If there are N people in the world and are using secret key…
2016
If there are N people in the world and are using secret key encryption/decryption for privacy purpose, then number of secret keys required will be :
- A.
\(N\) - B.
\((N - 1)\) - C.
\(\frac {N(N - 1)} {2}\) - D.
\(\frac {N(N + 1)} {2}\)
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Correct answer: C
Answer: Number of secret keys required = N(N - 1)/2.
Reason: With symmetric (secret) encryption, one secret key is shared by each pair of people who communicate. Keys are not directional, so we count unordered pairs.
Each of the N people can pair with (N - 1) others, giving N * (N - 1) ordered pairings.
Each unordered pair has been counted twice in that total (A with B and B with A), so divide by 2 to correct for double counting: N(N - 1)/2.
Example: For N = 4, keys needed = 4 * 3 / 2 = 6 (pairs: AB, AC, AD, BC, BD, CD).