I have copyrighted data block A.
I generate random, uncopyrighted data A1 and store on host X I XOR A1 with A and get A2, storing this on Y.
Y is derived from A (and A1) but A1 is totally original random data whose generation is totally unrelated to A.
So, who is hosting the derivative data? Y, possibly, but both A1 and A2 look like random data, there's no way to tell which is the random one.
The knowledge that "A = X(A1) xor Y(A2)" is also derived work. That fact will be known by someone, and will definitely be infringing.
Knowledge of how to combine them being a derived work is an interesting theory. One challenge is that facts aren't typically copyrightable. On the other hand you could argue contributory infringement instead.
> So, who is hosting the derivative data? Y, possibly
Y, definitely. Like you said yourself, Y's data is derived from A.
> both A1 and A2 look like random data, there's no way to tell which is the random one.
Any encryption scheme will cause the file to look like random data. All that means is that seeing the file contents alone is not enough to prove the crime. It doesn't mean that the file contents become free of infringement.
In any case, encryption schemes have keys, distinct from data and generated during encryption. In this case, there are two sets of data, either of which could be key or data, and one of which could of been generated before, and independently of the other. In fact, for any data block A, and random data X - there is a block Y that combines with X to produce A - any/all A, any/all X.
> In fact, for any data block A, and random data X - there is a block Y that combines with X to produce A - any/all A, any/all X.
That is true with basically any encryption scheme, the only peculiarity here is that key and data are the same length (which is irrelevant to the legality of the situation anyway).
Why? hosting derivative work is illegal, hosting random data (keys) isn't, the distinction between X's data and Y's data is the distinction between liable and not-liable. If you can't tell which is which, then both are innocent under reasonable doubt.
> That is true with basically any encryption scheme
What's isn't true is the ease with which the A can be generated from X given Y. In other encryption schemes, key and data are distinct components - and not just by size.
> In other encryption schemes, key and data are distinct components
Key and data are distinct components here too. You said yourself you generated the key data with no knowledge of the infringing content, so that makes them distinct. Size of the key is the only difference with this scheme compared to more typical ones.
> You said yourself you generated the key data with no knowledge of the infringing content, so that makes them distinct.
The 'key' differs by history, which isn't know from looking at the bits. There is no way to distinguish which is the key without knowing how they where generated.
But by "distinct" I mean that you cannot switch the roles of key and encrypted data in most encryption schemes, that is not true in this case.
> Size of the key is the only difference with this scheme compared to more typical ones.
That's not true, in traditional schemes the key of any size is still the key in how it's used to decrypt the encrypted data; you cannot decrypt the key using the encrypted data as a key; this is not true for OFFsystem - there is no key/data distinction, if E is the decryption function then E(A, B) = E(B, A)
Nope. X is still hosting infringing content (I doubt this would even be considered derivative and not simply the encrypted original), this just made the proof harder. But "it could theoretically have happened differently" is not "reasonable doubt" if this possibility is highly unlikely in face of all other evidence. A thief doesn't get out free because the thing "could have accidentally dropped into his bag".
You're demanding that the court, should only look at the tiny piece of the puzzle that you provide. They have no reason to do so.
In this case, I'd assume, instead of diving into the technicalities of the algorithm, they'd be more interested in the fact that the openly stated purpose of the whole system is to circumvent copyright.