I noticed something unusual, the green line (340 mirrored) often extends further than the red line, this may suggest that there are longer cycles to be found in that direction! Notice also at times a sharp drop for the red line, the wildcards are actually causing this.

The number of repeating ngrams also peaks in that direction: http://zodiackillerciphers.com/wiki/ind … tion_rates For the flipped (mirrored) 340, not only is the total number of ngrams at a maximum, but the size of the set of unique repeating ngrams also peaks.

I did a simple repeating fragment test which also showed a bias towards the mirrored 340: http://zodiackillerciphers.com/wiki/ind … e_analysis

So, it’s interesting that multiple measurements are producing peaks with the mirrored 340.

We have at least two simple ways to make more ngrams appear: 1) flip the 340 horizontally; 2) apply the period-3 transposition to re-order the columns. Are there others?

We have at least two simple ways to make more ngrams appear: 1) flip the 340 horizontally;

You mean mirror it? Hmm, interesting. I did the same to 1st half and 2nd half separately, and mirroring the 1st half alone *reduces* bigram repeats. Has no effect on 2nd half, as it still has a single bigram repeat (‘++’). This means that the newly formed bigrams from mirroring the whole Z340 are between 1st and 2nd halves. Not sure what that means exactly. Could be just a coincidence. Or maybe the first and last columns that are involved in forming these new bigram repeats are special in some way?

Are there others?

Here’s another one. 🙂

The problem with Z340 is that its bigram repeats are so low to begin with, it’s not that hard to come up with a way to rearrange the letters to increase the repeats. I’ve ran a test that did all possible symbol-wise transpositions of the width 9 (i.e. all groups of 9 symbols were rearranged/shuffled the same way). There are 362,880 possible ways. For Z340, nearly 5% of the transpositions increased its bigram repeats. For Z480, *none* of them increased the bigram repeats. Using width 9 transpositions alone, there are 581 distinct ways of increasing Z340’s bigram repeats by at least 30%.

From another end of the spectrum, for a random string of letters encrypted with 63 homophones with perfect cycles, out of all possible width 9 transpositions, full 48% increase the bigram repeats. Yet another metric that shows that Z340 doesn’t behave like a random text at all. It is just slightly more random than Z408.

Or maybe the first and last columns that are involved in forming these new bigram repeats are special in some way?

Another thing that makes the first and last columns special is the possible "fold line" appearing on row 10 as hyphens in those columns.

Another thing that makes the first and last columns special is the possible "fold line" appearing on row 10 as hyphens in those columns.

I always thought that the "fold line" theory was a bit unlikely. It doesn’t divide Z340 into equal halves — there are 9 rows above, and 10 below. The ‘-‘ symbol, while indeed new (it wasn’t present in Z408, as far as I can tell), is not exclusively used to signify the "fold line" — it is present a few more times throughout the rest of the cipher. How likely is it to happen by chance? There are 5 ‘-‘s present in 340 symbols. Which means it has the probability of 5/340=0.0147. The probability of 2 ‘-‘ appearing both at the beginning and the end of a row is the same as 2 of them appearing next to each other, and you just need to multiple the probability by itself (square it): 0.0147*0.0147 = 2.162e-4. Which means it will happen by pure chance about every 4,624 symbols. Or roughly in every 13th 340-symbol cipher (i.e. 1 in 13 chance for 340-symbol long sequences). Not at all improbable.

Here are my cycle score reports for M1_P1. I only copy and pasted the number grid into my spreadsheet and didn’t look at anything else, so I hope that I didn’t goof. I made some changes to my horizontal cycle hillclimber to make it more efficient, and it doesn’t work as well, so that is a work in progress. In any case, I tallied up the strings of consecutive alternations. And I randomized both the 340 and M1 ten times, and also included data from half of a randomized 340 and M1 for comparison.

Some of this stuff is a bit redundant, but included for thoroughness.

1. Compare A and B. Yes, Zodiac used cycles. Compare F and G. M1 has cycles. Compare B and G. Compare B and G. M1 is much more cyclic than Z340.

2. Compare C, D and E. The top half of the 340 is somewhat more cyclic than the bottom half. The bottom half is closer to how cyclic half of the 340 would be if randomized.

3. Compare H, I and J. The top half of M1 is much more cyclic than the bottom half. The bottom half is similar to what half of M1 would be if randomized.

4. Compare A and B and Compare F and G as you scroll down the rows. The general pattern is that a randomized message is going to have fewer long cycles and more short cycles, and the message is going to have more long cycles and fewer short cycles. There is a transition, which I cannot articulate an exact reason for. It’s just that if there are cycles, then there are going to be fewer AB’s than if there are not cycles.

