Illegal prime

http://en.wikipedia.org/wiki/Illegal_prime

by niyazpk • 17 years ago

152 76 17 years ago

en.wikipedia.org

wizard_2• 17 years ago

I bring this up whenever I want to point out how law lags behind technology and ends up doing silly things like making a number illegal, or making cracking cyphers like rot13 a felony. That is to say, breaking even simple encryption a felony, not rot13 specifically.

People always get amused that a prime number could get them in trouble.

k4st• 17 years ago

A more relevant example, as mentioned in a linked article, is that the binary data of images such as child pornography and state secrets are also numbers and as such may be considered illegal.

Rod14• 17 years ago

How can an image be a number? This is an honest question.

Isn't an image a list of numbers? These numbers could the RGB of each pixel, or the N higher Fourier coefficients, etc. From these numbers, one can compute a single number, sure. Nonetheless, the idea that an image is a number and, hence, can be made illegal, looks utterly ludicrous to me due to the fact that the image -> number mapping is certainly not injective.

Confusion3• 17 years ago

This has nothing to do with law lagging behind technology.

Even before computers, the ability to express language in a number was well known. If someone turned a defamatory sentence into a number and spread that number together with the key to turn it into the sentence, then they would be just as guilty of defamation as when they had spread the original sentence.

I surely hope you do not advocate getting rid of all laws that deal with information that could be expressed in a number, because you feel it should not count as the same incriminating information, just because it was masked with some mathematics?

WilliamLP• 17 years ago

This is pretty silly, isn't it? Is it that mind-boggling that data can be illegal to distribute, for example a movie or an unreleased game?

The prime number is a red herring. Given the prime number theorem, the probability that an n-digit number is prime scales as 1/log n, so it's easy to pad any data with random garbage that isn't executed until you get a prime. For a gigabyte of data that might be a few billion attempts. (Proving it's a prime will be harder.)

niyazpk4• 17 years ago

>> Is it that mind-boggling that data can be illegal to distribute...?

The DMCA has had an impact on the worldwide cryptography research community, since an argument can be made that any cryptanalytic research violates, or might violate, the DMCA.

- http://en.wikipedia.org/wiki/Digital_Millennium_Copyright_Ac...

That is mind-boggling.

fserb2• 17 years ago

I think the argument that "how can a number be owned or its posession be illegal" is mostly bogus. One could translate any string of text into a series of bits and back to a single number and say that a book or a picture is just a number. Then one could say that noone invented that number, and that it's just a number, so you couldn't have copyright nor protection because everything could be randomly generated, etc, etc...

I think the real issue is that in the case of prime numbers made "illegal/protected", the absurd is not that they are protected, but that they are not encoding any meaningful information that a human being produced. They are a particular number (probably randomly generated) and the fact that they are used in a particular context (to encrypt data) makes them protected.

jerf2• 17 years ago

"but that they are not encoding any meaningful information that a human being produced"

I was sort of with you up to that point; I don't agree, but I was with you. However, now I would say you need to read the article more carefully, as the entire point is that they do indeed encode something human-produced and usable. If you use Unix, you've almost certainly got the decoder for that number sitting right on your disk right now, it doesn't get much more concrete than that. Without that, you're missing the whole point. They aren't randomly generated at all.

Guess I might as well spell out the other objection I have, which is that you're subtly begging the question. You prove that the idea of owning a number is silly because the idea of owning a number is silly in your last sentence of your first paragraph. Let me give you a much better argument: flip your argument on its head, and say that of course it's perfectly sensible to own numbers.

All but the smallest works translate in any reasonable encoding scheme into enormous numbers, numbers that would simply never be chosen randomly. There 0 chance that sitting here and stringing together "random numbers" will ever produce anything like a movie or picture or even coherent sentence, that doesn't already exist in the encoding scheme. (Not literally 0, depending on the circumstances, but close enough.) Therefore, the actual problem is that it does indeed make sense to own numbers; in an infinite space when we are all choosing umpteen millions or billions or trillions or well beyond that of digits, one can very plausibly stake an ownership claim on the grounds that it is clear that if somebody else ends up with the exact same number, they got it from you.

Therefore, since it is sensible to own numbers, the objection that it is not collapses and then the rest of the argument against ownership does too.

As I said, I don't actually agree with that line of thought. There are a lot of intricacies in the issues of encoding, and some other objections I'm leaving out, but it's still a stronger line of argument. My feeling are more related to the classic bit color essay: http://ansuz.sooke.bc.ca/lawpoli/colour/2004061001.php If that doesn't seem related, think more; it is, it very much is.

fserb2• 17 years ago

yes it does represent something human-produced but the number is not said to be illegal because the human-produced thing is protected. The number is deemed illegal because there is a convoluted way in which it could be used illegally. My point is that the protected entity is a very abstract thing much disconnected from the number itself. And therefore it does not make sense to protect it.

Regarding your second point, it is obvious to me that it is related to the bit color issue. I was trying to make a similar point to yours, but maybe I failed. Let me try again: I don't think that making this rationale of "oh, it becomes a number therefore it can't be owned" is a proper argument. Exactly because anything can become a number and we do acknowledge properties to things (like a text of a book) that would be ridiculous for a pure number to have.

