Related papers: Some application of difference equations in Crypto…
Cryptography is an art and science of secure communication. Here the sender and receiver are guaranteed the security through encryption of their data, with the help of a common key. Both the parties should agree on this key prior to…
Nowadays, using cryptographic systems play an effective role in security and safety technologies. One of the most applied kind of cryptography is Symmetric Cryptography and its applications. New aspects of symmetric Cryptography…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
In this paper, we provide properties and applications of some special integer sequences. We generalize and give some properties of Pisano period. Moreover, we provide a new application in Cryptography and applications of some quaternion…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.
One-way functions are widely used for encrypting the secret in public key cryptography, although they are regarded as plausibly one-way but have not been proven so. Here we discuss the public key cryptosystem based on the system of higher…
A quantum theory is developed for a difference-difference system which can serve as a toy-model of the quantum Korteveg-de-Vries equation.
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
Krawtchouk polynomials appear in a variety of contexts, most notably as orthogonal polynomials and in coding theory via the Krawtchouk transform. We present an operator calculus formulation of the Krawtchouk transform that is suitable for…
Quantum cryptography exploits principles of quantum physics for the secure processing of information. A prominent example is secure communication, i.e., the task of transmitting confidential messages from one location to another. The…
We consider the quantum difference equation of the Hilbert scheme of points in $\mathbb{C}^2$. This equation is the K-theoretic generalization of the quantum differential equation discovered by A. Okounkov and R. Pandharipande. We obtain…
We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele $K$-theory to $KK$-theory for graded $C^*$-algebras with a real structure. Isomorphisms between $KK$-theory and complex or real $K$-theory…
We construct a family of graded isomorphisms between certain subquotients of diagrammatic Cherednik algebras as the quantum characteristic, multicharge, level, degree, and weighting are allowed to vary; this provides new structural…
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
We present the fundamental principles behind quantum key distribution and discuss a few well-known QKD protocols. Bearing in mind that the majority of our readers are from engineering and experimental optics, we focus more on the…
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction…