Publication Date
2019
Document Type
Thesis
Committee Members
Meilin Liu (Advisor), Junjie Zhang (Committee Member), Keke Chen (Committee Member)
Degree Name
Master of Science in Cyber Security (M.S.C.S.)
Abstract
Elliptic Curve Cryptography (ECC) is a public-key cryptography system. Elliptic Curve Cryptography (ECC) can achieve the same level of security as the public-key cryptography system, RSA, with a much smaller key size. It is a promising public key cryptography system with regard to time efficiency and resource utilization. This thesis focuses on the software implementations of ECC over finite field GF(p) with two distinct implementations of the Big Integer classes using character arrays, and bit sets in C++ programming language. Our implementation works on the ECC curves of the form y^2 = x^3 + ax + b (mod p). The point addition operation and the scalar multiplication are implemented on a real SEC (Standards for Efficient Cryptography) ECC curve over a prime field with two different implementations. The Elliptic Curve Diffie-Hellman key exchange, the ElGamal encryption/decryption system, and the Elliptic Curve Digital Signature Algorithm (ECDSA) on a real SEC ECC curve with two different implementations of the big integer classes are tested, and validated. The performances of the two different implementations are compared and analyzed.
Page Count
88
Department or Program
Department of Computer Science and Engineering
Year Degree Awarded
2019
Copyright
Copyright 2019, all rights reserved. My ETD will be available under the "Fair Use" terms of copyright law.
