Zodiackillersite.com

Your findings concerning misalignments make me wonder if Zodiac applied irregular columnar transposition. In irregular columnar transposition, some columns have length L while others have length L-1. When the columns are then written out, the periodic bigrams would then be misaligned, possibly only by 1 position. Did you already explore that possibility? I think we talked about it before. I recall running some brute force searches of short keys to try to find peak bigram counts, fragments, and L=2 cycles. It may be very interesting to see with test ciphers how often period 29 pivots appear for irregular columnar transpositions of plaintext written in 15 or 30 columns.

Jarlve wrote:Does there exist some structure (any combination of symbols at any positions) in any step of the transposition process which causes period 29 bigrams repeats?

Or alternatively, the transposition itself caused a misalignment. Mixing of periods or errors or for example skytale transposition does run into the same positions when the period number shares a divisor with the cipher length, but secondary rules can be added.

doranchak wrote:Your findings concerning misalignments make me wonder if Zodiac applied irregular columnar transposition. In irregular columnar transposition, some columns have length L while others have length L-1. When the columns are then written out, the periodic bigrams would then be misaligned, possibly only by 1 position. Did you already explore that possibility? I think we talked about it before. I recall running some brute force searches of short keys to try to find peak bigram counts, fragments, and L=2 cycles. It may be very interesting to see with test ciphers how often period 29 pivots appear for irregular columnar transpositions of plaintext written in 15 or 30 columns.

I haven't fully explored that possibility. Irregular columnar transposition is the hypothesis I put forward.

Jarlve wrote:The plaintext existed in a 23 by 15 grid and then was taken off by columns and transcribed into a 17 by 20 grid following either right-to-left, top-to-bottom or left-to-right, bottom-to-top. In that process some symbols were left out. I like it because it is a minimal hypothesis that can explain rare observations in the 340 such as pivots and periodical repeats (I understand that this hypothesis could be wrong and I would like to find out).

I would guess that the colums were taken off starting in either the upper-left or upper-right corner since that's where the highest AZdecrypt scores are returned from. Important to note is that there is an input and output direction. Which smokie describes as inscription and transcription, which are concepts of classical cryptology. I believe Zodiac transcribed (output direction) from right-to-left, top-to-bottom or left-to-right, bottom-to-top and that's why bigrams peak (41) after mirroring or flipping the 340.

smokie treats wrote:I spent some time on the 340 today. I have had some nagging issues about transposition, and one of them is whether a few transcription nulls, or transcription skips for the mirrored 340, could produce so many period 29 repeats and the pivots.

I did the same thing with a 340 character part of the 408. After period 15 transposition it created 46 period 15 bigrams repeats and 38 period 30 bigrams repeats. Then any combination of 2 characters were removed and period 29, 30 and 31 bigream repeats were measured. Here is the graph, the left square is period 29, the middle square is period 30 and the right square is period 31. The x-axis is the first character removed from position 1 to 340 and the y-axis is the second character removed from position 1 to 339. The color brightness are the bigram repeat values where brighter is more.

There is more bright in the left square, which is period 29, indicating that removing characters does shift the period but with only 2 characters removed the effect is minor at best. The highest bigram repeats recorded for period 29 were 31. So that seems to confirm smokie's results. If there is a structure misaligning period 30 into period 29 it must count quite a bit of characters. Interesting.

Yes to the post above. Maybe a structure and not just a few skips or nulls.

I have thought about this idea before. A 22 x 15 rectangle, except alternating 15 rows, then 14 rows, then 15 rows, etc. Period 1 would then be split between period 14 and period 15, and period 2 would become period 29.

However, when comparing the cross period bigram lists for all periods with period 15, I did not find a lot of period 14 bigrams that have symbols matching those of period 15 bigrams. The number is relatively low for period 14, at 67 ( red ). There are 99 bigrams with symbols that match period 15 bigrams at periods 16 and 26 ( blue ). The spike is not important because it is comparing period 15 with period 15.

