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Comment by sentinel | Hacker News Reader

Any recommendations for courses or books that give a 101 intro all the way to understanding these curves and why / how they are used?

I'd like to get a grasp on this from first principles. Thank you!

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This blog post from Cloudflare proved incredibly useful to me when I was trying to understand this stuff for the first time. The animated gifs about halfway down the page are particularly useful: https://blog.cloudflare.com/a-relatively-easy-to-understand-...

This is a pretty good intro article: https://andrea.corbellini.name/2015/05/17/elliptic-curve-cry...

Hankerson, Menezes, Vanstone [1] covers almost everything about Elliptic Curves and ECC (Theory and Implementation)

[1]:https://cacr.uwaterloo.ca/ecc/

Trying to render them in code, or with Desmos, is quite enlightening. Cryptographic tools are also helpful for testing it out in practise, such as OpenSSH. Then read up on the various forums and the Bitcoin Wiki, and try to make your own implementation to generate an address. Next step is trying out other cryptos and their algos, if that's the route you want to take.

Wikipedia, honestly. For background math you may want to rely on the citations or other provided texts but a lot of articles have great examples sections.

But... I think you need a more coherent goal than just "understand the math." You can superficially understand the math when guided, but without any reason to retain it I am not sure what you will gain from the experience.

> You can superficially understand the math when guided, but without any reason to retain it I am not sure what you will gain from the experience.

This has been my experience with almost everything I ever learned about math, much of which I have unfortunately not retained.

On my journey into this secret world I sadly had to conclude that understanding of the needed math was severely lacking, and that I'd have to start far back to ever get a grasp on it. But on the flipside it has motivated me to learn a bunch of things I never thought I would when I was younger, and also to program things that I never in my life thought I'd be able to.

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