Zodiackillersite.com

Largo wrote:Hi Jarlve,

this is an very intersting find. I can see that the orange and red squares form a structure, but I find it a bit hard to see the relationship between the structure and the bigrams in the image. When I apply period 29 to the z340 I count 33 bigram repeats, can you confirm that?

Today I fooled around a bit with period 19 / flipped period 15 and had an idea. What would happen when I shift the rows of the cipher by an offset of -2 per row? Row 1 has no offset, row 2 will then be shifted 2 letters to the left, row 3 will be shifted 4 letters to the left…and so on. This array represents the offsets for the shifting:
shifting_pattern = _list([0, -2, -4, -6, -8, -10, -12, -14, -16, 0, -2, -4, -6, -8, -10, -12, -14, -16, 0, -2]),

After the row shift I rotated the cipher by 270 degrees (respectively -90 degrees). Then I counted the repeated bigrams and found 39. This is nothing special since this kind of transposition has almost the same effect like a period 19 transposition. The only difference is that period 19 is consistent over the whole cipher and my row shift creates two „breaks“ (I hope you can decipher my broken english…I am still a bit tired from the new years party last night).
So I think that a regular shifting pattern can result in a cipher which looks like a cipher with a misalignment.

Code: Select all

H+MwICV9K-RR+4apIbID
EB+o7emLhu5JN0VMq+FH
RjUVFFuznc7IImUQL+eN
akZxPaLjMU1o7tZGRqhb
bOGb+gIG+VE7FV7gtWWe
clWO3Dkg0+ITB4-ITCnS
dDj+4j7J+dD4t1+t+uvu
VWq+eb+pZJYMj+rmLW1Z
PYLR5wK2R+Bm8+BxftBO
emkKyRQkgOb+wcXu#Pyw
InugzdlOFb03RGfBCOYA
foHSMF8+BvTBuFoKnSOI
LKJb+cgytnMF#Nsj+HBK
TpBbuOUNrFKgzd4OFTo8
Gqrv1-tYABOnSpzbc5-+
gNsd2oXu#rUtr7CdWjCa
hbtchhG+4-+ckgEmBqtM


Jarlve, smokie, David.......Do you think that could be the case? Maybe I missunderstand something...

The following sheet shows the differences between the repeated bigrams for period 19, flipped left to right + period 15 and shifted rows. I have used my own transcription of 340, so the symbols will not match with yours:

I am not really sure. It looks like the message above is 20 x 17. You redrafted the message into 19 columns, then rotated it so that the repeat symbols would be read horizontally, and then redrafted it again into 20 columns?

Jarlve.. It's very visually symmetrical its as if you could fold it and join it together like a mad magazine fold in. Do you remember them.. Which reminds me
AlfrEdEnEuman..13 letters haha..

Jarlve wrote:That is the right question, what is the relation, what is going on here? I don't understand it either, perhaps we are missing a simple fact. Here's an image of the 408 with the same thing at period 10.

I'm confused about the significance of this. Wouldn't any period N bigram repeats form repeating structures by definition when you mark them in the original cipher text? Each part of the bigram you highlight would always be 10 positions apart, for example, when looking at period 10 bigrams. It is like making a drawing with a pen that is attached to a rigid rod and another pen, where movements of the 1st pen create an equal image via the 2nd pen but offset a bit from the 1st pen's markings. Am I missing something?

doranchak wrote:I'm confused about the significance of this. Wouldn't any period N bigram repeats form repeating structures by definition when you mark them in the original cipher text? Each part of the bigram you highlight would always be 10 positions apart, for example, when looking at period 10 bigrams. It is like making a drawing with a pen that is attached to a rigid rod and another pen, where movements of the 1st pen create an equal image via the 2nd pen but offset a bit from the 1st pen's markings. Am I missing something?

Hey doranchak,

If you look at the image of the 408, the red squares are the start of each bigram repeat, and the orange squares are the end. What's special here is the regionality. If you look at the top-left square (the "9", blue one), it is a bigram that starts there and repeats 10 squares later (to the left). It does not share the regionality of the red structure. It seems that some of the periods are on another period so to say. I wonder if there is anything we could infer from this rather than it being some sort of harmonic between the cipher plaintext, encoding, period and physical dimensions.

