To understand the concept of secret-key distribution, assume a small private club has only 100 members (excluding the president). Answer the following questions:
a. How many secret keys are needed if all members of the club need to send secret messages to each other?
b. How many secret keys are needed if everyone trusts the president of the club? If a member needs to send a message to another member, she first sends it to the president; the president then sends the message to the other member.
c. How many secret keys are needed if the president decides that the two members who need to communicate should contact him first. The president then creates a temporary key to be used between the two. The temporary key is encrypted and sent to both members.