computation. It maintains privacy, safe key exchange, and tracing without heavy crypto, making it suitable for real-time vehicle communication. However, the paper does not explain how the system handles large numbers of vehicles, revokes misbehaving vehicles, or fast-moving cars switching between RSUs. It also lacks integration with standard VANET protocols and does not use edge computing to boost performance.

This study proposes an authentication framework for VANETs that exclusively uses Chebyshev polynomial-based mechanisms for the batch verification of messages and transfer authentication during vehicle handovers. The batch verification scheme allows an RSU or receiving vehicle to verify multiple message signatures together instead of individually, which drastically reduces the per-message delay when the traffic is heavily loaded⁸. The transfer authentication protocol enables a vehicle to remain continuously authenticated as it moves across different RSU coverage areas without performing a full and expensive handshake at each hop. Instead, a lightweight dynamic session mechanism is used to transfer the authentication state from one session or domain to another. By employing Chebyshev polynomials in both aspects, this scheme ensures that only simple mathematical operations (such as modular multiplication and addition from polynomial evaluation) are required for VANET entities, making it highly suitable for the constrained computational environment of OBUs.

Protocol

Preliminaries

System model: The VANET system consists of three primary entity types: trusted authority (TA), roadside units (RSUs), and vehicles with onboard units (OBUs). The TA is central to initiating the initialization, key management, and occasional revocation. It is fully trusted and typically government- or infrastructure-controlled. Each RSU is a stationary unit deployed along the road. This provides a communication infrastructure; in this model, RSUs are assumed to be connected to the TA via a secure backbone (e.g., fiber or a secure network) so they can send or receive updates from the TA as needed. Vehicles are equipped with OBUs that enable vehicles to vehicle (V2V) and vehicles to infrastructure(V2I) communications. This study assumes that OBUs have a tamper-proof device (TPD) or secure hardware module that can store cryptographic keys and perform cryptographic operations in isolation, protecting long-term secrets from physical compromise.

Communication model: Vehicles broadcast periodic one-hop messages (such as basic safety messages) over a wireless channel (e.g., IEEE 802.11p or C-V2X PC5) that can be received by other vehicles and RSUs in range. These messages must be authenticated by the receivers to ensure their validity. RSUs also send periodic information (traffic signals and warnings) to vehicles through vehicle-to-infrastructure (V2I) communication. In this work, the primary focus is on the authentication of vehicle-to-infrastructure (V2I) messages. It means that the vehicles are authenticated by an RSU through batch authentication when they enter the RSU’s coverage region. V2V authentication can be handled similarly by having vehicles use the same signature scheme; however, batch verification is most beneficial at RSUs, which may need to verify many vehicles’ messages simultaneously.

Figure 1: Batch verification in VANET network. This figure depicts the architecture used for batch authentication, illustrating how multiple OBUs in vehicle batches (e.g., BATCH1 and BATCH2) communicate wirelessly with RSUs at intersections or traffic points, which are connected via wired links to a central TA. The protocol enables collective verification of authentication requests in high-density traffic using Chebyshev polynomials. Each vehicle computes an authentication token by evaluating T_k(x) mod P, concatenates it with its identity and timestamp, hashes the value, and transmits it to the RSU. The RSU aggregates the tokens and verifies them collectively.
Abbreviations; VANET = Vehicular Ad Hoc Network; OBU = On-board Unit; RSU = Roadside Unit; TA = Trusted Authority. Please click here to view a larger version of this figure.

Batch authentication in VANETs: In high-density traffic environments, RSUs may receive authentication requests from multiple vehicles within a very short time frame. Performing individual authentication for each request can cause significant computational delays and increase communication overhead. As illustrated in Figure 1, the proposed batch authentication mechanism leverages the mathematical properties of Chebyshev polynomials to achieve efficient multi-vehicle-verification¹⁵. Each vehicle computes an authentication token α_i by evaluating a Chebyshev polynomial T_vi(T_r(x)) modulo a large prime p, where v_i​ is the vehicle’s private key, r is the RSU’s private key, and x is a public base. The output is concatenated with the vehicle’s digital identity and timestamp, hashed, and transmitted to the RSU. The RSU aggregates all received tokens into a single value and verifies them collectively using the relation T_r.∑vi(x) modulo p. This approach significantly reduces the number of expensive verification operations, thereby improving scalability in environments such as intersections, toll gates, and traffic choke points.

