

Illegal Prime Numbers - epenn
https://en.wikipedia.org/wiki/Illegal_prime

======
gilgoomesh
[ Ignoring the morality of making ideas illegal... ]

This demonstrates the difference between data (i.e. the number itself) and
information (the interpretation of data and use cases derived from that
interpretation).

What is "illegal" here is certain kinds of encryption and security software. A
prime number is not the same thing as encryption and security software. But
you can specify processes which allow encryption and security software to be
uniquely identified by a prime number. The interpretation _combined_ with the
data is what's important, not the data in isolation.

~~~
SilasX
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".

~~~
IanCal
Putting the number 07574635453 on a website can be illegal. Putting the number
35.672 on a website can be illegal. Terrible isn't it! I could be sent to jail
for sending someone
"1101001100111110110111001111101111110100111011101100111111010011011111101011110100111011001101100111100111011111110101"!

No, since the first could be in the context of me releasing personal
information, and the second could be the quarterly earnings before they're
released publicly. Or someones wages, or someones password, or the location of
a witness in hiding, or the binary representation of a libellous claim, or
harassment (but I only sent 0s and 1s in a message on facebook your honour!),
or a million other things that we all agree are illegal.

It's an incredibly boring, and over-repeated statement that you can represent
information as numbers and therefore you can have ILLEGAL NUMBERS! What will
the poor maths teachers do?

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

If you do so with the intent of breaking encryption I'm sure there are
situations where it would be illegal.

Intent, as is so often ignored when legal matters come up, is incredibly
important.

~~~
dllthomas
And if the intent is to watch legally purchased DVDs on a legally purchased
computer with a legally purchased DVD drive running my choice of operating
system, and I'm a 14 year old Norwegian kid, clearly prosecution is warranted.

~~~
IanCal
Are you accusing me of suggesting that is the case?

~~~
dllthomas
Not really. I understood you to be speaking in a more idealized mode, and was
criticising those who failed to live up to it.

------
wmf
Obligatory link: What Colour are your bits?
[http://ansuz.sooke.bc.ca/entry/23](http://ansuz.sooke.bc.ca/entry/23)

The fact that this Wikipedia article exists at all embarrasses me.

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

~~~
ryanthejuggler
"Now, the preceding paragraph is basically nonsense to computer scientists or
anyone with a mathematical background. (My friend is one; he'd done this as a
sort of elaborate joke.)"

Misunderstood in the way Douglas Adams "misunderstands" physics; i.e., the
best way possible.

------
davidw
It's also illegal to yell "fire!" in a crowded theater. Presumably, that can
also be encoded as a number.

While it's an interesting perspective, it does not strike me as particularly
_useful_ in the debate about intellectual property, free speech, etc...

~~~
waqf
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...](http://www.theatlantic.com/national/archive/2012/11/its-time-to-stop-
using-the-fire-in-a-crowded-theater-quote/264449/)

~~~
IanCal
As an alternative then, harassment over the internet and libellous statements.

------
fulafel
What's the big deal about this, are prime numbers so special that they should
be granted some kind of diplomatic immunity?

IOW what's the difference about this and ranting about illegal even numbers.

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

~~~
shawabawa3
The idea was to have a legitimate reason to publish the code.

He found a representation of the code that was also the tenth largest prime
found using ECPP meaning he could publish the finding and claim he wasn't
publishing the code. However, anyone who wanted the code could easily find it
by looking up the prime

------
joshfraser
Digg This: 09-f9-11-02-9d-74-e3-5b-d8-41-56-c5-63-56-88-c1

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

~~~
joshfraser
Good catch. I couldn't find the original post on Digg, so I used Google to
find other people discussing it. It looks like the publisher I copied was too
scared to publish the key verbatim.

------
easytiger
Why did it have to be Prime? Wh not just from the set of natural numbers
alone?

