Illegal Prime Numbers
en.wikipedia.org
en.wikipedia.org
This might be thought of as a human version of a covert channel: https://en.wikipedia.org/wiki/Covert_channel
E.g. publicizing the number and expiration date of Bill Gates' credit-card is illegal but what if we wrote a text commentary about Shakespeare's Hamlet that when SHA-1 hashed, it gives you that same information? Yes, it would be very computationally intensive to generate a plausible literary text but it could be done. Or one embeds Bill Gates credit-card number as "transactions amounts" on Bitcoin blockchain.
The theme is the same: find a "legitimate" information channel to transmit illegitimate data. This then allows the philosophical arguments about information:
- How can commentary about Shakespeare be illegal? It's education!
- How can you censor transactions on the bitcoin blockchain? There are already 100,000+ copies of it on nodes around the globe! And so on...
That would imply that it would be practical to create a document that hashes to a specified value. The SHA-1 pre-image resistance would prevent that.
Even MD5 is safe from a pre-image attack, it means, for example, that it is safe to use for storing passwords (but not recommended for other reasons).
No, I'm talking about computing something much less ambitious than solving pre-image resistance.
Consider the example SHA-1 hash[1]:
SHA1("")
gives hexadecimal: da39a3ee5e6b4b0d3255bfef95601890afd80709
gives Base64 binary to ASCII text encoding:
2jmj7l5rSw0yVb/vlWAYkK/YBwk=
It's a similar concept to creating "vanity" public hashes for Tor or bitcoin addresses or finding a hash that has a certain number of leading zeros in "proof of work". Embedding arbitrary illegal information that way is more computationally feasible with brute force than perfect pre-image attacks.
The underlying idea of the hack is the same : Find some way to make illegal data be interpreted in a totally different way that _is_ legal. It's very hard to do for large amounts of information such as 9 GB mp4 rip of a Blu-ray disc -- but easier for small amounts of information... such as the DeCSS C source code converted to an "interesting" prime number.
Additional metadata, such as "it's a driver's license number", "it relates to person X" gives it context and makes it information. 4037 is a bank pin code for millions of people, but as long as you don't combine it with a person it's just a 4 digit number. When you combine it it becomes information protected in many countries.
The fact all data exists 'in nature' - while interesting, is not something I think should override the intent of data laws.
If you remove all knowledge of that information you destroy it. And by "all knowledge" I mean every known way to generate it, not just a simple representation.
There is nothing special among any single number in 160 byte string, but it contains all SMS ever sent. Some of those messages are of special interest to some people.
There is no right and wrong in this world; there are only parties with enough power to enforce their will upon others. Some of those parties believe that what they do serves some public interest.
It's why sharing child pornography is illegal, even though all the creators are really doing is sharing a set of instructions for someone's else's computer to generate the image/video.
The strange matter is that in the U.S.A., mens rea is an element of the crime of sharing and possessing child pornography, meaning that one can only be convicted if one knew, or could reasonably be expected to know the actor was under a certain age, but this is not the case for actual sexual intercourse with a minor, where one is criminally liable if one could not be expected to know.
In most jurisdictions, mens rea is an element of both.
For copyright, it really doesn't. Hence Disney threatening to sue daycares for having Disney character murals on their walls.
While we have since had the four factors of fair use introduced, it still doesn't care about intent; it cares about how the work is used/transformed, but that's different than intent.
are you quite serious? Disney doesn't think they own coming of age tales or intrepid children feeling out of place. Disney thinks they own the things they paid to create during the operation of their business.
the daycares Aren't making up their own stories, theyre directly benefiting by using Disney's products without licence or permission. this is the exact opposite of seeking.
To prove intent you'd have to prove the daycare knew the works were copyrighted (i.e., the distinction between public domain Snow White, and Disney's Snow White), knew the copyright law sufficiently to know this was infringing (i.e., painting on the interior of a daycare where you're clearly not economically benefiting), and to choose to do it anyway.
Hence why copyright law doesn't take intent into account; 'ignorance of the law is not a defense'.
