I have a new shuffle spreadsheet, where I can select or exclude any of the positions for regional shuffle tests.
Looks like you are doing some awesome work Smokie.
I have been considering the grille but i can’t not see any valid or worthwhile input that i can offer.
The pure definition of the Grille is such that I can not see any way of efficiently attacking it.
I have been looking through the ACA Cipher lists looking for potential ciphers that are not main stream yet show a similar trait – BTW no luck so far.Regards
Bart
Thanks. I doubt that it is a grille. I could not re-create the period 19 bigram stats with a grille. I have been scouring classical cryptography too, and have not found any ciphers that can do that except route transposition or bifid, unless it is a statistical anomaly.
I am working on route transposition, and currently think that maybe a handful of nulls ( 16 +/- ), which cause misalignment of plaintext after un-transposition, and a handful of polyphones, are the problem.
I am working on route transposition, and currently think that maybe a handful of nulls ( 16 +/- ), which cause misalignment of plaintext after un-transposition, and a handful of polyphones, are the problem.
I really like your methodic way of working on the cipher! Sometimes I think that Z was very lazy and had problems with long periods of concentration. So I do not believe that he used something like Vigenère or double columnar transposition. I also believe he purposed the cipher to be broken. Some kind of route transposition would kill two birds with one stone: a cipher which is harder to crack than z408 but still solvable. As I mentioned in my documentation I consider the possibility that he wrote the plaintext in a 17×20 grid, cut it into pieces, rearranged it and applied a homophonic substitution. A route transposition would have made it even more simple for him.
As always the problem is the huge amount of possibilities. I’ve implemented some route transpositions as well as ‘cut and rearrange’ cipher parts. Whenever I have a new idea I implement it, but I think it would be really helpful to develop some kind of an automatic route generation algorithm. But atm I don’t have any idea how to achieve that.
Thanks!
I was playing around with re-drafting the 340 into different shapes, and found that if in 20 x 17, and read the message vertically, the repeats can be either period 16 or 18, depending on which direction you read. With 17 x 20, the period 19 repeats are period 15 if the message is mirrored. So, the period for the repeats could be 15, 16, 18 or 19, among other, larger periods. The other fact that makes this attractive to me is that cryptography books of the time showed route transposition always with examples of diagonal inscription.
Straightforward untransposing doesn’t work. But seeing that the repeats could be at periods 16 or 18 would mean that Zodiac could have taken an extra transposition step. So I have an idea for a new project to try to detect nulls transcribed at regular intervals, thinking that Zodiac may have filled an incomplete rectangle at some intermediate transposition step. This would cause misalignments, and maybe a shift from period 38 to period 39 in the bottom half of the message.
Ain’t nothing else working, so here is the tentative plan ( not necessarily in this order ):
1. Delete sets of symbols at regular intervals to find what start positions and intervals increase the count of period 19, 38, 57 etc. repeats. Or perhaps period 18, 36, 54 repeats.
2. Use shuffle testing on the regular interval sets to see if shuffling has a propensity to destroy or create new repeats.
3. Maybe incorporate some of my unfinished cycle analysis, to see if the cycles have a tendency to end at some of these positions.
4. With a narrowed down the list of regular interval sets, look to see if they could cause a period shift that could cause the pivots.
5. If some of the sets look promising, delete those symbols and untranspose. And flip horizontally. Try to solve.
6. Possibly expand one or two suspected polyphones ( e.g. the + ).
It may take a while, so don’t hold your breath waiting for the results. But this is the direction that I want to take.
nice work Smokie.. good thought patterns in your above post.. I am still here watching and learning as you go along.
cheers
Just got back from a long vacation and hope to get caught up on all the posts soon.
But I was thinking about the biggest problem of the "generate a bunch of test ciphers" approach: Which cipher schemes to test next? At the moment it is a really blind search, since there are too many to pick from. Once I pick one, it takes a long time to generate the ciphers and then to move on to the next one.
Z340 has several unusual and seemingly improbable qualities. The pivots, the periodic bigram repeats, even/odd bigram bias, prime phobia, etc. We don’t have a good sense yet of which cipher schemes are more likely to generate such phenomena.
So I’m considering a new experiment. First, get a big pile of plaintext messages to draw from (such as from Project Gutenberg). Select a million of them at random. Then measure the pivots, periodic bigram repeats, even/odd bias, etc. of all the plaintexts. Calculate the averages and standard deviations for them all. These will serve as the reference (or control) of the experiment.
