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Illegal Prime Numbers

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Re: Illegal Prime Numbers

#21

Post by jdc »

praptak wrote: post #14

Primes 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.

And 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.

Re: Illegal Prime Numbers

#22

Post by karatinversion »

abhishekjha wrote: post #20
praptak wrote: post #14

Primes 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.

> 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?

No, everything but single characters are composite numbers in Gödel encoding

Re: Illegal Prime Numbers

#23

Post by isitdopamine »

teddyh wrote: post #7

This 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

Interesting read!

It’s essentially the opposite of Aaron Swartz’s famous “Bits are not a bug” writeup.

Re: Illegal Prime Numbers

#24

Post by praptak »

feanaro wrote: post #8
teddyh wrote: post #7

This 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

How would the concept of colour be used practically in this case? Am I allowed to mention the prime number or am I not?

> 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.

Re: Illegal Prime Numbers

#25

Post by upofadown »

jasode wrote: 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…

>...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.

Re: Illegal Prime Numbers

#26

Post by DataWraith »

praptak wrote: post #15
heroku wrote: 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…

You're probably thinking of the OFFSystem (https://en.wikipedia.org/wiki/OFFSystem)

Re: Illegal Prime Numbers

#27

Post by praptak »

DataWraith wrote: post #26
praptak wrote: post #15

Earlier quoted context omitted.

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…

You're probably thinking of the OFFSystem ( https://en.wikipedia.org/wiki/OFFSystem )

This seems to use the same underlying idea as Monolith (which is the one I thought of - edited)

Re: Illegal Prime Numbers

#28

Post by tantalor »

upofadown wrote: post #25
jasode wrote: 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…

>...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.

https://shattered.io/

Re: Illegal Prime Numbers

#29

Post by jasode »

upofadown wrote: post #25
jasode wrote: 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…

>...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.

>The SHA-1 pre-image resistance would prevent that.

No, I'm talking about computing something much less ambitious than solving pre-image resistance.

Consider the example SHA-1 hash[1]:

  SHA1("")
  gives hexadecimal: da39a3ee5e6b4b0d3255bfef95601890afd80709
  gives Base64 binary to ASCII text encoding: 
  2jmj7l5rSw0yVb/vlWAYkK/YBwk=
Embedded in that hex is "95601890" ... which could be somebody's driver's license number. Now that the number is publicly visible via some legitimate purpose other than illegally publishing drivers license numbers, we can then argue "How can a SHA-1 of a empty string illegal?!?"

It's a similar concept to creating "vanity" public hashes for Tor or bitcoin addresses or finding a hash that has a certain number of leading zeros in "proof of work". Embedding arbitrary illegal information that way is more computationally feasible with brute force than perfect pre-image attacks.

The underlying idea of the hack is the same : Find some way to make illegal data be interpreted in a totally different way that _is_ legal. It's very hard to do for large amounts of information such as 9 GB mp4 rip of a Blu-ray disc -- but easier for small amounts of information... such as the DeCSS C source code converted to an "interesting" prime number.

[1] https://en.wikipedia.org/wiki/SHA-1#Example_hashes

Re: Illegal Prime Numbers

#30

Post by antirez »

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, 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.

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