Let me make some clarifications and point out additional evidence for this solution being correct.

First, I should clarify that the above assumes no anagrams. There are many nice anagram suggestions, but an anagram would be inconsistent with previous ciphers, and the numerous additional degrees of freedom would preclude a unique solution. So in my view, anagrams must be excluded.

One can confirm the small p-value by testing modest expansions to the vocabulary or a controlled addition of degrees of freedom. For example, I tested the sensitivity to translations (if starting not from the first symbol, then the solution is ruined and no other sensible results emerge) and to permitting a word spelled backwards (cannot be excluded in light of Z340, although less likely in a short, simple cipher like Z13, where BTW this may reduce to a letter swap).

The key passes my sanity checks. For example, others have noted that the Z408 key is not quite random (and could even relate to a QUERTY keyboard); indeed, there is a similar structure in the proposed Z13 key. Interestingly, this key resembles Z408 more than one would expect randomly:

Importantly, the aforementioned homophonic deviation is precisely the K-to-S substitution common to Z408 and Z13 (first row in the above table). A confused Zodiac may have reverted in this one instance to the Z408 key.

Finally, let me point out that back in December, adrian already anticipated (see below "Edit") Z13 to be a simple non-homophonic substitution cipher with transpositions, recognizable and relatable to Zodiac’s past writings, without an actual name. Apologies for only noticing that comment yesterday.

Excellent methodology. I’m not convinced that "slaves slayer" is a truly coherent message though. Both of Zodiacs solved ciphers solved to a plain text that is coherent and easy to read. "slaves’ slayer" sounds silly, and suspiciously like gobbledygook, don’t you think?

Excellent methodology. I’m not convinced that "slaves slayer" is a truly coherent message though. Both of Zodiacs solved ciphers solved to a plain text that is coherent and easy to read. "slaves’ slayer" sounds silly, and suspiciously like gobbledygook, don’t you think?

Who would dare accuse the executioner costumed Gilbert & Sullivan reciter of silliness?

The cipher is only half the message. The line reads "My name is ___ [slaves’ slayer]", which looks coherent enough to me, as far as Zodiac texts go.

If you are saying that "slave’s slayer" is a ridiculous self-title (not really logically self-consistent, grammatically flawed, etc.), then I surely agree, but I doubt Zodiac would. Especially given his apparent obsession with slaves and slaying, his established desire to taunt the police with his name (as in Z408), and his apparently immature personality.

So, is "slave’s slayer" a self-title that would appeal and sound just right to some people? Evidently yes. Proof: you can find online quite a few gamers (even on minecraft…), athletes, and others who call themselves "slave slayer" or "slaves slayer". I’d rather avoid linking personal profiles here, but see for example this game clip. I can provide other links over PM, if you can’t find them.

Would this nickname appeal to people who are actually interested in slaves? Definitely, I believe there is even a TV show episode with that name. And if you search carefully, you will find several "slave slayers" with content I wish I could unsee…

The cipher is only half the message. The line reads "My name is ___ [slaves’ slayer]", which looks coherent enough to me, as far as Zodiac texts go.

If you are saying that "slave’s slayer" is a ridiculous self-title (not really logically self-consistent, grammatically flawed, etc.), then I surely agree, but I doubt Zodiac would. Especially given his apparent obsession with slaves and slaying, his established desire to taunt the police with his name (as in Z408), and his apparently immature personality.

So, is "slave’s slayer" a self-title that would appeal and sound just right to some people? Evidently yes. Proof: you can find online quite a few gamers (even on minecraft…), athletes, and others who call themselves "slave slayer" or "slaves slayer". I’d rather avoid linking personal profiles here, but see for example this game clip. I can provide other links over PM, if you can’t find them.