Then, get a crypto package, such as https://github.com/WilliamMason/crypto-py , which has implementations for very many cipher types. For each cipher type, encode a million random plaintexts with random keys and settings. Then repeat the measurements of pivots, periodic bigram repeats, even/odd bias, etc. of the ciphers. Compare the measurements to the reference (control) data.
With that data, we can then work out which cipher types are more likely to make pivots appear, or more likely to produce even/odd bigram bias, or more likely to increase periodic bigrams, etc.
I think this data will be very helpful to guide our searches, especially if all the standard pen-and-paper cipher types are covered by the crypto package. The results may also help determine if the scheme used for Z340 is truly unique/homemade (or completely bogus). So, I’m seriously considering beginning this experiment soon.
Just got back from a long vacation and hope to get caught up on all the posts soon.
But I was thinking about the biggest problem of the "generate a bunch of test ciphers" approach: Which cipher schemes to test next? At the moment it is a really blind search, since there are too many to pick from. Once I pick one, it takes a long time to generate the ciphers and then to move on to the next one.
Z340 has several unusual and seemingly improbable qualities. The pivots, the periodic bigram repeats, even/odd bigram bias, prime phobia, etc. We don’t have a good sense yet of which cipher schemes are more likely to generate such phenomena.
So I’m considering a new experiment. First, get a big pile of plaintext messages to draw from (such as from Project Gutenberg). Select a million of them at random. Then measure the pivots, periodic bigram repeats, even/odd bias, etc. of all the plaintexts. Calculate the averages and standard deviations for them all. These will serve as the reference (or control) of the experiment.
Then, get a crypto package, such as https://github.com/WilliamMason/crypto-py , which has implementations for very many cipher types. For each cipher type, encode a million random plaintexts with random keys and settings. Then repeat the measurements of pivots, periodic bigram repeats, even/odd bias, etc. of the ciphers. Compare the measurements to the reference (control) data.
With that data, we can then work out which cipher types are more likely to make pivots appear, or more likely to produce even/odd bigram bias, or more likely to increase periodic bigrams, etc.
I think this data will be very helpful to guide our searches, especially if all the standard pen-and-paper cipher types are covered by the crypto package. The results may also help determine if the scheme used for Z340 is truly unique/homemade (or completely bogus). So, I’m seriously considering beginning this experiment soon.
That is a very good idea.
I have to take a vacation from the 340 for a while, but will be here periodically.
In extension to the cipher library from bion that David posted (looks like you had a great trip BTW)
here is a list and statistical metrics for most ACA reference ciphers
http://bionsgadgets.appspot.com/gadget_ … stats.html
These may help some of you guys to get some insight with out having to number crunch yet.
Also there is a good ACA cipher site here
http://www.cryptoprograms.com/
select the cipher on the side and then make sure you check the description box to get very good information about the cipher.
I have been messing around with amsco cipher which is a type of incomplete columnar cipher.
The little testing i have done seems to show a imbalanced Odd even bigram counts. i hope to show with more testing that it has a similar odd phobia as z340 has.
I too am have a bit of time out solving some smaller transposition ciphers, getting my own code library up to date and reflect on z340.
Regards
Bart
That is a very good idea.
I have to take a vacation from the 340 for a while, but will be here periodically.
Enjoy your break, and I hope you return to the 340 with some renewed motivation!
In extension to the cipher library from bion that David posted (looks like you had a great trip BTW)
here is a list and statistical metrics for most ACA reference ciphers
http://bionsgadgets.appspot.com/gadget_ … stats.html
These may help some of you guys to get some insight with out having to number crunch yet.Also there is a good ACA cipher site here
http://www.cryptoprograms.com/
select the cipher on the side and then make sure you check the description box to get very good information about the cipher.I have been messing around with amsco cipher which is a type of incomplete columnar cipher.
The little testing i have done seems to show a imbalanced Odd even bigram counts. i hope to show with more testing that it has a similar odd phobia as z340 has.I too am have a bit of time out solving some smaller transposition ciphers, getting my own code library up to date and reflect on z340.
Regards
Bart
Thanks for posting those resources – they are very useful. AMSCO cipher looks interesting especially with regard to odd phobia.
Thanks for posting those resources – they are very useful. AMSCO cipher looks interesting especially with regard to odd phobia.
I only have done a small number of ciphers so far so too little to be of any statistical significance.
I hope to clarify it tonight and post back
Bart: There has been prior discussion about AMSCO in this thread, and perhaps others. But the cipher was not fully explored. Try a search for "AMSCO" in this thread. At first I thought that it was route transposition, with a combination of monoliteral and polyliteral transposition. But it is a keyed columnar transposition with a combination of monoliteral and polyliteral transposition. Perhaps Zodiac took inspiration from the AMSCO cipher and created an original of his own? Thanks for checking it out.
Here is a direct link to the prior AMSCO discussion:
http://zodiackillersite.com/viewtopic.php?p=45069
The psychology behind creating an unsolvable cipher is interesting. There’s no real reward there–it requires no special genius to make a one-time pad.
Just as a hypothesis, let’s assume his intention is to create a cipher that is the same, but harder. Let’s assume that he begins with basically the same cipher as the 408. How would he change it specifically to fool solvers? He knows people are looking for double letters and repeating strings. A very easy way to fake these is to rearrange the columns. Just as bad solvers lean heavily on anagramming, perhaps bad cipher constructors also lean on anagramming (maybe or maybe not underestimating just how difficult it becomes to solve). By replicating a random vertical string on the horizontal (RJI[], b.cV), you create the sense of a meaningful pattern, but perhaps it’s an intentional red herring. The double ++ and backwards P, in each quadrant–perhaps those column arrangements were chosen as red herrings as well. It’s notable that there are no double letters in the columns that make up the pivots. If he is rearranging to create the doubles and rearranging to create the pivots, this makes sense, because the column order of the pivots is fixed; he would have to make the doubles with the remaining columns.
One reason this hypothesis interests me is the weird pseudo "zodiac" signature at the end. It’s impossible not to notice it, but at the same time, why use a K? Why transpose A and I? Sure, he misspells things, but not "zodiac". I wonder though, if it is evidence of a crime of opportunity. Z-O-triangle-A are in the fixed column order of the b.cV pivot. Perhaps he saw that and couldn’t resist putting the I-K after it, just working with the remaining letters available. Not perfect, but an unmistakable sign nonetheless. In particular it would explain to me the transposition of the A and the I.
This idea is appealing, because it’s so easy to do. As an experiment, I made a similar rearrangement with the first 20 lines of the 408. It took longer to cut out the columns than to rearrange them into pivots. The downside is the impossible number of permutations without a key. Maybe there are other pieces of information or hypotheses that can help cut down the permutations. The pivots and doubles at least give a suggestion of columns that are in the wrong order. It’s not much to start with, but maybe it’s a reasonable place to start for building test ciphers for comparison.
That’s a very interesting exercise. I liked your example of pivot production. It made me wonder how many different ways there are to produce them that way from a given cipher text.
The reordering of columns could explain the pivots, and also why we don’t see too many repeating bigrams at period 1. If we assume the pivots were created by reordering the columns, then we have to answer the next question: Where did the period 19 / period 15 bigrams come from? Quick summary: There are 25 repeating bigrams at period 1, 37 at period 19, and 41 at period 15 (when first mirroring the ciphertext horizontally).
http://zodiackillerciphers.com/wiki/ind … ngram_bias
http://zodiackillerciphers.com/period-19-bigrams/
The period 15 bigrams seem particularly improbable: A periodic bigram count of 41 only occurs in about 1 in 12821 random shuffles of Z340. The pivots are even more improbable, but if the cipher author shuffled columns around, then wouldn’t that disturb the periodic bigrams as well?
I don’t know enough about the probabilities of the period bigrams. One possibility is that the homophonic substitution key switches at line 11. That’s a big assumption, of course, but another very simple change for him to make. If it’s two keys, then the period bigrams seems like randomness (I suspect). There would be 9 period 1 bigrams in section one and just 1 in section two. 9 period 19 bigrams in section one, 6 in section two. 7 period 15 bigrams in section one, and 8 in section two, if my counting is correct. The sample with 170 characters becomes very small, but those numbers seem less indicative of a route transposition–but again, others would be able to say better than I.
I believe the "two key" hypothesis has been tested by several people, by feeding both halves separately into auto solvers such as zkdecrypto and azdecrypt. Nothing turned up from it, but maybe 170 characters are too few to guarantee the solution would be found. We need to create some test ciphers to get a handle on this, and to measure the behavior of the bigrams.
