Related papers: Introduction to the RSA algorithm and modular arit…

Given the escalating importance of cybersecurity, it becomes increasingly beneficial for a diverse community to comprehend fundamental security mechanisms. Among these, the RSA algorithm stands out as a crucial component in public-key…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

In this paper we present a new efficient algorithm for factoring the RSA and the Rabin moduli in the particular case when the difference between their two prime factors is bounded. As an extension, we also give some theoretical results on…

Modern-day computer security relies heavily on cryptography as a means to protect the data that we have become increasingly reliant on. The main research in computer security domain is how to enhance the speed of RSA algorithm. The…

RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a…

A introduction to the syntax and Semantics of Answer Set Programming intended as an handout to [under]graduate students taking Artificial Intlligence or Logic Programming classes.

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one…

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.

Singular Spectrum Analysis (SSA) as a tool for analysis and forecasting of time series is considered. The main features of the Rssa package, which implements the SSA algorithms and methodology in R, are described and examples of its use are…

These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…

Representational Similarity Analysis (RSA) is a technique developed by neuroscientists for comparing activity patterns of different measurement modalities (e.g., fMRI, electrophysiology, behavior). As a framework, RSA has several advantages…

In this paper we give a polynomial time algorithm to compute $\varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer. This provides a new insight in the very important problem of factoring an RSA…

This article proposes a new method to inject backdoors in RSA and other cryptographic primitives based on the Integer Factorization problem for balanced semi-primes. The method relies on mathematical congruences among the factors of the…

These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…

This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience. The objective of this paper is to help the reader feel…

This is a short introduction to quantum computers, quantum algorithms and quantum error correcting codes. Familiarity with the principles of quantum theory is assumed. Emphasis is put on a concise presentation of the principles avoiding…

RSA cryptography is still widely used. Some of its applications (e.g., distributed signature schemes, cryptosystems) do not allow the RSA modulus to be generated by a centralized trusted entity. Instead, the factorization must remain…

This is a short introduction to Quantum Computing intended for physicists. The basic idea of a quantum computer is introduced. Then we concentrate on Shor's integer factoring algorithm.

We introduce DM-RSA (Dual Modulus RSA), a variant of the RSA cryptosystem that employs two distinct moduli symmetrically to enhance security. By leveraging the Chinese Remainder Theorem (CRT) for decryption, DM-RSA provides increased…

The cryptosystem RSA is a very popular cryptosystem in the study of Cryptography. In this article, we explore how the idea of a primitive mth root of unity in a ring can be integrated into the Discrete Fourier Transform, leading to the…