Elliptic curves and elliptic curve cryptography : an honors thesis (HONRS 499)

Abstract

The purpose of this thesis is to introduce elliptic curves and their properties in order to see how they can be used to form groups over different types of fields. These groups are then applied to a cryptographic scheme known as Elliptic Curve Cryptography, and the encryption and decryption processes are demonstrated through the use of examples. Topics from abstract algebra, such as groups, abelian groups, and fields are discussed, as well as some background information about cryptography. Finally, the processes of addition and the encryption and decryption schemes will be implemented using Mathematica code originated from the equations presented in the literature.