A public-key cryptosystem based on Diophantine equations and permutation p-polynomials over finite fields
Other Title(s)
نظام تشفير المفتاح العام المعتمد على المعادلات السيالية (الدايفونية) و كثيرات الحدود الأولية على حقول منتهية
Dissertant
Thesis advisor
Comitee Members
al-Marashidah, Muhammad Fathi
al-Shar, Khalid Ahmad Khalid
al-Qadiri, Muhammad Husayn
University
Mutah University
Faculty
Faculty of Science
Department
Department of Mathematics and Statistics
University Country
Jordan
Degree
Master
Degree Date
2016
English Abstract
A Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only.
A linear Diophantine equation of the form ax + by = c has solutions if and only if gcd(a, b) | c.
There is a similar result for linear Diophantine equations in more than 2 variables.
We present a new Public-Key cryptosystem for thissystem; the equation ∑_(i=1)^n▒〖a_i x_i 〗=C is solved modulo m, in which C and a_iare known and x_i∈ {0, 1, 2}.
It can be simply seen that in general case we need to investigate 2^n combinations, while in our system, one need to examine 3^ncombinations which means that the security of the new system is higher than that ofMerkle’s.
Moreover in this thesis we propose an efficient multivariate public key cryptosystem based on permutation p-polynomials over finite fields.
We first characterize a class of permutation p-polynomials over finite fields F_(q^m ) and then construct a trapdoor function using this class of permutation p-polynomials
Main Subjects
No. of Pages
59
Table of Contents
Table of contents.
Abstract.
Abstract in Arabic.
Chapter One : Introduction and preliminaries in number theory.
Chapter Two : Diophantine equations and finite fields.
Chapter Three : Cryptography based on Diophantine equations.
Chapter Four : Cryptography based on permutation P-polynomials over finite fields.
References.
American Psychological Association (APA)
al-Qudah, Rima Umar Awwad. (2016). A public-key cryptosystem based on Diophantine equations and permutation p-polynomials over finite fields. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-731522
Modern Language Association (MLA)
al-Qudah, Rima Umar Awwad. A public-key cryptosystem based on Diophantine equations and permutation p-polynomials over finite fields. (Master's theses Theses and Dissertations Master). Mutah University. (2016).
https://search.emarefa.net/detail/BIM-731522
American Medical Association (AMA)
al-Qudah, Rima Umar Awwad. (2016). A public-key cryptosystem based on Diophantine equations and permutation p-polynomials over finite fields. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-731522
Language
English
Data Type
Arab Theses
Record ID
BIM-731522
