Secure Compressive Sensing with Hyper-Chaos: A Simultaneous Encryption and Sampling Framework

Secure compressive sensing (SCS) mostly benefits scenes such as IoT with finite computer resources, the fields of spaceflight and medicine, etc. Recently, research on SCS has aroused widespread interest. Nevertheless, existing work on embedding security of CS usually requires an extra cryptographic routine applied to the measurement vectors. In this paper, we proposed an SCS scheme boosted by the hyper-chaotic system, which outperforms state-of-the-art methods and endows the SCS with a high level of inherent security. Encryption and sampling processing are accomplished simultaneously in our scheme, i.e., security is achieved when sampling with a measurement matrix, which is generated by an initial-value (secret key)-driven discrete hyper-chaotic (HC) system. Moreover, the application of the HC matrix decreases both the computing and bandwidth consumption costs of secret key streams transmission compared with traditional CS-based encryption methods. Experimentally, the HC-based matrix demonstrates excellent reconstruction performance, achieving an average SSIM of 0.91 and PSNR of 29.09 dB on the Set5 dataset at a sampling ratio of 0.5, outperforming conventional matrices such as Bernoulli and Hadamard. Security analysis confirms that the system exhibits asymptotic spherical secrecy and high key sensitivity—a deviation of 10−16 in the initial value results in complete decryption failure. Furthermore, the scheme shows strong robustness against additive Gaussian white noise and cropping attacks, maintaining a PSNR above 15 dB even under 50% cropping. Compared to existing methods, the proposed approach reduces bandwidth consumption by transmitting only the HC initial parameters rather than the entire measurement matrix. These results demonstrate that the HC-driven SCS framework provides inherent security, high reconstruction fidelity, and practical efficiency, making it suitable for secure sensing in constrained environments.