Question

R6. Suppose N people want to communicate with each of N - 1 other peo- ple using symmetric key encryption. All communication between any two people, i and j, is visible to all other people in this group of N, and no other person in this group should be able to decode their communication. How many keys are required in the system as a whole

Answer 1

Answer:

N(N-1)/2

Explanation:

You would need a symmetric key for each pair of people, so you need the number of pairs.

Mathematically this can be written as

$_NC_2 = \frac{N!}{2!(N-2)!} = \frac{N(N-1)}{2}$