Introduction to Cryptography - Old Questions

2.     a) Consider a Deffie-Hellman scheme with a common prime p = 11 and a primitive root g= 2.

i. Show that 2 is a primitive root of 11.

ii. If user A has public key Y_a = 9, what is A’s private key X_a?

iii. If user B has public key Y_b = 3, what is shared key K, shared with A.         (3x2=6)