If your intent is to comment on Shakespeare, and it happens that what you produced, when run through some process, produces something under copyright, but the thing you intended to express doesn't, I don't think that would violate copyright law? Or at least, no one would convict you.
I was trying to emphasize the people sharing the legitimate data and not the person who generated it from illegal data.
For example, the SHA256("Hamlet was a prince in Denmark.")=="4461565240549538f8888f5ac829800a79763479f28418dec7a13087a3e0d2a8".
Let's say the first 16 hex digits ("4461565240549538") is an "illegal number" ... e.g. somebody's credit-card or whatever.
Yes, the intent of starting with "4461565240549538" and using brute force to eventually find some a plausible sounding sentence that creates a hash with that 16-digit number can be prosecuted. Likewise, you can't just XOR a Blu-Ray mp4 file with digits of pi and claim "it's just a random number" to be immune from copyright laws.
I'm talking about the people downstream that do something like this by sharing on reddit, Twitter, etc:
- I ran across some Shakespeare trivia: "Hamlet was a prince in Denmark." I don't want anybody to hash it. I just thought that was interesting to know.
- Streisand Effect[1] the above tweet or forum post
- now everyone debates : How can the sentence "Hamlet was a prince in Denmark." -- be illegal?!? It's a factoid about a play that you can't remove from everyone's brain! We're now past the point of the criminal who brute forced the illegal data to publish it. I'm talking about the non-criminals sharing it. That's the information hack: Shift the illegal data into the realm of the legal data.
Maybe that hack hasn't been fully tested in courts but it seemed to work if we look at the DeCSS code repackaged as an interesting prime number. Neither Chris Caldwell and Phil Carmody have been put in jail.
It can also be especially effective if the would-be criminal who generated interesting hashes or prime numbers did it anonymously such as Satoshi Nakamoto's generation of the bitcoin genesis block. There's now no obvious person to prosecute.
However if you have, or circulate this number along with an implementation of the decoding algorithm, as a reader, then you're actually circulating the credit card number itself in a much more direct way. Yes, I know they also publish the unpacking algorithms, but If I walked round with a T-shirt with the encoded file on the front, and the decoding program on the back, that's clearly a much more direct and obvious transgression.
The joke about these illegal primes is that by themselves they seem innocuous, they're just seemingly meaningless numbers, but put the two halves of the puzzle together and the problem becomes a lot clearer. Handing out an unreadable, encrypted, encoded number with the latest Marvel movie in it but no way to play it seems harmless, hand it out with a bundled video player as well and that's a problem. Now it's a viewable movie and that's a different kettle of fish.
A friend of mine got very excited when we were CS students because he found a way to theoretically 'encrypt and compress' data to extremely small sizes, until I pointed out the binary compression key would end up being vastly bigger than the 'compressed' file. Basically he was just 'sucking' the complexity out of the data file and putting it in the key. These numbers are a bit like that, a large amount of the information in the 'encoded' content is actually sequestered in the unpacking algorithm.
With the right 'decoding scheme' the number 5 is an encoded copy of Infinity War. Wow, 5 is now an illegal prime!
Therefore I don't see how those numbers being prime changes anything. This looks to me like a weak argument that tries to take advantage of poor intuitions that some people have about primes.
Yes, the IP laws are ridiculous but this is not a good argument to support this opinion.
Isn’t this what godel’s encoding does?
It is also a reversible concept: you can create an "illegal painting" by encoding a number in the painting, so that interpreting the painting in some way (like, splitting it in a X*Y grid, and assigning 1 to the squares where the red component in RGB is greater than G, 0 otherwise) will result in such number.
What's the gist of all this? That reality can be represented by numbers and the other way around, however numbers representing illegal digital entities (violating copyright or other laws) are so unlikely to happen by chance, that they need to be chosen explicitly to have such a representation: the illegal prime is just a different way to write the same thing in a file, thus is the same blatant law violation, and the fact they happen to have a prime number (very dense and common numbers) is not interesting at all.
The point, per the article, is a protest against the censorship of information. People may not think twice about making a computer program illegal. However, banning a number would get more attention. The point is exactly as you have noted-- it's the same thing.