My point was that even though the "just a number" argument is bad, there are other points to be made on the stupidity of this particular protection.

tjic• 17 years ago

> you're subtly begging the question.

You are the first person to correctly use the phrase "beg the question" in something I've read in the last three weeks.

Congratulations!

Confusion3• 17 years ago

The argument is bogus, because it's not the number itself that is illegal: it is the number plus the necessary meta data required to turn the number into something that has been outlawed.

It is like saying that it is silly that we prosecute people for possessing television sets, when the case under consideration is someone possessing a television set previously in the possession of someone else. If you do that, you are hiding contextual information that changes the meaning of what is being said.

As in the case of the television set, someone would only be convicted of 'possessing' or 'distributing' the number, if it was beyond reasonable doubt that he intended to break the law using the number. The number itself doesn't break the law: the actions/intent of the user is what breaks the law.

jfager3• 17 years ago

it is the number plus the necessary meta data required to turn the number into something that has been outlawed.

Where in the DMCA does it say that? And even positing that it does (though I'm pretty sure it doesn't), would that mean my possession of this prime, a linux distro, and this article in my browser history constitutes a crime?

The number itself doesn't break the law: the actions/intent of the user is what breaks the law.

Again, you're not talking about the actual DMCA. The actual DMCA implies that the intent of the user may be irrelevant if the primary purpose of the thing itself is to circumvent DRM tech. That's the whole point: the law is so poorly written and broadly applicable that nobody really knows what you can and can't do under it.

njharman• 17 years ago

It is illegal to distribute a "device"(very broad definition) that can circumvent DRM.

The protest is against how broad and vague that prohibition is and that it prohibits items even if their normal/much more useful function has nothing to do with DRM. Such as prime numbers or Sharpie markers. A "Hey legislators, in your scramble to sell out to content industry you've just made these numbers illegal." kind of thing.

jfager3• 17 years ago

The provision in the DMCA that this addresses says you can't make or distribute anything that is designed or primarily intended for breaking DRM tech.

A DVD decryption algorithm obviously is designed and primarily intended to circumvent DRM, and a prime number obviously is not. The fact that the former can be expressed as the latter effectively means the provision is either absurdly lenient or absurdly draconian. It's a law that leaves you in the dark as to what you're actually allowed to do without the threat of prosecution or legal harassment.

jodrellblank• 17 years ago

"One could translate any string of text into a series of bits and back to a single number and say that a book or a picture is just a number. Then one could say that noone invented that number, and that it's just a number, so you couldn't have copyright nor protection because everything could be randomly generated"

You could be on to something big there, maybe a new kind of science, even.

jacquesm2• 17 years ago

On behalf of Stephen Wolfram, "Ouch".

wmf• 17 years ago

Except in NKOS-land, Wolfram has copyright on all the numbers that you might possibly ever generate...

oscardelben• 17 years ago

I still don't get how a prime number can reveal hidden information. Can someone please explain me the process?

niyazpk4• 17 years ago

From the article: Its binary representation corresponds to a compressed version of the C source code of a computer program.

etherealG• 17 years ago

it doesn't reveal information except that it is a constant that is used as part of a process of encryption where without the constant cracking that encryption would be effectively impossible and with it cracking the encryption is trivial.

effectively the number is the encryption, as having the number makes the encryption useless. the rest of the algorithm is pointless without the number and vice versa.

lt• 17 years ago

That's a different number, not the one the article is about.

The one in question is a compressed version of a c program that breaks encryption.

ErrantX3• 17 years ago

For all those commenting please read it carefully: the primes are not illegal, just number representations of apparently illegal programs.

randomwalker• 17 years ago

Y'all totally missed what's going on here.

Primepages (http://primes.utm.edu/) lists the largest known primes of various forms. One of the categories is primes that have no special form, which are the hardest to prove prime.

Chris Caldwell, the primepages maintainer, called up Phil Carmody and said, "Phil, if you can turn DeCSS into a 'general prime' that's big enough for the top 20 ever discovered, I'll be happy to host it on primepages." (Just as he would host any prime, DeCSS or not, that was big enough for the top 20.) So Phil did, cuz he's a smart guy and had a lot of computrons, and the prime went in the database.

The point here is that if you're merely turning data into a number, you have no legitimate reason to distribute it other than whatever reason you had to distribute the data itself. However, primepages existed long before DeCSS became a problem, and was arguably simply doing what it always did, which is to list the top tens.

I don't know if that would hold up in court -- it was never tested -- but the argument is a lot more subtle than what people are criticizing here.

