# An Efficient and Secure Certificateless Aggregate Signature Scheme for Vehicular Ad hoc Networks
## 2 Literature Review  
A VANET is a communication technology that enables V2V and V2I communications via the Internet, which can be affected by several cyber-attacks. So, to avoid such circumstances, the best solution is authentication, in which the participating nodes in the VANET environment can authenticate each other before transferring data or information. To achieve authentication, the best approach is to use a digital signature, which allows a sender to sign data with his private key and deliver it to the recipient, who can then use the sender's public key to verify the signature. In a typical PKC-based signature, each user needs to produce a valid digital certificate that contains information about the identity of the certificate owner and the public key ([PERSON], 1996). However, it not only requires certificate management but also contributes to an increase in the verification cost. To address certificate management issues, [PERSON] (2003) proposed ID-PKC, in which the user's identity is his public key, bypassing the need for certificates. However, the private keys are generated via the KGC, which might lead to a key escrow problem. [PERSON] and [PERSON] [PERSON] and [PERSON] (2004) proposed the idea of CL-PKC, in which the user's private key is made up of a secret value and a partial private key. The user chooses his secret key, while the KGC generates the partial private key. Since the KGC cannot access the user's complete private key without the user's secret key, the user's public key can be calculated from the secret value. Thus, the potential security issues associated with key escrow are eliminated. Secondly, the user's public key can be calculated from the secret value, so a certificate is no longer needed. In other words, the CLS technique has the potential to address issues in both the classic signature method and the ID-based method. CLAS has the benefits of CLS and AS. In 2003, [PERSON] et al. [PERSON] et al. (2003) proposed the concept of CLAS, which can combine the signatures of n (n \(>\) 1) different messages signed by n other users into a single signature. The receiver only needs to check the aggregated signature instead of all the signatures, thereby reducing the computational cost of signature verification and the communication overhead of signature transmission to some extent. The benefits of CLAS mentioned above have led to a lot of new research. [PERSON] and [PERSON] [PERSON] and [PERSON] (2003) proposed a CLAS scheme within the framework of the Random Oracle Model (ROM), but [PERSON] et al. [PERSON] et al. (2003) discovered that [PERSON] and [PERSON]'s [PERSON] and [PERSON] (2003) scheme is vulnerable to public key replacement attacks. [PERSON] et al. [PERSON] et al. (2004) designed and proved a secure practical CLAS scheme, although [PERSON] and [PERSON] [PERSON] and [PERSON] (2005) found that [PERSON] et al. [PERSON] et al. (2004)'s scheme could guarantee unforgeability. A new certificateless signature system was presented by [PERSON] et al. [PERSON] et al. (2003) for the use of V2I in a VANET's communication. However, [PERSON] and [PERSON] [PERSON] and [PERSON] (2005) demonstrated that the scheme proposed by [PERSON] et al. [PERSON] et al. (2003) was vulnerable to various attacks like replay attacks, modification attacks, impersonation attacks, and man-in-the-middle attacks and hence could not provide authentication and message integrity. [PERSON] et al. [PERSON] et al. (2006) addressed the limitation of [PERSON] et al. [PERSON] et al. (2003)'s scheme and designed an improved CLAS scheme. However, the scheme has high computational and communicational costs since it uses bilinear pairing and point-to-point hash functions. [PERSON] and [PERSON] (2006) came up with an open and small CLAS scheme in which the size of signatures stays the same, and any combination of signatures can be added together. However, the scheme is based on bilinear pairing, which necessitates higher computational and communicational costs. A highly effective AS scheme was developed by [PERSON] et al.