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How many keys are needed in a symmetric key scenario for 4 people?

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In a symmetric key scenario, each pair of individuals requires a unique key for secure communication. This is because symmetric encryption relies on the same key being shared between the two parties who want to communicate securely.

For four people, you can think of all possible pairings among those individuals. The mathematical formula for determining the number of unique pairs from a group is given by the combination formula \( C(n, 2) \), where \( n \) is the number of people. In this case:

- \( n = 4 \) (the four individuals)

- The number of unique pairs is calculated as \( C(4, 2) = \frac{n(n-1)}{2} = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = 6 \).

Thus, for every pair, one unique key would be needed, resulting in a total of 6 keys for 4 individuals. Each key is specifically assigned to a pair, ensuring that the communication remains private and secure among that specific pair only.

This understanding highlights the exponential growth of key management as more participants are added to a symmetric key system, making it crucial to consider the implications of

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