Many sources mention that IVs must not be reused with the same key in CTR mode, for encrypting 2 different pieces of data, because that totally destroys security - but I haven't found an explanation so far as to why this is the case.
The issue is obvious if the attacker can manage to obtain the plain text and its corresponding cipher text for one piece of the data - but if no known plain texts are available, how could an attacker reconstruct the key-stream from just the IV value?
Can the security issues be mitigated by keeping the IV secret too? E.g. would an attacker have any realistic chance of cracking the encryption by just knowing that key/IV-pairs have been reused in the creation of two different ciphertexts, but nothing more?