Doranchak — correct me if I’m wrong, but if we were to impose a "soft" adjacency constraint (of course, I don’t have all the logistics worked out, but I think you follow) on the key to the 340, wouldn’t that dramatically reduce the key space? And thus improve the odds that a genetic algorithm could crack the 340?

It would, but it will only help if we have the correct assumption about how the 340 was constructed. I believe the evidence is very strong that the 340 isn’t a straightforward substitution cipher. So even if you have correctly guessed some of the symbol/plaintext assignments, the message would still be inscrutable without correctly identifying other steps the cipher author may have gone through to put the 340 together. But, if you are exploring candidate construction methods, you could still limit the search space by imposing the adjacency constraint.

Interesting find,

This might be of use here:

That’s interesting. I’m not sure what to make of it yet. It reminds me of another observation which is that the person who typed the confession letter started out putting two spaces between sentences. Then, around 1/3 to 1/2 through, he stopped doing it and reverted to one space between sentences.

This suggests some superficial knowledge of typing, IMO. Being old enough to have actually learned how to type on a typewriter, I can say two things. (1) Typists were taught to put two spaces between sentences. (2) If you learned in a formal environment and typed long enough, it became second nature. These two points in conjunction with the confession characteristics suggest to me that the person who typed the confession had some type of nontrivial exposure to typing, but did not type on a regular basis. He knew he was supposed to have two spaces between sentences; but once he got going, we was no longer paying strict attention to the semantics of typing and lost track of it.

If the QWERTY aspect of the encoding is correct, it would be an additional indication of exposure to typing.

That’s a remarkably perceptive observation. I’m too young to have familiarity with a typewriter, so I’d have never known. Because you clearly have firsthand knowledge of the history, I’d like to ask a couple questions. How common was it in the 60s/70s to have had formal lessons, so that you’d know of the two-space rule? Does it make certain occupations or past experiences vastly more likely than others? Does it indicate anything about his possible social class/status?

Doranchak — correct me if I’m wrong, but if we were to impose a "soft" adjacency constraint (of course, I don’t have all the logistics worked out, but I think you follow) on the key to the 340, wouldn’t that dramatically reduce the key space? And thus improve the odds that a genetic algorithm could crack the 340?

It would, but it will only help if we have the correct assumption about how the 340 was constructed. I believe the evidence is very strong that the 340 isn’t a straightforward substitution cipher. So even if you have correctly guessed some of the symbol/plaintext assignments, the message would still be inscrutable without correctly identifying other steps the cipher author may have gone through to put the 340 together. But, if you are exploring candidate construction methods, you could still limit the search space by imposing the adjacency constraint.

Makes sense to me. Just as an aside, while quantum computation’s still a way’s away, I’m aware that major players like IBM are in the midst of significant research in that area; because a functional quantum processors will (apparently) be able to break 256-bit encryption within moments, and because the key space of the 340 cipher is very nearly 2^256, do you think it’s realistic to expect that, if we don’t crack the cipher before then, a quantum computer will (within a couple decades) be able to exhaustively test all realistic keys (not just homophonic) to finally determine (a) the cipher’s message, or (b) that the cipher’s a hoax? Because, then, at least we’ll know.

It would be pretty damned incredible if they ever made a computer that could make such large spaces easy to explore exhaustively via brute force. Many problems that require heuristics or "reasonable, but not optimal, educated guesses" would be directly solvable. So I imagine some large subset of cryptographic problems would become trivial to solve.

As for the 340, it’d be hard to quantify exactly how many "key types" you’d have to generate, to account for all the possible ways it could have been constructed. The space is practically infinite. It may be more effective to train an algorithm to classify categories of unknown cipher texts. So basically you’d have a humongous pile of known cipher texts, where you know how they are all constructed. Then you’d train your algorithm (with some whiz-bang machine learning algorithm) to get it to learn to detect differences between the cipher texts so it can automatically put them in different categories. Then you’d turn it loose on some cipher texts it hasn’t been trained on, so you can see how well it responds to the unknown. If it does well, then maybe then it would have a decent chance to guess how the 340 was made.

Once you have a strong guess at how the 340 was made, you can apply the appropriate cryptanalysis to concentrate your attack.

Machine learning is a very promising area of research. Consider this recent research: https://newscenter.berkeley.edu/2015/05 … and-error/ At Berkeley they made a robot that learns through trial and error how to perform tedious tasks, instead of pre-programming it to do them. So, you could apply a similar approach to cryptanalysis: Build an algorithm that learns through trial and error how to automatically detect encipherment methods of different cipher texts.

