3) A Coding Scheme uses triple (3, 10, 3). The public numbers are 3 and 10, and the private key (third number) is 3. These numbers come from following a procedure, starting with two prime numbers p = 2 and q = 5.

(a) Suppose that you want to send a message HI to a friend. You decided to first turn the letters H and I into two numbers using the following scheme: A will be the number 1, B the number 2, etc. Then, you encode each of the above two numbers using the Coding Scheme with public numbers 3 and 10. What two numbers will you be sending?

(b) Decode the two numbers that you obtained in part (a) using the private key 3. What are the two numbers? Do they correspond to the letters H and I?