# An Efficient and Secure Certificateless Aggregate Signature Scheme for Vehicular Ad hoc Networks
## 1 Introduction  
Vehicular ad hoc network (VANET) is an advanced version of the mobile ad hoc network (MANET), which was developed to enhance the safety, efficiency, and convenience of transportation [1]. VANET is a set of applications designed to offer new services connected to the traffic management system, designed to help various users to be better informed and use the transportation network to be safer, more connected, and significantly more intelligent. VANET can be established for monitoring and controlling traffic using the conceptof vehicle-to-everything (V2X) communication, which includes vehicle to infrastructure (V2I), vehicle to sensor (V2S), vehicle to pedestrian (V2P), and Vehicle to Vehicle (V2V) communication [2; 3]. The general architecture of a VANET is shown in Figure 1, which includes vehicles with built-in 5G-enabled onboard units (OBUs), 5G-enabled roadside units (RSUs), and trusted authorities (TAs). TA is a service provider, ensuring the safety of the VANET network and generating public and private keys for OBUs and RSUs [4]. In VANETs, each vehicle communicates through an OBU and broadcasts traffic-related information such as positions, speed, current time, traffic and road conditions to a nearby vehicle and an RSU [5]. Despite all the attractive features offered by a VANET, there are significant challenges regarding its security and privacy when information is shared among vehicles through an open wireless channel. In a VANET system, an attacker can send bogus messages to the RSUs or other OBUs, which might cause disturbance on the roads, so it is necessary to verify the authenticity and integrity of the message [6]. Digital signature-based authentication techniques for VANETs have been built in various cryptographic frameworks, including public-key infrastructure (PKI), identity-based (ID), and certificateless cryptography. In the standard implementation of public-key cryptography (PKC), each public key is required to produce a corresponding digital certificate [7]. Nevertheless, it not only involves certificate management but also contributes to an increase in the verification cost. To address the issues of certificate management, [PERSON] [8] came up with a novel technique in 1984 called ID-based public-key cryptography (ID-PKC). The public key consists of the user's identity, such as phone number, e-mail address, etc., eliminating the need for a certificate. However, the private key is generated by the Key Generation Center (KGC), which might lead to a key escrow problem. To overcome the shortcomings of key management in traditional PKC and the key escrow problem in ID-PKC, [PERSON] and [PERSON] [9] proposed Certificateless Public Key Cryptography (CL-PKC), which also requires the KGC to generate part of the user's private key. In contrast, the other part is generated by the user locally. As a result, key escrow is overcome, and CL-PKC does not need to create certificates. Many researchers combine certificateless cryptography with aggregate signature (AS) to create certificateless aggregate signature (CLAS) schemes, which minimize node authentication overhead and address certificate management and key escrow issues in classical cryptosystems. CLAS can prevent  
Figure 1: The general architecture of a VANET. the routing information from being forged, altered, or impersonated, as well as ensure its integrity and provide authentication and nonrepudiation for the sender. Some entities in VANETs, such as RSUs and OBUs, have limited computing and storage capacity; therefore, efficiency must be taken into account while designing a suitable authentication system for efficient communication in VANETs. In 2003, [PERSON] et al. [PERSON] et al. (2003) proposed the idea of an aggregate signature, which combines the signatures of multiple messages sent by various vehicles into a single, short signature. By using aggregate signatures, we can reduce computational and communicational costs and increase storage capacity to enhance the efficiency of a VANET system.