Public key cryptography - Diffie-Hellman Key Exchange (full version)

The history behind public key cryptography & the Diffie-Hellman key exchange algorithm.
We also have a video on RSA here: • Public Key Cryptograph...

[@dancarlson3045]

The color analogy is amazing. Great work simplifying a difficult and important concept.

[@human.earthling]

Yes! This is the first time I have understood this concept due to the color analogy.

[@1986xuan]

Analogies are so powerful

[@jacquelinecahill4836]

I really enjoyed this. Thanks for breaking it down.

[@Percavius]

It's good in that it's simple, however unlike the discreet logarithm problem, you would be able to make a good estimate of the secret colour based on the starting colour and one of the mixed colours. For example if Eve received the starting colour yellow, and a mixed colour green, she can infer that the secret colour mixed in must be some shade of blue, which makes her search much easier. Recognizing this threw me off a bit at first.

[@jsonkody]

The concept is simple and genius.

[@ChristopherCricketWallace]

by far the best explanation of public key encryption EVER.

[@ArtOfTheProblem]

thanks for watching! stick around

[@lennonmclean]

unfortunately, public key is completely different than key exchange. public key requires different keys to encrypt and decrypt, so there's no need for diffie hellman to agree on a secret key.

[@ArtOfTheProblem]

made another vid: kzbin.info/www/bejne/hXe2amNje71ppsk

[@wilkmasterflex]

A great illustration. Diffie-Hellman has a well-known, fun vulnerability. Spoilers: Eve, knowledgeable herself on color theory, intercepts messages between Alice and Bob not letting their messages go directly to them. Instead she creates a color of her own. Mixing it twice with each of Alice and Bob's colors she creates two keys. She can now read Bob's message, re-encrypt, and send to Alice and pose as Bob. Same goes in the other direction. If only Alice could trust Bob's color comes from him.

[@Germanywithtripti101]

an underestimatted comment

[@Arkalius80]

This is why you typically use a digital signing algorithm like DSA to authenticate the messages from each party.

[@lennonmclean]

if only (epic RSA foreshadowing)

[@alittax]

This is called the man-in-the-middle attack.

[@AnimMouse]

Key signing parties!

[@satnamo]

Martin Hellman said: The system...has since become known as Diffie-Hellman key exchange. While that system was first described in a paper by Diffie and me, it is a public key distribution system, a concept developed by Merkle, and hence should be called 'Diffie-Hellman-Merkle key exchange' if names are to be associated with it. I hope this small pulpit might help in that endeavor to recognize Merkle's equal contribution to the invention of public key cryptography.

[@albertoradice7713]

This is precisely how mathematical concepts should always be explained. You guys nailed it!

[@ArtOfTheProblem]

would love your feedback again kzbin.info/www/bejne/hXe2amNje71ppsk

[@AjayPoriya]

I nominate this video for OSCAR !!

[@barbell13]

Yeah Oscar would definitely like this video

[@alice_in_wonderland42]

Computerphille uses the same technique.

[@199NickYT]

"While Eve is stuck grinding away at the Discrete Logarithm Problem" Hahaha that's definitely the best part right there.

[@Nefariouspat]

I've watched a few videos on public key cryptography, but never really understood how it worked until I heard this colour analogy. Absolutely phenomenal video!

[@SomeOne-tb2sd]

One the best and simplistic explanation of what appears to be a complex algorithmic process. Thank you.

[@xetronchan1059]

Most amazing and simple and clean explanation of Diffie-Hellman algorithm I've came across. Great!!!

[@dm8144]

I am typing typing this message in 29/10/2020 and this is one of the best and easiest explanation about public and private key system ever. well done.

[@ArtOfTheProblem]

great to know people still find this

[@appapurapu]

Brilliant trick behind Diffie Hellman explanation is very clear. Thanks a Lot.

[@SanjayShelat]

This is an excellent explanation of what is usually a difficult issue to understand. Thank you!

[@wreilly09]

THIS DID IT!! You helped me understand a few points that, in my opinion, we’re not pearly presented in other videos. Thank you very much.

[@ninumedia]

Thank you for taking the time to record and produce this video! Beautiful explanation.

[@mash0000]

Use of mixing colors as an analogy to explain the DH concept was brilliant. I know DH concept well, but never thought of the color analogy. Good job!

[@davidcalderon6062]

this is the best explanation I've seen on anything.

