Largo: See the 5th post down for another interpretation of the unique symbol strings, and the discussion carries over to the next page.
I am considering excluding sequences that terminate at the end of the cipher because their length is uncertain. Good point Largo.
What about normalizing the ones at the end by the fraction of the max possible length?
For example, Z340 has a max possible unique length of 63 due to its alphabet.
Towards the beginning, a unique string of length 10, out of a possible 63, would score: 63/63 = 1. Add 1 to the "10" column in the histogram.
But let’s say towards the end, a unique string of length 10 is found, but a max length of only 40 is possible. So it would score: 40/63 = 0.63. Add 0.63 to the "10" column in the histogram.Not sure how much it would matter.
Only the sequences that terminate at the last position of the cipher are uncertain and normalization does not fix that.
Largo: See the 5th post down for another interpretation of the unique symbol strings, and the discussion carries over to the next page.
viewtopic.php?f=81&t=3196&start=70
Thank you smokie! I’ll read these posts.
Largo: See the 5th post down for another interpretation of the unique symbol strings, and the discussion carries over to the next page.
viewtopic.php?f=81&t=3196&start=70
…from that thread:
Conclusion: It does seem that there is some encoding mechanism at work besides just cycling homophones, and whatever is disrupting the cycles does not appear to be random symbol selection. And that slope, the sudden drop after x = 17 for the 340 may be another indicator of the mechanism.
Has anyone ever examined the 26 segments in more detail? For example, whether there are repeated bigrams within a segment, or whether the repeated bigrams extend over several segments. It would also be interesting to compare the unigrams of all 26 segments.
If so, and if I overlooked it: Sorry =)
I wonder how the start and stop positions for the unique strings of length about 17 compare with the period 19 bigram repeat symbol positions. My guess is that, since the + is highest count with 24, it is most frequently terminating unique strings. And because it is heavily represented in the period 19 repeats, I guess that those positions would match up. But I haven’t looked.
Has someone done this yet? It would be interesting to color the segments with Peek-a-boo, then apply P19 and see if there is any noticeable pattern. I’ll put that on my todo list. Let’s see if and when I can do that in the next few days.
3. Some sort of exotic cycling scheme which cuts the cycles short at some point.
Hm…that alone does not explain why z340 cannot be solved. AZDecrypt / TheRaccoon have no problems with completely random cycles. So maybe some kind of " interlocked parts " when creating the final cipher (e.g. 75% of the cipher is in the correct reading order, the other 25% are interspersed according to a pattern. Or a pattern of zeros inside a transposition. That sounds a little vague, but I have concrete ideas on this. I’ll give you an example soon.
PS: I am not sure if I understood everything in the linked posts correctly. There’s a lot for me to catch up.
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Has anyone ever examined the 26 segments in more detail? For example, whether there are repeated bigrams within a segment, or whether the repeated bigrams extend over several segments. It would also be interesting to compare the unigrams of all 26 segments.
If so, and if I overlooked it: Sorry =)
I started thinking about doing that just last weekend, but didn’t get very far. I have to get myself psychologically motivated to do stuff like that now, but it is starting to bother me I was thinking about the 26 segments on my commute to work this morning.
Has someone done this yet? It would be interesting to color the segments with Peek-a-boo, then apply P19 and see if there is any noticeable pattern. I’ll put that on my todo list. Let’s see if and when I can do that in the next few days.
Again, I have not done this. It would be pretty easy to do though.
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viewtopic.php?f=81&t=3196&start=70
It doesn’t appear that I transposed the plaintext first before encoding.
O.k., so we are measuring the distance between A and B2, where the segments can look something like this:
A…..B1………B2
A..B1…………B2
A…………B1..B2
Forgive if I cannot remember all before. I know that there is a measurement for the distance between B1 and B2, but I am not sure how it compares. Is there a measurement for the distance between A and B1?
Has anyone looked at the A to B2 segments for English plaintext?
The longer I look at the cycles, the more doubts arise in me whether they are really relevant.
I’m one of those people who don’t just rely on numbers and statistics. Instead, I try to reconstruct how I would have created z340 instead of Zodiac. I am absolutely aware that this is largely a game of chance. An example I have already mentioned:
Zodiac knew that repeated bigrams were the main target for cracking z408. A logical conclusion is that this point should be avoided in the future. This assumption is the easiest to explain the incomplete cycles. Of course, this assumption can be completely wrong. One fishes in the mud. However, we also do so if we look at all the known statistics. P15/P19, cycles, IOC, Unigram distribution and what else. All these are clues. Sure… the sigma says something else. I am not suggesting that these statistics are a coincidence or irrelevant. But they have not yet led us to a solution. Maybe we’re too focused on it and don’t see the essential things. Once a question is reasonably clarified, three new questions arise from these answers.
Another point to consider (I think smokie or I have described this somewhere before): If z340 is based on transposition, why bother to hide the cycles? In 1969 one could be very sure that a well transposed text in combination with homophonic substitution would be extremely difficult to solve. If at all. Moreover: Clean cycles would rather lead on the wrong track. Here, too, one enters the realm of speculation. It is difficult to put yourself in the position of a disturbed personality like Zodiac and to search for logical conclusions at the same time.
