GATE CS 2015 Set 1 — Question 24
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Computer Networks → Application Layer → Symmetric & Asymmetric Encryption
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Question
Suppose that everyone in a group of people wants to communicate secretly with the 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
Correct answer
(C) N(N-1)/2
Solution
In a symmetric key cryptographic system, for two people to communicate securely such that no one else can decode the message, they must share a unique secret key.
In a group of people, every possible pair of individuals needs such a unique key. The number of ways to choose a pair of 2 people from a group of is given by the combination formula:Thus, keys are required.
In a group of people, every possible pair of individuals needs such a unique key. The number of ways to choose a pair of 2 people from a group of is given by the combination formula:Thus, keys are required.
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