GATE | GATE-CS-2015 (Set 1) | Question 65

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: (C)

Explanation: In Symmetric Key Cryptography, access of key is with both the parties. It implies every person needs to communicate N-1 other users using different keys i.e 1+2+3…N-2+N-1

This is like number of edges needed in a complete graph with N vertices is N(N-1)/2.
Answer is therefore C

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