Colour of bits isn't a property of bits. It's provenance. It's facts about history of the things.
There may be no trace from pure noise to original work, but you didn't get that particular noise randomly, you in fact got it from the original work.
Once you understand that law cares less about the thing itself, and more about the causal chain that led to it, it stops seeming magical and becomes perfectly reasonable.
(Also, FWIW, it's not that far conceptually from code = data, but there's still tons of technical people who can't comprehend the fact that there is no code/data distinction in reality. "Code" vs "data" too isn't a property of bits, it's only a matter of perspective.)
In this particular case there's also the simpler, more technical/mathematical argument: you cannot possibly just "accidentally" have that exact noise. Getting those specific bits instead of any other sequence from the space of random numbers that much long requires you to extend effort at least equivalent to possession of the exact copyrighted work that happens to fall out of the XOR exercise.
Except there are two people, B and C with noise. The only thing you can prove is that if you XOR both noise vectors together, you have a copyrighted work.
Both people will say they are innocent and that the other person used the other's noise vector and the copyrighted work to produce their noise vector.
> Both people will say they are innocent and that the other person used the other's noise vector and the copyrighted work to produce their noise vector.
Simple: because you can't find out who tells the truth, simply jail both. :-)
If they are all posting their noise vectors up on xor-music.com, sure. If they have valid reasons for making available a specific 'noise' vector (maybe they can prove it decrypts to something useful), then probably not.
Judges and juries don't need to guilt to be mathematically proved, they just have to be pretty sure.
Yes. Or at least hint at it, at which point someone will probably volunteer or let slip some information that gives you a rough shape of the causal chain, at which point you know where to dig and pressure further, and eventually convince someone to confess or get a warrant to be sure.
If the prosecuting side has a reason to care that much, it doesn't matter whether it's 10 or 100 people - in fact, if it's 100 people, the original source is in deeper shit because this is now obviously not just personal use, but distribution.
Sounds nice on paper but it becomes exponentially difficult when many people are involved, and some groups of the vectors XOR'ed together also demonstrably result in legal content.
There may be no trace from pure noise to original work, but you didn't get that particular noise randomly, you in fact got it from the original work.
Once you understand that law cares less about the thing itself, and more about the causal chain that led to it, it stops seeming magical and becomes perfectly reasonable.
(Also, FWIW, it's not that far conceptually from code = data, but there's still tons of technical people who can't comprehend the fact that there is no code/data distinction in reality. "Code" vs "data" too isn't a property of bits, it's only a matter of perspective.)