Related papers: Perfect Secrecy Using Compressed Sensing
The Restricted Isometry Property (RIP) introduced by Cand\'es and Tao is a fundamental property in compressed sensing theory. It says that if a sampling matrix satisfies the RIP of certain order proportional to the sparsity of the signal,…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
We consider the problem of constructing an unconditionally secure cipher for the case when the key length is less than the length of the encrypted message. (Unconditional security means that a computationally unbounded adversary cannot…
This paper considers the problem of detecting a high dimensional signal (not necessarily sparse) based on compressed measurements with physical layer secrecy guarantees. First, we propose a collaborative compressive detection (CCD)…
In this paper, we consider a more general four-terminal memoryless relay-eavesdropper channel with state information (REC-SI) and derive an achievable perfect secrecy rate for it. We suppose that the state information is non-causally…
This paper establishes a sharp condition on the restricted isometry property (RIP) for both the sparse signal recovery and low-rank matrix recovery. It is shown that if the measurement matrix $A$ satisfies the RIP condition…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
This paper studies the problem of secure communication over the broadcast channel with receiver side information under the lens of individual secrecy constraints. That is, the transmitter wants to send two independent messages to two…
The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography…
We study the distributed multi-user secret sharing (DMUSS) problem under the perfect privacy condition. In a DMUSS problem, multiple secret messages are deployed and the shares are offloaded to the storage nodes. Moreover, the access…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
This paper is concerned with several security notions for information theoretically secure encryptions defined by the variational (statistical) distance. To ensure the perfect secrecy (PS), the mutual information is often used to evaluate…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than…
The paper proposes a method to secure the Compressive Sensing (CS) streams. It consists in protecting part of the measurements by a secret key and inserting the code into the rest. The secret key is generated via a cryptographically secure…
This paper concentrates on the recovery of block-sparse signals, which is not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear…
Reconfigurable Intelligent Surfaces (RISs) constitute a strong candidate physical-layer technology for the $6$-th Generation (6G) of wireless networks, offering new design degrees of freedom for efficiently addressing demanding performance…
Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional (2D) variant of compressed sensing…
Dimension reduction plays an essential role when decreasing the complexity of solving large-scale problems. The well-known Johnson-Lindenstrauss (JL) Lemma and Restricted Isometry Property (RIP) admit the use of random projection to reduce…
Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the…