View topic - Omnidirectional repetitions

I was intrigued by Smithy's observation of the "H-N-reverse P" or "H-N-9" sequence in the last row of the 340, which repeats in the upper left corner in an L-shaped configuration. The question is: Did the cipher author intentionally copy this sequence as filler to the last row, much as the last 18 symbols of the 408 appear to be filler copied from symbols that appear above it? Or, is there any other kind of intent we can infer from these kinds of patterns? Perhaps their appearances are clues into the construction of the cipher text.

So I wrote an algorithm that does an exhaustive search for such sequences. It is basically a search for repeated n-grams, where the n-grams are allowed to follow paths that can go in multiple directions, even wrapping beyond block boundaries. The result is that these kinds of sequences seem to occur on their own fairly often.

Here are the full results for the 408: http://imgur.com/a/meqG8 (39 repeated patterns)

Some interesting ones:



And here are the full results for the 340: http://imgur.com/a/Fi8nN (48 repeated patterns)

Some interesting ones:



The repetition of "-*|" is particularly appealing because of its resemblance to box corners.

I think the reason there are more overall repetitions of this sort in the 340 than the 408 is because of how often the "+" symbol appears, so it is easier for it to get randomly involved in these sequences. There are also several small variations for some of the matches.

The above results only show matches where the sequence is repeated by following horizontal and vertical directions only. The algorithm, however, also supports diagonal directions, where you are allowed to go from one position directly diagonally to a neighboring position. But the resulting matching sequences are a meaningless mess, since there are more degrees of freedom in finding matching symbols in multiple directions.

Example: Repetitions of the sequence ")eNMVB9#9Afcq_9%7\" in the 408:



and "+(cMBpp<7cBOF+O" in the 340:



My feeling is that we can't really derive any intent from these patterns, since they occur so often in both cipher texts. What do you think?

I had noticed the 'meaningless mess' ones when I was looking at diagonal patterns. M+Z in relation to each other clustered over at the left hand side of the top half.

I like the 3 symbol ones - kinda like mini-pivots. I dunno, is it just more likely patterns or does it hint at something in the construction that reached critical mass with the 2 largest pivots that we're familiar with?

EDIT: "No brain, no cry" sung to the tune of a popular Bob Marley song.

doranchak wrote:I was intrigued by Smithy's observation of the "H-N-reverse P" or "H-N-9" sequence in the last row of the 340, which repeats in the upper left corner in an L-shaped configuration..... Did the cipher author intentionally copy this sequence as filler to the last row.....?

Thanks D. - that otherwise seems to have been an observation greeted with complete apathy!

So I wrote an algorithm that does an exhaustive search for such sequences....

Where would we be without you?

I think the reason there are more overall repetitions of this sort in the 340 than the 408 is because of how often the "+" symbol appears, so it is easier for it to get randomly involved in these sequences.

Yes - that must be the case. Intuitively, I'd expected fewer, since it's a smaller space with more substitutes. What particularly pleases me are the 408 "qEHM" reps, which rather put me in mind of the 340 "pivots". Good! Seems like they please Trav too eh? Double good!

The above results only show matches where the sequence is repeated by following horizontal and vertical directions only. The algorithm, however, also supports diagonal directions.....

Those are an absolute hoot. I can really think of no valid use for them at this time - except that perhaps there might be some way to use them to confirm text direction or some transposition somehow (?) - but they're a hoot alright.

My feeling is that we can't really derive any intent from these patterns, since they occur so often in both cipher texts. What do you think?

Intent, no. Usefulness though? Yes, even if I for one can't think of what that might be right now.
Once again thanks very much for providing thought-provoking material. Just great.

Doranchak:

MU^R=HING P#BI= ILLT El@X= EASO 6qEHM= EMETH

Looks like it's occuring in the 408 mostly from common n-grams (such as 'ill', 'ea', 'so', etc), and ngrams that are built from letters we'd expect to be high frequency (EITLOA is the top 6 from 408). So I would suggest this means it's not necessarily intentional... but it may serve as a tool to identify ciphertext symbols that represent higher frequency letters in the 340.

