Zodiackillersite.com

Hey Mr lowe,

I'm not sure. Your first plaintext string scores 20k and your second plaintext string scores 30k+. Could you report the multiplicity of both cipher strings? You can find the stat with AZdecrypt under Stats -> Unigrams. Most readable plaintext score around 24k, since your second plaintext string scores over 30k its multiplicity may be very high which allows AZdecrypt to come up with very high scoring solutions which are not real solves.

AZdecrypt unigram stats for:
--------------------------------------------------
Length: 167
Symbols: 160
Dimensions: 17 by 10
Multiplicity: 0.9580838323353293
Entropy: 7.299871957144694
Index of coincidence:
- Raw: 14
- Normalized: 0.000505014068249044
Flatness: 0.5218749999999994
Unigram repeats per 17 characters: 0

hey jarlvie.. it must be the repeats of the pivots.

Mr lowe wrote:AZdecrypt unigram stats for:
--------------------------------------------------
Length: 167
Symbols: 160
Dimensions: 17 by 10
Multiplicity: 0.9580838323353293
Entropy: 7.299871957144694
Index of coincidence:
- Raw: 14
- Normalized: 0.000505014068249044
Flatness: 0.5218749999999994
Unigram repeats per 17 characters: 0

hey jarlvie.. it must be the repeats of the pivots.

For your cipher, 160 out of 167 symbols are unique so practically anything could be made fit. While using 5-grams I would not attempt multiplicities higher than 0.35, your string is 0.95! The very best AZdecrypt has cracked was a 6 line 408 with a multiplicity of 0.5 while using 7-grams.

Here are the first results of my tests of the effects of symbol merges on periodic ngrams. The motivation is: If there is a homophonic aspect to the cipher text, and the spikes in periodic ngrams are real indications of some transposition occurring in addition to substitution, then will we see higher ngram counts at interesting periods when we merge the correct symbols together?

I considered all possible combinations of pairs of symbols. For each pair of symbols:

1) Merge them in the Z340 cipher text (that is, replace all occurrences of the 2nd symbol with the 1st symbol)
2) Count the repeating ngrams in all periods from 1 to 170
3) Compare to repeating ngrams in all periods of the unmodified Z340. For example, if period 10 jumps from 20 bigrams to 25 bigrams when a symbol pair is merged, then the value I track is 25-20 = 5.

This generated a large amount of data so I made an interactive charting tool to help navigate it all:

http://zodiackillerciphers.com/symbol-merge-ngrams/

Screenshot:



Click the image or link above to open the charting tool. The x-axis is the period, and the y-axis is the gain in repeating bigrams after merging the shown symbols. You can hover your mouse over the chart to see data values. Here is an explanation for the controls:

- Next: Show the chart for the next symbol pair
- Skip 20: Jump past the next 20 symbol pairs
- Last: Jump to the chart for the last symbol pair

- Prev: Show the chart for the previous symbol pair
- Skip 20: Jump past the previous 20 symbol pairs
- First: Jump to the chart for the first symbol pair

- Sort by: Here you can change how the charts are sorted:

1) Sum of increases in ngram repeats: This is the sum of ngram gains for all periods. Charts with the highest sums are shown first.
2) Max increase: Charts with highest gains in ngrams are shown first
3) Sigma: To compute sigma, we first compute mean and max gain for all periods, and standard deviation. Sigma is (max-mean) divided by standard deviation.
4) Period of max increase: Charts are arranged in order of which periods had the maximum gain in ngrams.
5) Period P spikes first (P can be from 1 to 170): Charts with max gain occuring at period P are shown first
6) Show data for: Here you can show charts for periodic 2-grams, 3-grams or 4-grams.

Let me know if there are any problems with the tool.

I find that it is very hard to judge the significance of the results, so I’m running a shuffle experiment and will update with those results soon. An early and interesting result is that merging produces two 4-grams repeats at period 19 (because the merge produces one 5-gram repeat at period 19).





The shuffle experiment considers that to be significant since only 4% of shuffles for those merged symbols produced peaks of 1, and 96% of them were 0.

Nice stuff doranchak! Very well built tool.

