Compressive Sensing (CS) is a new sensing modality, which compresses the signal being acquired at the time of sensing. Signals can have sparse or compressible representation either in original domain or in some transform domain. Relying on the sparsity of the signals, CS allows us to sample the signal at a rate much below the Nyquist sampling rate. Also, the varied reconstruction algorithms of CS can faithfully reconstruct the original signal back from fewer compressive measurements. This fact has stimulated research interest toward the use of CS in several fields, such as magnetic resonance imaging, high-speed video acquisition, and ultrawideband communication. This paper reviews the basic theoretical concepts underlying CS. To bridge the gap between theory and practicality of CS, different CS acquisition strategies and reconstruction approaches are elaborated systematically in this paper. The major application areas where CS is currently being used are reviewed here. This paper also highlights some of the challenges and research directions in this field.

A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications

Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.

Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing

An image encryption algorithm based on chaotic system and compressive sensing

The applications of compressive sensing (CS) in the field of information security have captured a great deal of researchers’ attention in the past decade. To supply guidance for researchers from a comprehensive perspective, this paper, for the first time, reviews CS in information security field from two aspects: theoretical security and application security. Moreover, the CS applied in image cipher is one of the most widespread applications, as its characteristics of dimensional reduction and random projection can be utilized and integrated into image cryptosystems, which can achieve simultaneous compression and encryption of an image or multiple images. With respect to this application, the basic framework designs and the corresponding analyses are investigated. Specifically, the investigation proceeds from three aspects, namely, image ciphers based on chaos and CS, image ciphers based on optics and CS, and image ciphers based on chaos, optics, and CS. A total of six frameworks are put forward. Meanwhile, their analyses in terms of security, advantages, disadvantages, and so on are presented. At last, we attempt to indicate some other possible application research topics in future.

https://dro.deakin.edu.au/eserv/DU:30106242/zhang-reviewofcompressive-2016.pdf

A Review of Compressive Sensing in Information Security Field

An efficient visually meaningful image compression and encryption scheme based on compressive sensing and dynamic LSB embedding

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 \(\frac{1}{N}\), 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.

A Secure LFSR Based Random Measurement Matrix for Compressive Sensing

In this paper, a new approach for scrambling the compressive sensed (CS) audio data using two dimensional cellular automata is presented. In order to improve the security, linear feedback shift register (LFSR) based secure measurement matrix for compressive sensing is used. The basic idea is to select the different states of LFSR as the entries of a random matrix and orthonormalize these values to generate a Gaussian random measurement matrix. It is proposed to generate the initial state matrix of cellular automata using an LFSR based random bitstream generator. In order to improve the security and key space of the proposed cryptosystem, piecewise linear chaotic map (PWLCM) based initial seeds generation for LFSRs is used. In the proposed approach, the initial value, parameter value and the number of iterations of PWLCM are kept as secret to provide security. The proposed audio encryption method for CS audio data is validated with different compressive sensing reconstruction approaches. Experimental and analytical verification shows that the proposed encryption system gives good reconstruction performance, robustness to noise, high level of scrambling and good security against several forms of attack. Moreover, since the measurement matrix used for CS operation and the initial state matrix used for 2D cellular automata are generated using the secret key, the storage/transmission requirement of the same can be avoided.

Audio security through compressive sampling and cellular automata

In this paper, a novel approach for secure compressive sensing of images based on multiple one dimensional chaotic maps is proposed. The basic idea is to perform the random selection of a combination of two one dimensional chaotic maps to generate a random stream. One or more values from the random stream are used to generate each normal value in the random measurement matrix for compressive sensing. In the proposed approach, eight different one dimensional chaotic maps are used. For one measurement matrix generation, two of them are randomly selected based on a secret key. The number of iterations and the initial states of the chaotic maps are also decided by external secret keys. The chaotic output of iterations of the two selected chaotic maps are XORed to generate a new chaotic value so that the measurement matrix so generated can withstand known plaintext attack. The block-based compressive sensing (BCS) of images is adopted to validate the proposed system. Further enhancement in the security of the proposed system for BCS of images can be obtained by using different measurement matrices for different blocks of images. An algorithm for generating multiple measurement matrices is also presented in this work. It is experimentally proved that the proposed encryption system can maintain the robustness to noise of the compressive sensing system. The proposed robust encryption system is subjected to several forms of attacks and is proved to be resistant against all.

A novel approach for secure compressive sensing of images using multiple chaotic maps

This paper proposes a pseudorandom sequence generator for stream ciphers based on elliptic curves (EC). A detailed analysis of various EC based random number generators available in the literature is done and a new method is proposed such that it addresses the drawbacks of these schemes. Statistical analysis of the proposed method is carried out using the NIST (National Institute of Standards and Technology) test suite and it is seen that the sequence exhibits good randomness properties. The linear complexity analysis shows that the system has a linear complexity equal to the period of the sequence which is highly desirable. The statistical complexity and security against known plain text attack are also analysed. A comparison of the proposed method with other EC based schemes is done in terms of throughput, periodicity, and security, and the proposed method outperforms the methods in the literature. For resource constrained applications where a highly secure key exchange is essential, the proposed method provides a good option for encryption by time sharing the point multiplication unit for EC based key exchange. The algorithm and architecture for implementation are developed in such a way that the hardware consumed in addition to point multiplication unit is much less.

/pdf/pseudorandom-bit-sequence-generator-for-stream-cipher-based-1ogww5w49s.pdf

Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves

In this paper, an audio encryption scheme using compressive sensing (CS) and Arnold transform-based scrambling is presented. In the proposed method, compressive sensing is done by using a key-based measurement matrix and the scrambling is carried out with the help of a key-based Arnold matrix. The use of these key-based matrices not only provides better security but also do away with their transmission and storage requirement. The measurement matrix is constructed by using the random numbers generated by a linear feedback shift register (LFSR) whose initial state is generated by a piece wise linear chaotic map (PWLCM), using three 32-bit keys whereas the Arnold matrix is constructed by the random numbers generated by using another 32-bit secret key, PWLCM and a logistic map. By combining secure compressive sensing and Arnold scrambling techniques, very high security can be ensured in addition to efficient channel usage, good resistivity to noise, best reconstruction performance, little encoder complexity and excellent scrambling of data. Experimental results prove the effectiveness of the proposed scheme.

Deepthi P. Pattathil

Papers

A Secure LFSR Based Random Measurement Matrix for Compressive Sensing

Audio security through compressive sampling and cellular automata

A novel approach for secure compressive sensing of images using multiple chaotic maps

Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves

An audio encryption technique through compressive sensing and Arnold transform