Answer:
No. This is not more secure.
Explanation:
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.
Can prove they are not infringing on copyright
It makes the possibility of an unwanted user to break into your account much smaller.