5. Go back to 2. The increased randomization in the bottom half of the 340 is subtle as compared to M1. Didn’t Zodiac include some gibberish at the end of the 408? I am almost inclined to compare 340 rows 1-8 and rows 11-18 to see of they are more similar. I wonder if analyzing parts of a message for the presence of consecutive alternations can be used to flush out gibberish. No doubt many have tried to solve the 340 by deleting the last few rows and it didn’t work.

M1 has only a few non-cyclic symbols, and they are not of the highest count. I have a lot more work to do on my systems.

Smokie

Every once in a while, I check these cipher threads,and most times, I am lost
By the way Smokie, I like how you’re rocking the throwback Ross Sullivan pic in your avatar

Every once in a while, I check these cipher threads,and most times, I am lost

i’m often lost, but their posts give me good "go research that" ideas and i find what they do fascinating. oddly my favorite threads to read are the crypto ones.

5. Go back to 2. The increased randomization in the bottom half of the 340 is subtle as compared to M1. Didn’t Zodiac include some gibberish at the end of the 408? I am almost inclined to compare 340 rows 1-8 and rows 11-18 to see of they are more similar. I wonder if analyzing parts of a message for the presence of consecutive alternations can be used to flush out gibberish. No doubt many have tried to solve the 340 by deleting the last few rows and it didn’t work.
Smokie

Thanks for your analysis. Do you want me to say what I did or will you work on it some more, either is fine by me. Looking at your table there seems to be a negative correlation going on with some of the higher rows versus the bottom one.

I think it could be valuable to measure by a row width of 10 and slide through the cipher. You’d have 11 slides then including top and bottom.

5) Last 18 symbols of the 408 are thought to be filler. But the 3rd part of the 408 is as good as random.

– Some of the medium-high count symbols do not seem to cycle well, are these possibly wildcards/polyalphabetic or 1:1 substitutes? (smokie treats)

By the way, what do you mean exactly by "wildcards/polyalphabetic"? I think I have a pretty good idea, but I better ask to make sure we are exactly on the same page. 🙂

So, it’s interesting that multiple measurements are producing peaks with the mirrored 340.

Thank you for reminding us of your test results. I don’t know what to think of it but what comes to mind is this line in the old FBI documents: "Hand anagramming done with the message as written and on assumptions that message backwards, written columnary, first line forward and second line backward etc."

I’m not sure what they mean with columnary, do they mean vertical instead of horizontal? I’m going on assumption that they meant that the message was written horizontally. And I wonder what they saw and if it is possibly in relation with what we are observing now? Have you checked if cycles improve under some of these basic alterations (don’t remember). Thanks.

Is this their version?

340fbi1969.txt:

>MDHNÐËS¤ZO¾AIKƒ+
ÃC-»BOy¸BÔ½<WÄËFI
++£WC¤WÃPOSHT/¢£Ð
L£IBWÌF+<C°²L+TÃR
IÕ´¤BK¢OÐ^•ÆMÑG±
+-µZuV>EC¼³„»²XBŸ
ÌGFN^Ƶ±³Â•ÃV³Ô++
R¾ƒ¢ÃBFµIN+·ŸS¼°¤
±<ÃÌRJI»µT³M•+ˆBF
OKMTÂÐByDIEÔµ/R+u
-¤ÌuV+^J+Oн<FBŸ-
K³°AŸÃBF±RZ+Â+M<Ä
¢G±JÆÊ·O+¸Ny¤+¹L¼
IL¤•VGXÃu±ƒºÑK+µ·
оR^FÌO-»ÄCËF>±D¢
/˳ˆ+PFµIÄÊÔ¤+M¼¸
SÐн^̾»V´ÐO++RK±
JH¤·L£¢WGZu+MÄŸB
NÐ+B¢·OºDWy•<»KÆ£
ıGTL²IËPV^ÌÐ>REH

– Some of the medium-high count symbols do not seem to cycle well, are these possibly wildcards/polyalphabetic or 1:1 substitutes? (smokie treats)

By the way, what do you mean exactly by "wildcards/polyalphabetic"? I think I have a pretty good idea, but I better ask to make sure we are exactly on the same page.

In the original thread:

There are some high scoring long or multi-repeated sequences with a one or more missing symbols. My thinking is that there may be a few symbols that Zodiac used as wildcards, which often appear in the message where the missing sequence symbols should be. He did that with one or two symbols on the 408.

