I didn’t see a topic on this so I’m sorry if this has already been pointed out
One of the differences between z408 and z340 is that, in the former case, it’s obvious that Zodiac was systematically pulling homophones from his key when making substitutions. I’ve gone into exhaustive detail on this topic here: https://forum.zodiackillerciphers.com/community/zodiac-cipher-mailings-discussion/z408-encryption-mistakes-a-deep-dive/
Though I certainly would never have even thought about it on my own, I just found it interesting.
Since doranchak, jarlve and Sam Blake brought down Thor’s hammer on the 340, I thought I should try the same thing I did before if for no other reason than to develop a more accurate key than the ones I’ve found in circulation. One of the problems, as has been pointed out, is that the cycling behavior is much weaker in 340 than 408. In my own testing, I can’t even really prove it’s there at all. I think it is though, at least for the first section of the cipher. I also think it can explain the reason for Zodiac’s crossed out ‘K’, and it might also suggest that the anchor symbols (anchor with a dot on either side) started out as a single symbol.
When Zodiac mixed up symbols in z408, much of the time it was for a very specific reason. Since he had his homophones organized in a specific order, when he went to see which symbol he should substitute next, he would sort of ‘anticipate’ the next symbol in his list. He also had a few very similar looking symbols assigned to other plaintext letters and in the same ‘spot’ in the order for that letter’s homophones. Since it was where he was expecting it to be, and looked like what he was expecting to see, he ended up picking the wrong symbol. That wasn’t the only type of mistake he made, but he made it multiple times.
In z340, the Letter ‘A’ has (‘K’) as a homophone and the letter ‘I’ has (‘K’ backwards) as a homophone. I suspect that the (‘K’) was the 3rd symbol he had assigned to ‘A’ and (‘K’ backwards) was the 4th assigned to ‘I’. Up until the point where he mixes up (‘K’) with (‘K’ backwards), it seems like he was systematically making substitutions in a left-to-right reading order. Moreover, at the time that he accidentally wrote ‘K’, he was ‘anticipating’ the 3rd symbol assigned to plaintext ‘A.’ He had also already just used the 4th (‘K’ backwards) as a substitution for ‘I’.
The weak cycles I’m describing and the circumstances that may have caused the mistake are visible here [a larger version is attached to this post]:
Why he chose to use (‘K’ backwards) again, I haven’t a clue. It’s possible that he wanted to add further confusion to the cipher or that he simply lost his place. I just don’t know.
I’m being pretty loose with the cycles here. As I point out above, the order for ‘A’ gets a little bit finnicky in the second cycle and the cycle for ‘I’ is interrupted by the error. What is interesting to me is that the midpoint of the first 2 sections of the cipher (denoted by the purple line) is pretty close to where these cycles appear to end.
If it’s real, and I think it is but with some caveats, then there is also reason to believe that the two anchor symbols assigned to ‘T’ may have started out as the same symbol. If this is true, then the cycles for ‘T’ are visible, but are also interrupted
This is a big if, but if these are real cycles then it might be that Zodiac was trying to keep from making the same ‘double square’ type arrangements that showed up in z408 and which helped the Hardens find double LLs. There are three occasions in part 1 of z340 where the transposition has caused two TTs to appear next to one another. Of course that would do absolutely nothing to help a person crack the code and, in fact, would have made for an infuriating red herring, but maybe he didn’t notice. Again, only if these are real cycles.
I’m continuing to try and work this. If anyone notices anything faulty with the approach here or has any ideas as to what he may have been thinking, post away. Maybe we can build up some more data points as to whether he realized how hard he was making this thing.
[EDIT] First image is too small. Adding as an attachment
Let me add a better copy of the picture for ‘T’. I don’t know how to make these image hosts work and this new forum is impervious to rescaling in browser.
Regarding the 3 2 symbol ‘interruptions’, of note to me is that they all have either (‘phi’) or (‘G’) and each of these terms are in the 1st and 2nd position respectively.
In other words, if you break the 2 symbol interruptions up in the manner I’ve suggested…
[ (‘G’)(‘phi’)—–(‘square’)(phi)—–(‘G’)(‘square’) ]
you don’t get a symbol followed by (‘G’) and you don’t get (‘phi’) followed by a symbol. This makes them, arguably, variations on the symbol pair (‘G’)(‘phi’), which I have listed as the 4th and 5th substitutions for ‘T’
*I know this is an unwieldy way of talking about this subject. I’m trying to be as clear and concise as possible. Ultimately, if it seems complicated I promise, it isn’t. I’ve probably just over-described my point.
