There is a double entry in the wiki:
If you highlight all occurrences of certain symbols, they seem to avoid the middle of the cipher text. (Source: Jarlve)
Some symbols are exclusive to the first 6 and last 6 rows. An unusual number of symbols are missing from the middle 8 rows. (Source: smokie treats)
Oops! I seem to be losing track of all the observations. I went ahead and merged them together.
Okay…check this out:
Rows 1-6, followed by rows 15-20:
HERabcdVPeIfLTGgh Nb+BjkOlDWYmnoKpq BrstM+UZGWjqLkuHJ SbbvdcwoVxbO++RKg yzM+u12hI7FP+34e5 bwRdFcO-ohCeFagDj rBXfos4zCEaVUZ7-+ ItmxuBKjObdmpMQGg RtT+Lf#Cn+FcWBIqL ++qWCuWtPOSHT5jqb IFehWnv1ByYOBo-Ct aMDHNbeSuZOwAIK8+Perfect 5-Cycles:
VPDrsVPDrsVPD (72) PDrsUPDrsUPD (56) PDrsxPDrsxPD (56) PDrszPDrszPD (56) PDrs7PDrs7PD (56) PDrUxPDrUxPD (56) PDrU7PDrU7PD (56) PDrz7PDrz7PD (56) PDsUxPDsUxPD (56) PDsU7PDsU7PD (56) PDsz7PDsz7PD (56) PrsUxPrsUxP (42) PrsU7PrsU7P (42) Prsz7Prsz7P (42) GkrsUGkrsUG (42) GDrsUGDrsUGD (56) DrsUvDrsUvD (42) DrsUxDrsUxD (42) DrsUyDrsUyD (42) DrsU1DrsU1D (42) DrsU7DrsU7D (42) DrsU5DrsU5D (42) DrsvyDrsvyD (42) Drsv1Drsv1D (42) DrsxyDrsxyD (42) Drsx1Drsx1D (42) Drsx5Drsx5D (42) Drsz1Drsz1D (42) Drsz7Drsz7D (42) Drsz5Drsz5D (42) Drs75Drs75D (42) Drs45Drs45D (42) DrUvyDrUvyD (42) DrUv1DrUv1D (42) DrUxyDrUxyD (42) DrUx1DrUx1D (42) DrUx5DrUx5D (42) DrU75DrU75D (42) Drz75Drz75D (42) DsUvyDsUvyD (42) DsUv1DsUv1D (42) DsUxyDsUxyD (42) DsUx1DsUx1D (42) DsUx5DsUx5D (42) DsU75DsU75D (42) Dsz75Dsz75D (42) rsUvyrsUvy (30) rsUv1rsUv1 (30) rsUxyrsUxy (30) rsUx1rsUx1 (30) rsUx5rsUx5 (30) rsU75rsU75 (30) rsz75rsz75 (30)Perfect 6-Cycles:
PDrsUxPDrsUxPD (72) PDrsU7PDrsU7PD (72) PDrsz7PDrsz7PD (72) DrsUvyDrsUvyD (56) DrsUv1DrsUv1D (56) DrsUxyDrsUxyD (56) DrsUx1DrsUx1D (56) DrsUx5DrsUx5D (56) DrsU75DrsU75D (56) Drsz75Drsz75D (56)I haven’t quite understood the scoring yet, but compared to the unmodified z340 it seems amazing to me
Excuse my ignorance, but what is a perfect 5-cycle? The patterns looks highly fascinating but i grasp to understand what you did there 
Is it this stuff? viewtopic.php?f=81&t=3616 (Cycle types thread)
My Z340 widget for the two-ciphers hypothesis:
Thank you for your ciphers smokie. Are you sure that 2 keys sufficiently diffuse bigrams?
That’s what I came up with. I made smokie 64 last month, and had to select a chunk of the book Brave New World that would do it.
When I needed a new key for testing, I made it relatively easy and used a trick. It also works very well if you work with paper and pencil. That’s how it works:
As you can see, I left the order of the cipher symbols unchanged. Only the plain text letters were swapped in their order. Of course, this has an effect on the efficiency of the key, since the result is no longer "smooth". It would be interesting to know how this affects the cycles of a cake cipher. And the frequent occurrence of the "+"symbol could also be explained by this, since a correlation could take place depending on the key.
