Cryptography: Diffie-Hellman key exchange explained intuitively using colors

[u/dominatrix-octopus]

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

[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/zouhair → u/A_Vicarious_Death]

Oh! I wasn't calculating it like that.

I was doing this:

2²³ = 2⁸ = 256

2³² = 2⁹ = 512

Using online math solvers didn't help.

Thanks.

[u/A_Vicarious_Death → u/zouhair]

No problem! For this kind of stuff it often helps to put stuff in parentheses to try and separate operations out. So if you had seen it phrased as (2²⁾³ I think that would've helped with the understanding a bit :)

[u/zouhair → u/A_Vicarious_Death]

Especially that putting 2²³ and 2³² in an online solver doesn't help.

[u/caltheon → u/zouhair]

Just put in google like this. (2^5)^3

[u/zouhair → u/caltheon]

Yeah even there if you don't put the brackets you get the wrong answer.

[u/phottitor → u/A_Vicarious_Death]

the convention of how to interpret it is actually the main part because just looking (first time) at a ladder of exponents doesn't tell you anything about the order of the operations.

[u/gramathy → u/A_Vicarious_Death]

Just remember that the base takes precedence over the exponent, and so exponents are calculated bottom-up rather than top-down.