Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Illegal Prime Numbers

en.wikipedia.org

Post reply on HN
Print view View original

51–60 of 109 posts

Re: Illegal Prime Numbers

#51

Post by dane-pgp »

dTal wrote: post #43
ACS_Solver wrote: post #16

Taking the same idea further, there are plenty of (possibly) illegal numbers that don't even have to be prime, just because an ASCII-encoded string of text can be represented as a number. A pair of GPS coordinates with five decimal precision, written like 7.63941, -122.12825 is just 19 ASCII characters. So in ~400 characters you could have 20 such pairs. 400 ASCII characters being 400 bytes or 3200 bits, they can be…

The minimum reasonable size of an "illegal number" is fairly comprehensively explored here [0] (tl;dr 128 bits) (You needn't be kept up at night by the thought of accidentally publishing nuclear codes; as you say, the probability is 0 for all practical purposes, and the reluctance of government agents to dismiss it as a coincidence would be entirely reasonable ) [0] https://qntm.org/number

I don't know about "reasonable", but much smaller numbers have, in practice, been banned in various contexts by legal authorities (tl;dr 2 to 11 bits).

https://en.wikipedia.org/wiki/Illegal_number#Other_examples

Re: Illegal Prime Numbers

#52

Post by Zircom »

bostonpete wrote: post #45
KMnO4 wrote: 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…

Just to be clear -- b/c I got a bit confused reading this -- this example seems to assume "12345" and "71" are base-256 numbers and "256" is base-10.

Once you compress the number it becomes stored in base-256 due to how the gzip file format works was my understanding

Re: Illegal Prime Numbers

#53

Post by uuidgen »

grishka wrote: post #41
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…

Because "illegal information" is an entirely artificial concept that doesn't hold if you think too much about it. You can't exactly "own" information, neither can you "destroy" it.

If you're the only person that knows a particular sequence of letters or numbers you own it.

If you remove all knowledge of that information you destroy it. And by "all knowledge" I mean every known way to generate it, not just a simple representation.

There is nothing special among any single number in 160 byte string, but it contains all SMS ever sent. Some of those messages are of special interest to some people.

Re: Illegal Prime Numbers

#54

Post by lupire »

grishka wrote: post #41
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…

Because "illegal information" is an entirely artificial concept that doesn't hold if you think too much about it. You can't exactly "own" information, neither can you "destroy" it.

Law is an entirely artificial concept. That's the whole point of it.

Re: Illegal Prime Numbers

#55

Post by lupire »

sweezyjeezy wrote: post #33
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…

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…

It's really amazing how many experts and professionals in information technology seem to understand what information is less well than stodgy old lawyers and politicians.

Re: Illegal Prime Numbers

#56

Post by uuidgen »

jasode wrote: post #29
upofadown wrote: post #25

Earlier quoted context omitted.

>...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…

"95601890" is just an arbitrary number, the same as any other.

Additional metadata, such as "it's a driver's license number", "it relates to person X" gives it context and makes it information. 4037 is a bank pin code for millions of people, but as long as you don't combine it with a person it's just a 4 digit number. When you combine it it becomes information protected in many countries.

Re: Illegal Prime Numbers

#57

Post by dane-pgp »

vbezhenar wrote: post #46
praptak wrote: post #19

Earlier quoted context omitted.

The point of the protocol is that both Bob and Alice can claim they were publishing a fully random string of bits and there is no way to disprove it. I don't see how the known pass phrase achieves that.

There's a way to prove it by XORing their streams. Just like there's a way to prove that given stream is AES-encrypted by trying to decrypt it with key published by Alice.

I think that a crucial point about XOR-based systems is that both Bob and Alice can produce the "other half" of their random-looking file which produces a legitimate non-random file (e.g. a video of their holiday), while claiming that the other party maliciously used the "first half" as the random-looking input against which they XORed their forbidden file.

Unless an omniscient observer knows the publication date of all the "halves" in the system, it is impossible to say which of Bob or Alice are telling the truth.

Of course, both parties are inherently slightly suspicious for using such a system in the first place, but if it existed as part of a free public hosting service, and lots of people used it for legitimate purposes, it might only be as incriminating as using BitTorrent.

Re: Illegal Prime Numbers

#58

Post by lupire »

jasode wrote: post #29
upofadown wrote: post #25

Earlier quoted context omitted.

>...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…

The law doesn't have exceptions for "a part of of happens to look like something legal"

Re: Illegal Prime Numbers

#59

Post by lupire »

jdc wrote: post #21
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.

Why would it be illegal to publish that particular executable? Was it harmful?

Re: Illegal Prime Numbers

#60

Post by jasode »

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…

I'm replying to myself to address some of the skeptical comments about my scenario because I didn't make it clear what I was trying to communicate.

I was trying to emphasize the people sharing the legitimate data and not the person who generated it from illegal data.

For example, the SHA256("Hamlet was a prince in Denmark.")=="4461565240549538f8888f5ac829800a79763479f28418dec7a13087a3e0d2a8".

Let's say the first 16 hex digits ("4461565240549538") is an "illegal number" ... e.g. somebody's credit-card or whatever.

Yes, the intent of starting with "4461565240549538" and using brute force to eventually find some a plausible sounding sentence that creates a hash with that 16-digit number can be prosecuted. Likewise, you can't just XOR a Blu-Ray mp4 file with digits of pi and claim "it's just a random number" to be immune from copyright laws.

I'm talking about the people downstream that do something like this by sharing on reddit, Twitter, etc:

- I ran across some Shakespeare trivia: "Hamlet was a prince in Denmark." I don't want anybody to hash it. I just thought that was interesting to know.

- Streisand Effect[1] the above tweet or forum post

- now everyone debates : How can the sentence "Hamlet was a prince in Denmark." -- be illegal?!? It's a factoid about a play that you can't remove from everyone's brain! We're now past the point of the criminal who brute forced the illegal data to publish it. I'm talking about the non-criminals sharing it. That's the information hack: Shift the illegal data into the realm of the legal data.

Maybe that hack hasn't been fully tested in courts but it seemed to work if we look at the DeCSS code repackaged as an interesting prime number. Neither Chris Caldwell and Phil Carmody have been put in jail.

It can also be especially effective if the would-be criminal who generated interesting hashes or prime numbers did it anonymously such as Satoshi Nakamoto's generation of the bitcoin genesis block. There's now no obvious person to prosecute.

[1] https://en.wikipedia.org/wiki/Streisand_effect

Post reply on HN