In response to doranchak’s suggestion, I programmed a simple simulation.

Each run of the simulation randomly generates a key with a similar distribution to that of the 408 (i.e. ‘A’ must be represented by 3 other letters on the keyboard, ‘B’ must be represented by 1, ‘C’ must be represented by 1, ‘D’ must be represented by 1, ‘E” must be represented by 5, etc. Refer to the graphic in Jarlve’s post if you’re not clear on what I mean.).

Then, each run computes the average distance (on the QWERTY keyboard) from the plaintext character to its ciphertext equivalents. For example, in the 408, the V in the ciphertext represents B in the plaintext, so B is, on average, 1 unit of distance away from its ciphertext equivalent, V.

At the conclusion of N simulations, the program then computes the mean distance and its variance between each plaintext character and its ciphertext equivalent(s).

Here are the initial results for N = 10,000. I think the plot’s sufficiently descriptive of its content to omit further description here.

My interpretation: The plot shows that 8 of the 22 plaintext letters (A, E, I, N, O, P, R, and T) are closer than the simulation’s 95% confidence interval would predict. Should we consider that significant? I think so, but I’d like to hear from you.

In the interest of full disclosure, I wrote the program rather quickly, so it’s possible I’ve made an error somewhere. I’ll review the code further, and I plan to rewrite the program in another language when I’ve got a chance. But as of now, these initial results seem reasonable. If anyone wants me to upload the code, I’d be happy to upload the second (cleaner) draft at a later time.

I’d like to hear your thoughts.

Great work!

So at first glance it looks like random trials tend to NOT show the same "keyboard-adjacent" qualities in the letter/symbol assignments as the 408’s actual key.

It makes me wonder: Among all those trials, how many of them DID have roughly the same (or better) adjacency qualities as the 408’s key?

As the metric of success, I simply chose to count the number of plaintext letters which are highly keyboard-adjacent (to adopt your terminology); more specifically, I chose to count the number of plaintext letters with a mean distance outside and below the simulation’s 95% confidence interval. If we agree that that’s a reasonable metric, then if you look at the plot, it’s actually only possible for 11 of the 22 plaintext letters (A, B, E, F, I, N, O, P, R, S, and T) to fall outside and below the confidence interval, because the confidence intervals for all other letters include 0 (i.e. you can’t lie outside a confidence interval that includes 0, because you can’t get closer than 0 distance).

In the 408, as we’ve seen, 8 of those possible 11 letters do so; furthermore, letters B and F nearly exceed the confidence interval. In fact, the only letter that doesn’t come very close is the letter S.

While that’s not a quantitative answer, I think it’s a decent qualitative response to your question. If you’d like a quantitative answer, we’d have to develop a more quantitative measure of keyboard-adjacency; although I’m hesitant to conjure up a convoluted metric to do so. What do you think?

t makes me wonder: Among all those trials, how many of them DID have roughly the same (or better) adjacency qualities as the 408’s key?

If even just one of the "simulations" mirrors the 408’s keyboard adjacency, the usefulness of this discovery evaporates. Probably before then since the 408 contains many non-abecenarian symbols. That and there’s no reason to think the Zodiac used a typewriter, much less used one in the creation of his ciphers, which would make no sense.

t makes me wonder: Among all those trials, how many of them DID have roughly the same (or better) adjacency qualities as the 408’s key?

If even just one of the "simulations" mirrors the 408’s keyboard adjacency, the usefulness of this discovery evaporates. Probably before then since the 408 contains many non-abecenarian symbols. That and there’s no reason to think the Zodiac used a typewriter, much less used one in the creation of his ciphers, which would make no sense.

I suggest we hold most of our critical fire until they have actually done the computer runs. And if this type of placement happens only 1 out of 1, 000 runs by chance, that IS significant.

The thing is, as far as I can see, apart from a keyboard, I can think of no natural, spelling, English language or numeric relationship between say C-V, B-V, A-W, R-T, etc. Yet Zodiac relates those letters and they also coincide on a standard QWERTY typewriter keyboard! That is amazing and well worth the further careful study it is getting.

If even just one of the "simulations" mirrors the 408’s keyboard adjacency, the usefulness of this discovery evaporates. Probably before then since the 408 contains many non-abecenarian symbols. That and there’s no reason to think the Zodiac used a typewriter, much less used one in the creation of his ciphers, which would make no sense.

