Adaptive traffic signal control system can reduce waiting time of vehicles at intersection by dynamically changing traffic signals based on density of vehicles present on roads at intersection. One of the approaches used to find density of vehicles on roads at intersection is proposed in  called as CDRIVE. In this, cluster-head vehicle updates density information as vehicles join the cluster and cluster is formed based on direction of the vehicle, it takes after intersection. However, a malicious vehicle can join the cluster by providing wrong direction information. Therefore, to ensure correct density estimation, the participating vehicles in density estimation should be authenticated ones; otherwise, density estimation estimated by cluster head may not reflect correct density and hence may result in incorrect changing of signals. In this work, we propose secure adaptive traffic lights system (SATS) protocol for VANETs which is an enhancement to CDRIVE by adding security to it. By this, the malicious vehicles are prevented to join the cluster. This is achieved by using cluster symmetric key for cluster joining and cluster communication. Cluster symmetric key is obtained from roadside unit (RSU) present near intersection. It has been seen that our proposed algorithm achieves security parameters such as authentication, privacy, source non-repudiation, and density estimation estimated by cluster-head vehicle is correct. Further, it is analyzed that the computational overhead by adding security features does not affect the functioning of CDRIVE.