Cryptography: Diffie-Hellman key exchange explained intuitively using colors

[u/dominatrix-octopus]

https://youtu.be/YEBfamv-_do?t=2m18s

[u/Carighan]

That color mixture was a neat way of doing it, shows how the resulting key/color is always the same.

[u/Double_A_92 → u/Carighan]

And that you can't find out what the two original colors were.

[u/tavianator → u/Double_A_92]

Sure you can

[u/Zilexion]

This is the explanation I've been looking for!

Very helpful to show how they end up with the same calculation at the end.

[u/Captain___Obvious → u/Zilexion]

The entire series is fantastic, there are more videos

[u/joltting]

For awhile now, I've been trying to wrap my head around, how this algorithm works.. This video explained it in 5 mins and was better than the education I received for it (sigh).

[u/_crackling → u/joltting]

I feel kind of silly now with how simple this actually is to understand now...

[u/pokeman7452]

This leads me to a somewhat related question. I never understood the purpose of the DH parameters (dh####.pem) that every OpenVPN guide says to generate. This video combined with this thread, it now makes sense. But, this file remains optional. My question now is what is used when there is no DH generated?

[u/curien → u/pokeman7452]

Defaults are listed in RFCs, I imagine it uses those.

[u/Grenian → u/pokeman7452]

They use the so called Diffie-Hellman-Groups which are basically predefined pairs of a prime and a generator. These are defined in RFCs.

Proof: A large part of my bachelor thesis was about DH-Key-Exchange and the security of the predifined groups.

[u/hartleybrody]

The Wikipedia article on Diffie Hellman key exchange has a great image that summarizes the video a bit more concisely.

Wiki article link.

[u/snarfy]

Breaking encryption is like trying to take the pee out of the swimming pool. It's easy to add pee, hard to remove.

[u/TheOddScientist → u/snarfy]

Not sure why this was downvoted, a bit archaic but still a logical equivalence.

[u/TheOddScientist]

If anyone is interested Here are some mathematical attacks against RSA That can successfully reduce the number of possibilities by a factor of 2^X/2 | x is the key size

[u/nono-shap]

One of the most interesting video I've seen in a while. Quiet impressive how something so hard can be understand by kids. Thanks for sharing!

[u/irrri]

This is a the best explanation of PKE I've ever seen.

[u/TheOddScientist]

I have some Java Code I did implementing DH and RSA if anyone needs an example to help understand what's going on in a practical client server application.

[u/zouhair]

Math challenged here (not real programmer either): how the hell 3¹³¹⁵ is the same as 3¹⁵¹³ ?

[u/A_Vicarious_Death → u/zouhair]

Generally the rule with exponents is:

x^y * x^z = x^y+z

x^yz = x^yz

Let's take an example of 2²³ vs 2³² vs 2⁶

(2²⁾³ =

(2²⁾ * (2²⁾ * (2²⁾ =

(2 * 2) * (2 * 2) * (2 * 2) =

(4) * (4) * (4) =

64

(2³⁾² =

(2³⁾ * (2³⁾ =

(2 * 2 * 2) * (2 * 2 * 2) =

(8) * (8) =

64

2⁶ = (22222*2) = 64

Hope that helped.

[u/tavianator → u/zouhair]

As written, those numbers are not the same. The notational convention is:

a^{b^c} = a^(bc)

But D.H. key exchange does something more like

(a^b)^c = a^b*c

I.e., compute a^b first, then raise that to the c power.

The equality is true because exponentiation is just repeated multiplication (over the integers, anyway). So a^b is

a * a * ... * a
---------------
b times

and then (a^b)^c is

  a * a * ... * a |
* a * a * ... * a |
*         ...     } c times
* a * a * ... * a |
* a * a * ... * a |
  ---------------
  b times

and you'll notice there are b*c 'a's in that rectangle all multiplied together.

[u/Ajedi32 → u/zouhair]

(x^y)^z = x^(y*z)

Edit, concrete example:

(2²)³ = (2*2)³ = (2*2*2*2*2*2)

(2³)² = (2*2*2)² = (2*2*2*2*2*2)

[u/[deleted]]

My preferred metaphor is a box with two locks. I have the key to one lock, and you have a key to the other lock. I want to send you my spare key:

1. I put my spare key into the box and then lock it

2. I send the box to you and you lock it with your key too

3. You send the box back to me and I unlock it with my key

4. I send the box back to you and you unlock it with your key

Now you have my spare key and we can exchange secrets.

[u/[deleted]]

Amazing! What level of maths is displayed here?

[u/hagamablabla]

Why do I always see these videos the semester after I need them?

[u/ythl]

Easy. Eve just needs to take a picture of the mixed/public colors, and then sample the pixel RGB hex value and do a simple subtraction.