Since it is exhausting for me to write long texts in english I’ll cut the long story short because there is a good chance that my discoveries are not really new. If they are new however or my description is unclear, feel free to ask and I will go into detail.
Smokie: I’ve checked some of my ideas how to produce z340-like hoaxes and I’ve found a way to produce lots of pivots. If a short sequence like ABCD…XYZ is repeated over and over again and the text is transposed diagonally, then a lot of pivots appear. If a homophonic substitution is applied, then only a few pivots remain. This happens almost exclusively if the repeated text has an even length (20,22,24,26 etc). This is just a symmetrical fact.
It also happens if the text is not a pattern like "ABC…" but something like "BYFIREBYGUNBYROPEBYKNIFE". Depending on the starting corner of the diagonal transposition you get period n spikes at period(cipher width -1) or period(cipher width + 1). A few examples:
- Start "peek-a-boo 0.5" (Download at: http://zodiackillersite.com/viewtopic.php?f=81&t=3255)[/*:m:3q28gza2]
- Click "Tools -> Fill with sequence -> Apply (With default settings)"[/*:m:3q28gza2]
- Select "Patterns -> Pivots -> Checkmark" on transcription window[/*:m:3q28gza2]
- No pivots were found.[/*:m:3q28gza2]
- Now click "Transposition -> Diagonal -> Transpose", keep default settings and click "apply".[/*:m:3q28gza2]
- Now click "Patterns -> Pivots" again: A lot of them are appearing![/*:m:3q28gza2]
- Next click "Tools -> Encode / Decode -> Encode Cyclic (keep default settings".[/*:m:3q28gza2]
- Click "Patterns -> Pivots" again: Four pivots remain.[/*:m:3q28gza2][/list:u:3q28gza2]
- Create the "ABC…XYZ" pattern again[/*:m:3q28gza2]
- Resize the cipher to 20×17[/*:m:3q28gza2]
- Apply diagonal transposition (default settings)[/*:m:3q28gza2]
- Encode homophonic[/*:m:3q28gza2]
- Resize to 17×20[/*:m:3q28gza2][/list:u:3q28gza2]
Unfortunately I still can not upload images I will post a dropbox link. I’ll upload the image later to this forum:
https://www.dropbox.com/s/74dq6ppl9swu2a3/pivots_recipe.png?dl=0
Of course this is not a real method to create z340 like hoaxes because of the huge amount of ngrams. But it is interesting that the period n spikes are appearing at period 16 or 18 depending on the chosen diagonal transposition. Now try the following:
Now you get at spike at period 19 and flipped period 15 but the pivots are vanished.
The strange thing is that is seems that some common plaintexts are also show pivots if transposed diagonally. E.g. load "Testcases/340_test_message_plaintext.txt" and select the pivots. There is a "wrapped around" one. Now transpose diagonal and check the results: Spike at period 16 and a different pivot can be found.
Hoax, repeated sequences or valid text: z340 could be a diagonally transposed 20×17 cipher with the little bit of extra magic. Of course there is not enough evidence yet since my "z340 recipes" are not good enough at the moment. But maybe they point into the right direction.
The strange thing is that is seems that some common plaintexts are also show pivots if transposed diagonally
Could you summon up an example of this? Thanks.
Could you summon up an example of this? Thanks.
I ran a test with your plaintext library. First, I’ve counted how many of your texts contains pivots. Then I transposed all the texts diagonally and counted again. The amount of texts which contained pivots was significant higher and I had absolutely no explanation for that behaviour. But then I realized that I had a stupid bug in my source code. After fixing it the results were as expected: no difference between pivot counts in plaintext and diagonal transpositions. The occurence of pivots in a z340-sized text (without homophonic substitution) is nothing special. They occur very often by chance (transposed or not)
Anyway…my best explanation for the pivots in z340 so far is a very repetitive underlying plaintext like shown in my exeriment above. Maybe in combination with a diagonal transposition. And this is no new idea I think.
