Elliptic curves over finite fields

Abstract

The application of elliptic curves to the field of cryptography has been relatively recent. It has opened up a wealth of possibilities in terms of security, encryption, and real-world applications. In particular, we are interested in public-key cryptosystems that use the elliptic curve discrete logarithm problem to establish security. The objective of this memory is to assemble the most important facts and findings into a broad, unified overview of this field. To illustrate certain points, we also discuss a some cryptosystems of the elliptic curve analogue such as of the exchange key deffie-hellman and El Gamal cryptosystem.