Things I noticed about Z340

Re: Things I noticed about Z340

Postby daikon » Wed Aug 05, 2015 2:24 pm

Hmm, something else I just noticed that might fit the theory of odd symbols being nulls.
Looking at Z13 cipher:
z13-small.PNG

If we split it into odds and evens, we end up with,
Evens: ImageImageImageImageImageImage
Odds: ImageImageImageImageImageImageImage

Notice that the newly introduced, never before seen, 8-in-a-circle symbol falls entirely into odds. Also, odds have a lot of repeats, while evens don't have a single repeating symbol. If we follow the theory that odds=nulls, then this cipher could very well solve to simply: "ZODIAC" (notice no repeating letters). As in: "My name is ZODIAC".

One small kink. Technically, this symbol is also new:
z13-symbol.PNG

But it can be argued that it was supposed to be the same as Image, but Z's hand slipped. Or even Image, but Z forgot to add the line at the top.

It could also be completely coincidental, of course, as Z13 is just too short. :)


Let's also look at Z32 cipher (map code), while we are at it:
z32-small.png

Evens: ImageImageImageImageImageImageImageImageImageImageImageImageImageImageImageImage
Odds: ImageImageImageImageImageImageImageImageImageImageImageImageImageImageImageImage

Once again, the new, never before seen, symbol "omega" falls into odds (i.e. random filler, nulls). Otherwise I can't really make any other meaningful observations. Well, maybe that the odds seem to spell out "GOD THE (zodiac symbol)" towards the end (signature of sorts?). Since the odds are supposed to be random filler, I can sort of see Z having some fun with it, spelling out stuff to confuse decryptors.

P.S. I so wish Webtoy would use consistent ASCII mapping across all Z ciphers! I nearly missed the fact that the same letters in Z13/Z32/Z340 map to entirely different symbols in each cipher. For example, 8 in Z13 is not the same symbol as 8 in Z340. Which is why I'm using actual pictograms in this post, and not ASCII, to avoid any confusion.
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Re: Things I noticed about Z340

Postby smokie treats » Thu Sep 10, 2015 7:28 pm

daikon wrote:Here's a few things I noticed about Z340 when doing different experiments with it. Things that stand out, but didn't lead to any breakthroughs (obviously). I thought I'd share my observations just in case someone else can make some further conclusions, or it might help lead to the solution in some other way.

Splitting Z340 into odd and even symbols (i.e. only symbols at odd or even positions) produces 2 very different sequences:
Odd symbols
Even symbols

Statistically they should be very similar, as English language has absolutely no preference towards odd/even letters that I know of, or odd/even lengths of words, etc. And yet...

Odd symbols:
Very low number of bigram repeats (only 2!).
No trigram repeats, or higher N-grams.
58 unique symbols, so 5 symbols are missing: & 1 @ A t.

Even symbols:
Good number of bigram repeats (9). About the expected for the cipher this length — Z408 had 10 bigram repeats in the first 170 symbols.
2 trigram repeats. Again, about expected — Z408 also had 2 trigram repeats in the first 170 symbols. These 2 trigram repeats are not overlapping with the 2 trigram repeats in the full Z340 in any way, so they were created anew.
54 unique symbols, so 9 symbols are missing: 3 7 ; J M U X b j.

The 14 symbols that are not shared is especially significant, I think. That's 22% our of 63 symbols. I don't think it can happen by chance. For comparison, I've split Z408 the same way, and there is only 1 symbol that's present in odds and not in evens.

Symbol counts (frequencies) do not match at all either. For example, the 3rd most frequent symbol for "odds" ('M') is completely missing in "evens". 2nd most frequent symbol for "evens" ('2') only appears twice in "odds". The only exception is '+', which is the top symbol for both, but most of '+'s went into "evens": 14 vs 10 for "odds".

What could this possibly mean? The obvious conclusion — the odd symbols are just random noise, filler inserted to confuse decryptors, they are nulls that should be dropped. However, the odds sequence does have a fairly expected frequency distribution, so it might be part of the message, just encrypted differently from the evens sequence.

I tried feeding each of the 2 sequences into an auto-solver, but didn't get a coherent solution. The issue might be the very high multiplicity, so it could be that we have the correct extra transposition that Z did to Z340, but the resulting 170 symbol cipher is too short to be cracked. I've tried combining the 2 sequences, by appending one to another, and then the other way around, but didn't get a solve either way. Maybe they should be recombined in some other way?