Would this nickname appeal to people who are actually interested in slaves? Definitely, I believe there is even a TV show episode with that name. And if you search carefully, you will find several "slave slayers" with content I wish I could unsee…

I agree. Perhaps Zodiac really was deranged and delusional enough to take his own ridiculousness very seriously. Or perhaps it was a reflection of a darkly macabre sense of humour. Either way, I think a pretentious title like "slaves slayer" does fit with the rest of the persona.

Agreed, and there is also a third possibility: he was role-playing a character, inspired perhaps by big bad Zode. I admit that when my code highlighted “slaves slayer”, I had the same first reaction as replaceablehead, thinking it should be dismissed as gibberish. But I completely turned around after some thinking, rereading the Zodiac letters, and finding those websites. And doesn’t the SLA letter look to you now like a rather transparent hint?

Two more comments:

1. It is often said that ciphers like Z13 are hopelessly short or somehow corrupted by an abundance of previous flawed attempts, but neither claim is accurate. Cipher difficulty is a strong function of its structure, the allowed vocabulary, and other assumptions. If natural (not fine-tuned) assumptions limit the phase space such that a chance solution becomes improbable beyond some reasonable significance threshold, then a solution emerging against all odds is likely correct, regardless of cipher length or previous failures. Adjusted for the above assumptions, the corrected unicity distance-to-length ratio is much better in Z13 than it is in Z408 or Z340 (this incorporates homophones, so e.g. Z32 is far worse in this regard unless some rigid template or a drastic vocabulary trim are introduced).

2. Defects in a candidate solution must be demonstrated to be plausible with respect to the characteristics of the cipher origin (not too frequent or unusual, and in general also not too rare). Although we only have Z408 and Z340 to work with, they already demonstrate the defects we should expect, as Zodiac was so sloppy and arguably unoriginal. If you wish to see how defects could emerge, it is always helpful to use the key to encrypt the message yourself.

This exercise shows how Zodiac may have accidentally swapped the v and e in “slaves”: it’s easy to get confused when repeatedly skipping 3 letters backwards (or 10 forward), somehow encrypt the e first, and only then go back for the v. One way this could happen is if you simply skip a letter (Zodiac did something similar in Z340, thus shifting an entire row). Even if he didn’t miss the v, it’s possible to become confused by the coincidental v->E encoding in the present key (and there is evidence for similar confusion in Z340). Perhaps Zodiac even re-encoded the result: v->e->8 (8 representing the circled-8 symbol). There are alternative paths to error, of course. And who knows if some of this was deliberate.

After encrypting the last s in “slaves” (as the symbol A on the right), Zodiac introduced an incorrect e (encoded 8), either because of his tendency to do so (a few examples of redundant e’s are given above; there are others, and the literature discusses his dyslectic symptoms) or because he wasn’t sure if he did or did not already encrypt the e in “slaves” (he did, you would recall, but prematurely, which is confusing) or because he was thinking of an apostrophe or some separator. In any case, you see why he would now want to switch the s homophone (or temporarily revert to the Z408 key) for the s in “slayer”: two letters s here are encrypted consecutively/almost consecutively (although separated on paper by a 6-symbol jump).

One should of course be careful not to over-rationalize defects. But after seeing how Zodiac mistreated Z340, scenarios like the above seem plausible.

Interesting stuff.

There’s simply no way to verify a proposed solution like this. The cipher IS too short. There are plenty of words or phrases that fit perfectly without allowing for mistakes or flipping of letters, and there is no way to prove that any of those solutions are correct.

Also, I think your method of constricting the possibilities to include only words or phrases that Zodiac had been known to use in previous correspondences to be flawed. The solution to a cipher that’s supposed to be his name could be anything, including something we have not seen before.

The idea that he’s already basically given us the solution, and all we need to do is piece together words correctly that he’s already used is an interesting one, and it could be right, but I don’t see how it would be possible to know that for sure.

There’s simply no way to verify a proposed solution like this. The cipher IS too short. There are plenty of words or phrases that fit perfectly without allowing for mistakes or flipping of letters, and there is no way to prove that any of those solutions are correct.

