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New elliptic curve breaks 18-year-old record

quantamagazine.org

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Re: New elliptic curve breaks 18-year-old record

#21

Post by neom »

vessenes wrote: post #17
Noumenon72 wrote: post #6

I was going to ask if the math articles from Quanta magazine are a "Matt Levine" situation where only one person can write so well, but I see only six articles by this author there, so maybe it's an editor doing the magic. All I know is this makes math so accessible and that's not easy.

I too love Quanta. It's funded by an extremely wealthy math guy as a public service; they have the luxury of affording excellent journalists who all seem to me to have graduate degrees in the area they cover, but have not lost the power of communication in exchange. Just a very nice gift to the world.

I was curious about the rich math guy so I looked it up, leaving this here for the next curious person: https://en.wikipedia.org/wiki/Jim_Simons :)

Re: New elliptic curve breaks 18-year-old record

#23

Post by jrvieira »

unnouinceput wrote: post #9
commandlinefan wrote: post #5

Earlier quoted context omitted.

I understood a fair bit of it but only because I've been studying elliptic curves for a while - Quanta does a good job of straddling the line between informing and educating, but they usually err on the side of presenting results rather than proving or explaining them.

>...but they usually err on the side of presenting results rather than proving or explaining them And that's exactly what I like about it. They are a news site, hence they present the news. If the news presenters start to chime in you get what you see at CNN / Fox etc, and that's called propaganda, not news. I want news.

you're worried that they'll explain 3rd degree polynomials with a leftist bias?

Re: New elliptic curve breaks 18-year-old record

#24

Post by defrost »

jrvieira wrote: post #23
unnouinceput wrote: post #9

Earlier quoted context omitted.

>...but they usually err on the side of presenting results rather than proving or explaining them And that's exactly what I like about it. They are a news site, hence they present the news. If the news presenters start to chime in you get what you see at CNN / Fox etc, and that's called propaganda, not news. I want news.

you're worried that they'll explain 3rd degree polynomials with a leftist bias?

The overwhelming majority of their publication on organics has an unmistakable bias toward D- sugars ...

Re: New elliptic curve breaks 18-year-old record

#25

Post by syncsynchalt »

If like me you're interested in the basics of elliptic curves, point addition, and the abelian groups that result then check the first third of my page at https://curves.xargs.org. It only gets you half way to an understanding of this article but might leave you less mystified.

You can also continue through the rest of that page to see how we use this math in cryptography, such as in key exchange.

Re: New elliptic curve breaks 18-year-old record

#26

Post by CarpaDorada »

UI_at_80x24 wrote: post #15
fermigier wrote: post #3

This discovery was already commented a few months ago: https://news.ycombinator.com/item?id=41475177 As I wrote in the comments, I was the record holder, twice, in the 90s: Fermigier, Stéfane - Un exemple de courbe elliptique définie sur Q de rang ≥19. (French) [An example of an elliptic curve defined over Q with rank ≥19] C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 6, 719–722. Fermigier, Stéfane - Une courbe…

As a professional and expert I would love to hear your thoughts and opinions on the use of elliptic curve crypto with SSH. There was a concern (unsure of the validity) that NSA/NIST had compromised the algorithm used and ECC was unfit for 'secure' communication. 2048bit RSA has been deprecated since that declaration and while 4096bit is still viable, the smaller key-size of ed25519 is appealing.

2048bit RSA is not deprecated...

Re: New elliptic curve breaks 18-year-old record

#27

Post by CarpaDorada »

eddd-ddde wrote: post #12
lisper wrote: post #7

Earlier quoted context omitted.

[Not the OP but I think I understand it well enough to take a whack at an ELI5.] Elliptic curves are a particular kind of cubic equation, exactly like the quadratic equations you studied in junior high algebra, except with one term being raised to the third power instead of just squared (and a few other conditions). It turns out that these equations have vastly more complicated behavior than quadratics and give rise…

For the longest time I thought elliptic curves where quadratic curves. Wouldn't it had been more accurate to name them elliptic surfaces?

They're curves (one-dimensional), not surfaces. An example of an elliptic curve is y^2 = x^3 + 1. The polynomial P(x,y) = x^3 + 1 - y^2 has degree 3. A surface is a 2 dimensional geometric shape.

Re: New elliptic curve breaks 18-year-old record

#28

Post by DFHippie »

neom wrote: post #21
vessenes wrote: post #17

Earlier quoted context omitted.

I too love Quanta. It's funded by an extremely wealthy math guy as a public service; they have the luxury of affording excellent journalists who all seem to me to have graduate degrees in the area they cover, but have not lost the power of communication in exchange. Just a very nice gift to the world.

I was curious about the rich math guy so I looked it up, leaving this here for the next curious person: https://en.wikipedia.org/wiki/Jim_Simons :)

> Simons shunned the limelight and rarely gave interviews, citing Benjamin the Donkey in Animal Farm for explanation: "'God gave me a tail to keep off the flies. But I'd rather have had no tail and no flies.' That's kind of the way I feel about publicity."

I'm glad to read about billionaires with non-poisonous personalities. I'd prefer a world where no individual held such relative power, but next best is a world in which the dreadful oligarchs have foils to balance them out slightly.

Re: New elliptic curve breaks 18-year-old record

#29

Post by AlotOfReading »

CarpaDorada wrote: post #26
UI_at_80x24 wrote: post #15

Earlier quoted context omitted.

As a professional and expert I would love to hear your thoughts and opinions on the use of elliptic curve crypto with SSH. There was a concern (unsure of the validity) that NSA/NIST had compromised the algorithm used and ECC was unfit for 'secure' communication. 2048bit RSA has been deprecated since that declaration and while 4096bit is still viable, the smaller key-size of ed25519 is appealing.

2048bit RSA is not deprecated...

NIST has deprecated it for government use after 2030, just not today.

Re: New elliptic curve breaks 18-year-old record

#30

Post by ElijahLynn »

jjice wrote: post #11
lisper wrote: post #7

Earlier quoted context omitted.

[Not the OP but I think I understand it well enough to take a whack at an ELI5.] Elliptic curves are a particular kind of cubic equation, exactly like the quadratic equations you studied in junior high algebra, except with one term being raised to the third power instead of just squared (and a few other conditions). It turns out that these equations have vastly more complicated behavior than quadratics and give rise…

This is a fantastic ELI5, thank you!

Not exactly the 5 year old level though, "you studied in junior high algebra".

Thank you for sharing, and I'm still looking for ELI5 though, because I don't remember algebra class that well.

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