Another issue with this (and I'm playing devil's advocate now :)), is that Z clearly liked to use a matrix with 17 characters in a row. It's an odd number, so odd/even positions alternate (or flip around) for every other row. I'll demonstrate with a matrix of width 7, and use 0 for odd positions and 1 for even positions:
0101010
1010101
0101010
1010101

So if he did use odds/evens split, it would make more sense, and would be easier to do with a pen and paper, if done per row. I.e. restart odd/even counts for each new row. I've tried decomposing Z340 this way, but ended up with 2 unremarkable sequences, of slightly different lengths, but with very similar stats. On the other hand, maybe Z realized that doing odds/evens across the whole cipher would result in a "checkerboard pattern" I showed above, and maybe he thought that it would be more confusing and harder to crack, and went with it.


I spent a few minutes making my cycle spreadsheet so that conditional formatting shows whether a symbol is odd or even. Then I looked at the top scoring cycles on the 340 to see if any of the 34 highest scoring cycles (score 256 or more) are exclusively odd - even - odd - even, etc., or exclusively odd or exclusively even.

There are nine symbols unique to the odds:

37, 38, 41, 43, 45, 49, 58, 59, and 61.

38 is an even numbered symbol, but first appears at position 41 and 58 is an even numbered symbol but first appears at position 109.

There are five symbols unique to the evens:

12, 48, 52, 60 and 62.

37 cycles with 41 in the top thirty four cycles, and 38 cycles with 41 in the top thirty four cycles. EDIT: There are 1953 total cycles. Twenty three cycles score in the 256 range. When I randomize the 340, I get an average of 6.1 such cycles. The 37 - 41 cycle has the familiar repetition of the last symbol toward the end.

37 41 37 41 37 41 37 41 37 37 37
38 41 38 41 38 41 38 41 38

It could just be a coincidence and those are the only patterns that I can find. There is no high scoring cycle that is odd - even - odd - even, etc. I am going to try to conditional format for 3 parts and 4 parts and look for patterns there too.

EDIT: I checked the top 34 two symbol cycles for cycled 3 keys, 4 keys and 5 keys. My findings are that there are no other high scoring cycles that are all in the same parts or cycle with the parts. In other words, there is no other cycle that occurs on only one part, or Part 1, then Part 2, then Part 3, then Part 1 again, etc.

See: viewtopic.php?f=81&t=2617&start=210
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Re: Things I noticed about Z340

Postby Jarlve » Sun Nov 12, 2017 5:03 am

daikon wrote:Odd symbols:
Very low number of bigram repeats (only 2!).
No trigram repeats, or higher N-grams.
58 unique symbols, so 5 symbols are missing: & 1 @ A t.

Even symbols:
Good number of bigram repeats (9). About the expected for the cipher this length — Z408 had 10 bigram repeats in the first 170 symbols.
2 trigram repeats. Again, about expected — Z408 also had 2 trigram repeats in the first 170 symbols. These 2 trigram repeats are not overlapping with the 2 trigram repeats in the full Z340 in any way, so they were created anew.
54 unique symbols, so 9 symbols are missing: 3 7 ; J M U X b j.

The 14 symbols that are not shared is especially significant, I think. That's 22% our of 63 symbols. I don't think it can happen by chance. For comparison, I've split Z408 the same way, and there is only 1 symbol that's present in odds and not in evens.

Symbol counts (frequencies) do not match at all either. For example, the 3rd most frequent symbol for "odds" ('M') is completely missing in "evens". 2nd most frequent symbol for "evens" ('2') only appears twice in "odds". The only exception is '+', which is the top symbol for both, but most of '+'s went into "evens": 14 vs 10 for "odds".

What could this possibly mean? The obvious conclusion — the odd symbols are just random noise, filler inserted to confuse decryptors, they are nulls that should be dropped. However, the odds sequence does have a fairly expected frequency distribution, so it might be part of the message, just encrypted differently from the evens sequence.

Sorry to necro this old thread but I am looking more deeply into unigrams unique/exclusive to other periods in function of the unigram distance anomaly in a broad sense.

Looking at odd/even (2 columns) there are 31 unigrams unique to the first column and 12 unigrams unique to the second column for a total of 43. Versus randomizations of the 340 it is a 1.92 sigma observation and verus plaintext + encodings with cycle randomization to match the 340 it is a 2.03 sigma observation. It appears not to be a property of sequential homophonic substitution and it being a 2 sigma observation makes it at least a little bit curious.

Looking at 3 columns there are 6 unigrams unique to the first column, 9 unigrams unique to the second column and 5 unigrams unique to the third column for a total of 20. Versus randomizations of the 340 it is a 1.61 sigma observation and verus plaintext + encodings with cycle randomization to match the 340 it is a 1.02 sigma observation. With 3 columns there is a positive correlation with sequential homophonic substitution.

