This is an expository paper I wrote at the end of "A Math Summer Program for High School Students" in 2022. This was a reading program where I read A Friendly Introduction to Number Theory by Joseph Silverman with a UCSD graduate student. One of the last topics we covered was elliptic curves, so I wrote this paper after doing some research on how elliptic curves are related to cryptography.

Abstract In this paper, we discuss cryptography using elliptic curves. We start with the basics of cryptography and then go on to the RSA Algorithm for context as why elliptic curve cryptography is so useful. Then we discuss discrete logarithms which is needed for the final section of this paper where we study elliptic curves.