Over the years, the performance of devices used to gather sensitive medical information about individuals has increased substantially. These include implanted devices in the body, placed on or around the body, creating a Wireless body area network. Security and privacy have been a greater concern over a period of time due to the sensitive nature of the data collected and transmitted by the network. It has been noticed that various techniques have been applied to secure the data and provide privacy in WBANs but with a tradeoff of execution overhead. Although the latest available anonymous authentication schemes provide privacy and security but due to the limited computation capacity of WBAN devices, these schemes show greater time cost for authentication and consume more processing time. We review two latest anonymous authentication schemes for the WBAN environment in terms of computation cost. These two schemes provide anonymous authentication and use encryption to secure the data and ensure privacy. Then we analyze a recent lightweight authentication scheme proposed for wearable devices which provides anonymity and privacy along with security with very low computation cost. This scheme uses hash functions in order to obtain authentication and anonymity and doesn’t use encryption in the authentication process. This scheme is not proposed for the WBAN environment, but it can be applied on the WBAN environment with necessary variations. The comparison of these available schemes shows clearly that the computation cost is considerably decreased by applying the latest authentication scheme in the WBAN environment. We propose a new authentication scheme for the WBAN environment based on the light-weight scheme proposed for wearable devices. The detailed analysis shows that our proposed scheme minimizes the computation cost and maintains the privacy and security along with anonymous authentication.