Networking

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
(A) 2N
(B) N(N – 1)
(C) N(N – 1)/2
(D) (N – 1)2
Answer
We need to find the total number of possible pairs from the N given people, each pair will share a key.
So, number of ways to choose two persons from N people = NC2 = N! / ((N −2)!×2!) = N(N-1)/2
Therefore, correct answer is Option (C)

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