Applications of Elliptic Curve Cryptography: A Light Introduction to Elliptic Curves and a Survey of Their Applications

Elliptic curve cryptography (ECC) is a relatively newer form of public key cryptography that provides more security per bit than other forms of cryptography still being used today. We explore the mathematical structure and operations of elliptic curves and how those properties make curves suitable tools for cryptography. A brief historical context is given followed by the safety of usage in production, as not all curves are free from vulnerabilities. Next, we compare ECC with other popular forms of cryptography for both key exchange and digital signatures, in terms of security and speed. Traditional applications of ECC, both theoretical and in-practice, are presented, including key exchange for web browser usage and DNSSEC. We examine multiple uses of ECC in a mobile context, including cellular phones and the Internet of Things. Modern applications of curves are explored, such as iris recognition, RFID, smart grid, as well as an application for E-health. Finally, we discuss how ECC stacks up in a post-quantum cryptography world.