Related papers: Qusicryslals in Vernam cipher
Shannon presented the concept `unicity distance' for describing the security of secret key encryption protocols against various ciphertext-only attacks. We develop this important concept of cryptanalysis into the quantum context, and find…
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a…
In this paper, we propose a quantum version of the differential cryptanalysis which offers a quadratic speedup over the existing classical one and show the quantum circuit implementing it. The quantum differential cryptanalysis is based on…
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…
It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and…
After providing a concise overview on quasicrystals and their discovery more than a quarter of a century ago, I consider the unexpected interplay between nanotechnology and quasiperiodic crystals. Of particular relevance are efforts to…
We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching…
We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra…
Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
In 1949, Shannon proved the perfect secrecy of the Vernam cryptographic system,also popularly known as the One-Time Pad (OTP). Since then, it has been believed that the perfectly random and uncompressible OTP which is transmitted needs to…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the…
Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also…
The one-electron properties of a certain class of one-dimensional ternary quasicrystals are investigated. In particular, we show in detail the presence of a special kind of critical states called marginal critical states in these QCs. By…
The distinctive electronic properties of quasicrystals stem from their long range structural order, with invariance under rotations and under discrete scale change, but without translational invariance. d-dimensional quasicrystals can be…
Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of…
Shannon's perfect-secrecy theorem states that a perfect encryption system that yields zero information to the adversary must be a one-time pad (OTP) with the keys randomly generated and never reused. In this work we design the first…
In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…