Figure 2: Transfer authentication in VANET networks. This figure shows the proposed lightweight handover authentication protocol that allows a vehicle to move from the current RSU (Roadside unit 1) to the next RSU (Roadside unit 2) without full re-authentication, which can reduce latency. RSU1 generates an authorized card using hash-based concatenation of public keys and a random value, then applies Chebyshev polynomial operations to compute intermediate parameters (ω₁, ω₂), an initial key (IK), an encrypted session key, and a temporary key (TK). These values are sent to the vehicle and forwarded to RSU2. RSU2 verifies the data and recovers the session key using inverse Chebyshev operations, establishing a secure session key (SK) for uninterrupted communication. The protocol supports fast and secure handovers suitable for high-speed vehicular communication environments. Abbreviations; VANET = Vehicular Ad Hoc Network; RSU = Roadside Unit; IK = Initial Key; TK = Temporary Key; SK = Session Key. Please click here to view a larger version of this figure.

Transfer authentication for seamless handover: As vehicles move between RSU coverage zones, re-performing full authentication with every new RSU introduces latency and may disrupt secure sessions. The transfer authentication process, as depicted in Figure 2, enables a secure and lightweight handover. The current RSU generates an authorized card AC_i​ by hashing the concatenation of the vehicle’s and RSU’s public keys along with a random session parameter b_i. Using Chebyshev polynomial transformations T_AC(x) modulo p, the RSU computes intermediate values ω₁,ω₂ = ω₁  FPK_Ri​​, a session-specific key IK_i = H(ω₁FPK_vi) and an encrypted session key ω₃ = (E_IKi(SK_i)). Finally, a temporary key TK_i​ is derived from γ = b_i.IK_i^-1​ using another Chebyshev transformation T_γ(x). The tuple (TK_i,ω₂,ω₃) is sent to the next RSU, which uses it to verify and resume secure communication with the vehicle without performing full re-authentication. This mechanism ensures minimal disruption and ultralow latency for vehicles moving at high speeds.

Mobility and handover: Vehicles moving from one location to another in the network may encounter multiple RSUs along their route. By combining Chebyshev polynomial-based batch authentication for initial RSU access and transfer authentication for mobility handovers, the system achieves both scalability and continuity¹⁶. Batch authentication effectively handles many simultaneous vehicle authentications, whereas transfer authentication reduces re-authentication delays during RSU transitions. Together, these mechanisms form a strong, mathematically secure, and performance-effective framework for VANET authentication.

Chebyshev polynomial preliminaries

Chebyshev polynomials (T_n(x))are the mathematical core concept of the authentication scheme. They follow a recurrence formula and have features that make them suitable for one-way cryptographic functions. The main definitions and properties are as follows.

Definition: The Chebyshev polynomial of degree n (for integer n≥ 0):

T_n(x) = cos(n arccos x),

for x [-1,1]]. Equivalently, one can define it over the reals or modulo a prime P. The first few Chebyshev polynomials of the first kind T_n(x) up to n=4 (degree varies from 0 to 4) described in Table 2.

S.No	Degree	Description	Result
1	T0(x)	T0(x) = cos(0.arccros x) = cos(0) = 1	T0(x) = 1
2	T1(x)	T1(x) = cos(1.arccros x) = cos(arcos x) = 1	T1(x) = x
3	T2(x)	T2(x) = cos(2.arccros x) = 2cos2(arcos x)-1 = 2x2-1 (Since cos(2θ) = 2cos2θ-1)	T2(x) = 2x2-1
4	T3(x)	T3(x) = cos(3.arccros x) = 4x3-3x (Since cos(3θ) = 4cos3θ-3cosθ)	T3(x) = 4x3-3x
5	T4(x)	T4(x) = 8x4-8x2+1 (Since cos(4θ) = 8cos4θ-8cos2θ+1)	T4(x) = 8x4-8x2+1

Table 2: Evaluation of recurrence relation. This table presents the first few Chebyshev polynomials of the first kind T_n(x) (for degrees 0 to 4), computed using the recurrence relation that forms the mathematical foundation of the proposed authentication scheme. Abbreviations; T_n(x) = Chebyshev polynomial of degree n evaluated at x; n = Polynomial degree; x = Input variable.

In general, they satisfy the recurrence:

T_n+1(x) = 2xT_n(x) - T_n-1(x), with T₀(x) =1, T₁(x) = x .

