Question

An organization has 100 members. It is desired that each member of the organization be able to communicate securely with any other member, without any other member being able to decrypt their messages. How many unique keys are required if:

a. The organization uses a symmetric cipher.

b. The organization uses an asymmetric cipher.

Answer 1

SOLUTION-

a. For the symmetric cipher every pair of person must have their key . So in total no. of keys in symmetric cipher=

No. of pairs of people in the organisation.

= ^NC₂

Here no. of people is N= 100

So no. of keys required = ¹⁰⁰C₂

= 100! / (2!(100−2)!)

= 4950

b. In assymetric cipher every person must have their own private key and public key.

So organisation needs 2 keys per person to make communication secure.

So, in assymetric cipher ,

No. of keys = 2* no. of people in orgnisation

= 2 * N

= 2* 100

= 200.

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