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!
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!
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
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.
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.
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? ruclips.net/video/1w4Y_sCDeCE/видео.html
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.
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).
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.
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.
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.
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.
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! :)
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
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
This is sad to see the subscribers are only 71.3K. I have seen RUclips 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.
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.
Because Eve is in the middle. Alice wants to talk to Bob, however she talks to Eve about how she wants to talk to Bob, first. So Alice negotiates (performs Diffie Hellman) to Bob *through* Eve. Eve just switches out Alice's color with her own, and vice versa. Basically, Alice/Eve have a secure channel, and Eve/Bob have one too. But not Alice/Bob! This lets Eve talk as both Alice and Bob. She can read their messages *and* pass them along so Bob/Alice have no idea they have been compromised.
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: ruclips.net/video/OFS90-FX6pg/видео.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!
This is precisely how mathematical concepts should always be explained. You guys nailed it!
would love your feedback again ruclips.net/video/OFS90-FX6pg/видео.html
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 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
I nominate this video for OSCAR !!
Yeah Oscar would definitely like this video
Computerphille uses the same technique.
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!
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??!!
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
"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.
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
One the best and simplistic explanation of what appears to be a complex algorithmic process. Thank you.
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.
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...
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.
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? ruclips.net/video/1w4Y_sCDeCE/видео.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 :)
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.
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
Best explanation you can find on the internet about this. The color analogy is Godlike
"without letting Eve, who's always listening.."
brilliant video, amazing explanation
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.
Brilliant trick behind Diffie Hellman explanation is very clear.
Thanks a Lot.
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.
Perhaps the best explanation of private key exchange on the internet. Thanks very much for this video!
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.
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 called magic math. Great video. Very helpful. Now to watch the series.
Single best explanation on any cryptography concept I've seen.
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
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!
Still one of the absolute best videos for explaining asymmetric key pair encryption
she's an oldie !
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.
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 learned more from this video than 5 weeks worth of lecturing in my university class.
Most amazing and simple and clean explanation of Diffie-Hellman algorithm I've came across. Great!!!
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.
Videos like this are always remind me why I am fascinated about the cybersecurity field! This is a fantastic video!
I found your video while studying for a technical certification. Very well done. Thank you :D
if this was 2 hours, i'd still watch it. awesome explanation
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.
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! :)
Amazing and excellent explanation. Better than my lecturer!
This is an excellent explanation of what is usually a difficult issue to understand. Thank you!
Oml dude this is exactly what I have been looking for! A visual explanation on how it works ! 10/10
that colour analogy was mind blowing. made my day!
Man you should get a teaching award for this explanation and video! Please become a teacher and make our children happy! :-)
thank you, I have been thinking about this
This was dramatically more helpful than the meager amount of info my book offered on the subject; thank you.
LOL ... I came for Diffe Hellman lesson. Got a lesson in Cold war politik.
Finally a good explanation!
You are a legend!
glad you found this years later!
@@ArtOfTheProblem hahaha! I started life 3 weeks late, so it's definitely a trend for me =)
Your videos are great. They have interesting visuals as well as an easy voice to listen to.
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: ruclips.net/video/4qN9OvvEPr8/видео.html
you are a magician !
I love it! (this is the first thing I publicly love on the internet) :-)
wassollderscheiss33 That's so awesome. Thanks for the love
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 :)
why can't i like this video more than once? thank you for an excellent explanation
Great video explanation. I loved the demonstration of colors & Mod Calculus Clock rope.
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
This is sad to see the subscribers are only 71.3K. I have seen RUclips 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.
thank you kindly....
Thank you for taking the time to record and produce this video! Beautiful 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
Thanks! Now it's clear, much better than the previous "short" version. The end there was quite unclear.
Algorithm explanation was really simple and effective
This is such a good explanation, it makes so much sense logically to me now.
It was just awesome, u played wid the colors and dat made the algo go so simple to understand !!!
Great video and explanations. Wild coincidence at 1:35, he draws a pentagram.
Very well explained. I would recommend this video to anyone studying the arts of encryption/decryption.
Linked to my cryptography teacher, this is how he should explain this to the class.
fantastic video, explained something I've wondered for a long time, Thank you.
The best explanation on RUclips .. thank you very very much ❤️❤️
This video is so awesome! Had been looking for the answer to this problem.
Watched it twice - I got it the second time, but I'm still amazed by the fact that it works... what an amazing "hack"!
This video explanation is terrific! Best one I've seen!
cool to see old videos get found
definitely an awesome video show you how to understand Diffie-hellman key exchange
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.
this kind of learning material is actually i m looking for. Great explanation
.
Amazing explanation! The best video about DH Algorithm. Thank you, it really helped me a lot.
Deep concept but simply explained. Excellent!
Cryptography 101, the best intro ever!
Wow respect! I have rarely seen anyone explain anything that well before..
thanks for the feedback
Very nice i was thought about the color logic in my college but i wondered how it would work in numbers.Excellent video.
Best explanation I have ever seen. Well done!
First video to really explain it
This video is really amazing!!!!!!!! THE COLORS: incredible!!!!!
That's a wonderful example!!! Mind blowing 😍😍😍
Thank you sooo much for putting time and work into this video.
you've helped a lot of people around the world
Great video! It helped me an insane amount understanding the public key cryptography consept.
Lovely videos. .... awesome way of descriptions. .... awesome job.... very well done guys
AWESOME!!!! Please keep on teaching... You did a great job!!!
EXCELLENT EXPLANATION. Thank You!
Amazing!!!! This is the best explanation that i've ever seen.
This going to help me pass my networking exam, thanks!
The Best Explanation of Diffe Hellman, Thank you Good Sir! Subscribed
welcome to the family!
Thank you for making this video, great explanation and brief history of the concept! Keep on, keeping on!
Just......beautifully and succinctly explained!
thanks for the feedback, stay tuned for more
Excellent explanation of a hard thing to understand. Thank you! (Cool background music too!)
This is the best explanation by far.
Because Eve is in the middle. Alice wants to talk to Bob, however she talks to Eve about how she wants to talk to Bob, first. So Alice negotiates (performs Diffie Hellman) to Bob *through* Eve. Eve just switches out Alice's color with her own, and vice versa. Basically, Alice/Eve have a secure channel, and Eve/Bob have one too. But not Alice/Bob! This lets Eve talk as both Alice and Bob. She can read their messages *and* pass them along so Bob/Alice have no idea they have been compromised.