Also, the potential for high count of period 15 repeats would be significantly diminished, so I don't think that this is what he may have done. But maybe it is worth investigation.


Maybe the period 29 spike is possible with skips or nulls at regular intervals, but I don't know.

Here is an example of what three skipped plaintext will do to the readability of an untransposed message.

Very simple inscription rectangle 17 x 20, transcription rectangle 17 x 20. Inscription left right top bottom. Plaintext lifted from inscription rectangle top bottom left right. Transcription left right top bottom.


Skip three symbols in three locations in the area of the pivots ( although this would not create pivots ).


Untranspose. Message scroll to the right unreadable.


That is all it takes.

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

smokie treats wrote:I have thought about this idea before. A 22 x 15 rectangle, except alternating 15 rows, then 14 rows, then 15 rows, etc. Period 1 would then be split between period 14 and period 15, and period 2 would become period 29.

I replicated your idea.

I took the 408 (because it has many period 2 bigram repeats) and set it in a 23 by 15 grid and alternated the length of each column. Then took off the cipher by columns starting in the upper-left corner and set it in a 17 by 20 grid. Since the length of each column was alternated (15,14,15,14,...) the cipher length reduces from 345 to 334.

Graph: period(1-334) versus bigram repeats. The peak you see is period 29, it counts 36 bigram repeats. I find it interesting that mixing periods can create a "fake" period.

Code: Select all

Combinations processed: 334/334
Measurements:
- Summed: 5896
- Average: 17.65269461077844
- Lowest: 8 (Period(UTP,134))
- Highest: 36 (Period(UTP,29))


Code: Select all

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smokie treats wrote:Here is an example of what three skipped plaintext will do to the readability of an untransposed message.

From my testing it takes only 2 characters, depending on their positions.

I've tested the 340 with up to 2 characters added at any positions in any of the 4 period 15 directions. The results are that scores increase quite a bit (up to 21300+) with a visible bias for 2 of the 4 directions (normal and flipped). I did a few iterative runs and saw that after 2 characters were added, scores do not increase as much.

Mirrored 340, period 15 untransposed:
0 character(s) added: 20500+
1 character(s) added: 21000+
2 character(s) added: 21300+
3 character(s) added: 21400+

It makes me skeptic of a finding a structure. And think it is more likely that the misalignment is part of the transposition itself, though a character may still have been skipped. Complicated, I would say it is to early to rule out a structure.

I've put forward a test cipher in this thread that has 5 skipped characters. Here's what it looks like when I perform the test that looks for skipped characters (the same test as main post).

It shows at least 3 peaks. That are 3 out of the 5 skipped characters. So the question is, if a multitude of characters have been skipped in the 340, why is there only one peak? My thinking is that only 1 character was skipped (transcription error? or would appear to be skipped?) and the misalignment exists in the transposition itself.

Jarlve:



340:

Jarlve wrote:I've put forward a test cipher in this thread that has 5 skipped characters. Here's what it looks like when I perform the test that looks for skipped characters (the same test as main post).

It shows at least 3 peaks. That are 3 out of the 5 skipped characters. So the question is, if a multitude of characters have been skipped in the 340, why is there only one peak? My thinking is that only 1 character was skipped (transcription error? or would appear to be skipped?) and the misalignment exists in the transposition itself.

Jarlve:



340:

I really like your idea of using AZD to detect skip positions. It appears to be a very useful tool, and shows that replacement of a skip does not have to be the exact same position to re-align the message enough to affect AZD ability to get an improved solution.

Not sure about interpreting the graph for the 340. There are a lot of ways to create period 15 bigram repeats other than using just one inscription rectangle and on transcription rectangle.

I have half a mind to try something like this:



It would increase the count of period 15 repeats, and move the period 29 repeats to the bottom half of the message. It is easy for me to imagine him doing something like that. But before doing so I would have to compare the list of period 29 bigrams to the list of period 30 bigrams to see if they are similar. I have added that to my to do list.