Magic Number Redux

Magic Number Redux

Slashdot has a nice article continuing the discussion about the HD-DVD key. I had this idea a few days ago too (I swear!).

NZ is party to the Berne Convention for the Protection of Literary and Artistic Works, so any artistic work automatically falls under copyright. So, create such a work. Then, take a number of your choice. Use an cypher of your choice (see Trav for implementation details, or just use ROTx) to encrypt the work. Then, optionally and to make your case stronger, distribute the encrypted work along with a program to decrypt it in memory, on the fly (see me for implementation details).

The number you used, that, remember, was arbitrary, is now a component of a TPM protecting your work from being copied. Find someone who uses your number and take them to court. Rinse. Repeat if desired.

Now, I posted in the earlier story a number of different representations of the HD-DVD key. The great thing is that there are an uncountable infinity of different isomorphic representations of an number. For instance, you can convert back and forth between a number and a string trivially with a code like ASCII, or just A = 1, B = 2, etc. So, to be really tricky, use one of the isomorphisms of an important string as your key. Your key could be the entire text to the Copyright Act 1994 - so, publishing the law that prohibits publishing components of a TPM circumvention method would be publishing a component of a TPM circumvention method. Got self-reference?

To be really, really tricky we can use the following supposition. It's unproven, but fairly trivial. I also don't know if it has a name. It should. Counter-examples welcome.
For any pieces of information, i and j, there is a bijective (and so, invertible) function such that f(i) = j, regardless of the complexity of i or j, provided there is no limit to the complexity of f.
Convince yourself of this and we'll continue. Seriously. Let it sink in. No trouble, I'll wait.

Well, from this it follows that literally every piece of information is a component of a TPM circumvention method. Well, even more strongly, any piece of information is a component of any (information using) TPM circumvention method. The only thing that changes between different pairs (i,j) is the component's triviality. The situation is isomorphic (ha.) to capacitors and transistors: they're not TPM circumvention components, even if they are used to break Macrovision. But mod-chip ICs? Not trivial/general enough, so they are TPM circumvention components.

That's damn fucked up.


learnt a nice way to convert any given string into any other string you like just today in fact. works along the lines of that neat result that you can draw a unique parabola through any three points that are not in a straight line.


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It thought it might have worked like this:

Convert the text into coördinates. Then we know there are two parabolas that pass through those points (one is found with the axes interchanged - it runs parallel to the x axis, if you like). Then you can use some unique property of each of the parabolas?

But then I considered that you could just hold two of the points stationary and move the third along the parabola you've found previously.

How did it work?
well, I guess I kinda misinterpreted the way the lecture was going: we went on to study <a href="">Shamir's Secret Sharing</a>, but consider this:
Convert your message into n coefficients of a polynomial, then pick n distinct arbitrary points on the graph of that polynomial and you have a representation which refers uniquely to the original message. Then you just need a way of choosing those points so that they represent the string you had in mind. I thought of choosing their x co-ordinates according to a key word; so APPLE, say, would give us 4 points on the graph which, assuming the polynomial is of degree 3, would define that polynomial uniquely and hence its coefficients, which encode the message, but so could any other word with only 4 distinct letters.
Only trouble with that encoding is that the word alone is not enough, you'd have to append the y co-ordinates to define the points.... so,.. yeah, it kinda lets you convert any string into any string you like... plus some garbage. Oh, and it kinda restricts your message to 26 characters. and if it is that long, chances are your output will look like:

so, yeah, not that great; but i did come up with it on the fly just now, so... some credit?

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