08-16-2017, 10:23 PM
The ultimate purpose of this project has been the implementation in MATLAB of an Elliptic Curve Cryptography (ECC) system, primarily the Elliptic Curve Diffie-Hellman (ECDH) key exchange. We first introduce the fundamentals of Elliptic Curves, over both the real numbers and the integers modulo p where p is prime. Then the theoretical underpinnings of the ECDH system are covered, including a brief look at how this system is broken. Next we develop the individual elements that will be needed in the implementation of ECDH, such as functions for calculating modular square roots and the addition of points on an EC. We then bring these elements together to create a working ECDH program, and discuss the limitations of the MATLAB environment in which it was created. Finally we look at the real world application of ECC and its future in the realm of cryptography.