A few issues for me,

Skipping backwards skips 10 instead of 20.

doranchak wrote:1) Sum of increases in ngram repeats: This is the sum of ngram gains for all periods. Charts with the highest sums are shown first.
2) Max increase: Charts with highest gains in ngrams are shown first

This seems to produce exactly the same results. Also, select 4-grams and then switching between the two sorting options a couple of times produces strange results.

doranchak wrote:3) Sigma: To compute sigma, we first compute mean and max gain for all periods, and standard deviation. Sigma is (max-mean) divided by standard deviation.
4) Period of max increase: Charts are arranged in order of which periods had the maximum gain in ngrams.

I don't understand how these are sorted. Why does 1 of 1953 has a higher sigma then 2 of 1953? Many of the pages after 1 have much higher maximum increases.

Only untransposed/untransformed periods are included. Is it possible to find the maximum increase for a period? Would it be possible to weigh increases in repeats in another way that includes the signifance of the from-to range? For instance merging "+B" shows the highest increase with +16 at period 114. But when looking at the original 340, this period has only 15 repeats. So it goes up from 15 to 31, that may be special in its own way but I wonder if for instance going from 30 to 38 would be more statistically significant in terms of rating the period as interesting considering transposition etc.

I also find the results are difficult to interpret. What ASCII symbols are these that create a 5-gram repeat?

Thanks for your feedback - I will try to incorporate your suggestions.

Jarlve wrote:Skipping backwards skips 10 instead of 20.

OK, fixed.

Jarlve wrote:This seems to produce exactly the same results.

I think they are the same for the first few (since max seems strongly correlated to sum), but diverge at chart #6 when "Max increase" is selected (watch the Max values jump around as you scroll through).

Jarlve wrote:Also, select 4-grams and then switching between the two sorting options a couple of times produces strange results.

That is probably due to the fact that changes to repeating 4-grams are rare, so the stats for them aren't as useful. Let me know if you can point out any specific mistakes.

Jarlve wrote:I don't understand how these are sorted. Why does 1 of 1953 has a higher sigma then 2 of 1953? Many of the pages after 1 have much higher maximum increases.

It's just how the math works out for situations where only a few periods produce +1 increases, and a single spike is found to be at +2. I think it highlights the problem with calculating sigma for only a few samples. And, a higher max increase might not have higher sigma because it doesn't deviate from the mean as much. Also, it's possible that none of the spikes are sufficiently significant, otherwise they would have appeared at the beginning of the charts (for instance, if a max of 20 was found when the average was 3 or something).

Jarlve wrote:Only untransposed/untransformed periods are included.

Yes, I think I will run it again to generate data for transposed periods as well, since you found that anomaly for those.

Jarlve wrote:Is it possible to find the maximum increase for a period?

OK - I replaced the "show period p spikes first" sort with "sort by period p". When it is selected, the number of increased bigrams at the selected period is displayed below the controls. The max increase for the period will be in the first chart displayed.

Jarlve wrote:Would it be possible to weigh increases in repeats in another way that includes the signifance of the from-to range? For instance merging "+B" shows the highest increase with +16 at period 114. But when looking at the original 340, this period has only 15 repeats. So it goes up from 15 to 31, that may be special in its own way but I wonder if for instance going from 30 to 38 would be more statistically significant in terms of rating the period as interesting considering transposition etc.

That's a really good point. I'll have to think about how to approach that. Let me know if you have any suggestions. Right now I'm waiting for full results of a significance experiment based on shuffles, and looking for repeating ngrams from actual merges that diverge significantly from the expected ngrams of merges in shuffles. I was hoping to do 3-symbol merges too but it already takes too long just to run only 100 shuffles per symbol pair and count ngrams for n=2 through 5 across 170 periods (about 20 seconds per symbol group). The number of symbol groups would jump from (63 choose 2 = 1953) to (63 choose 3 = 39711). I need a cloud supercomputer.

Jarlve wrote:I also find the results are difficult to interpret. What ASCII symbols are these that create a 5-gram repeat?

They are: %4

doranchak,

Thanks for changing the periods to max increase.

When at 21 of 1953 it won't skip backwards and when at 1933 of 1953 it won't skip forward.

And try this, reload your tool and set show data to 4-grams. You will see three spikes to the right side 157, 158 and 159. Now change sort by to "max increase", nothing changes. Now change it back to "sums of increases..." and notice how the spikes change offset to positions 159, 160 and 161. This happens with IE11 but not with Chrome.

