CompTIA Security+ (SY0-701)General Security ConceptsHard
An organization has 12 employees who each need to communicate securely with every other employee using a unique symmetric key per pair, with no key reuse. How many total symmetric keys are required?
- A132
- B144
- C78
- D66
Show answer & explanationAnswer & explanation
Correct answer: D. 66
The number of unique symmetric keys needed for n users to each have a distinct pairwise key is n(n-1)/2. With n=12, this is 12x11/2 = 132/2 = 66 keys.
Why the other options are wrong
- A. 132 is 12x11 without dividing by 2, double-counting each pair.
- B. 144 is 12x12, incorrectly treating each user as needing a key with themselves too.
- C. 78 would be the result for n=13 (13x12/2), not 12 users.
Symmetric Key Scalability
The number of unique pairwise symmetric keys needed for n parties equals n(n-1)/2, illustrating symmetric encryption's key management challenge at scale.
- Formula: n(n-1)/2 unique keys for n users
- Grows quadratically as users increase
- Asymmetric cryptography avoids this scaling issue via key pairs per user, not per pair
Memory trick: Pairs, not squares: n(n-1)/2