Recent study has shown that compressive sensing (CS) based computationally secure scheme using Gaussian or Binomial sensing matrix in resource-constrained IoT devices is vulnerable to ciphertext-only attack. Although the CS-based perfectly secure scheme has no such vulnerabilities, the practical realization of the perfectly secure scheme is challenging, because it requires an additional secure channel to transmit the measurement norm. In this paper, we devise a practical realization of a perfectly secure scheme by concealing energy in which the requirement of an additional secure channel is removed. Since the generation of Gaussian sensing matrices is not feasible in resource-constrained IoT devices, approximate Gaussian sensing matrices are generated using linear feedback shift registers. We also demonstrate the implementation feasibility of the proposed perfectly secure scheme in practice without additional complexity. Furthermore, the security analysis of the proposed scheme is performed and compared with the state-of-the-art compressive sensing based energy obfuscation scheme.