Elliptical curve cryptography

Abstract

In cryptography, the aim is to achieve security through encryption and this involves transforming a message also known as plaintext to cipher text via an encryption method. This encrypted message is to be unravelled by legitimate parties that possess certain information called “keys”.

The usage of encryption is vast and wide when this method of providing security can be practiced by militaries and governments to facilitate secret communication. Encryption can also be used in safe guarding confidential information within many kinds of civilian systems, such as computers, storage devices like mobile phones, Bluetooth devices, networks and automated telling machines issued by banks.

Elliptical curve cryptography which is suggested by Neal Koblitz and Victor S. Miller is a method to encrypt data based on algebraic structure of elliptic curves over finite fields. It is a means to encrypt data as a means of achieving computer security. In this report, the author is working on Elliptical Curve Cryptography (ECC) in which this report looks at the math of ECC, the different key agreement and key exchange protocols of ECC and analyst their effectiveness against certain attacks.

Next, there is the coding section in which the author will be looking at two basic function of ECC which is simply point addition and point doubling. In this section, the author will be presenting C++ codes using the software DEV-C++ that perform the functions of point addition and point doubling and document the ideology behind the C++ codes.

Lastly, in the conclusion section, the author will comment on the limitation of this report, document the performance of the results obtained for point addition and point doubling and finally assess the efficiency of ECC as a method to provide computer security.