I like the idea of separating genuine lengths and sub lengths for analysis. I was wondering what would happen if I read the 340 right left bottom top. By definition, the same unique strings should be there and the column chart should be the same, but why? Because the genuine lengths are bracketed by symbols that exist within them. Either you can or I will just make a list of the original lengths, but include the symbol before and after. Then we can look at them and see if the lengths of 17, 18 and 19 have anything in common. Can we use numbers for symbols to make discussion and spreadsheet work easier? See below one genuine string of length 19, colored. Symbol 16 comes before, and a 16 can be found within the string. Symbol 21 comes after, and a symbol 21 can also be found within the string.

The 340 LRTB

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
18 05 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
20 34 35 36 37 19 38 39 15 26 21 33 13 22 40 01 41
42 05 05 43 07 06 44 30 08 45 05 23 19 19 03 31 16
46 47 37 19 40 48 49 17 11 50 51 09 19 52 53 10 54
05 44 03 07 51 06 23 55 30 17 56 10 51 04 16 25 21
22 50 19 31 57 24 58 16 38 36 59 15 08 28 40 13 11
21 15 16 41 32 49 22 23 19 46 18 27 40 19 60 13 47
17 29 37 19 61 19 39 03 16 51 20 36 34 62 63 53 31
55 40 06 38 08 19 07 41 19 23 05 43 29 51 20 34 55
38 19 03 54 50 48 02 11 25 27 20 05 61 14 37 31 23
16 29 36 06 03 41 11 30 50 14 53 37 28 19 52 20 51
40 63 47 42 34 22 19 18 11 50 51 20 36 21 58 44 03
06 15 51 18 07 32 50 16 53 61 28 36 08 53 48 19 19
34 20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19
11 36 28 45 40 20 31 21 23 05 07 28 32 37 57 15 16
03 36 14 19 13 12 63 56 29 19 51 06 26 20 11 33 13
19 19 33 26 56 40 26 36 09 23 42 01 14 54 21 33 05
11 51 10 17 26 29 43 48 20 46 27 23 20 30 55 56 36
04 37 25 01 18 05 10 42 40 39 23 44 62 11 31 58 19

And RLBT

19 58 31 11 62 44 23 39 40 42 10 05 18 01 25 37 04
36 56 55 30 20 23 27 46 20 48 43 29 26 17 10 51 11
05 33 21 54 14 01 42 23 09 36 26 40 56 26 33 19 19
13 33 11 20 26 06 51 19 29 56 63 12 13 19 14 36 03
16 15 57 37 32 28 07 05 23 21 31 20 40 45 28 36 11
19 55 50 39 38 08 04 02 56 47 53 35 30 12 59 20 34
19 19 48 53 08 36 28 61 53 16 50 32 07 18 51 15 06
03 44 58 21 36 20 51 50 11 18 19 22 34 42 47 63 40
51 20 52 19 28 37 53 14 50 30 11 41 03 06 36 29 16
23 31 37 14 61 05 20 27 25 11 02 48 50 54 03 19 38
55 34 20 51 29 43 05 23 19 41 07 19 08 38 06 40 55
31 53 63 62 34 36 20 51 16 03 39 19 61 19 37 29 17
47 13 60 19 40 27 18 46 19 23 22 49 32 41 16 15 21
11 13 40 28 08 15 59 36 38 16 58 24 57 31 19 50 22
21 25 16 04 51 10 56 17 30 55 23 06 51 07 03 44 05
54 10 53 52 19 09 51 50 11 17 49 48 40 19 37 47 46
16 31 03 19 19 23 05 45 08 30 44 06 07 43 05 05 42
41 01 40 22 13 33 21 26 15 39 38 19 37 36 35 34 20
33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 05 18
17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01

Good idea with the 408, it looks very different. Not a cluster of genuine lengths all together like L17, L18 and L19 in the 340. I have to get ready for work.

Here’s my post from 2014 with the original observation: viewtopic.php?f=81&t=2114

The links are not working anymore.

Here’s my post from 2014 with the original observation: viewtopic.php?f=81&t=2114

Ah ha. There’s my heat map you copied from me minus 5 years ago.

[…] the 408, it looks very different. Not a cluster of genuine lengths all together like L17, L18 and L19 in the 340.

I think that’s very telling. I’m not sure what it’s telling, but it feels very relevant.

More hints this could just be someone trying to avoid repetition (of some sort)? Who knows.

(Notwithstanding the conversation I started this thread with) I wonder how rare a clustered peak of 3 genuine lengths of those sort of magnitudes would be, for a shuffled 340? My guess is mighty rare. And more evidence if needed that 340 is created by some human process – attempted random or enciphering.

One might argue that a well enciphered message (by any significant cipher, or multiple passes with different ciphers) would not show these patterns, hinting that it is just a human-random sequence.