Largo, I agree that writing the plaintext diagonally could create pivots because with period 2 there are a lot of E_E in the English language, period 3 there are a lot of E__E, and period 4 there are a lot of E___E. They are the most frequent and there are others like I_I and T__T and T___T.
If you make a list of all of the period 19 bigrams reading the message left right top bottom, and make a list of bigrams of all periods reading the message right left bottom top. Then compare the list of period 19 bigrams with all other periods from the other lists, period 16 has more matching symbols than any other period. See second post here:
viewtopic.php?f=81&t=3196&start=400
There is a spike. Then read the subsequent posts showing the strange herringbone pattern and the period 64 repeats, the most improbable of all repeat arrangements. I have been working on complex route transposition, trying to make a scheme to create period 19 repeats, pivots, and the herringbone.
Here is one. Scroll down through the picture to see the steps. The numbers in the cells are the position numbers of the plaintext message.
Step 1 start with a 15 x 22 grid, and write the message top to bottom vertically in columns 1, 3, 4, 6, 7, 9, 10, 12, 13, 15 ( grey cells ).
Step 2, write the remaining part of the message upward at an angle, right to left, starting at column 2 row 22 and working up to column 14 row 1 ( yellow cells, grey cells omitted for clarity ).
Step 3, re-draft into 17 columns.
Step 4, mirror the matrix. The matrix can create a lot of period 19 repeats, some pivot like structures, and sometimes herringbone structures as well. But not quite like the 340.
Here is the matrix. Thanks for working on the 340 with us. Hope you have further ideas.
315 2 199 330 177 155 329 133 111 327 89 67 324 45 23 320 1
47 25 310 3 200 328 178 156 326 134 112 323 90 68 319 46 24
70 309 48 26 305 4 201 325 179 157 322 135 113 318 91 69 314
308 93 71 304 49 27 300 5 202 321 180 158 317 136 114 313 92
138 116 303 94 72 299 50 28 295 6 203 316 181 159 312 137 115
161 302 139 117 298 95 73 294 51 29 290 7 204 311 182 160 307
301 184 162 297 140 118 293 96 74 289 52 30 285 8 205 306 183
10 207 296 185 163 292 141 119 288 97 75 284 53 31 280 9 206
33 270 11 208 291 186 164 287 142 120 283 98 76 279 54 32 275
269 56 34 265 12 209 286 187 165 282 143 121 278 99 77 274 55
101 79 264 57 35 260 13 210 281 188 166 277 144 122 273 100 78
124 263 102 80 259 58 36 255 14 211 276 189 167 272 145 123 268
262 147 125 258 103 81 254 59 37 250 15 212 271 190 168 267 146
192 170 257 148 126 253 104 82 249 60 38 245 16 213 266 191 169
215 256 193 171 252 149 127 248 105 83 244 61 39 240 17 214 261
230 19 216 251 194 172 247 150 128 243 106 84 239 62 40 235 18
64 42 226 20 217 246 195 173 242 151 129 238 107 85 234 63 41
87 225 65 43 223 21 218 241 196 174 237 152 130 233 108 86 229
224 110 88 222 66 44 221 22 219 236 197 175 232 153 131 228 109
340 339 338 337 336 335 334 333 332 331 220 231 198 176 227 154 132
Hi Smokie,
thank you for this enlightening explanation. Yesterday I’ve experimented a bit with different plaintexts and I can confirm that after diagonal transposition most of the pivots containing the letters you have mentioned. Now I understand what causes this.
The comparison between the bigrams at different period / transposition schemes is also very interesting. I’ve done that too, but not very accurate. Maybe I’ll implement a comparing system into my library. E.g. the bigrams at „z 340 + p19“ and „z340 + odd before even columns + flip + p16“ are almost the same (which is no surprise though).
I will have a deeper look into you complex route transposition experiment in the next few days.
