Period 19 corresponds to this reading rule (as an example):
– Start at top left of cipher (the "H"), and print the symbol there.
– Go down 1 row
– Go right 2 columns and print the symbol there.
(When you fall off the grid, wrap back around as if the text has no "edge")
Continue until you’ve read all 340 symbols. Here’s the result:
H+M8|CV@Kz/JNbVM) +kN^D(+4(5J+JYM(+ y.LWBOLKJp+l2_cFK 29^4OFT-+EB+*5k.L dl5||.UqL+dpVW)+k p+fZ+B.;+B31c_8Tf BpzOUNyBO<Sf9pl/C >R(UVFFz9<Ut*5cZG R)WkPYLR/8KjROp+8 lXz6PYAG)y7t-cYAy Ucy5C^W(cM>#Z3P>L (MVE5FV52cW<Sk.#K _Rq#2pb&RG1BCOO|2 N:^j*Xz6-+l#2E.B) |DpOGp+2|G++|TB4- |TC7z|<z29^%OF7TB zF*K<SBKdpclddG+4 -RR+4>f|pFHl%WO&D #2b^D4ct+c+ztZ1*H SMF;+B<MF6N:(+H*;
Its repeating trigrams:
And bigrams:
Was hoping to find some better cycles in the result, but they don’t seem any different.
Jarlve, I assume you already ran the above transposition through your solver. Here’s one that I got:
nnsesonortheronsi
ntralindisenersin
thedefereinatpeor
thadforintenasthe
lassshopenlindint
incynehunecleperc
eitfortefedchiaho
msionootheoraseya
sidtoreshermsfine
artforsaiturierst
oetsoadiesmaycome <== resembles "bodies may come" or "ladies may come"
isntsonstededthar
pspatiousaleoffst
reamartfinaatthei
slifaintsannsredi
sroutsetthanfoure
toarederliealland
issndmcsionandful
atoaldernentrylan
dsouneesofreinnau
Here are a few variants, using this rule instead:
– Start at first symbol at top left ("H"). Print the symbol.
– Skip 19 symbols and print the next symbol.
Repeat. When falling off the very end of the cipher at the bottom right, wrap around to the top left.
Below is the result, followed by a full reversal, and mirrored versions for both. Each is shown with its azdecrypt result.
The 2nd one has the words "police" and "anger" in it, but other than that, none of them pan out.
Score:20337 Ioc:692 M:185 C:340 S:63 mersdgingeandairi ahtmittohoutbyiri dalohleddomfansth esbeatertheedarrt hitsconhuntetorte dagoodoodsgwholes eintrongthenotoar asofcowhileadistg otagourgleoftsowe dherotatelsallher msengettsareansin thheracdlrantican landdimentmantoca triantindellities ndyearsfestousing lecterineseofteam ihendlychriesisac urtnerorthergoodd rloomberofbuteman buewasoftouchlaug H+M8|CV@K+l#2E.B) >R(UVFFz9z/JNbVM) |DpOGp+2|<Ut*5cZG +kN^D(+4(G++|TB4- R)WkPYLR/5J+JYM(+ |TC7z|<z28KjROp+8 y.LWBOLKJ9^%OF7TB lXz6PYAG)p+l2_cFK zF*K<SBKdy7t-cYAy 29^4OFT-+pclddG+4 Ucy5C^W(cEB+*5k.L -RR+4>f|pM>#Z3P>L dl5||.UqLFHl%WO&D (MVE5FV52+dpVW)+k #2b^D4ct+cW<Sk.