I think that the pivots may be connected to the misalignment and I have some new results that point in this direction. Will try to share soon. I do like your idea of the pivots being a visual clue.
Ok, check this: viewtopic.php?f=81&t=3206
When I say cut by the edge of the message, I mean that the two symbols of a period n bigram occupy different rows in the message. For example, period 1 could be two symbols next to each other, or one symbol in column 17 and the other symbol in column 1. When reading the message mirrored, it will be a period 33 bigram.
Reading the message in different directions counts different bigram repeats. For example, on the left is the 340 reading left right top bottom. The colored symbols are period 19 bigrams that occupy two rows and where there is a corresponding period 15 reverse bigram that occupies only one row ( the symbols not shaded, but outlined in red ). If the message is mirrored, then those period 15 reverse bigrams activate because all of the sudden they are not reverse and they have symbols that match the new period 15 bigrams that occupy two rows.
I circled one in blue. See the 31 – 29 period 19 bigram that occupies rows 16 and 17 and has matching symbols period 15 on row 9. When the message is mirrored, suddenly the symbols on row 9 are 31 – 29 period 15 and the 31 – 29 on rows 16 and 17 are also period 15.
There are a lot of these, accounting for some of the difference in repeat counts depending on reading direction. Some period 15 repeats would also be destroyed by the mirroring process, but overall the count of bigram repeats for the mirrored is higher. A lot of symbols turn on and off when reading the message in different directions.
Because the message is written into a 17 x 20 rectangle, we are stuck with interpreting this problem. If the message was drafted into a 10 x 34 rectangle, we would have the same problem but with different periods and different repeats being counted.
Cycle scores 8 different encoding directions from 4 corners
Score is calculated by adding all cycle scores for all possible combinations of symbols, where consecutive alternations ABA = 2 ^ 2, ABAB = 2 ^ 3, ABABA – 2 ^ 4, etc.
64418 Left right top bottom
64418 Right left bottom top
42608 Right left top bottom
42608 Left right bottom top
32444 Top bottom left right
32444 Bottom top right left
31516 Top bottom right left
31516 Bottom top left right
The message is much more cyclic reading left right top bottom OR right left bottom top
14888 Left right top bottom OR right left bottom top positions 1 – 170
13324 Left right top bottom OR right left bottom top positions 171 – 340
4710 Left right top bottom OR right left bottom top positions 1 – 85
4510 Left right top bottom OR right left bottom top positions 86 – 170
4272 Left right top bottom OR right left bottom top positions 171 – 255
4328 Left right top bottom OR right left bottom top positions 256 – 340
The message is somewhat more cyclic in the top half as compared to the bottom half
For comparison, here is a message where the plaintext is the first 340 of the 408, with perfect cycles:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 1 26 7 27 28 29 30 31 32
33 34 23 35 7 36 10 37 38 39 40 5 41 31 42 43 44
45 46 4 1 2 8 3 11 47 48 7 9 49 12 50 30 14
10 35 51 33 18 34 52 53 40 20 24 26 54 25 21 55 23
27 5 38 22 42 1 28 36 44 14 30 15 37 43 56 45 46
47 18 53 29 31 24 50 11 3 38 55 17 39 41 22 2 8
51 52 6 7 9 17 27 15 30 20 26 33 10 35 12 47 1
57 25 28 38 5 36 44 14 30 29 37 43 51 33 40 3 2
8 7 42 12 18 58 13 20 53 25 46 32 5 10 26 1 24
14 59 18 11 19 20 36 43 25 40 51 44 45 35 47 5 26
36 3 42 12 60 39 23 53 40 52 21 4 27 15 34 41 61
7 43 33 50 47 10 53 9 51 44 14 54 18 28 26 16 55
