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O.k., thanks. Just curious and thought that you may have already experimented with this.

smokie treats wrote:Largo. The matrix wasn't intended to make P19, but perhaps future ones will.

I know, but I was just curious which nGram peaks the matrix would produce and whether P19 might play a random role.

I found a way to make pivots with a cipher. I added a new spreadsheet to my transposition utility which takes a matrix and uses a mod function to repeat the same short portion over and over again in the matrix. Just changes a transposition matrix so that a short message can be repeated.


Then, I added my pivot detector, and can adjust the length of the message by adding 1 over and over again to see what lengths, if any, create a lot of pivots. Here is the original matrix at period 20.

001 018 035 052 069 086 103 120 137 154 171 188 205 222 239 256 273
290 307 324 002 019 036 053 070 087 104 121 138 155 172 189 206 223
240 257 274 291 308 325 003 020 037 054 071 088 105 122 139 156 173
190 207 224 241 258 275 292 309 326 004 021 038 055 072 089 106 123
140 157 174 191 208 225 242 259 276 293 310 327 005 022 039 056 073
090 107 124 141 158 175 192 209 226 243 260 277 294 311 328 006 023
040 057 074 091 108 125 142 159 176 193 210 227 244 261 278 295 312
329 007 024 041 058 075 092 109 126 143 160 177 194 211 228 245 262
279 296 313 330 008 025 042 059 076 093 110 127 144 161 178 195 212
229 246 263 280 297 314 331 009 026 043 060 077 094 111 128 145 162
179 196 213 230 247 264 281 298 315 332 010 027 044 061 078 095 112
129 146 163 180 197 214 231 248 265 282 299 316 333 011 028 045 062
079 096 113 130 147 164 181 198 215 232 249 266 283 300 317 334 012
029 046 063 080 097 114 131 148 165 182 199 216 233 250 267 284 301
318 335 013 030 047 064 081 098 115 132 149 166 183 200 217 234 251
268 285 302 319 336 014 031 048 065 082 099 116 133 150 167 184 201
218 235 252 269 286 303 320 337 015 032 049 066 083 100 117 134 151
168 185 202 219 236 253 270 287 304 321 338 016 033 050 067 084 101
118 135 152 169 186 203 220 237 254 271 288 305 322 339 017 034 051
068 085 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340

I found out that at period 20 which I like to experiment with because it fills a 17 x 20 grid perfectly, if the message length is 11, 33 or 67, you get a lot of pivots. At any other length up to 170, no pivots at all. Here is the matrix with message length of 67.

01 18 35 52 02 19 36 53 03 20 37 54 04 21 38 55 05
22 39 56 02 19 36 53 03 20 37 54 04 21 38 55 05 22
39 56 06 23 40 57 03 20 37 54 04 21 38 55 05 22 39
56 06 23 40 57 07 24 41 58 04 21 38 55 05 22 39 56
06 23 40 57 07 24 41 58 08 25 42 59 05 22 39 56 06
23 40 57 07 24 41 58 08 25 42 59 09 26 43 60 06 23
40 57 07 24 41 58 08 25 42 59 09 26 43 60 10 27 44
61 07 24 41 58 08 25 42 59 09 26 43 60 10 27 44 61
11 28 45 62 08 25 42 59 09 26 43 60 10 27 44 61 11
28 45 62 12 29 46 63 09 26 43 60 10 27 44 61 11 28
45 62 12 29 46 63 13 30 47 64 10 27 44 61 11 28 45
62 12 29 46 63 13 30 47 64 14 31 48 65 11 28 45 62
12 29 46 63 13 30 47 64 14 31 48 65 15 32 49 66 12
29 46 63 13 30 47 64 14 31 48 65 15 32 49 66 16 33
50 67 13 30 47 64 14 31 48 65 15 32 49 66 16 33 50
67 17 34 51 01 14 31 48 65 15 32 49 66 16 33 50 67
17 34 51 01 18 35 52 02 15 32 49 66 16 33 50 67 17
34 51 01 18 35 52 02 19 36 53 03 16 33 50 67 17 34
51 01 18 35 52 02 19 36 53 03 20 37 54 04 17 34 51
01 18 35 52 02 19 36 53 03 20 37 54 04 21 38 55 05

Here is the what the pivot detector looks like with message length 67.