#K p+fZ+B.;+c+ztZ1*H _Rq#2pb&RB31c_8Tf SMF;+B<MFG1BCOO|2 BpzOUNyBO6N:(+H*; N:^j*Xz6-<Sf9pl/C Score:20501 Ioc:739 M:185 C:340 S:63 ndenndoutforheall thmaillfisallions tsiinsinprusatpro ducoriescountheco mhidioaratesaddan thesoutrairsgauth saatontateopedori goitsemphelesseet heredhernsdesacct hesehasdritanearl santternatupisant agertimattsouthpo tproteanangerfore sumpisandthisthea canicetctousomnus airedadedcherstac tssusaanisaigalsa ndrehilustannings aroulddonoppolice asedtheationscram C/lp9fS<-6zX*j^:N ;*H+(:N6OByNUOzpB 2|OOCB1GFM<B+;FMS fT8_c13BR&bp2#qR_ H*1Ztz+c+;.B+Zf+p K#.kS<Wc+tc4D^b2# k+)WVpd+25VF5EVM( D&OW%lHFLqU.||5ld L>P3Z#>Mp|f>4+RR- L.k5*+BEc(W^C5ycU 4+Gddlcp+-TFO4^92 yAYc-t7ydKBS<K*Fz KFc_2l+p)GAYP6zXl BT7FO%^9JKLOBWL.y 8+pORjK82z<|z7CT| +(MYJ+J5/RLYPkW)R -4BT|++G(4+(D^Nk+ GZc5*tU<|2+pGOpD| )MVbNJ/z9zFFVU(R> )B.E2#l+K@VC|8M+H Score:20382 Ioc:716 M:185 C:340 S:63 hirfreishionefoss hoofmegarallouton ehademugerstelthe usinessetssthemis stonesedgoanditho fstlochfrageaanne inallherehalitarc hlarristheandpari canaumacthinghela ssettiatsunllserr aridesifattendcau andthenoteinssoou holthislatureedit ishtottsrdoldfoot heringtasmashefre sechmasascrishist infractiooftretor rellnicelogisclon cesstimplicmulati ngitringupareceim )B.E2#l+K@VC|8M+H )MVbNJ/z9zFFVU(R> GZc5*tU<|2+pGOpD| -4BT|++G(4+(D^Nk+ +(MYJ+J5/RLYPkW)R 8+pORjK82z<|z7CT| BT7FO%^9JKLOBWL.y KFc_2l+p)GAYP6zXl yAYc-t7ydKBS<K*Fz 4+Gddlcp+-TFO4^92 L.k5*+BEc(W^C5ycU L>P3Z#>Mp|f>4+RR- D&OW%lHFLqU.||5ld k+)WVpd+25VF5EVM( K#.kS<Wc+tc4D^b2# H*1Ztz+c+;.B+Zf+p fT8_c13BR&bp2#qR_ 2|OOCB1GFM<B+;FMS ;*H+(:N6OByNUOzpB C/lp9fS<-6zX*j^:N Score:20306 Ioc:752 M:185 C:340 S:63 tohismanymontralg rraoithrontoteest oaltermalhurgoodd isandronsrousinan renterateseastuse ndoherssesimonano talpillidetrlicen taiddaianleatione ysserindraintowin ishighitspresinan dthrolayersatther alsomorothesysith amanwithcreadislo hanironofthtolear dageadmadnoisoren scinwinslifefiate enthetertheedarry derohreddmissisth istilllatalftolac eeandglooeandparc N:^j*Xz6-<Sf9pl/C BpzOUNyBO6N:(+H*; SMF;+B<MFG1BCOO|2 _Rq#2pb&RB31c_8Tf p+fZ+B.;+c+ztZ1*H #2b^D4ct+cW<Sk.#K (MVE5FV52+dpVW)+k dl5||.UqLFHl%WO&D -RR+4>f|pM>#Z3P>L Ucy5C^W(cEB+*5k.L 29^4OFT-+pclddG+4 zF*K<SBKdy7t-cYAy lXz6PYAG)p+l2_cFK y.LWBOLKJ9^%OF7TB |TC7z|<z28KjROp+8 R)WkPYLR/5J+JYM(+ +kN^D(+4(G++|TB4- |DpOGp+2|<Ut*5cZG >R(UVFFz9z/JNbVM) H+M8|CV@K+l#2E.B)
BTW, Jarlve, didn’t you observe some other phenomenon a while back involving diagonal routes, perhaps involving the non-repeat scores? This period 19 stuff reminds me of that.
