Newcomer's thoughts on the 340

[Duman Profile]

Right, yes, my first thought was also that distances between letters would approach what you'd expect from their frequency, but it might not be so really due to the bigrams that the letters usually form and some more complex features of the text. The idea here obviously is to take suspected homophone cycles and look at the distances between symbols there and the typical distances between letters. For some reason though this statistic isn't here among the typical reference tables I use.

[jan Profile]

An idea that I had was that the plaintext was first Caesar-shifted and then homophonically encrypted

Although Glurk already pointed this out, his post may be a bit too long/empirically based for most to immediately understand why a caesar shift or similar techniques make no difference at all. Since this question or proposal comes up often, here's my stab at it to get it out of the way for good:

Code: Select all

plain text        : Seen  me   here ?
Caesar shift(1) : Tffo   nf    ifsf   ?
Substitution     : -++)  )+  {+}+  ?


Based on letter frequencies with 'e' being the most common letter in English, it's quite obvious that you'd go straight from '+' to 'e' and would never know about the 'f-stage'. It does not matter how many shifts there were in between because it does not change the letter frequencies.
(I used simple substitution in this example to make it more clear, but this holds equally true for homophonic substitution.)

"In quadrant 1, the double is qq"

The key in encryption is to hide as much information as possible: remove spaces (hides word boundaries), remove punctuation(hides sentence boundaries), use padding/filler (hides how the text should be held for reading), remove doubles (hides impossible/improbable pairs like kk, qq, aa), use homophonic substitution(hides/flattens out letter frequencies) etc.

In the 408 his concern seemed to be more about reoccurring combinations. For example, suppose you have symbols '*' and '+' for the letter 'L'.
To encrypt 'LL' he would use '+*' and '*+' but after that his combinations are exhausted. Another 'LL' would again use '+*' or '*+'. To avoid this repetition he used doubles like '++' and '**' (and thereby give away valuable information).
The 340 is clearly created to generate fewer reoccurring combinations. This leads to the only possible explanation for the doubles: he had no other choice! There is only one symbol for that plaintext letter. Suppose he used the '* symbol' to represent the letter 'z'. Then he had no other choice than to use '**' for a word like puzzle because there was only one symbol(*) for the letter 'z'.

But to let you in on a little secret: it's not a double 'qq' It's a reverse 'p' and a 'q' and .
Examine them very closely and you'll see that those are not the same symbols. While all/most other symbols are always written in the same fashion, these are clearly not. So, 'my' 340 does not use 63 symbols but 64.

There is also some 'psychology' involved in this (which I mentioned in another post about the reverse 'k' not being a reverse 'k' but more like a rotated pi-symbol, (even though the pi-symbol looks a bit differently, but don't know how else to describe).
There are quite a few horizontally mirrored letters, and when writing these (doing the individual strokes) one is surely thinking about the original letter but then horizontally mirrored. You can even see he constructed the horizontally mirrored versions in a similar fashion as the original. But with the rotated pi-symbol he was not thinking 'reverse k' and the first symbol of that double 'qq' is clearly written as a reverse 'p' and not like a 'q'. I have been running zdkrypto for about 3 years and have just about never seen it decrypt the ' reverse p and q' to a double letter. Many times I see it generate a double letter one position earlier where the 'reverse p' is the second letter of the double.

"What if each of the symbols utilized is intened to have a symbolic representation?"

That would be code (instead of encryption).
http://en.wikipedia.org/wiki/Encryption

"Codes operate at the level of meaning; that is, words or phrases are converted into something else. Ciphers work at the level of individual letters, or small groups of letters"

http://en.wikipedia.org/wiki/Code_(cryptography)

I have tried it numerous times and at some moments even thought I was on to something but without context it is much harder to crack than encryption. I also tried a combination of code and encryption. For example replacing some symbols with complete (common) words as 'me', 'the', 'and' instead of letters. One of my experiments was to decypher/decode the + symbol into 't' or 'and'. (That was his 'thing', not? ) I still don't exclude the possibility but I'm no longer exploring it.

