  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 the resultant security level is not evaluated in depth.
They can only be considered as a preliminary exploration on SCS, but a concrete
and operable encipher model is not given yet. In this paper, we are going to
investigate SCS in a systematic way. The relationship between CS and
symmetric-key cipher indicates some possible encryption models. To this end, we
propose the two-level protection models (TLPM) for SCS which are developed from
measurements taking and something else, respectively. It is believed that these
models will provide a new point of view and stimulate further research in both
CS and cryptography. Specifically, an efficient and secure encryption scheme
for parallel compressive sensing (PCS) is designed by embedding a two-layer
protection in PCS using chaos. The first layer is undertaken by random
permutation on a two-dimensional signal, which is proved to be an acceptable
permutation with overwhelming probability. The other layer is to sample the
permuted signal column by column with the same chaotic measurement matrix,
which satisfies the restricted isometry property of PCS with overwhelming
probability. Both the random permutation and the measurement matrix are
constructed under the control of a chaotic system. Simulation results show that
unlike the general joint compression and encryption schemes in which encryption
always leads to the same or a lower compression ratio, the proposed approach of
embedding encryption in PCS actually improves the compression performance.
Besides, the proposed approach possesses high transmission robustness against
additive Gaussian white noise and cropping attack.
