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Illegal Prime Numbers

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31–40 of 109 posts

Re: Illegal Prime Numbers

#31
Quote: "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.

Re: Illegal Prime Numbers

#32
The 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.

Re: Illegal Prime Numbers

#33
post #17

There 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 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…

I think this is less a philosophical argument than a legal one. If a court can prove that you explicitly owned the illegal data in its raw format, and used that to generate something (even if it has secondary value), they should be free to prosecute in my opinion. That includes searching through and highlighting data that already exists in the wild such as large prime numbers. Presumably showing statistics of how often random data would decode to someone's credit card number would prove this beyond reasonable doubt.

The fact all data exists 'in nature' - while interesting, is not something I think should override the intent of data laws.

Re: Illegal Prime Numbers

#35
post #32

The 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 (12345x…

Do 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"?

Re: Illegal Prime Numbers

#36
post #17

There 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 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…

I think this is less a philosophical argument than a legal one. If a court can prove that you explicitly owned the illegal data in its raw format, and used that to generate something (even if it has secondary value), they should be free to prosecute in my opinion. That includes searching through and highlighting data that already exists in the wild such as large prime numbers. Presumably showing statistics of how oft…

Yes. A commentary on Shakespeare that just happens to hash to Bill Gates' personal details is so monumentally unlikely to occur by accident that its existence constitutes proof of intent beyond all reasonable doubt. Disingenuously asserting that "it's education!" is a bit like the mafia boss asserting that no, the front business really is a laundromat.

https://qntm.org/number

Re: Illegal Prime Numbers

#37
post #30

Not 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,…

> 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.

Re: Illegal Prime Numbers

#38
post #15
post #11

Earlier quoted context omitted.

You can still distribute as a sum of legal numbers.

There'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…

That's covered by this essay: https://ansuz.sooke.bc.ca/entry/23

Re: Illegal Prime Numbers

#40
> 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=ExecutablePrim...

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