Efficient Lattice-Based Heterogeneous Multi-Receiver Signcryption Scheme in VANET

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Efficient Lattice-Based Heterogeneous Multi-Receiver Signcryption Scheme for VANETs

Introduction

Vehicular Ad Hoc Networks (VANETs) play a crucial role in intelligent transportation systems by enabling real-time communication between vehicles and roadside units (RSUs). However, the open nature of wireless communication in VANETs raises significant concerns about data privacy and security. Sensitive information, such as vehicle location and speed, can be intercepted or tampered with, leading to potential safety hazards. To address these challenges, cryptographic techniques like signcryption have been proposed to ensure confidentiality, integrity, and authentication in data transmission.

Traditional signcryption schemes are designed for homogeneous cryptographic environments, where all entities use the same encryption system. However, in VANETs, vehicles and RSUs may operate under different cryptographic frameworks, such as Certificateless Cryptography (CLC) for RSUs and Identity-Based Cryptography (IBC) for vehicles. This heterogeneity necessitates the development of secure and efficient communication protocols that bridge these systems while maintaining real-time performance.

This article presents a novel lattice-based heterogeneous multi-receiver signcryption scheme tailored for VANETs. The proposed solution enables secure communication between CLC-based RSUs and IBC-based vehicles while reducing computational and communication overhead through multi-receiver signcryption. By leveraging lattice-based cryptography, the scheme also provides resistance against quantum attacks, ensuring long-term security.

Background and Motivation

VANETs consist of vehicles, RSUs, and a trusted authority (TA) that manages cryptographic keys. Vehicles communicate wirelessly with each other and with RSUs to exchange traffic information, such as congestion updates and accident reports. However, the dynamic and open nature of VANETs makes them vulnerable to eavesdropping, message forgery, and privacy breaches.

Existing signcryption schemes often focus on point-to-point communication, which becomes inefficient in VANETs where multiple vehicles may need to receive the same message simultaneously. Repeated signcryption operations for each receiver increase computational load and communication latency, undermining real-time performance. Additionally, many existing schemes rely on number-theoretic problems, such as integer factorization or discrete logarithms, which are vulnerable to quantum computing attacks.

Lattice-based cryptography offers a promising alternative due to its resistance to quantum attacks and efficient algebraic operations. However, previous lattice-based signcryption schemes suffer from high computational costs due to the use of preimage sampling and multiple Gaussian sampling algorithms. This work addresses these limitations by introducing a more efficient lattice-based signcryption scheme that supports heterogeneous cryptographic environments and multiple receivers.

System Model and Security Requirements

The proposed system involves four main entities:

  1. Trusted Authority (TA): Generates system parameters and manages cryptographic keys.
  2. Roadside Units (RSUs): Operate under CLC and facilitate communication between vehicles.
  3. Vehicles: Operate under IBC and exchange messages with RSUs and other vehicles.
  4. Private Key Generator (PKG): Generates private keys for vehicles based on their identities.

The scheme must satisfy the following security requirements:

  1. Confidentiality: Ensures that only authorized receivers can decrypt the message.
  2. Integrity: Guarantees that the message has not been altered during transmission.
  3. Authentication: Verifies the identity of the sender.
  4. Unforgeability: Prevents adversaries from forging valid signcrypted messages.

The security of the scheme is formalized under the random oracle model, with two adversarial models considered:

  1. Type I Adversary (A1): Can replace public keys but does not have access to the master secret key.
  2. Type II Adversary (A2): Has access to the master secret key but cannot replace public keys.

The scheme must resist adaptive chosen ciphertext attacks (IND-CCA2) and existential unforgeability under chosen message attacks (EUF-CMA).

Proposed Scheme

The proposed lattice-based heterogeneous multi-receiver signcryption scheme consists of five phases: system initialization, CLC key generation, IBC key generation, signcryption, and unsigncryption.

  1. System Initialization:
    The TA generates public parameters, including a lattice dimension n, modulus q, and Gaussian distribution parameters. Three hash functions are defined for cryptographic operations. The TA also generates a master public key and a master secret key using a trapdoor generation algorithm.
  2. CLC Key Generation:
    • Partial Private Key Extraction: The TA generates a partial private key for RSUs based on their identity. • Key Generation: RSUs combine the partial private key with a randomly chosen secret value to generate their full private and public keys.
  3. IBC Key Generation:
    The TA generates private keys for vehicles based on their identities using a matrix sampling algorithm. The corresponding public keys are derived from the private keys.
  4. Signcryption:
    When an RSU needs to broadcast a message to multiple vehicles, it performs the following steps:
    • Samples a random vector from a Gaussian distribution. • Computes a hash value to bind the message, sender identity, and random vector. • Uses rejection sampling to generate a signature component without preimage sampling, reducing computational overhead. • Encrypts the message for each receiver by concatenating their public keys and applying lattice-based encryption. • Outputs the signcrypted ciphertext, which includes the encrypted message and signature components.
  5. Unsigncryption:
    Each vehicle decrypts the ciphertext using its private key and verifies the signature. If the verification succeeds, the original message is recovered; otherwise, an error symbol is returned.

Security Analysis

The security of the scheme is proven under the random oracle model, relying on the hardness of the Learning With Errors (LWE) and Small Integer Solution (SIS) problems.

  1. Confidentiality:
    The scheme is shown to be IND-CCA2 secure against both Type I and Type II adversaries. An adversary cannot distinguish between signcryptions of two equal-length messages without knowing the private keys. The proof involves simulating the adversary’s queries and reducing the security to the LWE problem.
  2. Unforgeability:
    The scheme is EUF-CMA secure, meaning an adversary cannot forge a valid signcrypted message without the sender’s private key. The proof reduces the security to the SIS problem, demonstrating that any forgery would imply a solution to SIS.

Performance Evaluation

The proposed scheme is compared with existing lattice-based and number-theoretic signcryption schemes in terms of communication and computational overhead.

  1. Communication Overhead:
    The scheme reduces the size of public keys and ciphertexts by leveraging efficient matrix operations and rejection sampling. For example, the public key size is nk log q, and the ciphertext size is m + 2Lk log q, where L is the number of receivers. This is more efficient than schemes that use preimage sampling or larger matrix dimensions.
  2. Computational Overhead:
    The scheme avoids costly preimage sampling and reduces the number of Gaussian sampling operations. Experimental results show that the signcryption time is significantly lower than comparable schemes, especially as the number of receivers increases. For instance, the scheme achieves a 70% reduction in signcryption time compared to previous lattice-based schemes.

Conclusion

This article presents an efficient lattice-based heterogeneous multi-receiver signcryption scheme for VANETs. The scheme enables secure communication between CLC-based RSUs and IBC-based vehicles while minimizing computational and communication overhead. By leveraging lattice-based cryptography, the solution provides resistance against quantum attacks and ensures long-term security.

The proposed scheme outperforms existing solutions in terms of efficiency and scalability, making it suitable for real-time VANET applications. Future work may explore aggregation techniques to further reduce verification delays and improve performance in large-scale deployments.

DOI: 10.19734/j.issn.1001-3695.2024.05.0266

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