If you don’t mind jumping me in. If your theory is true/statistically significant then it is an exciting discovery. Your wildcards would essentialy be a hint towards polyalphabetism of some kind right?

If we consider each + to be a wildcard, each standing for one of the symbols that is involved in high-scoring homophone sequences, then maybe we could conduct a brute force search for all replacements of the + symbol that yield "fixed’ sequences.

Could the Zodiac possibly have tried to mask bigrams visually with the "+" symbol etc? That would also be very much in line with smokie treats wildcard idea. And it was a problem with the 408.

It is suggested that up to 4 or 5 symbols could possibly be wildcards.

Hope that helps.

Those FBI notes suggest that they, too, suspected some kind of transposition going on. Difficult to rule out specific systems.

It would be interesting to revisit their ideas with more modern techniques.

Do you want me to say what I did or will you work on it some more, either is fine by me. Looking at your table there seems to be a negative correlation going on with some of the higher rows versus the bottom one. I think it could be valuable to measure by a row width of 10 and slide through the cipher. You’d have 11 slides then including top and bottom.Last 18 symbols of the 408 are thought to be filler. But the 3rd part of the 408 is as good as random.

I looked last night after making my post. M1 is highly cyclic in the first half, and with random symbol selection starting at the second half. Or thereabouts. Today I thought of maybe doing a consecutive alternation search in the 340 starting with Column 1, Row 1, and advancing one symbol at a time, adding up the alternations and making a graph with lines for each consecutive alternation number. See if a portion of the message, the end for instance, causes the graph lines to level out.

Yes, there is somewhat of a negative correlation in my findings. Basically, the more cyclic a message is, you get more of these: ABABABA, and fewer of these: ABA. If the symbol selection is more random, you get fewer of these: ABABABA and more of these: ABA. Makes sense.

Right now I have to work on my hillclimber, as I messed it up and have to merge an old spreadsheet and a new one to fix it.

So, it’s interesting that multiple measurements are producing peaks with the mirrored 340.

Thank you for reminding us of your test results. I don’t know what to think of it but what comes to mind is this line in the old FBI documents: "Hand anagramming done with the message as written and on assumptions that messaghim ackwards, written columnary, first line forward and second line backward etc."

I’m not sure what they mean with columnary, do they mean vertical instead of horizontal? I’m going on assumption that they meant that the message was written horizontally. And I wonder what they saw and if it is possibly in relation with what we are observing now? Have you checked if cycles improve under some of these basic alterations (don’t remember). Thanks.

Is this their version?

340fbi1969.txt:

>MDHNÐËS¤ZO¾AIKƒ+
ÃC-»BOy¸BÔ½<WÄËFI
++£WC¤WÃPOSHT/¢£Ð
L£IBWÌF+<C°²L+TÃR
IÕ´¤BK¢OÐ^•ÆMÑG±
+-µZuV>EC¼³„»²XBŸ
ÌGFN^Ƶ±³Â•ÃV³Ô++
R¾ƒ¢ÃBFµIN+·ŸS¼°¤
±<ÃÌRJI»µT³M•+ˆBF
OKMTÂÐByDIEÔµ/R+u
-¤ÌuV+^J+Oн<FBŸ-
K³°AŸÃBF±RZ+Â+M<Ä
¢G±JÆÊ·O+¸Ny¤+¹L¼
IL¤•VGXÃu±ƒºÑK+µ·
оR^FÌO-»ÄCËF>±D¢
/˳ˆ+PFµIÄÊÔ¤+M¼¸
SÐн^̾»V´ÐO++RK±
JH¤·L£¢WGZu+MÄŸB
NÐ+B¢·OºDWy•<»KÆ£
ıGTL²IËPV^ÌÐ>REH

– Some of the medium-high count symbols do not seem to cycle well, are these possibly wildcards/polyalphabetic or 1:1 substitutes? (smokie treats)

By the way, what do you mean exactly by "wildcards/polyalphabetic"? I think I have a pretty good idea, but I better ask to make sure we are exactly on the same page.

In the original thread:

There are some high scoring long or multi-repeated sequences with a one or more missing symbols. My thinking is that there may be a few symbols that Zodiac used as wildcards, which often appear in the message where the missing sequence symbols should be. He did that with one or two symbols on the 408.

If you don’t mind jumping me in. If your theory is true/statistically significant then it is an exciting discovery. Your wildcards would essentialy be a hint towards polyalphabetism of some kind right?

If we consider each + to be a wildcard, each standing for one of the symbols that is involved in high-scoring homophone sequences, then maybe we could conduct a brute force search for all replacements of the + symbol that yield "fixed’ sequences.

