I would like an answer that could be sustained by a mathematical proof.
Let's say I'm using AES-CCM to encrypt a lot of messages, and I always use a different nonce.
I know that when the nonce space gets exhausted, the encryption key needs to be changed.
The question is: even though my encryption key has not been compromised and the nonce space is not exhausted, do I have any benefit from changing the encryption key at random times?
My intuition is that whenever I encrypt some data and someone can see the result of the encryption, I somehow "lose" a tiny bit of entropy, even though I change the nonce every time. So, by changing the encryption key at some point, it feels like I'm gaining because the attacker has never seen messages encrypted with this key before.
Is it really worth the effort of changing the key periodically or is assuring an unique nonce really enough?