Here are the substitutions. The + symbol was just the letter H! 
Really good to hear from you again smokie! Thanks again for all your past contributions to this effort. You brought a lot of really interesting ideas (and colorful spreadsheets 
)
I hope this isn’t the end of the crypto journey for you – there are plenty of cipher mysteries ahead!
Really good to hear from you again smokie! Thanks again for all your past contributions to this effort. You brought a lot of really interesting ideas (and colorful spreadsheets
I hope this isn’t the end of the crypto journey for you – there are plenty of cipher mysteries ahead!
You are welcome and thanks to you! It is not the end of the journey for me. I have picked up some javascript and can write simple solver programs. That’s why I am so glad that the 340 is solved now. I can move on. I am so glad that Sam showed up. We were always talking about and wondering if someone would show up with a new approach to the old ideas. Someone with a different perspective and talent set to help out. And it happened. He is truly a blessing to us all.
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. 
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.
I was thinking the exact same thing. A freaking H
We have our answer to the pivots question! Pivots in cleartext are not uncommon, and it is not uncommon to even have two. Here it looks like there was one pivot in the cleartext, and one "almost" pivot of five out of six letters, except for the letter I instead of E in the blue pivot.
This is the cleartext before transcription. All of the letters that appear in the pivots are part of correctly spelled words that are parts of complete sentences.
On left, cleartext after likely one direction knight’s tour inscription. On right, the ciphertext. At bottom the substitutions for the letter I. The backwards B symbol maps to the letter E, but this one use of the backwards B that maps to I is in the pivot.
EDIT: Did he do this on purpose to make another pivot? If so, he must have stared at this for a long time, had an original encryption, and then subtly manipulated it to play a game with us. Otherwise, the backwards B was an encoding error.
EDIT 2: Here are all of the substitutions for the pivot cleartext. All pivot symbols, except for that one backwards B, appear to map exclusively to only one cleartext. Looking at the whole key in post above.
Hi again all! Great work Doranchak, Jarlve and Sam on the solution. Must be satisfying (and a little frustrating!) to see how close some of the theories on here were to the final encryption.
On the pivots – what do we think the odds are that he saw the first one appear naturally during encryption and fiddled to force the second one out as a red herring?
Hi again all! Great work Doranchak, Jarlve and Sam on the solution. Must be satisfying (and a little frustrating!) to see how close some of the theories on here were to the final encryption.
On the pivots – correct me if I’m wrong, but the horizontal arm for the second pivot is on the "one character too far to the left" row isn’t it? If he hadn’t have messed up this row the second pivot wouldn’t have appeared. Do we think this may have been a deliberate red herring he put in, with the bonus of knowing he was breaking the encryption method and making the crack harder? Otherwise still a funny coincidence!
It looks like what may have been an inscription / encoding skip was on the line below the pivot.
You were too quick for me smokie! I had another look and yeah that is how it seems. So maybe just the backwards B could have been forced to make the pivot? I suspect there’s lots of interesting tidbits we’ll find now we have a solve
I am just rolling with laughter over here, reading through some of the old threads.
Friday, November 13, 2015:
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.
Doranchak, your work answers the question I posed here. It does look like the cipher could possibly be split into quadrants on column 8 and row 9 (the "center" being the most logical place), though there are many other possibilities as your "heat map" demonstrates. Did you try the "knight’s tour" as one of the transposition schemes for the quadrants?
Friday, November 13, 2015:
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 8×8 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.
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!
Friday, November 13, 2015:
<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
Friday, February 5, 2016:
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.
Friday, February 5, 2016:
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.
Friday, February 5, 2016:
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
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 8×8 board alone has over 26 trillion tours.
Friday, February 5, 2016:
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.
Saturday, February 5, 2016:
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.
I am very happy about how this turned out in the end. Sam showed up and worked on the one direction Knight’s Tour idea. At some point, I would like to hear more about how he came up with all of the 650,000 routes. It was a brute force attack on the routes, combined with hillclimbing the substitutions, right?
Sam did not enumerate knight’s tour variations:
In regards to the transposition – it was by enumerating all possible proper 2D decimation of the cipher. That didn’t turn anything up, so we started splitting the cipher horizontally and vertically into all possible (2,3,4) segments, then for each all possible proper 2D decimations. Of all of these one turned up a fragment of a partial solution.
Decimation is not a word in my vocabulary but I suppose he meant the variations in 2-dimensional reading rules, (+2 horizontal, +1 vertical), (+3 horizontal, -2 vertical), etc… But only the variations in which the transposition does not run into itself.
It’s pretty amazing that it happened and we are now celebrating.
EDIT: Did he do this on purpose to make another pivot? If so, he must have stared at this for a long time, had an original encryption, and then subtly manipulated it to play a game with us. Otherwise, the backwards B was an encoding error.
Good observation, it is really odd.
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.
I was thinking the exact same thing. A freaking H
I said it many times over that it was most likely a 1:1 substitution. It happens in the Z408 also, the most frequent symbol is a 1:1.
I said it many times over that it was most likely a 1:1 substitution. It happens in the Z408 also, the most frequent symbol is a 1:1.
Yes, I remember you stating that. Was just also remembering the many discussions of the + being nulls and the uncanny way it landed dead center and inline with the dashes on line 10. That one in particular had me going unconventional by ruling line 10 out along with 19 and 20. I was currently working the quadrant angle with all four split into 8 by 9 sections, un-transposing them diagonally such as HNEB9R in the top left quadrant.
I am very happy you three kept the drive alive. The dedication was very impressive and I have much respect for what you all accomplished.
