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.
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.
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.
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.
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!
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).
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
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.
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
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!
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.
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? th-cam.com/video/1w4Y_sCDeCE/w-d-xo.html
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.
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.
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.
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.
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.
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.
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!
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*
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
The color analogy is amazing. Great work simplifying a difficult and important concept.
Yes! This is the first time I have understood this concept due to the color analogy.
Analogies are so powerful
I really enjoyed this. Thanks for breaking it down.
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.
The concept is simple and genius.
by far the best explanation of public key encryption EVER.
thanks for watching! stick around
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.
made another vid: th-cam.com/video/OFS90-FX6pg/w-d-xo.html
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.
an underestimatted comment
This is why you typically use a digital signing algorithm like DSA to authenticate the messages from each party.
if only (epic RSA foreshadowing)
This is called the man-in-the-middle attack.
Key signing parties!
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.
This is precisely how mathematical concepts should always be explained. You guys nailed it!
would love your feedback again th-cam.com/video/OFS90-FX6pg/w-d-xo.html
I nominate this video for OSCAR !!
Yeah Oscar would definitely like this video
Computerphille uses the same technique.
"While Eve is stuck grinding away at the Discrete Logarithm Problem"
Hahaha that's definitely the best part right there.
this is the best explanation I've seen on anything.
One the best and simplistic explanation of what appears to be a complex algorithmic process. Thank you.
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!
Most amazing and simple and clean explanation of Diffie-Hellman algorithm I've came across. Great!!!
Brilliant trick behind Diffie Hellman explanation is very clear.
Thanks a Lot.
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).
Even I was stuck here
Yo yall are smart AF
Thank you for taking the time to record and produce this video! Beautiful explanation.
Single best explanation on any cryptography concept I've seen.
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.
great to know people still find this
Colors made it wonderful to comprehend... really impressing!
Akash Verma now. I think that I understand how my Gizmo (for online banking) from HSBC works........
I actually needed the numbers to kinda grasp the concept...
This is an excellent explanation of what is usually a difficult issue to understand. Thank you!
Best explanation you can find on the internet about this. The color analogy is Godlike
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
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.
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
+Malmizaur Episode 3 is up next: th-cam.com/video/4qN9OvvEPr8/w-d-xo.html
you are a magician !
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.
Videos like this are always remind me why I am fascinated about the cybersecurity field! This is a fantastic video!
Oml dude this is exactly what I have been looking for! A visual explanation on how it works ! 10/10
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!
dafuq YEARS? i grasped it in about 15 minutes lol
Perhaps the best explanation of private key exchange on the internet. Thanks very much for this video!
LOL ... I came for Diffe Hellman lesson. Got a lesson in Cold war politik.
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!
fantastic video, explained something I've wondered for a long time, Thank you.
Amazing explanation! The best video about DH Algorithm. Thank you, it really helped me a lot.
This was dramatically more helpful than the meager amount of info my book offered on the subject; thank you.
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.
Thank you sooo much for putting time and work into this video.
you've helped a lot of people around the world
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??!!
That's called magic math. Great video. Very helpful. Now to watch the series.
Great video explanation. I loved the demonstration of colors & Mod Calculus Clock rope.
This is such a good explanation, it makes so much sense logically to me now.
that colour analogy was mind blowing. made my day!
Very well explained. I would recommend this video to anyone studying the arts of encryption/decryption.
Amazing and excellent explanation. Better than my lecturer!
Oh my god, your content would fit SO WELL into a podcast format! It's something we need!
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? th-cam.com/video/1w4Y_sCDeCE/w-d-xo.html
@@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 :)
Much better than the short version which confused the hell outta me @4:35!
Thank you very much for posting this!
I found your video while studying for a technical certification. Very well done. Thank you :D
I learned more from this video than 5 weeks worth of lecturing in my university class.
EXCELLENT EXPLANATION. Thank You!
if this was 2 hours, i'd still watch it. awesome explanation
Thank you for making this video, great explanation and brief history of the concept! Keep on, keeping on!
Your videos are great. They have interesting visuals as well as an easy voice to listen to.
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.
this kind of learning material is actually i m looking for. Great explanation
.
very smart.. my teacher also explained it in a wonderful way so it stuck in our minds .. bless him
This is ingenious. Thanks for sharing your knowledge and creativity and helping people to understand so easily.
appreciate the feedback and comment, stay tuned!
The articulation is excellent! Great read
Best explanation I have ever seen. Well done!
Deep concept but simply explained. Excellent!
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.
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.
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.
This is really a great set of videos. Thanks and great work.
why can't i like this video more than once? thank you for an excellent explanation
The best explanation on TH-cam .. thank you very very much ❤️❤️
Still one of the absolute best videos for explaining asymmetric key pair encryption
she's an oldie !
This video is so awesome! Had been looking for the answer to this problem.
Amazing!!!! This is the best explanation that i've ever seen.
Great video! It helped me an insane amount understanding the public key cryptography consept.
"without letting Eve, who's always listening.."
brilliant video, amazing explanation
thank you!
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.
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.
It was just awesome, u played wid the colors and dat made the algo go so simple to understand !!!
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!
appreciate the feedback. I always watch every video on a topic before making a new one, so i'm glad you noticed :)
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*
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
Not clear how A^b = B^a
Paste this into console: Math.pow(Math.pow(3,15)%17, 13)%17
Result should be 10
I don’t know what your background is just amazing explanation of concepts
I did a degree in CS and Engineering however I've always enjoyed explaining things. thanks for the feedback
That's a wonderful example!!! Mind blowing 😍😍😍
Very nice i was thought about the color logic in my college but i wondered how it would work in numbers.Excellent video.
I love it! (this is the first thing I publicly love on the internet) :-)
wassollderscheiss33 That's so awesome. Thanks for the love
I just love this, everything is so much easier!
LOL I've been explaining this idea using colors for about 6 months, then I find your video! love it!
Outstanding explanation.
Seriously mind blowing...
This is the best explanation by far.
definitely an awesome video show you how to understand Diffie-hellman key exchange
Thank you so much. Really helped me understand the concept. And I thought I was just going to have to fail my certification exam.
Now i understand clearly about diffe Hellman method. Lovely and lively demo video. Thanks for making this wonderful video.
thanks please share and stick around for more content.
@@ArtOfTheProblem yes.thanks for your valuable reply.
AWESOME!!!! Please keep on teaching... You did a great job!!!
Algorithm explanation was really simple and effective
Lovely videos. .... awesome way of descriptions. .... awesome job.... very well done guys
Amazing you fully explained this using paint!
such a beautiful explanation
simply great video ......
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
that means a lot
This is so beautiful theory. Really amazing!! Thank you for showing:)
Very well explained. Thanks a tone for your effort.
Just......beautifully and succinctly explained!
thanks for the feedback, stay tuned for more
Really good explainded. Helped me a lot, thank you for making this!
Just a amazing explanation
fantastic explanation. loved it
Outstanding explanation
Really great explanation with the color paints!
Awesome! Thank you! Great job guys