CK

Highlighted z340 17L, 18L and 19L genuine start points.

Looks a bit diagaonally to me (def: "diagonally" /dʌɪˈaɡ(ə)n(ə)li/, adjective. To have the appearance of diagonal patterns. Example: That pattern looks a bit diagonally to me).

That might just be what happens when you fit sections of 17,18 and 19 symbols into a 17 wide grid. Or it might indicate a some periodic behaviour, or scytails.

Or early signs of madness of someone spending too much time looking for patterns in a random grid of symbols.

More hints this could just be someone trying to avoid repetition (of some sort)? Who knows.

I fished up my encoder that applies homophonic substitution this way and the number of symbols, no repeat window and raw ioc target can be specified.

Here follows a cipher with 63 symbols, no repeat window 12 and raw ioc target 2236. It can be seen that this hypothesis creates very high spikes at higher lengths, in this case L18=31, even higher than the 340.

At the time I thought the hypothesis had some issues but it seems relevant again now that you are suspecting the same. Of course, the encoder is very mechanical and Zodiac would not have done it this strictly. The hypothesis explains L17=26 and also why we are not able to identify homophone groups like with the 408.

1  2  3  4  5  6  7  8  9  10 11 12 13 1  14 15 16
17 18 19 20 21 22 23 6  24 11 24 1  25 14 3  26 27
28 13 29 30 31 32 10 15 21 6  14 11 16 33 25 13 34
28 29 30 35 1  36 9  5  37 22 2  38 21 6  3  39 40
41 42 24 28 16 27 43 17 44 19 44 29 45 6  41 46 15
42 1  30 31 47 12 13 48 44 32 2  3  10 17 42 24 37
40 35 1  49 15 28 44 11 26 43 17 42 16 50 38 37 45
36 51 14 30 41 20 18 43 1  25 32 2  3  42 11 52 45
40 35 53 48 44 54 42 32 36 9  42 12 14 11 25 33 1
49 38 29 3  39 36 30 17 13 9  53 55 18 8  11 16 48
44 23 56 32 19 30 42 40 13 24 55 3  38 33 22 25 41
44 16 37 6  15 56 9  54 57 11 24 55 42 17 58 32 48
30 44 19 45 54 20 29 50 28 34 55 31 48 58 21 8  18
43 17 56 25 14 59 12 32 24 11 58 40 6  23 1  48 25
42 45 49 28 38 13 60 21 44 55 61 17 32 48 30 42 42
25 22 62 44 40 47 44 23 37 45 10 15 46 19 18 48 1
17 13 43 30 6  16 28 13 38 35 32 2  3  50 5  6  63
8  15 10 28 12 13 45 39 17 20 33 25 6  14 15 16 48
42 35 38 13 1  49 9  50 6  40 32 15 56 45 19 25 44
17 42 24 26 41 1  5  21 18 54 42 32 9  6  11 20 45

Z@(V)PN6#"O!%Z;S^
I-3CT'PGOGZ4;($Y
D%02K."SCP;O^M4%1
D02_Z?#)UT@*CP(H8
BWGD^Y:]-]0&PB5S
WZ2K9!%F].@("WGU
8_ZLSD]O$:W^>*U&
?7;2B3I:Z4.@(WOA&
8_+F]/W.?#W!;O4MZ
L*0(H?2%#+XI6O^F
]'<.-2W8%GX(*MT4B
]^UPS<#/JOGXWQ.F
2]-&/30>D1XKFQC6I
:<4;,!.GOQ8P'ZF4
W&LD*%[C]XE.F2WW
4T=]89]'U&"S5-IFZ
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6S"D!%&H3M4P;S^F
W_*%ZL#>P8.S<&-4]
WG$BZ)CI/W.#PO3&

That might just be what happens when you fit sections of 17,18 and 19 symbols into a 17 wide grid. Or it might indicate a some periodic behaviour, or scytails.

Me and smokie looked at various types of cycle periodicity and we did not find it. I also looked at periodicity within the cycle sequences and found nothing. The 340 just like the 408 tests positive for increasingly random cycles though.

[…] the 408, it looks very different. Not a cluster of genuine lengths all together like L17, L18 and L19 in the 340.

I think that’s very telling. I’m not sure what it’s telling, but it feels very relevant.

More hints this could just be someone trying to avoid repetition (of some sort)? Who knows.

(Notwithstanding the conversation I started this thread with) I wonder how rare a clustered peak of 3 genuine lengths of those sort of magnitudes would be, for a shuffled 340? My guess is mighty rare. And more evidence if needed that 340 is created by some human process – attempted random or enciphering.

One might argue that a well enciphered message (by any significant cipher, or multiple passes with different ciphers) would not show these patterns, hinting that it is just a human-random sequence.

