Illegal Prime Numbers

You could slippery slope that argument ad infinitum, though. Even the interpretation combined with the data mean nothing if you don't have intent. And even with intent you have to have a computer. And even with intent and computer it has to be reasonable that you could use the computer. Let's imagine I am laying in my bed by the computer completely unable to speak or move. I can only breathe. But, I intended to copy a rights-protected DVD and then fell ill for 10 years while I had everything in place to do it sitting right there beside me? Are you going to charge me as I think there in a semi-comatose state? What if I was copying a copy-protected DVD, but in got stuck in the process, while I laid in my bed in a coma? What if the coma started immediately before the computer started executing the copy, and my pet mouse stepped on the keyboard, starting the copy? What if both the pet mouse and I had the intent to copy the DVD? What if the pet mouse's friend was watching in a nearby corner and had egged the pet mouse to touch the keyboard knowing that the copy-protection would be circumvented, but the pet mouse had no intent to circumvent, but I did, and I fell into a coma prior to the enter key being pressed by the mouse? What if the mouse spontaneously combusted atop the keyboard, pressing that key that the other mouse and I intended to be pressed, and the other mouse was an illegal, but had applied for citizenship of both the U.S. and Britain simultaneously while holding a non-resident visa for Australia while vacationing in the states, and was smoking a cigar in an area clearly marked as non-smoking?

All true, but there are cases where the jump from the primality to the lawbreaking is really really short.

For example, if the authorities compromise a CA/ISP/website's private key, they'll be prohibited from "tipping off" others that the corresponding public key is insecure. But (in the case of RSA), that knowledge is equivalent to "the authorities know that the factors of X are Y and Z" or even "X = Y times Z".

Yep, announcing a number's factors can be illegal.

That seems like a more interesting, non-convoluted kind of "illegal prime".

The interpretation of the data exists solely in our minds. Would that not make it, quite literally, thoughtcrime?

I think that it is better to think about it in terms of the 'colour of bits'. Bit colour can be thought of as an invisible property that follows a bit around whenever that bit is computed in a way that depends on another coloured bit.

Suppose n_1 is picked randomly (from a distribution that doesn't take into account any 'coloured' bits). Suppose n_2 is computed from illegally obtained data. Now suppose that numerically, n_1 == n_2. Mathematically, n_1 and n_2 are indistinguishable, but in the eyes of the law, n_1 is not coloured and therefore legal, while n_2 is illegal.

In practice, courts cannot see the colour of bits, so they have to infer the colour. If you claim that some data on your hard disk was randomly generated, but it is exactly the same as, say, a 100 GB copyrighted movie file. The probability of randomly generating such a small file (unless your distribution is stacked towards that file - which doesn't count as being uncoloured) is so small that it is not credible that you coincidentally generated it randomly, so the court will likely infer that the bits in that file are coloured.

Another more complex example: suppose I give you four bitstrings, A, B, C, and D. Let ^ represent bitwise XOR. Suppose that A is a representation of the complete public domain works of Arthur Conan Doyle, A^B is a public domain representation of War & Peace, B^C is a copyrighted novel (and the person distributing the strings doesn't have permission to distribute it). C^D is a public domain representation of the bible. Which bitstrings are illegal? To decide, a court will need to infer how you generated the strings. A is clearly not illegal because it matches a public domain work exactly. B is completely determined by A and the contents of War & Peace. To compute C, you would take a copyrighted work and xor it with B, so that makes C illegal to distribute without permission because it was derived from a copyrighted work. To compute D, you need C and the bible, and since C is coloured, D is also coloured.

But only data (i.e. the number itself, as bits) is transmitted over the Internet, not interpretations.

Off-topic: Wow, that author's friend really dramatically and thoroughly misunderstood 4'33".

It's not illegal to do that, and in the context in which it was illegal, that decision was overturned: http://www.theatlantic.com/national/archive/2012/11/its-time...

Ha! It was pretty funny to see practically the entire front page full of nothing but the key. I had friends who had their accounts banned by Digg at the time (I don't think they were ever reinstated), but soon afterwards, they threw their hands up and gave in to the swarm.

According to Wikipedia (http://en.wikipedia.org/wiki/AACS_encryption_key_controversy) the last 1 has to be a 0.

I would also like to know this. Why is it important that the number representing some code must be prime? Why not any number?

