Suppose that everyone in a group of $N$ people wants to communicate secretly with the $N-1$ others using symmetric key cryptographic system. The communication between any two persons should not be decodable by the others in the group. The number of keys required in the system as a whole to satisfy the confidentiality requirement is

In a symmetric key cryptosystem, every communicating pair of users requires a dedicated secret key to ensure that no third party in the group can decrypt their communication.

For a group of $N$ people, the number of distinct pairs of individuals is given by the combination formula:

Hence, the system as a whole requires $N(N-1)/2$ keys, which corresponds to option (C).