40 36 29 34 1 43 3 37 51 33 22 26 48 44 20 46 7
49 10 25 1 61 3 17 2 19 5 53 14 54 39 40 11 7
35 13 45 53 50 56 10 32 18 55 42 49 22 8 9 36 33
20 1 44 45 57 25 6 3 17 2 5 56 48 7 8 9 19
14 21 52 38 18 30 62 24 17 50 59 20 27 10 61 1 2
8 46 15 43 12 3 57 25 60 29 31 38 62 11 55 30 5
54 14 32 22 23 28 18 60 39 31 48 7 9 17 51 40 62
1785226 Left right top bottom
1785226 Right left bottom top
112846 Right left top bottom
112846 Left right bottom top
33998 Top bottom left right
33998 Bottom top right left
33774 Top bottom right left
33774 Bottom top left right
EDIT: Here is the same message with all random homophonic symbol selection:
1 2 3 4 5 4 1 6 7 3 8 9 10 11 12 13 7
14 15 11 16 17 18 19 20 21 22 1 23 24 12 25 26 27
28 29 18 8 3 30 1 19 25 31 32 5 33 18 34 35 36
37 34 38 21 6 39 3 8 9 40 3 39 41 9 17 25 20
3 34 22 36 5 33 42 43 32 11 44 35 15 45 16 17 18
23 5 46 37 8 47 23 30 36 45 46 42 19 48 49 17 8
50 14 32 51 18 23 52 34 47 25 53 6 12 33 52 6 2
35 31 38 21 7 6 24 12 46 45 30 28 3 34 9 50 47
54 11 24 25 5 35 28 11 25 12 24 48 30 28 32 47 39
6 47 55 9 11 56 10 5 32 45 55 16 14 3 48 47 23
45 57 5 55 15 11 22 48 11 43 22 28 52 34 9 5 22
48 1 55 9 58 31 26 32 43 12 16 4 23 31 29 29 59
1 35 36 17 50 21 32 39 22 36 5 60 20 19 35 13 37
43 48 31 33 21 35 1 19 30 36 53 35 59 28 45 34 47
49 1 11 3 40 21 7 39 60 5 32 11 60 31 32 8 1
8 10 52 32 17 41 3 16 5 52 61 49 37 7 7 35 28
5 21 36 53 54 11 4 1 2 2 20 41 40 1 2 6 60
11 27 51 25 45 46 58 23 2 52 57 5 19 1 40 3 6
6 55 51 22 9 1 57 14 62 12 26 25 62 55 17 46 20
60 20 27 37 26 44 5 58 12 18 40 1 7 2 30 32 58
33756 Left right top bottom
33756 Right left bottom top
38526 Right left top bottom
38526 Left right bottom top
33184 Top bottom left right
33184 Bottom top right left
28420 Top bottom right left
28420 Bottom top left right
Visual Clue Pivot Hypothesis
Unless some new transposition has not yet been discovered, the odds of the pivots being created by a transposition, whether by skipped symbols, nulls, or whatever, are astronomical. Under the "visual clue pivot hypothesis," Zodiac put the pivots there on purpose to give a clue about the encoding or transposition. He knew that the message would be very difficult to solve, and installed two pivots so that they would be noticed.
Here is one possibility, although it is just a general idea about what Zodiac may have done:
1. Zodiac transposed the plaintext with a 22 x 15 inscription rectangle, or whatever;
2. Zodiac encoded the message right left bottom top ( although seemingly unlikely );
3. When Zodiac got to row 14, he decided to leave a clue, and copied three symbols vertically;
4. Zodiac continued to encode around the three symbols until he got to row 12, where he decided to double his clue so that it would be noticed;
5. Zodiac copied another 3 symbols vertically; and
6. Zodiac continued to encode around the pivots.
It was a way of giving us some clue as to what he did. Maybe he was saying, "I transposed the plaintext and transcribed it left right bottom top" or something like that.
Hey smokie,
I like your visual clue hypothesis on the pivots. He did a similar thing in the 408 by adding filler in the form of dropping down a trigram. Since period 15 returns higher than period 19 it seems likely that the transcription was either right left top bottom or left right bottom top. Encoding happened after final transcription left right top bottom. Somewhere along the line he introduced the pivots as filler. My encoding measurement rank the pivot rows and columns (or smaller parts) as best options for being non-cyclic. What I don’t like is that it is also unlikely since the pivots are made out of period 29 bigram repeats.
