Zodiackillersite.com

Quick rundown:

The Zodiac 408 cipher is encoded with something that is called homophonic substitution (suppression of frequencies, multiple substitutions per plaintext letter). This means that every letter in the plaintext could be assigned more than 1 substitution. For example the letter E in the plaintext could be given 7 unique substitutions (homophones, symbols) in the ciphertext. These substitutions can be used randomly or sequentially (cycles). In the Zodiac 408 cipher the substitutions are used mostly sequentially with increasing randomness nearing the end of the cipher (mostly the third part).

The general consensus is that the Zodiac 340 cipher is also encoded with homophonic substitution, though it is not nearly as sequential as the Zodiac 408 cipher. Clearly something more must be going on because otherwise the cipher would have been solved ages ago.

More information can be found at: http://zodiackillerciphers.com/wiki/ind ... =Main_Page

Cycle types:

A while ago moonrock suggested many different cycle types, which refers to the order in which the substitutions are used. Perhaps some of these cycle systems could help us classify more precisely what is going on with the Zodiac 340 cipher.

1. The perfect cycle, which has substitutions arranged in an unchanging pattern throughout the entire cipher: 12345 - 12345 - 12345 - 12345. (moonrock)
2. The increasingly random cycle, which has substitutions start off in an organized cycle and gradually become random: 12345 - 12345 - 12435 - 24153. (moonrock)
3. The decreasingly random cycle, which is the opposite of the increasingly random cycle: 24153 - 12435 - 12345 - 12345. (moonrock)
4. The random cycle, which has the substitutions arranged in random order: 32415 - 12543 - 41352 - 53124. (moonrock)
5. The concurrent cycle, which has two separate cycles existing at the same time for a single substitution; 1 and 5 cycling, and 2, 3, and 4 cycling in the following example: 12345 - 21354 - 23154 - 23415. (moonrock)
6. The palindromic cycle, which has the substitutions arranged in an order that reads the same forward and backward: 11211 - 11211 - 11211, 12321 - 12321 - 12321, and 123454321. (moonrock)
7. The inverted cycle, which has a uniform cycle inverted to be the opposite of what it was beyond a certain point: 12345 - 12345 - 54321 - 54321, and 11211 - 11211 - 22122 - 22122. The former example is an example of a perfect cycle being inverted, which creates a palindrome, and the latter example is of a palindromic cycle being inverted. (moonrock)
8. The shortened cycle, which has a cycle decrease in length as the ciphertext progresses: 12345 - 12345 - 1234 - 1234 - 123 - 123. (moonrock)
9. The lengthened cycle, which is the opposite of the shortened cycle: 123 - 123 - 1234 - 1234 - 12345 - 12345. (moonrock)
10. The regional cycle, which restricts substitutions to or from specific regions, or areas, of the ciphertext; this restriction typically manifests as either a restriction to specific rows or to specific columns, and, if used exclusively, is the equivalent of a series of simple substitutions. (moonrock)
11. The semi-regional cycle, which has the frequency of substitutions fluctuate between different regions, or areas, of the ciphertext in a similar way to regional cycling. When regional and semi-regional cycles are combined, it increases their level of security. Both regional and semi-regional cycles are capable of being accompanied by non-regional assignment of substitutions. (moonrock)
12. The sequential cycle, which is when one type of cycle is followed by another type of cycle: 12345 - 12345 - 123454321 - 1234321 - 12321; in this example, a perfect cycle changes to a palindromic cycle, which is then shortened. (moonrock)
13. The anti cycle, which is exactly the opposite of the perfect cycle: 11111 - 22222 - 33333 - 44444 - 55555. (Jarlve) viewtopic.php?f=81&t=3599
14. The offset cycle, which offsets its repeating pattern in a systematic way: 12345 - 23451 - 34512 - 45123 - 51234. (Jarlve, smokie treats)
15. The pattern cycle, which repeats a pattern that includes at least one repeat of a substitution: 122333 - 122333 - 122333, 1233455 - 1233455 - 1233455. (doranchak, smokie treats)
16. The alternating length cycle, which alternates between shorter and longer substitution cycles: 12 - 1 - 12 - 1 - 12 - 1, 123 - 12 -123 - 12 - 123. (Jarlve)
17. The random shift cycle, which shifts the position at which the substitution is selected in its homophone group to the left or to the right randomly. (smokie treats)

