Enhancement of elliptic curves cryptography methods

Dissertant

Saghir, Ali Makki

University

University of Technology

Faculty

-

Department

Computer Sciences Department

University Country

Iraq

Degree

Master

Degree Date

2004

English Abstract

The group of the elliptic curve points forms a Belian group that is suitable choice for constructing a good problem similar to Discrete Logarithm Problem.

This led to create cipher system based on the difficulty of solution elliptic curve discrete logarithm problem that greats a clear change in the cryptography, and open the new windows for treatment with special group and new operations.

This thesis provides the definition and mathematical characteristics of the elliptic curves, gives the properties of constricted group with its points.

Gives how it is possible to be implemented in the cryptography and analyzing the weakness for such group.

This thesis proved a new theorem that can contribute in facilitating the computational process and give method to conclude that each point in the elliptic curve-except the point at infinity-is generator point, if the order-the number of points-is prime.

Also, this thesis provides four proposed methods as a modification of ElG Ama cryptosystem with the elliptic curves, as well as, design a program implementing process of these proposed methods, compute the computational complexity of these methods compared to the original methods, compare these methods with the original methods in running time pot several messages have different sizes, a great reduction in calculation is resulted.

Main Subjects

Mathematics
Information Technology and Computer Science

Topics

• Mathematics
• Data processing
• Encryption

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-305873