Z340 Kasiski Examination

[smokie treats]

For the 340, I found all period x bigram repeats where x is a divisor of the position spacing of the repeat. Here is the table. On the left is the period. On the right are the position spacings. I must have gotten lucky when checking period 26 before, as I did not find any other period with such a high count of the same position spacings.

There are a lot of period 2 and period 3 bigram repeats where the period is a divisor of the position spacing of the repeats. But that is to be expected, because a lot of numbers can be divided by 2 or 3.

Besides the period 26 bigram repeats, I don't see anything particularly interesting.

coincidence.counting.26.png

[BartW]

For the 340, I found all period x bigram repeats where x is a divisor of the position spacing of the repeat. Here is the table. On the left is the period. On the right are the position spacings. I must have gotten lucky when checking period 26 before, as I did not find any other period with such a high count of the same position spacings.

There are a lot of period 2 and period 3 bigram repeats where the period is a divisor of the position spacing of the repeats. But that is to be expected, because a lot of numbers can be divided by 2 or 3.

Besides the period 26 bigram repeats, I don't see anything particularly interesting.

coincidence.counting.26.png

This is an interesting observation.
I feel this points to a cipher parameter like rail size in railfence foe example. Hence why i see the spikes i posed before that correlate to your numbers. Now we just need to track down what it is.
EDIT i also feel that this indicate the exsistance of a valid message rather than a troll.

Regards
Bart

[smokie treats]

By "rail size", do you mean the number of rows in a rail fence cipher like this one?

coincidence.counting.27.png

I would say that this is a 25 x 3 railfence cipher because there are 25 columns and 3 rows. Just checking.

[BartW]

By "rail size", do you mean the number of rows in a rail fence cipher like this one?
I would say that this is a 25 x 3 railfence cipher because there are 25 columns and 3 rows. Just checking.

Yes, My plot the other day shows the Rail number (key) verse Bigrams.
I am exploring other versions of Railfence including inverse, offset and Redefence.
As it is a zigzag every rail number would line up so this is why i have hits at 13,26 etc etc
That is why i think we are seeing a cipher artifact but have not identified it yet.

EDIT
http://codepad.org/MEPN90S2
Click the output link for the output data, I will be adding another score metric suggested by Doranchak when i get time
Regards
Bart

[smokie treats]

I am glad that you are bringing this up, not just railfence but any transposition idea, because there is something that I have wanted to do for a while and haven't gotten around to it.

Below are the period 19 bigram repeat positions shaded yellow. The message on the left and right are both the 340, but I show it twice for clarity. There are a lot of consecutive diagonal shaded positions. Some are shown boxed blue on the left, and others boxed green on the right for clarity. I made the picture last year, and I think that I only boxed where there are at least three consecutive diagonal ( period 19 ) positions.

340trigramsearch.png

Let's say we have a railfence cipher that is 38 columns x 2 rows, and we transpose 38 plaintext at a time. That is the easiest way to re-produce the period 19 repeats - except that is still not easy because we are only transposing 38 plaintext at at time. Each individual transposed message chunk is independent of the previous and following message chunk for transposition purposes, making it difficult to result in so many consecutive diagonal positions that test positive for period 19 repeats. Even with a railfence that is designed to maximize the count of period 19 bigram repeats, it is still very difficult to cover 35% of the entire message.

I am going to update my spreadsheets so that they count the number of consecutive diagonal positions where there is at least a group of three; I want to find some type of way to count them and compare with other messages, including route transpositions, railfence transpositions, non-transpositions, etc.

[doranchak]

For the 340, I found all period x bigram repeats where x is a divisor of the position spacing of the repeat. Here is the table. On the left is the period. On the right are the position spacings. I must have gotten lucky when checking period 26 before, as I did not find any other period with such a high count of the same position spacings.

There are a lot of period 2 and period 3 bigram repeats where the period is a divisor of the position spacing of the repeats. But that is to be expected, because a lot of numbers can be divided by 2 or 3.

Besides the period 26 bigram repeats, I don't see anything particularly interesting.

Interesting! I tried to run the same experiment, but instead of using the original position numbers, I used the new position numbers of the bigrams as they repeat in the untransposed ciphertext. I found an unusual spike at period 39, where some of the bigram repeats have positions that share a common factor of 25. I tested periods 1 through 170, and the average number of bigram repeat spacings sharing a factor of 25 was only 0.84, with a standard deviation of 0.99. At period 39, there are 7 bigrams whose position spacing have a common factor of 25. That's 6.22 standard deviations from the mean!

To visualize this, untranspose Z340 at period 39, then write it to 25 columns like this:

Then you can see these repeating bigrams lining up by columns:

Some of the bigrams overlap. Makes me wonder if that causes overcounting.
For comparison, here are all the repeating bigrams at period 39:

Also, these "triples" stood out to me:

[doranchak]

I ran the same experiment on Z408 for all periods and the untransposed cipher (period 1) has a strong spike for factor 17, corresponding to the bigrams that line up along columns. Here's what they look like in the cipher:

And the plaintext:

Seems to be a mix of naturally occurring bigrams (that seem to line up by chance), and the "filler" section at the end.
Perhaps some of the untransposition schemes for Z340 are uncovering some echoes of the similarly naturally occurring bigrams in the Z340's plaintext.

[doranchak]

I am glad that you are bringing this up, not just railfence but any transposition idea, because there is something that I have wanted to do for a while and haven't gotten around to it.
Below are the period 19 bigram repeat positions shaded yellow. The message on the left and right are both the 340, but I show it twice for clarity. There are a lot of consecutive diagonal shaded positions. Some are shown boxed blue on the left, and others boxed green on the right for clarity. I made the picture last year, and I think that I only boxed where there are at least three consecutive diagonal ( period 19 ) positions.

If you untranspose the cipher text at period 19, the "consecutive diagonal positions" can be interpreted as repeating bigrams that are directly adjacent (or overlapping) with one another:

If I'm not mistaken, any area there with more than 2 symbols in a row highlighted will show up in the unmodified Z340 as consecutive diagonals. Here's another view, with the non-consecutive bigrams outlined instead of highlighted:

[smokie treats]

Those graphics look awesome.

[BartW]

They are great visualization but i find the 408 experiment very interesting. Thanks for sharing.