This week’s Zodiac Killer cipher thoughts…

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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?

Oops, that was a nice conference I just missed… :-(

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The NSA’s 2011 Cryptologic History Symposium (held in Johns Hopkins) ran yesterday and today, and had plenty of names long-suffering Cipher Mysteries readers will doubtless recognize in a flash:-

* Dr. Jim Reeds, Institute for Defense Analyses: “Editing the ‘General Report on TUNNY’”
* Dr. Benedek Lang, Budapest University of Technology and Economics: “Towards a Social History of Early Modern Cryptography”
* Elonka Dunin, Independent Scholar: “Kryptos–The Decades-Old Enigma at Langley”

(Personally, I’d also love to have heard this presentation:-
* Erin Higgins, Department of Defense: “Humanism, Magic, and Cryptology in the Renaissance”)

However, arguably the big cipher mystery story of the conference was the fact that Panel session 4B, moderated by David C. Cooley from the NSA/CSS Center for Cryptologic History, was devoted to “Investigating the Voynich Manuscript” and with two Voynich speakers well-known from recent talks and results (respectively):-
* Klaus Schmeh, Independent Scholar: “New Research on the Voynich Manuscript”
* Dr. Greg Hodgins, University of Arizona: “Radiocarbon Dating and the Voynich Manuscript”

Could I perhaps tempt any attendee to email me a short description of the conference that I can put up here as a guest post? Cheers!

Today’s Da Vinci claim…

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Some days I wonder if I should forget all about cipher mysteries – which are, quite frankly, far too much like hard work – and instead start up a news feed that promises subscribers one thing and one thing only: a freshly hatched cracked Leonardo da Vinci theory every day.

But even if such a tragic nadir of historical non-journalism were to prove possible (and, unfortunately, I suspect it probably would), it would surely be no more than a postmodernist anti-triumph: for what would it prove? That “war, war is stupid, people are stupid, and love means nothing in some strange quarters“? I rest my case, m’lud.

Yet despite the obvious foolishness of sending yet another Leonardo theory floating off into the ether like some flying Chinese lantern, even the very best Leonardo writers still feel the need to do just that. For example, Martin Kemp – Emeritus Professor of History of Art at Oxford, the crème de la crème of da Vinci-studying historians – recently co-write a book (“La Bella Principessa: The Story of the New Masterpiece by Leonardo Da Vinci”, summarized here) arguing that a picture long thought to be a 19th century fake is in fact a real 15th century drawing of Bianca Sforza by none other than Leonardo. Is it definitely by Leonardo (to be honest, Kemp’s not-quite-smoking gun proof is a fingerprint identification that seems more tendentious than tentative), or a German “Nazarene Brotherhood” creation from closer to 1820, as Christie’s wrote in their auction catalogue? Given the strong arguments both ways, I suspect Kemp may have subtly damaged his credibility by not really balancing his case out. He of all people should know that when it comes to Leonardo, things are rarely that one-sided. 🙁

But actually, that’s all by the by. Today’s fruity Mona Lisa story comes courtesy of p.22 of the Sunday Times, which reports “a startling theory about the work’s background” proposed by “Canadian doctor and amateur art historian” (do those words fill you with dread as well?) Donato Pezzutto. If, the good doctor claims, you join the right-hand edge of the Mona Lisa to the left-hand edge, you end up with a depiction of “Lake Trasimeno in Umbria” verrrry similar to the one that Leonardo depicted in his 1502-3 topographical map of Val di Chiana. If you want more, all I can do is refer you to Pezzutto’s article in the journal Cartographica: but… being honest… I have to say it sounds to me a lot like superficial nonsense built around a single rather unconvincing datapoint.

All of which of course points to why I couldn’t be the brains behind dailyleonardotheory.com: having to bite my tongue every day would kill me. Or rather, I’d probably need a new tongue every couple of days. Not my idea of fun, not by a long way. 🙁

German cipher mystery found and solved!

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Here’s a nice story that should bring heart to researchers struggling with uncracked homophonic ciphers (e.g. Zodiac Killer Ciphers, Beale Papers, etc). Kevin Knight, who Voynich Manuscript researchers may remember from various posts here, has now co-authored a 2011 paper with Beáta Megyesi and Christiane Schaefer from Uppsala University on how they cracked a hitherto unknown (to me, at least) 105-page ciphertext dated 1866 they call the Copiale Cipher.