Cycle type example ciphers:

jarlve_26percentrandomhomophones1: https://drive.google.com/open?id=1R3xdZ ... FmRnH75YV-
jarlve_anticycles1: https://drive.google.com/open?id=1Tkhae ... 3D_0tCzDXx
jarlve_palindromiccycles1: https://drive.google.com/open?id=1uZkyG ... fZ4SIRtzfO
jarlve_perfectcycles1: https://drive.google.com/open?id=19GDyl ... 9SV6a2-P6b
jarlve_randomshiftcycles: https://drive.google.com/open?id=1V-bEU ... DqcVVsBJT6
moonrock_regionalcycles1: https://drive.google.com/open?id=1b562G ... yvrl4uhP6-
moonrock_regionalcycles2: https://drive.google.com/open?id=15DcFQ ... wW_Vx4Xqhj
moonrock_regionalcycles3: https://drive.google.com/open?id=1naM0f ... w7BbLlCevk
smokie_palindromiccycles1: https://drive.google.com/open?id=1tp7L2 ... pyzt1NSBhs
smokie_palindromiccycles2: https://drive.google.com/open?id=1zzbW3 ... jMM4ahI-2-
smokie_shortenedcycles1: https://drive.google.com/open?id=1uNhEM ... _4bshnrX9K
smokie_shortenedcycles2: https://drive.google.com/open?id=1Hw6Pq ... tDhUaQYzeg

Let me know if you have more cycle types suggestions or examples and feel free to do any cycle busy work in this thread.

At the moment I'm working with z340 only from time to time and I'm mainly looking at diagonal transpositions related to the pivots. Sometimes I extend my C# cipher library. Since I have some personal things to take care of right now, I can unfortunately only follow the discussion about the cycles superficially. However, I am pleased that the team has apparently been strengthened with Moonrock.
I find the cycle analysis interesting, but I don't quite understand what you're aiming for. In my experience, AZDecrypt does not really care whether perfect cycles or completely random cycles were used. The solution for almost every test cipher is found anyway. How do you get closer to the solution with the knowledge gained?

my understanding from your work is that you would have cracked a homophonic substitution even if he, say, used 20 symbols for "e" or took a left to right message and encoded it vertically, right?

i'm not much help with the technical stuff, although i enjoy reading it, but i think psychologically you're looking at someone who used a trick or gimmick to make the cipher more difficult. what i understand of your findings thus far seem to back that up. he would likely mimic the 408 but do something weird (and simple) to make it harder to break. i like the idea that he used regions and perhaps the "+" symbol in the first half is the letter "e" and in the second half is the letter "t" or something similar.

we should remember that he had an advantage in his coded message that most don't have - he didn't have a recipient who needed to be able to decode it.

Largo wrote:I find the cycle analysis interesting, but I don't quite understand what you're aiming for. In my experience, AZDecrypt does not really care whether perfect cycles or completely random cycles were used. The solution for almost every test cipher is found anyway. How do you get closer to the solution with the knowledge gained?

Rule in/out different cycle types. I do not feel like I have to get closer to the solution with every piece of work on the 340. Since the problem is so complicated a better general understanding of how the 340 works is very beneficial. Example: understanding how the cycles work could lead to better cycle merges which in turn reduce the multiplicity of the cipher.

masootz wrote:perhaps the "+" symbol in the first half is the letter "e" and in the second half is the letter "t" or something similar.

My program, AZdecrypt has some excellent solvers that could easily deal with polyalphabetism like this. And if you are suggesting that the key changed half way through that is statistically unlikely. If not a hoax then the 340, in some way, or ways, is very complicated and something simple and weird does not cut it.

Largo wrote:I find the cycle analysis interesting, but I don't quite understand what you're aiming for. In my experience, AZDecrypt does not really care whether perfect cycles or completely random cycles were used. The solution for almost every test cipher is found anyway. How do you get closer to the solution with the knowledge gained?

I want to know what he did. I figure we don't know what we can do with any knowledge gained until we have the knowledge. Maybe we will gain knowledge and gain nothing, but we won't know unless we have the knowledge.

I have some ideas. Maybe instead of adding to the cycle type list, I think that, since we can find all of the consecutive alternations like ABABAB and score them, then we can also find, count and score other arrangements, like AABAAB or ABAABA as well. I am thinking about a new simple project. Break down all 1,953 two symbol combinations into strings and then into small chunks. Chunks of 2,3,4,5,6 etc symbols. Convert all symbols to A's and B's to keep things simple. Then start counting all of the different arrangements of A and B for each size chunk. And consecutive alternations of the chunks or consecutive alternations of different chunks. Maybe there will be some that have more than the others. Then shuffle the message a bunch of times and see if the shuffles have as many. We can score the ABABABs, so I wonder if there are other arrangements, that if we score the entire message, will score higher. Just two symbols for starters because even if some of the cycles are with three symbols, there will be a patterns with two. Then maybe with three later.

