Embedding cryptographic features in compressive sensing

Compressive sensing (CS) has been widely studied and applied in many fields. Recently, the way to perform secure compressive sensing (SCS) has become a topic of growing interest. The existing works on SCS usually take the sensing matrix as a key and can only be considered as preliminary explorations on SCS. In this paper, we firstly propose some possible encryption models for CS. It is believed that these models will provide a new point of view and stimulate further research in both CS and cryptography. Then, we demonstrate that random permutation is an acceptable permutation with overwhelming probability, which can effectively relax the Restricted Isometry Constant for parallel compressive sensing. Moreover, random permutation is utilized to design a secure parallel compressive sensing scheme. Security analysis indicates that the proposed scheme can achieve the asymptotic spherical secrecy. Meanwhile, the realization of chaos is used to validate the feasibility of one of the proposed encryption models for CS. Lastly, results verify that the embedding random permutation based encryption enhances the compression performance and the scheme possesses high transmission robustness against additive white Gaussian noise and cropping attack.