Related papers: Some application of difference equations in Crypto…
Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical…
The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…
In quantum information, the role of entanglement and disentanglement is itself a subject of research and debate. Earlier works on quantum cryptography have almost established that entanglement has no special advantage in quantum…
This chapter describes the application of lasers, specifically diode lasers, in the area of quantum key distribution (QKD). First, we motivate the distribution of cryptographic keys based on quantum physical properties of light, give a…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
With the rapid development of quantum computers the currently secure cryptographic protocols may not stay that way. Quantum mechanics provides means to create an inherently secure communication channel that is protected by the laws of…
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…
In quantum cryptography, the level of security attainable by a protocol which implements a particular task $N$ times bears no simple relation to the level of security attainable by a protocol implementing the task once. Useful partial…
The discrete heat equation is worked out in order to illustrate the search of symmetries of difference equations. It is paid an special attention to the Lie structure of these symmetries, as well as to their dependence on the derivative…
The aim of this paper is to elucidate the implications of quantum computing in present cryptography and to introduce the reader to basic post-quantum algorithms. In particular the reader can delve into the following subjects: present…
While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy…
Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already…
The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the…
Owing to its fundamental principles, quantum theory holds the promise to enhance the security of modern cryptography, from message encryption to anonymous communication, digital signatures, online banking, leader election, one-time…
In this brief review, we discuss the role that quantum correlations, as quantified by quantum discord, play in two interesting settings. The first one is discerning which unitaries have been applied on a quantum system, by taking advantage…
Quantum Key Distribution (QKD) is currently being discussed as a technology to safeguard communication in a future where quantum computers compromise traditional public-key cryptosystems. In this paper, we conduct a comprehensive security…
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
The problem of implementation security in quantum key distribution (QKD) refers to the difficulty of meeting the requirements of mathematical security proofs in real-life QKD systems. Here, we provide a succint review on this topic,…