Current thoughts/observations: it seems as if the first 10 rows of the 340 are homophonically substituted in reverse (mirrored), starting from character 170,169,168,etc. Or, the top and bottom part (10 rows each) are independently transposed somehow (probably after homophonic substitution symbol assignment).
Additional to the pivots there is a whole charlie foxtrot of diagonal repetitions at the center of the 340. Diagonal repetitions with a distance of 1 to 3 are colored orange. I’ve compared this to the 408 and several other ciphers and this is not a tendency that seems to occur.
I also want to note that there seems to be a tendency for certain symbols to cluster (grid wise, visually observed) and this is something that I have noticed from the beginning I started to work on the 340. Maybe I should try to come up with a way to generate statistics for this.
https://www.dropbox.com/s/97quwptpux8ah … 3.png?dl=0
There is a difference between the top and the bottom (about 10 rows) part of the 340 for the data of the uniques. My algorithm calculates the score by considering each character as a starting point and then moving on in one direction until a repeat is found. These values are counted and then multiplicated by the length of the unique string to give a greater weight to longer strings. As I have observed there is a difference for this data when you consider different directions/orientations, and the direction in which the cyclic homophonic substitution is done will have a significantly higher score.
So I generally compare a direction to its mirrored counterpart because this interrupts the homophonic cycle.
Now comparing the 340 between normal reading direction and its mirrored counter part. Note that the first value is highly likely to be higher for cyclic homophonic substitution.
For the whole cipher: 4462, 4260. 104,7%
For the first 10 rows: 2084, 2250. 92,6% <— ???
For the last 10 rows: 2273, 1879. 120,9%
The second part is making up for the first part.
For the first 9 rows: 1887, 2124. 88,8% <— ???
for the last 11 rows: 2477, 2109. 117,4%
I have tested this to be true for groups of 4 and 5 rows and largely true for groups of 2 rows. All three parts of the 408 have a higher value in the primary direction and as a whole. The same goes for all cyclic homophonic substitution ciphers I have tested. It is really not supposed to happen.
I’ve recently tested the 340 (17 by 20) with AZdecrypt, for:
Rotation and removal of rows or columns, twice 2^20 and 2^17 unique combinations. With rotation I mean: string "abcdefg" becomes "gfedcba".
Removal of symbols, columnar transposition, also considering the first and last 10 rows to be individually columnary transposed.
Treating the cipher as 2,4,5,10 parts and changing orientations for each part, doing and undoing, very thorough, millions of combinations.
None of the above had interesting results except (maybe) for the removal of rows or columns, but that is probably multiplicity related stuff. I’m thinking of redoing some of these tests with a 20 by 17 grid.
To test all columnar transpositions (17!) in for example one year of computing time you need to check 17! divided by 31536000 (seconds in a day times 365 days in a year) = 11278774. Give or take 10 millions ciphers a second for a year. That would require a big supercomputer. Maybe it is possible to write a specific algorithm, for instance, scoring each rows as an annagram. Or come up with some statistics that could indicate transposition of this kind.
Once I decided that transposition was probably involved, and saw what a large number 17 (factorial) was, I just lost hope.
I am not telling you to, of course, I’m only saying that I did.
-glurk
——————————–
I don’t believe in monsters.
Yes it’s daunting!
My current thoughts are that the 340 indeed has columnar transposition, going under the assumption that this was done after the homophonic substitution. I’m not sure if either it is a whole cipher transposition or that the top and bottom 10 rows are individually transposed.
I devised some kind of sketchy test to see if columnar transposition – or possibly any other – was done after symbols assignment (probably more accurate for cyclic h.s.) where I average data from the non-repeats (unique strings) for a large number of random columnar transpositions. I found that then multiplying this average by 1.05 gives the likely score (approximation) the cipher would have, for the 408 this is: 4683.5/4692. Where the bold number is the approximation. For the 340: 4457/4462. I think it could mean that the cipher was not columnary transposed after the symbols were assigned as I have thought earlier since then the number of the non-repeats would likely have shifted away and the approximation would not match. I’m less sure of the whole columnar transposition thing atm.
