Smart Grid is the advanced power grid system that combines renewable energy resources like wind, solar, biogas with the existing power system. Besides that, it provides two-way communication using a large number of electronic devices between the customer and providers which is also known as Advanced Metering Infrastructure (AMI). The devices are resource constraint devices and sensitive information is communicating through them. Therefore, in this paper, these constraints are taken under consideration and designed a lightweight encryption authentication scheme for AMI. The lightweight RECTANGLE and chaotic Logistic map algorithms are taken under consideration. These algorithms encrypt the information along with generating authentication tags. These tags are used on the receiver side to verify the authenticity of the data. The algorithm is simulated in MATLAB and various performance parameters calculated for it. After that, it is compared with the existing algorithms.