I did something similar last month where I transposed and encoded 768 messages from the book Brave New World. First I transposed at period 20, then I used a tabula recta to encode the top / bottom and a different shift for the middle. I even checked all of the shift differentials to find out how to come up with a middle section of 8 rows that had only four unique symbol positions. EDIT: Then I encoded homophonic. There is a very detailed explanation about the experiment starting at the top post here:
viewtopic.php?f=81&t=3196&start=750
It seems like so much longer than a month ago.
Excuse my ignorance, but what is a perfect 5-cycle? The patterns looks highly fascinating but i grasp to understand what you did there
Here is an illustration. Largo’s modified cipher:
Highlight all occurrences of the symbols V, P, D, r and s:
Read them out in order, and you get: VPDrs VPDrs VPD
It is a perfectly alternating sequence, potentially of homophones for a single plaintext letter. Z408 was filled with such patterns.
borkky:
You can find this feature in Jalve’s "AZDecrypt" at menu "Stats 2".
Okay…check this out:
Rows 1-6, followed by rows 15-20:
I had the same idea, but these cycles may be an artifact of smaller pieces of cipher, hard to say. The first half of the 340 also has many of these. The scoring is based on the ioc formula: cycle_alternations*(cycle_alternations-1).
If different keys were used alternately, this could be the cause of incomplete but not completely absent cycling. Has anyone ever done some tests before? For example, rows 1-6 and 15-20 with key A, then rows 7-14 encoded with key B and check the cycling? If not, I’d like to put that on my todo list.
Good idea. Should be easy to check since there are only 2^20 row combinations for 2 keys.
I’m bored right now, but I don’t feel like programming or analyzing any complicated statistics. So I look at the connections of the different observations again. I noticed the following:
What is characteristic for homophonic encryption? Right! As a rule, the first rows of a the encryption usually contain the fewest repetitions of characters from a statistical point of view. This is especially true if a cyclical encryption was used. z408 was an exception, since the plaintext letter "L" appeared relatively often and the key was not chosen well. This is also an indication that Zodiac chose his key based on the letter frequency of general English texts, not those of the plaintext of z408.
Let’s say the following three assumptions are correct:
– Zodiac was able to learn and he improved his key(s)
– Zodiac has used several keys in z340.
– The observation that the upper 6, the middle 8 and the lower 6 rows consist of at least two keys is correct.
Let’s take a look at the following picture (source: http://zodiackillerciphers.com/images/z … olumns.jpg)
It is noticeable that this actually fits together. If several keys have been used, the observations of the character repetitions within the individual rows could be an indication of this.
What do you think?
Hi Largo.
What I tried to do here:
viewtopic.php?f=81&t=3196&start=750
is basically the same as this:
I tried to make a message that would have a P20 spike with transposition at period 20, about 39 symbol positions unique to top and bottom 6 rows, and only four symbol positions unique to the middle 8 rows. "Cake" 6-8-6.
It was very difficult to transpose the plaintext at P20 and use two different keys to get a spike at P20. Assuming, of course, that Zodiac transposed the plaintext before encoding. I had to take an entire book and find the chunk of 340 plaintext that would do it the most. It may be that more than one key was used and the P19 spike is a phantom.
The P20 repeats for smokie 64 were mostly within their 6-8-6 regions, meaning that there could be a P20 bigram in the top 6, but the repeat would occur in the top 6 or bottom 6. Or there would be P20 bigram in the middle 8, but the repeat would also be in the middle 8. There were few that crossed over from one region into the other. And with the 340, the P19 bigram repeats occur in all regions ( right? someone check me on this ).
It was easy to make a message that had a lot of symbols unique to the top and bottom 6 rows.
But I was unable to make a message that only had a few symbols unique to the middle 8 rows. The reason is because with homophonic encoding, a lot of symbols appeared in the middle 8 rows and did not appear in the top and bottom 6 rows. As different from the 340, where only two symbols, or a total of four symbol positions are unique to the middle 8 rows.
