authorities (TAs), RSUs and onboard Units (OBUs) mounted on vehicles [14; 15; 16]. The OBUs constantly cast the traffic related messages about vehicles facilitating various smart applications and technologies such as current vehicle location, time, speed, direction and traffic condition in every 100-300  ms [13; 17; 18]. As is the case with many communication network based technologies, VANETs is not an exception to face various cyber-security challenges in terms of data security and user privacy [19; 20; 21; 22]. With secure and privacy protection addressed, the applications of VANETs in traffic management and control, traffic accident avoidance features, traffic vigilance, gas emission, EV charging and fuel consumption will be fully implementable [23]. So if the VANETs network system is not protected, adversaries may launch all sorts of attacks like data modification, impersonation, replay, denial of service attacks among others. For instance, there are attacks launched by rogue vehicles broadcasting fake instructions to cause traffic accidents and general confusion. Thus, in terms of message senders' legitimacy there should be security features when sending messages to check authentication and integrity [23; 24]. To this effect many authentication schemes have been proposed using traditional public key cryptography (PKC) to secure a VANETs system [25; 26]. In terms of privacy concerns, anonymity must be provided in the design of securing the message from an eavesdropping adversary. In this way the real identity of communicating party will not be known nor communication transactions be analyzed and linked to a particular VANETs participant. However, due to abuse of the anonymity feature, the pseudonym given to participating entities should be traceable and revocable, so that the TA can reveal the real identity of malicious vehicle under certain conditions [27]. Since OBUs have limited computation and storage capabilities, the use of less computation intensive cryptographic techniques is promoted so as to handle large message flow in the system and improve smooth communication. Certificate-less aggregate signature (CLAS) is one efficient technique that improves message authentication by utilizing batch calculation of which saves bandwidth. In CLAS \(n\) signatures on \(n\) distinct messages from \(n\) distinct users, are aggregated into a single short signature that can be verified at once as combined [28]. This approach is very helpful in VANETs where RSUs collects and aggregate a large number of signatures from individual participants signatures into one signature that is broadcasted to vehicles in the system to achieve a particular VANETs enhanced smart grid application, and this greatly enhances efficiency in verification and communication overhead [13; 29]. Achieving efficiency by design is much encouraged to cope up with the computation capabilities of RSUs and OBUs by constructing the algorithms with lighter computation operations. To this effect, employing elliptic curve cryptography (ECC) based cryptosystems improves computation efficiency by a great margin and thereby a recommendable approach. Thus, we propose an efficient certificate-less aggregate scheme with conditional privacy-preservation by using the ECC approach. The proposed scheme satisfies security and privacy requirements for VANETs with optimal efficiency and rigorous security proof is provided. There are different modes of communications in VANETs such as vehicle-to-vehicle (V2V), vehicle-to-grid (V2G) and vehicle-to-infrastructure (V2I) and vehicle-to-everything (V2E), which use the short medium range communication protocol called dedicated short range communication (DSRC) to facilitate various vehicular network applications [30]. These computer sophisticated vehicles are being adopted for various smart services in intelligent transportation systems (ITS).