Also, I think your method of constricting the possibilities to include only words or phrases that Zodiac had been known to use in previous correspondences to be flawed. The solution to a cipher that’s supposed to be his name could be anything, including something we have not seen before.

The idea that he’s already basically given us the solution, and all we need to do is piece together words correctly that he’s already used is an interesting one, and it could be right, but I don’t see how it would be possible to know that for sure.

Do I understand correctly your second and third points as saying that limiting the Z13 vocabulary to previous Zodiac correspondences is flawed, interesting, and could be right? In my view, if it’s right, it can’t really be flawed.

More importantly, if you categorically dismiss the possibility of limiting the vocabulary, regardless of where this might lead you, then of course it is impossible to verify any resulting solution (your first point). But I already explained above (comment 1 in my last post) why this approach is wrong – quite generally (it flies in the face of a great deal of scientific progress over more than a century) and specifically here (e.g., may I dismiss the Harden Z408 solution if I find an alternative solution in French or Arabic or one of the ~6500 non-English languages spoken today?). We really have no choice but to examine the statistical significance of a result given its priors, and this underlines most any cryptographic solution (including Z408 and Z340) even if one doesn’t bother to actually compute p-values. It’s fine to deprioritize priors that seem unreasonable to you, but I think you are saying that you can reject them even for arbitrarily small and robust p-values (i.e. incorporating multiple-trial corrections, within a natural phase space, passing consistency/sanity checks, etc.), which seems to me like an indefensible conviction, and contradictory if the idea ‘could be right’.

I can share some quantitative analyses, anecdotal evidence in favor of the above solution, and thoughts about its implications, but I think it is more appropriate to first see if any of you cipher warriors would like to challenge or support the solution. The statistical significance I get when weighing in the strong priors (mainly, a tiny vocabulary, and paying of course for the very short cipher length) exceeds the threshold for a scientific paper, even without additional support (and I already showed some supporting evidence above), but I don’t know what exact criteria are required here, if my error penalty may be too liberal, and if a long exposition is even worth the trouble. So I’m leaving this particular line of study for a while; let me just clarify first why I was expecting the transposition jump j to be a small prime number (and should have probably anticipated j=|3|…), as I left this unjustified earlier and it affects the p-value.

Zodiac clearly had some notion of the importance of prime numbers, as he took the block width w to be prime in all four ciphers: w=17 in Z408 and Z340, w=13 in Z13, and w=17 again for the first line in Z32 (tellingly splitting Z32 as 17+15 instead of the more natural and symmetric 16+16). But why did he use a large prime j=19 transposition in Z340? That seems an inconveniently large and unnecessary choice; he could have covered each 17-by-9 block fully and with no self-crossing using any constant j that is not a multiple of 3 or 17 (that’s without the “life is” stopper, otherwise the exact stopper-crossing rule should be incorporated). It was conjectured that he wanted a tightly wrapped text (i.e. every two symbols consecutively added to a line are adjacent, as in a scytale), which requires j=19 if we take w=17, a block height h=9, and left-to-right reading.

But why did he split the cipher into two such 17-by-9 blocks, leaving him with a third awkward 17-by-2 block which required a different reading rule? He could have avoided this block entirely and still tightly wrapped the text, using for example j=29 for a cipher split into two 17-by-10 blocks, or j=23 for a single 17-by-20 block. He may have added unplanned text for two additional lines, but I think a more reasonable answer is that he insisted on chess-knight moves, which conveniently require only three local steps (one down, two to the right), with no large and confusing jumps except at the edges. Here, h=17 immediately fixes j=19, and a tight text then requires h=9, leading to the specific choice of three blocks and their given unequal heights. Presumably, all this was discussed here before.

