Route Transposition and Phenomenon

[smokie treats]

But here is a link to the same image, 4th post down.

Thank you very much!

Good luck with your taxes.

Thanks. I have a new theory: Zodiac is still alive and is working in germany. He is creating all the tax laws to torture the people. He says: "You guys think z340 was complicated? Try this!"

I am thinking about making peace with the 340.

This would definitively be a pity since you have contributed so much! But it is totally understandable. Sometimes I am thinking the same but then I have new ideas to test. I am one of those who can easily gets obsessed by things like z340. So I always try to make a pause and do other things (again obsessively ). At the moment I use the z340 to learn new things like statistics, general cipher techniques and new programming languages. So I think I am controlling z340 and not the other way around.
Will you still read the forum if you decide to stop you work on z340? I think I have dug out something interesting concerning your hoax hypothesis and I would be glad to hear your opinion.

I would very much like to read anything that you have to say or show regarding a hoax. Not making peace quite yet.

[smokie treats]

ADFGX cipher ( but without transposition )

Jarlve, check this out. I have been considering fractionating ciphers, where one letter of the alphabet becomes two ciphertext. But then after that homophonic substitution. The World War I ADFGX cipher encodes with a 5 x 5 polybius square, then uses keyed columnar transposition to scramble the ciphertext up. I made a spreadsheet suite that encodes the plaintext with a polybius square. Then encodes again homophonic. There is no transposition so far. So far it seems very easy to generate messages with a high count of period 1 bigram repeats. Even easier than with straightforward homophonic, much to my surprise.

Message, bottom half of 34 of the Jarlve plaintext library

F F E R I N C E R T A I N S E C O
N D A R Y R E S P E C T S F R O M
T H E F I N D I N G S S E T F O R
T H H E R E I N D O N O T C O N S
I D E R T H E S E D I F F E R E N
C E S S U F F I C I E N T T O W A
R R A N T T H E F I L I N G O F A
M I N O R I T Y R E P O R T I T I
S O U R E A R N E S T H O P E T H
A T T H E F R U I T S O F O U R D

Simple polybius square

...A D F G X
A A B C D E
D F G H I K
F L M N O P
G Q R S T U
X V W X Y Z

ADFGX encoded message ( row, column )

D A D A A X G D D G F F A F A X G
D G G A A D G F F G F A X A F F G
F F A G A A G D X G G D A X G F F
X A X A F G G G F D A G D F G F D
G G D F A X D A D G F F A G D G F
F D D G F G F A X G G D A F G G D
G G D F D F A X G D A X D G F F A
G F G F F F G G G A F F G F F G F
D G A G A X G D G G D F A X G F A
X A G D G D A D A A X G D A X F F
A F A X G F G F G X D A D A D G A
F D G A X F F G G G G F G X D A A
G D G D A A F F G G G G D F A X D
A D G F A D G F F D D F G D A A A
F D D G F F F G G D D G G G X G G
D A X F X F G G D G G D G G G D G
G F F G G X G D A X A A G D F F A
X G F G G D F F G F X A X G G D F
A A G G G G D F A X D A G D G X D
G G G G F F G D A F G G X G D A G

Homophonic key

A 1 2 3 4 5 6 7 8 9 10 11 12 13
B
C
D 14 15 16 17 18 19 20 21 22 23 24 25 26
E
F 27 28 29 30 31 32 33 34 35 36 37 38 39
G 40 41 42 43 44 45 46 47 48 49 50 51 52
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X 53 54 55 56 57 58 59 60 61
Y
Z

Cryptogram, with about 20% random symbol selection within homophonic groups

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

The lower the randomization, the higher the period 1 repeats. I can make messages very easily that have a high count of period 1 repeats, if no randomization. As I increase randomization, then it become more difficult.

There should be a big spike at period 1, AND, also a spike at period 1 mean repeat score.

The first two symbols, 14 and 1 map to D and A on the homophonic key. The D and A symbols map to the letter F on the polybius square. And so on.

For some reason I cannot upload pictures anymore. I am going to rest a little bit, and double check things. But I think that this cipher may produce ngram repeats even more frequently than just homophonic substitution. If anyone wants to check be my guest.

