One smart city component that has been revolutionized by integrating advanced technologies such as the Internet of Things, big data, artificial intelligence, and such into urban mobility is smart transportation, also known as intelligent transportation systems (ITS). The main purpose of the systems is to optimize transportation efficiency and safety by fully harnessing the integrated technologies. However, security and privacy issues that come along with the use of technologies have become constant challenges in ensuring the systems are safe and secure against cyber threats and attacks. Robust access control may mitigate these issues by strengthening the security and protecting the data privacy in ITS, but developing one without compromising the confidentiality, integrity, and availability of the ITS is quite challenging, and traditional access control is not compatible with ITS because of the dynamicity and a numerous of vehicles. In this study, an authentication that employs identity-based encryption and edge computing to enhance the privacy in ITS has been proposed and it considers all layers in ITS in the architecture design to further enhance the security at each layer.