Slightly unhelpfully, the authors refer only to the manuscript as having come “from the East Berlin Academy”: in fact, as far back as 1992/1993 the East Berlin Academy of Arts and the West Berlin Academy were merged into a single Academy of Arts, Berlin (i.e. the Akademie der Künste). I searched the Akademie’s archives to see if I could find the source but only managed to find one plausible-sounding hit:-

Record group: Döhl – Reinhard-Döhl-Archiv
Classification group: 6.1. Fremde Manuskripte
Lauf. Nummer: 3625
Dat. => Findbuch: o.O., o.D.
Titel: [ohne Verfasser]: die sentenzen verschlüsselter deutbarkeit […]

Perhaps someone with better German and more persistence than me will find the actual manuscript reference.

Anyway, Knight/Megyesi/Schaefer give a nice account of how they went about analysing the neatly-written ciphertext, the various hypotheses they came up with along the way, and how they finally managed to decrypt it (though admittedly they initially only transcribed 16 pages), apart from eight mysterious logograms (i.e. an eight-entry nomenclator “for (doubly secret) people and organizations”). Here’s their translation of the first few lines, which make it quite clear what kind of a book it is:-

First lawbook
of the [1] e [2]
Secret part.
First section
Secret teachings for apprentices.
First title.
Initiation rite.
If the safety of the [3] is guaranteed, and the [3] is
opened by the chief [4], by putting on his hat, the
candidate is fetched from another room by the
younger doorman and by the hand is led in and to the
table of the chief [4], who asks him:
First, if he desires to become [1].
Secondly, if he submits to the rules of the [2] and
without rebelliousness suffer through the time of
apprenticeship.
Thirdly, be silent about the [5] of the [2] and
furthermore be willing to offer himself to volunteer
in the most committed way.
The candidate answers yes.

The interesting thing about the date is that it predates the 1887 founding of the Hermetic Order of the Golden Dawn by 20 years or so: and many (if not most?) regular Cipher Mysteries readers will recall that that was founded with a (quite different) mysterious cipher document allegedly referring to a certain “Fraulein Anna Sprengler” mentioned in the enciphered text. By way of comparison, Aleister Crowley’s favourite Ordo Templi Orientis was founded only in 1895 or thereabouts.

Hence the really big question about this enciphered document is whether there is any connection (perhaps even Anna Sprengler) between it and the Golden Dawn Ciphers. The answer may well lie in the 89 pages as yet untranscribed by K/M/S… hopefully we shall see!

Update: since writing this, I found that K/M/S have put up a detailed web-page including scans, transcriptions, and English translations of the whole 105 pages. Codicologically, they say it is “beautifully bound in green and gold brocade paper, written on high quality paper with two different watermarks [and] can be dated back to 1760-1780.”

They also note that they think it is a document of an “18th century secret society, namely the “oculist order”. A parallel manuscript is located at the Niedersächsisches Landesarchiv, Staatsarchiv Wolfenbüttel.” Which of course rules Fraulein Sprengler out. 🙂

To be honest, the part in the ceremony described where they pluck a hair from the eyebrow of the initiate reminds me not a little of the Simpsons’ Stonecutters episode (“Who holds back the electric car? Who makes Steve Gutenberg a star? We do! We do!”), but perhaps let’s not dwell on that too much… 🙂

Leonardo da Vinci fruity theory roundup…

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What would it feel like to be a footballer with no goal? An actor with no stage? A projector with no screen? Or (finally getting to the point) a pseudohistorian with no infamous historical figure to attach his/her nutty theories onto?

All of which is why I feel sorry for poor old Leonardo da Vinci. He barely counts as a genuine historical figure any longer, for he has transformed into merely a blank canvas to be doodled upon by every new generation of messed-up researchers. Even the mention of his name in The Da Vinci Code is largely risible (he no more invented the ‘cryptex’ than the microwave oven). For every nutjob theory about Michelangelo, there must be a hundred crazy Leonardo ones: how they must be laughing at him in the Florentine Renaissance fama corner of Heaven.

