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RE: RE: Rubix

by kilinrax (Deacon)
on Oct 02, 2000 at 23:26 UTC ( [id://34962]=note: print w/replies, xml ) Need Help??


in reply to RE: Rubix
in thread Rubix

I was under the impression that a more common notation was 'U,D,F,B,L,R for 90° clockwise turns, 'U²,D²,F²,B²,L²,R²' for 90° turns, and either 'U',D',F',B',L',R'' ('prime') or 'U-1,D-1,F-1,B-1,L-1,R-1' for 90° anti-clockwise. The obvious advantage of this system is that U' or U-1 imply the inverse of U.

I would be inclined to agree with you to the security of the cryptosystem. Istr that a 2x2 cube has only ~107 permutations, which strikes me as a rather small number compared to those people throw around when talking about PGP (but then, i am not a cryptologist). The number of permutations increases exponentially with cube size, so if you a use a bigger one, this may cease to be a problem.

It would be really cool if you could use the resulting cryptosystem using nothing but a Rubik's cube, some paper, and a lot of free time (à la '<cite>Pontifex</cite>'), but maybe that's a little optimistic.....


Some interesting cube-related links from my bookmarks:

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RE: RE: RE: Rubix
by BlaisePascal (Monk) on Oct 03, 2000 at 00:28 UTC
    Yes, that notation is more common, but the problem is that it doesn't scale well for NxNxN cubes. It fixes the centers for 3x3x3 cubes, and it doesn't handle the inner slices for 4x4x4 or higher order cubes. The notation I described was reasonably compact, and handled cubes up to 9x9x9. That's why I went with it.

    The security really gets worse the larger the cube -- mainly because of key-length. True, the total number of permutations goes up exponentially (and how! one -factor- in the number of permutations is 24!floor((N-1)/2). I don't have time to compute the other factors, but with that exponential base, who cares?), but the number of permutations that can be reached within m quarter-turns is less than 12Nm. If you want to reach anywhere near a decent subset of the permutations, you are going to quickly need huge keys. If you use too small of keys, you get too little mixing, which ruins your cipher. I'd be interested to know when the length of good keys exceeds the length of the datablock (6N2). I suspect it happens quite low -- I know 3x3x3 cubes require at least 22 quarter-turns to reach all permutations, with a datablock size of 24 characters.

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