We see that not only line widths w, but also many of the valid transpositions j values turn out to be prime numbers (although this is not strictly required), so I suspected that Zodiac would consider primes safer for j, not only for w. And I can’t believe he would opt for a large prime, given the added work and higher risk of error. That is my justification for the higher priority given to a small prime |j| in my code. Let me now loosely speculate further on the reading rules.

I had a hunch Zodiac might try a negative prime j to show-off (knight and more sophisticated moves being impossible on one line…), but didn’t incorporate that in the code, giving equal weights to positive and negative j. In retrospect, I should have considered |j|=3 and perhaps specifically j=-3 as the most reasonable choice. First, |j|=2 or 3 make sense as the smallest primes, to avoid long jumps which may confuse: even knight moves proved too difficult for Zodiac in Z340. Second, |j|=3 simply as a knight move, flattened. Third, as a recurring Zodiac number (three blocks, three moves of the knight, three-itemizations in letters). But mainly fourth, because Zodiac may have given us the reading rules for Z340 and Z13 (and perhaps even Z32) in October 1970, frustrated after Z340 remained unsolved for almost a year, Z13 for six months, and Z32 for four months. In both his Halloween card and envelope, he drew a symbol suspected as unoriginal (perhaps copied from comics or a brand catalog), but added four points of his own, uncharacteristically neatly spaced in a (,’’,) pattern. Perhaps this should be read upside down (’,,’). In either case, and as illustrated in the image below, this looks to me in retrospect like reading rules: some combination of “one step down, two to the right” and (there is at least one more rule, otherwise why the fourth point?) “three steps left”. This feels hauntingly familiar and not original to Zodiac, but I cannot recall where I saw it done before; perhaps someone else would know. Again, apologies if all this was discussed in this forum and I missed it.

Edit:
The most elegant interpretation of the symbol, I think, is as follows, suggesting also the Z32 rule:

Edit:
The results in this thread are summarized in this post with free-access figures.

Posted by: @urik

Method: Z13 can be convincingly deciphered if the allowed vocabulary is drastically trimmed, otherwise 13 characters are insufficient for a unique solution. It is natural to assume that like its predecessor Z340, Z13 is a substitution cipher with transpositions (preferably but not necessarily with prime-number jumps, like j=+19 in Z340), thus being more complicated than Z408 due to the additional degree of freedom. However, Z13 is simplified by frequent symbol multiplicities (one triple and three doubles), suggesting that the cipher is almost, or entirely, non-homophonic (perhaps Zodiac wanted a simpler cipher, as Z340 remained unsolved for five months prior to Z13, or wanted his proclaimed name to be more readily known). The text may have been padded to obtain a line of prime-number length, as in the other ciphers. Now consider an additional constraint: based on the Z408 and Z340 solutions, Z13 too is likely to consist of the ramblings found in Zodiac letters and ciphers.

Results: Thus limiting Z13 to words derived only from established Zodiac texts, passed through a substitution cipher with transpositions, the frequent symbol multiplicities reduce the problem to a small set of possible constrained solutions, with a vanishingly small probability of producing an exact sensible solution by chance. One and only one of my trials makes sense as an approximate solution: ‘slaevseslayer’, obtained for j=-3 (minus meaning backward jumps) or equivalently j=+10, +23, etc. The self-title “slaves’ slayer” (with misplaced e’s discussed below) is consistent with subsequent Zodiac letters and recurring themes. The key, provided below, is non-homophonic with one exception (the letter ‘s’ is decoded twice as “A” in ‘slaves’, but once as “K” in ‘slayer’).

Discussion: Unlike previous suggestions, this solution is demonstrably of high probability when taking into account the very limited allowed vocabulary, frequent symbol multiplicities, and previous sloppy work by Zodiac. Moreover, with this solution, the Halloween card and bizarre SLA letter make sense as deliberate hints (see below). The p-value of the solution being coincidental depends on vocabulary size and tolerance to errors. My first test consisted of 12 prioritized Zodiac expressions, {killer, slaves, own, slayer, zodiac, murder, collect, sanfran, bomb, meannie, cop, paradice} (sic.), with a negligibly small p-value for a chance hit realized already at the fourth priority with modest errors. For comparison, a control sample of 24 viable words based on the Zodiac killer Wikipedia page (including for example the names of all suspects, but excluding Zodiac’s own words) produced no hits for arbitrary j and a very liberal error tolerance.

