1. A network consists of n hosts. Assuming that cryptographic keys are distributed on a per-hostpair basis, compute how many different keys are required.

2. One cryptographic checksum is computed by applying the DES in CBC mode to the message or file and using the last n bits of the final enciphered block as the checksum. (This is a keyed hash; the parties must agree on the key and the initalization vector used.) Analyze this hash function. In particular, how difficult is it to find two different messages that hash to the same value? How difficult is it to generate a second message that produces the same hash value as the first message?