Curves which make Bitcoin possible.

Elliptic curves are exciting- they have beautiful mathematical properties which found very wide applications in cryptography. In this video, we study the particular elliptic curve which is responsible for Bitcoin security (secp256k1) and understand why elliptic curves are so complex !

(00:00) - Intro
(01:04) - Adding a point to itself
(02:24) - Cryptography
(04:03) - Curves over finite fields
(05:37) - Bitcoin !

#EllipticCurve
#Bitcoin
#Manim

[MaximumBan]

Please make it a sequel! This is an amazing explanation! We want to learn more!

[Jesus-kpml]

just the best video I've ever found about elliptic curves, congrats!!

[김정-nd]

I was studying cryptography in math and this just pops out thanks for this wonderful video

[brandonwalker]

Really cool video. I have always though of elliptic curves as something unaccessibly when hearing about them in the context of proofs such as Prof Wiles proof of Fermat but this was very understandable and an application I did not know existed.

[tamarpeer]

I’d love if you do make a video about hash functions

[anhluong]

This is a really good explainer on elliptic curves and their application! I wish I found this earlier lol

[joaquingutierrez]

Amazing video!! I would like to learn more about criptography here :)

[kattenelvis]

Very good video, I find this topic interesting and I should study it sometime

[aaronlee]

2:35 the text itself is showing a quadratic curve 😳 monospace font 🙌

[Cpt.Zenobia]

It'd be great if you could do a video about interactive proof systems to verify knowledge of a discrete logarithm or isomorphism between graphs.

[giorgos-]

very interesting video keep up the good work :)

[pravinrao]

I always forget that you have so few viewers

[somgesomgedus]

Could you explain why it is so hard to find the key? It doesn't seem so complicated to me at first glance.
And why only use finite fields of prime order? Wouldn't it be also an idea to take F_p^m for some m?

[evanparshall]

I don't understand where those numbers at 2:17 come from. Like where is 72 from the previous points shown.

Edit: I went through your code and found you made a mistake at 1:52. You miss a point with X coordinate 72.

[avionmission]

what software do you use for these amazing animations??

[Jop_pop]

Can you explain why the computation is easy in one direction (finding nP) but hard in the other (finding n)?

[КоляВасильев-ои]

Thanks for video! Please, can you explain how we can calculate "n" at the first time (for private key)? As i understand, we do not do that iterative because iterative way can take very-very long time

[artahir]

0:43
why you show the third point as P+Q
as it doesn't seem to be equal to the sum of the P and Q ?

[viniciusteixeira]

there a some bibliography for this topic? I am a former Mathematician, nowadays i work with data, and i'm got a love for criptology

[michalchik]

It almost seems like the beginning of this video is cut off and he starts in mid idea