This recurrence allows efficient iterative computation of T_n(x).

Semi-group property:  Similar to multiplicative exponents, Chebyshev polynomials display a composition property specifically:

T_m(T_n(x)) = T_m.n(x) ,

for any positive integers m,n. In words, if one first applies a Chebyshev polynomial of degree n to x, and then applies another Chebyshev polynomial of degree m to the result, it is equivalent to applying a Chebyshev polynomial of degree m * n directly to x. This property is central to using Chebyshev polynomials in Diffie–Hellman like key exchange and authentication protocols, because it resembles the property (g^a)^b = (g^b)^a of exponentiation in a cyclic group.

Chaotic behavior: For degrees n>1 , the map x T_n(x) (when x is in [-1,1]) has been shown to be chaotic mapping under specific conditions. Informally, a small change in x can cause large changes in T_n(x) when  n is large, and T_n(x)is distributed in [-1,1] in a way that for large n can appear random. This "pseudo-randomness" is useful in cryptography for producing non-predictable outputs.

Chebyshev polynomial discrete logarithm problem (CPDLP): This is similar to the discrete logarithm problem but uses Chebyshev polynomials. Given a prime modulus P and public values x and y = T_n(x) mod P, it’s very hard to find the integer n. In other words, if one knows x and y, figuring out n is extremely difficult when the numbers are large. This is similar to the classic discrete log problem, where finding a from g^a mod P is tough.

Chebyshev polynomial Diffie–Hellman problem (CPDHP): Given x, T_a(x), and T_b(x) (for random secret integers a,b), it is hard to compute T_a.b(x) without knowing either a or b. This mirrors the Diffie–Hellman problem: give g^a and g^b, an adversary cannot compute g^ab. In the Chebyshev context, note that T_ab(x) = T_a(T_b(x)) = T_b(T_a(x)) by the semi-group property; so if two parties each know one of a,b they can each compute T_ab(x) easily, while an eavesdropper knowing only the individual results cannot.

The security of the scheme relies on these assumptions (CPDLP and CPDHP are intractable). For practical implementation, this study operates in a finite field (modulo a large prime P) to guarantee distinct behavior. Typically, a random number x in [2,P-2] is chosen as a system parameter (this plays a role like a generator in a multiplicative group). The TA will choose such an x and publish it as part of the public parameters. Then the Chebyshev polynomials can be computed mod P via the recurrence formula. Although x is not in [-1,1] in this case, one can use the isomorphism between Chebyshev polynomials and hyperbolic cosine for values outside [-1,1], or simply treat the recurrence algebraically mod P. The chaotic property, in a strict sense, applies to real intervals; however, for cryptographic usage, study relies on the unpredictability due to the hardness of the CPDHP in the finite field.

Attack model

In the proposed batch and transfer authentication framework for VANETs using Chebyshev polynomials, researchers consider a realistic threat landscape in which both external and internal adversaries may attempt to disrupt secure communication. External attackers are entities outside the vehicular network that aim to intercept, alter, or inject malicious messages without possessing any legitimate authentication credentials¹⁷. Internal attackers, on the other hand, are compromised or malicious vehicles or RSUs that already hold valid credentials but misuse them to impersonate others, forge data, or launch coordinated attacks.

Man-in-the-middle (MIM) attack: The adversary intercepts and relays messages between two legitimate parties while potentially altering their content. The protocol mitigates this by employing mutual authentication and session key agreement based on the hardness of the Chebyshev polynomial problem, ensuring that any intercepted data is computationally infeasible to manipulate without detection¹⁸.

Replay attack: An attacker resends previously captured valid messages to gain unauthorized access or cause network confusion. Researchers address this issue by incorporating timestamps and session identifiers into the authentication process, ensuring that messages are valid only within a short time window and cannot be reused later.

Impersonation attack: is also considered, where an attacker attempts to pose as a legitimate vehicle or RSU. By tightly binding the authentication process to unique Chebyshev polynomial keys and verifying digital signatures during batch and transfer authentication, the system ensures that only genuine participants can communicate.

Eavesdropping attacks: where adversaries passively monitor communications to extract sensitive information. The proposed scheme ensures confidentiality through secure session key generation; therefore, even if data packets are intercepted, they remain unintelligible without the secret key.

