Doranchak. Can you do the pivots and the box corners in the same spreadsheet highlighted differently just to see if they become (related)….39s 19s
Thanks
Doranchak. Can you do the pivots and the box corners in the same spreadsheet highlighted differently just to see if they become (related)….39s 19s
Thanks
OK – it is done. I marked the box corners in yellow:
http://zodiackillerciphers.com/period-calculator/
Doranchak. Can you do the pivots and the box corners in the same spreadsheet highlighted differently just to see if they become (related)….39s 19s
ThanksOK – it is done. I marked the box corners in yellow:
http://zodiackillerciphers.com/period-calculator/
Thanks..
I’ve updated it so you can choose between showing: 1) Positions, 2) Z340 (numeric), and 3) Z340 (symbolic).
http://zodiackillerciphers.com/period-calculator/
I just updated it to mark and count the repeated bigrams as well.
I wanted to know how often a random 340-character cipher text would yield the same high numbers of bigram repeats at different periods, so I ran a shuffle test.
1) Randomly shuffle the original Z340
2) Test periods 1 through length/2 (170)
3) Untranspose the shuffled cipher at each of those periods
4) Save the maximum repeated bigram value (for example, for the original Z340, the maximum is 37 at period 19, compared to 25 at period 1).
I ran this test 1,000,000 times and here are the results:
The average max repeated bigram value was 30.6155 (variance 3.16546, standard deviation 1.77917).
68% of the shuffles fall in this range of max repeated bigram values: [28.83633, 32.39467] (1 sigma)
95% of the shuffles fall in this range of max repeated bigram values: [27.05716, 34.17384] (2 sigma)
99.7% of the shuffles fall in this range of max repeated bigram values: [25.27799, 35.95301] (3 sigma)
Based on those results, I estimated the chance that what we see in Z340 is happening by pure accident:
For the normal Z340:
The estimated probability that it has a max repeated bigram value of 37 at some period by chance is: 0.00463199 (1 in 216 chance)
This is about 3.6 sigma away from the mean.
For the mirrored Z340:
The estimated probability that it has a max repeated bigram value of 41 at some period by chance is: 0.0000779998 (1 in 12821 chance)
This is about 5.8 sigma away from the mean. (Trivia: 5 sigma was the strict threshold required to declare that the Higgs boson found by the Large Hadron Collider was real and not some random phenomenon).
Conclusion: The bigram peaks for the Z340 seem significant, especially for the mirrored Z340.
Here’s a plot of the distribution of bigram peaks for all 1,000,000 shuffles. X-axis is the number of bigram repeats observed at the peak period. Y-axis is the number of shuffles that produced the peak bigram repeats:
And here’s the data: https://docs.google.com/spreadsheets/d/ … sp=sharing
For the normal Z340:
The estimated probability that it has a max repeated bigram value of 37 at some period by chance is: 0.00463199 (1 in 216 chance)
This is about 3.6 sigma away from the mean.For the mirrored Z340:
The estimated probability that it has a max repeated bigram value of 41 at some period by chance is: 0.0000779998 (1 in 12821 chance)
This is about 5.8 sigma away from the mean. (Trivia: 5 sigma was the strict threshold required to declare that the Higgs boson found by the Large Hadron Collider was real and not some random phenomenon).Conclusion: The bigram peaks for the Z340 seem significant, especially for the mirrored Z340.
I like the Higgs Boson comparison.
A lot of people have tried to solve the 340. It has received a lot of scrutiny from experts to novices. I am wondering how many people and who has treated the 340 as a route transposition or any other explanation for the repeats. And what they came up with. I would like to see work of others in that direction. Does anyone know?
EDIT: I am starting to look. So far I have found some information about columnar transposition, but not so much about the period 15/19 repeats or route transposition. Funny, because route transposition is thousands of years old and very classical. Here is a nice paper written by a guy named Jeffery Yi. He put a lot of work into trying to solve via columnar transposition, and is undoubtedly a very smart guy. Never once as I could find did he mention, however, the period repeats.
That’s a good question. People have looked into different transposition schemes but I don’t recall anyone mentioning the specific symptom embodied by the period 15/19 phenomenon in Z340.
