Finder's Theory on QWERTY keyboard and Zodiac 408

[Jarlve]

If anyone is interested, I drew up a new key for the 408 that Includes what I think are the correct cycle positions for each symbol and which is organized by a standard keyboard layout.

Thanks, very handy!

[Teg>Ean]

I'm telling you, there's something going on here. This cannot be my imagination.

Orientation relationships in the 408 key 4.png

There is something systemic about how he makes the symbol assignments. I don't think this was a table with substitutions. Maybe it was more like some kind of matrix

Has anyone ever seen something that looks like this?

what is this.png

[Teg>Ean]

I don't know what to make of this, but, without reading too much into it, it's just weird.

If we give some leeway for reflections and dots in the symbol assignments, it seems like "E" ends up substituting to the four corners of the keyboard and snuggling up to the weirdo letters [M, Q, X, O]

z408 ZPW and MQ 1.png

Also, the first substitution for "N" is [O], which is weird since [dotO-N-E] concludes the substitution sequence for "E."

I don't know exactly where I'm going with this. It could be the result of sampling too many letters and their substitutions, or over-analyzing similarities in the symbols. I just find it so utterly bizarre that the statistical outliers in Finder's graph seem so bunched up in the four corners, particularly since "E" also seems to be doing that. Particularly odd since "everything comes back to 'E'." Did I mention I find this weird?

EDIT: Also, I know this graph was updated later but the statistical outliers were still the same. This seems like a really hard connection to map statistically, too. As has been pointed out, special characters didn't have a consistent location on old school QWERTY keyboards. There's a ton of ambiguity when you throw reflected or rotated symbols into the mix because so many letters are vertically and/or horizontally symmetrical. What does a backwards [X] look like, anyways?

[Teg>Ean]

There might be one more thing to consider here.

I didn't realize that the history of keyboard layouts was such a controversial subject mired in folklore, but the impression I get is that QWERTY and the like are optimized for bigrams in English (and similar Latin Script). In other words, QWERTY is full of n-grams, and I'm just wondering if this is such a straightforward observation because I imagine you could get similar distributions by taking all the vowels in English and putting them on either side of all the consonants in English, measure the mean distance and get a similar deviation from randomly generated keys. That's basically what QWERTY is after all.

That's not to say that an actual keyboard layout is unrelated to the construction of the 408 key, but maybe there's a risk of confirmation bias here (If you've read my posts, you probably know I am consistently guilty of this exact thing)

[Jarlve]

Particularly odd since "everything comes back to 'E'." Did I mention I find this weird?

This is marie's or margie's observation right? I've been wanting to look into this sometime.

That's not to say that an actual keyboard layout is unrelated to the construction of the 408 key, but maybe there's a risk of confirmation bias here.

I think it is simple what to do here, we need to statistically test if the keyboard observation has any significance.

[Jarlve]

I think it is simple what to do here, we need to statistically test if the keyboard observation has any significance.

My memory is failing me, it seems this was already done by _pi:

Here are the corrected values by keyboard layout. The error I initially made in the post I deleted was to compare, for example, a random key applied to the azerty layout with the z408 key applied to the qwerty layout, as opposed to comparing it to the z408 key applied to the azerty layout.

I generated 10 million random keys to compare them to the z408 key on how many directly adjacent letter symbols can be found, per keyboard layout.

qwerty: 1.3% of random keys exhibit an equal or higher adjacency than the z408 key (as seen in previous posts)
azerty: 6.48% of random keys exhibit an equal or higher adjacency than the z408 key
qwertz: 7.37% of random keys exhibit an equal or higher adjacency than the z408 key
Dvorak: 14.25% of random keys exhibit an equal or higher adjacency than the z408 key

The z408 key exhibits a higher affinity with the qwerty keyboard than with the others, in terms of number of symbol letters being directly adjacent to their plaintext letter.

[Jarlve]

And also this:

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.

QWERTY 408 Simulation.jpg

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.

[Finder]

Hi guys! It’s been a while since I’ve logged on! I was blown away by the news about the 340. Congratulations to all of you who’ve worked so hard on this! What an incredible, incredible achievement. I’m so happy for all of you.

I’ve just taken a look at the 340 key alongside the QWERTY keyboard, and we can immediately notice some parallels between the keyboard layout and the 340 key. Here are my observations:

Reversed L and O and K decode to A. L, O, and K are right next to each other on the keyboard.
S and A decode to D, which is next to S and A on the keyboard.
B and N, which are adjacent on the keyboard, decode to E.
Reversed K decodes to I, which is next to K on the keyboard. H and reversed Y decode to I, and H and Y are adjacent on the keyboard.
E and T decode to R, which is next to E and T on the keyboard.
U and J, which are adjacent on the keyboard, decode to S.
G decodes to T, which is next to T on the keyboard.
C and X, which are next to each other on the keyboard, decode to Y.

I’m not sure that these observations are statistically significant, but I was drawn to make the comparison once I’d heard the 340 had been cracked. Maybe I’ll write another program to test the likelihood of the observations.

Once more: congratulations, congratulations, congratulations!