a) A newly graduated cryptologist proposes to encrypt the first 80 bits of the message with a secret key (known only to the sender and receiver) and use this 80-bit as a signature, thus saving time compared to standard signature techniques. What is wrong with this idea?

b) The same novice expert, this time, is given the task of developing a method to prevent the modification of messages from outside intruders. Our expert offers to add the hash of that message to each message. Why this method does not solve this problem?

Note: The hash function used is a powerful hash function.