Learning Elliptic Curve Cryptography with Curve25519

As of late, I’ve been trying to learn about cryptography more rigorously. I quite enjoyed Real-World Cryptography by David Wong, but there’s a lot of group theory and low-level machinery to continue learning. Martin Kleppmann has an exemplary tutorial on Implementing Curve25519/X25519: A Tutorial on Elliptic Curve Cryptography that I worked through. I think I mostly understood the theory as I worked through it; but here’s some thoughts: TweetNaCl is really cool! I love the idea of tweet-sized algorithms for educative purposes. There’s a lot of different ways to implement finite-field arithmetic (efficiently) – something I want to dig into more. I don’t feel comfortable with the point at infinity. I understand that we’re augmenting the group with an identity element that satisfies criteria that are a pre-requisite for the elliptic curve structure to hold. But I feel like I need a more rigorous perspective to fully grok how it functions. I suspect that some projective geometry and an…