Could the Zodiac possibly have tried to mask bigrams visually with the "+" symbol etc? That would also be very much in line with smokie treats wildcard idea. And it was a problem with the 408.

It is suggested that up to 4 or 5 symbols could possibly be wildcards.

Hope that helps.

This cipher stuff is not my cup of tea. I come in to the cipher threads from time to time just to admire all of you guys work. However, there was an observation I made with the card that might be in line with the wildcard topic mentioned. Please keep in mind its just an observation/idea and that I more than likely will not interrupt your conversations again.

OK. The dripping pen card was the very first time that the Zodiac ever used the word "thing" to sum up what pleased him most. But "thing" was not an original thought, meaning, he didn’t view his actions as "thing" prior to acquiring the card. He pulled it straight from the card itself. Its almost like he was browsing cards in the local store, saw the word "thing" and said yup, this is the card. "Thing", for whatever reason, had meaning to him the second he saw the card.

Well I guess my thought here is that, if the zodiac can steal the word thing and claim it for his own then, why can’t he with the cipher? The card is about a freshly washed pen that’s ink bleeds when written with. The blotches on the card illustrate this. The zodiacs cipher is filled with blotchy writing that’s first introduced with this card: filled in circle (number one choice for a wildcard), filled in square, filled in triangle, filled in p, filled in theta and I believe a filled in crosshair.

I don’t know. Maybe I shouldn’t post. As I said this isn’t my cup of tea. I just couldn’t help but think that the Zodiac would be crazy enough to steal ink blotches for wild cards.

Soze

I believe it will be very hard to really distinguish between real and chance cycles. I would start with a textbook example which cycles without error. Hill climb your probability system to increasingly better results (fake/real cycles). Use all information you can extract about cycles, positions, distances, symbols in between. A cycle which is real will probably have a better spread throughout the cipher since that is the nature of cyclic homophonic, etc.

See viewtopic.php?f=81&t=267&p=34835&hilit=spread#p34835

I got my hillclimber fixed and am experimenting with formulas. I have been trying log10, and using spread to give weight to a cycle. I am thinking that different formulas and working with different parts of a message will be useful, depending on the cycle structure. One formula or approach may not work for all cycle structures. The horizontal hillclimber has some major limitations in that it can only show 64 symbol relationships at a time. The grid may be useful, and could show about 63*4 or 63*8 symbol relationships at a time. That list could subsequently be culled for different factors. Just trying different formulas and sorting the whole list of 63 * 62 of symbol relationships may work just as well.

Just wondering at the outset, what is a practical list of possible merges to work with when we are talking about permutations of merges? How many?

I thought that you might want to see this also, since no cycle that you made in M1 is perfect. There is a relatively short list of perfect two symbol cycles that was generated by the overlapping your imperfect cycles.

By comparison, here is the list of all perfect two symbol cycles in the 340:

I am just sort of thinking that a message with overlapping of all true perfect cycles is going to generate more false perfect cycles than a message with all true imperfect cycles. Another way to try to figure out what Zodiac did may be to compare statistics from lists of perfect cycles… Ha, ha, ha!

I looked last night after making my post. M1 is highly cyclic in the first half, and with random symbol selection starting at the second half. Or thereabouts.

Yes, first half is perfectly cyclic and second half is fully random (starting from character position 171). Well done! Since your system is able to detect it I will say that the m2 is more of the same, just that it is the other way around. I will move them away from the mystery list. I believe you’ve ruled out this scheme and possibly also columnar transposition but to be on the safe side with columnar transposition you should do a few more samples but it can wait. Whenever your up to it I’d like to create a new mystery cipher with another idea I have that could possibly relate to the 340.

This cipher stuff is not my cup of tea. I come in to the cipher threads from time to time just to admire all of you guys work. However, there was an observation I made with the card that might be in line with the wildcard topic mentioned. Please keep in mind its just an observation/idea and that I more than likely will not interrupt your conversations again.

Hey. As far as I’m concerned anyone can jump in and share their ideas! One wonders if clues to the 340 can be found in the card that accompanied it, especially since there was a hint to the proper order of the 408 in its accompanied communications.

Just wondering at the outset, what is a practical list of possible merges to work with when we are talking about permutations of merges? How many?

It all depends on how we decide to do it. With the system I use for my tests – which is quite thorough and gives a wealth of feedback – about 10. And maybe up to 13 with less thorough settings and increased CPU power next year. http://www.wolframalpha.com/input/?i=10%21 If the system works we could try a hill climber and then more may be possible.