They could probably convince a judge that there is no reason anyone would ever use such a program for anything else.

I can't think of any other reason why someone would want to convert a string to a decimal number to binary, then dump it as a zip file, then unzip it. The separate components would be fine (i.e. base converter, bit writer, unzipper). But put it together, and you have a provable intent, unless you can show that it can be used for other legal things.

It's no different than the innumerable YouTube videos showing how to lock pick. They're not picking the locks of any specific location, just showing the methodology.

But high-powered lawyers can be persuasive to your detriment if you do distribute it so you may have to get crafty with the method. I.E. Print it up on paper and distribute calling it Free Speech ;)

Yup, I wish I could find my essay, but I wrote an essay in the 90's on this. That one day, numbers and arithmetic will be outlawed, because any data (program, image, movies, etc) can be presented by a number, and those numbers can be represented by a bunch of mathematical operations. So if we can copyright programs, then those numbers and any possible arithmetic operation to generate them will also by be copyright able and anyone possessing them without permission is breaking the law. This also applys to all possible forms of IP.

There's no compression. It's expansion, since null bytes were added to increase the digit length of the resulting prime, making it long enough to publish. For an arbitrary binary, the original (most likely non-prime) zipped representation is more useful since it's smaller.

Because then you'd have new dvd's that don't work on most dvd players... consumers would get mad... and DVD is kindda getting obsolete now that there's bluray.

because it allows control of hardware vendors via anticircumvention laws.

Roughly: 1. The letters and punctuation which comprise a computer program in human-readable form can be translated into a string of numbers.

2. That list of numbers can be looked at as if it were one really large number instead of a list of smaller ones.

3. By being a bit clever about how the original program text was translated into numbers, the resulting very-large-number was made to be prime, i.e. not evenly divisible by any numbers other than itself and one. Prime numbers hold a special place in the hearts of many mathematicians.

4. The social implication of all this is that what would have been illegal (rightly or wrongly) in the form of a computer program entered the public record instead in the form of a large number with mathematical significance.

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TL;DR:

The genius of this story is that Phil Carmody found a way to just ADD BITS to the end of a zipped, illegal program to make it a large publishable prime number. Even more brilliant is that if you convert the prime number back to binary (trivial) and unzip it, you get the illegal program. That is amazing.

----------------------------------------

  For the curious:

  Let "k" be your illegal program zipped in binary, interpreted as a number.
  
  Carmody created a buffer of zeroed-out bytes to the right of "k" to allow for a
  free space to search for prime numbers without tampering with the illegal bits
  on the left that he still wanted intact.  The unzip program will ignore
  everything after it anyway (either because of null terminating zeros or because
  the file size listed in the header would ignore it).


        (illegal bytes)                   (zero buffer)
                |                               |
                v                               v
  |---------------------------||--------------------------------|
  kkkkkkkkkkkkkkkkkkkkkkkkkkkkk0000000000000000000000000000000000

  
  He created this "zero buffer" of size "n" bytes by multiplying k by 256^n.  You
  already know that multiplying a base-10 number by 10^n adds "n" zeros to the
  right.  Multiplying a base-2 (binary) number by 2^n similarly adds "n" zeros to
  the right.  This is what "bit-shifting" is.   So, multiplying a binary number
  by 2^(8n) will add increments of 8 zeros (a zero byte) to the right of the
  number.  And if you know your rules, 2^(8n) = (2^8)^n = 256^n.

  Then, he modified the bits in this zero buffer to make the whole thing a
  prime number.


        (illegal bytes)           (left-over zero buffer)   (prime-making bytes)
                |                            |                |
                v                            v                v
  |---------------------------||---------------------------||---|
  kkkkkkkkkkkkkkkkkkkkkkkkkkkkk00000000000000000000000000000bbbbb
  

  He didn't do this directly of course.  We know from a popular theorem that
  there are an infinite number of values of "n" that make (k * n + b) a prime
  number, as long as "k" and "b" don't share any factors.  He presumed with
  high probability that (k * 256^n + b) would hit on that infinite space of
  primes, and he was right.  He found values of "n" and "b" to match his
  illegal "k" value to create a prime.

  To relate the equation to the visualization above:  "k" is the illegal bytes
  in the beginning.  "n" is the size of the zero buffer.  "b" is the prime-making
  bytes.