Diffie Hellman Key Exchange Algorithm? (x,y value)

[shivajikobardan]

Homework Statement

What should be the value of x and y in Diffie Hellman Key Exchange Algorithm?

Relevant Equations

Diffie-Hellman Key Exchange Algorithm

I'm not asking it from "will it be secure" point of view, rather I'm asking textbook kind technically correct or not.

This is the algorithm (in the 3rd step of right figure, it should be generate y, typo)

I took p=23,g=5.
And picked x=4,y=5
I got the secret key as 12 and both got 12, so it looks like the algorithm worked. But were there any restrictions and if this was a fluke?

What I'm aware?
x,y should be random. And x,y range from 1 to p.

 

[pbuk]

But were there any restrictions and if this was a fluke?

No it wasn't a fluke, just a poor resource: I suggest you use https://en.wikipedia.org/wiki/Diffie–Hellman_key_exchange#Cryptographic_explanation.

To prove it is not a fluke you need to show that $A^y \pmod p \equiv B^x \pmod p$ i.e. $(g^x \pmod p)^y \pmod p \equiv (g^y \pmod p)^x \pmod p$.

 

[shivajikobardan]

No it wasn't a fluke, just a poor resource: I suggest you use https://en.wikipedia.org/wiki/Diffie–Hellman_key_exchange#Cryptographic_explanation.

To prove it is not a fluke you need to show that $A^y \pmod p \equiv B^x \pmod p$ i.e. $(g^x \pmod p)^y \pmod p \equiv (g^y \pmod p)^x \pmod p$.

Thanks for the information sir.