1. You are Alice. You have agreed with your friend Bob that you will use the Diffie-Hellman public-key algorithm to exchange secret keys. You and Bob have agreed to use the public base g = 3 and public modulus p = 809. You have secretly picked the value SA = 17. You begin the session by sending Bob your calculated value of TA. Bob responds by sending you the value TB = 291. What is the value of your shared secret key?

2. A particular cipher is implemented by combining the ASCII representation of plaintext characters with pseudorandom bytes (eight-bit binary strings of 1s and 0s) using the XOR function. In the process of encrypting a message, a character in the plaintext, a capital H, is XORed with the pseudorandom byte 10111100.

a. What is the ciphertext (in binary form) generated by the encryption of the character D? (show your work.)
b. How is the plaintext for this encrypted D recovered? (show your work.)

3. An organization has 300 members. It is desired that each member of the organization be able to communicate securely with any other member, without any other member being able to decrypt their messages. How many unique keys are required if:

a. The organization uses a symmetric cipher.
b. The organization uses an asymmetric cipher.