To complete the 'illegality' you need three pieces of information used in tandem:
1) the prime number (which is innocent in its own right)
2) the decompression algorithm (also innocent in its own right)
3) the knowledge that some specific prime number, when viewed through the lens of the decompression algorithm, yields an 'illegal' interpretation. (not illegal in its own right?)
The issue only comes from all three being present. If you have #2 and #3, #1 can be the last puzzle piece needed to create the required set, but no one piece is in-and-of-itself the source of the issue.
Of course, if the compression algorithm is one that's very commonly used like gzip or jpeg, a jury will infer intent from the totality of the circumstances and your lawyer will have a really hard time talking them out of it.
For instance, if you encoded the entire design of a nuclear weapon (or some other highly classified military secret) inside a prime, saying "but it's just a prime!" is a very silly excuse for exchanging that information. The question is: "what kind of information should be illegal to exchange", not "which format of information should be protected".
"11234349387298245791029384857" may or may not be an illegal number. Nobody cares and mathematicians can use it to their heart's content. That is, until I attach the metadata to it: "This number is the AES key embedded in every YthnVideo Disc Player". Now it's illegal. Number = legal. Number + metadata = illegal.
At least, that's how it should be.
If from a completely different domain, someone who has no relationship whatsoever to the maintainer of that first site creates a page explaining how DVD players contain AES keys and then links to one of the pages on the first page, from the perspective of a web user, that's number + metadata = illegal, right? And yet the number itself is legal. And the text by itself is legal. The combination is illegal, but the combination doesn't really exist.
Of course, the answer is probably that the text is illegal in the US, because the DMCA overrides the first amendment. Whether the text includes the number or a link to the number, it all interferes with the ability of a company to make money, so it's illegal.
The link is the illegal metadata. It's fine to explain that DVD players use cryptographic keys. It's fine to explain how said keys work. It's fine to have a list of prime numbers on your website for fun. It's not okay to link the two together. The link itself is exactly the type of illegal metadata I'm talking about.
Any type of pointing, eyebrow wiggling, coughing, etc. providing people with metadata on why certain numbers have cryptographic significance for a particular product is not okay (in my opinion).
Encoding as a prime doesn’t impose any special requirements on the data. All you have to do is append a bit of junk to make the whole thing prime. The rest of it can be plain text or whatever.
In that case, the knowledge that information is encoded in that specific number and the drawing attention to that fact is the illegal metadata. In other words, numbers are just numbers - until you draw attention to specific numbers with metadata, that's when you cross the line.
If you make a website with a prominently displayed huge prime number with flashing lights and arrows, you've added illegal metadata that says "try decoding me" or "I am probably a cryptographic key to something"
Someone who knowingly hosts a base-256 encoded secret should be held as accountable as if they had hosted the same information in picture form, morse code form, or plaintext.
By having enough capacity for organised violence to make their will stick. And if they lose that, they are no longer a government.
The only major dispute between governments is which groups of minorities to target.
Yes, but that would be a silly definition; governments rarely persecute as an end goal.
A more sensible one would be: a government is what controls a state, and a state is an organisation with a monopoly of legitimate force on an area of land.
The persecution perspective raises several ideas to the surface that get buried under the monopoly of force definition. The latter is concerned with collection of power, but the former is concerned with the use of power. Further, in countries such as the US, there are numerous arms among the citizens and the government cannot be truly said to have a monopoly of force (disproving the definition at least in part).
To what end is a monopoly of force? There is always a moral judgement in the use of power and always a line in the sand concerning who should be persecuted. Sometimes that line is murderers and sometimes it is homosexuality or saying things the majority disagree with.
Further, the persecution definition is more accurate in that it places the responsibility into the correct hands. Governments are formed by the people who consent to them and have no life of themselves. Even in a place like North Korea, most people endorse a government that most of us find horrible. The position of that line of persecution isn't determined solely by government fiat -- it is a result of the people's consent and inaction.
A government would find catching murderers impossible if the general population did not (as a majority) support and help them. Slaves would not have escaped from the South in any significant number if so many people in the North had not consented. Likewise, lynchings, kangaroo courts, and Jim Crow would not happen if the majority of people had not consented.
Very importantly, this view forces home the effects of intolerance. When a large group of people silence their opposition "freedom of speech isn't freedom from repercussions" they are in fact exercising this exact type of governmental persecution power, but without the tolerance that is otherwise "agreed" upon.
This raises what is (to me) the most interesting argument of all. Speaking of the US. We agree that the government cannot punish people for controversial, but non-inciteful speech. We are the government ("by the people"). We simultaneously agree that we can do the exact opposite in our personal lives and ruin someone we disagree with. This shows our true line in the sand is very much not in sync with the one we voted for and illustrates a very complex, but dangerous cognitive dissonance.
I could go on, but this lens is the most useful one I've seen for looking at how society, morality, and government interact.
If they dont do this, no one cares about 'the law'.
I think that intent and plausibility play the most important roles here.
Also, if the number of bits you need to describe an illegal prime is of the same order as the number of bits in the prime itself, then you have a weak case.
To point to the "Nth prime" would require almost as many digits as the prime itself. Mabe it's more efficient for very large primes, but I don't think so.
source?
As you increase length, the number of possible strings grows exponentially. There are only a few (relatively) much smaller strings you can map to.
I sometimes make the joke that unicode sequences make people extremely angry. It's a gentle reminder not to take everything so seriously. But everyone still understands that it isn't actually the sequential placement of glyphs that make people angry.
Are you really surprised that most of them comply? What other choice do they have?
Definition weapon - a thing designed or used for inflicting bodily harm or physical damage.
By itself, it is harmless, but when paired with an appropriate device, by a user with malicious intent, it can then be used to cause harm.
But certainly information can be used for extortion, or to otherwise coerce people against their will, and maybe that's enough?
"Information" is a noun, hence it is a "thing".
Furthermore, the 'physical damage' it can inflict is the destruction or manipulation of physical memory cell states.
Whenever this attempt at reductio-ad-absurdem comes up, I find it pretty unconvincing. It's not that they are banning a number, just like if you make certain images illegal you're not banning "light" and if you make slander illegal you're not banning "sound, which is just vibrations in the air." Describing the medium of speech is kind of silly, because the point is the information contained in the media. The fact that the law addresses abstract concepts isn't exactly groundbreaking.
Everything is information. How can murder be forbidden? It's just an arrangement of quarks?!
The interesting part here is the obvious contradiction that prime numbers seem innocent but in the end, they are numbers, and numbers can represent anything.
Again, the obvious question to rise here is: How is it possible that a government can forbid information?