Related papers: Quasigroups in cryptology
Quasirandomness is a general mathematical concept meant to encapsulate several characteristics usually satisfied by random combinatorial objects, and which we regard as describing when a given object 'looks random'. In this survey we…
This work is intended as an introduction to cryptographic security and a motivation for the widely used Quantum Key Distribution (QKD) security definition. We review the notion of security necessary for a protocol to be usable in a larger…
Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate…
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…
I present examples of mathematical objects that are of interest for public key cryptography. Text for the Journ\'ee Annuelle 2007 of the SMF.
We explain, on the example of Wigner's quasiprobability distribution, how negative probabilities may be used in the foundations of probability.
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…
Quantum computing has recently appeared in the headlines of many scientific and popular publications. In the context of quantitative finance, we provide here an overview of its potential.
This article presents the application of homomorphic authenticators, replication encodings to be precise, to multigroup fully homomorphic encryption schemes. Following the works of Gennaro and Wichs on homomorphic authenticators in…
In this paper we generalize the definition of a multilinear map to arbitrary groups and develop a novel idea of multilinear cryptosystem using nilpotent group identities.
Most currently used cryptographic tools for protecting data are based on certain computational assumptions, which makes them vulnerable with respect to technological and algorithmic developments, such as quantum computing. One existing…
In this survey we propose to cover the prose of post-quantum cryptography over classical cryptography. We talk about the various cryptographic methods that are being practiced to safeguard our information. The future of secure communication…
In this paper we introduce the notion of weak Hopf quasigroup as a generalization of weak Hopf algebras and Hopf quasigroups. We obtain its main properties and we prove the fundamental theorem of Hopf modules for these algebraic structures.
We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian…
We review the theory of Cheeger constants for graphs and quantum graphs and their present and envisaged applications.
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…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
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…
We announce a new approach to the octonions as quasiassociative algebras. We strip out the categorical and quasi-quantum group considerations of our longer paper and present here (without proof) some of the more algebraic conclusions
Quasiprobability representations are well-established tools in quantum information science, with applications ranging from the classical simulability of quantum computation to quantum process tomography, quantum error correction, and…