To solve the problem, make assumptions for missing data and justify. Given: a) Prime number: p=97
b) p=97 has 32 primitive roots, and they are 5, 7, 10, 13, 14, 15, 17, 21, 23, 26, 29, 37, 38, 39, 40, 41, 56, 57, 58, 59, 60, 68, 71, 74, 76, 80, 82, 83, 84, 87, 90, and 92.

Select one primitive root (>20)from the set randomly for the below computation.

Compute:
1. Assuming the last three digits of your Roll number as your public key(Ya), then compute your private key (Xa) using the given data.

2. Assume one of your classmate's (no collusion) last three digits of his/her Roll number as a public key(Yb), then compute private key (Xb) using the given data.

3. What will be the shared key, if you both use the Diffie-Hellman Key exchange technique?

4. Using the ElGamal scheme encrypt your first name by selecting some random integer k. What will be the ciphertext?

5. Explain how decryption is done to retrieve your name.