11 ms·
Illegal Prime Numbers
- dezmou 6y agoI understand that one number can be the binary equivalent of a protected source code, but I don't understand why the fact that it is a prime number is important.
- bjornsing 6y agoIf it was composite then at least you could factor it into (hopefully) legal numbers and distribute those. :P No, jokes aside I don’t know either.
- heroku 6y agoYou can still distribute as a sum of legal numbers.
- st_goliath 6y ago"Any integer can be expressed uniquely as a sum of unique powers of even primes."
- praptak 6y agoThere's a proof-of-concept file sharing protocol (Monotone? I cannot remember the name. Edit: it's monolith.sourceforge.net) that distributes numbers as xor of legal numbers. 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.
- vbezhenar 6y agoBob publishes encrypted data. If it’s legal, just use AES with known pass phrase, its output looks random enough.
- praptak 6y agoThe point of the protocol is that both Bob and Alice can claim they were publishing a fully random string of bits and there is no way to disprove it. I don't see how the known pass phrase achieves that.
- vbezhenar 6y agoThere's a way to prove it by XORing their streams. Just like there's a way to prove that given stream is AES-encrypted by trying to decrypt it with key published by Alice.
- dane-pgp 6y agoI think that a crucial point about XOR-based systems is that both Bob and Alice can produce the "other half" of their random-looking file which produces a legitimate non-random file (e.g. a video of their holiday), while claiming that the other party maliciously used the "first half" as the random-looking input against which they XORed their forbidden file. 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.
- vbezhenar 6y agoThat makes sense, thanks.
- DataWraith 6y agoYou're probably thinking of the OFFSystem (https://en.wikipedia.org/wiki/OFFSystem https://en.wikipedia.org/wiki/OFFSystem)
- praptak 6y agoThis seems to use the same underlying idea as Monolith (which is the one I thought of - edited)
- MauranKilom 6y agoThat's covered by this essay: https://ansuz.sooke.bc.ca/entry/23 https://ansuz.sooke.bc.ca/entry/23
- dezmou 6y agoI Missread it "...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."
- sweezyjeezy 6y agoJust because it has a secondary reason of interest, it doesn't negate the original intent (especially when the original intent has been documented by the author). I doubt this would stand up if legally challenged. 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.
- panosfilianos 6y agoWhat's interesting in this case is that I may know that an entity has such a number in possession. By encrypting sensitive IP with that number, do I force that entity to break the law?
- dane-pgp 6y agoHopefully the targeted entity could prove that they had the number in their possession for longer than your encrypted data existed, but this is an interesting question. 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.
- dezmou 6y agoDoes the guy actualy had to test many version of the code by adding some useless instruction only to change the binary final number ? like mining a bitcoin
- teddyh 6y agoThis is pretending that bits don’t have color¹. In one way they don’t, but in another they do. 1. https://ansuz.sooke.bc.ca/entry/23 https://ansuz.sooke.bc.ca/entry/23
- feanaro 6y agoHow would the concept of colour be used practically in this case? Am I allowed to mention the prime number or am I not?
- teddyh 6y agoIt depends of the color of the number. If the color is that of a simple prime number, which you mention purely for its characteristics as a number, then you would theoretically be allowed. Otherwise not.
- feanaro 6y agoLet's assume my intent for publishing the paper was clean and I was not attempting to subvert colour. What happens if word spreads around on the internet that the prime number in my paper is actually the illegal DeCSS prime number, making it into an efficient avenue of its dissemination and distribution? Is my paper going to get censored or not?
- teddyh 6y ago> Is my paper going to get censored […]? 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.
- praptak 6y ago> Am I allowed to mention the prime number or am I not? 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.
- nxpnsv 6y agoThis rabbithole led me to http://fatphil.org/maths/illegal2.html http://fatphil.org/maths/illegal2.html - non-trivial executable primenumbers are amazing.
- sleavey 6y agoJust goes to show that copyright laws are incompatible with reality.
- NaturalPhallacy 6y agoCopyright laws exist exclusively for the benefit of lawyers.
- praptak 6y agoPrimes are pretty dense. If you can encode something as a number, then you can encode it as a prime number with enough padding. 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.
- abhishekjha 6y ago> If you can encode something as a number, then you can encode it as a prime number with enough padding. Isn’t this what godel’s encoding does?
- karatinversion 6y agoNo, everything but single characters are composite numbers in Gödel encoding
- jdc 6y agoAnd yet regardless debate about hypotheticals, Phil Carmody discovered the first non-trivial executable titanic prime, Professor Caldwell published it and neither of them faced repercussions.
- dTal 6y agoExactly. Primality is nothing more than a misleading intuition pump to make you think in terms of "innocent bit of number theory", instead of "encoded data file". Even the term "illegal number" is designed to make you think this way; somehow, "legally protected secret" doesn't sound quite so absurd.
- ACS_Solver 6y agoTaking the same idea further, there are plenty of (possibly) illegal numbers that don't even have to be prime, just because an ASCII-encoded string of text can be represented as a number. 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.