Here’s a printout from my take on your excellent 2 symbol cycles measurement. There’s something I’d like you to check out, some diagonal transpositions of the 340 seem to have high encoding scores compared to the 408 (see arrow). A 17 by 20 408 sample does not score over 700 on the transposed diagonals, but the 340 goes over 1100? I wonder about your numbers here.
Normal: 1626.452102524174 Mirror: 1531.387861369969 Flip: 1420.695336079445 Reverse: 1518.393544750901 ------------------------------- Columnar 1 (transposed): 736.4058657007797 Columnar 2 (transposed): 790.8818545519781 Columnar 3 (transposed): 794.7181464173056 Columnar 4 (transposed): 734.8074362170063 ------------------------------- Diagonal 1 (transposed): 718.6289061289619 Diagonal 2 (transposed): 1134.842018070604 Diagonal 3 (transposed): 1136.136454401513 Diagonal 4 (transposed): 688.2150467485983 Diagonal 5 (transposed): 724.5091453366368 Diagonal 6 (transposed): 1161.151305138606 <--- Diagonal 7 (transposed): 1112.24619433296 Diagonal 8 (transposed): 683.1066835763855 ------------------------------- Columnar 1 (untransposed): 883.3881806407487 Columnar 2 (untransposed): 887.7496692598623 Columnar 3 (untransposed): 879.2200056046327 Columnar 4 (untransposed): 892.1323783679032 ------------------------------- Diagonal 1 (untransposed): 947.2925194245371 Diagonal 2 (untransposed): 896.3105754457064 Diagonal 3 (untransposed): 1028.076451417183 Diagonal 4 (untransposed): 1061.154355555342 Diagonal 5 (untransposed): 1084.653703864863 Diagonal 6 (untransposed): 1049.816383587005 Diagonal 7 (untransposed): 873.1772161081185 Diagonal 8 (untransposed): 918.8201487911971 Diagonal 6: 31 47 21 19 6 50 3 43 21 34 27 20 15 10 6 3 1 55 53 13 11 50 51 11 19 5 26 20 26 19 14 9 5 2 23 34 63 60 13 22 7 17 19 5 15 33 25 5 13 8 4 51 31 20 62 19 40 21 3 49 23 42 39 32 24 18 12 7 44 20 37 51 34 40 28 25 44 48 5 41 38 31 23 17 11 53 58 52 14 29 36 27 8 16 5 40 45 1 19 30 22 16 4 8 21 19 61 43 20 18 15 4 54 19 8 40 37 29 21 31 2 36 36 28 5 5 51 46 59 51 10 37 30 22 36 28 36 20 56 28 20 37 20 23 16 19 36 10 53 47 44 13 35 26 3 40 47 61 51 53 27 19 3 23 38 56 52 46 6 33 40 6 16 45 53 53 50 14 25 41 39 22 16 17 19 16 7 21 56 51 15 28 35 16 11 50 11 7 19 49 58 30 9 31 29 54 26 19 57 36 30 50 18 30 2 19 61 32 24 55 51 20 26 14 33 29 37 11 12 32 19 11 48 8 19 41 57 23 37 23 17 1 19 56 32 19 59 7 22 41 50 38 37 16 31 10 4 27 10 42 19 63 28 55 20 18 34 3 54 6 29 15 23 5 36 46 51 23 13 12 7 50 34 51 42 6 3 40 17 11 39 18 56 20 11 9 33 13 5 39 19 15 47 36 19 55 58 62 40 1 55 48 5 36 11 19 23 38 19 6 63 29 38 19 31 44 42 25 30 43 33 26 20 14 21 8 48 3 40 16
I came up with 35236 for the above message.
I was thinking about the pivots being period 29 / 39 while driving to work this morning. Although there is a spike at period 29, and it could be a coincidence that Zodiac put the pivots at period 29, wouldn’t it be more probable that he did that than the pivots naturally occurring by some transposition? In other words, we have two improbable things, but one may be more probable than the other. We have a spike at period 29 and he put the pivots at period 29 versus the pivots naturally created.
The message could be upside down.
I am still working on detecting the count of columns for your chunk anagram message in the other thread. I have sort of a system, made two test messages. One was a partial success, one was a failure. But I am still working on it for a little bit each day.
