Talk:Chaocipher: Difference between revisions
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(A Latin Square) |
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==Latin Suares== |
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The relationship between encryption and Latin Squares has been mentioned recently on RC. I thought it might be interesting to look at the Latin Squares associated with this task. |
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===Latin Square for left wheel=== |
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<pre> |
<pre> |
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0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 |
0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 |
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13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 |
13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 |
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</pre> |
</pre> |
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If p is the position of the ciphertext letter then given a current ciphertext alphabet, HXUCZVAMDSLKPEFJRIGTWOBNYQ say, then applying the bijection<br> |
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:new ciphertext alphabet[n]=current ciphertext alphabet[LS[p][n]] |
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one obtains ONYQHXUCZVAMDBSLKPEFJRIGTW when p is 21.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 17:59, 20 July 2019 (UTC) |
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: Why is there the (Latin) lowercase letter '''o''' in the 9<sup>th</sup> row of this Latin square? -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 19:49, 9 August 2019 (UTC) |
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===Latin Square for right wheel=== |
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<pre> |
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25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 |
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24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 |
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23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 |
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22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 |
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21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 |
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20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 |
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19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 |
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18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 |
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17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 |
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16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 |
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15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 |
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14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 |
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12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 |
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11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 |
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10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 |
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9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 |
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8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 |
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7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 |
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6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 |
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5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 |
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4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 |
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3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 |
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2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 |
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13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 |
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1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 |
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0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 |
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</pre> |
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Now I just need a way to generate random Latin Squares of order 26 to program a better Chaocipher--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 10:59, 21 July 2019 (UTC) |
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Latest revision as of 19:49, 9 August 2019
Latin Suares
The relationship between encryption and Latin Squares has been mentioned recently on RC. I thought it might be interesting to look at the Latin Squares associated with this task.
Latin Square for left wheel
0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 18 19 20 21 22 23o 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 14 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 12 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 11 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 10 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 9 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 8 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 7 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 6 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 5 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 4 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 3 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 2 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 1 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 13 13 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0
If p is the position of the ciphertext letter then given a current ciphertext alphabet, HXUCZVAMDSLKPEFJRIGTWOBNYQ say, then applying the bijection
- new ciphertext alphabet[n]=current ciphertext alphabet[LS[p][n]]
one obtains ONYQHXUCZVAMDBSLKPEFJRIGTW when p is 21.--Nigel Galloway (talk) 17:59, 20 July 2019 (UTC)
- Why is there the (Latin) lowercase letter o in the 9th row of this Latin square? -- Gerard Schildberger (talk) 19:49, 9 August 2019 (UTC)
Latin Square for right wheel
25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 12 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 11 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 10 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 9 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 8 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 7 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 6 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 5 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 4 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 3 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 2 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 13 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 1 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 0 0 1 13 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25
Now I just need a way to generate random Latin Squares of order 26 to program a better Chaocipher--Nigel Galloway (talk) 10:59, 21 July 2019 (UTC)