Oh my gosh. I thought this said Homophobic substitution.

Great to hear that you’re still on it doranchak, your transposition explorer is a very exciting project! I’ve just fired up a big test of 8 million transposition variations for smokie’s scheme but with a period 15 interpretation. Will get back with the results.

@smokie, whatever you do, don’t pick up Gareth Penn’s book TIMES 17. It makes things worse.

From that book:

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I have been taking a little break but thinking about skipped and added symbols during transposition. I have my spreadsheets set up for a diagonal row analysis, but am also thinking about some type of analysis of an un-transposed message, which is easier to visualize. I am also thinking about how to add or delete symbols to maximize the total number of transposed period 19 bigram repeats and/ or their scores, or to maximize the total number of untransposed period 1 bigram repeats and/ or their scores.

Smokie14 has been ready for a while now, and it has two skipped symbols in the first few rows which emulate the 340’s number of period 18 bigrams that have matching period 19 bigrams in the remainder of the message. Similar to what would happen if the message was 319-321 plaintext long and the transposition started at column 17 rather than column 1. There are also two added symbols with separated distortion zones, although I do not see strong evidence that Zodiac did that, except for the high number of period 39 bigram repeats. But I have not yet worked the analysis. It will be a bit murky I think.

I have also been making a lot of messages privately. With 63 symbols, it is much easier to emulate the 340’s number of period 19 bigram repeats by making the key "inefficient" as Jarlve would call it. Making the key so that a slightly higher count of ciphertext map to low count plaintext and a lower count of ciphertext map to high count plaintext, in addition to making at least one ciphertext polyalphabetic and map to at least a few high count plaintext that are also high count with plaintext bigram repeats. With the 340, the + symbol is heavily represented on the list of period 19 bigram repeats (EDIT: and doesn’t cycle well with other symbols). That makes me suspicious. There are also several situations where you have A19B and A19C and B and C cycle together.

I know that you guys have been working on a lot of different complicated transposition schemes. My thinking is that maybe the transposition scheme is simple, but has several skipped symbols, which would cause several misalignments in an untransposed message making it more difficult to solve. My argument is that Zodiac made the message in 1969 or 1970 or whenever, and did not have any idea of what computer abilities we would have today. But I am waiting to see what your results are and hoping that you guys solve the message so that I can move on with my life.

Let me know when you want smokie14. The transposition scheme is very simple. But Jarlve, I am not asking you to write a computer program to try all different combinations of two skipped and two added symbols in a 340 symbol message. I am thinking about ways to detect them, but still resting too. Either way it is o.k. In the big scheme of things, I think that we are on the right track and I appreciate your efforts.

Smokie

EDIT:

Here is one example of A19B and A19C where B and C cycle:

OF are a period 19 bigram repeat, and so is MF. O am M cycle together, although not perfectly. But their cycle score is 15th highest out of 1953 two symbol cycle scores.

Is that a coincidence? I am saying that O and M map to the same plaintext. That is why they cycle and are also in a period 19 bigram repeat with F. Maybe O and M map to plaintext "T" and F maps to plaintext "H", or whatever two plaintext are in high frequency bigram repeats for the message.
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Here is another one. The G and + are in three period 19 bigram repeats. The phi symbol and + are also in three period 19 bigram repeats. The G and phi symbol cycle together, and although not perfect, their score ranks 17th out of 1953 two symbol cycle scores. That is in the top 1%.

There is a missing G in rows 3-6. I wonder if the cycle not being perfect is evidence of intent, sloppiness, or the cipher.

If the + symbol is part of multiple cycles making it look like a high count 1:1 substitute, then maybe these period 19 bigrams can help us to group them with their respective cycles. In the above example I am saying that the G and phi symbol likely map to the same plaintext and the + symbol in those period 19 bigrams map to the same plaintext. Those period 19 bigrams map to English language high frequency plaintext period 1 bigrams. I have not explored this yet, but the + symbols in those period 19 bigrams should cycle well with a few other symbols.

Basically I am saying that we have A19C A19C A19C and B19C B19C B19C. A and B map to the same plaintext. C is a high count symbol that doesn’t cycle well with other symbols. Except that if you segregate those particular C’s, they should cycle with E and F, irrespective of the other C’s.
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Let me know when you want smokie14. The transposition scheme is very simple. But Jarlve, I am not asking you to write a computer program to try all different combinations of two skipped and two added symbols in a 340 symbol message. I am thinking about ways to detect them, but still resting too. Either way it is o.k. In the big scheme of things, I think that we are on the right track and I appreciate your efforts.

I would like to write a routine to (un)verify your scheme for the 340. So that we can move onto another interpretation.

