Towards Secure Compressive Sampling Scheme.

There have been some pioneering works concerning embedding cryptographic properties in Compressive Sampling (CS) but it turns out that the concise linear projection encoding process makes this approach ineffective. Here we introduce a bi-level protection (BLP) model for constructing secure compressive sampling scheme. Then we propose several techniques to establish secret key-related sparsifying basis and deploy them into our new CS model. It is demonstrated that the encoding process is simply a random linear projection, which is the same as the traditional model. However, decoding the measurements requires the knowledge of both the key-related sensing matrix and the key-related sparsifying basis. We apply the proposed model to construct digital image cipher under the parallel compressive sampling reconstruction framework. The main properties of this cipher, such as low computational complexity, compressibility, robustness and computational secrecy under known/chosen plaintext attacks, are thoroughly studied. It is shown that compressive sampling scheme based on our BLP model is robust under various attack scenarios although the encoding process is a simple linear projection.

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