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Relevant bibliographies by topics / Prime factorization / Dissertations / Theses

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Dissertations / Theses on the topic 'Prime factorization'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Eppens, Daniel. "Prime Factorization by Quantum Adiabatic Computation." Thesis, KTH, Fysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-138164.

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2

Bollinger, Patrick James. "Prime Factorization Through Reversible Logic Gates." Youngstown State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1558867948427409.

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3

Jacobsson, Mattias. "Bitwise relations between n and φ(n) : A novel approach at prime number factorization". Thesis, Blekinge Tekniska Högskola, Institutionen för datalogi och datorsystemteknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-16655.

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Cryptography plays a crucial role in today’s society. Given the influence, cryptographic algorithms need to be trustworthy. Cryptographic algorithms such as RSA relies on the problem of prime number factorization to provide its confidentiality. Hence finding a way to make it computationally feasible to find the prime factors of any integer would break RSA’s confidentiality. The approach presented in this thesis explores the possibility of trying to construct φ(n) from n. This enables factorization of n into its two prime numbers p and q through the method presented in the original RSA paper. T

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4

Wilson, Keith Eirik. "Factoring Semiprimes Using PG2N Prime Graph Multiagent Search." PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/219.

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In this thesis a heuristic method for factoring semiprimes by multiagent depth-limited search of PG2N graphs is presented. An analysis of PG2N graph connectivity is used to generate heuristics for multiagent search. Further analysis is presented including the requirements on choosing prime numbers to generate 'hard' semiprimes; the lack of connectivity in PG1N graphs; the counts of spanning trees in PG2N graphs; the upper bound of a PG2N graph diameter and a conjecture on the frequency distribution of prime numbers on Hamming distance. We further demonstrated the feasibility of the HD2 breadth

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5

Puffenberger, Owen. "Uniqueness of Bipartite Factors in Prime Factorizations Over the Direct Product of Graphs." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3017.

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While it has been known for some time that connected non-bipartite graphs have unique prime factorizations over the direct product, the same cannot be said of bipartite graphs. This is somewhat vexing, as bipartite graphs do have unique prime factorizations over other graph products (the Cartesian product, for example). However, it is fairly easy to show that a connected bipartite graph has only one prime bipartite factor, which begs the question: is such a prime bipartite factor unique? In other words, although a connected bipartite graph may have multiple prime factorizations over the direct

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6

Rezola, Nolberto. "Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/205.

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The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order of the factors. This

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7

Borg, Caroline W., and Erik Dackebro. "A Comparison of Performance Between a CPU and a GPU on Prime Factorization Using Eratosthene's Sieve and Trial Division." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-208678.

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There has been remarkable advancement in Multi-cored Processing Units over the past decade. GPUs, which were originally designed as a specialized graphics processor, are today used in a wide variety of other areas. Their ability to solve parallel problems is unmatched due to their massive amount of simultaneously running cores. Despite this, most algorithms in use today are still fully sequential and do not utilize the processing power available. The Sieve of Eratosthenes and Trial Division are two very naive algorithms which combined can be used to find a number's unique combinataion of prime

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8

Hedenström, Felix. "Trial Division : Improvements and Implementations." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-211090.

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Trial division is possibly the simplest algorithm for factoring numbers.The problem with Trial division is that it is slow and wastes computationaltime on unnecessary tests of division. How can this simple algorithms besped up while still being serial? How does this algorithm behave whenparallelized? Can a superior serial and a parallel version be combined intoan even more powerful algorithm?To answer these questions the basics of trial divisions where researchedand improvements where suggested. These improvements where later im-plemented and tested by measuring the time it took to factorize a

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9

Kišac, Matej. "Distribuované aplikace s využitím frameworku Windows Communication Foundation." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-242060.

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This thesis deals with distributed applications and WCF framework. The first part is based on theoretical information about distributed systems and we also concentrate on models of distributed systems. Next part describes WCF framework and key elements of WCF application. The following chapter is designated to introduce information about prime factorization. Then the knowledge from previous parts is used to create examples of service-oriented applications. In conclusion we discuss main parts of designing distributed application to solve factorization problem. Finally the comparison of distribu

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10

Johansson, Angela. "Distributed System for Factorisation of Large Numbers." Thesis, Linköping University, Department of Electrical Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1883.

