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

[@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

[@FosterPinnock]

Hey, could you possibly help me with this issue? USDT TRX20 is in my OKX wallet and I know the recovery phrase [ clean party soccer advance audit clean evil finish tonight involve whip action ] How do I transfer it to Binance?

[@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

[@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.

[@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!

[@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

[@AjayPoriya]

I nominate this video for OSCAR !!

[@barbell13]

Yeah Oscar would definitely like this video

[@alice_in_wonderland42]

Computerphille uses the same technique.

[@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!

[@davidcalderon6062]

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

[@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??!!

[@SomeOne-tb2sd]

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

[@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

[@199NickYT]

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

[@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.

[@AgglomeratiProduzioni]

For a few months, my teacher didn't manage to explain this to a class. In 8 minutes, this video can explain it to every dummy. If it's simple, keep it simple.

[@tonyc3668]

Finally a good explanation! You are a legend!

[@ArtOfTheProblem]

glad you found this years later!

[@tonyc3668]

@@ArtOfTheProblem hahaha! I started life 3 weeks late, so it's definitely a trend for me =)

[@mort8568]

I'm not even a math guy or even like numbers that much but every once in a while I come back to this video purely because of how entertaining it is

[@ArtOfTheProblem]

that means 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 :)

[@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.

[@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

[@mmuarc]

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

[@5mwa]

Good explanation, better than those explanations given by the professors in lectures... My tutors can explain this to me for 1 day and I still don't get it. Now I find this concept extremely simple.

[@AkashVermaNITian]

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

[@MEANASSJAMSTER]

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...

[@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.

[@kanaverum]

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

[@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.

[@fireflies15]

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

[@appapurapu]

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

[@mipmap24]

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

[@xetronchan1059]

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

[@skidude9800]

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

[@jon_hodl]

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

[@ArtOfTheProblem]

she's an oldie !

[@garykubiak]

This video explanation is terrific! Best one I've seen!

[@ArtOfTheProblem]

cool to see old videos get found

[@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.

[@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!

[@roxiogamer]

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

[@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.

[@mfratto]

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

[@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 :)

[@ROCDUC]

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

[@exdunn]

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

[@KILO993]

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

[@duallancers001]

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

[@SanjayShelat]

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

[@valor36az]

I don’t know what your background is just amazing explanation of concepts

[@ArtOfTheProblem]

I did a degree in CS and Engineering however I've always enjoyed explaining things. thanks for the feedback

[@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.

[@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

[@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!

[@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 !

[@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.

[@CarlitoProductions]

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

[@abeer_nawaf_sul]

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

[@KautilyaSave]

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

[@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

[@ForcefighterX2]

Man you should get a teaching award for this explanation and video! Please become a teacher and make our children happy! :-)

[@ArtOfTheProblem]

thank you, I have been thinking about this

[@ninumedia]

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

[@thomaspribitzer5373]

that colour analogy was mind blowing. made my day!

[@MohammadNadeem1]

This is sad to see the subscribers are only 71.3K. I have seen KZbin Channels with Billions of Subscribers and what they are doing is just insulting others in the name of comedy. The way this guy has explained the topic is amazing. I am subscribing to this channel because he won by subscription.

[@ArtOfTheProblem]

thank you kindly....

[@fubonte]

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

[@MohamedAnsari_H]

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

[@willydafunkykid]

Wow respect! I have rarely seen anyone explain anything that well before..

[@ArtOfTheProblem]

thanks for the feedback

[@IAmSinister5]

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

[@mortenbrodersen8664]

Best explanation I have ever seen. Well done!

[@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

[@rschintalapati]

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

[@adityamenon]

Watched it twice - I got it the second time, but I'm still amazed by the fact that it works... what an amazing "hack"!

[@milo10001]

That's why modulus is used. When you add two values, like secret + x = y, it's easy to substract and calculate secret = y - x. But when you use mod infinite number of "secret" values produce the same result "y", so you cannot reverse using substraction.

[@Yashuu96]

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

[@felixmintah8632]

Very good example. Thanks for making me smart this last 8:37 minutes.

[@mustafarangwala5657]

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

[@blackcheetah4550]

The best explanation on KZbin .. thank you very very much ❤️❤️

[@hdlopesrocha]

Cryptography 101, the best intro ever!

[@jacquesvanderwesthuizen7287]

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

[@silastube_]

If you can't explain it simply, you don't understand it well enough - Albert Einstein. You guys are the very definition of the above quote. Subscribed! :)

[@jaketarren]

Linked to my cryptography teacher, this is how he should explain this to the class.

[@AXDOOMER]

What's the name of the music at 3:55 ?

[@carlossiverio3570]

This is the best explanation by far.

[@ketansanil6046]

Algorithm explanation was really simple and effective

[@godfreytan1001]

Deep concept but simply explained. Excellent!

[@ashutoshnautiyal9625]

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

[@atom2ueki]

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

[@h.kkhandelwal9142]

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

[@aymanjabali]

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

[@SomdeepSengupta]

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

[@danyellbaptiste1055]

EXCELLENT EXPLANATION. Thank You!

[@houyao2147]

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

[@tasoskontos10]

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

[@jackdrost7291]

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

[@thor0707]

Great video and explanations. Wild coincidence at 1:35, he draws a pentagram.

[@SibteAli-p1d]

Solves the non-quantum problem. Advancements in quantum computation tech has got the exact implementation in this video (using discrete log problem) on its toes. Diffie-Hellman continues to be just an idea like it always has been - you can implement it in lots of different ways. I was looking at an interesting one which explored the idea of a point in three dimensional space which is reachable by some linear combination of two unique vectors... anyone know what I am remembering? Something like lattice-based cryptography?

[@TheLexusAlexey]

I just love this, everything is so much easier!

[@Derbauer]

Just......beautifully and succinctly explained!

[@ArtOfTheProblem]

thanks for the feedback, stay tuned for more

[@notallthatbad]

Great explanation and visual demonstration of a seemingly complex topic. The only part I may be a bit fuzzy on is when the users add their private colors to the "mixture". Wouldn't they come up with different colors? I'd think the resulting colors would have to match on both sides in order for decryption to take place. I guess my basic question is - does the "shared secret color" have to be the same exact color for decryption to happen, or is there more to it? Maybe I'm thinking too much on the concept within the bounds of colors rather than numbers, or there are more sophisticated mathematics at work here - but I love the visual explanation. Thank you!

[@seppet0ni]

+tubez4321 They would come up with the same color, because on both sides they are adding their own color to a mixture of the base color and the other's private color. Basically, with public color P, secret color left L and secret color right R: Start: P, L P, R Sending mixtures: P+L -> < - P+R After sending: P + R, L P + L, R Mixing: P + R + L P + L + R ==

[@AlexU2be]

Thanks! Now it's clear, much better than the previous "short" version. The end there was quite unclear.

[@federicocreti4699]

This video is really amazing!!!!!!!! THE COLORS: incredible!!!!!

[@piriyaie]

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

[@19RedX91]

The Best Explanation of Diffe Hellman, Thank you Good Sir! Subscribed

[@ArtOfTheProblem]

welcome to the family!