The value of the pattern isn’t dependent on its utility as a clue to the solution of the 340 or any other cipher. I’ve never, at any time, suggested that it was some remarkable key that’d unlock everything.

The value lies in the idea that if he did, in fact, apply this pattern, then it offers insight into his background and how he thinks. It, together with other small bits of evidence, might help further characterize the invisible man.

Furthermore, why would it make no sense? We are, each of us, reflections of our environments. We draw from them both intentionally and unintentionally.

I suggest we hold most of our critical fire until they have actually done the computer runs. And if this type of placement happens only 1 out of 1, 000 runs by chance, that IS significant.

The thing is, as far as I can see, apart from a keyboard, I can think of no natural, spelling, English language or numeric relationship between say C-V, B-V, A-W, R-T, etc. Yet Zodiac relates those letters and they also coincide on a standard QWERTY typewriter keyboard! That is amazing and well worth the further careful study it is getting.

There’s a 1/20 probability that any given plaintext letter has a mean distance below its associated confidence interval. As such, there’s a (1/20)^N chance that N letters have a mean distance below their confidence interval.

Therefore, unless I’m mistaken, the 408’s pattern seems to have odds somewhere around (1/20)^8, or 1 in 25,600,000,000 (rough estimate, but I believe the order of magnitude’s on point).

Not to get off topic here, but if the cipher does include some sort of clues based on the QWERTY keys, possible that Z had an interest or background in typewriters,maybe? Got me thinking, the confession letter writer in Riverside knew enough about typewriters to used many carbons in the letter to keep his typewriter from being identified. ‘If’ Z used the QWERTY, and if he was the same person that prepared the confession letter, maybe he has a background with typing??? Maybe had a typing class, typing instructor,etc? How readily avail was info that a typewriter could be traced?

morf13, that’s not off topic at all; that’s an interesting detail I hadn’t heard before now. If you look at AK Wilks’ initial post, zodiacrevisited also mentioned that the confession letter began with 2 spaces between sentences, which was indicative of familiarity with typewriters.

I’m also interested in the answers to the questions you pose.

Finder – Absolutely. I have no idea what the final numbers will show, just off the top of my head I was trying to say if something happens by chance 1 out of 1,000 times or 1 out of 10,000 times, if we see that pattern, it would be regarded as significant enough for further study. I suspect your idea of the numbers is correct, and if so, then this is truly significant.

My point to jroberson was just to suggest let us hold off on heavy criticism until you and doranchak have actually finished your study and present us with something to evaluate and criticize and/or praise and/or question.

At first glance IMO your discovery is quite amazing. It was right there staring us in the face from our computer keyboards yet you were the first person to think of it! I can think of no reason that letters like C & V, B & V. A & W, etc., should be linked. Yet it seems Zodiac linked them, and they are linked on a typewriter keyboard.

If the computer numbers study verifies that this would happen by chance only by incredibly small odds, which I think it will, orders of magnitude as you suggest, then this is definitely a major discovery IMO. It would indicate beyond any reasonable doubt that this was intentional by Zodiac.

As you note it may tell us something more about Z – maybe that he was more likely to be involved in a school, program, field of study, job or profession that used a typewriter. A student, a writer, a professor, a newsman, office worker, etc. Somebody who at least was exposed to typewriters in his education, job or profession. And conversely many types of jobs have little to no use of a typewriter – mechanic, truck driver, factory worker, soldier, sailor, etc. Though there are (fairly rare) exceptions like a factory worker who is also an amateur novelist. And as finder said it tells us something about the way Z thinks. Like hiding things in plain sight? Teasing clues? A facility for words, letters patterns, spaces & distances? What else?

But it also provides something much more important IMO, at least a potential clue as to an approach to the 340, MNI Code & Map Code. Certainly we would then look at the unsolved codes chiefly the 340 and see if a QWERTY analysis, perhaps with variations like going two spaces out, diagonal, etc., bears any fruit to helping solve any of the symbols, which so far nobody has done with anything like a consensus acceptance. It might also lead us to consider other similar methods Z could have used on the 340, such as getting ideas from the periodic table, Greek alphabet, Latin, letters to numbers, etc. If he used something like a keyboard to create not all but a substantial part of his 408 code, he might well have used something similar in the construction of the 340.

Thanks again for posting this information. Excellent work! And welcome to the board.