Jarlve, maybe he wrote a vertical message with 19 columns and then re-drafted it with 17 columns. Did you try that?
EDIT: Nevermind, I tried it and it didn’t work.
I’ve created a start for the 340 spreadsheet: https://drive.google.com/open?id=1VrAwV … gJ8Rb7sEKs You should have permission to fill in your numbers and if you don’t mind I’d like to create all the necessary fields and maintain the spreadsheet (tell me if you want anything added). I’ve added links to download the transformations of the 340 measured, do you want me to include a numeric version as well? If so, re-numbered by appearance or with the original 340 numbered by appearance kept so you are able to compare cycles more easily? The spreadsheet may seem ill-formatted on some browsers, I recommend Google Chrome. If anyone wants to contribute to the spreadsheet let me know, you’ll need a Google account/e-mail.
I went to the spreadsheet and do not mind if you want to manage the fields or format it any way that you want. I have numeric versions of the messages on the first post in this thread. I have Google Chrome. I saw on the spreadsheet that you included smokie1 and smokie2. Are those the messages that you want cycle measurements for? I noticed that you named your messages Jarlve 2c Cpl, Jarlve 3c Cpl, and Jarlve NR. I am not familiar with those message names.
EDIT: My message experiment that I have been working on (in my head only so far) did involve the low number of bigram repeats in the bottom half of the 340 and the possibility of two keys with increasing randomization values. The more cycles are randomized, the fewer bigram repeats we get. But I think that the period 19 bigram repeat statistics are very important and would like to explore that further; try to figure out a method of encipherment that would cause that. I also have plans for other experiments to find out what plaintext false cycles could map to.
EDIT: Did you try combinations of horizontal and vertical transposition to make some, but not all, period 19 bigram repeats into period 0 bigram repeats? What about horizontal transposition of columns and then diagonal message?
ANOTHER EDIT: Let’s keep it simple. If I just encoded a message and wanted to hide a bunch of bigram repeats, it would be easy to just switch one of the symbols with a nearby symbol.
12345678
90679123
16345678
90279123
Piece of cake. Has anyone tried messing around with this idea? You would have to change out maybe half of them (?) to get normal statistics for period 19 bigrams. I will take a closer look tomorrow. Look to see if there are a lot of matching "unchanged" bigrams:
12345678
90679123
ANOTHER EDIT: The nice thing about this idea is that it reduces period 0 bigram repeats. He could have encoded with nearly perfect cycles and just done a lot of diagonal switching around. If he did that more in the bottom half, that would explain the one bigram repeat in the second half and the lower cycle scores in the second half. It would also explain how either 37, 38 or 41 could have gotten switched from an even to an odd, making it look like he used two keys. I did this with r3_s4_p3, which is 30% random and got 25 remaining bigram repeats and cycle score went down from 76,000 range to about 66,000. But I didn’t have enough period 19 bigram repeats. However, with a different message or more cycling with a lot of bigram repeats to start with, I see this as a plausible explanation for what you are seeing, Jarlve. The only issue is making more period 0 or fewer period 19 bigram repeats when switching stuff around.
If you want me to make a test message to try to duplicate the 340 stats this way, let me know.
Jarlve: You may have already done this, but here is a list where Period 0 bigrams = Period 19 bigrams in the 340. For example see the top row. At position 171, there is Symbol 3 and Symbol 54 one space to the right. At position 66, there is Symbol 3 with Symbol 54 nineteen spaces to the right. There are a whole lot of candidates for diagonal switching here. Maybe abnormally too many. I only checked for right side, diagonal switch down to the right. I didn’t check for left side diagonal switch up to the left.
I see that you are up late tonight, Mr. Lowe. Or perhaps up early this morning. Thanks for stopping by; we are going to solve it this time!
I see that you are up late tonight, Mr. Lowe. Or perhaps up early this morning. Thanks for stopping by; we are going to solve it this time!
tis late afternoon in the land of OZ..
I am watching your progress.. trying to follow ..this is way way above my level..you guys are advancing to a resolution I feel. I can not offer much assistance but you never know what might fall into place.. I have been analyzing your "partial" solves to see if any nuggets are missed. sifting through the tailings one might say.
