Embedding cryptographic features in compressive sensing

Abstract

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 twolevel 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.Index Terms-Secure compressive sensing, two-level protection models, symmetric-key cipher, parallel compressive sensing, random permutation, chaotic measurement matrix.

Bi-level Protected Compressive Sampling

“…As we mentioned earlier, there exists some effort to support CS-based cipher for MTS usage [20]- [22], [25]- [28]. In this section, we report the fact that all of them fail to resist CPA.…”

“…In the subsequent sections, we will show that almost all the CS-based product ciphers mentioned above, i.e., those proposed in [20]- [22], [25]- [28], fail to resist the CPA under MTS scenario due to the fact that these product ciphers work only under the RIP framework.…”

“…As described in the previous sections, it is more practical if the same measurement matrix can be re-used multiple times. To this end, there are some attempts trying to incorporate other low-complexity cryptographic primitives to fix the intrinsic security defect of CS in a manner of constructing product ciphers [20]- [22], [25]. A common cryptographic technique suitable for this purpose is scrambling (also known as random permutation), which has been widely used in the field of multimedia security [6], [23].…”

“…Scrambling is performed on the measurements, such as [20], [21]; II. Scrambling is done in the frequency domain, such as [22], [25]. The scrambling process can be characterized by a permutation matrix, which is a square binary matrix that has exactly one non-zero element with value 1 in each row and each column and 0s elsewhere.…”

“…A similar idea was later applied for secure remote image sensing [21]. For the purpose of image acquisition and confidentiality, Zhang et al [22] suggested scrambling the frequency coefficients before the CS encoding instead of scrambling the CS samples. Note that scrambling the frequency coefficients is a mature technique for multimedia confidentiality in traditional coding system [23], the main advantage of employing this technique in the CS paradigm is that a so-called "acceptable" permutation can make the column (or row) sparsity level of 2D signals uniform [24], thus relaxing the restricted isometry property (RIP) of the measurement matrix and flavoring a parallel CS (PCS) reconstruction model.…”