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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

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    $\begingroup$ Broad question: you could study the math behind elliptic curves, you could look at implementing them securely (and efficiently), you could study the basic protocols (ECDH, ECDSA and friends, ECIES), you could study pairing based crypto (e.g. IBE), you could study isogeny based crypto (although, at your level, I wouldn't start there). How comfortable are you with math (e.g. abstract algebra)? Or, is implementations more your thing? $\endgroup$ – poncho Dec 31 '20 at 15:44
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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:

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