Route Transposition and Phenomenon

[Jarlve]

Try this transposition matrix, it creates a period 19 bigram cipher with a guaranteed better peak at column period 2 + period 18 or what Largo calls columns odd before even. The matrix is based off the magic square found in the Zodiac FBI files and the reading rules differ from the regular periodic transpositions we have been considering. For the record, columnar, diagonal and skytale transposition do not seem to produce this behaviour.

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141 81  21  301 241 181 121 61  1   281 221 161 101 41  321 261 201
260 200 140 80  20  300 240 180 120 60  340 280 220 160 100 40  320
39  319 259 199 139 79  19  299 239 179 119 59  339 279 219 159 99
158 98  38  318 258 198 138 78  18  298 238 178 118 58  338 278 218
277 217 157 97  37  317 257 197 137 77  17  297 237 177 117 57  337
56  336 276 216 156 96  36  316 256 196 136 76  16  296 236 176 116
175 115 55  335 275 215 155 95  35  315 255 195 135 75  15  295 235
294 234 174 114 54  334 274 214 154 94  34  314 254 194 134 74  14
73  13  293 233 173 113 53  333 273 213 153 93  33  313 253 193 133
192 132 72  12  292 232 172 112 52  332 272 212 152 92  32  312 252
311 251 191 131 71  11  291 231 171 111 51  331 271 211 151 91  31
90  30  310 250 190 130 70  10  290 230 170 110 50  330 270 210 150
209 149 89  29  309 249 189 129 69  9   289 229 169 109 49  329 269
328 268 208 148 88  28  308 248 188 128 68  8   288 228 168 108 48
107 47  327 267 207 147 87  27  307 247 187 127 67  7   287 227 167
226 166 106 46  326 266 206 146 86  26  306 246 186 126 66  6   286
5   285 225 165 105 45  325 265 205 145 85  25  305 245 185 125 65
124 64  4   284 224 164 104 44  324 264 204 144 84  24  304 244 184
243 183 123 63  3   283 223 163 103 43  323 263 203 143 83  23  303
22  302 242 182 122 62  2   282 222 162 102 42  322 262 202 142 82


Code: Select all

ebceetowilaeaiado
asmtevirtgyippdtn
iyrkssbadelnrktxt
esnmaceeelitlites
vegouupovrlsntall
llabnmfonrirpyeef
boiiheiehyirgoomh
ewnlkwihlhcenugfe
epmteanuetltuvron
yihgoavmaohlismio
gbghtncheihytrrio
nstentnietsntelih
gtasorieilbsiansl
uaatminetmellitsu
ufadhsetlbtomilti
ieoecntosillesaki
ewfcrreaimueilglg
ldkdoneobeweaswin
wailietegmecfhcui
asihkillrrnsmifte


[smokie treats]

It is the thing about cutting column 17, shifting columns 1-16 to the right, and pasting column 17 into column 1. What you have been talking about for a long time. As if he wrote the message at an angle, but when coming to the edge, instead of dropping down two rows like what you would see with simple columnar transposition, he just dropped down one row. There are misalignments created when un-transposing.

You should be able to repeat and get the same results, right? Cut the new column 17, shift the new columns 1-16 to the right, and paste column 17 into column 1. Like splicing two halves of a jigsaw puzzle.

I think that it is very plausible, especially because it is simple. Detecting anything but the predominate period is so hard with homophonic diffusion. Sometimes it works and sometimes it doesn't. If this is the case, then there would be some period 2 bigrams that have their leftmost symbol in columns 16 or 17, and their rightmost symbol in columns 1 or 2. And the symbols should match up with other period 19 bigrams. I could take a look at it later, but also looking for other predictable bigram existences or non-existences. Lack of bigrams in certain areas. Several things all at once.

[smokie treats]

I have an idea. I think that I will make 17 cut - scroll - paste versions. Highlight the cells involved with period 19 repeats for each version. Then count the cells that are highlighted for each column and for each version of the message ( any message ). With all of that, it would seem to me that columns 1 and 17 should have lower totals than columns 2 - 16. And make some test messages to see if it works. Then try it on the 340.

[Jarlve]

If I remember correctly then it was doranchak who premiered the column/row period operation with his transposition explorer. It is period on columns/rows and can be used to solve multiple inscription rectangles and polyliteral transposition. In AZdecrypt it is called Period column/row order and Largo has dubbed column period 2 as Columns: Odd before even in Peek-a-boo. Check the transposition matrix below for what is happening.

