Diffie–Hellman key exchange

Diffie–Hellman is a specific method of exchanging cryptographic keys.allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel. This key can then be used to encrypt subsequent communications using a symmetric key cipher.

My eavesdropping
My homework for this week is eavesdrop a key exchange between two friends and use the key exchange public information to brute-force their secret key. Because this is an example the brute-forcing has to be done with hand and pencil.

First i calculated all the possible "x", "y" lowercase that could use them to calculate their public parts of the key. Then, i calculated all the keys for every "x", "y" that give me a public part "X", "Y" of the key, seeking for a pair of values "x", "y"  that their keys have the same value. And in the case of that more than one pair have the same key-value then i just going to try all the keys of all pairs.

Now i know Key value is = 3, but is hard to know what was the original values of "x", "y"  so i decide to ask to my friends what of the possible values "x: 1, 6,11" , "y: 2, 7" was the original value.

The final values (asking to my friends) are:

Key = 3
y = 7
x = 6

Reference:
http://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange