Z340 Kasiski Examination

[doranchak]

Smokie, that's an interesting way to link the phenomena. Based on https://docs.google.com/spreadsheets/d/ ... sp=sharing I suspect there are also 20 shared positions among bigrams at period 39 and kasiski shift 78. At period 39, do you also find ngrams that are spaced apart by multiples of 13?

So strange, all these multiples of 13. And the "my name is" cipher happens to have a length of 13.

[doranchak]

Smokie, your "periodic bigrams that are also periodic" are easier to spot when you write the cipher to width 26:

[doranchak]

Besides the coincidence with the "my name is" cipher of length 13, a typical plaintext alphabet has 26 letters in it, which produces another coincidence with your observation.

[BartW]

Last night i ran through the Railfence cipher 2 to 100 and used
Akdecrypt test the output All scored around 19k to 20k with no solution.
I currently have no plausible answer to the pivots except an angular striping transposition.
Thans David for having a look at my PT idea but i think we can conclude i am pretty much pissing in the wind with it.

Smokie those are some interesting observations
Thanks for sharing

Regards
Bart

[smokie treats]

At period 39, do you also find ngrams that are spaced apart by multiples of 13? So strange, all these multiples of 13. And the "my name is" cipher happens to have a length of 13.

I haven't looked at any other spacing or at the number 13 yet, but was also thinking about it.

Besides the coincidence with the "my name is" cipher of length 13, a typical plaintext alphabet has 26 letters in it, which produces another coincidence with your observation.

I have also been thinking about the plaintext alphabet length of 26.

I have considered some type of multiple transposition, with more than one consecutive inscription shapes that could put the plaintext period 1 bigram repeats at period 19. One that also causes these other phenomenon that we are looking at. I have played around briefly with multiple consecutive inscription rectangles, and they do move plaintext around in patterns.

Or some type of encryption where, although not a Vigenere step before homophonic substitution, ciphertext is conditioned upon position. Some system that uses the number 13.

I have also considered that he may have just written out the alphabet forward, backwards, forwards, and then backwards again, etc. Then encoded it with the homophonic symbols. But that wouldn't explain the period 19 repeats. Maybe I should consider this in more detail.

The number 13 reminds me of the ROT13 cipher.

I am definitely not ready to dismiss the period 78 unigram repeat spike. I would like to explore these spacing phenomenon in more detail, and it may take some time. I don't want to miss something important. And of course, find the most improbable and compare with other messages.

Last night i ran through the Railfence cipher 2 to 100 and used
Akdecrypt test the output All scored around 19k to 20k with no solution.
I currently have no plausible answer to the pivots except an angular striping transposition.
Thans David for having a look at my PT idea but i think we can conclude i am pretty much pissing in the wind with it.

Smokie those are some interesting observations
Thanks for sharing

Thank you. I have really enjoyed your contributions and appreciate your participation. I am excited about your findings.

I have experimented with railfence to try to explain the period 19 bigram repeats, using chunks of plaintext with two rows and I think 39 columns. It is the same as using an inscription rectangle that is two columns wide, which is found in some of the cryptography books of the time. But I found that it is very difficult to generate so many period 19 bigram repeats because one message chunk transposed doesn't have any relationship with a following message chunk transposed so that we get diagonal rows of period 19 repeats.

I use my subconscious a lot to work on the 340. Last night I made my post showing that both the leftmost and rightmost symbols of the period 78 unigram repeats shared positions with the period 26 bigram repeats. This morning I woke up wondering if the period 26 bigram repeats were spaced at a period of 78. I got up, checked it, and they were. That was a really weird experience.

[BartW]

At period 39, do you also find ngrams that are spaced apart by multiples of 13? So strange, all these multiples of 13. And the "my name is" cipher happens to have a length of 13.

I haven't looked at any other spacing or at the number 13 yet, but was also thinking about it.
I have also been thinking about the plaintext alphabet length of 26.

Well here is some more 13 and 19 spikes for you guys to chew on. I have no spike at 26 but i do at 27 and not 39 but at 40 and not at 78 but at 77.
This is a bigram hit vs Railfence cipher at X rails.

Fence rail.png

Due to the nature of the Homophonic layer it really is knocking my tools and intuition forcing me to revisit my thinking.
I have written a program where I can drop in simple transposition programs and quickly score the output based on the key input using bigram counting.
I can then drop the output to a csv for plotting in excel.

Thank you. I have really enjoyed your contributions and appreciate your participation. I am excited about your findings.

I am glad that I am bring some value to the group and pleased to be working with serious people in a co-op manor.
I have not found any one in the ACA community that is active on Z340

I have experimented with railfence to try to explain the period 19 bigram repeats, using chunks of plaintext with two rows and I think 39 columns. It is the same as using an inscription rectangle that is two columns wide, which is found in some of the cryptography books of the time. But I found that it is very difficult to generate so many period 19 bigram repeats because one message chunk transposed doesn't have any relationship with a following message chunk transposed so that we get diagonal rows of period 19 repeats.

I think i will ponder your statement some more.... All these clue point to something

I use my subconscious a lot to work on the 340.

Lol same. I have had many experiences in the past when I have dreamt the solution to a problem.
Regards
Bart

[BartW]

Hi Guys,
Just want to consolidate some of my ideas/assumptions and theories or at least kick them around so as to try and focus and take stock of what we know.
I would appreciate any input.

1/ There is at least another layer of encryption below the Homophonic due to no one being able to solve with hill climbers.

2/ From the KE experiments we know that there is little to no change of a underlying Vigenere cipher.

3/ From my PT CHI2 experiment I would be more inclined to consider an underlying transposition cipher. however the validity of this questionable.

4/ The KE has highlighted some quirks which correlate to an anomaly in the periodic bi gram search

5/ My recent rail fence experiment is showing similar anomalies at same/very similar locations to the KE and Periodic experiments.

6/ Pivots could be explained by an angular (diagonal) striping method.

7/ The prime phobia observation is likely to be tied in with the Odd /even observation as only odd values are potential candidates for prime.

Regards
Bart

[smokie treats]

Hi Guys,
Just want to consolidate some of my ideas/assumptions and theories or at least kick them around so as to try and focus and take stock of what we know.
I would appreciate any input.

1/ There is at least another layer of encryption below the Homophonic due to no one being able to solve with hill climbers.

2/ From the KE experiments we know that there is little to no change of a underlying Vigenere cipher.

3/ From my PT CHI2 experiment I would be more inclined to consider an underlying transposition cipher. however the validity of this questionable.

4/ The KE has highlighted some quirks which correlate to an anomaly in the periodic bi gram search

5/ My recent rail fence experiment is showing similar anomalies at same/very similar locations to the KE and Periodic experiments.

6/ Pivots could be explained by an angular (diagonal) striping method.

7/ The prime phobia observation is likely to be tied in with the Odd /even observation as only odd values are potential candidates for prime.

Regards
Bart

Will give input soon. But I have to make this post and get going for a short while.

EDIT:

1/ I agree.
2/ I agree.
3/ There are 121 positions covered by the period 19 repeats, which is 35.6% of the entire message. By contrast, there are only 80 positions covered by the period 1 bigram repeats, which is 23.5% of the message. Doranchak and I both proved that messages can be created with comparable stats, but without transposition. When I did it, there were a statistically high count of period 19 repeats in the plaintext, and I manipulated the key so that the period 1 plaintext repeats would be diffused more and the period 19 plaintext repeats would be diffused less. However, Doranchak and Jarlve untransposed the message in a lot of different way to re-connect the period 19 repeat ciphertext as period 1 ciphertext, and there was no solve. There could be an untried transposition, some other complications with the transposition, or another cipher step.
4/ I agree, but I don't know how significant it is.
5/ I don't know.
6/ I agree.
7/ I think so also, if it is not just a statistical anomaly.

I made a coincidence count chart for the period x bigram repeats. I found all of the period 1 bigram repeats, and then found the spacing of them. Then I found all of the period 2 bigram repeats and found the spacing for those. And so on through to period 170 bigram repeats.

There are 147 occurrences ( a massive spike ) where you have AxB exactly 78 positions away from another AxB, where A is the first symbol in the bigram repeat, x is the count of positions to B, and B is the second symbol in the bigram repeat. There is another curious spike at x = 35, and little spikes at 71, 48, 39 and 32. I think that I may be just multiple counting the period 78 unigram positions as they relate to each other, but not sure. Will have to take a closer look.

EDIT: The spikes are just the period 78 unigram positions counting each other because they create a lot of different period x bigram repeats. Same thing with the spike at 35, but I haven't looked at the different periods yet.

coincidence.counting.22.png

[smokie treats]

I checked all of the period x bigram repeats, and made a tally of those spaced by 78 positions. Left column is the period, and right column is the count. Only those with count of 2 are listed. I don't really see any interesting patterns, except period 26 and a few at period 19 and 38 ( NOT period 39 ).

26 4
19 3
23 3
38 3
45 3
47 3
58 3
69 3
111 3
116 3
135 3
2 2
5 2
13 2
15 2
16 2
20 2
21 2
22 2
31 2
32 2
46 2
49 2
51 2
64 2
65 2
66 2
67 2
77 2
84 2
85 2
90 2
93 2
95 2
103 2
109 2

Here are the period 19 bigram repeats spaced by 78 positions. There is one repeated trigram:

coincidence.counting.23.png

And here are the period 38 ( NOT period 39 ) bigram repeats spaced by 78 positions:

coincidence.counting.24.png

[smokie treats]

I only found one period 13 bigram repeat spaced at 39 positions:

coincidence.counting.25.png