You probably haven’t considered the period 15 version of your scheme. Mirror the 340 and then cast it into a 23 by 15 grid and do/undo the vertical transposition.

Let’s decide on all the possible variations of your scheme,

– Period 15 or 19 scheme.
– Normal or reversed string.
– 4 different starting corners for the transposition.
– Cipher length range.
– Add, remove a number of symbols in the process.

So I want to know from you what kind of limits you would feel sufficiently comfortable with to rule out your scheme for the 340. And also if you want to consider other possible variations. We previously used a cipher length range of 21 and that, I think, is more than broad enough. But we only considered one symbol removed and/or added and that seems to be on the low side. We didn’t consider the period 15 scheme and using the reversed string of the 340.

So tell me what I need to know and I’ll look into the feasability and get to work on some changes to my routine. Then you could remake the smokie14 into the ultimate test for the limits we agreed on. If it solves the routine will versus the 340.

I agree with all of the above limitations, including message length range, and your variations of plaintext message shape far exceed anything that I ever dreamed of. Except that I think that a mirrored period 15 bigram repeat could be caused by writing a period 19 transposed message from right to left, bottom row to top row. I think that there could be more skipped or added symbols, your idea. It seems like the most pragmatic explanation for the message not getting solved at this point and I think that you like that idea.

Regardless of the type of transposition, what about making alterations to un-transposed messages before or during the solve process. If you add a symbol to replace a suspected skipped symbol, then contiguous symbols are shifted with respect to each other at the misalignment line. Elsewhere, contiguous symbols are not shifted with respect to each other. What do you think about randomly adding or deleting a symbol once every 500 ( or whatever ) solve iterations? If the score increases over the next 500 ( or whatever ) iterations, then keep the change. If the score does not increase over the next 500 ( or whatever ) iterations, then don’t keep the change. Make another random change.

My lunch break is over, I have to go. Ttyl.

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K so let’s go back to the first example.

Here we have O19F O19F ( my 23 – 51 ):

There are ten O’s and ten F’s in the message. I figure that the odds of getting O19F O19F with random shuffles as:

[(10/340)*(10/340)]^2 = 1 in 1,336,336.

Here is M19F and M19F ( my 37 – 51 ):

There are seven M’s and ten F’s. I figure the odds of getting M19F and M19F with random shuffles as:

[(7/340)*(10/340)]^2 = 1 in 2,727,216.

Here is the cycle with O and M ( my cycle 23 – 37 ), where we have O M O M O O M O M O M O M O O M O:

Scoring that is a bit more difficult for me when it is not a perfect cycle, but one of my formulas adds the scores of perfect segments of cycles:

[(10/340)*(7/340)*(10/340)*(7/340)*(10/340)]+[(10/340)*(7/340)*(10/340)*(7/340)*(10/340)*(7/340)*(10/340)*(7/340)*(10/340)]+[(10/340)*(7/340)*(10/340)]

= 1 in 92,725,355 plus 1 in 252,882,102,317,634 plus 1 in 56,149.

In any case, I have 1,953 two symbol cycles and this is the 15th highest scoring cycle with all of them using the same scoring formula.

What are the chances of all three of these things happening with random shuffles? Pretty astronomical I would think. But I am not totally sure. The second example has two sets of three period 19 bigram repeats, even more astronomical I think.
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Let’s say that you have this, with the symbols and otherwise blank spaces:

How many times to shuffle to get a similar pattern?

EDIT: This comparison is wrong because there are other symbols with similar counts in the message. You would have to take into account the other symbols with similar counts. You would probably have to shuffle a similar example that includes all of the other symbols with similar counts.
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Good to see so many people are trying to break the Zodiac’s code!

Except that I think that a mirrored period 15 bigram repeat could be caused by writing a period 19 transposed message from right to left, bottom row to top row.

Plausible but unlikely. I will include the reversed cipher in my routine so that will be considered as well.

I think that there could be more skipped or added symbols, your idea.

I’d like to go as high as possible here. I’m willing to spend about a month of computer time.

Regardless of the type of transposition, what about making alterations to un-transposed messages before or during the solve process.

Hill climbing is probably a good idea although I don’t want to consider it at the moment. I’d like to (un)verify the scheme to some respectable limits.

Thanks, Jarlve. I have some quiet time and not feeling burned out right now. I am working on a massive new spreadsheet that detects possible locations for skipped and added symbols. It won’t be perfect, but will give the best guess as to where to add or delete symbols so that misaligned period 1 bigrams are re-aligned when the message is untransposed. I don’t know if it will work, but it is going to be much more efficient than a diagonal row analysis, and have cool charts and heat maps and stuff. Coming soon.