If the vocabulary is expanded further, then the very short length of Z13 motivates an enhanced role for context and content in the solution-acceptance criteria. It should then be noted that contemporary news headlines often referred to the Zodiac killer with variations on <word>+”slayer”. Related Zodiac correspondences include the subsequent Halloween card, which explicitly taunts at his identity and emphasizes “slaves” (the only element in the card that, as others have noted, does not seem to be based on 1950s comics). There are conflicting interpretations of the later SLA letter, but it certainly makes an effort to introduce the word “slay”. Note that Zodiac is known to provide clues to his ciphers, explicitly in his “radians+#inches” clue for Z32, and likely in his “I hope you” clues for Z340 (as others have noted, this opening phrase of Z340 is uncharacteristically repeated three times in the two letters breaking the subsequent five-month hiatus).

The misplaced e’s in the proposed solution are similar to mistakes seen in previous Zodiac ciphers. In particular, note that:
(1) As in other ciphers, Zodiac apparently forced a prime-number line length, thus adding an ‘e’ between words.
(2) Zodiac is known to add redundant e’s, e.g. “haveing” and “fireing” (in debut of Zodiac), or “oute” (bus bomb letter).
(3) Alternatively, the added ‘e’ may represent an apostrophe. Zodiac omitted apostrophes from previous ciphers, but used them (albeit inconsistently) in letters, and Z13 may have been special to him if proclaiming his title.
(4) The swapped ‘e’ and ‘v’ may well arise from the unfortunate encoding of ‘v’ in the proposed key as the symbol “E”.
(5) Indeed, Zodiac tends to confuse characters adjacent to such encoding coincidences, as seen in Z340.
(6) The homophonic deviation (‘s’ decoded once as “A”) is adjacent to the swapped ‘e’, consistent with some localized confusion.

Bottom line: if the ‘e-v’ swap is deemed acceptable, then this solution seems correct based on the very small p-value. Indeed, I challenge you to find a better solution constrained to Zodiac ramblings only, with or without transpositions, consistent with all symbol multiplicities. And consider: the Z340 solution shows a high frequency of Zodiac errors or variations in reading rules, in addition to spelling and other mistakes (deliberate or perhaps due to his suspected dyslexia). So, would you expect to find a 13-letter cipher by Zodiac which includes transpositions, yet doesn’t have at least one error?…

Proposed key:

 

 

Hey @urik.

I don’t know if you are — or if anyone is, for that matter — still around on this board, but still, I have a few questions.

Primarily, I would be interested for you to perhaps say a little more about how you arrived at your assessment of “a vanishingly small probability of producing an exact sensible solution by chance” from your analysis. You note, at several points in this discussion, your use in some manner of applying p-values in support of your conclusions. If possible, I’d like to understand in more detail what exact process you are referring to here. In particular, I’m wanting to get past my initial sense that, having in some apparently arbitrary manner started with a dataset of merely “12 prioritised Zodiac expressions,” you are then apparently wanting to make some probability assessment as to “producing an exact sensible solution” from these alone then, it seems, to propose that this has meaning. To me, that seems a little like seeking to calculate the probability of drawing three consecutive diamonds from a deck of cards, whilst from the outset choosing to ignore that there are, in fact, more than just three diamonds in the deck. Also, what were your criteria for limiting you data set down to these specific 12? (‘OWN’? No ‘CID’, ‘BUSS’, ‘NEEDLE’, ‘PIG’, ‘GIRL’, ‘BOY’, ‘ROCKS’?)

