Information security and customers' privacy in smart grid are significant concerns. Existing security and privacy preserving schemes consider that the consumption reports for electricity consumption aggregation and billing purposes are sent periodically. These periodic messages increase the computation and communication burden on restricted-capabilities smart meters. In this paper, we propose a lightweight security and privacy preserving scheme that is based on forecasting the electricity demand for a cluster of houses in the same residential area; it limits the cluster's connection with electricity utility only when the cluster needs to adjust its total demand. The scheme efficiently satisfies the security and privacy requirements in customer-side networks, i.e., communication between customers and power utility. At the same time, it significantly reduces the communication and computation overhead. Moreover, the proposed scheme utilizes NTRU cryptosystem to further reduce the computation complexity.