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Jarlve wrote:Oh I see. Well, in general the operation does not improve things on my end.

That's not the goal either. A demonstration, nothing more. But I have some ideas based on "interlocked" ciphers. Let's see how much time I can invest the next few days.

Jarlve wrote:Sorry to be so persistent on the matter.

That's exactly what we need...different points of view! If we all had the same view, this would not be the most efficient way to look for a solution. Perhaps I am completely barking up the wrong tree, but I may also find a new clue tomorrow. Who knows?
Thinking up possibilities and discussing them is what takes us forward. And that's exactly why I appreciate this forum

Indeed. I really hope that you find something new!

I took a look at the effects of the ioc and encoding randomization on the unique sequences. Each graph/mountain is the average of 10,000 sequential homophonic substitution ciphers. None of the options listed is a good match for the 340. Either something funny is going on in the 340 or it is a significant outlier.

1) A higher ioc compresses the mountain horizontally:







2) More encoding randomization also compresses the mountain horizontally:

Jarlve wrote:Yeah. These images are from December 2014. But have not tried to interpret patterns:

Nice - have you done a similar plot of Z408?

Jarlve wrote:The mountain most offset to the right is generally the true direction of the sequential homophonic substitution.

And this can be generalized to this aspect of the substitution: When encoding, symbols undergo a "spreading out" effect (in the normal reading direction) due to cycling of symbols within groups of homophones. Is that correct?

Does the effect still occur for homophonic substitution that is completely randomized (i.e., no cycles)? You probably already answered that long ago.
EDIT: Just studied your "average mountain" plots and I would interpret your results like this:

1) A cipher with more repetition of symbols (higher IoC) will have a harder time maintaining longer non-repeating sequences.
2) A cipher with more randomization in homophone groups will also have a harder time maintaining longer non-repeating sequences, since members of the groups are allowed to repeat sooner than if they were fully sequential.

So this makes some intuitive sense. Does that match your interpretations?

doranchak wrote:

Jarlve wrote:Yeah. These images are from December 2014. But have not tried to interpret patterns:

Nice - have you done a similar plot of Z408?

Here are some new ones.

340:

Code: Select all

18 17 16 15 14 29 28 27 26 25 24 23 22 21 20 19 18
17 16 15 14 22 21 20 19 18 17 18 17 16 15 14 13 12
19 18 17 16 15 14 13 12 11 10 9  8  7  6  5  4  3
2  1  8  10 9  8  7  6  5  4  3  2  1  7  15 14 13
12 11 10 9  17 16 15 14 13 12 11 17 16 15 14 13 13
12 11 10 9  8  19 18 17 16 15 14 13 12 11 10 19 18
18 17 16 15 14 13 12 11 10 9  8  7  17 16 15 15 14
13 12 11 10 9  8  7  6  5  11 10 9  8  7  8  7  6
5  4  3  2  18 17 19 18 17 16 15 14 13 12 11 10 9
8  7  6  5  4  3  12 11 10 18 17 16 15 14 13 23 22
21 20 19 20 19 18 17 16 18 17 16 15 14 13 14 25 24
23 22 21 20 19 18 17 16 15 14 13 12 11 10 13 12 11
19 18 17 16 15 14 13 12 11 10 9  17 16 17 16 15 14
13 12 11 10 9  8  7  6  5  7  6  5  4  3  2  1  17
22 21 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12
11 10 9  23 22 21 20 19 18 17 16 15 14 13 12 11 10
9  8  7  6  12 12 11 10 9  8  8  7  6  5  4  3  2
1  5  4  3  17 16 15 21 20 19 19 18 17 16 15 14 13
12 11 10 9  8  7  6  5  4  18 17 16 22 21 20 19 18
17 16 15 14 13 12 11 10 9  8  7  6  5  4  3  2  1


408:

Code: Select all

5  4  3  2  11 10 9  8  7  6  5  4  3  19 18 17 16
15 14 13 12 11 10 13 12 11 10 9  8  7  6  5  4  14
13 12 11 24 23 25 24 23 22 21 20 19 18 17 16 15 14
13 12 11 10 9  8  7  6  5  27 26 25 24 23 22 21 28
27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11
10 9  8  17 16 15 14 13 17 16 15 14 13 18 17 16 17
16 15 14 13 12 11 10 9  8  7  6  5  9  8  7  6  6
15 14 13 12 11 10 9  8  7  6  5  4  3  2  1  10 9
8  7  6  5  32 34 33 32 33 32 31 30 30 29 28 27 26
25 24 23 22 21 27 26 25 25 24 23 22 21 20 19 19 18
17 16 15 14 13 12 11 13 12 11 10 9  8  7  6  23 22
21 20 19 18 30 29 28 27 29 28 27 26 25 24 23 24 23
22 21 22 21 21 20 19 18 17 19 18 26 25 24 23 22 21
20 19 18 17 16 16 15 14 13 12 11 10 9  16 15 14 13
12 11 10 9  8  7  6  5  4  22 21 20 19 18 17 16 15
14 13 12 11 10 9  8  7  6  5  4  3  2  1  11 11 10
9  8  7  6  5  4  3  2  1  13 12 11 10 9  8  7  6
5  4  3  2  11 10 9  8  7  6  5  4  3  2  15 14 13
12 11 10 9  8  7  6  5  4  6  5  4  12 13 12 11 10
9  8  7  6  5  11 10 9  14 13 12 11 12 11 10 9  8
7  6  5  4  3  14 13 12 11 10 9  10 9  8  7  6  5
4  3  2  1  21 20 19 18 17 16 15 14 13 12 11 10 9
8  7  6  17 16 15 14 13 12 11 10 9  10 9  8  7  8
9  8  13 12 11 10 9  10 9  8  7  6  5  4  3  2  1


doranchak wrote:

Jarlve wrote:The mountain most offset to the right is generally the true direction of the sequential homophonic substitution.

And this can be generalized to this aspect of the substitution: When encoding, symbols undergo a "spreading out" effect (in the normal reading direction) due to cycling of symbols within groups of homophones. Is that correct?

Yes. Symbols spread out evenly throughout and around the middle point of the cipher. It is very easy to see and determine the properties of sequential homophonic substitution by scaling down the problem. For instance "ABCABCABC" versus "CAABACBCB". Of course all these properties are emergent from one single phenomena. But there seems to be no one single measurement/property that perfectly captures the phenomena in practice because of the randomness of the underlying plaintext.

doranchak wrote:Does the effect still occur for homophonic substitution that is completely randomized (i.e., no cycles)? You probably already answered that long ago.

No. These are quite random.

doranchak wrote:EDIT: Just studied your "average mountain" plots and I would interpret your results like this:

1) A cipher with more repetition of symbols (higher IoC) will have a harder time maintaining longer non-repeating sequences.
2) A cipher with more randomization in homophone groups will also have a harder time maintaining longer non-repeating sequences, since members of the groups are allowed to repeat sooner than if they were fully sequential.

So this makes some intuitive sense. Does that match your interpretations?

Yes. That is a very good interpretation and it is indeed as intuitive and simple as that.

Unique sequences, 340 versus 408:





408 without the last 8 rows, this graph/mountain looks allot more natural:



408 with and without the last 8 rows superimposed on top of each other, the area colored red is the difference between the two. This area is more left shifted and less significant, the last 8 rows do not add very long sequences to the result. Just a simple example of the system:



It is odd that the 340 has such a high spike that is so much shifted to the right.

Jarlve wrote:It is odd that the 340 has such a high spike that is so much shifted to the right.

Within a sequential homophonic substitution 25% encoding randomization hypothesis the length 17 spike on its own it is a ~2.5 sigma observation. Not strong but I still hold some value to it.

Jarlve wrote:But there seems to be no one single measurement/property that perfectly captures the phenomena in practice because of the randomness of the underlying plaintext.

What about unigram distance? http://zodiackillersite.com/viewtopic.p ... 902#p53902
It seems to capture two phenomena: Anomalous gaps between symbols, and the overall spreading out of symbols.
My own implementation of the measurement in randomization tests shows a 2.6 sigma for Z408 and 4.4 for Z340.