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Diffie-hellman key exchange | Journey into cryptography | Computer Science | Khan Academy
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- Опубликовано: 27 апр 2014
- Walkthrough of Diffie-Hellman Key Exchange
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Thanks. Perfectly explained in 2mins.
wrr
yeah, cus they just cut out a part of someone else's video
@@johnprice4847 whose video
the music in the background is very ominous, sounds like I'm exploring a cave in Minecraft.
Best video on Diffie Hellman, quick, to the point.
WOW! So clear in such little time. Thank you a lot!
Khan Academy is the one. Teaches this better than anybody
Thank you.
my question is if Eve intercept this connection as man-in-the-middle, and he build a connection with bob and alice separately, so it means he generate his own keys and numbers and share it.
will this work?
The way you explained is excellent.
Thanks a lot.
wrg
damn that was too easy this way. I've been studying this for the past 20-30 minutes without any clue.
Great video! Noticed a couple of mistakes though. In 1:18 it falsely shows 3^(13^15) mod 17. It should be (3^13)^15 mod 17 = 3^(13*15) mod 17 = 3^(15*13) mod 17 = (3^15)^13 mod 17.
I wasted 45 minutes on this. Honestly, this error makes it NOT a great video. A key element has crippling error for someone learning this for the first time.
What happens to the second [mod 17]? I see that 12 is replaced by (3^13), for example, but do we just throw away the [mod 17] that was used in the calculation of that 12??
Well. I think (3^13)^15 = 3^(13*15).
For example
(2^2)^3 = 4^3 = 64
2^(2*3) = 2^6 = 64
Another Example
(3^3)^4 = 27^4 = 3^12
3^(3*4) = 3^12
I think there is no error...?
wrr
@@baatar its called the modular exponentiation property sorry for 4 year late reply
That background music creeps me out...
wuhan?
Really? I actually like it. Reminds me of the Minecraft OST, personally.
Loved the explanation!
But what's the name of the music in the background?
This is a Copy content from "Art of the Problem" channel you can check it out by yourself. And the credit also not given in description
they really did tho
@@DaBoi808D where?
this is the most understandable explanation of an asymmetric cryptography.
what a good and simple explanation, thanks
Guys is it just me or anyone else noticed in the beginning of the video that he stated that both Alice and Bob agreed publicly agreed on the " 3 mod 17"... and he did not include THIS information on the diagram, only the number 6 and number 12....
Is this a flaw on the Diffie-hellman security???
They never share the private keys
And they are needed to get the final result
So no
no, as everyone can know the public key. In fact, it would be good for them to have everyone know their public keys, because the only way to actually interfere as a MIDM at the DHE would be to listen the conversation from t=0. Because then the MIDM could give fake key information to the two parties each. By having the Public key literally public, they can ask for a third party, that a safe connection can be established to by both parties, to sign the public key and therefore prevent MIDM / detect an Intruder that interferes even from t=0 on.
great whole concept in 2 minutes
I have been reading about this for hours, and you just made it make perfect sense in 2 minutes... fml
Would be nice to talk about finite fields, and Galois field.
Thanks for this clear explanation
Really good explained!!! Thanks!
thanks
Dude we had a whole lecture on this the professor tried explaining with colors and what not and u blew it out the water in 2 minutes
The best and most laconic explanation!
wrr, no such thign as more or few or loconx, doesn mtatter
So do the secret keys not need to be prime? In this example Alice's secret key is 15 = 3*5
Right now i understand this, thanks
I'm having a hard time understanding part of this, but then again I am not very familiar with the ideas themselves. If A and B publicly agree to the formula, then wouldn't their private number, and thus the ciphertext itself, be vulnerable since the attacker knows both the equation and the result of the variable that is the private number?
If I am correct on this point then does the security come from the fact that very big numbers are used? I just looked up that part and it seems that these problems are harder to work backwards than they are forwards.
With that said however, my next question regards the vulnerability of the device doing the actual calculations. There must be special software to manage the calculations and do the other things necessary since it cannot be done by hand, and therefore the actual encryption may not be vulnerable but the software itself could be right? And software vulnerabilities seem much easier than trying to break encryption in general. And does this hold true for public-key cryptography in general?
The last thing I wanted to touch upon is the fact that it seems dangerous to base the cipher on the difficulty in working an equation backwards on the computer's part, because computing power is increasing at a relatively steady rate. If quantum computers ever reach the point of being more like the personal computers of today, it is hard to imagine that, eventually, such algorithms will remain secure. I suppose that there could be multiple possible solutions in some cases, but this should not be a problem for figuring out the plaintext. If that day ever comes, are there other practical ways that provide message security? I know that the one-time pad system is quite inefficient and harder to implement in a digital manner, while by hand it is relatively easy, and thus it is hard to imagine this system ever gaining popularity despite its perfect encryption with proper use.
Then there is the fact that if there needs to be a secure channel to exchange a secret key or password, then why not just transfer the message via that secure channel?
1. Yes the secret is that very large numbers are used. Any form of security in computer science is breakable and brute forceable, but the amount of time it would take even on a supercomputer is so much longer than how long humans can live.
2. The software cannot have a mistake in it. If the software did, then there will be instances where the shared secret would be different and thus the process fails. Securing software is a whole other problem in computer science.
3. Again, back to the first point, it takes millions or hundreds of millions of years to brute force it. We won't be alive for that long even if computing power increases exponentially. If it does, we just make the number even larger, as we can work with bigger numbers to make the keys safer.