"It doesn't mention anything significant about using a symbolic character representation for cipher text instead of just using enciphered standard alphabet. I wonder why Zodiac made such an (apparent) effort to do that with his ciphers."

Because he could.
In real life (think about (older) military communication for example) you want a technique that is fast and easy to use for both encrypting and decrypting. Ideally you'd like a technique that can be somewhat automated (think of a typewriter). Using symbols like he did is much too cumbersome for daily use. The major difference is that he has to use it only a couple of times. It is more of a 'puzzle' than what encryption is regularly is used for.
It is also quite common when you use homophonic substitution. You can even be (almost) certain he used that technique simply based on the use of 'symbols'. No other technique (apart from code) would require the use of symbols. And also what others have said: it looks more mysterious and is much more appealing to the general public. It is in line with what the public expects from a 'secret message' because that is how it is most often portrayed in books or movies.

Cheers,

John

[Duman Profile]

Some more musings.

I'm afraid the quadrant approach has to be dismissed. After trying various things with the individual quadrants, there is simply nothing useful to be extracted. There are some cycles that can be found, but even if all of them turned out to be real homophone cycles and not due to chance, then a couple suspected letters in quadrant 1 is the best that can be obtained without starting to really stretch this. The main problem is that each of the quadrants has a very high amount of unique symbols. In quadrant 2 we get 46 different symbols for 72 characters, or 43 different symbols in Q1. That's not workable.

Now I am looking at lines 13 and 14. It might be worth indeed to try and match those two lines against plaintext from some corpus. These lines give us 34 characters with 27 different symbols. The lines are interesting because they include some of the noteworthy features of the 340. Line 14 ends with the incredibly annoying ++ digram, while 13 contains the 3-gram FBc , which is one of the only two 3-grams that get repeated in the cipher. As an interesting coincidence, the first suggestion by ZKD for these two lines was that 13 ends in "was" and 14 begins in "tortured", which also makes "t?er" appear earlier in 13. This is the sort of creepy thing that happens when working on the ciphers. Oranchak, do you perchance have a readily usable corpus from Gutenberg or whatever?

That darn + symbol is killing me. At a whopping 24 appearances out of 340 characters, it's too common if a proper attempt to mask frequency was made. Compare to the 408's most frequent character only appearing 16 times. And in the 408, the two most frequent characters never form doubles, and the third forms one double. While our esteemed + appears in an impressive 3 ++ doubles. This should not appear if the 340 was encrypted similarly to the 408. Problem is, we already know that much, in essence.

[doranchak Profile Website]

Below are some raw results from a previous search I ran. Not exactly the two lines in question, but close. The last number is the zkdecrypto score for the plaintext that appears in the rest of the cipher when the crib is applied. The score does not include the crib itself. The list is in descending order of zkdecrypto score.

Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, SPUEBLOSDEESTASRENTASDEBERANPAGARS, 1633.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EAPOSTLEPETERTHATTHEEPISTLETOTHEHE, 1626.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, HRONOMETERTHEESCAPEWHEELTEETHEXERT, 1625.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ENCETOGETTHECOMMITTEETOTHROWYOUOVE, 1607.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, SCUSTOMSANDSITUATIONSALLDESPOTISMS, 1603.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TPOINTWHERETHEYHADINTENDEDTORESTTH, 1591.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EINERKRIEGSERLEBNISSEERNSTUNDLAUNI, 1586.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, OFETCHYOURSONTOHELPYOUTOSTEALTHEHO, 1578.25
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, THEYFURTHERTESTIFIEDTHEIRSATISFACT, 1557.125
BFz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ETHEYFURTHERTESTIFIEDTHEIRSATISFACT, 1557.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TOCCURSTOMETOTESTIFYTOTHEFACTTHATT, 1553.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TBESAIDTHATTHEYAREWITHOUTGUILEBUTT, 1542.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ETELLEOUDETELLEFAUSSEDENTDETELLEOU, 1538.25
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, HRISTIANITYHADLIFTEDHIMBYHEHADBEEN, 1536.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, OWNANDWERENOTTOBESUBORDINATEDTOTHE, 1512.625
BFz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TOWNANDWERENOTTOBESUBORDINATEDTOTHE, 1512.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, AISSESVERSLATERREETPARMILESQUELSJE, 1511.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ERIORMESENTERIESPROCEEDSTOTHEINTES, 1509.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, OFLEARNINGTOREADASSOONASTHEYWEREGI, 1503.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, SETLESDESSESVENUESAUSSILENNAGEANTE, 1501.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TGOTOSEEHIMTOSPEAKWITHHIMTORESTORE, 1499.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EADLEAVESTHEHEATOFTHESUNHATCHESTHE, 1493.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ETJEVISENTRERAGRICOLENCORELAPAILLE, 1491.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ENDEUXLONGUESTRESSESENTOURESETRECO, 1472.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t++, EADLEAVESTHEHEATOFTHESUNHATCHESTHEE, 1465.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TBEENMISSEDTHESERVANTSHADRUSHEDUPS, 1460.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, TOOGOODTOBETEMPTEDORTOOWEAKTOMAKET, 1458.375
BFz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ETOOGOODTOBETEMPTEDORTOOWEAKTOMAKET, 1458.375
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EMORETHANTHEPAINSTAKENBYHISTRANSLA, 1449.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ENWIJREDENEERDENMETVEELGELEERDHEID, 1421.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ORMETURNUNTOHERWHOWROUGHTTHESETHIN, 1419.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, NOVIOLAORSINOICHERINNREMICHDAICHVO, 1394.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, AYSDIRECTLYANDIMMEDIATELYORINDIREC, 1383.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, RMYTHEPREPARATIONSWEREATANENDTHEAR, 1372.5
BFz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ARMYTHEPREPARATIONSWEREATANENDTHEAR, 1372.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, IRITHEPERCEIVEDTHATHIRASEYESWEREBE, 1363.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ANDLANDEDLEAVINGTHELADSSEATEDINTHE, 1357.25
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EPROPERTOTHEBESTLANCEOFTHEORDEROFT, 1344.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ROACHEBUNDIRKLARPLAIRNEPIERRELARQU, 1324.25
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, NTEDCARDTHENFORAMOMENTTHEYSTOODSID, 1319.375
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EIVEDUPONPIECESOFLINENWHICHARETHRO, 1317.0
BFz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, CEIVEDUPONPIECESOFLINENWHICHARETHRO, 1317.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, NJURYOBSSPENSERSYNCENSUREREPREHENS, 1315.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, IOUSFACETHEIROWNSPIRITSWENTUPONTHE, 1295.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ILEQUISERAVISEQUIALAIRDAVOIRDESIDE, 1295.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ESTEILLUSTRECITOYENDESPARTEQUIDEPU, 1278.375
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, HANDSOFTOMWHITEAMANWHOMIWOULDTRUST, 1275.75
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, AGNAYKSINNSALINIKKUNANRESSJAKIRJOI, 1269.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, OPPEDMYINDOORWORKISDONEGOLDENWEDDI, 1260.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ENACHTELIJKEEENZAAMHEIDIKTELDEDESL, 1253.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ERSTELDVANDEONDERGANEAANDOENINGENV, 1245.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, AVAAOSPSDOMARIDOELAVADAEMLAGRIMASS, 1241.0
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ARIUSVIIDENARIUSVIQUADRANSXIIINXII, 1234.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, STASGENTESASDELASQUESELLAMANDECAST, 1193.5
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, NIGODPUTSMUNISDEPLEINSPOUVOIRSDONT, 1190.875
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, EERMEHRUNDMEHRMENSCHENKAMENHERANAU, 1182.625
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, ABUKTUTANGGAWAGAYONMANANGPAGKAMAPA, 1063.125
Fz69Sy#+N|5FBc(;8RlGFN^f524b.cV4t+, LKABOUTITBELIEVEMEALLTHEEXAGGERATI, 1034.125

[Duman Profile]

Heh, Apostle Peter... do you mind posting the corpus? I assume you collected it. Also, what is it? Maybe I am not thinking clearly, but I can not see any plain English in some of those strings. The top pick seems to be Spanish, I also see Dutch and Portugese?