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<p>This thesis aims at implementing methods for factorisation of large numbers. Seeing that there is no deterministic algorithm for finding the prime factors of a given number, the task proves rather difficult. Luckily, there have been developed some effective probabilistic methods since the invention of the computer so that it is now possible to factor numbers having about 200 decimal digits. This however consumes a large amount of resources and therefore, virtually all new factorisations are achieved using the combined power of many computers in a distributed system. </p><p>The nature of the

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11

Vychodil, Petr. "Softwarová podpora výuky kryptosystémů založených na problému faktorizace velkých čísel." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2009. http://www.nusl.cz/ntk/nusl-218146.

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This thesis deals with new teaching software, which supports asymmetric encryption algorithms based on the issue of large numbers´ factorization. A model program was created. It allows to carry out operations related to encryption and decryption with an interactive control. There is a simple way to understand the principle of the RSA encryption method with its help. The encryption of algorithms is generally analysed in chapters 1,2. Chapters 3 and 4 deals with RSA encryption algorithm in much more details, and it also describes the principles of the acquisition, management and usage of encrypt

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12

Bértolo, Mónica Calvário. "Inteiros Gaussianos." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16826.

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13

"Elliptic curve over finite field and its application to primality testing and factorization." 1998. http://library.cuhk.edu.hk/record=b5889507.

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by Chiu Chak Lam.<br>Thesis submitted in: June, 1997.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.<br>Includes bibliographical references (leaves 67-69).<br>Abstract also in Chinese.<br>Chapter 1 --- Basic Knowledge of Elliptic Curve --- p.2<br>Chapter 1.1 --- Elliptic Curve Group Law --- p.2<br>Chapter 1.2 --- Discriminant and j-invariant --- p.7<br>Chapter 1.3 --- Elliptic Curve over C --- p.10<br>Chapter 1.4 --- Complex Multiplication --- p.15<br>Chapter 2 --- Order of Elliptic Curve Group Over Finite Fields and the Endo- morphism Ring --- p.18<br>Chapter 2.1 --- Hasse'

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14

WANG, LI-CHUN, and 王莉淳. "Research on 5th Graders' Performance on Solving Prime Factorization Problems Using Virtual Manipulatives " Factor tree"." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/44871484784358326023.

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碩士<br>國立臺中教育大學<br>數學教育學系<br>104<br>The purpose of this study was to investigate 5th graders’ performance on solving prime factorization problems via virtual manipulatives “factor tree”. Both quantitative and qualitative methods were used in this study. The participants were 26 fifth grade students from on elementary school located at Banqiao District, New Taipei City. Self-constructed examinations were given before and after instruction. In addition, ten students were selected based on their responses of the tests for further semi-structured interviewed. The results were as follows: 1. Ov

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15

WANG, TZ-CHI, and 王姿淇. "The Effects of Integrating Digital Board Game into Prime Factorization Learning on Elementary Students’ Technology Acceptance and Flow Experience." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/4t8gnu.

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碩士<br>國立屏東大學<br>資訊科學系碩士班<br>106<br>Mathematics is an important subject to students for further learning other domain knowledge. However, since mathematics learning process is usually uninteresting, many students thus lack learning motivation to learn mathematics and further have low learning performance with regard to mathematics. In recent years, various board games have been proposed and evaluated the effectiveness on education. With the advance of the technology, it is possible to integrate information technology with traditional board games to develop digital board games. Different from tr

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16

Rebenich, Niko. "Counting prime polynomials and measuring complexity and similarity of information." Thesis, 2016. http://hdl.handle.net/1828/7251.

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This dissertation explores an analogue of the prime number theorem for polynomials over finite fields as well as its connection to the necklace factorization algorithm T-transform and the string complexity measure T-complexity. Specifically, a precise asymptotic expansion for the prime polynomial counting function is derived. The approximation given is more accurate than previous results in the literature while requiring very little computational effort. In this context asymptotic series expansions for Lerch transcendent, Eulerian polynomials, truncated polylogarithm, and polylogarithms of neg

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