Elliptic Curves - Computerphile

Just what are elliptic curves and why use a graph shape in cryptography? Dr Mike Pound explains.

This video was filmed and edited by Sean Riley.

[zusurs]

Up till now Tom Scott was hands down my favourite Computerphile presenter, but Mike is now taking over that role. :) as always - great video and nice simplified explenation.

[ewenchan]

I LOVE the fact that he's able to take something that is really, quite complicated, and break it down into vastly simpler terms so that the knowledge is more accessible to a wider range of audience members.

This is how you truly know your stuff -- the test of it is how well can you "dumb it down" so that other people who don't do this daily, would understand this, at least conceptually.

This is what I strive for with some of the stuff that I've learned, is to be able to learn it enough to be able to pass on that knowledge (correctly) to other people. :)

[ElagabalusRex]

I always appreciate new entries in the Diffie-Hellman Cryptographic Universe.

[xdmeister]

Wow, I just got out of my 2 hour lecture where the professor attempted to explain elliptic curves and this 8 minute video explained it much better. Quite impressive!

[jimkd]

7:32 "What you would normally do in this kind of situation if you're were deriving a key from this, is scrap the y and just use the x cuz it's long enough and secure enough." That's wrong! It got nothing to do with x being long end secure enough. It's just that x holds all information necessary to describe what point on the curve you're talking about when the curve you're using is known (which it is) when you just add the information of which side of the curve the point is on. This is why you don't just use x but also add a single bit denoting the side of the curve the point is on. If you look at the formula he wrote down, you can see that you can calculate y^2 when given x, a, and b. a and b are just publicly known parameters. After calculating y^2, you can calculate y except for its sign. If you're given x, a, b, and the sign of y, you can calculate y.

[alemutasa]

Finally a new Mike Pound video. I missed you, man <3 Frankly, I'd listen to him talking about anything, he's so damn charismatic

[Petertronic]

He just loves saying "Diffie-Hellman" 😆

[wesleyesterline]

Would love to see a video about the back door mentioned!

[StreuB]

As a 1st year Calculus student, the maths and geometry was extremely EXTREMELY beneficial to me. It tied several different things I have learned into one real about x x about the x VERY cool!

[christiandalton]

Amazing instructor who has the very unique ability to break very technical topics into an easily understandable video. Thank you!

[lirothen]

I've been thrown into an encryption project at work and these videos are massively helpful, thanks!

[amandacapsicum]

A cryptographer, flirting with someone in a monogamous relationship:
"Other curves are available..."

[harveyp.]

This is the best explanation abt ECC I can find in the internet

[LightTheMars]

Yeah, it's Mike again! Always glad to see that cheeky guy.

[AdamReece]

I really like these videos from Dr Pound. Already looking forward to a video on different curves. :)

[richardjohnson]

Thanks for another cracking explanation.

[benjaminwilson]

Thank you for making these videos. I assume making those Diffie-Hellman videos was annoying but seeing the math all the way through really helped me. Thanks again.

[lukepapapetrou]

I'd love to see a video about security backdoors! And please be as long and thorough as possible.

[Roberto-ddte]

Love this series about cryptography. Please keep on with it.

[andrewxc]

4:43 - "Eventually they will cycle back around..."
At this point, you can also use the number of complete cycles that your number goes around as an additional verification element. All those which have the right modulus, but have a different number of cycles should automatically get locked out, because, c'mon... They're trying to break in...