Column period 2 untransposed + period 18 untransposed creates a variation of the 340 with 44 bigrams and 5 trigrams. Which poses the feature or a phantom question. I believe that there is a good chance that it is a feature and I found at least one periodic transposition that actually has this as a feature. For that, see my previous post. It is a periodic transposition which wraps around the cipher in 2 dimensions X and Y.

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Column period 2 untransposed:

1   3   5   7   9   11  13  15  17  2   4   6   8   10  12  14  16
18  20  22  24  26  28  30  32  34  19  21  23  25  27  29  31  33
35  37  39  41  43  45  47  49  51  36  38  40  42  44  46  48  50
52  54  56  58  60  62  64  66  68  53  55  57  59  61  63  65  67
69  71  73  75  77  79  81  83  85  70  72  74  76  78  80  82  84
86  88  90  92  94  96  98  100 102 87  89  91  93  95  97  99  101
103 105 107 109 111 113 115 117 119 104 106 108 110 112 114 116 118
120 122 124 126 128 130 132 134 136 121 123 125 127 129 131 133 135
137 139 141 143 145 147 149 151 153 138 140 142 144 146 148 150 152
154 156 158 160 162 164 166 168 170 155 157 159 161 163 165 167 169
171 173 175 177 179 181 183 185 187 172 174 176 178 180 182 184 186
188 190 192 194 196 198 200 202 204 189 191 193 195 197 199 201 203
205 207 209 211 213 215 217 219 221 206 208 210 212 214 216 218 220
222 224 226 228 230 232 234 236 238 223 225 227 229 231 233 235 237
239 241 243 245 247 249 251 253 255 240 242 244 246 248 250 252 254
256 258 260 262 264 266 268 270 272 257 259 261 263 265 267 269 271
273 275 277 279 281 283 285 287 289 274 276 278 280 282 284 286 288
290 292 294 296 298 300 302 304 306 291 293 295 297 299 301 303 305
307 309 311 313 315 317 319 321 323 308 310 312 314 316 318 320 322
324 326 328 330 332 334 336 338 340 325 327 329 331 333 335 337 339


[Jarlve]

Here is the column period 2 matrix applied to the matrix I based off the magic square, which can be seen as skytale in a grid. As you can see it reduces period 19 to period 18. I am not exactly sure why this would improve bigrams but I think that it has to do with there being less shorter period lines because of the period downgrade. That may then indicate that the period line order in the 340 is out of order of what we are expecting.

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141 21  241 121 1   221 101 321 201 81  301 181 61  281 161 41  261
260 140 20  240 120 340 220 100 320 200 80  300 180 60  280 160 40
39  259 139 19  239 119 339 219 99  319 199 79  299 179 59  279 159
158 38  258 138 18  238 118 338 218 98  318 198 78  298 178 58  278
277 157 37  257 137 17  237 117 337 217 97  317 197 77  297 177 57
56  276 156 36  256 136 16  236 116 336 216 96  316 196 76  296 176
175 55  275 155 35  255 135 15  235 115 335 215 95  315 195 75  295
294 174 54  274 154 34  254 134 14  234 114 334 214 94  314 194 74
73  293 173 53  273 153 33  253 133 13  233 113 333 213 93  313 193
192 72  292 172 52  272 152 32  252 132 12  232 112 332 212 92  312
311 191 71  291 171 51  271 151 31  251 131 11  231 111 331 211 91
90  310 190 70  290 170 50  270 150 30  250 130 10  230 110 330 210
209 89  309 189 69  289 169 49  269 149 29  249 129 9   229 109 329
328 208 88  308 188 68  288 168 48  268 148 28  248 128 8   228 108
107 327 207 87  307 187 67  287 167 47  267 147 27  247 127 7   227
226 106 326 206 86  306 186 66  286 166 46  266 146 26  246 126 6
5   225 105 325 205 85  305 185 65  285 165 45  265 145 25  245 125
124 4   224 104 324 204 84  304 184 64  284 164 44  264 144 24  244
243 123 3   223 103 323 203 83  303 183 63  283 163 43  263 143 23
22  242 122 2   222 102 322 202 82  302 182 62  282 162 42  262 142


[smokie treats]

Try this transposition matrix, it creates a period 19 bigram cipher with a guaranteed better peak at column period 2 + period 18 or what Largo calls columns odd before even. The matrix is based off the magic square found in the Zodiac FBI files and the reading rules differ from the regular periodic transpositions we have been considering. For the record, columnar, diagonal and skytale transposition do not seem to produce this behaviour.

