In a smart grid system, the utility server collects data from various smart grid devices. These data play an important role in the energy distribution and balancing between the energy providers and energy consumers. However, these data are prone to tampering attacks by an attacker, while traversing from the smart grid devices to the utility servers, which may result in energy disruption or imbalance. Thus, an authentication is mandatory to efficiently authenticate the devices and the utility servers and avoid tampering attacks. To this end, a group authentication algorithm is proposed for preserving demand-response security in a smart grid. The proposed mechanism also provides a fine-grained access control feature where the utility server can only access a limited number of smart grid devices. The initial authentication between the utility server and smart grid device in a group involves a single public key operation, while the subsequent authentications with the same device or other devices in the same group do not need a public key operation. This reduces the overall computation and communication overheads and takes less time to successfully establish a secret session key, which is used to exchange sensitive information over an unsecured wireless channel. The resilience of the proposed algorithm is tested against various attacks using formal and informal security analysis.