[@mmuarc]

Best explanation you can find on the internet about this. The color analogy is Godlike

[@skidude9800]

Single best explanation on any cryptography concept I've seen.

[@KautilyaSave]

Great video explanation. I loved the demonstration of colors & Mod Calculus Clock rope.

[@AkashVermaNITian]

Colors made it wonderful to comprehend... really impressing!

[@ANTHONYBOOTH]

Akash Verma now. I think that I understand how my Gizmo (for online banking) from HSBC works........

[@Appoxo]

I actually needed the numbers to kinda grasp the concept...

[@supernanotech1]

Time hardened Encryption just like safe hardening how much time is needed to open it. I love this, this is the best way to explain encryption ever. I love how they have IBM sage running for this video also. Amazing

[@jasoncorrigan9937]

My background in advanced math concepts is somewhat limited, and so it's always been difficult for me to intuitively grasp how DH worked. After years of struggling, this is the one video that really drove the point home for me. Thank you!

[@oliverbeck6839]

dafuq YEARS? i grasped it in about 15 minutes lol

[@roxiogamer]

Oml dude this is exactly what I have been looking for! A visual explanation on how it works ! 10/10

[@marelloeg6988]

Videos like this are always remind me why I am fascinated about the cybersecurity field! This is a fantastic video!

[@orionjonesy226]

Thank you for making this video, great explanation and brief history of the concept! Keep on, keeping on!

[@jacquesvanderwesthuizen7287]

Very well explained. I would recommend this video to anyone studying the arts of encryption/decryption.

[@duallancers001]

This was dramatically more helpful than the meager amount of info my book offered on the subject; thank you.

[@Malmizaur]

wow finaly the video i was looking for with the best explanation and number proving examples thank you very much I also checked your chanel realy awesome

[@ArtOfTheProblem]

+Malmizaur Episode 3 is up next: kzbin.info/www/bejne/aqKxaoKsq6qDqJo

[@dangerlibya2010]

you are a magician !

[@rschintalapati]

Amazing explanation! The best video about DH Algorithm. Thank you, it really helped me a lot.

[@georgiepentch]

Oh my god, your content would fit SO WELL into a podcast format! It's something we need!

[@ArtOfTheProblem]

Funny you say that, i'm working on developing a podcast right now. I was town between just using the audio from these or doing a new conversational approach. can you listen to the demo I posted last week and give feedback? kzbin.info/www/bejne/Z6iXipKpeKmYeac

[@georgiepentch]

@@ArtOfTheProblem wow sorry, I don't know why I just got this notification now, but I did listen to the demo and I loved it! Keep it up :)

[@kanaverum]

Perhaps the best explanation of private key exchange on the internet. Thanks very much for this video!

[@MohamedAnsari_H]

fantastic video, explained something I've wondered for a long time, Thank you.

[@KILO993]

I found your video while studying for a technical certification. Very well done. Thank you :D

[@blackmouthblackface]

Much better than the short version which confused the hell outta me @4:35! Thank you very much for posting this!

[@aymanjabali]

Thank you sooo much for putting time and work into this video. you've helped a lot of people around the world

[@KevinElamMusic]

Excellent video! My only complaint is the explanation of "how Alice did the same calculation as Bob" from 7:27 to about 7:40. Starting at 7:27, we see that "12 = 3^13mod17". Then conveniently, right at 7:34, when that figure is substituted into Alice's original expression, the "mod 17" DISAPPEARS and the 12 is simply replaced by "3^13". Although this IS mathematically correct, it REQUIRES a rather advanced principle of modular arithmetic: namely, that [(a*mod c)^ b]*mod c = (a^b)mod c. (In the example from the video, a = 3^13, b is 15, and c is 17). So, you effectively CAN simply remove the extra "mod c" term, but the video glosses over this difficult but crucial step. My sister and I just spent 2 hours figuring out the proof for this principle. If anyone's interested I can share a photo of the completed proof. (It can be found online also).

[@dhanushshetty7840]

Even I was stuck here

[@ukee31]

Yo yall are smart AF

[@laurv8370]

Very nice! Hat off! One of the best explanations I have seen, and nice put into the story. however, when you swap those powers, you should use parenthesis, that is because generally, powering is not commutative. That is, a^b^c is not equal to a^c^b, modular or non modular powering. Powering is right-associative. But (a^b)^c=a^b*a^b*...a^b (c times) which is a^(b*c)=a^(c*b)=a*a*a*a.... (b*c times), which is (a^c)^b always, modular or not. This is due to the commutativity of the _multiplication_ operation. Not the powers.

