A Secure LFSR Based Random Measurement Matrix for Compressive Sensing

In this paper, a novel approach for generating the secure measurement matrix for compressive sensing (CS) based on linear feedback shift register (LFSR) is presented. The basic idea is to select the different states of LFSR as the random entries of the measurement matrix and normalize these values to get independent and identically distributed (i.i.d.) random variables with zero mean and variance $$\frac{1}{N}$$1N, where N is the number of input samples. The initial seed for the LFSR system act as the key to the user to provide security. Since the measurement matrix is generated from the LFSR system, and memory overload to store the measurement matrix is avoided in the proposed system. Moreover, the proposed system can provide security maintaining the robustness to noise of the CS system. The proposed system is validated through different block-based CS techniques of images. To enhance security, the different blocks of images are measured with different measurement matrices so that the proposed encryption system can withstand known plaintext attack. A modulo division circuit is used to reseed the LFSR system to generate multiple random measurement matrices, whereby after each fundamental period of LFSR, the feedback polynomial of the modulo circuit is modified in terms of a chaotic value. The proposed secure robust CS paradigm for images is subjected to several forms of attacks and is proven to be resistant against the same. From experimental analysis, it is proven that the proposed system provides better performance than its counterparts.