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".
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.
> 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.
I'll disagree. I think that things like publishing passwords, quarterly earnings, wages, locations of people, etc. should only be "illegal" in the civil sense: if people have contractually agreed to not release such information, then they should be liable for damages if they violate the contract. I don't think libel should be illegal, and surprisingly, the UN Human Rights Committee seems to agree: http://www.mediadefence.org/news-story/un-rules-against-crim.... I'll concede that harassment is a tricky one, because it's a rather vague term that can range from "frequently annoying someone" to "threatening someone with violence."
The example I gave involved a lot more than the pedestrian observation that "arbitrary strings can be interpreted to mean illegal stuff". And it did not in any way attempt the sleight-of-mind involved in the "it's all 1s and 0s" reduction.
My example involved explicitly stating the mathematical fact of a number's factors, requiring no steganographic reinterpretation. The crucial point is that the (boring mathematical) information about factors alone, with no further interpretation, suffices for the authorities' opponents to be tipped off. That is, all they have to do is search the web for "known semi-primes" and check them against public keys.
>It's an incredibly boring, and over-repeated statement that you can represent information as numbers and therefore you can have ILLEGAL NUMBERS!
Which wasn't my point at all; in the example I gave the numbers and encoding are not intended to represent anything other than the fact of a semi-prime's factorization.
>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.
It would actually be the breaking of the breaking of encryption. And I'm no so naive to think this would be a legally-defensibly way to circumvent snooping, to suppose that judges would just say, "herp derp, all you did was announce a semi-prime's factors, you're free to go!"
But it is a much less trivial example that you're making it out to be, and it is not at all the same as the OP's example, which required applying a specific encoding to an arbitrary string to get arbitrary meaning. In my example, it is nothing more and less than a mathematical fact that also happens to be used to conceal or authenticate data by other parties.
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.
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".