I do like the recent findings on the 19 bigram repeat statistics.. interesting to see where that leads you.. I am pensive to the methology Z used to mix it up.
just playing around with the tailings
mersdgingeandairiahtmittohout by iridalohleddomfansthes beat ertheedarrthitscon hunt etorted a good oodsg whole seintrong then otoaras of cow hile a distgotagourgleoft so wed her otatelsall her msengettsareansinthheracdlrantican land dime nt man to
catriantindel litiesnd years festou single cterineseof team i hendlychries is a curtnerorther good dr loom be rofbute man bue wasoftouch laug
And this one
urd manical the cosmedis the work for us govern alor the hand
i dating relatin dream analys them i call and genesis element
shirt was ar the fact the substice band compauny name north egu
es then is it a to move and will nobody care ep and strica long seas
on this the sas and y the sis is a foregon its this america l is i
trolas used iful the drone he monents the ingrestrati now that
most polock to remail one don alen t buy i
all the best to you Guys n Gals hope a solve comes soon.
It sounds like you worked on the "tailings" by making the diagonal switch. I see "this america" at the bottom half of the message often in my solver attempts. Thanks for helping; did you try to switch all of them?
Thanks for your work in the meanwhile on the matter.
When you consider bigrams towards the end of the cipher text, are you allowing the 2nd symbol to "wrap" around to the beginning? If not, I wonder what effect doing so would have on your numbers.
No, will look into it.
The other interesting thing about period 19 ngrams is that they cover exactly 20 spots in the grid, which is precisely the number of rows occupied by the cipher. Is there some connection to rows?
What do you mean with spots?
BTW, Jarlve, didn’t you observe some other phenomenon a while back involving diagonal routes, perhaps involving the non-repeat scores? This period 19 stuff reminds me of that.
Check my spreadsheet. The related fields are marked in yellow/orange. Usually, when encoding horizontally, the horizontal directions are highest and then come the vertical directions. That is to say, somehow a small bit of the horizontal information leaks into the vertical direction when measured in a grid. And less so for the diagonal directions, but in the 340 some of the diagonal directions are a bit higher. In other words, a diagonal reading of a horizontally encoded cipher usually offers increased randomization over a vertical reading.
These are the averages for the 408 (17 by 20 and normalized):
Horizontals: 4515
Verticals: 3266
Diagonals 1: 2734
Diagonals 2: 2990
340:
Horizontals: 4361
Verticals: 3108
Diagonals 1: 2939
Diagonals 2: 3376 <– higher than vertical
These directions are SE-SW and NW-NE (primary direction-secondary direction). The statistical weight of this observation is probably not as strong.
The other interesting thing about period 19 ngrams is that they cover exactly 20 spots in the grid, which is precisely the number of rows occupied by the cipher. Is there some connection to rows?
What do you mean with spots?
I just mean positions in the cipher text. For example, the ngram AB has period 1, A?B has period 2, A??B has period 3, etc. AB occupies 2 spots, A?B occupies 3 spots, A??B occupies 4 spots, etc. So, an ngram of period p occupies p+1 spots. Period 19 ngrams cover 20 spots, which happens to be the number of rows in Z340.
I went to the spreadsheet and do not mind if you want to manage the fields or format it any way that you want. I have numeric versions of the messages on the first post in this thread. I have Google Chrome. I saw on the spreadsheet that you included smokie1 and smokie2. Are those the messages that you want cycle measurements for? I noticed that you named your messages Jarlve 2c Cpl, Jarlve 3c Cpl, and Jarlve NR. I am not familiar with those message names.
Okay that’s cool. Do you want me to include numeric versions of the cipher alterations in the spreadsheet? If so, do you want me to re-number them by appearance or do you want me to keep the 340 numbers by appearance? smokie 1, smokie 2, Jarlve 2c Cpl, etc, these are all measurement systems, not ciphers. I want my spreadsheet to be for the 340 only (in-depth) so perhaps you could maintain a spreadsheet that compares different ciphers. Like the one you have been using and then we can draw ideas from each other and we both have something of our own to work. How about that?
