I always thought it would be a cool investigation to look at the distribution of entropy signals coming from celestial bodies and group them. I'd bet there is a non-'natural' entropic signal coming from planets with biological processes on them.
The only way alien civilizations will pick up each others' signals is if they're intentionally directed at those systems with highly focused emitters. If you're intentionally sending a signal in hopes another civilization will see it you're definitely not going to encrypt it. Compression also serves little purpose as there's no shared context to decompress the message.
By the same token, if humanity disappeared but left a bunch of encrypted hard drives around and aliens came and found them, they may have no hope of distinguishing the bits from random bits, but they'd be able to tell that no natural process encodes any kind of bits at all onto magnetic discs or flash drives or whatever else we manage to come up with.
The actual issue is what the other commenter said about the impossibility of detecting such low power radio at all.
historical forms of signal modulation like ook and fm don't look very much like white noise, because they're designed to be demodulated by circuits with 1-10 vacuum tubes, but more modern modulations can look pretty white. they'd look a lot whiter if they weren't constrained by regulation to strongly attenuate bands used by obsolete forms of signal modulation