[@thomaspribitzer5373]

that colour analogy was mind blowing. made my day!

[@mfratto]

That's called magic math. Great video. Very helpful. Now to watch the series.

[@IAmSinister5]

This is such a good explanation, it makes so much sense logically to me now.

[@scienceblossom6197]

Can't thank you enough. Awesome video. I wish you also explained how the digital signature works in order to avoid Eve pretending to be either Bob or Alice.

[@akshaymahale6521]

It was just awesome, u played wid the colors and dat made the algo go so simple to understand !!!

[@princyep8409]

The articulation is excellent! Great read

[@danyellbaptiste1055]

EXCELLENT EXPLANATION. Thank You!

[@ashutoshnautiyal9625]

this kind of learning material is actually i m looking for. Great explanation .

[@johnmacward]

Brilliant explanation about key exchange for those of you interested in how your data is encrypted over the web. Ok, when the maths comes you need to pay attention but all in all the best explanation I've found.

[@godfreytan1001]

Deep concept but simply explained. Excellent!

[@notmychairnotmyproblem]

THIS IS THE EASIEST EXPLANATION OF MODULAR MATH I'VE EVER SEEN Why didn't I have this channel 10 years ago when I was in college??!!

[@tasoskontos10]

Great video! It helped me an insane amount understanding the public key cryptography consept.

[@CarlitoProductions]

if this was 2 hours, i'd still watch it. awesome explanation

[@LGM4]

LOL I've been explaining this idea using colors for about 6 months, then I find your video! love it!

[@fubonte2272]

why can't i like this video more than once? thank you for an excellent explanation

[@SomdeepSengupta]

LOL ... I came for Diffe Hellman lesson. Got a lesson in Cold war politik.

[@atom2ueki]

definitely an awesome video show you how to understand Diffie-hellman key exchange

[@IgorAherne]

This helped me understand it: Imagine Bob and Allice want to teleport to some secret planet without Eve joining them. 1) *Neither Alice nor Bob have a planet in mind where they would like to meet*. They want to use their own piece of puzzle to mutually arrive at the same planet. Depending on which private keys they've chosen initially the final planet will be in the very different locations of universe. 2) They publicly pick which galaxy they want to be in 3) They can pick any number they want, scramble it with the publicly known galaxy's name, and send it over to each other. 4) now each one has the scrambled piece of another person. Both pieces were scrambled with the same galaxy. 5) scrambling Allice's piece with the scrambled code received from Bob will teleport her to planet XYZ. 6) Bob will do the same thing with the scrambled code received earlier from Alice, which will teleport him to planet XYZ because Eve didn't mix-in any of her information into the exchanged (scrambled) messages and was only listening to their conversation, she is unable to align herself with the planet XYZ where those two went. Even if Eve would substitute her message instead of Bob', this would only result Alice and Eve arriving to FZK, without Bob. Alice would see that it's not Bob and no information would be disclosed.

[@Yashuu96]

This video is so awesome! Had been looking for the answer to this problem.

[@Konraden]

I'm reading wiki trying to understand how public-key encryption works (I'm told its better than symmetrical encryption). I remember someone tried to explain this before using colors, so a quick search--and I find your video. This is a great video.

[@ROCDUC]

Your videos are great. They have interesting visuals as well as an easy voice to listen to.

[@earavichandran]

Now i understand clearly about diffe Hellman method. Lovely and lively demo video. Thanks for making this wonderful video.

[@ArtOfTheProblem]

thanks please share and stick around for more content.

[@earavichandran]

@@ArtOfTheProblem yes.thanks for your valuable reply.

[@HariKrishnaReddy7696]

such a beautiful explanation

[@mustafarangwala5657]

Very nice i was thought about the color logic in my college but i wondered how it would work in numbers.Excellent video.

[@chetanrane724]

fantastic explanation. loved it

[@MahmoudHammad1]

amazing description . Thank you

[@asdunn2]

I learned more from this video than 5 weeks worth of lecturing in my university class.

[@richardgreenstone1095]

Outstanding explanation.

[@Kevi_N.]

