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For 6 people, how many symmetric key pairs are required?

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15

To determine the number of symmetric key pairs required for a group of 6 people, it's important to recognize the nature of symmetric key cryptography. In symmetric key scenarios, each pair of individuals requires their own unique key for secure communication. This means that for every unique pair of people, a separate key must be generated.

The formula to calculate the number of unique pairs from a group of n people is given by the combination formula C(n, 2), which is n(n-1)/2. For 6 people, we can calculate it as follows:

1. Substitute n with 6 in the formula:

C(6, 2) = 6 * (6 - 1) / 2

= 6 * 5 / 2

= 30 / 2

= 15.

This calculation shows that 15 unique pairs can be formed from 6 individuals. Therefore, 15 unique symmetric key pairs are required to ensure that each pair can communicate securely without sharing their keys with anyone else. In this context, the response indicating that 15 is the correct answer aligns with the necessary number of key pairs for the communication needs of the group.

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