UP NEXT: Nested Cycles within substitutions for ‘E’
To finish out the gambit for letters with 5 or more homophone assignments, here is the substitution order for ‘N’
Like with the letter ‘A’ the only difference between the first set of substitutions and the second is that the order of 2 symbols (‘y’) and (‘dot’) is reversed, although it’s admittedly weaker here since there are only two potential cycles to compare.
I would say that, since the first 5 assignments have no repeats, and 5 is the total count of symbols assigned to ‘I’, ‘A’, and ‘N’ it supports the suggestion that substitutions were made in a left-right reading direction and with attention given to diversifying the substitutions, presumably to maintain the flatness of their distribution. Again, only if these are real cycles and only for the first section of the cipher.
Moreover, this doesn’t apply to ‘T’, although I’ve made the argument that there is still a pattern for ‘T’ substitutions, admittedly a weaker one than in the other three cases and which requires more assumptions.
Which brings us to ‘E’
There is no obvious pattern for ‘E’ substitutions, nothing like what can be seen in the other cases.
Regarding the flatness of symbol distribution for ‘E’, if you survey all of the substitutions made for ‘E’ then it’s clear that there is a major preference for the (‘B’) symbol. (‘B’) is used 12 times, versus 10 for (‘I’) and (‘C’ backwards), 6 for (‘half moon’), 5 for (‘N’) and 3 for (‘B’ backwards).
So it isn’t flat, which is one of the primary goals of homophonic substitution and a possible explanation as to why he might have made systematic assignments in z408.
It is possible to tease some more flatness out of the distribution, however, if you eliminate lines 19 and 20 and the section that decodes to [LIFEIS] (which weren’t included in his 1-2 decimation transposition)
Doing this causes (‘B’), (‘C’ backwards) and (‘I’) to be flattened out to 9 substitutions each. Additionally, if you combine (‘B’ backwards) with either (‘N’) or (‘half moon), then the overall distribution becomes even flatter, with only one outlier remaining in the total.
This, in turn, begs the question; If we restrict our survey to just a few of the substitutions, let’s say 3 of the 6 symbols assigned to ‘E’, can we find any patterns?
………….sort of maybe? I haven’t checked all possible groupings, but this one stood out to me.
The pattern of (‘N’)(‘C’)(‘half moon’)(‘C’) remains stable in the first part of the cipher, although it’s admittedly not much to go off of. If it’s real, though, it might offer some insight into the ordering of his key, which is the whole point here. At least it’s something to ponder.
A note on the other two sections of the cipher; I have only looked for cycles in part 2 using the letter ‘A’. Since there aren’t any on a left-right reading direction, I also looked for vertical patterns (top-bottom-left right, bottom-top-right-left, etc.) and I didn’t find anything. I may revisit section 2 at some point, however, using the other letters.
In conclusion, if these are real cycles, then it may suggest that the transposition was performed first and the substitution second. Thinking about it, it does seem easier to transpose plaintext than a set of symbols since it’s easier to keep track of words in your head than an arbitrary group of homophones.
Since I haven’t seen any contemporary sources that talk about ‘cycles’ in z408 being relevant, then I would submit that there is no reason for Zodiac to pay any attention to disguising that type of pattern in the cipher. He seems to have been oblivious to this concept the first time so I can’t think of any reason for him to have such an insight prior to creating z340. Bigrams, however, might have been a point of concern after z408 was solved so quickly. This is all speculation, of course.
Moreover, if these are real cycles, then I think it supports the notion that the two (‘anchor’) symbols assigned to ‘T’ probably started out as a single symbol, which he then convoluted by adding a dot to either side. I can’t think of a reason to make this distinction other than to throw further confusion into the mix, since this distinction has no bearing on the underlying plaintext. It’s also a very simple change to make, requiring no corrections (which we know he made in the cipher). He could have used liquid paper or started over, but he didn’t. He scratched out (‘K’) and replaced it with (‘K’ backwards). The dot on the anchor symbols would require nothing more than a pen to incorporate, so this may have also been a ‘correction’ of sorts.
I’m sure there are a number of reasons for him to do this, but at the end of the day I just don’t see that it makes the cipher that much harder to decode, certainly not as much as the other steps he took. But who knows. Again, I’m speculating, but I don’t think I’m extrapolating beyond what is reasonable.
Love to hear if anyone else notices anything.