Here is the plaintext 67 long that repeats itself a lot of times.

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

The plaintext written over and over again at period 20 into a 17x20 grid.

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

The key ( symbol 00 is a polyphone to simulate the + ).

E 00 01 02 03 04 05 06 07
T 08 09 10 11 12 13 14 00
A 15 16 17 18 19 20 00
O 21 22 23 24 25 00
I 26 27 28 29 30 00
N 31 32 33 34
S 35 36 37 38
R
H 39 40 41
D 42 43 44
L 45 46 47
C
U 48 49
F 50 51
M 52 53
W 54 55
G 56 57
P 58 59
Y 60
B 61
V
K 62
X
J
Q
Z

Randomization matrix.

15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35
35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35

And the cryptogram, which has two pivots that resemble the 340 pivots. Ha ha!

21 00 15 42 50 31 52 08 08 56 00 22 16 27 10 40 32
11 40 17 51 33 53 12 13 57 01 23 18 28 14 41 34 00
39 19 43 54 01 58 08 56 03 21 20 29 09 40 31 00 41
00 44 55 04 59 58 15 54 59 20 30 11 39 32 12 40 17
42 55 03 58 59 18 54 58 00 35 19 06 33 13 41 18 43
55 07 59 58 00 54 59 26 36 15 00 14 35 60 34 43 54
01 58 59 16 54 58 27 38 17 02 00 35 60 31 28 29 08
61 59 18 55 59 30 36 19 06 09 37 60 32 00 26 10 61
50 52 39 60 30 38 20 04 14 35 60 33 28 29 12 61 51
53 40 60 48 59 26 13 14 36 60 31 28 26 10 61 50 52
41 60 49 58 27 12 46 46 31 40 27 30 09 61 51 53 40
60 48 58 26 08 47 45 32 41 46 60 57 03 50 52 39 60
48 58 00 10 45 45 33 40 46 60 56 00 25 00 37 11 48
59 29 13 45 45 34 41 46 60 57 07 00 15 38 00 25 38
39 27 47 47 31 40 46 60 56 02 22 19 35 00 23 37 41
28 62 39 17 23 47 60 57 04 25 16 38 08 00 36 40 29
62 39 19 21 30 20 42 51 22 00 36 14 23 37 40 28 62
41 15 24 26 16 43 50 32 53 10 11 25 38 41 27 62 39
17 21 30 00 44 51 33 52 12 13 56 02 21 19 62 41 20
22 29 15 42 50 34 52 14 00 56 03 22 15 30 09 41 33


But the P16, 32 and 48 unigram repeats are way more than in the 340 and I haven't checked the other stats and also wonder if a message of a certain length that does not make pivots would if nulls or skips are in certain positions, or vice versa.

It should solve at P20.

The bigram repeat chart shows a pattern unlike the 340 and the coincidence count spike is way, way higher.


But, my hypothesis is that there is a pattern of letters written over and over again, at least in the region of the pivots. Or something like that because of the cluster of P16, 32 and 48 unigram repeats in the area of the pivots. Especially the one on the right.

I have a new, adjusted hypothesis. Here is what might create pivots in the middle of the message and P29 or P39. He used a cylinder with a paper taped to it, and vertically wrote the same word or short phrase over and over again in certain columns at certain intervals. Then, he wrote vertically an actual scytale message, skipping over the word or short phrase. Then the plaintext was transcribed into the 17x20 grid, and the letters of the word or short phrase lined up diagonally and that made pivots and P29 or P39.

I got a pretty good partial solve in just a few seconds with AZD. Thanks!