On this board back in 2013, pi did an investigation into routes: http://www.zodiackillerciphers.com/?p=401
The forum at zodiackillerfacts.com had some discussions about different transpositions but I don’t recall which types came up. And many of the posts have been lost.
Do you recall who on this forum was the first one to notice the period 15/19 phenomenon? I think it is a very important discovery and whoever found it should be acknowledged. I’ve been trying to collect all the observations here: http://zodiackillerciphers.com/wiki/ind … servations. If you get a chance to look at that, let me know if I left anything out.
Here’s another gadget. A "repeating fragments explorer":
http://zodiackillerciphers.com/fragment-explorer/
Choose a cipher from the dropdown list, then hover over the buttons to highlight the patterns. The patterns are shown in order from least probable to most probable. Also, notice how the number of patterns increases as you go through the different Z340 schemes in order.
Great program mr doranchak Can you drop the link onto the front page of this homophonic substitution thread with the other ones..
Jarlve and Daikon have both mentioned it. Jarlve mentioned it on page 27 of this thread, and I am sure that he mentioned it somewhere before that.
http://zodiackillersite.com/viewtopic.p … &start=260
Daikon mentioned it here:
http://zodiackillersite.com/viewtopic.p … &start=300
and here:
I agree that it is very significant. Daikon seems to have thought that he wasn’t the first, but I don’t know any more than that. A lot of people talk about "columnar transposition," but the correct term is "route transposition". I know what "keyed columnar transposition" is, but that is not the same thing as route transposition.
I am still thinking about it, and wondering if anyone a long time ago explored route transposition. It seems the easiest way to create so many period x ( period at a distance ) repeats.
EDIT: I checked out the new gadget. It is interesting that the 408 has much lower probabilities than even the horizontally flipped untransposed period 15. Especially since there were fewer symbols used. What does that tell us? What is "untransposed column period 2 then linear period 18"?
hi guys..the other day i was running AZdecrypt for the first time just experimenting around, and after about two hours i checked it and the top line read a perfect sensible line. Is this a normal happening. Does it do this because of the way the first few lines of the 340 have no repeats. any ways what spiked my interest is that it read DEARANNAFRAIDTHAT..ANN being the wife of my poi at the time. Just more really weird zynchro shit i suppose. I took a screen shot a little later and it was changing around a little but kept coming back to that line ..left it running to see what would come out a day or two later but i forgot to flick switch at power outlet too on..DOH.. lost it except the screen shot.
Great program mr doranchak Can you drop the link onto the front page of this homophonic substitution thread with the other ones..
Oh! I keep forgetting about that. OK – I added the links to the period calculator, fragment explorer, and the old word search gadget.
Jarlve and Daikon have both mentioned it. Jarlve mentioned it on page 27 of this thread, and I am sure that he mentioned it somewhere before that.
Thanks for digging up those references – I added them to the wiki.
EDIT: I checked out the new gadget. It is interesting that the 408 has much lower probabilities than even the horizontally flipped untransposed period 15. Especially since there were fewer symbols used. What does that tell us?
All I can think of is the obvious stuff: 1) Z340 has some scheme that conceals the original patterns that would have appeared if only normal substitution had been applied in a normal reading order. 2) Z408 has fewer symbols to randomly select from, so its underlying plaintext patterns are more likely to be preserved after substitution.
I am trying to come up with more refined measurements of how well the patterns appear in cipher texts, so I can compare them to random distributions. People have used IoC for unigrams and bigrams; perhaps I should extend that to include the other types of repeating fragments. Ideally, the measurements will be highest when the correct un-transposition is identified.
What is "untransposed column period 2 then linear period 18"?
A while back, I ran some "transposition explorer" experiments, and it found high-scoring manipulations that involved those operations (original post).
The "PeriodColumn(2)" operation means to step through the columns with period 2. Say you have columns {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}. The operation results in this new column ordering: {1, 3, 5, 7, 9, 11, 13, 15, 17, 2, 4, 6, 8, 10, 12, 14, 16}.
Then, applying linear period 18 is just our familiar period operation (untransposition of period 18). I call it "linear" simply to distinguish it from the columnar variation.
That particular combination of operations is interesting because it produces a very high number of repeating bigrams with just two steps.