Great explanation, thanks!
Amazing video!!
I agree for sure!
What's keeping an intercepting hacker to get the public key and simply act as a negotiating peer?
theonlyrobg
Nothing.. Downgrading to a 512bit Crypto .. Does the job.
Precise and perfectly made
x^2^3 != x^3^2 , you made a mistake there its not 3 raised to the 13 raised to the 15 its 3 raised to 13*15, of which multiplication is commutative thus equivalent to 3 raised to the 15*13
True that!
Iove the dramatic music
Please assist to give key length & block size of following Asymmetric Encryption Algorithms: RSA - ECC- ELGANAL - DSA -Diffie-Hellman. Thank you
Fantastic video
Excellent!
so easy to understand! thank you!
Where is this method used nowadays?
ok but what if i can only relay my messages through eve and there's no way for me to verify that who im talking to is actually bob (assuming im alice)
then what? because that's basically me sending msgs through my isp and the isp doing a dh key exchange with me as well as bob so now my isp and the gov can easily eavesdrop on my msgs
awesome good job
Would you know how to implement this into Python code?
excellent calculations. wow 👌
is 1 considered a primitive root of 2?
what if Eve interrupted Bobs value and sent her own ??
Then Eve can read whatever she want, but that's actually not a problem of this algorithm. DH is used for encryption, you kinda have to trust who is on the other side. For that, there are signing algorithms (like RSA), that are used to determine whether the person on the other side is the one who he's pretending to be or not.
Basically:
DH - you can be sure, that the communication can be read only by the person on the other side, but you don't know anything about the actual other side
RSA - if you use it in combination with DH, you can be sure about who is on the other side, and that no one except you two can read the communication.
We'll explained
Thanks
Beautiful
I had to study what mod is to understand this video.
Yeah until the Discrete log problem is solved!
goated
can i know what software is this?
can someone please explain what mod 17 is?
modulus is a remainder like if you want '50 mod 12' answer will be 2 ..and there is nothing like 'mod 17' but if you consider it is same as like ' 1 mod 17' which is 1
it's explained in the full video they took this from, which they didn't mention in the description: ruclips.net/video/3QnD2c4Xovk/видео.html&ab_channel=ArtoftheProblem
engineering yaako madtaidiya loude
Wow
what must be going on in the person's mind who made the algo while making this lol
At 1:53; Eve can only get 3 as 12^6 mod 17 or get 13 as 6^12 mod 17. We know that 13 - 3 = 10, and 10 is the shared secret. Is this just a coincidence?
Yes this is just coincidence. Also remember that in real life, this example could be decrypted very easily. We would be using much larger numbers. Currently, the standard key size for Diffie-Hellman key exchange is 2048 bits which gives a maximum key size of something like 3.23 x 10^616, which is a number that is 617 digits long!
I still not get the 3 pow mod 17 how comes? sos
The mod is a math technique to get a value. You can determine easily the final number.. But it is impossible to get the originating numbers because it could be tons of combinations. They agree to send a generator and a prime mod. In this case 3 and 17. It could be any pair of numbers.
can someone explain why the initial modulus and the generator are prime?
+exxodas I'm guessing it's to guarantee that secret does not end up to be zero, but I'm not sure :/
+exxodas The shortened version: In order to make sure that a hacker cannot break this key, the numbers have to be extremely large. Extremely large numbers will take a computer a very long time to calculate. But there are certain mathematical principles that you can apply to reduce the computation time for the modulus. This is a very quick explanation. Look up Little Fermat's Theorem, Euler's Theorem, and Square Modulo Rule, and theres one more theorem that is important, but I cant seem to remember the name.
The generator is not prime, it's a primitive root of the modulus. Making the modulus prime ensures that this generator produces a uniformal distribution of all the numbers from 0 to "modulus-1" (as said in the video, it's from 0 to 16 for a modulus 17).
Not quite true, you are mixing RSA (prime factorization) with discrete logarithm problem.
This has to do with some mathematical stuff he didn't explain in the video. +exxodas Go read about finite fields, specifically, Galois Field .
to anyone else wondering, it's explained in the full video they got this from (which they forgot to mention): ruclips.net/video/3QnD2c4Xovk/видео.html&ab_channel=ArtoftheProblem
For sure you are a student of Dr.Chuck, aren't you?
L
I think in this case it would have been alot clearer if you explained everything in terms of variables instead of using an example
'Art of the problem' v=3QnD2c4Xovk He is, as far as I know the owner of this material. You have hereby been reported to 'Art of the problem.'
aaaa what?!
With all four public number and some algebra the password can be uncovered 😈
ruclips.net/video/jLeNX2jYuUs/видео.html
The words spoken in this video do not match the animation.
Here is one way for eve to hack it, he can pretend to be Bob and send Alice a message sighed by her secret number, in this example, alice does not have a way to identify the coming message is signed by Bob or Even, if she was tricked it was Bob and signed with her secrete number and send to public, eve can then use her secrete number to crack the information, while bob can not.
No, there are many ways that Alice would be able to verify the source of the information.
短小精干，牛逼！୧(๑•̀◡•́๑)૭
what in the Western sorcery is this.
This video is misleading. Eve can find the solution by pursuing the prime and the primitive root. Disliked. Obfuscating the attack.
Good luck doing that
hi , can i contact you pls ?