With the rapid growth of Vehicular Ad-Hoc Networks (VANETs), huge amounts of road condition data are constantly being generated and sent to the cloud for processing. However, this introduces a significant load on the network bandwidth causing delay in the network and for a time-critical application like VANET such delay may have severe impact on real-time traffic management. This delay maybe reduced by offloading some computational tasks to devices as close as possible to the vehicles. Further, security and privacy of vehicles is another important concern in such applications. Thus, this paper proposes a secure road condition monitoring scheme for fog-based vehicular networks. It considers Road-Side Units (RSUs) with computational capabilities, which act as intermediate fog nodes in between vehicles and cloud to reduce delay in decision making and thereby increases scalability. Apart from fulfilling basic security features, our scheme also supports advanced features like unlinkability and untraceability. A detailed security analysis proves that the proposed scheme can handle both internal and external adversaries. We also justify the efficiency of our scheme through theoretical overhead analysis. Finally, the scheme is simulated using an integrated SUMO and NS-3 platform to show its feasibility for practical implementations while not compromising on the network performance. The results show an average 80.96\% and 37.5\% improvement in execution time and end-to-end delay respectively while maintaining at par results for packet delivery ratio over a state-of-the-art scheme.