Code: Select all

141 81  21  301 241 181 121 61  1   281 221 161 101 41  321 261 201
260 200 140 80  20  300 240 180 120 60  340 280 220 160 100 40  320
39  319 259 199 139 79  19  299 239 179 119 59  339 279 219 159 99
158 98  38  318 258 198 138 78  18  298 238 178 118 58  338 278 218
277 217 157 97  37  317 257 197 137 77  17  297 237 177 117 57  337
56  336 276 216 156 96  36  316 256 196 136 76  16  296 236 176 116
175 115 55  335 275 215 155 95  35  315 255 195 135 75  15  295 235
294 234 174 114 54  334 274 214 154 94  34  314 254 194 134 74  14
73  13  293 233 173 113 53  333 273 213 153 93  33  313 253 193 133
192 132 72  12  292 232 172 112 52  332 272 212 152 92  32  312 252
311 251 191 131 71  11  291 231 171 111 51  331 271 211 151 91  31
90  30  310 250 190 130 70  10  290 230 170 110 50  330 270 210 150
209 149 89  29  309 249 189 129 69  9   289 229 169 109 49  329 269
328 268 208 148 88  28  308 248 188 128 68  8   288 228 168 108 48
107 47  327 267 207 147 87  27  307 247 187 127 67  7   287 227 167
226 166 106 46  326 266 206 146 86  26  306 246 186 126 66  6   286
5   285 225 165 105 45  325 265 205 145 85  25  305 245 185 125 65
124 64  4   284 224 164 104 44  324 264 204 144 84  24  304 244 184
243 183 123 63  3   283 223 163 103 43  323 263 203 143 83  23  303
22  302 242 182 122 62  2   282 222 162 102 42  322 262 202 142 82


Code: Select all

ebceetowilaeaiado
asmtevirtgyippdtn
iyrkssbadelnrktxt
esnmaceeelitlites
vegouupovrlsntall
llabnmfonrirpyeef
boiiheiehyirgoomh
ewnlkwihlhcenugfe
epmteanuetltuvron
yihgoavmaohlismio
gbghtncheihytrrio
nstentnietsntelih
gtasorieilbsiansl
uaatminetmellitsu
ufadhsetlbtomilti
ieoecntosillesaki
ewfcrreaimueilglg
ldkdoneobeweaswin
wailietegmecfhcui
asihkillrrnsmifte


I describe this as a guy back in 1969 with a pencil and paper writing the message at an angle, but not dropping down a row when crossing over from column 17 to column 1. On left is your matrix, on right is a matrix made by a route transposition using a 18 x 19 inscription rectangle. Then below I took out all symbols except for one angled row for better visualization.

matrix.discussion.1.png

If I cut column 17, scroll the message to the right, and paste it into column 1, your matrix continues the angled row, but the route transposition matrix angled row is misaligned. Two iterations of this.

matrix.discussion.2.png

Two more iterations. There are vertical misalignments, and horizontal misalignments created when scrolling the route transposition message, but not with your matrix. I have started a spreadsheet to explore this for detection, have to do some stuff today but definitely will continue with it very soon. We should be able to scroll the message and see what happens to detect what type of message it is.

[smokie treats]

Here is the result of a scrolling experiment.

Here is the 340. X axis is the leftmost column ( 1 means undisturbed message, 17 means 17th column shifted to the leftmost position, etc. ). Y axis is the count of cells highlighted because they are part of a period 19 repeat. For the 340, Y varies between about 100 to 120.

matrix.discussion.4.png

I LIKE KILLING using Jarlve's first matrix. Y varies between about 100 to 120.

11 5 7 12 13 50 40 58 22 28 1 14 2 23 3 10 39
3 46 33 51 15 57 24 45 52 18 61 25 42 43 9 52 34
22 62 44 26 47 48 6 1 9 11 28 35 44 27 52 60 51
12 49 36 33 1 8 13 14 15 30 22 52 31 23 53 11 46
56 12 19 40 54 55 42 41 56 45 11 46 37 51 3 28 29
30 31 4 5 34 32 16 40 35 44 24 45 43 61 13 14 17
6 39 25 11 20 14 23 11 21 62 22 44 18 40 41 33 20
12 59 36 11 26 58 25 21 28 20 7 13 37 54 18 16 14
15 43 32 50 11 2 34 55 11 53 31 53 55 57 45 40 35
61 11 21 18 39 2 56 33 3 40 20 30 11 48 32 22 41
18 5 18 21 51 36 8 20 13 23 21 62 51 45 45 24 38
37 49 52 14 34 53 35 25 15 50 47 36 51 15 28 11 20
19 52 4 47 39 45 22 14 23 11 6 48 24 1 37 49 28
55 2 3 51 33 25 34 13 50 32 14 29 30 11 51 47 55
55 17 4 9 21 49 15 52 31 5 53 40 33 22 31 50 23
25 11 41 12 7 35 51 38 48 11 29 30 14 49 4 27 23
14 59 17 7 45 44 15 2 25 32 55 11 23 30 18 31 19
11 9 26 10 41 37 12 40 6 13 58 14 3 47 59 23 37
58 4 25 28 11 15 52 15 18 33 12 7 17 21 8 55 23
1 47 23 21 27 24 29 30 45 44 36 48 32 25 16 53 13

