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Written by phryk 🏴 on 2025-01-17 at 14:34

And not a single fucking video I find even attempts to explain what the fuck the "elliptic" in elliptic curve means.

This is beyond abysmal.

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Descendants

Written by Arne Babenhauserheide on 2025-01-17 at 14:40

@phryk isn’t that because geometry of ellipses is a hard to reverse problem?

Wikipedia has you covered: https://en.wikipedia.org/wiki/Elliptic-curve_cryptography

"the base assumption is that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible"

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Written by phryk 🏴 on 2025-01-17 at 14:43

@ArneBab Yeah, that part I get, but I don't get why and none of the other lower-level stuff either.

Like, beginning at "elliptic" – literally none of the elliptic curve plots I have seen was actually an ellipsis? And many actually contained a closed curve plus another curve?

Like, the more I look into it, the less sense it all makes.

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Written by Arne Babenhauserheide on 2025-01-17 at 14:50

@phryk Wikipedia states that it’s a three dimensional ellipsis with the third point in the infinity. That ellipsis gets projected on a two dimensional plane.

Why it’s often open, I don’t know.

But I’m also not deep in the details.

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Written by Arne Babenhauserheide on 2025-01-17 at 14:51

@phryk (and I like it a lot that you are actually asking that question! Though I can’t answer it … can you ping me if you find an answer?)

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Written by phryk 🏴 on 2025-01-17 at 14:55

@ArneBab Huh, so the plots are actually of intersections of a 3D structure on some plane?

Then, shouldn't it be called spheroid cryptography or something like that?

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Written by Arne Babenhauserheide on 2025-01-17 at 16:01

@phryk that might be — I’m really not deep enough in it to give you definite answers.

But it sounds plausible.

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Written by chebra on 2025-01-17 at 16:27

@phryk @ArneBab The wiki article actually answers that:

correspond to embeddings of the torus into the complex projective plane

and

An elliptic curve is not an ellipse in the sense of a projective conic, ... However, there is a natural representation of real elliptic curves with shape invariant j ≥ 1 as ellipses in the hyperbolic plane

(and that's enough math language for a month) Anyway have you seen https://www.youtube.com/watch?v=NF1pwjL9-DE ?

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