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