A pair of GPS coordinates with five decimal precision, written like 7.63941, -122.12825 is just 19 ASCII characters. So in ~400 characters you could have 20 such pairs. 400 ASCII characters being 400 bytes or 3200 bits, they can be represented by a number that's < 2^3200. What if the 20 pairs of coordinates are current locations of US nuclear submarines? That would make the ~900 digit number very dangerous from the US military's point of view.
400 characters is surely also enough for many other bits of highly classified information. Several names of CIA agents under non-official cover in China. A concise description of the purpose and capabilities of the X-37 spacecraft. The top item on the President's Daily Brief for today.
It raises some interesting questions about the legality of numbers, and what would happen to someone publishing one. What if I'm writing an article that happens to contain the nuclear-submarine-coordinates-encoding number? What if I'm writing about a debugging problem and I show a memory dump that happens to contain it? The actual probability of that happening is of course zero, but something tells me that anyone who did publish such a number would suddenly find themselves in the company of government agents very willing to overlook that person's rights.
(You needn't be kept up at night by the thought of accidentally publishing nuclear codes; as you say, the probability is 0 for all practical purposes, and the reluctance of government agents to dismiss it as a coincidence would be entirely reasonable)
I guess the counterpoint here is, a government that wanted to put you behind bars by justifying it with 5 random bytes would have no problems with fabricating some much stronger evidence against you instead.
Is my paper going to get censored or not?
No, but that is not a problem, since that will never happen. There are too many prime numbers for you to accidentally stumble upon that prime number while doing something else. The theoretical possibility that you might is not a problem for the law, which only concerns itself with problems which occurs in practice.
Since "the colour" is the whole context which led to you mentioning the prime number, the answer is "it depends".
In practice you can publish it as a part of mathematical paper on primes. You cannot publish it saying "here's a prime that decoded as X does illegal thing Y".
Anything in-between is gray zone, with the disclaimer that courts don't like "clever" schemes that try mess with the "colour". So if you try to publish a fake mathematical paper to thumb your nose at the illegality of publishing something, the court will be unsympathetic.
It’s essentially the opposite of Aaron Swartz’s famous “Bits are not a bug” writeup.
No, jokes aside I don’t know either.
Alice publishes a truly random string of bits, Bob publishes a XOR of Alice's string with an "illegal" number. Information theory says you cannot tell which is which (and publishing a random string of bits is supposedly legal) but you can still retrieve the "illegal" number by xoring Alice's and Bob's strings.
I don't see how the known pass phrase achieves that.
Unless an omniscient observer knows the publication date of all the "halves" in the system, it is impossible to say which of Bob or Alice are telling the truth.
Of course, both parties are inherently slightly suspicious for using such a system in the first place, but if it existed as part of a free public hosting service, and lots of people used it for legitimate purposes, it might only be as incriminating as using BitTorrent.
"...worthy of being published on the lists of the highest prime numbers.[1] In a way, by having this number independently published for a completely unrelated reason to the DeCSS code, he had been able to evade legal responsibility for the original software."
Primes are pretty dense in the integers - unless you're going to say 'data can't be illegal' - including e.g. CP, then highlighting illegal primes is simply not a valid evasion.
https://math.stackexchange.com/questions/216343/does-pi-cont...
The other idea I've always liked is a length that, to enough precision, encodes something in the decimal places. Then in theory you could just cut something, say a diamond, to this impossible precision, and then measure it later. I assume that, like the Pi example, this is impractical not only in practice but even in theory, even if we had impossibly-accurate cutters and measurers.
1. Take illegal number
2. GZip it, or at least store it in a format that discards trailing null bytes.
3. Multiply it by a power of 256
Every power of 256 adds a zero to the end, in the same way that multiplying 5x10=50, 5x100=500, etc.
4. Add a an integer and check primality; repeat.
So if the illegal number was 12345 your could have an illegal prime 1234500000071 represented by (12345x256^8+71).
The only reason you’d want to do this is because people actually share seemingly random prime numbers online. There’s no legal reason to share the DeCSS encryption code, but a prime number with a length of 2000 is “interesting” enough to avoid legal issue.