The more cycles are randomized, the fewer bigram repeats we get.
Yes, both our numbers show increased randomization for the bottom 10 rows over the top 10 rows and that goes some way for the bigrams too.
EDIT: Did you try combinations of horizontal and vertical transposition to make some, but not all, period 19 bigram repeats into period 0 bigram repeats? What about horizontal transposition of columns and then diagonal message?
A normal bigram is period 1 I think, if not then the other is period 18. Anything that involves row or column transposition is a bit of a nightmare but I guess it’s possible. Would love to see some examples of what you mean.
I don’t think switching of symbols in the manner you described would create allot of bigrams. But who knows?
Edit: I think that looking for things in the encoding that could both explain the bigram peak and randomization of the cycles is certainly a good direction.
@Mr lowe, thanks for rechecking our solves.
Deleted my previous post because I managed to confuse unigram with bigram repeats.
I’m also considering that the peak at 19 is somehow related to the positions of the "+" symbol in a horizontal scheme, that whatever is actual (endocing system/plaintext) in the 340 prefers a distance of 19 between the "+" symbol. That’s another interpretation. I count 10 repeats for the "+" symbol alone. So what is the chance of a peak of 37 at period 19 with 10 of the repeats sitting among the "+" symbol.
It is very interesting. But when asking a question such as this: "What is the chance of finding this very specific interesting pattern", I often think of this related question: "What is the chance of finding any interesting pattern"? Since we are looking for such specific interesting patterns in shuffles of Z340, we may overlook other interesting patterns that are very specific but not yet detected by our approach.
For an example, consider the qwerty keyboard layout idea here: viewtopic.php?p=34394#p34394 A shuffle test might suggest there is significance to the QWERTY idea, but the test fails to consider other layouts that would be of interest to us if they turned up (DVORAK keyboard, international keyboards, periodic table of elements, a 5×5 square of letters alphabet order, etc).
UPDATE: Original post deleted but my point is still relevant to other aspects of the Z340 analysis.
It is very interesting. But when asking a question such as this: "What is the chance of finding this very specific interesting pattern", I often think of this related question: "What is the chance of finding any interesting pattern"? Since we are looking for such specific interesting patterns in shuffles of Z340, we may overlook other interesting patterns that are very specific but not yet detected by our approach.
I’ve thought the same thing. When considering a 340 character cipher and a near infinite different ways to measure it, would you not always find exceptionally rare artifacts? But then you could very well throw every individual observation out of the window. So I guess we need to find a patch of observations that point in one direction.
The message I deleted basicly pointed out that there may be something going on with a distance of 19 or a multiple of it between the "+" symbols but at that time I was actually confusing unigrams with bigrams. It may not be rare at all.
I’ve thought the same thing. When considering a 340 character cipher and a near infinite different ways to measure it, would you not always find exceptionally rare artifacts? But then you could very well throw every individual observation out of the window. So I guess we need to find a patch of observations that point in one direction.
That makes sense. An analogy might be this: You have a handful of suspects, and each has a set of suspicious connections to the crime. Each connection by itself is rare, but because there are so many rare coincidences to choose from, they are bound to happen by chance. But the right suspect may be associated with the rare connections that all point in one direction.
Okay that’s cool. Do you want me to include numeric versions of the cipher alterations in the spreadsheet? If so, do you want me to re-number them by appearance or do you want me to keep the 340 numbers by appearance? smokie 1, smokie 2, Jarlve 2c Cpl, etc, these are all measurement systems, not ciphers. I want my spreadsheet to be for the 340 only (in-depth) so perhaps you could maintain a spreadsheet that compares different ciphers. Like the one you have been using and then we can draw ideas from each other and we both have something of our own to work. How about that?
Yes, maintain a spreadsheet for the 340 and I will maintain the comparison spreadsheet. If you allow me to edit my making a separate spreadsheet, then I can just copy it in. Not sure what you mean by my measurement systems. I only have one, I think. But maybe I have more.