I also noticed that transposing rows, for instance interlacing the first and last 10 rows, or swapping parts of 2 rows or more here and there – but not necessarily swapping stuff between the first and last 10 rows – decreases overal cipher randomness. Putting the cipher in a much more likely state. I have tried this also with some other ciphers and it did not happen to a significant degree, what is going on?
The 408 scores 4692 on my non-repeat test and the 340 only 4462, since this number is supposed to go up with more symbols for cyclic h.s. I still feel that the cipher is transposed in some way after the symbols were assigned. So I redid the same sketchy test for row transposition and seem to have found clear indication that rows were transposed or something similar was done. 4933/4462. Again the bold number is the approximation and there is a big difference. A number around 4900 would make much more sense for the 340 in contrast with the 408.
But transposing rows alone does not make a cipher unsolveable…
A new theory everyday. 
I believe the whole block of rows from 6 to 15 may have a specific transposition. I had the best results with undoing rotation so something like that might be actual there. Nothing came close to a solve though.
This area very specifically:
https://www.dropbox.com/s/d4ogk4vc59e7x … 2.png?dl=0
340 example cipher, SN-EW rotation undone:
HER>ÐÌ^VPËI²LTG±Ä NÐ+B¢·OºDWy•<»KÆ£ BŸ„ÃM+uZGW¢£L·¤HJ SÐн^̾»V´ÐO++RK± ¸¼M+¤ÔÊÄIµFP+ˆ³Ë/ ++RFO-K¼I¢-+¾BKŸ³ LLDµÔƒˆMB°¹¤±Z³¢+ TFA+•>uVÕÂ<Ÿ¤VFV ÃBMнÃyGË>•F³BÐBN XCEµTyOF¸ÃÄC³IµD +±+u»¼±N»IJRO±-³µ +IE^Z·ƒO„Æ·JÔ++ʺ Ì»^ŸRµVÂÆÑF²NSÌ/u +JK^XF¼ÃRÌM±+RBG° <+¤<Gµ¾ŸÌ¤±u-Ä¢·Ð IÕ´¤BK¢OÐ^•ÆMÑG± RÃT+L²°C<+FÌWBI£L ++£WC¤WÃPOSHT/¢£Ð IFËÄW<½ÔB¸yOB»-Cà >MDHNÐËS¤ZO¾AIKƒ+
Visual aid for example cipher, darker grays are transpositioned further away from the original position.
https://www.dropbox.com/s/6pumb3jbghma0 … 1.png?dl=0
A quick post/start about bifid encoding.
Found this interesting post from Paul_Averly in the Ross Sullivan section:
His name, RossMSullivan has the same amount of characters as the MY NAME IS cipher but not the same symbol to letter distribution
For years I have been playing with the idea Z used a Bifid Cipher for the 340 and Name Codes. I’m thinking Bifid because the halloween card ‘By fire’ might be a hint.
RossMSullivan encoded with Bifid (and no key) turns into: stosMvMsMpaqc.
Notice the M’s.
It still doesn’t line up with the Name Cipher but I was amazed at the 3 M’s positions on the first try.
This video explains the encoding, it is quite simple and is open for everyone using a pen and paper method: https://www.youtube.com/watch?v=LQCy_7KFyZk
Online tool: http://rumkin.com/tools/cipher/bifid.php
Paul_Averly said that though the M’s are in place it still doesn’t line up but it may be considered that he did the encoding in a slightly different way. (mirroring the numbers perhaps) Still need to look into it.
408 plaintext first 340 characters (no errors) bifid encoded, no key.
hgbhmmlnlaatbrtnq gsiinqiofmhmmwlfl hrboqtaatccircoqc fstchcmcomhondgmg vsdfntrrnhfxdcaii ecatdrcfthkotlimk ifgsradsdsgrtfufm bbwnaqcshlqbacanr bfvgnawnaclpsedkh nogvxsxcaadqxuhou quzqdmzueklxytnrx lxtsikeolpqdmidfk ssvrkoklxwcsswstc kixcraqaduqcryomi emypiosiaskpwxpts vxktwscktsiugsxqb tlifswxubtdtolrpo tyiakkihsvftpcqas yleyayiakokilaxrq ctietwsbwxeptwqdi
Same thing homophonically substituted 63 symbols.
