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Compressive sensing (CS) has been widely studied and applied in many fields.Recently, the way to perform secure compressive sensing (SCS) has become atopic of growing interest. The existing works on SCS usually take the sensingmatrix as a key and the resultant security level is not evaluated in depth.They can only be considered as a preliminary exploration on SCS, but a concreteand operable encipher model is not given yet. In this paper, we are going toinvestigate SCS in a systematic way. The relationship between CS andsymmetric-key cipher indicates some possible encryption models. To this end, wepropose the two-level protection models (TLPM) for SCS which are developed frommeasurements taking and something else, respectively. It is believed that thesemodels will provide a new point of view and stimulate further research in bothCS and cryptography. Specifically, an efficient and secure encryption schemefor parallel compressive sensing (PCS) is designed by embedding a two-layerprotection in PCS using chaos. The first layer is undertaken by randompermutation on a two-dimensional signal, which is proved to be an acceptablepermutation with overwhelming probability. The other layer is to sample thepermuted signal column by column with the same chaotic measurement matrix,which satisfies the restricted isometry property of PCS with overwhelmingprobability. Both the random permutation and the measurement matrix areconstructed under the control of a chaotic system. Simulation results show thatunlike the general joint compression and encryption schemes in which encryptionalways leads to the same or a lower compression ratio, the proposed approach ofembedding encryption in PCS actually improves the compression performance.Besides, the proposed approach possesses high transmission robustness againstadditive Gaussian white noise and cropping attack.

Embedding Cryptographic Features in Compressive Sensing