EDIT: Did you try combinations of horizontal and vertical transposition to make some, but not all, period 19 bigram repeats into period 0 bigram repeats? What about horizontal transposition of columns and then diagonal message? I don’t think switching of symbols in the manner you described would create allot of bigrams. But who knows?
I think that making two symbol transpositions in any direction to hide bigram repeats is a possibility, similar to the bigram masking experiment that we did earlier with daikon. I did find many examples of where period 0 bigrams and period 18 bigrams share the same symbols. Identifying them and reversing the switch would increase period 0 bigram repeats, decrease period 18 bigram repeats, and decrease randomization. I tried an experiment, which didn’t work, by doing just that where making the diagonal switch would increase cycle scores. There wasn’t a solve, but it is the general idea I guess that I am thinking about.
These are the symbol pairs that appear as both period 0 bigrams and period 18 bigrams:
3 54
5 6
5 19
5 23
5 61
11 25
12 30
16 46
18 7
19 11
19 19
19 20
19 40
20 5
20 31
21 15
23 5
25 21
26 20
26 21
26 29
29 37
30 31
33 5
33 19
33 26
34 20
36 6
36 34
38 8
38 36
39 15
40 48
40 63
41 19
43 48
48 19
50 16
51 40
54 50
55 19
58 19
I reversed the suspected diagonal shift and increased the overall cycle scores substantially, and increased the top half cycle scores. I increased the period 0 bigram repeats to 61, increased the bottom half period 0 repeats, and decreased the period 18 bigram repeats to 28. But… the solver has been working on it for 15 minutes now and is clogged up at about 32k.
Here is the altered message ( not that it has any value ):
1 2 3 4 5 6 7 8 9 10 11 12 30 14 15 16 17
18 5 19 20 21 22 23 24 25 21 27 28 29 13 31 32 33
20 5 35 36 6 19 38 39 15 26 26 33 19 22 40 1 41
42 5 34 43 7 37 44 30 8 45 5 23 19 13 3 31 16
46 47 37 19 40 48 49 17 11 50 51 9 19 52 53 10 54
5 19 3 7 51 6 23 55 30 17 56 10 51 4 16 25 21
22 50 44 31 57 24 58 16 38 36 59 15 8 28 40 13 11
21 15 16 41 19 49 22 23 19 20 18 27 40 63 60 13 47
17 29 37 19 61 32 39 3 16 51 46 36 34 62 19 53 31
55 40 6 38 8 19 11 41 19 23 5 43 29 37 20 34 55
38 19 3 54 50 48 2 7 25 27 20 5 61 14 51 31 23
16 29 36 6 3 41 11 30 53 14 50 37 28 19 52 20 51
40 63 47 42 34 33 19 18 11 50 51 20 36 21 58 19 3
6 15 51 18 7 32 50 16 53 61 28 36 8 53 48 19 44
34 20 59 12 30 35 53 47 56 2 4 8 38 39 15 55 19
11 36 28 45 40 20 31 21 23 5 7 28 32 37 57 50 16
3 36 14 19 13 12 16 56 29 19 51 6 26 20 11 33 13
19 19 33 26 56 40 48 36 9 23 42 1 14 54 21 33 5
11 25 10 17 26 29 43 26 20 46 27 23 20 31 55 56 36
4 37 51 1 18 5 10 42 40 39 23 44 62 11 30 58 19
I am thinking about possible switches and identifying them.
123456
789712
345608
EDIT: With two or more similar occurrences and in another location there is a 90 bigram.
I am saying that there may be a simple explanation for the period 18 repeats. Trying simple easy ways for Zodiac to make the message unsolvable.
I am getting tired and should probably take a break if I can. Not a total break, but minimal involvement for a short period of time. I have other ideas that I would like to work on in the future as well. I think that if we keep exposing ourselves the the possibility of solving the 340, then it may happen.
I am also glad that Mr. Lowe is looking over this stuff. It would be cool if he solved it with one of our ideas. Thanks.