Edit: ahh he wanted an excuse to publish it which you wouldnt get with a non
prime

~~~
felipelalli
[http://en.wikipedia.org/wiki/Illegal_number](http://en.wikipedia.org/wiki/Illegal_number)

------
bromagosa
These stupid scenarios are direct consequences of software patents.

I remember an article that used Haskell to show how absurd software patents
are by showing how any piece of software is actually just a mathematical
formula that turns some input (however big) into some output.

------
stevetursi
Earlier this year, Numberphile (which is a fantastic youtube channel) created
a very accessible video about this topic.
[http://www.youtube.com/watch?v=wo19Y4tw0l8](http://www.youtube.com/watch?v=wo19Y4tw0l8)

------
wbhart
If you have a strong RSA modulus, e.g. 2048 bits, then the primes we are
talking about are about 1024 bits.

There is no way you are going to hit such a prime number at random. Not even
if you set a million fast computers going in a million universes on every
planet in those universes. Certainly not before heat death of this universe.

The only way you are going to have an interest in this prime is as a factor of
someone's RSA key (for which you will need not-yet-invented algorithms of
great sophistication and probably an enormous amount of computer time to find
in the first place).

On principle, the idea of illegal numbers is stupid. Actually, on second
thoughts, it is stupid either way. It is basically serving only as a legal
backstop for a situation that by definition shouldn't need one.

------
auggierose
The question is: The program that recovers from the illegal prime number the
original source code, is that program legal and freely distributable?

~~~
eksith
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 ;)

------
praptak
Hey, I can append a bit to a string of bits...

Behold! Illegal odd numbers!

------
jostmey
Simply outrageous. What is next? Intellectual property on arithmetic?

~~~
segmondy
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.

~~~
schoen
Eben Moglen talked about the different legal regimes that were applied to
different classes of information (which programmers might view as different
numbers) in "Anarchism Triumphant", at
[http://emoglen.law.columbia.edu/publications/anarchism.pdf](http://emoglen.law.columbia.edu/publications/anarchism.pdf)

I think it's an interesting read in conjunction with "What Colour Are Your
Bits" (suggested above).

------
vignesh_vs_in
Prime numbers can provide the ultimate form of compression. If only there was
a way to find a corresponding prime number per code base.

~~~
theatraine
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.

~~~
IgorPartola
I think he is saying that for example the Linux kernel version 3.11 would be
the Nth prime.

------
qwerta
I have question: If DVD encryption was broken several years ago, why is it
still used?

~~~
NKCSS
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.

~~~
aw3c2
I think he meant dropping the encryption all together. Would players not be
able to play non-encrypted discs?

~~~
Zak
DVD encryption combined with anticircumvention laws mean DVD players that can
skip no-skip content or play out-of-region DVDs aren't sold to mainstream
consumers.

Without anticircumvention laws, there would be no incentive to use encryption.
Such laws have nothing to do with piracy; they're about maximizing revenue
from paying customers.

------
LordHumungous
Someone explain for us normals.

~~~
undershirt
\----------------------------------------

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.

~~~
edolstra
I'm sorry, but how exactly is this "amazing"? That you can find some bits to
append to a number such that it becomes prime is rather obvious, given that
there are an infinite number of primes and (probabilistic) primality tests are
readily available. As other have pointed out, this is no more interesting than
the fact that adding a "1" bit yields an odd number.

And what's the point? Yes, illegal information can be encoded as bits, those
bits interpreted as numbers, and then you can apply transformations to those
numbers. So what?

~~~
homeomorphic
The point is that certain large prime numbers (of certain forms) are curated
and published in a catalogue because they are notable (in and of themselves).
The process you dismiss as trivial allowed Carmody to encode the illegal
program as such a prime, and hence have it independently published in said
catalogue, where it belongs _entirely independently of whether it happens to
turn into the illegal program when run through gunzip_.

------
felipelalli
This is why libertarians are against intellectual "property".

