User A and B use Diffie-Hellman algorithm to exchange a shared key and generate public keys of their own. Consider a common prime number q=71 and α (a primitive root of q)=7. Determine the followings:
1. If user A has private key=5, what is A's public key?
2. If user B has private key=12, what is B's public key?
3. What is the shared key?
Show the full working process of your work in at least three steps in both encryption and decryption