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Official PYQ · 2015Set 1 · Q21Concept of Layering: OSI and TCP/IP Protocol StacksMCQ1 mark

GATE CS 2015 Set 1 Q21 — Concept of Layering: OSI and TCP/IP Protocol Stacks

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Suppose that everyone in a group on NN people wants to communicate secretly with the (N - 1)(\text{N - 1}) others using symmetric Key cryptographic system. The communication between any two person should not be decodable by the others in the group. The numbers of keys required in the system as a whole to satisfy the confidentiality requirement is

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Answer: C

In a symmetric key cryptographic system, the same key is used for both encryption and decryption. For secure and private communication between any two individuals, they must share a unique secret key that is not known to anyone else in the group.

To find the total number of keys required for a group of NN people where every pair needs to communicate securely:

  • We need to select a unique pair of people from the group of NN people.
  • The number of ways to choose a pair of 22 people from a set of NN is given by the combination formula (N2)\binom{N}{2}:
Total keys=(N2)=N(N−1)2\text{Total keys} = \binom{N}{2} = \frac{N(N-1)}{2}

Thus, the total number of keys required in the system as a whole is N(N−1)2\dfrac{N(N-1)}{2}.

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