Question 3: Diffie-Hellman (DH) is a key exchanged algorithm which allows two entities to agree on a shared key. In DH, Alice and Bob each independently choose secret keys, a and b respectively. Alice and Bob computes their public keys, A and B. Then, they exchange their public keys over the internet. Alice calculates the shared secret key S. Similarly, Bob calculates shared key S.

1. Prove that, Alice and Bob obtain the same symmetric key (i.e. prove S = S).

2. With p=11 and g=2, suppose Alice and Bob choose private keys a=5 and b = 12, respectively. Calculate Alices and Bobs public keys, A and B.

NOTE: Plz, NO handwriting and NO Pictures.