Say I have a bunch of data encrypted with a secure block cipher (such as AES). A

Question

Say I have a bunch of data encrypted with a secure block cipher (such as AES). An attacker has unlimited access to this encrypted data. The attacker doesn't know whether the data is encrypted or if it's just purely random bits. Is it possible (even theoretically) for the attacker to distinguish the encrypted data from purely random bits?

There seems to be many questions asking whether or not it's possible to identify a particular encryption scheme from the ciphertext, but what I want to know is if it's even possible to determine that the data is encrypted in the first place (as opposed to being random bits).

Explanation / Answer

In theory, there is a simple distinguisher for encrypted data: Try all the possible keys, decrypt the stream and look if the result is something which makes sense.

Of course, this will not work if you encrypted garbage (and one could say that encrypted random data is really indistinguishable from random data itself, ignoring block sizes).

And practically, the key space of all modern block ciphers is large enough that trying all (or even a large part of all) keys is impossible.

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