What topics does Elliptic curve cryptography lie under? I know this is a weird question to ask. Basically for my Math Internal Assessment, I want to explore Elliptic curve cryptography. (
Due to the lack of time, I'm unable to properly study it and I'm suppose to hand in a proposal very soon.
Therefore I was wondering what topics come under Elliptic curve cryptography?
I think the main topic is functions?
For example: If my topic was calculating surface area of an egg; I guess the main topic it would lie under would calculus & maybe algebra

Put it under Number Theory. I would recommend Ketheth Rosen's Book as it is a pleasure to read, even as an undergrad, and its section on ECC is written by Larry Washington, an expert on the subject matter.
To see this stuff is real and in use, from the linux command line if you type
openssl s_client -host website -port 443

You can see what cipher suite the website is using. Hit CTRL-C to break. For example
openssl s_client -host google.com -port 443

will contain in its extensive output
ECDHE-RSA-AES128-GCM-SHA256

Elliptic Curve Diffie Hellmen Exchange is being used so that the site and the user can have a shared secret.