If you look at the image of the 340, the orange squares are the start of each bigram repeat, and the red squares are the end. Again there is strong regionality here, with hints of up to 4 structural repeats (period on period). It is indicative that the pivots owe their existance to this phenomena. We are getting tantalizingly close to explaning the pivots.

OK - so you are highlighting clusters where bigrams tend to start and end. Is that right?

doranchak wrote:OK - so you are highlighting clusters where bigrams tend to start and end. Is that right?

I highlighted a repeating structure. It is possible that not all of these bigram repeats connect properly, in the 340 the repeating structure overlaps with itself and its boundaries are unclear. And there are indications of a third and fourth repeat (periodical). I think it will prove to be highly subjective to the grid dimensions.

I guess I'm getting confused about the distinction between clusters and structures.

What you are calling structures, I am seeing as a tendency for repeating bigrams to start near certain columns and to end near certain columns. The latter is a consequence of the former due to the fixed period. Are you seeing something to the structures that isn't just this clustering phenomenon?

There's something periodical about it.

In the 340, certain parts of the structure repeat 4 times. Let's say that there are 4 structures, from left to right 1, 2, 3 and 4 and some of them are partial. Then some of the bigrams in structure 1 connect to structure 2, allot of bigrams in structure 2 connect to structure 3, some of the bigrams in structure 3 connect to structure 4. The shape of the structure and the offset it repeats in seems dominant here, and not for instance a clustering effect that creates a copy.

Jarlve wrote:I like your idea but how would Zodiac have transposed it then? That seems a bit strange.

smokie treats wrote:I am not really sure. It looks like the message above is 20 x 17. You redrafted the message into 19 columns, then rotated it so that the repeat symbols would be read horizontally, and then redrafted it again into 20 columns?

I am sorry if my description of what I did was a bit confusing. Here is a more detailed version:

Period 19 is the same like resizing the cipher to width 19 and reading it top to bottom, left to right. As we know, we get 37 bigram repeats by doing so.
Now imagine a slightly different transposition which has almost the same effect like period 19. To keep things easy I have created a „cipher“ made of „ABCD…“:



As you can see in the image each row is shifted to the left by formula „rowIndex * -2“ until -16 is reached. If you read this cipher (of course with the z340 symbols) top to bottom, left to right you will get 39 bigram repeats. The bigrams are of course almost the same like the bigrams from the period 19 version (see table from my last post in this thread). The sample cipher from my last post in this thread was created like that (z340 read top to bottom, left to right after applying the row shifts). Thus it is 20x17 (not redrafted).
As you can see in the image the shifting process has two breaks which can be seen as period 18 repeats. Maybe such breaks causes the misalignment you mentioned earlier smokie.
Long story made short: The high peak of repeated bigrams in period 19 may be the effect of a row shift like the one shown above. If you mention the 3 purple lines in the table you can imagine the row shifts as some sort of rail fence transposition too. Since period 19 / flipped + period 15 causes significant bigram peaks but do not lead to a solution we may have to look for slightly different modifications that are close to period 19.

Mr lowe wrote:Nothing much in that...but I do like that whole simplistic method of z making the 340 difficult using such a method.

I totally agree with you! Sometimes I think we don’t see the forest for the trees (is this translation correct?). Some sort of a home grown transpositioning method could lead to a cipher that remains unsolved for so many years.

OK I tried to reproduce the highlighted mirrored period 29 bigrams:



In my version, orange is only used to mark the 1st symbol of each bigram, and red is only used to mark the 2nd symbol of each bigram.

I think a lot of the "repeating structure" occurs only because they are already linked by period 29, which shows up in the grid as your x=5 y=2 rule. For example:



The structures formed by and are the same because they belong to the same set of bigrams linked by period 29.

Maybe there is some additional regularity you have noticed that I still don't understand yet, but it just looks like the natural outcome of showing period 29 mirrored bigrams in a 17x20 non-mirrored grid. Which is still one possible explanation for the pivots: clusters of mirrored repeating period 29 bigrams.

Are you looking specifically at exceptions to the normal period 29 behavior? In other words, parts of the repeating patterns that aren't explained by the above?