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Re: Evidence of transposition misalignment in the 340

PostPosted: Tue Jan 03, 2017 10:55 am
by Jarlve
Ok Largo. Then the difference is that you would still need to undo the row shifts after untransposing period 19? Changing the order or offset of rows that are sufficiently long will not cause the cipher to become unsolvable. Maybe I misunderstood something.

doranchak wrote: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.

I realize now what is causing the structure to exhibit hints of multiple repeats. If you look at period 1 bigrams then they may group together and form longer blocks. Translate that to period 29 and add some bigram regionality et voila. I suppose that's what you meant with clustering.

Here's my bigram map for period 29 in 29 columns, there is indeed quite allot of clustering here.

Image

Re: Evidence of transposition misalignment in the 340

PostPosted: Tue Jan 03, 2017 7:24 pm
by smokie treats
Largo wrote:
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…“:

Row shifts.pdf


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.


Largo, check out the Department of the Army Technical Manual published 1955 Discussion of Route Transposition: https://www.nsa.gov/news-features/decla ... 078809.pdf. There is a lot of discussion of simple route transposition in Chapter 2, and Chapter 8, which discusses different geometric shapes. Your idea reminds me of maybe a parallelogram or some similar shape.

Re: Evidence of transposition misalignment in the 340

PostPosted: Wed Jan 04, 2017 11:54 am
by Jarlve
Jarlve wrote:Ok Largo. Then the difference is that you would still need to undo the row shifts after untransposing period 19? Changing the order or offset of rows that are sufficiently long will not cause the cipher to become unsolvable. Maybe I misunderstood something.

Row offset can cause the cipher to become unsolvable, my bad.