Looking at 6 columns ... (2, 5, 3, 2, 0, 2) for a total of 14. Versus randomizations of the 340 it is a 3.35 sigma observation and verus plaintext + encodings with cycle randomization to match the 340 it is a 1.51 sigma observation. With 6 columns there is a positive correlation with sequential homophonic substitution.

I have tested only the column sizes that appeared interesting. For column sizes larger than 2 it appears to be a property of sequential homophonic substitution.

Code: Select all
AZdecrypt periodic unique unigrams stats for: 340.txt
--------------------------------------------------------
Period 1:
- Row/column 1: 340, 340 (100%)
Period 2:
- Row/column 1: 5, 31
- Row/column 2: 0, 12 (11.62%)
Period 3:
- Row/column 1: 2, 6
- Row/column 2: 1, 9
- Row/column 3: 0, 5 (15%)
Period 4:
- Row/column 1: 0, 2
- Row/column 2: 1, 3
- Row/column 3: 0, 0
- Row/column 4: 0, 0 (20%)
Period 5:
- Row/column 1: 0, 0
- Row/column 2: 3, 2
- Row/column 3: 0, 0
- Row/column 4: 0, 8
- Row/column 5: 0, 2 (25%)
Period 6:
- Row/column 1: 0, 2
- Row/column 2: 0, 5
- Row/column 3: 1, 3
- Row/column 4: 0, 2
- Row/column 5: 0, 0
- Row/column 6: 0, 2 (7.14%)
Period 7:
- Row/column 1: 0, 1
- Row/column 2: 0, 0
- Row/column 3: 1, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 0
- Row/column 7: 0, 0 (100%)
Period 8:
- Row/column 1: 0, 2
- Row/column 2: 0, 2
- Row/column 3: 0, 0
- Row/column 4: 1, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 1
- Row/column 7: 0, 0
- Row/column 8: 0, 0 (20%)
Period 9:
- Row/column 1: 0, 2
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 1, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 0
- Row/column 7: 0, 2
- Row/column 8: 0, 1
- Row/column 9: 0, 0 (20%)
Period 10:
- Row/column 1: 0, 0
- Row/column 2: 0, 2
- Row/column 3: 0, 0
- Row/column 4: 1, 1
- Row/column 5: 0, 2
- Row/column 6: 0, 0
- Row/column 7: 0, 0
- Row/column 8: 0, 0
- Row/column 9: 0, 3
- Row/column 10: 0, 0 (12.5%)
Period 11:
- Row/column 1: 0, 0
- Row/column 2: 0, 1
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 1, 0
- Row/column 6: 0, 2
- Row/column 7: 0, 0
- Row/column 8: 0, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0 (33.33%)
Period 12:
- Row/column 1: 0, 0
- Row/column 2: 0, 1
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 1, 0
- Row/column 6: 0, 0
- Row/column 7: 0, 0
- Row/column 8: 0, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 2
- Row/column 11: 0, 0
- Row/column 12: 0, 0 (33.33%)
Period 13:
- Row/column 1: 0, 0
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 1
- Row/column 5: 0, 0
- Row/column 6: 1, 0
- Row/column 7: 0, 0
- Row/column 8: 0, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0 (100%)
Period 14:
- Row/column 1: 0, 0
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 1, 0
- Row/column 7: 0, 0
- Row/column 8: 0, 1
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 0 (100%)
Period 15:
- Row/column 1: 0, 0
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 1, 0
- Row/column 7: 0, 2
- Row/column 8: 0, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 1
- Row/column 15: 0, 0 (33.33%)
Period 16:
- Row/column 1: 0, 2
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 1
- Row/column 7: 1, 0
- Row/column 8: 0, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 0
- Row/column 15: 0, 0
- Row/column 16: 0, 0 (33.33%)
Period 17:
- Row/column 1: 0, 0
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 0
- Row/column 7: 1, 0
- Row/column 8: 0, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 0
- Row/column 15: 0, 1
- Row/column 16: 0, 0
- Row/column 17: 0, 0 (100%)
Period 18:
- Row/column 1: 0, 0
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 0
- Row/column 7: 0, 2
- Row/column 8: 1, 1
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 0
- Row/column 15: 0, 0
- Row/column 16: 0, 0
- Row/column 17: 0, 0
- Row/column 18: 0, 0 (33.33%)
Period 19:
- Row/column 1: 0, 1
- Row/column 2: 0, 0
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 0
- Row/column 7: 0, 0
- Row/column 8: 1, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 0
- Row/column 15: 0, 0
- Row/column 16: 0, 0
- Row/column 17: 0, 0
- Row/column 18: 0, 0
- Row/column 19: 0, 0 (100%)
Period 20:
- Row/column 1: 0, 0
- Row/column 2: 0, 2
- Row/column 3: 0, 0
- Row/column 4: 0, 0
- Row/column 5: 0, 0
- Row/column 6: 0, 0
- Row/column 7: 0, 0
- Row/column 8: 1, 0
- Row/column 9: 0, 0
- Row/column 10: 0, 0
- Row/column 11: 0, 0
- Row/column 12: 0, 0
- Row/column 13: 0, 0
- Row/column 14: 0, 1
- Row/column 15: 0, 0
- Row/column 16: 0, 0
- Row/column 17: 0, 0
- Row/column 18: 0, 0
- Row/column 19: 0, 0
- Row/column 20: 0, 0 (33.33%)
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Re: Things I noticed about Z340