But also, as pointed out elsewhere in this thread, your hypothetical is more or less what happened with the DeCSS primes Phil Carmody published. Except it never even got to a judge.
I found that to be an interesting rabbit hole: https://primes.utm.edu/glossary/page.php?sort=ExecutablePrim...
Well, I suppose a government could try to ban the numbers 2 and 3, but it might have trouble complying with that law itself.
If the source code to Microsoft Windows is illegal, is the source code plus one bit of padding at the end illegal? How about two bits? How about an XOR transform with some random number, which I also publish online? How can Microsoft copyright an infinite number of variations of their source code?
The answer is that they obviously can't, but all those variants are illegal if the purpose is to get back to that same source code. If you're transforming their source code, and providing some obvious or non-obvious key for how to get from your transformation to the original, you're violating copyright.
It seems like it's logically or legally equivalent to setting your password to someone else's date of birth and then claiming that they have hacked you because they know your password.
Hiding number is not a proper way to address the issue. We should address the core of it - drm which should be made illegal.
What is strange for me is that making digital rights management program that does who knows what and thus breaks any privacy by definition is not illegal but some number that merely describes a computer program that bypasses such program is. This is not crazy? Why it should be illegal to protect own computer from malware?
Actually, I believe we are going towards information being the thing that has value, we should arrive there, assuming abundance (on a human scale of course, energy is still required to sustain any patterns), material goods being just things that can be copied.
So where do you draw the line? If you get caught with my private keys is that ok & legal? What if I get caught with internal documents of some company? Espionage? Facebook just keeping some big numbers around? How do you implement privacy that you seem to care about without some numbers being illegal?
Also remember you bought/installed that malware or agreed to it. And no, I don't like DRM, I do agree that it is insane, but without presenting a coherent view where that problem is not present it's just being angry about the sky being blue.
A reasonable suggestion would be to draw the line around private data.
By design, DRM is intended to restrict people's use of data which the publisher wants to spread as widely as possible (on the condition that they are paid for every copy). This data is therefore not private in any sense.
All your other examples work with this line: Private keys are obviously private; internal company documents are "private" in the same sense that corporations are people; government secrets are private (and countries are legal people); and Facebook should be keeping people's personal data secret on their behalf.
But then, if a company implements DRM using its private key and somebody steals that private key?
For example, I don't think that all information created by a government should be given the same protections as information about individual humans, which is why we have Freedom of Information laws. I would even go so far as to say that this principle should apply to corporations, at least for information that is no longer commercially relevant.
We already have "public interest" exceptions for things like reporters exposing the private lives of politicians, and that sort of careful consideration also has to be applied to requests invoking "the right to be forgotten".
Anyway, even if a society didn't make DRM systems illegal outright, it could accept a legal judgement that "private keys" which are distributed to end user devices are not to be considered private. As a practical matter, though, if your DRM system relies on the secrecy of a key that can fit in a QR code, then you shouldn't expect the law to put that genie back in the bottle for you.
I think actually it is very simple. Obviously when you wish to watch some movie your privacy should not be compromised to the end of your life or the life of your computer. It's too much to demand from customer.
Just like when you buy an ice cream you do not expect that seller will be granted rights to visit your home whenever he wants from now on. Very simple. No DRM no problem.
If seller sells movies he should not install DRM to the customer nor demand it nor imply it. Because in attempt to control things that are impossible to control one can endanger much more important things which can lead to loosing rights, freedom and democracy and those are much more serious problems then some additional copies of some stupid movies which cannot be prevented anyway.
Ethereum is also DRM.
2. Because once you allow such things then soon any seller would feel safe to add any degree of tracking/ breaking privacy to any product... Oh wait,isn't it what is happening these days?
3. If you do not understand the value of privacy for the democracy then perhaps selling kidney when you buy ice cream example would work for you. Even if it is written between the lines it should be illegal, isn't it ?
That's a stretch. Same as Botswana's currency (Pula) which is a slang in Romania for male genitalia. Or India's ancient swastika symbol that is pretty much illegal in Western countries.
Mathematicians (in my humble experience) are also pretty clueless about law, but at least they can’t just make up shit that is fundamentally incompatible with reality[0]