Not sure if this belongs here but could not find the other closest section to my query.
The question is :Suppose that everyone in a group of N people wants to communicate secretly with the N–1 others using symmetric key cryptographic system. The communication between any two persons should not be decodable by the others in the group. The number of keys required in the system as a whole to satisfy the confidentiality requirement is
The options are :
A) 2N
B) N(N – 1)
C) N(N – 1)/2
D) (N – 1)2Need this for a project I'm working on.Logical explainations appreciated.
Sounds like Im doing your homework here. Oh well. We are using symmetric keys so each pair of people that wants to communicate need 1 key. If
n is 3 and the names are Alice, Bob and Claire we get the following pairs.
A-B
A-C
B-C
All other possible pairs (like B-A) are doubles. I will leave it for you to find the general formular for any
n. If you have trouble finding a solution start from 3 and ask yourself how many additional(!) keys you need to add for the 4th person. Repeat adding more people until you see a pattern and test for a higher number.
