\indent in the last 25 years, elliptic curve cryptography has become a mainstream primitive for cryptographic protocols and applications. this talk will give a survey of elliptic curve cryptography and its applications, including applications of pairing-based cryptography which are built with elliptic curves. one of the information-theoretic applications i will cover is a solution to prevent pollution attacks in content distribution networks such as bittorrent which use network coding to achieve optimal throughput. another application i will cover is to privacy of electronic medical records and billings systems.