Question

There are 67 people in a company where they are using secret key encryption and decryption system for privacy purpose. Determine the number of secret keys required for this purpose?

(a) 887

(b) 6529

(c) 2211

(d) 834

The question was posed to me in an online quiz.

This intriguing question comes from Cryptography topic in section Number Theory and Cryptography of Discrete Mathematics

Answer 1

Correct choice is (c) 2211

For explanation: Since every two employee have their own secret key encryption and decryption. Both users have to agree on a secret key to communicate using symmetric cryptography. After that, each message is encrypted with that key it is transmitted and decrypted with the same key. Here, key distribution must be secret. For n = 67 we would need  \(\frac{n(n-1)}{2} = \frac{67(67-1)}{2}\) = 2211 keys.