matrix.discussion.5.png

I LIKE KILLING using route transposition with an 18 x 19 inscription rectangle. Y varies between about 80 to 120. Scrolling disturbed a lot of the repeats.

24 5 54 23 11 24 1 38 32 12 50 26 13 20 44 51 6
28 13 29 13 34 30 16 47 35 33 39 34 21 47 48 11 37
20 12 34 8 25 8 11 31 38 52 22 13 49 7 2 41 53
35 23 14 8 38 3 27 1 50 24 45 21 32 51 52 15 37
17 42 25 37 24 39 53 55 11 54 23 34 45 12 1 20 50
23 18 16 2 9 42 21 33 19 46 26 48 48 18 13 32 11
24 20 51 14 58 44 22 1 4 15 11 12 22 12 33 59 49
40 41 35 44 23 52 24 52 13 45 56 32 57 61 28 25 38
23 50 47 17 19 22 47 51 52 39 23 1 14 62 15 40 29
50 44 11 5 50 2 18 31 11 24 20 16 58 10 27 48 61
55 25 11 12 9 15 10 11 22 28 56 36 3 23 24 25 11
29 41 59 37 49 17 19 7 4 30 57 22 11 18 19 51 31
8 31 4 54 23 19 49 55 3 3 34 53 11 35 36 62 22
25 28 11 29 56 33 30 42 38 36 32 54 19 39 47 18 6
40 44 48 5 4 12 13 61 31 14 33 53 15 49 11 26 33
14 13 55 11 50 14 34 9 46 35 52 41 54 20 11 15 45
22 11 60 52 45 53 21 44 10 59 23 4 45 43 7 2 36
32 40 28 50 42 50 44 20 1 12 3 24 59 33 62 31 21
37 52 1 55 30 20 13 14 39 15 50 6 31 11 25 11 5
12 16 27 21 34 49 48 13 44 44 8 6 58 41 28 29 29

matrix.discussion.6.png

It seems as though the 340 behaves more like your matrix than route transposition, Jarlve.

[Jarlve]

It seems as though the 340 behaves more like your matrix than route transposition, Jarlve.

Yes, my point exactly and thanks for confirming.

[Jarlve]

So what I am trying to get at is that with periodic transposition we may have been over assumptious with the order the plines are in. To give a crude and extreme example, here follows a cipher with the plaintext of the 408 where the row order has been randomized in a 5 by 68 configuration. Bigrams are high but the solution is junk with an AZdecrypt score of 20780.

Code: Select all

KM!O"6WS'Y;-(:=$<
]%A1,8Z@LH;K<?W-;
F9/\1DPYV]K]58N3&
(0C=M2\%4SCR/)7JW
=AV$^E]AH!683I*]_
CG2D5F&8ZJY-(+/\1
^4];-/[>)DEK:MA-;
Z#Y-P=BO,]7C(<8L2
.">A@=/TQU;]X86W!
#&H/*$NFJ]?)Z7Y4E
'(-;AZ!YEFI_^V65;
7&81,/9]0PK-;OD_G
S(B,IM8.^:!9O5@A/
Z>Y-*2H7[M5]4!;-N
)F/0(P($SC/M7J1:C
]A!YE;985/]<8@XI%
(-;-;FML9/B7R"DNA
!]!FZ0Y-;98/E(#AZ
<]H_SQK5KO47!68!F
/M]F&8,Z_W-2G)^>Y


[Jarlve]

Looking at the 17 by 20 configuration of the 340, with a transposition reading rule of "go left by 2 and go down by 1" (period 19 bigram peak) then there are whopping 55 plines/fragments that can be out of order. While with a regular period 19 transposition there are only 18 plines/fragments to consider.

I am trying to formulate some attack plan, possibly a hill climber.