# GATE Papers >> CSE >> 2015 >> Question No 24

Question No. 24

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

Solution of Question No 24 of GATE 2015 CSE Paper

Every pair of nodes need a separate key. There are NC2 pairs required for N people.

$\therefore$  NC2 $=\frac{\mathrm N\left(\mathrm N-1\right)}2$ keys are required.

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