- dTal 6y agoThe minimum reasonable size of an "illegal number" is fairly comprehensively explored here [0] (tl;dr 128 bits) (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) [0] https://qntm.org/number https://qntm.org/number
- dane-pgp 6y agoI don't know about "reasonable", but much smaller numbers have, in practice, been banned in various contexts by legal authorities (tl;dr 2 to 11 bits). https://en.wikipedia.org/wiki/Illegal_number#Other_examples https://en.wikipedia.org/wiki/Illegal_number#Other_examples
- jasode 6y agoThere are several past threads of this article but this comment about how the DeCSS illegal prime was created seemed the most interesting: https://news.ycombinator.com/item?id=1045394 https://news.ycombinator.com/item?id=1045394 This might be thought of as a human version of a covert channel: https://en.wikipedia.org/wiki/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...
- upofadown 6y ago>...what if we wrote a text commentary about Shakespeare's Hamlet that when SHA-1 hashed, it gives you that same information? 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.
- tantalor 6y agohttps://shattered.io/ https://shattered.io/
- GuB-42 6y agoThis is a collision attack, much weaker than pre-image. It means that you can make two different texts with the same hash, but you can't create a text that matches a specific hash. 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).
- 6y ago
- antirez 6y agoNot only this concept has a great deal of triviality, because everything you can digitally encode will have a corresponding prime (often you can change the encoding slightly, yet the binary format is still valid, so you can perform random changes and run a fast primality test, until you find a good candidate). 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.
- batch12 6y ago> What's the gist of all this? 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.
- unnouinceput 6y agoQuote: "Its binary representation corresponds to a compressed version of the C source code of a computer program implementing the DeCSS decryption algorithm, which can be used by a computer to circumvent a DVD's copy protection" 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.
- KMnO4 6y agoThe process is fairly simple. 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.
- Y_Y 6y agoDo you imagine a judge would just say "well fuck it, he published the illegal number, but appended some shit to the end, so maybe it's just an astronomical coincidence"?
- bzbarsky 6y agoThe point is, if the resulting prime number is large enough to be in the very public "list of N largest known primes", how do you keep it out of that list, exactly? 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.
- bostonpete 6y agoJust to be clear -- b/c I got a bit confused reading this -- this example seems to assume "12345" and "71" are base-256 numbers and "256" is base-10.
- Zircom 6y agoOnce you compress the number it becomes stored in base-256 due to how the gzip file format works was my understanding
- 6y ago
- amelius 6y agoIf N is illegal, then could N+1 be legal or not?
- dane-pgp 6y agoI think all we can say is that if N is an illegal prime, then N+1 is not an illegal prime. Well, I suppose a government could try to ban the numbers 2 and 3, but it might have trouble complying with that law itself.
- SamBam 6y agoI think the purpose is the intent. 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.
- amelius 6y agoPeople believe (although there is no proof) that any finite sequence of bits appears somewhere in pi, making pi an illegal number :) https://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations https://math.stackexchange.com/questions/216343/does-pi-cont...
- curryst 6y agoIf true, that could be an exceptionally interesting method of compression. Any volume of data can be compressed to two numbers: an offset and a length. Presuming we have a way to "stream" the numbers, rather than having to calculate the entire value.
- thestoicattack 6y agoWe do have such a digit-extraction algorithm: https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...
- tyilo 6y agoThis has been done: https://github.com/philipl/pifs https://github.com/philipl/pifs
- zild3d 6y agoalso means the offset can be larger than the data
- SamBam 6y ago...and almost always is, except in the trivial cases of tiny numbers right near the start. Which is why it doesn't actually work as an encryption algorithm. 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.
- MayeulC 6y ago> Following this, Carmody discovered an 1811-digit prime—this one being non-compressed, directly executable machine language in the ELF format for Linux i386, implementing the same DeCSS functionality. I found that to be an interesting rabbit hole: https://primes.utm.edu/glossary/page.php?sort=ExecutablePrime https://primes.utm.edu/glossary/page.php?sort=ExecutablePrim...
- lovelyviking 6y ago>it describes a computer program that bypasses the digital rights management scheme used on DVDs. 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?
- comboy 6y agoObviously. But the issue is not that simple. Do you think any kind of information should be protected by law? Because I can think of a few examples. 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.
- dane-pgp 6y ago> So where do you draw the line? 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.
- cannabis_sam 6y agoHow clueless about mathematics do you have to be, as a professional in the legal field, to propose this type of garbage? 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] [0] https://en.m.wikipedia.org/wiki/Indiana_Pi_Bill https://en.m.wikipedia.org/wiki/Indiana_Pi_Bill
- FrozenVoid 6y agoIf any number is illegal, all numbers in such size range A xor B can be made illegal(even though A or B are both perfectly mundane, xoring them creates an illegal number, so they're now illegal too). * Xoring the original illegal number with any random legal number A of same size creates a new (also random) number B that (A xor B) restores the original.
- whatgoodisaroad 6y agoI could imagine a somewhat cynical science fiction story where Earth manages to communicate with an intelligent alien species using fundamental constants and rules of mathematics. But then, the aliens transmit a prime that the humans have happened to have declared illegal and have no choice but descend into interplanetary copyright war.
- dane-pgp 6y agoSlightly more realistic would be a story about a technocratic nation that changed its flag to something like a "Free Speech Flag" (as mentioned in another comment) containing a representation of an illegal number, with the global media industry then conspiring to generate support amongst the public for regime change in that nation.
- goatcode 6y agoThat's how you deal with trolls from countries with very strict language laws.
- deleted 6y ago[deleted]