Question

. A small private club has only 100 members. 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

Answer 1

Answer:

(a) The number of keys = n × (n − 1) / 2 = (100 × 99) / 2 = 4950

(b) Just 100 keys are required. One secret key will be shared  between the president  and each member.

(c ) Only 100 keys are needed: This can be established using session key. Member A sends a request to president to talk to B. The president creates a session key and encrypts using secret key shared between him and A. He also encrypts the session key by secret key between him and B. This A will be delivering to B. After the session key is  established, the two members can use the one-time session key.