Zodiackillersite.com

smokie treats wrote:Each symbol selection he would move to the left or right, but not repeat a symbol. If he was encoding E, then he didn't stay on one symbol and repeat. He would move to the left or right, but not stop, repeat, then change direction. That would be consistent with your idea that he was trying not to repeat symbols by row. Rather, instead of avoiding repeats by row, he kept shifting to the right or left, but didn't stop and make a period 1 repeat. It's just an idea, but could explain what you were talking about, not repeating symbols by row. Always shifting left or right would make it look like that. Just an idea, maybe too soon to say.

And by far the majority of 3 symbol cycles do not have any period 1 unigram repeats.

That is a good idea. It could go from left-to-right and then from right-to-left, alternating, this would create perfect palindromic cycles. I have created such a cipher and it scored very high on my palindromic test so it is not that. A random shift does not create enough cycles. And a left-to-right to right-to-left + random shift still scores high on my palindromic test. Perhaps you need to try a few ciphers.

doranchak wrote:

Jarlve wrote:@doranchak, you said that the cycles in the 340 are easily improved by simple manipulations, I was wondering if my cipher would have the same result.

Oh! OK. I should dust off my hillclimber and give it a try.

Sure, I would like to know if the 340 is special in that way.

doranchak wrote:To me an isomorphism is like an equivalence category.

Cycles DEFDEF and XYZXYZ are isomorphic because they can both be represented by the new sequence ABCABC.
So, multiple cycles can be included in this same "category" or isomorphism. It is a mathematic term that I'm probably not using correctly.

I just was not familiar with the term, ofcourse I understood that ABC could represent different groups of symbols, that is a given. Cycle ngram analysis is very interesting!

doranchak wrote:2) Additionally, when considering substrings, I recompute the isomorphism. For example, "BCABCAB" is converted back to "ABCABCA".

Our routine differs in this point. ABC could be BCA or CBA. ABA could be BAB, CBC, CAC, ACA or BCB right? I thought about it and concluded it complicates quickly and dismissed it for the sake of computing time and consistency.

Quicktrader wrote:This is way worse than Powerball lottery..one might focus on letters with less homophones, however, which could still make sense (e.g. finding the homophones for the letters YOU), just wanted to comment on that before someone starts to crash his calculation with some memory error

Try a hill climber. AZdecrypt has a cycle merge hill climber which works on the 408 and reduces it to a 1:1 substitution cipher. So bad that the 340 is more random...

Jarlve wrote:

smokie treats wrote:Each symbol selection he would move to the left or right, but not repeat a symbol. If he was encoding E, then he didn't stay on one symbol and repeat. He would move to the left or right, but not stop, repeat, then change direction. That would be consistent with your idea that he was trying not to repeat symbols by row. Rather, instead of avoiding repeats by row, he kept shifting to the right or left, but didn't stop and make a period 1 repeat. It's just an idea, but could explain what you were talking about, not repeating symbols by row. Always shifting left or right would make it look like that. Just an idea, maybe too soon to say.

And by far the majority of 3 symbol cycles do not have any period 1 unigram repeats.

That is a good idea. It could go from left-to-right and then from right-to-left, alternating, this would create perfect palindromic cycles. I have created such a cipher and it scored very high on my palindromic test so it is not that. A random shift does not create enough cycles. And a left-to-right to right-to-left + random shift still scores high on my palindromic test. Perhaps you need to try a few ciphers.

I am starting to make messages to see how my own cycle chunk ( "isomorphic pattern" ) test works. So far using 5-gram ABCBA for high frequency letters and 6-gram ABAABA for low frequency letters is creating a lot of false perfect cycles ABABAB in many instances. But I am only checking the first six positions in the pattern and I should change that.

The isomorphic pattern test could be applied in different ways. Encoding start position and direction, odd / even positions, etc.

Are you comfortable with the reliability of the test? Do you think that we need to try simple messages with designated patterns to see more about how the test works? You probably have already done that, I see some work on other messages above.

