This thread covers an (ongoing) investigation into "multiple period 19 transcription rectangles" on the Z340. In the following image you can see an example of that:
For the record, "multiple inscription/transcription rectangles" is something that is covered in old army cryptography manuals and something smokie first brought up. AZdecrypt’s simple transposition solver is able to solve it if (all) the rectangles are even/of the same size and the period operation is similar enough.
It shows two 17 by 9 rectangles followed by 17 by 2 rectangle stacked on top of eachother. The division is then 9, 9 and 2, but it really could be anything. The period 19 transposition is not the "standard columnar transposition by 19 columns" but rather a special rule in a 17 wide grid I came up with on the fly. Untransposing the Z340 with this matrix yielded a surprisingly 42 bigrams:
H+M8|CV@KEB+*5k.L dR(UVFFz9<>#Z3P>L (MpOGp+2|G+l%WO&D #2b^D(+4(5J+VW)+k p+fZPYLR/8KjRk.#K _Rq#2|<z29^%OF1*H SMF;+BLKJp+l2_cTf BpzOUNyG)y7t-cYA2 N:^j*Xz6dpclddG+4 -RR+4>f|pz/JNbVM) +l5||.UqL+Ut*5cZG R)VE5FV52cW+|TB4- |TC^D4ct+c+zJYM(+ y.LW+B.;+B31cOp+8 lXz6Ppb&RG1BCO7TB zF*K<S<MF6N:(+HFK 29^4OFTBO<Sf9pl/y Ucy5C^W(-+l#2E.B) |DFHkNdpWk<S7ztZB O_8YAO|BK*;-+C>cM 1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 137 146 2 11 20 29 38 47 56 65 74 83 92 101 110 119 128 120 129 138 147 3 12 21 30 39 48 57 66 75 84 93 102 111 103 112 121 130 139 148 4 13 22 31 40 49 58 67 76 85 94 86 95 104 113 122 131 140 149 5 14 23 32 41 50 59 68 77 69 78 87 96 105 114 123 132 141 150 6 15 24 33 42 51 60 52 61 70 79 88 97 106 115 124 133 142 151 7 16 25 34 43 35 44 53 62 71 80 89 98 107 116 125 134 143 152 8 17 26 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 9 154 163 172 181 190 199 208 217 226 235 244 253 262 271 280 289 298 290 299 155 164 173 182 191 200 209 218 227 236 245 254 263 272 281 273 282 291 300 156 165 174 183 192 201 210 219 228 237 246 255 264 256 265 274 283 292 301 157 166 175 184 193 202 211 220 229 238 247 239 248 257 266 275 284 293 302 158 167 176 185 194 203 212 221 230 222 231 240 249 258 267 276 285 294 303 159 168 177 186 195 204 213 205 214 223 232 241 250 259 268 277 286 295 304 160 169 178 187 196 188 197 206 215 224 233 242 251 260 269 278 287 296 305 161 170 179 171 180 189 198 207 216 225 234 243 252 261 270 279 288 297 306 162 307 309 311 313 315 317 319 321 323 325 327 329 331 333 335 337 339 338 340 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336
I say surprisingly because using the same matrix to transpose a 17 by 20 Z408 only yields 30 period 19 bigrams (down from 46 untransposed):
9kVPYN9fZW9zl#Xkq c!%O+@^Q#RJeKSOBq LEZ8PReKUYBld8I(8 RqdHK5/=G!IDPqrY) @6NG/MqLZpYqk5OE kp+qtBPUpM/XFY7)R SA^FqXIT#^IrU=6eq MT(ULHG8YQBR)9BB9 WHJt/%MVD5ES@RW#% BNcLD/8Ek)9tUI9V# p8P(p)R@RK5Z#OeM% N%ecDeOl_XUH9(BP6 ^7kZX+REV^TJt=8PV zW=D)fq@+UWRYQ%GL rMUSzSAW9jHI6rAL P)Ilp+rGcPqA=k5H Id5N!NkVl%E#_96F+ Zt9eMVJAATf%/BFB %TRc_Y_SWZGK_Y9#t L_O5U+dq^qVeYETA%
The effect of multiple transcription rectangles, even and uneven, and the use of more exotic period 19 transpositions can easily disrupt the spread over the standard period 19 lines mentioned in: viewtopic.php?f=81&t=4632
As I reasoned that:
Bottom line: if the Z340 is a homophonic substitution cipher + period 19 or 15 transposition, then the transposition for some reason is not properly divided over the aforementioned period lines.
