Research Guidance on Elliptic Curve Cryptography I am a freshman who want to research elliptic curve cryptography.
There are a few questions I have:
Firstly, I am not sure about how I should narrow down the topic. Where should I focus on? Can I examine a specific application of elliptic curve cryptography? Or should I basically compare Elliptic Curve Cryptography and RSA algorithms.
Secondly, which prerequisite knowledge do I need? Also, do you suggest any foundational books on the topic?
Thank you
Firstly, I am not sure about how I should narrow down the topic.

It is better to ask your advisor to help you for selecting a good research topic.

Secondly, which prerequisite knowledge do I need? Also, do you suggest any foundational books on the topic?

A roadmap for learning Elliptic Curve Cryptography:

Beginner: you can learn the basic of ECC by reading Chapter 9 of Understanding Cryptography book and/or some good online tutorials and/or by ECC workshop schools.
Intermediate: for a better understanding, you can read these three books: Elliptic Curves: Number Theory and Cryptography, Guide to elliptic curve cryptography and Handbook of elliptic and hyperelliptic curve cryptography.
Advanced: for a deep dive into the mathematics of elliptic curves, you can read Joseph H. Silverman's books.
Implementation: Implementing Curve25519/X25519: A Tutorial on Elliptic Curve Cryptography by Martin Kleppmann.
Research: for selecting a research topic, you can read last research papers of the Workshops on Elliptic Curve Cryptography.