Homophonic substitution

[smokie treats]

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.

[doranchak]

Here is a direct link to the prior AMSCO discussion:

http://zodiackillersite.com/viewtopic.php?p=45069

[versaceversace]

408 column shifted.jpg

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.

[doranchak]

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/

viewtopic.php?p=46618#p46618

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?

[versaceversace]

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.

[doranchak]

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.

[versaceversace]

Yes, I've put the halves through zdecrypto as well. And surely with all the quadrant work, a solution would've been found if that's all that was done. But if there are two keys, plus columns are rearranged after the enciphering, it's no surprise that zdecrypto turned up nothing. In fact, it seems borderline impossible. But yes, if test ciphers can reliably show the same bigram patterns, that could at least give a focus to the work. Is there a best way to create/share test ciphers on this board?

[doranchak]

Trying out all the possible column rearrangements would be one hell of an undertaking. There's only, oh, 355,687,428,096,000 of them!

If you have test ciphers, a good place to post them might be this thread of documented ideas:

viewtopic.php?f=81&t=3093

I've been trying to track different schemes from here (but I think it is a little out of date):

http://zodiackillerciphers.com/wiki/ind ... variations

So, I could link to your post from there to keep it organized with the rest. I also collect the wide variety of test ciphers here, including measurements that compare them to aspects of Z340:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

[Mr lowe]

Hi Mr doranchak ..
when you get time can you drop your Hypothesis Testing: Overview and Tool onto the start of this homophonic substitution thread with all the other programs ..it may even be time to package them all up and drop them on to the board index? for ease of finding.
i have been busy of late trying to organise a holiday ... going to India for a few weeks so have not had time to do to much.. i still have to go back and see what that last column scytale i put up divulged a few pages back . it did have a few words and phrases . it had a series of 1 2 1 2 3 4 3 4 , in it which i think is very very rare, i need to go back and see if it was a pivot. (not sure why no one else thought a sequence like that important). something like that could be the end of a code filler or junk .. moving on i ask this question... has anyone bothered to make a real scytale to see how they actually work? they have lots of unique values and i feel its something a computer program does not give you. Again i reiterate i have not been able to use an online scytale programme to emulate a hand made period 19 of the 340..

cheers all keep at it

[Largo]

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.

...

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 agree with you and no one can deny the many odd things in z340 (pivots, even/odd, prime phobia and so on). Like others I spent a lot of time to find out which cipher methods can produce these characteristics. But there is still a chance that some (or even all) of them could be coincidences (doubt it). So here is a little story:

I like to listen a german Podcast called "Alpha Centauri" which is all about astrophysics. An episode about the search of dark matter begins with a story about a man who is searching for something in a dark night below a street lamp. A policeman comes around and asks the man what he is searching for. The man answers: "I am searching my car keys". The policeman starts to help him in his search for the keys. Half an hour later he asks: "Are you sure that you have lost your keys right here?". The man answers: "No, I think I have lost them somewhere else but this is the only illuminated place".

My approach is "what would I have done if I created a cipher which has been cracked in a couple of days?". Which strategies could lead to a harder but still solvable cipher? Well, this approach will become totally useless if he never intended to produce a crackable cipher.
I think your approach is the more sophicsticated one and the one which has the better chances to lead to a solution. I look forward for your results!

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.

I had tested a couple of columnar transpositions in the past. I agree with you that this could explain a lot of the characteristics of z340 and it would be a good way to disturb double letters and repeating strings. If he did it that way I am sure that he used a keyword or a pattern since I still believe he wanted the cipher to be solved. But maybe he used a „home grown“ idea and did not realized how complicated it can be to solve it. Another way to fool solvers would be to simply skip all repeating letters like that:

Code: Select all

Plaintext:
THISSHORTTESTSHOWSSKIPPINGDOUBLELETTERS

Skipped version:
THISORTESTSHOWSKIPINGDOUBLELETERS


Code: Select all

Another idea which takes the „plus“-symbols into account:
IHADNOSUCCESSSOIKEEPTRYING
IHADNOSUC+ES++OIKE+PTRYING


The plus means „repeat the last letter“.

I have tested a lot of ideas like these. Obviously without success

It took longer to cut out the columns than to rearrange them into pivots.

This would implicate that he had to rewrite the whole letter (the scan of z340 shows an intact one). Personally I think Zodiac was very lazy. He could have mailed the whole z408 three times to the newspapers. The reason for cutting it into pieces was maybe just a lack of effort and he did’nt want to write the cipher three times.
If this is the case then I think he did the „cut and rearrange“ trick with the plaintext before applying the homophonic substitution.

What do you think?