Image of a standard period 19 line:
To start off the investigation I began work on a transposition solver to handle multiple transcription rectangles.
At the moment it can handle any number of complete rectangles and the rectangles do not have to be of the same size, for example one could stack a 17 by 2, 17 by 3, 17 by 4, 17 by 5 and 17 by 6 rectangle on top of each other, each having an individual period 19 transposition (using the same operation), and the solver will crack it easily.
Example cipher:
77?R5D%F[:BJ^/7NL CV+2)GP=[Q/.SAW4T 8;#*CK5((VRG4<,]_ "P)N)0>;?9W^82>< *.XKH/!N1:C5)W*0 >D8C,'QG2YJ/$KN6S &.*7I_UTW:VZGRW /B8*VN%@XGW,WU58 ;*[U2QAC:N).4I*H KW/7<+,E-KCP_0B$ >OX*<Q8'72_FW."C( ,,A^X@5*SJZ!^29R >C-6T9YOF*<&VG8_ M",IX$7=B+/JS)2> T))*H:JV9>/GXZ)J. ($/->O6>W*:P8KC& 5<Y[&*TN)CVTJ*@ WCL2VJ*'WC0Q6G8K C3_(/<N:JF*4TUC ,#"R?+M5C2VEX0.A=
Solve:
Score: 24515.33 IOC: 0.06550 Multiplicity: 0.18529 Repeats: 906 PC-cycles: 834 Minutes: 1.97 Key(2,5,9,14) IFIAMOUTOFMYMINDI TSALLRIGHTWITHMET HOUGHTMOSESHERDOG SOMEPEOPLETHOUGHT HEWASCRACKEDANDFO RATIMEHEHIMSELFHA DDOUBTEDTHATHEWAS ALLTHEREBUTNOWTHO UGHHESTILLBEHAVED ODDLYHEFELTCONFID ENTCHEERFULCLAIRV OYANTANDSTRONGHEH ADFALLENUNDERASPE LLANDWASWRITINGLE TTERSTOEVERYONEUN DERTHESUNHEWASSOS TIRREDBYTHESELETT ERSTHATFROMTHEEND OFJUNEHEMOVEDFROM PLACETOPLACEWITHA
I’ve only implemented the standard period operation so far and tried it on the Z340 trying both period 15 and 19 but nothing came out. In time I will follow up with more exotic period 19 operations.
Very interesting, Jarlve. Seems like there is still a lot of unexplored territory around these ideas.
Have you guys done anything with "irregular scytale?" Scytale with period 19 could generate repeating bigrams. But what if each "wrap" of the scytale was a different period within a cycling set?
For example, instead of a constant period: {19, 19, 19, …}
How about a set of cycling periods: {19, 15, 19, 15, …}
or: {19,15, 5, 19, 15, 5, …}
Perhaps such a scheme could produce periodic bigrams at a "major" period p1 and a "minor" period p2.
In physical terms, the rod used for this kind of scytale would be lumpy instead of having a constant diameter.
Have you guys done anything with "irregular scytale?" Scytale with period 19 could generate repeating bigrams. But what if each "wrap" of the scytale was a different period within a cycling set?
No but It’s an interesting idea worthy of exploring.
For the record, "multiple inscription/transcription rectangles" is something that is covered in old army cryptography manuals
Do you recall which manual had it? I was thinking it was in Friedman’s manual but I couldn’t find where it mentioned multiple inscription.
Anything related in this?
https://www.nsa.gov/Portals/70/document … 078809.pdf
“I don’t know Chief, he’s very smart or very dumb.“
Have to ask smokie.
That’s a great idea! Have you ever tried to rotate z340 by 90 or 270 and then test with your new solver mode? It could also be that the individual transcription rectangles are not stacked on top of each other, but side-by-side. I recently did a small test that deals with the relatively high number of nGrams in a rotated z340. I’m not ready to post this yet, though.
Translated with www.DeepL.com/Translator
Not yet, haven’t had so much time to work on it yet, but it is probably on the menu.
Very interesting, Jarlve. Seems like there is still a lot of unexplored territory around these ideas.