CK

"human process". yes. the same human who created the 408 that was solved more quickly than he had hoped. what would a person do to make their next cipher more challenging? the hardens suggested expected words like "kill" helped them solved the 408. if i was the cipher creator i’d avoid words that are closely associated with me or, alternately, i’d get trickier at disguising those words. i’d misspell them if i was lazy.

what you see in the first row of the 340 is exactly what an amateur would do – no repeats. in fact, only one repeat in the first two rows. he uses 33 of his 63 symbols in the first 34 characters. i’m sure that seemed like it would make the cipher harder. but why is row 2 column 2 the sole repeating symbol? he’s not hiding what he’s doing, he’s telling us he’s not going to repeat symbols for a while, but then he does for one. why? he’s lazy so maybe it was just a mistake.

i’d also avoid cycling symbols like he did in the 408. i’d attempt to randomize my system. use some of the symbols only in certain areas to make them seem special. occasionally repeat a symbol in two adjacent spots. they’ll know it’s a double letter, but maybe the end of one word and beginning of another. tricky enough right?

i would skip words, misspell words, use uncommon words, whatever it took to make things hard.

what i wouldn’t do is anything that made encoding the cipher a pain in the ass. if i’m not going to bother rewriting the cipher when i mess up the backward "k" in row 6 then im definitely not going to do too much with transposing columns and rows or tricky mathematical clues because at the end of the day the message probably doesn’t say anything important and i don’t care if someone solves it, i just don’t want it solved so quickly.

just my 2 cents.

just my 2 cents.

All good points.

Obviously the only way to know what was done for sure, is to find a reasonable solution and plaintext. Until then, all patterns and lack of patterns are just hints at what might be.

To me, these patterns above seem to contribute equally to the theory of a hard cipher, and a theory of no cipher. Which isn’t much help at all.

But I completely agree that the Zodiac (probably) wouldn’t be in the mood for a long and complex cipher process, with just the pen and paper he had to hand.

Here follows a cipher with 63 symbols, no repeat window 12 and raw ioc target 2236. It can be seen that this hypothesis creates very high spikes at higher lengths, in this case L18=31, even higher than the 340.

So I’ve run the same analysis on your cipher, and get this distribution (the same as your chart, but showing the contribution of real-new length stacked with sub-lengths)

That appears very different to smokie’s equivalent for the 340 below

My point being the 3 real value (red) spikes in z340 L17,L18 and L19 are the defining signature of z340 IMO.

Does any tuning of your parameters generate anything similar?

[Edit – Is there any sort of nasty plaintext that leads to this output, using this encipher algorithm – like ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ etc]
[Editx2 – bad example by the way, obviously all arbitrary, nonsense solutions to 340 lead to this distribution, so forget that]

CK

what you see in the first row of the 340 is exactly what an amateur would do – no repeats. in fact, only one repeat in the first two rows. he uses 33 of his 63 symbols in the first 34 characters. i’m sure that seemed like it would make the cipher harder. but why is row 2 column 2 the sole repeating symbol? he’s not hiding what he’s doing, he’s telling us he’s not going to repeat symbols for a while, but then he does for one. why? he’s lazy so maybe it was just a mistake.

Outstanding post. It suggests a method of attack. If each letter is on average represented by 2.4 symbols, and if he avoids repeats in the first two lines, he is severely constraining the rest of the cipher. It also strongly suggests that +, which does not appear in the first two lines but is the most frequent symbol overall, is either a null or a wildcard. Or that the whole thing is fake. Or perhaps even that it isn’t a cipher at all, but something else, like a word game.

My point being the 3 real value (red) spikes in z340 L17,L18 and L19 are the defining signature of z340 IMO.

Does any tuning of your parameters generate anything similar?

No 2 ciphers will have a similar chart even with exactly the same encoding properties. The main point that I wanted to make with the original observation is that the 340 L-peaks are right-shifted from the expected. For example, in the 408 the highest is L9=27 while in the 340 we have L17=26. Looking purely at that, the "no repeat window" hypothesis does generate such ciphers on demand. It seems that you guys are on a tangent with looking at the defining properties of the measurement and that may be interesting in its own, I will follow the discussion.

Thanks for the observation, Jarlve. At the least it is providing some good entertainment right now.

Here are the genuine lengths in order for you to copy into a spreadsheet, except that the repeated symbols at the beginning and end are included. So if you look at the first symbol, you will find it in the length. And if you look at the last symbol, you will also find it in the length. I am interested in L17-L19 and above mostly since they are primarily responsible for 26 L=17, and any possible relationship or pattern concerning these pairs of symbols or relationship between the pairs and the same pairs in other observations. I took out the first and last length because there is no pair to look at. I plan on casting the message into different widths to look at the repeats by rows also and maybe do some other stuff but it is the work week so I will pick at it. Have fun.