Collusion attacks: where multiple compromised entities collaborate to break the authentication protocol. The use of aggregated verification in batch authentication and independent verification in transfer authentication prevents compromised nodes from collectively forging valid credentials.

Symbol	Description
Ui	i-th vehicle in the VANET
RSU	Roadside Unit
TA	Trusted Authority
TSi	Timestamp generated by vehicle
TARSU	Timestamp generated by RSU
TSTA	Timestamp generated by TA
ΔT	Maximum allowed clock difference for message validity
DIDUi	Pseudonym-based identity of vehicle Ui
DIDRSU	Pseudonym-based identity of RSU
Tv(x)	Chebyshev polynomial with vehicle's private key  "v"
Tv(x)	Chebyshev polynomial with Trusted authority private key "b"
TPKRi(x)	Chebyshev polynomial with RSU’s public key
αi	Identity hash computed by vehicle Ui
βi	Identity hash computed by RSU for  Ui
θi	Polynomial verification token from Ui  used for aggregation
θ'agg	Expected aggregated polynomial (TA computed)
θagg	Aggregated polynomial product from all vehicles Θi
mi,ni	Random session key seed values from  generated by TA
ri,ui	Secret scalar values assigned to RSU and vehicle respectively
PUBRSU	Public key of RSU
PUBui	Public key of vehicle Ui
E1(i),E2(i)	Masking values computed via hash for confidentiality
IK(i)	Components of authentication/session key exchange messages
SKi	Final session key established between vehicle and RSU
H(.)	Collision-resistant hash function
ESK(.)/DSK(.)	Symmetric encryption/decryption using session key
||	Concatenation operator
mod P	Modular operation over a large prime p

Table 3: Notations. This table lists the key symbols, parameters, and cryptographic notations employed throughout the paper.

Proposed Schema:

This proposed scheme consists of two main components: (i) a batch message verification mechanism using Chebyshev polynomials and (ii) a transfer authentication protocol for vehicle handovers between RSUs. This study first provides an overview of the system setup and then describe each component in detail in the following sections along with that the terminology and the notation were illustrated in Table 3.

Vehicle registration:

Step 1: Each vehicle initiates the authentication process. Let there be n vehicles u₁,u₂,u₃....,u_n attempting authentication with the same RSU at time t. Each vehicle u_i computes:

α_i = H(DID_ui|| T_vi(T_b(x)) || TS_i)  (1)

Then, u_i sends:

I₁⁽ⁱ⁾ = (α_i,DID_ui,TS_i)  (2)

to the RSU.

Step 2: RSU aggregates and prepares for batch authentication after receiving all I₁⁽ⁱ⁾, RSU performs:

1. Timestamp validation: |TS_c - TS_i| ≤ ΔT
2. Compute RSU response hash for each vehicle: β_i = H(DID_RSU||T_ri(T_b(x))||TS_RSU)
3. Compute Chebyshev tokens: θ_i = T_vi(T_PKRi(x)) mod P 
4. Aggregate all tokens:   
5. Prepare batch message:  and send to TA.

Step 3: TA verifies batch signatures

1. Verify timestamp: TS_TA - TS_RSU ≤ ΔT 
2. Check RSU hash: β_i^* = H(DID_RSU || T_b(T_ri(x)) || TS_RSU) = β_i 
3. Check vehicle hash: α_i^* = H(DID_ui|| T_b(T_vi(x)|| TS_i) = α_i 
4. Aggregate verification: θ'_agg = T_∑vi(x)mod P 
H(θ_agg) = H(θ_agg^')  If all passes, authentication is successful.

Step 4: Session key establishment (in batch) for each u_i , TA performs:
1. Compute: E₁⁽ⁱ⁾ = H(PUB_RSU||r_i||TS_RSU) 
E₂⁽ⁱ⁾ = H(PUB_ui||v_i||TS_i) .
2. Generate random values m_i,n_iZ^*_P 
3. Compute session key: SK_i = H(m_i||n_i||r_i||v_i) 
4. Construct encrypted components:
I₃⁽ⁱ⁾ = H(m_i)E₁⁽ⁱ⁾ 
I₄⁽ⁱ⁾ = H(n_i)E₂⁽ⁱ⁾
I₅⁽ⁱ⁾ = SK_iH(m_i) 
I₆⁽ⁱ⁾ = SK_iH(n_i) 
Send bundle: {I₃⁽ⁱ⁾,I₄⁽ⁱ⁾,I₅⁽ⁱ⁾,I₆⁽ⁱ⁾,TS_TA}ⁿ_i=1 