[smokie treats]

This cipher results in a high count of period 1 bigram repeats, which is really just the frequency statistics of the letters in the message:

1. Encode ADFGX
2. Encode homophonic with about 12 ciphertext allocated to each of A, D, F, G and X

This cipher results in a low count of period 20 bigram repeats, because when a message is transposed after ADFGX encoding, the period is diffused because there are only 5 different ciphertext:

1. Encode ADFGX
2. Transpose with a 17 x 20 inscription rectangle, so that the period = 20 and there do not need to be any nulls
3. Encode homophonic with about 12 ciphertext allocated to each of A, D, F, G and X

However, this cipher results in a high count of period 20 bigram repeats, because when a message is transposed after homophonic encoding that occurs after ADFGX encoding, the period is not diffused because there are 60 ciphertext:

1. Encode ADFGX
2. Encode homophonic with about 12 ciphertext allocated to each of A, D, F, G and X
3. Transpose with a 17 x 20 inscription rectangle, so that the period = 20 and there do not need to be any nulls

But what about the cycles? If I use perfect cycles on step 2 of the above cipher, most of the time I get relatively low overall cycles scores. But it took me only several tries to get this. EDIT: It is the bottom half of message # 12 in Jarlve plaintext library. Polybius square same as post above, exactly 12 homophonic symbols allocated to each of A, D, F, G and X.

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

Cycle scores are just slightly lower than the 340, but homophonic encoding occurred before transposition. There is a big spike at period 20 for repeats, similar to the period 15 / 19 repeat spike, and a big spike at period 20 for average repeat score, similar to the period 15 / 19 average repeat score spike.

Here is the matrix:

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

[Jarlve]

But what about the cycles? If I use perfect cycles on step 2 of the above cipher, most of the time I get relatively low overall cycles scores. But it took me only several tries to get this. EDIT: It is the bottom half of message # 12 in Jarlve plaintext library. Polybius square same as post above, exactly 12 homophonic symbols allocated to each of A, D, F, G and X.

These ADFGX plaintext have only 5 letters so very long cycles become possible and thus the cycle scores inflate for allot of periods. For example the average cycle score for all periods of your cipher is 1732.08 (very high). And it peaks at a whopping 8600 at period 20 untransposed. The 340 has a period 1 cycle score of 2137 and no other period betters it so that seems to leave the hypothesis in the dust.

Your ADFGX plaintext has 314 or 315 bigrams in all periods and it is the sequential homophonic substitution direction which introduces the bigram peak. Sequential homophonic substitution increases the bigram count in its direction and the ADFGX plaintext is a prime example of this effect. An even better example would be to encode a plaintext with only one letter. The most sequential configuration of any text also has the maximum amount of bigrams, it goes hand in hand: ABCDEABCDEABCDE.

[smokie treats]

The 340 has a period 1 cycle score of 2137 and no other period betters it so that seems to leave the hypothesis in the dust.

Thanks for checking into that. I agree. The hypothesis is in the dust. It is very interesting that that I can very easily make a ADFGX + homophonic cryptogram that has period 1 repeats similar to the 340 period 15 / 19 repeats. The numbers are consistently very close.

Bifid very tiny chance. Rotating grille no way. Digraph most likely not. Fractionating the plaintext before homophonic in the dust. Various route, simple columnar, or complex route transposition trying to make pivots or whatever so far unsuccessful. Multiple small inscription rectangles unlikely. If you cannot make one with a particular cipher, then Zodiac couldn't have made one with the same cipher.

I will keep looking at classical ciphers for a little while. Thanks again.

[smokie treats]

Jarlve, I am starting a new project. Swapping symbols at period 18 to see what happens to the cycle scores, and looking for a pattern that dramatically increases cycle scores. It is slow going, but I have some spreadsheets made up. If you are interested, maybe work on this a little bit with me. I was wondering how many randomly located period 18 symbol swaps in a homophonic message would make the message look like period 19 instead of period 1, but unsolvable. I can check into that myself later as well, but for now looking for patterns.

Attempt at sharing an image in Google Drive ( I don't know what I am doing yet ):

https://drive.google.com/drive/folders/ ... WRzbF9mWm8

EDIT: Best results so far, swapping the green with the red starting at position 0, interval 32, period 18.

