The vehicular ad hoc network presents a very complex cyber-physical system with intricate interplay between the physical and cyber domains. In the physical domain, vehicles need to frequently broadcast their geographic information. The safety message broadcasting in an area with a high density of vehicles tends to incur a large data traffic rate that should be properly processed in the cyber domain. In this paper, we address the issue of large computation overhead caused by the safety message authentication. Especially, a cooperative message authentication protocol (CMAP) is developed to alleviate vehicles' computation burden. With CMAP, all the vehicles share their verification results with each other in a cooperative way, so that the number of safety messages that each vehicle needs to verify reduces significantly. Furthermore, we study the verifier selection algorithms for a high detection rate of invalid messages in a practical 2-D road scenario. Another important contribution in this paper is that we develop an analytical model for CMAP and the existing probabilistic verification protocol , considering the hidden terminal impact. Simulation results over a practical map are presented to demonstrate the performance of the proposed CMAP with comparison to the existing method.