I just coded something up for you. A superfast ngramsize 2 to 5 repeat counter. It counts ngramsize repeats in the array with a single pass while building a new array with enumerated couples to iterate ngramsize+1 on and so forth. It short circuits when less than 2 repeats are found since that is the minimum requirement for a ngramsize+1 repeat. You may only need to worry about the speed that your programming environment can handle the initializing and clearing of the arrays gram and iden. This is the FreeBASIC code where I had to use a constant to define the array sizes to be able to use the erase keyword, (339) which is the cipher length minus the minimum ngramsize-1 considered.

Code: Select all

function m_ngramreps(array()as integer,byval l as integer)as string
   
   'array()=cipher numbered by appearance from 1 to 63 for example
   'l=cipher length
   
   dim as integer i,e,a,b,r,n
   dim as string reps
   dim as integer gram(339,339) 'l-1 ,l-1
   dim as integer iden(339,339) 'l-1 ,l-1
   
   for n=2 to 5 'n-gram range
      for i=1 to l-(n-1) 'single pass
         a=array(i)
         b=array(i+1)
         gram(a,b)+=1
         if iden(a,b)=0 then
            e+=1
            iden(a,b)=e
         end if
         array(i)=iden(a,b)
         if gram(a,b)>1 then r+=1
      next i
      if r>0 then reps+=str(r)+" "
      if r<2 then return reps 'short-circuit
      e=0
      r=0
      erase gram,iden 'clear arrays
   next n
   return reps
   
end function


EDIT:

Function output for 408.txt:
"62 11 2 "
2-grams: 62
3-grams: 11
4-grams: 2

Function output for p1.txt:
"191 87 41 20 "
2-grams: 191
3-grams: 87
4-grams: 41
5-grams: 20

Works perfectly.

I've updated the tool to include significance measurements for shuffles:

http://zodiackillerciphers.com/symbol-merge-ngrams/

Select "Shuffle Sigma" in the "Sort by" dropdown list. You'll then see spikes that seem significant shown first among the charts. Each pair was compared to only 100 shuffles, so the comparison might not be fully adequate, but it does make the more visually obvious spikes show up first.

Jarlve wrote:When at 21 of 1953 it won't skip backwards and when at 1933 of 1953 it won't skip forward.

Thanks for reporting that. It is fixed now.

Jarlve wrote:And try this, reload your tool and set show data to 4-grams. You will see three spikes to the right side 157, 158 and 159. Now change sort by to "max increase", nothing changes. Now change it back to "sums of increases..." and notice how the spikes change offset to positions 159, 160 and 161. This happens with IE11 but not with Chrome.

I was able to reproduce this in IE. I noticed that the spikes change offset but they correspond to real data for another set of symbols. I think IE is not guaranteeing the sort order of the data when we change the sort criteria. So when the value it uses for sorting is the same, Chrome gives the same ordering but IE does not, for some reason. Strictly speaking, the result of the sort is still correct. I suppose I could add a secondary criteria to force a guaranteed order but it doesn't seem like that big of a problem.
[code="Jarlve"]I just coded something up for you. A superfast ngramsize 2 to 5 repeat counter.[/code]
Thank you for sharing that. I'm always impressed with how much speed you get out of your algorithms. My ngram counter has a lot of unnecessary overhead that I stapled onto it from other experiments (such as a tracking a sorted list of frequency distributions). I should whittle it down for speed and incorporate your algorithm.

Thanks doranchak,

I've added some new stuff to AZdecrypt which reveal interesting behaviours about the encoding properties of the 340. The following ciphers are compared with my 2-symbol cycles measurement and a couple of transposition operations: the 340, a 340 character part of the 408, the smokie2 and a cipher of my own with 18% encoding randomization.

1. Directional:

This goes through the typical directional transposition. It stands out that the 340 shows high scores for some of the diagonal transpositions (1627). The other ciphers do not exhibit this behaviour.

