Master the 2026 CRISC Challenge – Grab Your Risk Control Superpowers!

The formula for the number of symmetric key pairs required in a group of N individuals is derived from the need for each individual to have a unique key pair with every other individual in the group. Symmetric key encryption means that both parties involved in the communication need to share the same key.

In a scenario where every individual needs to establish a secure connection with every other individual, you first recognize that each individual can pair with N-1 other individuals (since one cannot pair with themselves). However, when establishing a symmetric key, the pairing between Person A and Person B is the same as the pairing between Person B and Person A. Thus, counting each pair twice needs to be addressed.

The correct formula reflects this by taking the total number of pairings (N times (N-1)) and dividing it by 2 to account for the fact that each pairing has been counted twice. Therefore, the formula to calculate the number of unique symmetric key pairs required is (N x (N-1)) / 2.

This understanding is critical in scenarios involving cryptographic protocols and secure communications, where minimizing the number of required keys can lead to reduced complexity in key management.