Step 5: RSU sends session info to each vehicle u_i 
1. Recover: H(m_i) = I₃⁽ⁱ⁾E₁⁽ⁱ⁾ 
SK_i = I₅⁽ⁱ⁾H(m_i) 
2. Send to u_i : {I₄⁽ⁱ⁾,I₆⁽ⁱ⁾,TS_RSU+1} 

Step 6: Vehicles complete session key extraction for each u_i 
1. Compute: H(n_i) = I₄⁽ⁱ⁾E₂⁽ⁱ⁾ 
SK_i = I₆⁽ⁱ⁾H(n_i) 
2. Use the session key to encrypt messages:
E_SKi(m_i||PUB_ui||PUB_RSU) 

Step 7: Transfer authentication for seamless handover
Step 7.1: Authorized card generation by RSU will compute
AC_i = H(FPK_vi|| FPK_Ri|| b_i) 
ω₁ = T_AC(x) mod P,ω₂=ω₁FPK_Ri 
IK_i = H(ω₁||FPK_vi) 
ω₃ = E_IKi(SK_i) 
TK_i = T_γ(x) mod P 
γ = b_i.IK_i^-1 
Send (TK_i,ω₂,ω₃) to the next RSU.
Step 7.2: Validation by the neighboring RSU
T_AC(x) = ω₂FPK_Ri^-1 
IK_i ^'= H(T_AC(x)||FPK_vi) 
T_TKi(IK_i^'(HOR_i))mod P = T_t(x)mod P 
Step 7.3: Session key recovery (New RSU decrypts)
SK_i = D_IKi^'(ω₃) 

The vehicle u_i​ is now authenticated within the new RSU zone and can continue secure communication, with all notations used in the algorithm detailed in Table 3.

In Figure 3, researchers have explained in detail about the transfer authentication with a swim lane diagram, how the current RSU transfers the authorization to the new RSU by sending its parameters (TK_i,ω₂,ω₃) and after receiving these parameters from the new RSU, it validates the verifies by using
T_TKi(IK_i^'(HOR_i))mod P = T_t(x)mod P . From this session, the key will be recovered by the new RSU and sent to the Vehicle.

Figure 3: Transfer authentication between two RSUs. This figure illustrates the flowchart of the transfer authentication protocol in a VANET, where a vehicle facilitates secure handover between the current Roadside Unit (RSU 1) and the next Roadside Unit (RSU 2). The process begins with authenticated card generation and cryptographic computations at RSU 1, followed by transmission of parameters to the vehicle, validation, and session key recovery at RSU 2, concluding in the establishment of a secure session key. Abbreviations; VANET = Vehicular Ad Hoc Network; RSU = Roadside Unit. Please click here to view a larger version of this figure.

Results

Security analysis

Informal security analysis

Impersonation attack: An adversary may attempt to impersonate a legitimate vehicle u_i or roadside unit (RSU) to gain unauthorized access or disrupt authentication, but such impersonation is computationally infeasible due to the robust security mechanisms in place. Each vehicle and RSU employs Chebyshev polynomial-based signatures, which involve their respective private keys (v<...

Discussion

The proposed batch and transfer authentication scheme significantly enhances VANET performance by overcoming the limitations of traditional one-to-one verification. Through batch authentication, multiple vehicles can be authenticated simultaneously by an RSU, reducing computational and communication load and enabling efficient large-scale operation in dense traffic conditions. This mechanism ensures faster authentication cycles and better bandwidth utilization, making it suitable for real-time vehicular networks that dem...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Component	Specification / Details
Batch Size (n)	10 to 100 vehicles
Comparison Schemes	[20],[21],[22] (analytical from literature)
Cryptographic Primitives	Chebyshev polynomials (custom recursive implementation), SHA-256 hash
Hardware Platform	Intel Core i7 processor, 16 GB RAM, Windows 11 (or your specific OS)
Key Libraries	hashlib (for SHA-256), time (for measurements), built-in math operations
Measurement Method	Average execution time over 1000 iterations using time module
Prime Modulus (p)	256–512 bits (small values like 7919 used for testing; scaled for security analysis)
Programming Language	Python 3.10
Simulation Type	Cryptographic operation timing (no network simulator used)