I have to wonder if this would ever hold up in court. I don't know much about the UK justice system, but in America it would be pretty rare to be convicted of a crime that they can't actually prove you committed. You could be jailed for refusing to comply with a court order to decrypt the file, but if you can prove it's not actually encrypted, they can't do anything about it.
You're saying: "prove that there does not exist any decryption method or key that will turn this blob into incriminating data."
You can never prove that such a decryption method doesn't exist.
In fact, maybe it does exist? Given a blob of random data and infinite time, couldn't you find a way to "decrypt" that into pre-defined data? (I'm not really sure of that.)
It's really quite simple. Just xor it with some publicly available text, and then present the result of that xor as the "encryption key". When you xor that result with the original data, you get the publicly available text back.
To all the people commenting about how you can't prove it: in America, proof means "beyond a reasonable doubt". If you really did have random radio telescope data, the prosecution would have to prove beyond a reasonable doubt that your random data is actually encrypted. The proof for the defense would be called an alibi, wherein you would just say where you downloaded it from and what you used it for.
You don't need to prove that it could never be decrypted, you need to provide an alibi and then the prosecution needs to prove beyond a reasonable doubt that your alibi doesn't hold true. Your alibi is your proof.
You can decrypt random data to anything if you want to. Say R is your random data and M is the message you want. Compute Key=R+M, then decrypt R-Key=M.
This argument is interesting because it both a) makes the law worthless and b) removes the "scary slippery slope" argument.
After all, if you can provide a key to anything, then all you have to do (whether it's encrypted financial documents or random noise) is say, "Yep, it's encrypted, here's the key, it's the text of the Wikipedia page for 'kittens.'"
Prove that's not the correct key. If the onus for producing a key (whether one exists or not) is on the defendant, isn't the onus for proving the validity of the decrypted file on the prosecution?
All this comes back to cases like the one from CA (I think) where the guy who refused to decrypt the evidence that would prove his guilt.
And from another perspective, if you're Bernie Madoff and the evidence that will convict you is encrypted, won't you refuse to decrypt with a smile and take the 2-year punishment (with $500M in the bank) over life for financial fraud (and bankruptcy)?
Assuming the encryption method can create the bit sequence that is the random data. It very well might not. There may be gaps in the encrypted data's number space.
For any non-trivial encryption method, you'd be brute forcing your way through a bunch of them to find the key that can decrypt the random noise to that message. Typical "20 times longer than the existence of the universe" warnings apply. :)
The law's been around for quite a long time (since 2000, but it didn't come into force for a while after that). The answer to your question about unproven crime with random data is simply that it hasn't been tested in court yet. When a case comes along where the prosecution is claiming something is encrypted data, and the defendant's side is claiming it's random data, then this will be tested. Until then it's anyone's guess what'll happen.
In America a suspect can be jailed for years, even in solitary confinement, no conviction or trial required. The actual number of cases may be small but it's still scary.
In theory the accused is innocent until proven guilty, and thus should only need to suggest that the data is random, and pass the burden of proof back to the prosecution, who now have to prove the random data is encrypted.
File headers, existence of cryptography software and manuals, etc might be useful. Admission that the data is encrypted is stronger.
