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Vehicular Ad hoc Networks (VANETs) are emerging as the first commercial implementation of mobile ad hoc networks. There has been a significant rise in the use of secure group communication as a result of the growth in the applications that require confidentiality and authorized access to multicast data. Numerous Group Key Management (GKM) schemes have been proposed to meet the security and QoS requirements. The highly dynamic nature of VANETs can cause significant overhead in the form of re-keying communication, if these existing GKMs are to be used. Hence, we identify the need for new solutions specific to VANETs and introduce a multivariable symmetric polynomial based GKM which eliminates the need for the re-distribution of keys upto a configurable number of membership changes, without compromising the forward or the backward secrecy. Furthermore, our scheme reduces the effect of mobility on the re-keying overhead by allowing vehicles to handoff between road side units (RSUs) within the group without re-keying.