For the moment I will focus my further efforts in a different direction. I try to look as little as possible at statistics and prefer creative transpositions or interlocked encryption instead. I have found some other, quite simple possibilities that cannot be solved by the AZDecrypt transposition solver. Perhaps this will also help in favouring other points of view.
And as always: Maybe tomorrow I will change my mind again =)
https://en.wikipedia.org/wiki/Occam%27s_razor
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The longer I look at the cycles, the more doubts arise in me whether they are really relevant.
I agree and this is why sometimes I stop looking at them.
Another point to consider (I think smokie or I have described this somewhere before): If z340 is based on transposition, why bother to hide the cycles?
I don’t know who said it but I have thought it. I agree.
Check out the first post here. Maybe he just did some creative pattern with his homophone groups. He may not have been trying to hide anything.
http://www.zodiackillersite.com/viewtop … f=81&t=267
It is annoying though to not know the answer. It would be interesting to know why there are 26 segments of length 17.
The cycles still baffle me. There’s just enough left in Z340 to seem statistically significant. For example, my perfect L2 cycle score is only met or exceeded in 1 in 5,000 shuffles of Z340 (compared to 1 in 500,000 shuffles for Z408). 6 sigma vs 32 sigma. But if higher-order cycles were ever present, they got really destroyed by whatever extra steps Zodiac did. For example, about 1 in 30 shuffles have L4 scores as good as Z340’s score. The sigma goes up with L *a lot* for Z408, but down with L for Z340.
Z408 cycle shuffle sigmas:
L2: 31.5
L3: 78.0
L4: 160.7
Z340 cycle shuffle sigmas:
L2: 5.8
L3: 3.9
L4: 2.2
Perhaps the transposition is brutal to higher order cycles but leaves a bit of L2 cycling behind, since they are harder to fully disrupt than higher-order cycles.
Or we’re not really looking at a cycling phenomenon. What about a shifting alphabet?
Check out the first post here. Maybe he just did some creative pattern with his homophone groups. He may not have been trying to hide anything.
http://www.zodiackillersite.com/viewtop … f=81&t=267
Let’s say z340 is solved. Let’s also say, there was a transposition and it was substituted with a creative pattern. Since we would then know the solution, we would also see the pattern. How would you rate the pattern then? In what way would it have helped us to find a solution in retrospect? I really think that a possibly existing cycle pattern is only important if there is a transposition/route in the final cipher and not only in plain text.
Or we’re not really looking at a cycling phenomenon. What about a shifting alphabet?
I’ve thought of that, too. This might also explain the frequent occurrence of the + symbol. But I thought there was a thread where multiple alphabets were excluded. Otherwise, we could really look at it again. I had done some tests earlier with heavily repeated text fragments. The 26×17 phenomenon can also be caused by this. However, I never managed to get as few ngrams as z340, so repeated text would definitely become apparent.
But…multiple alphabets / shifted alphabet + P15/P19? I don’t think both can be at the same time.
Or we’re not really looking at a cycling phenomenon. What about a shifting alphabet?
I like that. How do you imagine the shift?
I like that. How do you imagine the shift?
No idea. Vigenere comes to mind. Or what if he did something to the alphabet every X assignments, where X is chosen to sufficiently explain the oddities we see in Z340’s stats? If X is greater than one, maybe that would make the cipher only partially polyalphabetic while making the stats reflect some echoes of monoalphabetic substitution. Maybe he periodically cycled the alphabet just like he cycled individual homophones.
I like that idea too. An Alberti, or Caesar shift, maybe on a period.
See several posts here where I toyed with the idea in a different context to try to explain the regional bias symbols. Depending on the shift, of which there are 25 possible, the resulting ciphertext, which looks just like letters of the alphabet, the frequencies will be different. I called it the shift differential. And with the right period, or number of letters before shifting the key, maybe that could explain 26×7 and some other things.
viewtopic.php?f=81&t=3196&p=56084&hilit=alberti#p56084
In other words, I use a particular key on my Alberti disk to encode X number of letters. Then I rotate the disk, and encode X number of letters again. Repeat until I get to the end of the message. Then encode homophonic.
Consider trying a lot of different combinations of rotations and X number of letters to see what happens. Could that cause P19 too somehow?
I also like it because in a cryptography book that is organized chronologically, the Alberti cipher will be in the chapter next to the homophonic cipher. They were both Renaissance era.
Interesting. I wonder if something like an Alberti cipher could explain the Kasiski spike at shift 78: http://www.zodiackillersite.com/viewtop … 225#p48225
I have been messing around with it. No transposition, Alberti, odd rows one random alphabet key, even rows the other random alphabet key, perfect cycles, homophone keys of varying efficiency ( number of symbols in proportion to number of Alberti letters in the message to almost same number of symbols, 3 to 4, per Alberti letter ).
The bigram spike is almost always at period 1, and at any other period higher than 17 ( the next row ) not even close to 340 P19. The lengths of the segments vary, and the spike can be at longer than 17, especially for inefficient homophone keys, but no spike very close to 26. And we have already seen that randomization shortens the segments. The coincidence count graphs look similar, and there is often a lone spike that is fairly close.
In my opinion, that ain’t it.
EDIT: Source of plaintext random selections from a novel.
