Curves which make Bitcoin possible.
HTML-код
- Опубликовано: 11 июн 2024
- 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 !
Source code: github.com/univalency/Manim-a...
(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
Please make it a sequel! This is an amazing explanation! We want to learn more!
I was studying cryptography in math and this just pops out thanks for this wonderful video
Thanks for watching !
Yeah, sometimes, _the algorith_ is actually good for something :-)
I’d love if you do make a video about hash functions
Me too!
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.
Perfect video, congratulations!
I always forget that you have so few viewers
Same lol
Wonder when this channel will blow up
I love this format. Really good work!
2:35 the text itself is showing a quadratic curve 😳 monospace font 🙌
This is a really good explainer on elliptic curves and their application! I wish I found this earlier lol
Wonderful video!
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.
Cool video!
Such interesting video!
very interesting video keep up the good work :)
Very good video, I find this topic interesting and I should study it sometime
Amazing video!! I would like to learn more about criptography here :)
I love you videos ♥ keep it up
new metamathsh upload lets gooo
Do a vid on Hash Functions
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
It almost seems like the beginning of this video is cut off and he starts in mid idea
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?
you would need to start at a base point P and calculate 2P, 3P and so on until you see the right coordinates. This is computationally expensive. The reality is even harder: read about hash functions, they scramble the coordinates.
I never said that a field must have prime order- it is indeed of p^m cardinality. An elliptic curve becomes an Abelian group under such conditions which makes math easy.
@@MetaMaths I think the point that was potentially being made is why it is harder to find n given nP and P than to calculate nP given n and P (i.e. why elliptic curve point multiplication isn't just as hard). I believe the reason is that you can use the method of repeated squares as elliptic curves form groups (called double-and-add in this case).
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 ?
what software do you use for these amazing animations??
Manim for animations, Final Cut for editing
Can you explain why the computation is easy in one direction (finding nP) but hard in the other (finding n)?
Read about fast exponentiation. For example, 10P is 8P + 2P and 8P can be computed in just 3 steps !
@@MetaMaths thanks!
Wow
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.
Great, thanks for noticing ! The point was to demonstrate quadratic growth of numerators/ denominators
@@MetaMaths really good video! One question for you. What happens when the intersection point with the curve goes outside of the finite field?
Can you make a video about parabola and circles and eclipses.
well like if you are interested in making them .
Would be kinda useful for jee adv.
I feel so weird asking this.
it's your choice. ok dude. no pressure.
problems plus in iit mathematics is good book for jee adv
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
Funky!
BCTR - Ready for Takeoff
4:54
how this second equation is true ?
4/3 = 4*3^-1 ok
4*2 = 3 mod 5 ok
but
4/3 = 4*3^-1 = 4*2 = 3 mod 5 how ?
I go like. wait a second why does this zach star video just has one like and 1 view
Nice ! Let' s hope for some explosive dynamic !
THE EGG CURVE
Why 4*3^-1 = 4*2?
only in mod 5.
3^-1 = 2 mod 5 because 3*2 = 6, which is 1 mod 5
@@Errenium Thanks!
I wonder if the crypto spam bots can find this video.
@@s4br3 i invested my bitcoin with Mr Williams and got a 230% return in just 15 days
@@s4br3 messge him on telegram hackerthomas and get yours
Mathematicians and their goofy jargon... "Elliptic" curve - 3rd or 4th order. Yet ellipses, to non-cryptographers, are simple 2nd order curves.
This "adding a point" stuff sounds like something arbitrary made up. Some explanation or rationale would would be in order. Stopped watching after that and disliked.
If you have point 1 and point 2 on an elliptic curve, a line through them will almost always give you a third point on the curve.
So 1 'plus' 2 equals '3', this was the motivation