Low power has become an essential design imperative in the era of nanotechnology. In this paper, we propose a new design of energy efficient reconfigurable Linear Feedback Shift Registers(LFSRs). The reconfigurable LFSR design allows an increase in the randomness at the output. Furthermore, several low power design techniques are utilized to help achieve energy savings. This improves the applicability of the design for security applications in portable embedded systems. The LFSR building blocks are presented in this paper. The design implementation and analysis were performed using HSPICE. Simulation results show reduction in the energy consumed by the circuit.