# Number of keys when using symmetric and asymmetric encryption?

Quoting part of my homework/assignment:

How many keys are required for secure communication among 1000 person if:

1. Symmetric key encryption algorithm is used?
2. Asymmetric key encryption algorithm is used?

My guess:

For symmetric they each need to maintain and transfer their own key, so probably $1000 \times 1000$, and for asymmetric maybe just $2000$, each having one public one private.

Is that correct?

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The answer depends on the security requirements, it could be just 1 symmetric key if everyone is supposed to read the messages of everyone else (group key) –  Richie Frame May 8 at 19:24
Its secure communication. –  Prakash Wadhwani May 8 at 19:31
Its secure communication. That was rather obvious. The question is: “What exactly are the security requirements which are expected in this secure communication?” Which somewhat asks for a protocol description… in case your homework/assignment provides that. –  e-sushi May 8 at 20:20
Nope, the question is here as it is. Doesn't provide anything else. But its assumed logically on such questions that the parties involved would be able to communicate secretly from one another. –  Prakash Wadhwani May 9 at 2:21
Do they really need a symmetric key to communicate with themselves? –  mikeazo May 9 at 12:25