An aside: Phil and I worked together on some other primality records. I wrote most of that Wikipedia article back in 2002 or so, and they went and featured it.. this was all before the rules for citations/references on Wikipedia became tighter than a mouse's arsehole. So if anyone is in the mood to add some citations, that would be much appreciated.

tshaddox• 17 years ago

I don't see how "a reason to distribute it" is necessary. What if I just choose a completely random integer with 2000 digits and host it? I don't have any reason to do so, and it's certainly not illegal. Then someone comes along and generates a program that's equivalent to that number, or some digital media rights developer happens to use that number as a key for encrypting some copyrighted media. Does my original act of hosting suddenly become illegal, because I had no good reason to host the number in the first place?

yoden2• 17 years ago

The probability of you doing that without piracy is so vanishingly small as to be irrelevant.

yoden2• 17 years ago

This is actually a really interesting idea I can't believe I haven't heard of yet. No matter what the angry neckbeards might say, just because content is a number doesn't mean copyright is invalid.

Obviously, we can generalize this approach to more than primes. Still, I imagine any idea would be extremely hard to scale up to mp3/video/game sizes, so it looks like those content industries are safe for now.

mixmax3• 17 years ago

A Danish Social security number consists of two numbers - the first one being four arbitrary digits, and the second one being the six digits of your birthday.

My two numbers aren't only prime, which in and of itself would be pretty unlikely. No they're Twin primes. (http://en.wikipedia.org/wiki/Twin_prime)

This is the only place I know where information like that would be considered pretty cool :-)

Now somebody guess my birthday.

yan• 17 years ago

Now someone can guess your entire social security number :P

mixmax3• 17 years ago

Calculated risk

pvg2• 17 years ago

Which two numbers? It's quite difficult for a six digit and four digit number to be twin primes. Some zany Danish date format?

_cbsz• 17 years ago

Impossible? Danes write dates as dd-mm-yy according to http://en.wikipedia.org/wiki/Calendar_date, so your birthday can have at most one leading zero and thus is >= 10100. 9973 is the largest 4-digit prime number, and 9973 + 2 is 1) not prime and 2) not a 5-digit number.

mixmax3• 17 years ago

We're talking about two sets of twin primes, each part of the social security number being in each set. I'm sorry I didn't make it clear in the OP.

niyazpk4• 17 years ago

Assuming that (1) you were born between 1950 and 1985 and (2) the danish date format is (dd-mm-yy), here are the possible DOBs:

    10-01-51    30-01-51    17-03-51    14-05-51    26-05-51    27-05-51
    13-06-51    16-06-51    16-07-51    18-07-51    25-07-51    25-09-51
    15-10-51    21-10-51    24-10-51    21-11-51    13-12-51    17-12-51
    19-12-51    28-12-51    10-01-53    17-03-53    27-05-53    16-07-53
    25-07-53    21-11-53    17-12-53    24-02-57    29-06-57    25-10-57
    13-02-59    24-02-59    21-03-59    29-06-59    14-07-59    17-07-59
    22-08-59    15-09-59    25-10-59    26-10-59    10-11-59    24-12-59
    13-02-61    10-03-61    21-03-61    31-03-61    27-04-61    23-05-61
    14-07-61    17-07-61    27-07-61    22-08-61    23-08-61    26-08-61
    15-09-61    12-10-61    18-10-61    21-10-61    26-10-61    10-11-61
    17-11-61    24-12-61    25-12-61    10-03-63    31-03-63    27-04-63
    23-05-63    27-07-63    23-08-63    26-08-63    12-10-63    18-10-63
    21-10-63    17-11-63    25-12-63    13-03-67    19-03-67    11-05-67
    19-06-67    15-07-67    14-08-67    20-08-67    16-09-67    25-09-67
    24-10-67    17-11-67    26-11-67    29-11-67    27-02-69    13-03-69
    17-03-69    19-03-69    22-04-69    11-05-69    19-06-69    29-06-69
    15-07-69    28-07-69    14-08-69    20-08-69    16-09-69    25-09-69
    22-10-69    24-10-69    12-11-69    15-11-69    17-11-69    26-11-69
    29-11-69    11-12-69    23-12-69    27-02-71    17-03-71    22-04-71
    29-04-71    29-06-71    23-07-71    28-07-71    22-10-71    12-11-71
    15-11-71    22-11-71    11-12-71    23-12-71    29-04-73    23-07-73
    22-11-73    15-03-77    11-04-77    19-05-77    16-08-77    22-08-77
    17-10-77    25-11-77    27-12-77    18-01-79    15-03-79    11-04-79
    19-05-79    11-08-79    16-08-79    22-08-79    17-10-79    14-11-79
    25-11-79    10-12-79    27-12-79    18-01-81    20-03-81    16-04-81
    30-05-81    14-06-81    11-08-81    15-08-81    24-08-81    14-11-81
    30-11-81    10-12-81    20-03-83    16-04-83    30-05-83    14-06-83
    15-08-83    24-08-83    30-11-83

smokinn• 17 years ago

Thanks for the list but he said 6 digits... So the format is probably dd-mm-yy.

pvg2• 17 years ago

Assuming you're talking about splitting your SSN down the middle (two 5 digit numbers) and it looks something like this

http://en.wikipedia.org/wiki/Personal_identification_number_...

The candidates are (unless I horked something up, these are pairs of 5 digit twin primes that start with a sensible 6 digit date and checksum as Danish SSNs)

0212702129 0608706089 2105721059 2210722109

That's assuming you were not born in '90 or '91.

Illegal prime

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