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.
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).
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.
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
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
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
