Related papers: Introduction to the RSA algorithm and modular arit…
We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
A new scheme of probabilistic subgroup-related encryption is introduced. Some applications of this scheme based on the RSA, Diffie-Hellman and ElGamal encryption algorithms are described. Security assumptions and main advantages of this…
Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and let M be an R-module. The aim of this paper is to introduce the notion of S-secondary submodules of M as a generalization of secondary submodules of…
This tutorial provides an introduction to the development of fast matrix algorithms based on the notions of displacement and various low-rank structures.
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations…
Representational similarity analysis (RSA) is a multivariate technique to investigate cortical representations of objects or constructs. While avoiding ill-posed matrix inversions that plague multivariate approaches in the presence of many…
These notes are an expanded version of a short course of lectures given for graduate students in particle physics at Oxford. The level was intended to be appropriate for students in both experimental and theoretical particle physics.The…
Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA at sublinear cost -- by using much fewer memory cells and…
We present a method to increase the dynamical range of a Residue Number System (RNS) by adding virtual RNS layers on top of the original RNS, where the required modular arithmetic for a modulus on any non-bottom layer is implemented by…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some…
We give a short introduction to the theory of modular metric spaces. This is a corrected version of the paper [1], which had some errors. We are grateful to V. V. Chistyakov for bringing these to our attention.
The notes provide a short introduction to de Branges--Rovnyak spaces. They cover some basic facts and are intended to give the reader a taste of the theory, providing sufficient motivation to make it interesting.
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…
We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that…
I give an introduction to algorithmic uses of the principle of inclusion-exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness.
The standard RSA relies on multiple big-number modular exponentiation operations and longer key-length is required for better protection. This imposes a hefty time penalty for encryption and decryption. In this study, we analyzed and…
In this overview article we will consider the deliberate restarting of algorithms, a meta technique, in order to improve the algorithm's performance, e.g., convergence rates or approximation guarantees. One of the major advantages is that…
In recent years there has been a great deal of work done on secret sharing scehemes. Secret Sharing Schemes allow for the division of keys so that an authorised set of users may access information. In this paper we wish to present a…