05 06 07 08 09 10 11 12 13 14 15 16 17 18 05 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 20
20 21 22 23 24 25 26 27 28 29 30 31 32 33 20 34 35 36 37 19 38 39 15 26
26 27 28 29 30 31 32 33 20 34 35 36 37 19 38 39 15 26 21 33
33 20 34 35 36 37 19 38 39 15 26 21 33 13 22 40 01 41 42 05 05
05 05 43 07 06 44 30 08 45 05
05 43 07 06 44 30 08 45 05 23 19 19
19 19 03 31 16 46 47 37 19
19 03 31 16 46 47 37 19 40 48 49 17 11 50 51 09 19
19 40 48 49 17 11 50 51 09 19 52 53 10 54 05 44 03 07 51
51 09 19 52 53 10 54 05 44 03 07 51 06 23 55 30 17 56 10
51 06 23 55 30 17 56 10 51 04 16 25 21 22 50 19 31 57 24 58 16
16 25 21 22 50 19 31 57 24 58 16 38 36 59 15 08 28 40 13 11 21
15 08 28 40 13 11 21 15 16 41 32 49 22 23 19 46 18 27 40
19 46 18 27 40 19 60 13 47 17 29 37 19
19 60 13 47 17 29 37 19 61 19
19 61 19 39 03 16 51 20 36 34 62 63 53 31 55 40 06 38 08 19
19 39 03 16 51 20 36 34 62 63 53 31 55 40 06 38 08 19 07 41 19
19 07 41 19 23 05 43 29 51 20 34 55 38 19
19 23 05 43 29 51 20 34 55 38 19 03 54 50 48 02 11 25 27 20
20 34 55 38 19 03 54 50 48 02 11 25 27 20 05 61 14 37 31 23 16 29 36 06 03
03 54 50 48 02 11 25 27 20 05 61 14 37 31 23 16 29 36 06 03 41 11
11 25 27 20 05 61 14 37 31 23 16 29 36 06 03 41 11 30 50 14
14 37 31 23 16 29 36 06 03 41 11 30 50 14 53 37
37 31 23 16 29 36 06 03 41 11 30 50 14 53 37 28 19 52 20 51 40 63 47 42 34 22 19
19 52 20 51 40 63 47 42 34 22 19 18 11 50 51
51 40 63 47 42 34 22 19 18 11 50 51 20 36 21 58 44 03 06 15 51
51 20 36 21 58 44 03 06 15 51 18 07 32 50 16 53 61 28 36
36 21 58 44 03 06 15 51 18 07 32 50 16 53 61 28 36 08 53
53 61 28 36 08 53 48 19 19
19 19 34 20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19
19 34 20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19 11 36 28 45 40 20
20 59 12 30 35 53 47 56 02 04 08 38 39 50 55 19 11 36 28 45 40 20 31 21 23 05 07 28
28 45 40 20 31 21 23 05 07 28 32 37 57 15 16 03 36 14 19 13 12 63 56 29 19
19 13 12 63 56 29 19 51 06 26 20 11 33 13
19 19 33 26 56 40 26
26 56 40 26 36 09 23 42 01 14 54 21 33 05 11 51 10 17 26
26 36 09 23 42 01 14 54 21 33 05 11 51 10 17 26 29 43 48 20 46 27 23
20 46 27 23 20 30 55 56 36 04 37 25 01 18 05 10 42 40 39 23

I am interested in L17-L19 and above mostly since they are primarily responsible for 26 L=17, and any possible relationship or pattern concerning these pairs of symbols or relationship between the pairs and the same pairs in other observations. I took out the first and last length because there is no pair to look at. I plan on casting the message into different widths to look at the repeats by rows also and maybe do some other stuff but it is the work week so I will pick at it. Have fun.

I think that all the genuine lengths (including the interesting L17,L18 and L19) represent the gap between the first symbol in a pair of identical symbols, and the last symbol in the next pair.

Obviously a length starts when you pass over the first symbol in a pair (the pair that was creating the previous length), and the end of the new length is the second symbol from the next pair by definition (of the end of a unique sequence). And the gap is in-between those.

Which is a rather odd pattern. Might just be coincidence. But the high count of L17-L19 is quite distinctive. I can’t think of a simple non-cipher process, like trying to avoid a repeat, that would lead to such a relationship.

Certainly my computer randomised z340s never (yet) show anything like this.

Certainly my computer randomised z340s never (yet) show anything like this.

doranchak calculated L17=26 to happen 1 in 400,000,000 shuffles. On the other hand, the cycles have a very strong signature, and the 408 would likely be able to beat these odds in some way.

Within the hypothesis of sequential homophonic substitution + 25% random homophone selection the odds increase to about 1 in 100 for L17=26.