Code: Select all

340:

Directional: (transposition, untransposition)
--------------------------------------------------
Normal: 2152, 2152 <---
Mirror: 2029, 2029
Flip: 2029, 2029
Reverse: 2152, 2152 <---
--------------------------------------------------
Columnar 1: 1125, 1341
Columnar 2: 1208, 1325
Columnar 3: 1208, 1325
Columnar 4: 1125, 1341
--------------------------------------------------
Diagonal 1: 1010, 1336
Diagonal 2: 1590, 1281
Diagonal 3: 1627, 1478
Diagonal 4: 1027, 1520
Diagonal 5: 1027, 1520
Diagonal 6: 1627, 1478
Diagonal 7: 1590, 1281
Diagonal 8: 1010, 1336
--------------------------------------------------
Transposition average: 1471
Untransposition average: 1557.75

408:

Directional: (transposition, untransposition)
--------------------------------------------------
Normal: 2861, 2861 <---
Mirror: 2281, 2281
Flip: 2281, 2281
Reverse: 2861, 2861 <---
--------------------------------------------------
Columnar 1: 982, 1144
Columnar 2: 1089, 1294
Columnar 3: 1089, 1294
Columnar 4: 982, 1144
--------------------------------------------------
Diagonal 1: 983, 1044
Diagonal 2: 951, 1036
Diagonal 3: 905, 1137
Diagonal 4: 928, 1067
Diagonal 5: 928, 1067
Diagonal 6: 905, 1137
Diagonal 7: 951, 1036
Diagonal 8: 983, 1044
--------------------------------------------------
Transposition average: 1372.5
Untransposition average: 1483

smokie2:

Directional: (transposition, untransposition)
--------------------------------------------------
Normal: 2197, 2197 <---
Mirror: 1796, 1796
Flip: 1796, 1796
Reverse: 2197, 2197 <---
--------------------------------------------------
Columnar 1: 918, 1002
Columnar 2: 987, 932
Columnar 3: 987, 932
Columnar 4: 918, 1002
--------------------------------------------------
Diagonal 1: 1129, 1089
Diagonal 2: 1098, 1028
Diagonal 3: 1047, 935
Diagonal 4: 1087, 985
Diagonal 5: 1087, 985
Diagonal 6: 1047, 935
Diagonal 7: 1098, 1028
Diagonal 8: 1129, 1089
--------------------------------------------------
Transposition average: 1282.37
Untransposition average: 1245.5

jarlve18:

Directional: (transposition, untransposition)
--------------------------------------------------
Normal: 2178, 2178 <---
Mirror: 1824, 1824
Flip: 1824, 1824
Reverse: 2178, 2178 <---
--------------------------------------------------
Columnar 1: 1044, 928
Columnar 2: 1102, 973
Columnar 3: 1102, 973
Columnar 4: 1044, 928
--------------------------------------------------
Diagonal 1: 1158, 1165
Diagonal 2: 1242, 1035
Diagonal 3: 1161, 1166
Diagonal 4: 1103, 1213
Diagonal 5: 1103, 1213
Diagonal 6: 1161, 1166
Diagonal 7: 1242, 1035
Diagonal 8: 1158, 1165
--------------------------------------------------
Transposition average: 1351.5
Untransposition average: 1310.25


2. Offset row order:

This shifts the entire cipher downwards. The 340 seems normal here.

Code: Select all

340:

Offset row order: (transposition)
--------------------------------------------------
Offset rows 1: 2080
Offset rows 2: 2112
Offset rows 3: 2118
Offset rows 4: 2009
Offset rows 5: 2044
Offset rows 6: 2129
Offset rows 7: 2113
Offset rows 8: 2101
Offset rows 9: 2125
Offset rows 10: 2139
Offset rows 11: 2121
Offset rows 12: 2012
Offset rows 13: 2091
Offset rows 14: 2013
Offset rows 15: 2150
Offset rows 16: 2077
Offset rows 17: 2014
Offset rows 18: 2070
Offset rows 19: 2065
Offset rows 20: 2152 <---
--------------------------------------------------
Transposition average: 2086.75

408:

Offset row order: (transposition)
--------------------------------------------------
Offset rows 1: 2861 <---
Offset rows 2: 2833
Offset rows 3: 2731
Offset rows 4: 2655
Offset rows 5: 2636
Offset rows 6: 2665
Offset rows 7: 2725
Offset rows 8: 2599
Offset rows 9: 2640
Offset rows 10: 2702
Offset rows 11: 2646
Offset rows 12: 2656
Offset rows 13: 2644
Offset rows 14: 2633
Offset rows 15: 2480
Offset rows 16: 2503
Offset rows 17: 2562
Offset rows 18: 2572
Offset rows 19: 2710
Offset rows 20: 2861 <---
--------------------------------------------------
Transposition average: 2665.7

smokie2:

Offset row order: (transposition)
--------------------------------------------------
Offset rows 1: 2135
Offset rows 2: 2123
Offset rows 3: 2011
Offset rows 4: 2013
Offset rows 5: 2007
Offset rows 6: 2022
Offset rows 7: 2026
Offset rows 8: 2026
Offset rows 9: 1980
Offset rows 10: 2054
Offset rows 11: 2061
Offset rows 12: 2101
Offset rows 13: 2029
Offset rows 14: 2115
Offset rows 15: 2096
Offset rows 16: 2001
Offset rows 17: 2061
Offset rows 18: 2040
Offset rows 19: 2144
Offset rows 20: 2197 <---
--------------------------------------------------
Transposition average: 2062.1

jarlve18:

Offset row order: (transposition)
--------------------------------------------------
Offset rows 1: 2092
Offset rows 2: 2058
Offset rows 3: 1983
Offset rows 4: 2038
Offset rows 5: 2092
Offset rows 6: 2025
Offset rows 7: 1984
Offset rows 8: 1893
Offset rows 9: 1946
Offset rows 10: 2050
Offset rows 11: 2113
Offset rows 12: 2075
Offset rows 13: 2033
Offset rows 14: 2051
Offset rows 15: 2090
Offset rows 16: 2035
Offset rows 17: 2049
Offset rows 18: 2108
Offset rows 19: 2170
Offset rows 20: 2178 <---
--------------------------------------------------
Transposition average: 2053.15


3. Offset column order:

This shifts the entire cipher rightwards. The 340 peaks at offset 15, though it is not much higher than its base. There is also less indication of suppression in the 340 scores at the midrange offsets compared to the other ciphers.

Code: Select all

340:

Offset column order: (transposition)
--------------------------------------------------
Offset columns 1: 2085
Offset columns 2: 2025
Offset columns 3: 2080
Offset columns 4: 2066
Offset columns 5: 2090
Offset columns 6: 1995
Offset columns 7: 2040
Offset columns 8: 2024
Offset columns 9: 1963
Offset columns 10: 1994
Offset columns 11: 2031
Offset columns 12: 2023
Offset columns 13: 2094
Offset columns 14: 2113
Offset columns 15: 2212 <---
Offset columns 16: 2157
Offset columns 17: 2152
--------------------------------------------------
Transposition average: 2067.29

408:

Offset column order: (transposition)
--------------------------------------------------
Offset columns 1: 2752
Offset columns 2: 2720
Offset columns 3: 2698
Offset columns 4: 2523
Offset columns 5: 2515
Offset columns 6: 2503
Offset columns 7: 2427
Offset columns 8: 2449
Offset columns 9: 2362
Offset columns 10: 2412
Offset columns 11: 2429
Offset columns 12: 2453
Offset columns 13: 2507
Offset columns 14: 2538
Offset columns 15: 2596
Offset columns 16: 2699
Offset columns 17: 2861 <---
--------------------------------------------------
Transposition average: 2555.52

smokie2:

Offset column order: (transposition)
--------------------------------------------------
Offset columns 1: 2088
Offset columns 2: 2015
Offset columns 3: 1968
Offset columns 4: 1968
Offset columns 5: 1922
Offset columns 6: 1965
Offset columns 7: 1867
Offset columns 8: 1854
Offset columns 9: 1856
Offset columns 10: 1829
Offset columns 11: 1851
Offset columns 12: 1870
Offset columns 13: 1926
Offset columns 14: 2035
Offset columns 15: 2052
Offset columns 16: 2097
Offset columns 17: 2197 <---
--------------------------------------------------
Transposition average: 1962.35

jarlve18:

Offset column order: (transposition)
--------------------------------------------------
Offset columns 1: 2095
Offset columns 2: 2085
Offset columns 3: 2089
Offset columns 4: 1987
Offset columns 5: 1973
Offset columns 6: 1975
Offset columns 7: 1956
Offset columns 8: 1922
Offset columns 9: 1874
Offset columns 10: 1874
Offset columns 11: 1863
Offset columns 12: 1912
Offset columns 13: 1990
Offset columns 14: 1997
Offset columns 15: 2099
Offset columns 16: 2100
Offset columns 17: 2178 <---
--------------------------------------------------
Transposition average: 1998.17


4. Period row order:

This changes the order of the rows according the period operation. In the 340 the scores in general do not drop as low as the other cipher, are less suppressed. The lowest values observed for each cipher, usually near the midrange periods: 340: 1297, 408: 1096, smokie2: 1069, jarlve18: 1115. The average scores are also much higher for the 340 due to this behaviour when compared to the other ciphers excluding the 408 which has a much higher base score.