CZG?HjQ27!D3W"Na. El@i2U6(IdCHjFm0Q ?XG[-O#3]^KPRB.8 IVN]C^dR(H?[a_ZjE 4pA02O"XaCITg8'>@ ;]!3_P^0N?kBO7id/ 6IZ)"DALglEX30eIH WGf2#URVCm-W8'aP G04Z2!FaD]Qbp;_o? 2(E41)T^#A.1eC[e Uec-gjce;k7T9Na"1 mTOLK/;BQb._d>AIo lV4Xk(/71fRp)FL38 o@T]P'U!ge-^"9[Hi ;j9b6BlKDVkbf1bNp 4T/OF)Ro3L>eZl1.W Nm@0VfTeGO_3(QXb[ N9i#k/6?p4IOb8U) 97;9'9K!oBk>mD1P- ]3@;NFLWfT;bOF.Ai
Observations about bifid encoding with no key: (need to do test with keys later, might be different)
Bifid encoding splits up the cipher in 2 different data streams and then recombines them in another way. There is a very strong tendency of letters and thus symbols spreading more unevenly over the grid from what is expected. Because of this the 340 just cannot be a bifid cipher in the straightforward manner, which is, encode plaintext with bifid and then encode bifid plaintext with homophonic substitution. Maybe the result will be different if for instance bifid encoding was adjusted to output directly to symbols. Thinking of an input 8×8 polybius square filled in with "abcdefgh" and an output 8×8 square with the symbols filled in.
What does seem to correlate with the 340 is that the IoC (index of coincidence: http://en.wikipedia.org/wiki/Index_of_coincidence ) is more even throughout the cipher. For example the first and last 10 rows of the 340 strangely have the same IoC and bifid encoding does produce ciphers and plaintexts with this tendency.
Bigrams steer heavily towards diagonals and very low counts, much different from the 340.
the practical cryptography analyzer listed 6×6 bifid highly when looking at the 340. i don’t think zodiac was an expert cryptographer. i think it’s more likely he read half of a cryptography book and got to work. the 408 wasn’t impressive, and he obviously didn’t like that it was solved, so what would an amateur do to improve the complexity? if it were me (a true amateur), i’d just combine two methods to make it harder. it’s not like he said "this is my final ultimate cipher". if it gets solved, he could just make an even harder one. his point was to aggravate law enforcement, not win a world war.
anyway, i read a thread that touched on this – http://www.zodiackillerfacts.com/forum/ … 038#p22038 – about using a bifid then homophonic substitution. the gist i get from this is it would be obvious because we should see lots of homophone sets since there are only 63 ciphertext characters, but isn’t it possible he artifically manipulated the results? he could leave out rarer letters so we start with 20 instead of 26 (i.e. – no v,k,j,x,q,z). he could include letters twice in the bifid. etc etc.
i guess i’m hoping to know if some of you have looked at bifids combined with homophonic substitution and also ruled it out. thanks.
the practical cryptography analyzer listed 6×6 bifid highly when looking at the 340. i don’t think zodiac was an expert cryptographer. i think it’s more likely he read half of a cryptography book and got to work. the 408 wasn’t impressive,
I wouldn’t be so sure that Z408 wasn’t impressive. Yes, knowing the solution, it doesn’t seem to be all that impressive. But don’t forget, originally it was solved pretty much using a crib, or a lucky guess. If Z didn’t use the word "kill" so many times in Z408, it is quite possible that it would’ve taken much longer to crack. After all, Z408 wasn’t solved purely algorithmically, i.e. without any lucky guesses, until over 30 years later, right?
i guess i’m hoping to know if some of you have looked at bifids combined with homophonic substitution and also ruled it out. thanks.