Postby doranchak » Sun Nov 12, 2017 5:48 am

Interesting observations, Jarlve. I also re-read this thread and updated http://zodiackillerciphers.com/wiki/ind ... servations. There are so many observations to keep up with. I'm wondering if there is a better way to keep it all organized. For example, I have a separate extensive spreadsheet that tracks all of my "features or phantoms" experiments, which compare observations to randomizations.

I still want to drive towards comparing all of these unusual observations to a wide assortment of classical cipher schemes.

Also, Jarlve, why do you think column period greater than 2 shows unigram biases that reflect sequential homophonic substitution? Why would specific symbols still tend to fall in specific columns (versus more random placement)? I can't think of why certain high frequency letters would align with specific columns.
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Re: Things I noticed about Z340

Postby Jarlve » Sun Nov 12, 2017 7:05 am

doranchak wrote:Interesting observations, Jarlve. I also re-read this thread and updated http://zodiackillerciphers.com/wiki/ind ... servations. There are so many observations to keep up with. I'm wondering if there is a better way to keep it all organized. For example, I have a separate extensive spreadsheet that tracks all of my "features or phantoms" experiments, which compare observations to randomizations.

Thanks to mention the update. You could create a document "observation sigmas" that lists a description of the observation and test, the observer and sigma.

doranchak wrote:I still want to drive towards comparing all of these unusual observations to a wide assortment of classical cipher schemes.

I think we are slowly getting there anyway.

doranchak wrote:Also, Jarlve, why do you think column period greater than 2 shows unigram biases that reflect sequential homophonic substitution? Why would specific symbols still tend to fall in specific columns (versus more random placement)? I can't think of why certain high frequency letters would align with specific columns.

It must have to do with the sequential property of the ciphertext.

Example cycle:

Code: Select all
ABCDEABCDEABCDEABCDEABCDE

Example cycle by 5 columns:

Code: Select all
ABCDE
ABCDE
ABCDE
ABCDE
ABCDE

Sensible?
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Re: Things I noticed about Z340

Postby doranchak » Sun Nov 12, 2017 7:09 am

Jarlve wrote:It must have to do with the sequential property of the ciphertext.

Example cycle:

Code: Select all
ABCDEABCDEABCDEABCDEABCDE

Example cycle by 5 columns:

Code: Select all
ABCDE
ABCDE
ABCDE
ABCDE
ABCDE

Sensible?


Right, but why would they prefer certain columns? For example, there are other symbols occurring somewhat randomly between A and B, then between B and C, etc.

For instance, here are all the Z408 symbols that stand for plaintext E:

Image

There are 5 strong cycles of the 7-symbol pattern. Are the individual symbols lining up with columns more than expected?
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Re: Things I noticed about Z340

Postby Jarlve » Sun Nov 12, 2017 7:55 am

doranchak wrote:Right, but why would they prefer certain columns? For example, there are other symbols occurring somewhat randomly between A and B, then between B and C, etc.

Why? Because repeats are pushed out of the rows into the columns and the other symbols that may occur between A and B and so forth do not entirely destroy/randomize this property. Cycles also happen to be multiplicative, that is why measurement systems like smokie's way of measuring all the symbol cycles work so well.

Code: Select all
ABCDE
ABCDE
ABCDE
ABCDE
ABCDE
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Re: Things I noticed about Z340

Postby doranchak » Sun Nov 12, 2017 7:59 am

Ah, yes - I can see it being a relative effect, i.e. when compared to row-level repeats.
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Re: Things I noticed about Z340

Postby doranchak » Sun Nov 12, 2017 4:39 pm

daikon wrote:P.S. I so wish Webtoy would use consistent ASCII mapping across all Z ciphers! I nearly missed the fact that the same letters in Z13/Z32/Z340 map to entirely different symbols in each cipher. For example, 8 in Z13 is not the same symbol as 8 in Z340. Which is why I'm using actual pictograms in this post, and not ASCII, to avoid any confusion.

I finally corrected that particular annoyance. I've updated the transcriptions of Z13 and Z32 on the wiki as well as in CryptoScope.
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