Question

Symmetric-key encryption scheme

In my notes, it says there are three problems associated with symmetric-key encryption schemes. One of them is complex key management. It states that for n users, we have nC2 keys. Why is it nC2?

Answer 1

If you want to use symmetric keys, every combination of two users should have an unique key. nC2 is the number of possible combinations of two users.

If you have a list of n users you need to find sequences which select precisely two elements. It's combination since (User1, User2) is the same as (User2, User1) (both users will get the same key).