Have you guys done anything with "irregular scytale?" Scytale with period 19 could generate repeating bigrams. But what if each "wrap" of the scytale was a different period within a cycling set?
For example, instead of a constant period: {19, 19, 19, …}
How about a set of cycling periods: {19, 15, 19, 15, …}
or: {19,15, 5, 19, 15, 5, …}Perhaps such a scheme could produce periodic bigrams at a "major" period p1 and a "minor" period p2.
In physical terms, the rod used for this kind of scytale would be lumpy instead of having a constant diameter.
I’ve been thinking about this, and from a period 19 perspective, if you want the main period to be at 19 – as in the Z340 – then most of the Scytale columns have to be length 19. I also realized that AZdecrypt’s "Substitution + nulls and skips" solver is perfectly capable of handling it if the total amount of band changes is equal to the amount of "nulls and skips". For example (19, 19, 19, 18, 19, 18) has a total of minus 2, that is equal to 2 skips, and can thus be solved with 2 skips. The problem with (19, 15, 5, 19, 15 , 5, …) or even (19, 19, 15, 19, 19, 15, …) is that it diminishes the bigram information at period 19 allot. Not much irregularity seems allowed bigram wise.
When smokie and I did viewtopic.php?f=81&t=4125 we went up to any distribution of a total 10 nulls or skips (3+7, or 5+1, or 2+2, …) and I also asked the following question:
Is it likely that there are more than 10 nulls and/or skips given the increased amount of bigram diffusion?
Interesting points and questions. And I wonder if he’d have been so evil as to combine an irregular transposition with multiple transcription rectangles. That’d be such overkill!
There are just so many combinations of things that could have been done.
The work you have done on AZDecrypt to try out all these ideas may not yet have unraveled the 340 but it has become so powerful at unlocking both common and very uncommon cipher types! Even without cracking the 340, you have made a huge accomplishment.
Someone really should write a paper that summarizes all the different cipher types that can be unlocked by AZDecrypt. Could make a good entry in Cryptologia some day.
I wish we could come up with a very accurate cipher type detector that could look at all the test ciphers and automatically put them in the right categories. It could point the Z340 research in interesting directions.
Have you guys done anything with "irregular scytale?" Scytale with period 19 could generate repeating bigrams. But what if each "wrap" of the scytale was a different period within a cycling set?
No but It’s an interesting idea worthy of exploring.
i have been down the scytale path and physically made them by the hundreds. they can result in a period 19. But my opinion is that it is way to difficult to make on a long string like 340. short messages yes, maybe two or three lines at a time as you would need that to bring in period 19.
i like rectangles as the 408 was cut into three rectangles and distributed out. also really simple.
but i like the concept of cutting each row or column and rearanging the order of them basicaly 17 or 20 long skinny rectangles. again very simple.
EG: 17 columns rearanged odds evens and then each column up one gives a great period 19.
Bigrams: 41
– Normalized: 0.1547169811320755
Bigram IOC: 98
– Normalized: 0.0008552826796529996
Trigrams: 4
16 14 32 12 30 1 10 28 22 31 8 26 33 19 10 6 24
26 23 52 25 4 22 39 45 9 4 13 2 20 19 30 50 10
28 13 17 5 36 6 17 17 15 19 53 15 33 34 43 48 55
36 27 62 34 13 31 41 5 19 6 16 46 36 51 31 11 29
40 16 47 7 24 23 51 43 14 20 9 27 13 3 54 44 31
49 3 23 5 19 44 7 25 21 19 53 21 50 41 19 41 27
37 21 19 5 23 15 5 19 16 11 15 19 19 11 14 20 53
55 3 21 38 8 51 51 40 47 29 38 48 30 50 36 39 15
1 19 37 44 11 56 8 60 31 40 54 41 18 61 8 37 33
18 35 7 49 30 59 40 63 55 19 6 22 16 2 28 20 33
20 5 40 23 38 18 34 20 23 29 42 32 47 5 6 54 56
42 37 51 58 19 20 29 37 51 63 18 35 21 19 1 30 58
46 3 57 22 16 5 61 52 3 15 12 20 56 23 23 11 5
19 32 39 19 20 28 58 19 20 45 12 36 46 44 22 16 61
7 25 53 36 48 19 36 19 40 48 39 21 37 8 2 50 51
8 50 16 36 26 29 42 17 6 50 11 11 28 38 57 13 19
17 5 55 3 3 19 53 4 32 11 5 51 1 38 36 34 50
56 7 26 21 36 37 16 47 7 53 23 51 14 55 19 40 51
30 31 29 42 20 31 6 59 40 63 9 27 62 34 28 13 26
20 23 11 14 56 43 40 3 33 26 10 19 10 18 11 25 4
the solve not very good apart from the first line DON (C)ARDON which i think is very cool if thats how he started off the 340 and the second last line USS TO BEAT
AS OURS A WAR (M)ATION.