During the work week I get hasty and forget to be artful about making test messages that emulate as many of the 340 stats as possible. Would trying to match other 340 stats matter? Except that there should be about 63 symbols I think. Any other specific stats that you want, like cycle score, unigram repeat distances, etc.? It would be nice to be able to say that the test has been applied to a variety of different patterns, etc. and get a better feel for interpreting the results and tinker with the test. Maybe you guys already have that.

Do you want a random left right shift message to see if the highest scoring patterns mostly do not have P1 repeats?

I just had an idea. But before I start implementing, I would like to ask you for advice:
Let's say that in z340 the order of the columns was changed (e. g. with a keyword), but after substitution. Like most others, I believe that if there was a transposition, it was performed before the substitution. However, in this case it would still be possible because such a transposition only has a horizontal effect (I hope my description is not too confusing). Even observations like the high amount of rows without repeats would not be affected.
This could lead to the fact that in the final cipher you occasionally find cycles that are simply overlays / correlations of the original.
If I haven't said any total rubbish so far: Would a hillclimber or genetic algorithm find the original sequence if you use the cycle score as fitness function? Or would there be too many false positives? Has this been tried yet?

Another possibility would be that Zodiac did several steps in the substitution process. For example, he first substituted columns 1,5,9,10,11,13,16 and 17 from left to right, top to bottom. After that he substituted columns 2,3,4,6,7,8,12,14 and 15. Regarding to the cycles this would have the same effect like the first idea in this post. Well... in this case that can't be everything, because otherwise z340 would already be solved.

Largo, that idea sounds very plausible to me. In my transposition experiments, I found that certain rearrangements cause more bigrams/fragments to appear, and some cause better cycles to appear. But I don't think I've come across rearrangements that amplify both phenomena. I think it's definitely still worth exploring.

Allright, perhaps I can contribute to the cycle investigation in the next days. But I have one more question: does anyone have a piece of source code with an efficient way to find cycles? I don't want to reinvent the wheel =) I remember an older post from Jarlve, but unfortunately I can't find it any more. Thank you in advance!

I've been using brute force searches lately but the most efficient algorithm I'm aware of is REMOVE_HOMOPHONES mentioned in the King and Bahler paper.

Here's my old crappy Java implementation of it:

viewtopic.php?p=38871#p38871

But I would first recommend reading the paper, because it goes into detail about the speed efficiencies of their algorithm:

http://www.oranchak.com/king-homophonic-ciphers.pdf

Unfortunately, I think the algorithm gets easily confused when the cycles are imperfect.

Jarlve wrote:

doranchak wrote:

Jarlve wrote:@doranchak, you said that the cycles in the 340 are easily improved by simple manipulations, I was wondering if my cipher would have the same result.

Oh! OK. I should dust off my hillclimber and give it a try.

Sure, I would like to know if the 340 is special in that way.

Here are some row swaps that boost your m2 cycles measurement:

Code: Select all

01 +E7'D*!$3*.)HSF1$    04 ITC#X3>E14#]+H\LX
02 M&^*%Y6[ZU=($VQ,*    02 M&^*%Y6[ZU=($VQ,*
03 $R+>)*'/KG$(*8V$B    01 +E7'D*!$3*.)HSF1$
04 ITC#X3>E14#]+H\LX    03 $R+>)*'/KG$(*8V$B
05 -3*=$)*@II^1HQ$[>    06 !YP^<R\U:T,<?$IO;
06 !YP^<R\U:T,<?$IO;    07 #QK*5A"$9I0&CE*^.
07 #QK*5A"$9I0&CE*^.    05 -3*=$)*@II^1HQ$[>
08 +0D]M/JV$!K'*QR46    08 +0D]M/JV$!K'*QR46
09 )-4Z"MI$8H1?9'?E&    20 @K$*#$U:?RW2,Y*9E
10 7^A?(!-B)\V?Z+55A    10 7^A?(!-B)\V?Z+55A
11 *Q_M9KX+G_/$2-4%E    12 ]R!;SFL)_<*8"1I3&
12 ]R!;SFL)_<*8"1I3&    11 *Q_M9KX+G_/$2-4%E
13 #N=#HL';Y$O0Z*F@[    13 #N=#HL';Y$O0Z*F@[
14 S!X.V"':$*-^V\:DK    14 S!X.V"':$*-^V\:DK
15 3UF,*E!8AB"TQ$7K>    15 3UF,*E!8AB"TQ$7K>
16 [4=*["^\H#$XME*T3    16 [4=*["^\H#$XME*T3
17 C49+[]PG>-;%5#X*\    17 C49+[]PG>-;%5#X*\
18 &N)T/RE1@?N3>2S\I    18 &N)T/RE1@?N3>2S\I
19 Q#]P$P'[JU*;O*:1@    19 Q#]P$P'[JU*;O*:1@
20 @K$*#$U:?RW2,Y*9E    09 )-4Z"MI$8H1?9'?E&

m_2s_cycles goes from 2202.52 to 2678.40
pcs2 goes from 312.40 to 422.92
pcs3 goes from 112.04 to 289.30

Here are dumps of the L3 cycles for the "before" and "after" ciphers:

http://zodiackillerciphers.com/jarlve-c ... cycles.txt
http://zodiackillerciphers.com/jarlve-c ... cycles.txt

The row swap operations have caused more cycles to appear. Here are the counts by run length (example: ABCABCABC has a run length of 3):

Before swaps:
Run length 2: 4059
Run length 3: 236
Run length 4: 11

After swaps:
Run length 2: 6395
Run length 3: 478
Run length 4: 27

Incidentally, it only takes a single row swap operation (swap rows 9 and 20) to boost the m2 score from 2202.52 to 2415.13:

Code: Select all

01 +E7'D*!$3*.)HSF1$    01 +E7'D*!$3*.)HSF1$
02 M&^*%Y6[ZU=($VQ,*    02 M&^*%Y6[ZU=($VQ,*
03 $R+>)*'/KG$(*8V$B    03 $R+>)*'/KG$(*8V$B
04 ITC#X3>E14#]+H\LX    04 ITC#X3>E14#]+H\LX
05 -3*=$)*@II^1HQ$[>    05 -3*=$)*@II^1HQ$[>
06 !YP^<R\U:T,<?$IO;    06 !YP^<R\U:T,<?$IO;
07 #QK*5A"$9I0&CE*^.    07 #QK*5A"$9I0&CE*^.
08 +0D]M/JV$!K'*QR46    08 +0D]M/JV$!K'*QR46
09 )-4Z"MI$8H1?9'?E&    20 @K$*#$U:?RW2,Y*9E
10 7^A?(!-B)\V?Z+55A    10 7^A?(!-B)\V?Z+55A
11 *Q_M9KX+G_/$2-4%E    11 *Q_M9KX+G_/$2-4%E
12 ]R!;SFL)_<*8"1I3&    12 ]R!;SFL)_<*8"1I3&
13 #N=#HL';Y$O0Z*F@[    13 #N=#HL';Y$O0Z*F@[
14 S!X.V"':$*-^V\:DK    14 S!X.V"':$*-^V\:DK
15 3UF,*E!8AB"TQ$7K>    15 3UF,*E!8AB"TQ$7K>
16 [4=*["^\H#$XME*T3    16 [4=*["^\H#$XME*T3
17 C49+[]PG>-;%5#X*\    17 C49+[]PG>-;%5#X*\
18 &N)T/RE1@?N3>2S\I    18 &N)T/RE1@?N3>2S\I
19 Q#]P$P'[JU*;O*:1@    19 Q#]P$P'[JU*;O*:1@
20 @K$*#$U:?RW2,Y*9E    09 )-4Z"MI$8H1?9'?E&