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The original (3×3×3) Rubik's Cube has eight corners and twelve edges. There are 8! (40,320) ways to arrange the corner cubes. Seven can be oriented independently, and the orientation of the eighth depends on the preceding seven, giving 37 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, since an even permutation of the corners implies an even permutation of the edges as well. (When arrangements of centres are also permitted, as described below, the rule is that the combined arrangement of corners, edges, and centres must be an even permutation.) Eleven edges can be flipped independently, with the flip of the twelfth depending on the preceding ones, giving 211 (2,048) possibilities.[24] [8! \times 3^7 \times 12!/2 \times 2^[11]] = 43,252,003,274,489,856,000 which is approximately forty-three quintillion.[25] The puzzle is often advertised as having only "billions" of positions, as the larger numbers are unfamiliar to many. To put this into perspective, if one had as many 57-millimeter Rubik's Cubes as there are permutations, one could cover the Earth's surface 275 times. The preceding figure is limited to permutations that can be reached solely by turning the sides of the cube. If one considers permutations reached through disassembly of the cube, the number becomes twelve times as large: [8! \times 3^8 \times 12! \times 2^[12]] = 519,024,039,293,878,272,000. which is approximately five hundred and nineteen quintillion[25] possible arrangements of the pieces that make up the Cube, but only one in twelve of these are actually solvable. This is because there is no sequence of moves that will swap a single pair of pieces or rotate a single corner or edge cube. Thus there are twelve possible sets of reachable configurations, sometimes called "universes" or "orbits", into which the Cube can be placed by dismantling and reassembling it.
Originally posted by tinfoilman
reply to post by The X
Yeah that shouldn't be a problem. You would have to convert the cube positions to numbers that can be transmitted. This is easy. Then use whatever key exchange method you wish to use to transmit the numbers. Then your friend reconstructs the cube, either real or virtual, on his side from the numbers. Also easy.
Then after you've transferred the cube positions you would have each others cube keys from then on. Then you could use the cube position to generate keys for whatever encryption algorithm you wanted and send messages back and forth.
From then on If you wanted to change keys you could just send the changes, rotations, flips or whatever, but not the starting position. If he makes the same changes as you make you'll end up with the same thing. But the hacker won't know what position you guys started from and won't be able to recreate your changes after you've transmitted the first key.
Originally posted by The X
Originally posted by tinfoilman
reply to post by The X
Yeah that shouldn't be a problem. You would have to convert the cube positions to numbers that can be transmitted. This is easy. Then use whatever key exchange method you wish to use to transmit the numbers. Then your friend reconstructs the cube, either real or virtual, on his side from the numbers. Also easy.
Then after you've transferred the cube positions you would have each others cube keys from then on. Then you could use the cube position to generate keys for whatever encryption algorithm you wanted and send messages back and forth.
From then on If you wanted to change keys you could just send the changes, rotations, flips or whatever, but not the starting position. If he makes the same changes as you make you'll end up with the same thing. But the hacker won't know what position you guys started from and won't be able to recreate your changes after you've transmitted the first key.
Thanks!.
So it wouldn't be too difficult to implement something like this in a program such as tyler, so that every communication could be transmitted outside of standard encryption keys?.
I started to think about this a few days ago when i read that the NSA have made some breakthroughs vastly reducing the amount of time it takes to break standard encrypted messages coded in 128 and 256 bit keys.
I did wonder if all those server farms they built have been working on producing vast swathes of the encryption block, and now use a process similar to that used by the Enigma codebreakers at bletchley park, of matching up parts of the code against a database of held strings of encryption.
I am a writer/ artist not a mathematician, all just conjecture that passes through my "fractal factory".
Originally posted by The X
reply to post by tinfoilman
It's nice to know that the NSA could bankrupt america if the encryption was strong enough, and the desire to read it, compulsive enough.
What ideas do you have for where the future of cryptography goes?.