Cryptography

Describe the process used for creating a shared secret key using the Diffie-Hellman Key Exchange protocol. What "hard problem" is the security of the DH protocol based on? Define a primitive element of the group Z^+_p. Why is it important that element g in Diffie-Hellman is primitive modulo p? Say Alice and Bob generate a public key for Diffie-Hellman where p = 53 and g = 23. Should Alice and Bob use this key? Why or why not