That is why I think that one possibility is not two different keys, but that Zodiac selected his symbols from the homophonic groups of symbols that map to the individual plaintext by some pattern that would cause the regional bias.
That’s just my two cents, and I could be wrong.
What if the reason the symbols are sparse in the middle but are lush at the top and come back in the bottom is the following:
Instead of a key that looks like this:
E = ABCDEABCDEABCDE (cyclic)
it looks like this:
E = ABCDEFGHGFEDCBA
i.e. palindromic
?
We really need a webtoy that has both Ciphertext and Key, shown side by side.
What if the reason the symbols are sparse in the middle but are lush at the top and come back in the bottom is the following:
Instead of a key that looks like this:
E = ABCDEABCDEABCDE (cyclic)
it looks like this:
E = ABCDEFGHGFEDCBA
i.e. palindromic
?
I agree that something like that could be possible.
What if the reason the symbols are sparse in the middle but are lush at the top and come back in the bottom is the following:
Instead of a key that looks like this:
E = ABCDEABCDEABCDE (cyclic)
it looks like this:
E = ABCDEFGHGFEDCBA
i.e. palindromic
?
I agree that something like that could be possible.
It will be very hard to have a say about it as with so many symbols many many millions of cycles are to be considered and such things are bound to happen.
Here are a few of the best palindromic cycles in the 340:
5-symbol: H>OYHOO>XOYOYOX>OOHYO>HO: 11 H>OYHOO>;OYOYO;>OOHYO>HO;: 10.08 H>H35>5;555;5>53H>H;: 9 6-symbol: H>YH3>;Y@Y;>3HY>H;: 8 H>YH3>XY@YX>3HY>H: 8 H>YH3>XYAYX>3HY>HA: 8 >Yf3>XfY@YfX>3fY>: 8 >Yf3>XfYAYfX>3fY>A: 8
It is noticeable that this actually fits together. If several keys have been used, the observations of the character repetitions within the individual rows could be an indication of this.
What do you think?
I do not recommend to use repeats per row to gauge multiple keys. Your vision is then limited to the length of these rows. Rows 11, 12 and 13 are unlikely to be the start of a new key:
– Rows 1, 2 and 3 of the 340 have 41 unique symbols and ioc of 0.0078. Row 2 has 1 symbol that repeats from row 1.
– Rows 11, 12 and 13 of the 340 have 37 unique symbols and ioc of 0.0149. Row 12 has 7 symbols that repeat from row 11! These are: "+R5|BTM".
It was very difficult to transpose the plaintext at P20 and use two different keys to get a spike at P20. Assuming, of course, that Zodiac transposed the plaintext before encoding. I had to take an entire book and find the chunk of 340 plaintext that would do it the most.
My results speak against that. I suspect that your ciphertexts have a low ioc and that this diminishes the bigram repeats a whole lot.
I would be happy if someone could make a few more test ciphers that are in line with borkky’s hypothesis
Here you are:
Largo_Sing_Along
8z0Oap:sI7n;WGkRN 2XvArxKhPlzMS8QVO nL9:sJ4t3iZNabfBo uVUx;AF38isL14qyN lwuMk2erx8o07sVLd :=r2vpy8e+aCGxTY0 a5K-p7:qPaRdw0PHM Vit1o3ZGyTFmSIsji RmbX=uYvZwBp+T;Lj Ohn:cNS3;yPFQWfA- 0EkZJWUePFxF9T34J b;z+Q:VA0LFwCyNBP 0UhtDUePFOMonXlaa zq2U0pmvaeuuVKDx9 awSVgLiucj:37QyCP L0rd5pmGw8iVHFtp= Fox3G1jvMWq9SLPY4 FbI+QwCh57OZVpR0: VRveZTxkuV;3rIXz5 EB=SoF4WfYb1uuOmw
My workstation has been running this for 2 days now without any interesting result. Largo, I am a bit worried that your cipher is harder than the 340, it has 66 symbols and a low ioc, which diminishes internal structure. Please tell me how the keys are distributed so that I can find out if AZdecrypt can crack this cipher when the distribution is known.
