Pivots and repeating reversible trigrams

[smithy Profile]

Trav, those batwings are a hoot, thanks. It's more than 10 years since Ed first posted "Zynchronicity (noun): a term used to describe the various baffling yet bizarre coincidences, synchronicities and other assorted oddities that surround the infamous Zodiac case of the Bay Area in Northern California and its investigators...".

10 years eh?

Yes the pivots seem to be the focus of some interesting "events". They're central-ish I suppose, but hmmm.
D. - diagonals in the 340.....?

[doranchak Profile Website]

D. - diagonals in the 340.....?

I don't understand the question.

If it's "What the hell are you talking about?" then the answer is:

I did a search in the 408 to find patterns similar to what Trav found in the 340:



Turns out they are common in the 408.

[smithy Profile]

D. - diagonals in the 340.....?

I don't understand the question.
If it's "What the hell are you talking about?" then the answer is:
I did a search in the 408 to find patterns similar to what Trav found in the 340.....
Turns out they are common in the 408.

Sorry D., it was, it is, they are.
Doh!
I'm now wondering if I should be surprised at that.

[Wrench Profile]

I was thinking of looking at repeat ngrams diagonally, both this way / and this way \, last night, but then a good movie came on (A Shot in the Dark). That doable in CryptoCipherScope?

If nothing else, it would give us another comparison to the vertical and horizontal ngrams.

[doranchak Profile Website]

I was thinking of looking at repeat ngrams diagonally, both this way / and this way \, last night, but then a good movie came on (A Shot in the Dark). That doable in CryptoCipherScope?

If nothing else, it would give us another comparison to the vertical and horizontal ngrams.

"Repeated sequences (any direction)" does that, but only for n-grams where n is greater than 2. This is easy to change, though.

It also does not consider the types of diagonal repeats Trav found (I call them "n-grams with gaps").

[Wrench Profile]

I think I may have just answered my own question I was about to ask, but, never being afraid to be an ignoramus, I'll ask it anyway.

Always wondered what the value of these gap-grams (ggrams?) was, being that if you have A_B_C with different cihphertext in the blanks, many different words would fit these situations. However, I then realized that repeats of this type could be the same word, with different subs for the non matching characters. Right? Likely?

[doranchak Profile Website]

To me the gapped n-grams may reveal more about the internal structure as a whole (such as ciphertext orientation), rather than specifics about words that fit. This is because there are still too many possibilities on word boundaries within the repeated gapped n-grams to make a conclusion.

For example, if the repetition is AxByC (A, B and C are the fixed symbols while x and y can vary), and we represent word boundaries with "|", the possibilities are:

AxByC
A|xByC
Ax|ByC
AxB|yC
AxBy|C
A|x|ByC
A|xB|yC
A|xBy|C
A|xB|y|C
A|x|B|yC
A|x|By|C
A|xB|y|C
A|x|B|y|C

We could make a reasonable guess based on the distribution of such patterns by looking at a large corpus of text. For example, I'd expect that repeated patterns of the form "A|x|B|y|C" are quite rare because that's just too many one-letter words in one spot.

But, if many such gapped n-grams are repeated in a certain orientation of the cipher text, more so than for other orientations, then perhaps it is reasonable to conclude that that orientation is the correct one. Also, if a certain symbol tends to occur at the same distance from another symbol, then perhaps this says something about whether or not the symbol represents a single plaintext letter versus multiple plaintext letters. (For instance, what if the author cycles between plaintext letters for certain cipher symbols, to confuse decryption attempts? Similar to the A/S cycle for the filled triangle of the 408.)

[traveller1st Profile]

12 vs 7 on the 408 and 9 vs 4 on the 340. A difference of 5 in both cases...hmmm.

A 'hoot' Smithy? That's my very scientific research your talking about I'll have you know lol.

Ok I had a look at widening the gaps so if we take the first example as a gap of one the next ones are 2, 3, 4 and so on up to 7. I don't want to flood the thread with images so here's them all in one. Some had more hits than others and some gaps had no reverses.

0GAP - 5 to 4
1GAP - 9 to 4
2GAP - 7 to 4
3GAP - 4 to 2
4GAP - 4 to 4
5GAP - 0 to 2
6GAP - 2 to 1
7GAP - 5 to 1
8GAP - 0 to 3

Bear in mind these are only the bi-grams. Bear in mind I also have no idea what I'm doing except documenting simple patterns. It could all be a load of 'gnupung' for all I know.

gaps-1-to-7.jpg [ 216.13 KiB | Viewed 259 times ]

GAPS-comp.jpg [ 218.26 KiB | Viewed 225 times ]

EDIT: added GAPs 0 and 8 to list. Added comp image of those GAPs separated and with all GAPs shown and one showing just GAPs 0-3 inline with amount of matching GAPs in the pivots. There were no matches for GAPs 9 or 10. Ok so that just matching symbols on the diagonals. I'm off to show how the batwing explains why the taxi was parked the way it was

PS. If anyone wants readable versions of those let me know and I'll post them separately.

[Wrench Profile]

To me the gapped n-grams may reveal more about the internal structure as a whole (such as ciphertext orientation), rather than specifics about words that fit. This is because there are still too many possibilities on word boundaries within the repeated gapped n-grams to make a conclusion.

I'm with you, had considered that. Also, I suppose a repeat A_B_C could be a transposed ABC__.

"Repeated sequences (any direction)" does that, but only for n-grams where n is greater than 2. This is easy to change, though.

Let me know when you're done jaw-jakin' with AK and get to this.

Bear in mind I also have no idea what I'm doing except documenting simple patterns. It could all be a load of 'gnupung' for all I know.

It's all good. The cipher-wits haven't solved it yet, maybe it's up to us half-wits.

[Jazzerman Profile]

If you really want to get liberal with these pivot patterns there are a few more examples I can find in the 340 that seem rather odd. I don't think there is really much to say about these pivots for credibility, but there is definitely some symmetry here (whether or not it was intended is another question).

340coordi.JPG [ 80.75 KiB | Viewed 199 times ]

Notice that 3 places from the center pivot (marked with the red dot) the symbols are reversed in each example and then branch out into two symmetrical symbols thereafter that are consistent with each other. I don't put much credence into this, and I'm now thinking these pivot patterns might just be common in cryptography...as they seem to occur with some degree of frequency within both the 340 and the 408. Make of it what you will...