###### Abstract  
The privacy and security vulnerabilities in fifth-generation (5G)-enabled vehicular networks are often required to cope with schemes based on either bilinear pair cryptography (BPC) or elliptic curve cryptography (ECC). Nevertheless, these schemes suffer from massively inefficient performance related to signing and verifying messages in areas of the high-density traffic stream. Meanwhile, adversaries could launch side-channel attacks to obtain sensitive data protected in a tamper-proof device (TPD) to destroy the system. This paper proposes a Chebyshev polynomial-based scheme for resisting side-channel attacks in 5G-enabled vehicular networks. Our work could achieve both important properties of the Chebyshev polynomial in terms of chaotic and semi-group. Our work consists of five phases: system initialization, enrollment, signing verification, and pseudonym renew. Moreover, to resist side-channel attacks, our work renews periodically and frequently the vehicle's information in the TPD. Security analysis shows that our work archives the privacy (pseudonym identity and unlikability) and security (authentication, integrity, and traceability) in 5G-enabled vehicular networks. Finally, our work does not employ the BPC or the ECC; its efficiency performance outperforms other existing recent works, making it suitable for use in vehicular networks.  
Cabyshev polynomial; side-channel attacks; 5G-enabled vehicular networks; semi-group; privacy and security; chaotic map +
Footnote †: journal: Accepted: 8 June 2022  
Due to the nature of the public environment, vehicular networks are vulnerable to various privacy and security issues. Therefore, many scholars have focused on satisfying privacy and security requirements for vehicular networks by proposing sophisticated authentication schemes. Nevertheless, more precisely, some existing schemes are vulnerable to side-channel attacks to obtain the sensitive information saved on the tamper-proof device (TPD) of the vehicle. Thereby, if the attacker compromises the private key of \"trusted authority (TA)\" saved of any TPD, the entire system will be insecure and exposed. Furthermore, the existing schemes use more complex and time-consuming operations such as \"bilinear pair cryptography\" and \"elliptic curve cryptography\" to sign and verify the messages.  
As a result, this paper proposes a Chebyshev polynomial-based scheme for resisting side-channel attacks in 5G-enabled vehicular networks, which could achieve both important properties in terms of chaotic and semi-group. To the best of the author's knowledge, our work is the first Chebyshev polynomial-based scheme for 5G-enabled vehicular networks without using bilinear pair cryptography or elliptic curve cryptography. More precisely, the main contributions of this paper are threefold.  
* First, a Chebyshev polynomial-based scheme for resisting side-channel attacks in 5G-enabled vehicular networks that fulfills the design goals with regard to the privacy and security requirements;
* Second, a scheme that resists side-channel attacks by regularly renewing the system's sensitive information (pseudonym) preserved in the TPD;
* Third, a scheme that outperforms other works based on bilinear pair cryptography and elliptic curve cryptography schemes; therefore, it the suitable for large-scale deployment in vehicular networks.  
The remainder of this paper is arranged as follows. In Section 2, the previous existing works are reviewed. The architectural design, design goal, threat model, and mathematical foundations are introduced in Section 3. We propose a Chebyshev polynomial-based scheme for secure 5G-enabled vehicular networks in Section 4 and the security analysis of our work in Section 5. Section 6 evaluates the efficiency performance. Ultimately, we conclude the paper in Section 7.