= Diffie Hellman =

Diffie Helman is a secret sharing algorithm where a shared secret can be
created between two parties via an unsecure channel.

* Diffie hellman is not for encryption
* used to generate private key

== algorithm ==

1) For some prime `q`
2) Select some `alpha` such that `alpha < q` and `alpha` is a
   [[primative_root|Primative root]] of `q`
   * known as global elements
3) X,,a,, and X,,b,, are the private keys of alice and bob respectively
   * known as private elements/keys
4) Y,,a,, is `alpha^x,,a,, mod q`
   * Same for Y,,b,,
   * Known as public elements/keys
5) Both parties then calculate the shared secret via
   `K,,a,, = Y,,b,,^X,,a,, mod q`
   * same for K,,b,,
   * K,,a,, should be same as K,,b,,

== example ==

```
q = 7
alpha = 5

X,,a,, = 3
Y,,a,, = 5^3 mod 7 = 6

X,,b,, = 4
Y,,b,, = 5^4 mod 7 = 2
```