I’ve actually explored the possibility that bifid was used prior to homophonic substitutions. I’m by no means an expert in the field, so please take everything I say with a handful of salt. 🙂 But according to my analysis, it is unlikely. Here’s why. As Jarlve pointed out above, bifid mixes up the letters quite a bit. Two properties that make a good (i.e. secure) cipher — confusion and diffusion. Confusion means that changing the encryption key a little bit should result in a big change in the ciphertext — somewhat true for bifid, unless the Polybius square was chosen poorly. Diffusion means that changing one letter in the plaintext should change multiple characters in ciphertext (and vice versa) — very true for bifid. Even for the classic bifid, as described in Military Cryptanalysis book Part IV, it generally ends up reducing all 3-gram repetitions to 2-gram reps, 4-gram reps to 3-gram reps, and so forth. Using the later/improved version of bifid, with recombining the rows from coordinates written in columns, it completely destroys all N-gram repetitions altogether (* see note below).
Looking at Z340, the 2-gram repeats are just too high for a bifid cipher, let alone a bifid that was further encoded using homophonic substitution, which also reduces N-gram repeats even further. I haven’t done an exhaustive test using a large number of variety of ciphers encoded with bifid and homophonic substitution, but out of a few that I’ve encoded as a test, the highest number of repeats barely approached half of the repeats in Z340. So it can’t be completely ruled out, but it is unlikely that bifid was used in Z340. I’d love to get an independent confirmation from someone else though?
(*) With the rare exception of the same word being encrypted in the same position along the bifid period, then there will be a repeat in the ciphertext, and that’s how bifid ciphers are often cracked. There are only 2 separate 3-gram repeats in Z340, one 69 positions apart (1, 3, 23, 69) and another 136 positions apart (1, 2, 4, 8, 17, 34, 68, 136). They happen not to share a single factor (other than 1), so they cannot be an artifact of a bifid encryption. (actually, both of the 3-grams are mixed together in one of the repeats, so I didn’t even have to analyse factors) I was going to analyse the 2-gram repeats for common factors as well, but when I saw that the repeats are too frequent, I just abandoned the whole idea.
Bifid may not be impossible, I think glurk did some work on it because I saw some samples included with ZKDecrypto.
@glurk, if you are reading this and did some work on Bifid could you please share it? Thanks.
It’s hard to compare computer generated ciphers to the ones which the Zodiac created. There will be more bigrams in hand made ciphers, also from what I’ve seen the encoding seems to create it’s share of bigrams in its direction.
Another question is, which has probably been discussed before, why are there so few patterns in the 340 versus the 408? If not subtly transposed after encoding it does hint towards some randomization of the plaintext.
I’ve looked at bigrams at a distance for the 340 and found some unusual peaks (for my system) at distances of 15, 19 and 29. A distance of one would be a standard bigram, I’m not sure if it’s something or just a fluke in the cipher. It could be related to the "+" symbol only landing on a prime number just once. The 340 is trouble, and the way the cipher is throws of many tests, I have wondered if he was really that smart. Let’s hope not!
I’ve looked at bigrams at a distance for the 340 and found some unusual peaks (for my system) at distances of 15, 19 and 29.
Are you talking about the same "bigrams at a distance" stats described here? I’ve actually looked at it as well, when working the bifid theory, and got the following. First "graph" is for bigram IoC, and the second is for bigram variance. Both are a measure of bigram repeats, but they have a slightly different "sensitivity" to the distribution of repeats.
I’m only seeing a weak spike at 19, and it’s a weird one, as it suggests a bifid period of 2*19=38, as the spikes in bifid tests are at half the period (which is why odd periods are more secure, as you’ll have 2 smaller spikes at (period/2) and (period/2+1)). I’ve done a few tests with bifid subsequently encoded as homophonic substitution, and I saw similar weak spikes, so bifid should be plausible in Z340, but I really don’t see someone using a period of 38. You usually go with small periods of maybe up to 10, or across the whole message. There are also really weak spikes at 5 and 16, but they are barely above the baseline (the first line in each graph).
