Diffie-hellman protocol

A little introduction:

The Diffie-Hellman cryptographic protocol, one due to Whitfield Diffie and Martin Hellman (Diffie-Hellman Problem-> DHP) is a key establishment protocol between parties who have had no previous contact, using an insecure channel, and anonymously (not authenticated).

It is generally used as a means to agree to be symmetric keys used for encryption of a session (session key establishment). Unauthenticated being, however, provides the basis for various protocols authenticated.

Your safety lies in the extreme difficulty (conjectured, not proven) to compute discrete logarithms in a finite field.

Excercise

Data are:

• p = 11
• g = 9
• X = 4
• Y = 9

The formulas are:

• X = (g^x) mod p
• Y = (g^y) mod p
• k = (Y^x) mod p
• k = (X^y) mod p

So,we had to find

• x = ?
• y = ?
• k = ? 

for this task, i used the method of trial and error until the numbers were equal, so here is how we realize:

first find y with the following numbers:
first try :(
Y = 9^8 mod 11 = 9x9x9x9x9x9x9x9 mod 11 = 43046721 mod 11 =  3

second try :(
Y = 9^4 mod 11 = 9x9x9x9 mod 11 =  6561 mod 11 =  5

third try :(
Y = 9^9 mod 11 = 9x9x9x9x9x9x9x9x9 mod 11 = 387420489 mod 11 = 5

fourth try :(
Y = 9^10 mod 11 = 9x9x9x9x9x9x9x9x9x9 mod 11 = 3486784401 mod 11 = 1

fifth try :)
Y = 9^6 mod 11 = 9x9x9x9x9x9 mod 11 = 531441 mod 11 = 9

y = 6

then the x:

first try:
X = 9^5 mod 11 = 9x9x9x9x9 mod 11 = 59049 mod 11 = 1


second try:
X = 9^7 mod 11 = 9x9x9x9x9x9x9 mod 11 = 4782969 mod 11 = 4

x = 7

then find k:

k = 4^6 mod 11 = 4096 mod 11 = 4

k = 4 

here my calculations:

that's all.

sorry for my bad english

Bibliography:
http://es.wikipedia.org/wiki/Diffie-Hellman
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