The Mathematics of Diffie-Hellman Key Exchange | Infinite Series

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Symmetric single-key encryption schemes have become the workhorses of secure communication for a good reason. They’re fast and practically bulletproof… once two parties like Alice and Bob have a single shared key in hand. And that’s the challenge -- they can’t use symmetric key encryption to share the original symmetric key, so how do they get started?

Written and Hosted by Gabe Perez-Giz
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow and Meah Denee Barrington

Thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!

And thanks to Nicholas Rose, Jason Hise, Thomas Scheer, Marting Sergio H. Faester, CSS, and Mauricio Pacheco who are supporting us at the Lemma level!

[pbsinfiniteseries]

We intended the animation to show Alice using asymmetric (i.e. public key) encryption to encrypt the symmetric key and send it to Bob. To do that, Alice should have encrypted the key with *Bob's* public key so that only Bob could decrypt it (with his private key). What this animation instead shows (accidentally, b/c we inserted the wrong animation and didn't catch it before uploading) is Alice *digitally signing* the symmetric key with her own *private* key, i.e. *authenticating* that it came from her, since *anyone* in the outside world (not just Bob) could decrypt it now using Alice's (and only Alice's) public key.

Sorry about this! I'm really pissed at myself for not catching it before we uploaded. I'll do a better job of that in the future. Thanks for having eagle eyes and catching our mistakes. It's hugely helpful.

[naftilos]

Crystal-clear English, no silly jokes, precise descriptions and for god's name no camera trying to focus on a whiteboard. Excellent work.

[ryanmcnamara]

This series was amazing, I'm so sad it's no longer being produced.

[brianhorne]

I encrypt my messages by exchanging corn muffin mix and mayonnaise keys: Jiffy-Hellman's.

[deepjoshi]

Computerphile also made video for it. This is what we want. More options for the same contents.
Both are good.

[shubhamshinde]

Gabe teaching diffie hellman!! Now, thats gotta be good...

[lovaaaa]

Only a physicist could make a video on a math channel and feel like he has to excuse himself for talking about math

[AceHack]

Also would be great if you guys could go over Quaternions, Octonions, Sedenions, i.e. Cayley-Dickson constructions and how they relate to Clifford Algebras, Lie Groups, and Lie Algebra including good books to read up more on the subject. Thanks, love the show.

[ihatethesensors]

I like the speed! Thanks man great video. To anyone saying he was going too fast, that's what the pause button is for.

[skebess]

Almost tuned out at the beginning, but then he started talking about gt and nt, then I was like: ah! Here's something I can work with. Then I stayed.
These videos are much better when you understand what's going... Nice episode.

[BeCurieUs]

Ya, I wish creators didn't shy away from getting "scooped" by other youtubers. Like you said, it is always nice to hear it twice cause a lot of times you just hear different things from different presenters, even if the material is nearly identical!

[Kabitu]

Gemoetric one-way functions.. oh goodness, you're gonna cover that elliptic curve nonsense I've never understood jack shit of, aren't you? Can't wait.

[mattiarosso]

Amazing video as usual! Keep on going on cryptography! Gabe and Tai-Danae are amazing hosts: definitely on par with the great Kelsey!!!

[Rattiar]

As a more-computery guy, I really liked watching Computerphile's take on DH and then you guys'. They gave me the concepts and then you nailed down the nitty gritty. I thought the two shows were perfect complements. While I know you didn't actually plan it that way, I'm going to pretend you did and applaud your amazing accidental colab. ;)

[ludvercz]

Look mommy! I'm famous!
I also totally agree. One of the many wonderful things about YT is that you guys aren't forced to compete for a time-slot like in old media, we can just have it all. It was still a funny coincidence though.
Great video, as usual. Keep it up!

[ThomasJedi]

i barely comment on YT but this needs to be said: this is the only channel where i enjoy the speed a lot. however it could be a bit faster.

[DanielFoland]

13:18 A bigger plot twist at the end than Usual Suspects. Good show.

[ChurchOfThought]

Great video. I don't think you talk too fast at all. You are my favorite host of all Gabe!

[ReaperUnreal]

I remember proving the exponentiation in cyclic groups thing in my abstract algebra class in university. Thanks for making me remember that.

[nagoshi]

Can't wait for the next episode, what a cliffhanger