The GATE Grind

GATE 2015 CS – Question 24

Computer Networks · Application Layer: DNS and HTTP · 1 mark · Multiple choice

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

  1. $2N$
  2. $N(N-1)$
  3. $N(N-1)/2$
  4. $(N-1)^2$

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Correct answer: (C) $N(N-1)/2$

Explanation

Every pair of people needs its own secret key, shared only by the two of them. The number of pairs among $N$ people is $\binom{N}{2} = \frac{N(N-1)}{2}$.