[doranchak Profile Website]

The corpus is the Project Gutenberg "April 2010 DVD" available here:

http://www.gutenberg.org/wiki/Gutenberg:The_CD_and_DVD_Project

Yes, the search results include English as well as non-English books. Here is an expansion of the matches which shows the book titles, authors, and excerpts:

http://zodiackillerciphers.com/corpus-matches-lines-13-and-14.txt

[Duman Profile]

A thought I had last night - it's been mentioned numerous times how Zodiac might have done something that was intended to add some complexity, but actually ended up adding far more complexity than he expected. Has the possibility been considered that he encrypted the 340 homophonically and then just rearranged the lines randomly, not realizing that 20 lines can be arranged in an absolutely insane amount of combinations?

Then again, it is highly unlikely. If the cipher simply had rearranged lines, it should be possible to obtain meaningful words in the middle part of each line, but that hasn't been the case.

[doranchak Profile Website]

I scrambled the 408 cipher: http://zodiackillerciphers.com/408.zodiac.solved.scrambled.lines.txt

Then fed it into zkdecrypto, which solved it without any problems:

YCOLLECTINGORSLAV
ILIKEKITLINGPEOPT
HEORIETEMETHHPITI
GERTUEANAMATORALT
HECAUSEYOUWILLTRY
TOKILTSOMETHINGGI
LNOTGIVEYOUMYNAME
RTOFITIATHAEWHENI
TOSTOIDOWNOBUTOPM
NPARADICEUNDALLTH
EHECAUSEITISSOMUC
ITHAGIRLTHEHESTPA
SEMANISTHEMOATDAN
ECOMEMYSLAVESIWIT
ESFORMYAFTERTIREE
TINGYOURBOCKSOFRW
HFUNITIUMORERUNTH
EVENHETTERTHANGET
EIHAVEKILLEDWILTH
INTHEFORBESTHECAU
ANKILTINGWILDGAME
DIEIWILTHEBEHORNI
TINGECPEBENCEITIS
VESMETHEMOATTHRIL

So, it seems like the 340 would have fallen easily if it were similarly constructed.

[Duman Profile]

Feel like I need to take a step back and see if I can correctly summarize the findings about the encryption method used, so please correct me if I am wrong on some count.

First we assume of course that the 340 is a normal cipher in the sense that it's encrypted plaintext also of length 340.

Traditional homophonic encryption has been essentially ruled out due to repeated failure to get a solution through ZkDecrypto or manually through familiar methods of attacking homophonics. ZkD also rules out traditional homophonic encryption if the message is in German, French, Italian or Spanish.

Homophonic encryption that was preceded by a Caesar shift of the plaintext has been ruled out - it's been shown that ZKD deals with such ciphers with no extra difficulty.

Vigenere, either pre- or post-homophonic step, has been ruled out due to the lack of familiar IoC peaks expected for Vigenere encrypted messages.

Bifid encryption preceding homophonic encryption has been ruled out through analysis here on the forum.

Columnar or diagnoal transposition ruled out by FBI.

Linear transposition not ruled out, but has to be more complex than rearranging lines at random or inserting a couple of filler lines.

Message being split into 4 quadrants with a different key in each is ruled out as unsolvable because the quadrants contain too few repeats.

Message being split into halves at line 10 with 2 different keys is ruled out because the halves do not solve indidivually, either.

What am I missing here?

[doranchak Profile Website]

Good summary! I can't think of any others you haven't mentioned.

Doing something like this for the Zodiac ciphers wiki is on my wish list:

https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/index.php/Cipher_Cross-off_List