Adam

Good observation; thanks!

Doranchak, has this pattern been noticed already in the 408? Alternating the A,S after the solve really cleans up a lot of the spelling mistakes in the 408.



I am guessing someone has already posted this somewhere, so that's why I am hiding in it your thread :)

Potentially, he could have applied this type of approach to every symbol in the 340 to make it "harder".

Adam

Yes, the sequence has been noted before, most recently by Nick:

http://www.ciphermysteries.com/2011/10/18/this-weeks-zodiac-killer-cipher-thoughts

http://www.ciphermysteries.com/2011/09/13/thoughts-on-the-zodiac-killer-z408-and-z340-ciphers

Applying this sort of duality to each symbol would indeed make decryption attempts of the 340 more difficult. I wonder if a flavor of zkdecrypto that permits such dualities would result in successful decryption of test ciphers.

If the A/S cycle was intentional, why did he limit it to one symbol of the 408? And perhaps the rapid solution of the 408 may have encouraged him to apply such cycles to more symbols.

More questions than answers. :)

Doranchak:

Great, thanks! we'll save those questions for another thread...

This algorithm you designed seems like it would be invaluable for transposition ciphers.

doranchak wrote:Yes, the sequence has been noted before, most recently by Nick:
http://www.ciphermysteries.com/2011/09/13/thoughts-on-the-zodiac-killer-z408-and-z340-ciphers

Haven't seen that, and hadn't realised that those "poly's" were a "duality" before. Didn't get the memo.
Wow.
Is it entirely intentional do you think? Because if so, when would that have been done? During the first pass at encoding, or...?
Hmmm.
Later, when the cipher was written out, as an "extra"...?
That would be difficult.
I'm looking hard at that "s" in "stop".

Lots more questions.
Re:

ALisowsky wrote:Doranchak:

MU^R=HING P#BI= ILLT El@X= EASO 6qEHM= EMETH

Looks like it's occuring in the 408 mostly from common n-grams (such as 'ill', 'ea', 'so', etc), and ngrams that are built from letters we'd expect to be high frequency (EITLOA is the top 6 from 408). So I would suggest this means it's not necessarily intentional... but it may serve as a tool to identify ciphertext symbols that represent higher frequency letters in the 340.

Adam

Well yes, maybe, accent on the "may"!
This is why our harking back to the 408 can sometimes be a nuisance, as I occasionally opine. As ever, it depends on the 340 plain text, and the number of substitutions against the "most common" letters within that plain text...
Still, you all have that in mind I know. Sorry.

Ok,

Hope this qualifies for this thread. One thing that struck me looking at this previously with other patterns was the symbol R appearing quite frequently near the + symbol so I decided to have a look with this omni repeat thing in mind. I've tried to keep it simple by using 3 symbol combinations although I have left one bi-repeat in as it pertains to the R and + relationship.

I started with R and + then noticed other combinations adjacent and another that I had previously considered a 2 symbol combination became a 3 symbol combination - that would be the CROSSHAIR and the + as there was always a + adjacent to a CROSSHAIR with only one exception. The R,+ naturally became R,+,+

So the green represents the R,+,+ combo and also the R,+
Yellow represents the start point of CROSSHAIR, R, +
Red represents K, H/CIRCLE,J but could be extended to R,+,CROSSHAIR
Blue represents F/TRIANGLE,R,+

The point of note I suppose is those two large cluster in the top half that have so many of the combinations in each of them. I tried to avoid diagonals as this would bring in many more combination and just be a mess but I couldn't help myself on the left hand cluster as it was so close in regards the CROSSHAIR, R, + combination and the R,+,+ in that one.

As usual no idea what it could mean if anything.