Image Encryption and Stegenography Based on Computational Single Pixel Imaging

Multiple layers of information security are introduced based on computational ghost imaging (CGI). We show, in the first step, that it is possible to design a very reliable image encryption scheme using 3D computational ghost imaging with two single-pixel detectors sending data through two channels. Through the Normalized Root Mean Square scale, it is then shown that a further level of security can be achieved by merging data-carrying channels into one and using a coded order for their placement in the sequence of bucket data carried by the single channel. Yet another layer of security is introduced through hiding the actual grayscale image inside another image such that the hidden image cannot be recognized by naked eyes. We then retrieve the hidden image from a CGI reconstructed image. It is shown that the proposed scheme increases the security and robustness such that an attacker needs more than 96 percent of the coded order to recover the hidden data. Storing a grayscale image in a ghost image and retrieving different intensities for the hidden image is unprecedented and could be of interest to the information security community

Provably secure and efficient audio compression based on compressive sensing

The advancement of systems with the capacity to compress audio signals and simultaneously secure is a highly attractive research subject. This is because of the need to enhance storage usage and speed up the transmission of data, as well as securing the transmission of sensitive signals over limited and insecure communication channels. Thus, many researchers have studied and produced different systems, either to compress or encrypt audio data using different algorithms and methods, all of which suffer from certain issues including high time consumption or complex calculations. This paper proposes a compressing sensing-based system that compresses audio signals and simultaneously provides an encryption system. The audio signal is segmented into small matrices of samples and then multiplied by a non-square sensing matrix generated by a Gaussian random generator. The reconstruction process is carried out by solving a linear system using the pseudoinverse of Moore-Penrose. The statistical analysis results obtaining from implementing different types and sizes of audio signals prove that the proposed system succeeds in compressing the audio signals with a ratio reaching 28% of real size and reconstructing the signal with a correlation metric between 0.98 and 0.99. It also scores very good results in the normalized mean square error (MSE), peak signal-to-noise ratio metrics (PSNR), and the structural similarity index (SSIM), as well as giving the signal a high level of security

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X \in \mathbb{C}^{n \times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j a_j^*$ for some measurement vectors $a_1,...,a_m$, i.e., the measurements are given by $y_j = \mathrm{tr}(X a_j a_j^*)$. The case where the matrix $X=x x^*$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements, $y_j = |\langle x,a_j\rangle|^2$ via the PhaseLift approach, which has been introduced recently. We derive bounds for the number $m$ of measurements that guarantee successful uniform recovery of Hermitian rank $r$ matrices, either for the vectors $a_j$, $j=1,...,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective $t$-design with $t=4$. In the Gaussian case, we require $m \geq C r n$ measurements, while in the case of $4$-designs we need $m \geq Cr n \log(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank $r$-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate $4$-designs generalizes and improves a recent bound on phase retrieval due to Gross, Kueng and Krahmer. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.Comment: 24 page

A review of compressive sensing in information security field

The applications of compressive sensing (CS) in the fi eld of information security have captured a great deal of researchers\u27 attention in the past decade. To supply guidance for researchers from a comprehensive perspective, this paper, for the fi rst 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. Speci fically, 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