Jarlve wrote:I do not feel like I have to get closer to the solution with every piece of work on the 340. Since the problem is so complicated a better general understanding of how the 340 works is very beneficial.

smokie treats wrote:I want to know what he did. I figure we don't know what we can do with any knowledge gained until we have the knowledge. Maybe we will gain knowledge and gain nothing, but we won't know unless we have the knowledge.

I totally agree with you. That's why I like to experiment with paper and pencil and think about how Zodiac might have done it. Maybe the examination of cycles give you the right idea.

Jarlve wrote:Example: understanding how the cycles work could lead to better cycle merges which in turn reduce the multiplicity of the cipher.

And this is exactly where my doubts come into play: There are some ways in which phantom cycles appear that lead you in the wrong direction. Don't get me wrong... of course you have to try things out before you can evaluate them. And perhaps it is exactly this cycle analysis that leads to the final realization and thus to the solution. For my part, however, I see too many possible red herrings.

Here is an example, which would be quite easy to make with paper & pencil. I have not tried to imitate z340 (period spikes, pivots etc.). I haven't been working intensively on the cycles yet, so I only compared z340 with my test cipher. Both have some perfect 2,3 and 4 cycles. Although it is very easy to encode and decode by hand, I think it is impossible to solve without knowledge of the method. Anyway, I would be surprised and impressed if someone succeeded.

PS: I don't want to spread discontent, I'm just not convinced that investigating the cycles helps.

Code: Select all

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smokie treats wrote:I have some ideas. Maybe instead of adding to the cycle type list, I think that, since we can find all of the consecutive alternations like ABABAB and score them, then we can also find, count and score other arrangements, like AABAAB or ABAABA as well.

I implemented some code to do that a while ago. It takes a set of symbols then looks for the longest repeating sequences involving those symbols.

Here are the raw results:

http://zodiackillerciphers.com/longest- ... ng-cycles/

A few interesting examples:



I feel that cycle detection often leads to many spurious patterns, similar to searching for repeating fragments. You can see this by looking at my raw z408 results in the above link, which includes whether the cycle is true or not. It may take more finesse to separate out true cycles from false ones, such as by comparing the shapes of probability distributions, at least to answer the overall question of "does a particular rearrangement of the cipher produce more TRUE cycles than the others?" I found that arbitrary re-arrangements of rows of Z340 produces drastic increases in statistically significant cycles. Many such rearrangements are likely false positives.

Jarlve,

I agree with you regarding the different cycle types representing the sequences of homophones used. Some homophones have been used frequently in one part of the cipher, others only in other parts of the cipher. This indicates some sort of regional or semi-regional sequence type as the cycles had been broken up by purpose to complicate the cipher even more. It could also be the reason why the ZDK tool alone can't handle the cipher.

I currently do some runs with my (Python) FCCP model. In fact it works fine and due to its focus on certain regions of the ciper it works independently of any homophone cycles, too. Depending on the basic configuration, one run does between 200m and 2,000m variations on one region only, with approximately 500,000 to a million 'results' (e.g. words found of length >4). Most of those are duplicates, only a few hundred (200-300) words remain (plaintext). First I'll finish the runs on one sequence, a later goal will be to cross-check the results of different strings to each other. It's a good way to completely avoid the cycles..

QT

Largo wrote:And this is exactly where my doubts come into play: There are some ways in which phantom cycles appear that lead you in the wrong direction. Don't get me wrong... of course you have to try things out before you can evaluate them. And perhaps it is exactly this cycle analysis that leads to the final realization and thus to the solution. For my part, however, I see too many possible red herrings.

Here is an example, which would be quite easy to make with paper & pencil. I have not tried to imitate z340 (period spikes, pivots etc.). I haven't been working intensively on the cycles yet, so I only compared z340 with my test cipher. Both have some perfect 2,3 and 4 cycles. Although it is very easy to encode and decode by hand, I think it is impossible to solve without knowledge of the method. Anyway, I would be surprised and impressed if someone succeeded.

Different homophonic substitution keys for odd and even positions? If yes, then you underestimate the work that has been done so far.