Investigation into the Cryptographic Properties of Elliptic Curves Defined over a Prime Field

Bachelor Thesis from the year 2014 in the subject Computer Science - IT-Security, grade: 90.00, , course: Computer Security & Digital Forensics, language: English, abstract: Elliptic curves, as used in cryptography, are essentially points bounded by a finite prime field which display group properties that facilitate their usage in a cryptosystem. The Discrete Log Problem (DLP) - based on a large prime order subgroup of (Zp)* - constitutes the essence of Elliptic Curve Cryptography (ECC) and can be summed up as such; find an integer, k, such that Q = kP where k = logp(Q) and P, Q (Zp)*. Compared to the Integer Factorisation Problem - upon which RSA is constructed - the DLP achieves a greater level of complexity in terms of resistance to attack. This project seeks to describe the mathematical properties that enable ECC to outperform RSA, culminating in the construction of a software system to demonstrate ECC's ability to securely encipher and decipher files and text, according to the National Security Agency's (NSA) Cryptographic Interoperability Strategy (CIS) or Suite B Cryptography.