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

Image compression based on 2D Discrete Fourier Transform and matrix minimization algorithm

In the present era of the internet and multimedia, image compression techniques are essential to improve image and video performance in terms of storage space, network bandwidth usage, and secure transmission. A number of image compression methods are available with largely differing compression ratios and coding complexity. In this paper we propose a new method for compressing high-resolution images based on the Discrete Fourier Transform (DFT) and Matrix Minimization (MM) algorithm. The method consists of transforming an image by DFT yielding the real and imaginary components. A quantization process is applied to both components independently aiming at increasing the number of high frequency coefficients. The real component matrix is separated into Low Frequency Coefficients (LFC) and High Frequency Coefficients (HFC). Finally, the MM algorithm followed by arithmetic coding is applied to the LFC and HFC matrices. The decompression algorithm decodes the data in reverse order. A sequential search algorithm is used to decode the data from the MM matrix. Thereafter, all decoded LFC and HFC values are combined into one matrix followed by the inverse DFT. Results demonstrate that the proposed method yields high compression ratios over 98% for structured light images with good image reconstruction. Moreover, it is shown that the proposed method compares favorably with the JPEG technique based on compression ratios and image quality