Here are the substitutions. The + symbol was just the letter H!

I thought that was funny too. All our ideas about how crazy that symbol must have been but it was just a straight up substitution.

Basically, I test all possible ways to split the cipher into 4 quadrants. I ran it for all possible (i,j) values that define the "split point" (the intersection of the four quadrants). For each possible (i,j), I reorder the 4 quadrants in all possible ways, and apply all possible combinations of flips and rotations to each quadrant before combining them back into a single cipher text. Then I count the bigram repeats, and track the highest count across all the permutations for a given (i,j) split point.

Did you try the "knight's tour" as one of the transposition schemes for the quadrants?

I did not try that. There are too many possibilities, unless you limit the kinds of knight's tours (for instance, the period 19 pattern follows one specific movement, rather than allowing for multiple directions). Even just an 8x8 board has 26,534,728,821,064 possible complete tours. So the search space is high. Still, I doubt Zodiac would have implemented a random knight's tour - since the bigrams are peaking at period 19 (and period 15 for the flipped version), maybe simple variations of basic knight's tours could be explored exhaustively. Still, in those cases, the periodic bigrams reduce to a normal bigram counting problem once the cipher is untransposed with a simple procedure. Side note: I thought this was interesting. It's the site of a guy who spent a lot of time trying to count how many possible knight's tours exist for various grid sizes. http://magictour.free.fr/

I'm no longer interested in magic knight's tours and don't want to encourage others to waste time on it.

His frustration is amusing, but we all feel it to some degree with this damned Z340!

<OFFTOPIC> There was an old computer game with puzzles ' "The 7th Guest" that required completing a Knight's Tour as part of the game. HARD!! </OFFTOPIC> -glurk

The knight's tour transposition was discussed by Barry S. and doranchak above. Glurk may also have mentioned it. The Army Manual explains it under 107. Complex Route Transposition on the actual book pages 121 and 122. https://www.nsa.gov/public_info/_files/ ... 078809.pdf Would you like me to make a knight's tour message to see if it can be detected or what it would look like? I would think that it should have a lot of period 15, 19, 32 and 35 repeats. And comparing those periods should yield two symbol sets that have matching symbols. Otherwise I will continue working on my simple rectangular route detection methods.

I think we should continue with our current hypothesis but I'd like to re-mention some really interesting period 19 zynchronities. There is a magic square in the Zodiac FBI files which has the same pattern, something like that could have been used as a transposition matrix. Or a more classic magic square 18 by 18 transcribed to 17 by 20. In Gareth's Penn book TIMES 17, there is a section on how to construct a magic square. Supposedly he received some one ring phone calls over the span of 2 years which he wrote down on his calender, true or not, he somehow managed to interpret a "Knight's move" out of it. Check the following image I put together from his book.

Another chess connection is the alleged 7/19/78 "I am in control" letter mentioned in Graysmith's "Zodiac Unmasked" but has not been independently confirmed to exist:

But maybe you play chess with me. I have several cheap sets in closets all over

viewtopic.php?f=69&t=726 As far as I know, there is no direct reference to chess from the authenticated Zodiac correspondences and other evidence; they are only coming out of these secondary sources. Still, I agree that it's worth exploring the possibility of knights' tour transposition. But unraveling such a transposition sounds very daunting, since there is an intractable number of possible tours for a "board" as large as the 340's grid. An 8x8 board alone has over 26 trillion tours.

I will put knight's tour somewhere on my to-do list. Although trying to solve the 340 by figuring out a knight's tour transposition would be very difficult ( as if we don't have enough problems already ), it would not be difficult to try to make a lot of practice messages with the same knight's tour scheme but many different plaintexts to see if 340 stats can be emulated. The repeats show up primarily as diagonal rows going in one direction, and I suspect a knight's tour scheme would make it difficult to make so many period 19 repeats because the repeats would be diffused in other directions. Maybe at some point, if other schemes don't work out for us, I can try something similar to knight's tour so that it can be eliminated as a possibility. Maybe constructing such a cipher will teach us something.

The repeats show up primarily as diagonal rows going in one direction, and I suspect a knight's tour scheme would make it difficult to make so many period 19 repeats because the repeats would be diffused in other directions.

Good thinking. That is my conclusion also. Sometimes the Zync gets at me.

It looks like a 16 x 21 grid, inscribed vertically and then transcribed right to left horizontally. Or a 21 x 16 grid inscribed horizontally and transposed vertically. Somewhere inscription or transcription is backwards. I am going to keel working on my spreadsheets, which are pretty crude. But even with a far from perfect untransposition, I was able to get a decent score and find a lot of words.

Yes, you solved it rather decently. Let me know when you want to know what exactly I did to create these ciphers.

Here are the substitutions. The + symbol was just the letter H!