Code: Select all

340:

Period row order: (transposition, untransposition)
--------------------------------------------------
Period rows 1: 2152, 2152 <---
Period rows 2: 1809, 1451
Period rows 3: 1392, 1578
Period rows 4: 1297, 1629
Period rows 5: 1629, 1297
Period rows 6: 1796, 1691
Period rows 7: 1578, 1392
Period rows 8: 1409, 1513
Period rows 9: 1570, 1605
Period rows 10: 1451, 1809
Period rows 11: 1498, 2000
Period rows 12: 1451, 2081
Period rows 13: 1581, 1750
Period rows 14: 1593, 1618
Period rows 15: 1552, 1640
Period rows 16: 1603, 1784
Period rows 17: 1646, 1855
Period rows 18: 1856, 1922
Period rows 19: 1958, 1974
--------------------------------------------------
Transposition average: 1622.15
Untransposition average: 1723.21

408:

Period row order: (transposition, untransposition)
--------------------------------------------------
Period rows 1: 2861, 2861 <---
Period rows 2: 1786, 1539
Period rows 3: 1262, 1340
Period rows 4: 1445, 1256
Period rows 5: 1256, 1445
Period rows 6: 1096, 1501
Period rows 7: 1340, 1262
Period rows 8: 1494, 1578
Period rows 9: 1415, 1605
Period rows 10: 1539, 1786
Period rows 11: 1531, 1773
Period rows 12: 1433, 1882
Period rows 13: 1555, 1978
Period rows 14: 1586, 1863
Period rows 15: 1812, 2211
Period rows 16: 2114, 2272
Period rows 17: 2142, 2391
Period rows 18: 2307, 2525
Period rows 19: 2516, 2811
--------------------------------------------------
Transposition average: 1710
Untransposition average: 1888.36

smokie 2:

Period row order: (transposition, untransposition)
--------------------------------------------------
Period rows 1: 2197, 2197 <---
Period rows 2: 1450, 1276
Period rows 3: 1230, 1350
Period rows 4: 1167, 1214
Period rows 5: 1214, 1167
Period rows 6: 1189, 1124
Period rows 7: 1350, 1230
Period rows 8: 1166, 1069
Period rows 9: 1160, 1313
Period rows 10: 1276, 1450
Period rows 11: 1383, 1281
Period rows 12: 1375, 1442
Period rows 13: 1509, 1680
Period rows 14: 1569, 1814
Period rows 15: 1659, 1778
Period rows 16: 1742, 1853
Period rows 17: 1771, 1865
Period rows 18: 1894, 1983
Period rows 19: 2034, 2122
--------------------------------------------------
Transposition average: 1491.31
Untransposition average: 1537.26

jarlve18:

Period row order: (transposition, untransposition)
--------------------------------------------------
Period rows 1: 2178, 2178 <---
Period rows 2: 1435, 1329
Period rows 3: 1425, 1241
Period rows 4: 1496, 1175
Period rows 5: 1175, 1496
Period rows 6: 1115, 1219
Period rows 7: 1241, 1425
Period rows 8: 1280, 1504
Period rows 9: 1357, 1308
Period rows 10: 1329, 1435
Period rows 11: 1349, 1358
Period rows 12: 1326, 1476
Period rows 13: 1322, 1718
Period rows 14: 1360, 1888
Period rows 15: 1540, 2037
Period rows 16: 1670, 1875
Period rows 17: 1779, 1899
Period rows 18: 1895, 1970
Period rows 19: 2010, 2112
--------------------------------------------------
Transposition average: 1488.52
Untransposition average: 1612.78


5. Period column order:

This changes the order of the columns according the period operation. Again the 340 has a peak not a the main period although the difference is small. Other ciphers show a drop in scores around the midrange periods but the 340 does not.