Another query about your data selection would be in regard to your inclusion of ‘SLAYER’. I get that you are wanting to start with your limited set of “Zodiac expressions,” but what criteria are you applying that would permit the inclusion of ‘SLAYER’? By every reasonable assessment, the ‘SLA’ letter is not among the confirmed Zodiac correspondences and, unless I have missed something, this is not a word he has ever used elsewhere. So, I’m just questioning the validity of providing a solution of two words of which the second hardly meets the criteria you have wanted to start with.

Aside from my curiosity on the above, I would just add — as I can see has already been discussed — that your solution must, again on any assessment, fail against the criterion of readability being, as I think you have noted yourself, grammatical nonsense.

A ‘climber of hills’ is a ‘hill climber’, a ‘decorator of houses’ is a ‘house decorator’, a ‘slayer of slaves’ is a ‘slave slayer’. The ‘of’ in ‘slayer of slaves’ is not an instance of a possessive, and so ‘slave’s slayer’ is likewise a nonsense. The subject of ‘slayer of slaves’ is ‘slayer’, slaves the object. Likewise with ‘slave slayer’.

These last are just some thoughts on your conclusion, but I am nonetheless interested still to understand a bit more about your method.

Posted by: @urik

Discussion: Unlike previous suggestions, this solution is demonstrably of high probability when taking into account the very limited allowed vocabulary, frequent symbol multiplicities, and previous sloppy work by Zodiac.

…

Bottom line: if the ‘e-v’ swap is deemed acceptable, then this solution seems correct based on the very small p-value. Indeed, I challenge you to find a better solution constrained to Zodiac ramblings only, with or without transpositions, consistent with all symbol multiplicities. …

Although I’m still not at all clear as to what is intended by “the very small p-value” argued for starting with an arbitrary and severely limited vocabulary, I had thought it worthwhile just to throw together a simple computer programme for constructing possible solutions “constrained to Zodiac ramblings only, with or without transpositions, consistent with all symbol multiplicities,” just to see what it might come up with.

For the first criteria, use can be made of the word list compiled by Glen Claston from the Zodiac correspondence, available on Dave Oranchak’s Cipher Wiki, here.

For the second, the following gives the breakdown of the available straight transpositions of the Z13.

The row number gives the shift steps for each transposition against the given cipher, which is transposition 1 (T1). After T12, of course, the pattern just repeats (modulo 13).

Program runs were made building length-13 strings out of words from Claston’s list, in the first instance (to limit run time) reduced to those of length 2 to 9 letters inclusive, just as a test. Separate runs were also made based on whether homophones were or were not to be permitted. Null cipher symbols were not allowed, and no consideration was made to the possibility of ordering errors having been made in such a small cipher. Spelling errors were, however, acceptable according to Claston’s dictionary.

No detailed study was made (nor need it be) of the complete set of results obtained, as it is sufficient to purpose just to provide one or two random examples. So …

On T7, no homophones:

AME0N[zN0AKM0
NICETRYTENDIE

as a possible comment on the previous line, rather than a completion of it, as:

My name is _______.

Nice try, ten die!

This would be consistent with the ‘kill count’ on the Z13 letter.

Equally, on T6, with homophones:

A0MKA0Nz[N0EM
ISTHISTHATSIT

as:

My name is _______;

is this. That’s it!

Other random examples that either complete or move on from the first line include

ECHOITWHENHIT (3.)
SAIDSATINTAXI (6.)
ISTHISBOMBSET (6.)

None of the above are offered to be taken seriously at all, just as examples of plausible text which meets the given criteria.

@shaqmeister Iam new to this site, I have always been intrigued by not only Zodiak but serial killers in general. 

Iam ignorant when it comes to cryptology and deciphering codes. Not sure if you’d be willing to help me to begin to understand where to start I would appreciate it. If not I understand, seeing that it would take time out of your life. With that I’ll close, I pray your day is blessed.