A simple and provably secure encryption allowing encrypted data to be efficiently and additively aggregated. Only a modular addition is needed for cipher-text aggregation. Scheme security is based on the in distinguish ability property of a pseudorandom function (PRF), a standard cryptographic primitive. It was proved that aggregation based on this can efficiently compute statistical values, like mean, variance, and sensed data’s standard deviation, while achieving great bandwidth savings. To protect aggregated data’s integrity, an end-to-end aggregate authentication scheme was constructed which was secure against outsider-only attacks. Suggested a method to achieve optimal rate allocation for data aggregation in wireless sensor networks. A rate allocation problem was formulated as a network utility maximization problem., A couple of variable substitutions on the original problem was made due to its non-convexity and transformed it into an approximate problem, which is convex. Then duality theory was applied to decompose the approximate problem into a rate control sub-problem and a scheduling sub-problem. Based on this, a distributed algorithm for joint rate control and scheduling is designed, and was proved to approach arbitrarily close to the optimum of the approximate problem. Theoretical analysis/simulations prove that approximate solution can achieve near-optimal performance. Evaluated two representative SDA schemes realistically using TOSSIM simulator for analyses. To validate data aggregation techniques implementation of data was through use of an analytical model. Results reveal that it is important to reduce transmitted packets number than the overall number of bits transmitted. With low duty cycles and low sensor data generation probability, even simple concatenation of sensor data, which lowered the number of packets transmitted, was as effective as the more sophisticated SDA schemes; when sensor data are generated more frequently, SDA schemes that do not require intermediate nodes decrypt sensor data to give 10% higher network lifetime.