===================================================================== Bifid period test, bigram IoC: 1 = 2.00 |———————————————————————————————————————————————————————————— 2 = 1.52 |—————————————————————————————————————————————— 3 = 1.79 |—————————————————————————————————————————————————————— 4 = 2.00 |———————————————————————————————————————————————————————————— 5 = 2.27 |————————————————————————————————————————————————————————————————————— 6 = 1.45 |———————————————————————————————————————————— 7 = 1.45 |———————————————————————————————————————————— 8 = 1.45 |———————————————————————————————————————————— 9 = 1.52 |—————————————————————————————————————————————— 10 = 1.72 |———————————————————————————————————————————————————— 11 = 1.24 |—————————————————————————————————————— 12 = 1.17 |———————————————————————————————————— 13 = 1.72 |———————————————————————————————————————————————————— 14 = 1.17 |———————————————————————————————————— 15 = 1.65 |—————————————————————————————————————————————————— 16 = 2.20 |——————————————————————————————————————————————————————————————————— 17 = 1.93 |—————————————————————————————————————————————————————————— 18 = 1.45 |———————————————————————————————————————————— 19 = 3.10 |————————————————————————————————————————————————————————————————————————————————————————————— 20 = 1.38 |—————————————————————————————————————————— 21 = 1.93 |—————————————————————————————————————————————————————————— 22 = 1.52 |—————————————————————————————————————————————— 23 = 1.17 |———————————————————————————————————— 24 = 1.58 |———————————————————————————————————————————————— 25 = 1.65 |—————————————————————————————————————————————————— 26 = 1.38 |—————————————————————————————————————————— 27 = 1.65 |—————————————————————————————————————————————————— 28 = 2.07 |—————————————————————————————————————————————————————————————— 29 = 2.07 |—————————————————————————————————————————————————————————————— 30 = 1.58 |———————————————————————————————————————————————— 31 = 1.31 |———————————————————————————————————————— 32 = 1.86 |———————————————————————————————————————————————————————— 33 = 1.17 |———————————————————————————————————— 34 = 1.79 |—————————————————————————————————————————————————————— 35 = 1.72 |———————————————————————————————————————————————————— 36 = 1.38 |—————————————————————————————————————————— 37 = 1.17 |———————————————————————————————————— 38 = 1.58 |———————————————————————————————————————————————— 39 = 2.27 |————————————————————————————————————————————————————————————————————— 40 = 1.03 |——————————————————————————————— ===================================================================== Bifid period test, bigram variance: 1 = 0.098 |———————————————————————————————————————— 2 = 0.068 |———————————————————————————— 3 = 0.079 |———————————————————————————————— 4 = 0.095 |——————————————————————————————————————— 5 = 0.103 |—————————————————————————————————————————— 6 = 0.065 |—————————————————————————— 7 = 0.068 |———————————————————————————— 8 = 0.065 |—————————————————————————— 9 = 0.071 |————————————————————————————— 10 = 0.073 |—————————————————————————————— 11 = 0.062 |————————————————————————— 12 = 0.053 |—————————————————————— 13 = 0.083 |—————————————————————————————————— 14 = 0.053 |—————————————————————— 15 = 0.077 |——————————————————————————————— 16 = 0.104 |—————————————————————————————————————————— 17 = 0.102 |————————————————————————————————————————— 18 = 0.068 |———————————————————————————— 19 = 0.160 |————————————————————————————————————————————————————————————————— 20 = 0.065 |——————————————————————————— 21 = 0.092 |————————————————————————————————————— 22 = 0.068 |———————————————————————————— 23 = 0.056 |——————————————————————— 24 = 0.071 |————————————————————————————— 25 = 0.077 |——————————————————————————————— 26 = 0.062 |————————————————————————— 27 = 0.074 |—————————————————————————————— 28 = 0.101 |————————————————————————————————————————— 29 = 0.095 |—————————————————————————————————————— 30 = 0.074 |—————————————————————————————— 31 = 0.062 |————————————————————————— 32 = 0.089 |———————————————————————————————————— 33 = 0.050 |———————————————————— 34 = 0.079 |———————————————————————————————— 35 = 0.080 |———————————————————————————————— 36 = 0.065 |——————————————————————————— 37 = 0.050 |———————————————————— 38 = 0.067 |——————————————————————————— 39 = 0.114 |—————————————————————————————————————————————— 40 = 0.047 |———————————————————
Just had an idea. Is it possible that Z did something different with bifid, such as writing out Polybius square coordinates for plaintext letters in his usual matrix with 17-letter rows, and then reading/recombining them by columns? I.e. doing columnar transposition (without a key) as an intermediate step on the Polybius square coordinates. Might be worth exploring…
