Results 51 to 60 of about 125 (118)

Mersenne Primes in Real Quadratic Fields

, 2012
The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\sqrt{2})$ is studied in detail with a focus on representing Mersenne primes in the form $x^{2}+7y^{2}$. It is also proved that $x$ is divisible by 8 and $y\equiv \pm3\pmod{8}$ generalizing the result of F Lemmermeyer ...
Palimar, Sushma, Shankar, B. R.
openaire   +3 more sources

Stegocrypt: A robust tri‐stage spatial steganography algorithm using TLM encryption and DNA coding for securing digital images

IET Image Processing, Volume 18, Issue 13, Page 4189-4206, 13 November 2024.
This research work presents a novel secured spatial steganography algorithm consisting of three stages. In the first stage, a secret message is divided into three parts, each is encrypted using a tan logistic map encryption key with a unique seed value.
Wassim Alexan, Eyad Mamdouh, Amr Aboshousha, Youssef S. Alsahafi, Mohamed Gabr, Khalid M. Hosny   +5 more
wiley   +1 more source

Prospects for the Use of Quasi-Mersen Numbers in the Design of Parallel-Serial Processors

Applied Sciences
It is shown that a serial-parallel processor, comparable in bit capacity to a 16-bit binary processor, can be implemented based on an algorithm built on the residue number system, a distinctive feature of which is the use of the first four quasi-Mersenne
Aruzhan Kadyrzhan, Kaisarali Kadyrzhan, Akhat Bakirov, Ibragim Suleimenov   +3 more
doaj   +1 more source

Strong divisibility sequences and sieve methods

Mathematika, Volume 70, Issue 4, October 2024.
Abstract We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods.
Tim Browning, Matteo Verzobio
wiley   +1 more source

Generalizing the eight levels theorem: a journey to Mersenne prime discoveries and new polynomial classes

Arab Journal of Basic and Applied Sciences
Mersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Ibrahim
doaj   +1 more source

Variational approaches to the elasticity of deformable strings with and without mass redistribution

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 104, Issue 8, August 2024.
Abstract The catenary is a curve that has played a significant role in the history of mathematics, finding applications in various disciplines such as mechanics, technology, architecture, the arts, and biology. In this paper, we introduce some generalizations by applying the variational method to deformable strings.
Stefano Giordano
wiley   +1 more source

Trigger-Based Systems as a Promising Foundation for the Development of Computing Architectures Based on Neuromorphic Materials

Technologies
It is demonstrated that neuromorphic materials designed for computational tasks can be effectively implemented by drawing an analogy with trigger-based systems built upon classical binary elements.
Dina Shaltykova, Kaisarali Kadyrzhan, Jelena Caiko, Yelizaveta Vitulyova, Ibragim Suleimenov   +4 more
doaj   +1 more source

mid-pSquare: Leveraging the Strong Side-Channel Security of Prime-Field Masking in Software

Transactions on Cryptographic Hardware and Embedded Systems
Efficiently protecting embedded software implementations of standard symmetric cryptographic primitives against side-channel attacks has been shown to be a considerable challenge in practice.
Brieuc Balon, Lorenzo Grassi, Pierrick Méaux, Thorben Moos, François-Xavier Standaert, Matthias Johann Steiner   +5 more
doaj   +1 more source

Electronic Fourier–Galois Spectrum Analyzer for the Field GF(31)

Applied Sciences
A scheme for the Fourier–Galois spectrum analyzer for the field GF(31) is proposed. It is shown that this analyzer allows for solving a wide enough range of problems related to image processing, in particular those arising in the course of experimental ...
Kaisarali Kadyrzhan, Daulet Kaldybekov, Saltanat Baipakbaeva, Yelizaveta Vitulyova, Dinara Matrassulova, Ibragim Suleimenov   +5 more
doaj   +1 more source

The Mersenne Primes

This is a unique system for finding Mersenne Primes Deveolped by Branden Lee ...
openaire   +2 more sources