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==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.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk: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? -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk: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--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 10:59, 21 July 2019 (UTC)