One of the nice things about the unsolved Z340 Zodiac Killer cipher is that we have a previous solved cipher by the same encipherer (i.e. the Z408 cipher), which appears to exhibit many of the same properties as the Z340. Hence, if we could forensically reconstruct how Z408 was constructed (i.e. its cryptographic methodology), we might also gain valuable insights into how the later Z340 was constructed.

One interesting feature of the (solved) Z408 is that even though it is a homophonic substitution cipher (which is to say that several different shapes are used for various plaintext letters), the shape selection is often far from random. In fact, in quite a few instances Z408 shapes appear in a strict cycle, which has led to some recent attempts to crack Z340 by trying (unsuccessfully) to infer homophone cycles.

Curiously, one of the shapes (filled triangle) appears to encipher both A and S: and if you extract all these out, a homophone-cycle-like ASASASAS sequence appears. This intrigued me, so I decided to look at it a little closer: might this somehow be a second layer of cycling?

The answer (I’m now pretty sure) turns out to be no, though it’s still interesting in its own right. Basically, the Zodiac seems to have got confused between dotted triangle (for S) and filled triangle (for A), which caused his cycles to break down. He also miscopied an F-shape as an E-shape: perhaps his working draft wasn’t quite as neat as his final copy, and/or written in felt tip, causing letter shapes to soak into the paper and become slightly less distinct.

If we correct these mistakes and reconstruct what he seems to have intended, we see that he was following a fairly strict cycle most of the time, though getting less ordered towards the end (perhaps from enciphering nausea?):-

A: length-4 homophone cycle = (1) F – (2) dotted square – (3) K – (4) dotted triangle
–> 12341234123413234124211
—-> 16 decisions out of 22 follow the cycle pattern

S: length-4 homophone cycle = (1) 6 – (2) S – (3) reversed L – (4) filled triangle
–> 1241234123412341231412
—-> 18 decisions out of 21 follow the cycle pattern

L is interesting because though that seems to start out as a length-2 homophone cycle [diagonal square – B], the diagonal square then seems to morph into a filled square and then back again to a diagonal square. Hence there’s no obvious sign of an actual length-3 homophone cycle as such, only a miscopied length-2 cycle (which then breaks down halfway through, with four diagonal squares in a row).

Yet even though the Zodiac loves words containing LL (kill, thrill, will, all, etc), he only actually seems to be using a length-2 homophone cycle for L (if slightly miscopied). That is, he is probably using a generalized model of English letter frequency distribution rather than a particular model of his own English letter frequency distribution.

The odd thing is that if you go through Dave Oranchak’s list of Z408 homophone sequences, you’ll see that it doesn’t quite match the traditional “ETAOINSHRDLU” frequency ordering (I count L as length-2):
* Length-7: E
* Length-4: TAOINS
* Length-3: R
* Length-2: LHFD

Was there an American amateur cryptography book of the 1950s or 1960s that espoused this frequency distribution?

7 thoughts on “This week’s Zodiac Killer cipher thoughts…

  1. David Kahn’s book “The Codebreakers” came out in 1967, two years before the ciphers were published. The frequency distribution mentioned therein was:


    Helen Gaines’ book “Cryptanalysis: A Study of Ciphers and Their Solution” was published in 1939 and into the 40s. She also discusses ETAONIRSH.

  2. Ernest Lillie on October 19, 2011 at 1:34 am said:

    “Cryptography: The Science of Secret Writing” by L. D. Smith contains material on this as well. Both it and the book by Helen Gaines mentioned above have been in print since the mid-1950’s from Dover books.

  3. Smith’s book says this: “Authorities agree that the letters of highest frequency in our language are E-T-A-O-N-I-R-S-H.”

    Then there is ETAOIN SHRDLU from the old Linotype keyboards, which have been around since the late 1800s.

  4. Dave & Ernie: thanks for your replies! What I was puzzled by was why R has a shorter homophone cycle than both S and H, and why F has a homophone cycle at all when it comes so far down the list. As Dave pointed out, ETAONIRSH does makes more sense than ETAOINSHRDLU, but it’s still got the R and S out of order. Perhaps this was miscopied by the Zodiac? 🙂

    Also, I’m wondering if the letter shape assignments might help us reconstruct the order of letters in the Zodiac’s Z408 homophone key, which could possibly look like ETAONISRH rather than ABCDE. Dave, has anyone tried to do this?

  5. My last encounter with possible reconstruction of the 408 key’s order was this post.

    It was a humorous and pointless effort. 🙂

    And here is an interesting discussion about a key that was mailed in 1969, independently of the Harden’s solution.

  6. Dave: oh yes, how could I have possibly forgotten THEBUFFOONSSWEETGENITALIA? Also, if I’m right about miscopyings in Z408, the 1969 key wasn’t by the Zodiac at all.

  7. davonskevort on March 22, 2014 at 12:09 am said:

    The 340 is a crossword with phrases. Solved the my name code and the way to solve it is basicly the same. 340 has reverse text which taunt the FBI . You can’t crack a crossword . Think btk and his crosswords with someone a bit smarter.

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