Code: Select all

340:

Period column order: (transposition, untransposition)
--------------------------------------------------
Period columns 1: 2152, 2152
Period columns 2: 2097, 2177 <---
Period columns 3: 2126, 2116
Period columns 4: 2067, 2058
Period columns 5: 2023, 1955
Period columns 6: 2116, 2126
Period columns 7: 2073, 2049
Period columns 8: 2022, 1990
Period columns 9: 2177, 2097
Period columns 10: 2162, 2087
Period columns 11: 2167, 2036
Period columns 12: 2102, 2127
Period columns 13: 2107, 2088
Period columns 14: 2164, 2091
Period columns 15: 2154, 2034
Period columns 16: 2198, 2092 <---
--------------------------------------------------
Transposition average: 2119.18
Untransposition average: 2079.68

408:

Period column order: (transposition, untransposition)
--------------------------------------------------
Period columns 1: 2861, 2861 <---
Period columns 2: 2687, 2686
Period columns 3: 2612, 2685
Period columns 4: 2557, 2580
Period columns 5: 2580, 2587
Period columns 6: 2685, 2612
Period columns 7: 2703, 2627
Period columns 8: 2660, 2623
Period columns 9: 2686, 2687
Period columns 10: 2641, 2639
Period columns 11: 2558, 2650
Period columns 12: 2593, 2620
Period columns 13: 2644, 2596
Period columns 14: 2653, 2742
Period columns 15: 2661, 2756
Period columns 16: 2718, 2765
--------------------------------------------------
Transposition average: 2656.18
Untransposition average: 2669.75

smokie2:

Period column order: (transposition, untransposition)
--------------------------------------------------
Period columns 1: 2197, 2197 <---
Period columns 2: 2071, 1991
Period columns 3: 1982, 2005
Period columns 4: 1991, 1943
Period columns 5: 2031, 1917
Period columns 6: 2005, 1982
Period columns 7: 2058, 1932
Period columns 8: 2086, 1989
Period columns 9: 1991, 2071
Period columns 10: 1955, 2008
Period columns 11: 1956, 2080
Period columns 12: 1977, 2006
Period columns 13: 2003, 2021
Period columns 14: 2011, 2003
Period columns 15: 2022, 2042
Period columns 16: 2138, 2091
--------------------------------------------------
Transposition average: 2029.62
Untransposition average: 2017.37

jarlve18:

Period column order: (transposition, untransposition)
--------------------------------------------------
Period columns 1: 2178, 2178 <---
Period columns 2: 2030, 2060
Period columns 3: 1946, 2011
Period columns 4: 1972, 1984
Period columns 5: 2049, 2051
Period columns 6: 2011, 1946
Period columns 7: 1951, 1996
Period columns 8: 1992, 1924
Period columns 9: 2060, 2030
Period columns 10: 2048, 2030
Period columns 11: 2000, 2042
Period columns 12: 2013, 2034
Period columns 13: 2047, 2026
Period columns 14: 2038, 2119
Period columns 15: 2113, 2107
Period columns 16: 2136, 2094
--------------------------------------------------
Transposition average: 2036.5
Untransposition average: 2039.5


Conclusions:

In 4 out of 5 observations the 340 deviates in a consistent manner

Behaviour 1: some of the diagonal scores are quite high.
Behaviour 2: the operations in general seem to suppress the encoding scores much less for the 340 than the other ciphers.
Behaviour 3: encoding scores peak are not always where they are supposed to be.

Are these behaviours connected somehow?

Hypothesis 1: the row order of the 340 has been altered after the encoding.
Hypothesis 2: the encoding direction in the 340 is not quite as we think it is and possibly follows a route that has a diagonal component to it.

Interesting results, Jarlve. The bump in encoding score for diagonals is curious. There's something that "feels" diagonal about the pivots (namely, a pivot's line of symmetry is a diagonal line). I also noticed that a "Snake" transposition (read line 1 from left to right, line 2 from right to left, line 3 from left to right, etc) has only a small effect on your cycle score (I measured it as 2080.25). I also tried to find operations in my old transposition experiments that produced high repeating bigrams AND high cycle scores. PeriodColumn(2) FlipVertical() Diagonal(1) produces 41 repeating bigrams but kills your cycle score (1164.80).