Talk:Chaocipher: Difference between revisions

Latin Squares and Chaocipher
(A Latin Square)
 
(Latin Squares and Chaocipher)
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A ==Latin SuareSuares==
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===
<pre>
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
Line 28 ⟶ 30:
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
</pre>
The relationship between encryption and Latin Squares has been mentioned recently on RC. The above, LS, is the Latin Square corresponding to the left wheel. If p is the position of the ciphertext letter then given a current ciphertext alphabet, HXUCZVAMDSLKPEFJRIGTWOBNYQ say, then applying the bijection<br> new ciphertext alphabet[n]=current ciphertext alphabet[LS[p][n]]<br> one obtains ONYQHXUCZVAMDBSLKPEFJRIGTW when p is 21.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 17:59, 20 July 2019 (UTC)
: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)
===Latin Square for right wheel===
<pre>
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
</pre>
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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