DON CARDON SIDE EDAN
DS PRINT A MINOR E AND
ONT HEAT THESHEILL B
EATINSC HEAD LETSTO
AD GUNS TLOR MANY MAS
K YSHEAURIESINCECA
NIEHSHHEDTHEETORS
BYIFITTAGOFLANETH
RENATO IT SAM CAPINE
ALUKAWARBEANDOORE
R HAS FAIR SOUNG HAMO
UNTLERONTRALIERAL
LYANDHPPYH CROSS TH
EN TEROLERACE LAND P
URSE LEEEALTINIONT
INDEDOUTANTTOFANE
TH BY YES IN THTRFEIN
OUDIENDG USS TO BEAT
AS OURS A WAR MATION D
RS TOO LAYED DEDATRI
I wish we could come up with a very accurate cipher type detector that could look at all the test ciphers and automatically put them in the right categories. It could point the Z340 research in interesting directions.
I know this has been in your mind for a long time. I think that if you want to make it then you should just start somewhere, make something very simple that has a human approach. For example:
More than 26 symbols, homophonic substitution? look for cycles.
Low ioc, polyalphabetic? look for keyword length.
Periodic bigrams, transposition? calculate odds.
And keep adding/improving stuff over time and at one point you may have something magical.
i like rectangles as the 408 was cut into three rectangles and distributed out. also really simple.
Good point!
I worked a bit more on the solver and it can now also find irregular rectangles, example:
IELPPBAEIOCUTMENA
IILKIELEUISMHNIOF
TNLNIINOECSTSUFIS
RUHKLGKLG
WGIERBUA
TOARAAAOLENIANFEE
SNHSNONLLKSTGLMTO
SCEIETGUIOLIOHGDE
HRTAMSMDESMFTLMII
Full example cipher + solve:
#J!:FPQ!S4J1$@O,! Y_^H[5Z+1R:-21LVE XBSQ)!;?.:0+9^&ZA J;]1$,RC>I@8_9Q^% !G+7#ZR::E?)0X+4- J$/3PV%MWBN&).!P< G."O+:LX@A*1!CW41 V:D#-W6LG"7)SU+C. -BF:0XM.JQL+:+1$& G-!-@RJG]4VJ:8O!C GYPXO0;W*+B^?$QS@ 4%:0CM9J,<L13#2"R /T$@:!HV_E.S#XMC& ).BRS>4WE#UR&:^(V YBQPLXAY1CW)E9SO$ -;./#RU-:%D6G+IQL 6@01+C(WO^L#]K:V= *9-4_/L%.B_XGY!L: H-#E!8)SNQL=?%ZC 5490^RW'VO:!1%SE_ Score: 23699.95 IOC: 0.06534 Multiplicity: 0.18529 Repeats: 356 PC-cycles: 4695 Minutes: 1.80 By characters, key(59,136,195,299) THEREWASABLACKCLO UDANDHARDRAINTHEP UDDLESWEREYELLOWA NDGREENLIKESOMEON EHADTOUREDPAINTIN TOTHEMTHEYSAIDITW ASDUSTFROMTHEFLOW ERSGRANDMACADEUSS TAYINTHECELARSHEG OTDOWNONHERKNEESA NDTRAYEDANDSHETAU GHTUSTOOLOURSIPRA YITSTHEENDOFTHEWO RLDITSGODSPUNISHM ENTFOROURSNINSMYB ROTHERWASEIGHTAND IWASSIXWESTARTEDR EMEMBERINGEBROKET HEGLASSCANWITHTHE RASTHERRYVACANDSH
Tried it on the Z340 using the period 15 and 19 with no results. Also tried Scytale.
Next up will be to implement grid style period 19 transpositions, 2-dimensonal period 15 and 19 variations. And allowing a individual period for every rectangle. And vertical rectangles, etc…