Okay smokie, looking forward to it.

I’ve calculated that 4 symbols can be skipped or added. But not 4 of each, so 2 skips and 2 adds, or 3 skips and 1 add. What is your opinion here? Go with 2/2? The routine will also find anything less by the way and also when multiple skips or adds are on one transposition line.

I have a few recommendations to fight fatigue and burn out.

– Regular vitamin supplements or vitamin rich food/drinks.
– Don’t overdo on coffee, it will only exhaust you in the long term.
– About 20 mins of sweat inducing physical activity mostly every day.
– When feeling stressed/uneasy start monitoring your breathing and take slow deep breaths.
– Get enough quality sleep, unwind a few hours before going to bed. Don’t use alcohol to induce evening drowsiness, it should come naturally.

Two skipped and two added symbols is fine. I can make one of those if you want; I already have a tracing map made for two skipped symbols very close to each other and two added symbols not close to each other so that the distortion zones are easy to identify.

My new spreadsheet has about 580,000 formulas and takes about a minute to calculate everything.

You can select to add a skipped symbol or delete an added symbol in all of the 340 positions and the spreadsheet will compare the changes in number of period 19 bigram repeats, total probability score, and score / number of bigram repeats. I have a heat map showing where to add or delete symbols so that an untransposed message will have more or higher scoring period 1 repeats.

It doesn’t work perfectly, but when I use it on some of my former messages, it actually does work sometimes to highlight distortion zones and occasionally nails the position where the plaintext was skipped or deleted. I am still working on my scoring formula; currently I am using the ln function to make scores more comparable.

EDIT: Here is a preview of the heatmap with the 340 on it. The lighter colored squares are where adding a symbol would increase the number of period 1 bigram repeats after untransposition. The numbers in the squares are the rank for maximum impact. The scoring formula isn’t taken into consideration with this example, but all I have to do is change the value in one cell and it will take scoring into consideration. I can also change the value in one cell and look for where deleting a symbol will have maximum impact. The idea will be to trace the distortion zones for test messages onto the heatmap and make changes to the formulas to see if I can identify the distortion zones or even particular cells.

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Jarlve, here is smokie14. There are two skipped and two adds.

12 2 9 16 15 33 39 13 37 57 8 24 59 47 5 10 36
53 18 1 56 29 49 27 13 40 60 19 17 25 25 1 47 14
20 19 16 15 25 40 38 19 6 5 41 39 60 11 34 61 45
30 4 29 1 17 3 26 59 44 28 37 19 49 9 15 19 42
23 54 57 13 32 63 52 16 62 19 26 39 40 18 10 25 5
41 7 29 58 60 27 14 19 61 59 19 21 17 49 48 41 38
58 61 33 19 17 5 41 20 53 14 20 29 12 36 43 21 56
23 9 20 12 61 56 19 39 19 33 49 47 45 22 8 37 53
19 20 45 9 59 57 49 42 25 29 49 56 50 20 19 4 38
33 12 17 19 5 35 17 55 34 29 13 32 15 62 37 37 31
49 53 17 45 19 3 21 16 40 11 5 52 17 38 1 19 28
20 57 39 27 18 51 19 29 37 59 19 57 54 41 7 9 61
47 13 17 41 25 36 61 56 61 15 2 5 19 3 31 35 20
27 23 33 32 42 14 38 57 53 20 60 5 45 61 61 17 12
29 9 52 49 19 17 61 24 55 33 61 11 39 8 19 41 61
60 53 17 28 28 41 61 22 5 20 59 57 17 16 19 29 41
32 49 49 13 40 60 19 9 36 63 11 61 3 3 42 2 13
52 52 17 10 34 55 5 63 57 22 53 46 25 60 12 29 61
42 50 58 41 30 50 6 5 46 16 3 28 25 51 40 2 53
60 14 13 19 20 17 9 37 20 47 33 38 8 19 39 16 53

Here is the heatmap for smokie14, showing where ( maybe ) adding a symbol to replace a skipped symbol will increase the overall probability bigram repeat score:

Here is the heatmap for smokie14 showing where ( maybe ) deleting a symbol to replace an added symbol will increase the overall probability bigram repeat score:

When you solve and figure out where the skipped and added symbols are, I will show the distortion zones on the heatmaps to see if they work.

EDIT: The transposition scheme is very simple. The message is 323 plaintext long 17×19 both before and after the two skips and adds.
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By the way, smokie14 has two polyalphabetic symbols.

Here is the 340 scattergraph showing on the x axis symbol count, and on the y axis cycle activity:

Here is the smokie14 scattergraph showing the same:

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