In a smart grid environment, data for the usage and control of power are transmitted over an Internet protocol (IP)-based network. This data contains very sensitive information about the user or energy service provider (ESP); hence, measures must be taken to prevent data manipulation. Mutual authentication between devices, which can prevent impersonation attacks by verifying the counterpart's identity, is a necessary process for secure communication. However, it is difficult to apply existing signature-based authentication in a smart grid system because smart meters, a component of such systems, are resource-constrained devices. In this paper, we consider a smart meter and propose an efficient mutual authentication protocol. The proposed protocol uses a matrix-based homomorphic hash that can decrease the amount of computations in a smart meter. To prove this, we analyze the protocol's security and performance.