Suppose Alice, Bob, and Carol want to use secret key technology to authenticate each other. If they all used the same secret key
K, then Bob could impersonate Carol to Alicia (actually any of three can impersonate the other to the third). Suppose instead that each had their own secret key, so Alice uses KA, Bob uses KB, and Carol uses KC. This means that each one, to prove his/her identity, responds to a challenge with a function of his/her secret key and the challenge. Is this more secure than having them all use the same secret key K? (Hint: what does Alice need to know in order to verify Carol’s answer to Alice’s challenge?)
this is not more secure than having all of Carol, bob and Alice having the same key.
alice would be able to know Carol's key for her to be able to verify the answer Carol gave to a challenge by her. she would also have to know bob's key to do the same.
any of these 3 would have to know someone else's secret key to verify answers to any challenge.
the challenge is to know the secret keys if the other two and if done, decryption can easily be done and they can impersonate.