Can somebody let me know if you can see the image? Thanks.

[smokie treats]

Symbol Swapping To Obscure / Transpose Period 1 Repeats

Subtle transposition is possible and would be more local or act over shorter distances, it could also be a thing like a few swapped columns, rows or other small units that would nevertheless cause huge decryption issues.

That is the idea with this project. I was wondering if I swapped symbols at period 18, starting with position x, iterating through intervals of y, and swapping symbols at period 18, what would happen to the cycle scores. So far x = 0, and y = 1 to 64. Base cycle score for the 340 by my calculations is 64418.

The maximum increase is for y = intervals of 64. It is not a huge increase, but this is only with starting position at x = 0. Swap green with red, and you get a cycle score increase. See symbol.swap.2.

https://drive.google.com/drive/folders/0B5md-0QaS8QJQkZEcWRzbF9mWm8

Here is the table. Columns reading left to right: start position, interval, swap period, cycle score, cycle score rank ( sorted ). See symbol.swap.3. Note that most of the top scoring intervals are even numbers, 64, 32, 40, 10, 36, 54, 34 and 16. There are a couple of odd intervals, 27 and 59.

https://drive.google.com/drive/folders/0B5md-0QaS8QJQkZEcWRzbF9mWm8

That is it for today, probably, but the question is, could he have used some type of system to swap symbols, after homophonic encoding, that would make period 1 repeats look like period 19 repeats, and also disrupt the cycles?

EDIT: symbol.swap.4 top of table easier to read.

https://drive.google.com/drive/folders/0B5md-0QaS8QJQkZEcWRzbF9mWm8

I do not know why the post above included a link, and this post only shows a web address. I didn't do anything different.

EDIT: Period 64 is mentioned 7th post down here:

http://zodiackillersite.com/viewtopic.php?f=81&t=3196

[smokie treats]

Since my highest score was with start position 0, interval 64 and swap period 18, I iterated start position 0 to 64, interval 64 and swap period 18. The two highest scores were with start positions 39 and 21. See symbol.swap.5 and symbol.swap.6.

With the swaps at start positions 39 and 21, there is a shared symbol. They overlap each other. So here is the idea. A variation of a grille cipher. Encode homophonic perfect cycles, then take a grille with some holes punched in it, diagonal rows, and lay it on top of the message. Then swap the symbols with some type of pattern. Something like that.

https://drive.google.com/drive/folders/ ... WRzbF9mWm8

[Jarlve]

Jarlve, I am starting a new project. Swapping symbols at period 18 to see what happens to the cycle scores, and looking for a pattern that dramatically increases cycle scores. It is slow going, but I have some spreadsheets made up. If you are interested, maybe work on this a little bit with me. I was wondering how many randomly located period 18 symbol swaps in a homophonic message would make the message look like period 19 instead of period 1, but unsolvable. I can check into that myself later as well, but for now looking for patterns.

Is that the same as smokie18e but then after homophonic substitution?

Can somebody let me know if you can see the image? Thanks.

Yes, they are viewable.

That is it for today, probably, but the question is, could he have used some type of system to swap symbols, after homophonic encoding, that would make period 1 repeats look like period 19 repeats, and also disrupt the cycles?

I am skeptic, it is a very awkward thing to do and it would require a great deal of luck to have a proper bigram period conversion. Though it could be interesting to look at systematic swaps in a wide variety.

Since my highest score was with start position 0, interval 64 and swap period 18...

Can you share the cipher please?

[smokie treats]

Not smokie18e. Sort of like this, symbol.swap.7, but not exactly because with a few tries this method doesn't seem to be working to create enough period 19 repeats or disrupt the cycles enough. But similar.

https://drive.google.com/drive/folders/ ... WRzbF9mWm8

Yes, it would have been a lot of work. But we don't know if he was willing to do a lot of work or not, just assuming. Some of the cryptography books have lots of images of strange grilles and grille variations. Remain skeptical for the time being though. The previous images were of the 340. I am still working on trying to detect patterns where swapping two symbols at regular intervals would dramatically increase cycle scores.