Hi smokie,
Your idea that the pivots could be visual hints sounds good! I will try some patterns with pen+paper soon.
I had a similiar idea in which the + symbols represented some kind of a shape before the cipher was transposed (see second post in the following thread: http://zodiackillersite.com/viewtopic.php?f=81&t=3093&p=48590).
I tried to find a transposition which can produce z340-like plus patterns. Here is my result:
Plaintext in a 9×9 grid (to keep things simple):
Now read the plaintext diagonally. You can still recognize a pattern
Now re-draft to a 6 x 14 grid. The pattern is gone (I don’t see it anymore…anyone else?)
This idea fits with Jarvles observations:
– The ‘+’ symbol does not seem to cycle well with other symbols.
– The average of the position numbers for all occurrences of the ‘+’ symbol is 171, which is only one position from the midpoint of the cipher. This suggests the + symbols are very uniformly distributed throughout the ciphertext.
What do you think?
Another idea is that the plus symbols are nulls which have to be removed before applying any kind of transposition. (Regarding to Jarlve’s and yours hypothesis that a possible misalingment is the result of nulls in the cipher text).
Oh…by the way….I have re-drafted z340 into new sizes from width 2 to width 170 and generated .png-files which contains the plus-patterns. I have found nothing special. But feel free to have a look at those images and look for suspicious ones:
https://www.dropbox.com/s/3rxszvu44m6laym/Plus_Patterns_Resized_Width.zip?dl=0
Oh…by the way….I have re-drafted z340 into new sizes from width 2 to width 170 and generated .png-files which contains the plus-patterns. I have found nothing special. But feel free to have a look at those images and look for suspicious ones:
That’s a cool idea. It might be beneficial to run an automatic symmetry test (i.e., use an algorithm to count plus symbols that occupy symmetrical positions within each grid under consideration).
An interesting discussion of different ways to detect patterns in a grid: http://stats.stackexchange.com/question … ary-matrix
Replace the dots with Z340’s plus symbols (or any other symbol under consideration I suppose)
I liked this suggestion on that page: "You could rotate (flip to 90 degrees, than 180 degrees, etc) your matrix until the configuration concur with the original one". As you do the rotations, you can see how many of the symbols coincide, which may give you a quantitative sense of symmetry.
That’s a cool idea. It might be beneficial to run an automatic symmetry test (i.e., use an algorithm to count plus symbols that occupy symmetrical positions within each grid under consideration).
I have implemented that a couple of month ago. My python library creates a plus pattern for each of my tests and checks for horizontal and diagonal patterns (like "+++++" and "+ + + + +".
Maybe I will refactor my code and make it open source. I have implemented lots of tests and my library is very convenient (move rows/columns around, re-draft and all that stuff)
Preview:
----------------- -+--------------- -----+----------- ------------++--+ ------------+---- ----------------- --+-------------- -------+--------- -++--+----------- ----++----------- -+--------------- -------------+--- -----------+----- ---------------++ ----------------+ ----------------+ -----+----------+ -+--------------- ----------------- -----------------
Very nice!
I recently put all of my code up, warts and all, on github: https://github.com/doranchak/zodiac-killer-ciphers
It’s a huge mess and has zero documentation of course. 
But I highly recommend that you put your stuff up on github. It’s a really convenient way to preserve and share your work. Plus if you want to stage a multi-machine attack on some problem you’ve coded up, you can easily clone the repo on multiple computers and set them all to work.
Largo, I will definitely have to include a discussion about the + symbol in this thread so stay tuned. I made another post, much longer this morning, but for some reason having difficulties with the website having to constantly login to view pictures and not being able to preview my messages. I lost the one that I wrote.
I really like the idea of looking for patterns in rearranged messages, and consider that possibly related to prime phobia. I am so pleased that there are new people contributing to the 340 discussion on this website, yourself and BartW included.
I had a similiar idea in which the + symbols represented some kind of a shape before the cipher was transposed.
Incredibly you came up with roughly the same idea I posted a while ago in viewtopic.php?f=81&t=2810
