Low-complexity Multiclass Encryption by Compressed Sensing

The idea that compressed sensing may be used to encrypt information from unauthorised receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analysed: firstly, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.Comment: IEEE Transactions on Signal Processing, accepted for publication. Article in pres

On Known-Plaintext Attacks to a Compressed Sensing-based Encryption: A Quantitative Analysis

Despite the linearity of its encoding, compressed sensing may be used to provide a limited form of data protection when random encoding matrices are used to produce sets of low-dimensional measurements (ciphertexts). In this paper we quantify by theoretical means the resistance of the least complex form of this kind of encoding against known-plaintext attacks. For both standard compressed sensing with antipodal random matrices and recent multiclass encryption schemes based on it, we show how the number of candidate encoding matrices that match a typical plaintext-ciphertext pair is so large that the search for the true encoding matrix inconclusive. Such results on the practical ineffectiveness of known-plaintext attacks underlie the fact that even closely-related signal recovery under encoding matrix uncertainty is doomed to fail. Practical attacks are then exemplified by applying compressed sensing with antipodal random matrices as a multiclass encryption scheme to signals such as images and electrocardiographic tracks, showing that the extracted information on the true encoding matrix from a plaintext-ciphertext pair leads to no significant signal recovery quality increase. This theoretical and empirical evidence clarifies that, although not perfectly secure, both standard compressed sensing and multiclass encryption schemes feature a noteworthy level of security against known-plaintext attacks, therefore increasing its appeal as a negligible-cost encryption method for resource-limited sensing applications.Comment: IEEE Transactions on Information Forensics and Security, accepted for publication. Article in pres

On the secrecy of compressive cryptosystems under finite-precision representation of sensing matrices

In recent years, the Compressed Sensing (CS) framework has been shown to be an effective private key cryptosystem. If infinite precision is available, then it has been shown that spherical secrecy can be achieved. However, despite its theoretically proven secrecy properties, the only practically feasible implementations involve the use of Bernoulli sensing matrices. In this work, we show that different distributions employing a much larger finite alphabet can be considered. More in detail, we consider the use of quantized Gaussian sensing matrices and experimentally show that, besides being suitable for practical implementation, they can achieve higher secrecy with respect to Bernoulli sensing matrices. Furthermore, we show that this approach can be used to tune the secrecy of the CS cryptosystems based on the available machine precision

Minimizing Acquisition Maximizing Inference -- A demonstration on print error detection

Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition and compression of any signal by taking very few random linear measurements (M). The quality of reconstruction directly relates with M, which should be above a certain threshold for a reliable recovery. Since these measurements can non-adaptively reconstruct the signal to a faithful extent using purely analytical methods like Basis Pursuit, Matching Pursuit, Iterative thresholding, etc., we can be assured that these compressed samples contain enough information about any relevant macro-level feature contained in the (image) signal. Thus if we choose to deliberately acquire an even lower number of measurements - in order to thwart the possibility of a comprehensible reconstruction, but high enough to infer whether a relevant feature exists in an image - we can achieve accurate image classification while preserving its privacy. Through the print error detection problem, it is demonstrated that such a novel system can be implemented in practise

AN INVESTIGATION OF DIFFERENT VIDEO WATERMARKING TECHNIQUES

Watermarking is an advanced technology that identifies to solve the problem of illegal manipulation and distribution of digital data. It is the art of hiding the copyright information into host such that the embedded data is imperceptible. The covers in the forms of digital multimedia object, namely image, audio and video. The extensive literature collected related to the performance improvement of video watermarking techniques is critically reviewed and presented in this paper. Also, comprehensive review of the literature on the evolution of various video watermarking techniques to achieve robustness and to maintain the quality of watermarked video sequences