Compressive sensing (CS) can provide joint compression and encryption, which is promising to address the challenges of massive sensor data and data security in the Internet of Things (IoT). However, as IoT devices have constrained memory, computing power, and energy, in practice the CS-based computationally secure scheme is shown to be vulnerable to ciphertext-only attack for short-signal length. Although the CS-based perfectly secure scheme has no such vulnerabilities, its practical realization is challenging. In this article, we propose an energy concealment (EC) encryption scheme, a practical realization of the perfectly secure scheme by concealing energy, thereby removing the requirement of an additional secure channel. We propose three different methods to generate sensing matrix to improve energy efficiency using linear feedback shift registers and lagged Fibonacci sequences. Leveraging the signal’s maximum energy in the EC scheme, we design a new measure to evaluate reconstructed signal quality without the knowledge of the original signal. Furthermore, a new CS decoding algorithm is designed by incorporating the knowledge of maximum energy at the decoder, which improves the signal reconstruction quality while reducing the number of measurements. Additionally, our comprehensive security analysis shows that the EC scheme is secure against various cryptographic attacks. We implement the EC scheme using the three different ways of generating the sensing matrix in the resource-constrained TelosB mote using the Contiki operating system. The experimental results demonstrate that the EC scheme outperforms advanced encryption standard in terms of code memory footprint and total energy consumption.