Code: Select all

21   00   15   42   50   31   52   08   08   56   00   22   16   27   10   40   32
11   40   17   51   33   53   12   13   57   01   23   18   28   14   41   34   00
39   19   43   54   01   58   08   56   03   21   20   29   09   40   31   00   41
00   44   55   04   59   58   15   54   59   20   30   11   39   32   12   40   17
42   55   03   58   59   18   54   58   00   35   19   06   33   13   41   18   43
55   07   59   58   00   54   59   26   36   15   00   14   35   60   34   43   54
01   58   59   16   54   58   27   38   17   02   00   35   60   31   28   29   08
61   59   18   55   59   30   36   19   06   09   37   60   32   00   26   10   61
50   52   39   60   30   38   20   04   14   35   60   33   28   29   12   61   51
53   40   60   48   59   26   13   14   36   60   31   28   26   10   61   50   52
41   60   49   58   27   12   46   46   31   40   27   30   09   61   51   53   40
60   48   58   26   08   47   45   32   41   46   60   57   03   50   52   39   60
48   58   00   10   45   45   33   40   46   60   56   00   25   00   37   11   48
59   29   13   45   45   34   41   46   60   57   07   00   15   38   00   25   38
39   27   47   47   31   40   46   60   56   02   22   19   35   00   23   37   41
28   62   39   17   23   47   60   57   04   25   16   38   08   00   36   40   29
62   39   19   21   30   20   42   51   22   00   36   14   23   37   40   28   62
41   15   24   26   16   43   50   32   53   10   11   25   38   41   27   62   39
17   21   30   00   44   51   33   52   12   13   56   02   21   19   62   41   20
22   29   15   42   50   34   52   14   00   56   03   22   15   30   09   41   33

Iterations: 303/1000
Score: 23363.37 Ioc: 0.06491
Ngrams: 8875690302 PC-cycles: 2807

Columnar(20*17,TP,C:1)
Offset row order(11*31,Y:25)
Offset row order(134*3,Y:1)

IORTANORTANDPINIR
OLLOOKENGITWASSIM
PLYESHAMETHEWAYTH
INGSHADTOHAPPENBY
THENIORTANDPINFRO
LLOOKINGITWASSIMP
LYASHAMETHEWAYTHE
NGSHADTOHAPPENBYT
HATFORTANDPITFROL
LOEKINGFEWESSIMPL
YASHEMENHEWAYTHIN
GSHADNOHEPPANBYTH
EEIRREANDPIEERILL
EOKINGIEWASSIMPLY
ASHAMETHEWAYTHING
SHADTOHAPPENBYTHE
EFORTANDPENFROLLO
OKINGITWASSIMPLYE
SHAMATHEWAYTHINGS
HADTOHAPPENBYTHET

O F T A N D P I T I F U L L O O K I N G I T W A S S I M P L Y A S H A M E T H E W A Y T H I N G S H A D T O H A P P E N B Y T H E T I M
ORT AND PINIR OL LOOKENG IT WAS SIMPLY E SHAME THE WAY THINGS HAD TO HAPPEN BY THE NIO

At P19, if the repeated message was 53 long, it would make pivots. Or, if there was a word or short phrase repeated at intervals of 53, there would be pivots and also P19.

Or far simpler explanation, and simple is good. A word that is 8 long, repeated over and over again in the middle of the message. Would make P19, P39 and pivots!

The numbers are word positions, just imagine an 8 letter word there. Match up 4 and 7 = P19. Match up 1 and 8 = P39. Match up 3 and 2 = P39. And the diagonals P16, P32 and P48 unigram repeats will make pivots.

smokie treats wrote:But, my hypothesis is that there is a pattern of letters written over and over again, at least in the region of the pivots. Or something like that because of the cluster of P16, 32 and 48 unigram repeats in the area of the pivots. Especially the one on the right.

I also have considered this but did not get very far.

If you made a scytale message 19 x 18 and wrote vertically, and there was a section that was repeated over and over again at this interval, it would make pivots.

The message below, with only the repeated phrase in the creative pattern.


After recast into 17 x 20, it makes pivots.


Maybe we are looking at a very creative scytale message. If the phrase was just the right length I think it would make P39 but I will work on that later today or tomorrow.

hi smokie.. i have tried lots of times to get a scytale to wrap and form in a pivot with no success. i can see your line of thinking but i am not sure he would have done that.
cheers