Garg, Gentry and Halevi (GGH) described the first candidate multilinear maps using ideal lattices. However, Hu and Jia presented an efficient attack on GGH map, which breaks the GGH-based applications of multipartite key exchange (MPKE) and witness encryption (WE) based on the hardness of 3-exact cover problem. We describe a new construction of multilinear map using random matrix, which support...

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the meth...

In this paper we construct a class of random matrix ensembles labelled by a real parameter α ∈ (0, 1), whose eigenvalue density near zero behaves like |x|α. The eigenvalue spacing near zero scales like 1/N1/(1+α) and thus these ensembles are representatives of a continous series of new universality classes. We study these ensembles both in the bulk and on the scale of eigenvalue spacing. In the...

In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also given.

the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

Entries of a random matrix are random variables but a random matrix is equivalently considered as a probability measure on the set of matrices. A simple example of random matrix has independent identically distributed entries. In this paper random unitary matrices are studied whose entries must be correlated. A unitary matrix U = (Uij) is a matrix with complex entries and UU ∗ = UU = I. In term...