## 2 Related Work
### Pseudonym-Based  
The main motivation behind the pseudonym-based approach is to address the three main limitations and two main limitations arising from the PKI-based and GS-based vehicular networks, respectively. The rationale behind the pseudonym-based approach is that the public key is extracted from the vehicle's identification, and the master key is created by a trusted authority. At present, the two cryptographic methods could use the pseudonym-based approach. The following methods for this approach are introduced separately.  
* Bilinear Pair Cryptography (BPC): In 2008, [PERSON] et al. [23] were the first to propose the bilinear pair cryptography and pseudonym-based approach to achieve security communication in vehicular networks. The scheme of [PERSON] et al. [23] stores the secret key of the system (TA) in the TPD of the vehicle, which is claimed not to be compromised by the adversary. In 2013, [PERSON] and [PERSON] [24] highlighted the limitation arising from the scheme of [PERSON] et al. [23]: it could not achieve non-repudiation and replay attacks resistance. Therefore, [PERSON] and [PERSON] [24] proposed an enhanced scheme to satisfy privacy preservation in vehicular networks. Later, [PERSON] et al. [25], and [PERSON] et al. [26] highlighted the limitation arising from the scheme of [PERSON] and [PERSON] [24]: it could not resist the impersonation attacks in 2015 and 2014, respectively. In 2016, [PERSON] et al. [27] designed a pseudonym-based authentication scheme to resist side-channel attacks by periodically renewing the sensitive data preserved on the TPD of the vehicle.
* Elliptic Curve Cryptography (ECC): In 2015, [PERSON] et al. [28] were the first to propose the use of elliptic curve cryptography rather than bilinear pair cryptography to achieve privacy and security requirements in vehicular networks. [PERSON] et al. [28] also highlighted the limitation arising from the schemes of [PERSON] and [PERSON] [24] and [PERSON] et al. [26]: they could not resist forgery attacks. However, due to the secret key of the system (TA) being saved on the TPD, the scheme of [PERSON] et al. [28] suffers from side-channel attacks to retrieve the data for impersonating legal vehicles and sending fake messages in the vehicular networks. In 2017, [PERSON] et al. [29] designed a pseudonym-based scheme in which TA preloaded a batch of pseudonym identities for each enrolled vehicle to provide secure communication in vehicular networks. In 2020, [PERSON] et al. [30] presented a mutual authentication with privacy preservation to resist side-channel attacks by using operation ECC. In 2020, the TA in the scheme of [PERSON] et al. [31] preserved the secret key to the TPD of OBU for enrolled vehicles. In 2019, the scheme proposed by [32] employs time-consuming operations with regards to scalar multiplication-based ECC to check several messages in the urban area.  
In order to address the aforesaid issues existing in vehicular networks, this paper will propose the Chebyshev polynomial-based scheme for resisting side-channel attacks in 5G-enabled vehicular networks. Our work will regularly renew the sensitive data preserved in the TPD of the vehicle by using Chebyshev polynomial operations rather than a bilinear pair or ECC. Due to bilinear pairs or ECC not being utilized, our work has high efficiency; thereby, the computation and communication cost compared to other related schemes is lower.