– The "slope" of the sequence "1212321…" is -1. For example, the sequence "123123123123123" has a positive slope since it goes uphill and "321321321" has a negative slope since it goes downhill. The L homophones not having a positive slope may indicate that Zodiac did not pick these homophones from left-to-right from a table, but since we know the sequence is cyclic it must have meant that he at least tried to alternate the homophones to some extent. Interesting!
I’ve measured the slope of all homophone groups, all are positive except for L. While H, F and D only have a slope of 1 these letters only have 2 homophones each and the slope measurement is rendered ineffective because for example "12121212" goes both up and downhill almost equally.
Letter: slope ------------- I: 18 L: -1 E: 27 N: 10 O: 5 A: 4 S: 5 T: 11 H: 1 F: 1 R: 5 D: 1
It’s like everything he did is perfectly designed to make his encryption behavior ambiguous.
This is exceptionally true for the Z340.
My suspicion is that it was done by design (to some degree). There is a high quality picture of the Z340 and if you look at how the symbols were drawn it’s obvious that he was very consistent about it.
What also is little bit odd is that he cycled his homophones, we’ve done some searching here and there and it is not something that is commonly listed in cryptography books.
My suspicion is that it was done by design (to some degree). There is a high quality picture of the Z340 and if you look at how the symbols were drawn it’s obvious that he was very consistent about it.
What also is little bit odd is that he cycled his homophones, we’ve done some searching here and there and it is not something that is commonly listed in cryptography books.
I can’t imagine why it would be. If the goal is to hide letter frequency, cycling homophones seems to undermine the effectiveness of the cipher. It’s impossible to know for sure, but it looks like, overall, this behavior falls apart around position 290 (18 or so symbols after the start of part 3). That is with the exception of "L"
With "L", the first time he uses the same substitution for both terms in "LL" is before this. In fact, it’s at the end of part 2
I don’t know why he would stop caring about "L" before he stopped caring about the rest of the cycles. Especially weird is that, since the double L at 269 is the half filled square, it’s not like he started out with L3L1 or L1L3 and decided to go back and change it later.
If he had his plaintext and his key and then went one letter at a time with his substitutions, filling out the whole cipher for each letter before going back and starting over with another letter, I don’t know why the cycles would all fall apart at the same time, especially right in the middle of a section rather than between them. Add to that the weird choice to double up symbols for "L" at a completely different place in a different section and I don’t know what to make of it.
And if he was encrypting one letter at a time, that would make the cycles easier to maintain, sure, but then why is he mixing up A4 with S4 and E7 with S1? There’s just no obvious way I can think of to explain all of the behavior at once. It’s like, one minute he is careful to incorporate fake bigrams ("GG" [RR] in part 1) and the next he skips a whole word or line. He accidentally encrypts [DANGEROUE] wrong and then misspells the very next word, [ANAMAL], on purpose. And SLOI. Gosh darned SLOI.
There are very few historical ciphers that cycle homophones but I can see why it was done. Homophonic substitution was made to defeat frequency analysis and cycling homophones is a simple way to ensure that the frequencies are as flat as possible. In that regard it increases the effectiveness of the cipher. And pretty much a computer is needed to tap into its weakness.
I don’t know why he stopped cycling homophones in the third part but my two best bets are that he grew tired of it or it was by design.
Looking at the Z340 the cycles are much more random. And random enough so that we can’t be sure of any cycle. It may be that in the Z340 most of the cycles are similar to L in the Z408.
Hi there, do you think the omission at "all the[…] I have killed" part could explain how he screwed up the cycling and ended up with 18 surplus characters? I liked Oranchak’s suggestion that a full line was missed at this spot and he decided to just carry on. Thanks for the great thread!
Hi there, do you think the omission at "all the[…] I have killed" part could explain how he screwed up the cycling and ended up with 18 surplus characters? I liked Oranchak’s suggestion that a full line was missed at this spot and he decided to just carry on. Thanks for the great thread!
It makes a lot of sense. He might have even proven this statistically, but I don’t know where. Just saw someone mention it.
It’s weird though. If the 408 was his "first and final draft" then the mistake almost certainly happened during encryption because the cycles of his homophones is uninterrupted between parts 2 and 3 (where the line would have been missed). Maybe that suggests the cipher was always on three separate sheets of paper or he put enough space in between sections that he could trifurcate it on standard letterhead without bunching up at the top or bottom? I don’t know. It’s hard to say. It’s a very ambiguous situation in many ways.
Often, it’s pretty easy to see where the spelling errors come from, but in other cases its hard to separate intentional misspellings from accidental ones. Maybe he missed a letter first and then, at some point, realized he was moving to a new row in his plaintext before he was finished encrypting a row in the cipher. Then, when he moved from the second to the third part, for whatever reason he also skipped a line (maybe he went and tried unsuccessfully to find out what went wrong, lost his place, etc.) and saw that he was really messing up badly, so he rushed through the last part and slapped gibberish on the end.
The real questions are
1)what he knew/realized about the mistakes and when,
2)what’s intentional and what isn’t,
3)how good/experienced he was with encryption.
4)what the mistakes can suggest about his process
What Jarlve has said is probably exactly what happened; that this guy was systematically cycling homophones from his key in order to keep the distribution as flat as possible, then he just got tired of it towards the end. It’s a perfectly plausible explanation.
408 is just really hard to pin down as far as intentionality is concerned. Doesn’t mean we can’t tear the thing apart and speculate/make fun of the Zodiac.
These are really interesting thoughts. I think this big media entrance was important to him so he may have practised on rough paper but I also think he was arrogant so he may well have thought practise unnecessary, even though I doubt he had much experience creating ciphers or art. It may have been his last sheet of giant art paper so he decided to carry on rather than wait for the next day to resupply at Woolworths. It is pure conjecture of course but he did switch paper for his next letter four days later.
As far as his process, my guess is that he started with the key because coming up with the symbols is the fun part. For writing out assignments a typewriter would be helpful for anyone. Then I think he decided on the 408 character count because he knew he was sending it in three parts and it had to be divisible. Then he would compose his stupid message on rough before tackling the expensive paper. It may be easier to count typewritten (aligned) text than handwriting so I would expect him to use a typewriter for that as well. Why would handwrite letters if he had a typewriter? Because you can’t type a cipher? I don’t know but I think he typed the concerned citizen card so I am on board. Thanks for sharing your thoughts!
It’s an interesting observation. I wonder if the keyboard layout really did play a role in him making the cipher key. It’s hard to tell since a lot of the key doesn’t seem related to the layout.
So the observation is that (some) of the letters and their respective homophone mappings sit next/close/adjacent to each other on a Qwerty keyboard?
Have the odds ever been calculated?
Thanks for taking the time to answer. Best of luck on finding things out.
