Chinese remainder theorem and its applications
Other Title(s)
نظرية البواقي الصينية و تطبيقاتها
Dissertant
Thesis advisor
Comitee Members
Asad, Y. Asad
Abu Zayidah, Abd al-Salam Uthman
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2014
English Abstract
-The Chinese Reminder Theorem is an ancient but important calculation algorithm in modular arithmetic.
The Chinese Remainder Theorem enables one to solve simultaneous equations with respect to di erent moduli in considerable generality.
In this thesis I introduce an overview of the history of the Chinese Remainder Theorem, state the theorem in di erent algebraic structures and explain di erent uses for the theorem in managing large numbers, speed up calculation, and nding out some division criterion.
The tenor of the thesis revolves around how to calculate residues modulo composite number and consequently introducing divisibility criteria of those number and applying this in the binary system.
Also, I present criteria for calculating residues modulo all integers less than 100.
As well as I explain how to use the Chinese Remainder Theorem in integer factorization and managing large integers.
Also we use Chinese Remainder Theorem to obtain self-dual codes over Rings and to obtain the RSA cryptography.
Main Subjects
Topics
No. of Pages
74
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : Preliminaries.
Chapter Two : Chinese remainder theorem in di erent algebraic structures.
Chapter Three : Applications of the Chinese remainder theorem.
Conclusion.
References.
American Psychological Association (APA)
Abd al-Qadir, Khulud Khalid. (2014). Chinese remainder theorem and its applications. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-531306
Modern Language Association (MLA)
Abd al-Qadir, Khulud Khalid. Chinese remainder theorem and its applications. (Master's theses Theses and Dissertations Master). Islamic University. (2014).
https://search.emarefa.net/detail/BIM-531306
American Medical Association (AMA)
Abd al-Qadir, Khulud Khalid. (2014). Chinese remainder theorem and its applications. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-531306
Language
English
Data Type
Arab Theses
Record ID
BIM-531306