The trick in a nutshell: ( G^*a* mod P )^*b* mod P = G^*a*^*b* mod P = ( G^*b* mod P)^*a* mod P = *key* *a* and *b* - private numbers *key* - private key (same for both) G - public generator P - public prime module ( G^*a* mod P ) = *A* ( G^*b* mod P) = *B* *A* and *B* - public numbers both sites do: *A*^*b* mod P = *B*^*a* mod P = *key*

[@yc4295]

I try to calculate in Javascript but found it not the same, is there any wrong? According to the fomula "( G^a mod P )^b mod P = G^a^b mod P", Assume G = 3, a = 13, P = 17, b = 15 Math.pow(Math.pow(3, 13) % 17, 15) % 17 = 10 Math.pow(Math.pow(3, 13), 15) % 17 = 2 Math.pow(Math.pow(3, 15) % 17, 13) % 17 = 10 But 10 is not equal to 2

[@romanmandeleil]

Not clear how A^b = B^a

[@uid26]

Paste this into console: Math.pow(Math.pow(3,15)%17, 13)%17 Result should be 10

[@FyberOptic]

Great video, you described it in a perfect way to understand. Though I'm not sure if it was clear for everyone that this was merely for calculating a mutual key to use with a cipher, and not really for actually communicating information itself.

[@greg4529]

Amazing and excellent explanation. Better than my lecturer!

[@davidr.flores2043]

Fantastic. I've watched many videos on this same topic; nevertheless, this is The Best one. A million thanks for breaking down difficult concepts in an easy, understandable way. Kudos!

[@ArtOfTheProblem]

appreciate the feedback. I always watch every video on a topic before making a new one, so i'm glad you noticed :)

[@MalaAnsoo]

This is ingenious. Thanks for sharing your knowledge and creativity and helping people to understand so easily.

[@ArtOfTheProblem]

appreciate the feedback and comment, stay tuned!

[@jon_hodl]

Still one of the absolute best videos for explaining asymmetric key pair encryption

[@ArtOfTheProblem]

she's an oldie !

[@abeer_nawaf_sul]

very smart.. my teacher also explained it in a wonderful way so it stuck in our minds .. bless him

[@houyao2147]

Amazing!!!! This is the best explanation that i've ever seen.

[@mortenbrodersen8664]

Best explanation I have ever seen. Well done!

[@crazy-blue]

I really really like the music in this video. It mysterious. I like the fact that you take your time to explain and it is also visual. Nice creative video.

[@ArtOfTheProblem]

Took 2 years to finish this one, finally live would love your feedback: kzbin.info/www/bejne/hXe2amNje71ppsk

[@sukhrobkurbonov8327]

Just a amazing explanation

[@schedarr]

Outstanding explanation

[@fireflies15]

"without letting Eve, who's always listening.." brilliant video, amazing explanation thank you!

[@nabeel250575]

This is really a great set of videos. Thanks and great work.

[@TheLexusAlexey]

I just love this, everything is so much easier!

[@andyGPT101]

Nicely done. Makes a lot of sense

[@jayendrasingh9260]

simply great video ......

[@legoman777777777]

Awesome! Thank you! Great job guys

[@gowthamiirao9010]

Very well explained. Thanks a tone for your effort.

[@thefirstfishadvancetheland8980]

This is so beautiful theory. Really amazing!! Thank you for showing:)

[@AmanShaikh-qr5lh]

That's a wonderful example!!! Mind blowing 😍😍😍

[@aiayumi]

Amazing you fully explained this using paint!

[@jackdrost7291]

Excellent explanation of a hard thing to understand. Thank you! (Cool background music too!)

[@infinitybiff]

well this was an incredible video. such a good explanation. well done!

[@piriyaie]

AWESOME!!!! Please keep on teaching... You did a great job!!!

[@SninjaThirteen]

Thank you so much. Really helped me understand the concept. And I thought I was just going to have to fail my certification exam.

[@msjaeduval]

Really great explanation with the color paints!

[@arunraj5275]

Seriously mind blowing...

[@wassollderscheiss33]

I love it! (this is the first thing I publicly love on the internet) :-)

[@ArtOfTheProblem]

wassollderscheiss33 That's so awesome. Thanks for the love

[@maheshirk]

Fantastic explanation

[@sics993]

Really good explainded. Helped me a lot, thank you for making this!

[@h.kkhandelwal9142]

Lovely videos. .... awesome way of descriptions. .... awesome job.... very well done guys

[@frank4738]

Great video, clear explanation. Thanks

[@malikwaseem1983]

Excellent explanation