Still, when you put a load of these fruity theories together, I (for one) come away with a reassuring sense of constancy: that the pareidoiliac capacity of the mass of human minds remains just as capable of finding new (yet often just as manifestly false as ever) ways of reading Leonardo’s works. So here are some recent ones you may not yet have heard of… probably for good reason, in most cases. Just so you know, I’ve placed them in broadly decreasing order of plausibility, to lull you into a frog-in-a-saucepan sense of false security.

(1) Might Giorgio Vasari have sealed Leonardo’s “Battle of Anghiari” mural behind a wall to preserve it? San Diego “art diagnostic specialist” Maurizio Seracini suspects he did, for when he worked on Santa Maria Novella, he sealed Masaccio’s fresco “Trinità” behind the wall on which he painted part of his “Madonna of the Rosary” – we know this to be true, because Masaccio’s original was rediscovered in 1861. And so Seracini is trying to build the most amazing camera in the world to peer through the wall, to see if Leonardo’s fresco is still at least partially there. And the evidence? “A tiny painted green flag” in Vasari’s picture, reading “‘Cerca, trova’ — seek and you shall find.” It’s not much, but is it enough?

(2) Not many people know that top-drawer da Vinci art historian Carlo Pedretti has long been hunting for a nude Mona Lisa: it’s a kind of Holy Grail of wobbly art history. In fact, Leonardo may well indeed have painted one, for there are a number of copies originating from the school surrounding the Florentine, all apparently from an original “Monna Vanna”. But is the one in the link Leonardo’s? Almost certainly not: but keep searching, Professor Pedretti, keep searching!

(3) In his imaginatively titled (but as yet unwritten) book-and-forthcoming-feature-film-documentary “The Mona Lisa Code”, Scott Lund thinks that Mona Lisa is an anagram of “Anima Sol”, and that she stands in for Janus in a deviously-crafted stereoscopic illusion, constructed around a map of Rome. Well, if it’s good enough for the Huffington Post, who am I to disagree? Personally, I’m rather more troubled by the anagram “No Salami”: did Leonardo intend the painting as pro-vegetarian propaganda? Or perhaps “Sal (sapit) omnia“? Once you start down that idiotic road, there really is no end to it. *sigh*

(4)-(6) If you’re suffering from intellectual poverty, here’s a bargain you can’t afford to turn down: three Last Supper theories for the price of one, courtesy of at Artden. Read all about Slavisa Pesci’s 2007 mirrored image wonderment; Giovanni Maria Pala’s 2007 claim that you can read a musical score from the hand-positions; and Sabrina Sforza Galitzia 2010 claim that there are hidden signs of the zodiac, pointing to a deluge to end the world starting on March 21st 4006 (but don’t worry, it’ll all be over by November 1st 4006).

(7) But finally, arguably the best of the lot is from Michelle Legro, an editor at Lapham’s Quarterly. Her hilarious post Top Chef, Old Master starts from the seed of [I think] truth that Leonardo was commissioned to automate the Sforza kitchens (though it all ended in disaster), but which she then grows into a wonderful towering wedding cake of nonsense. Sadly, the problem is that such gentle, well-informed satire is wasted on a world for whom mad Leonardo theories are ten-a-penny. I mean, why didn’t he just use his microwave oven? Tcha!

Apologies for three missing posts!

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A quick apology to Cipher Mysteries email subscribers: some illegal text characters (now fixed) that accidentally sneaked into a recent post caused Feedburner (the Google service I use to email posts to you) to go all huffy for a few days. Hence I’m very sorry to say that you’ve missed out on three recent updates to the site.

They were (in chronological order):
(1) Harvard Professor nearly wades into Voynich swamp… – discusses an upcoming lecture at Cambridge University on various Slavic mystery documents and John Stojko’s Voynich theory.
(2) Voynich fruitiness back in season… – discusses two recent fruity Voynich theories that popped up on the Internet, one linking the VMs with Jewish pharmaceutical conspiracies, the other with the coelacanth (yes, really!).
(3) Decent 2010 paper on the Zodiac Killer Ciphers – discusses a paper by two Norwegian academics searching for homophone cycles in the uncracked Z340 Zodiac Killer cipher.

Feel free to click through and have a look at them, they were all good posts, well worth a read. Enjoy! 🙂

Decent 2010 paper on the Zodiac Killer Ciphers…

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Here’s some more on the Zodiac Killer ciphers, specifically the interesting uncracked one (“Z340”). Though most of the images of this on the Internet are both monochrome and somewhat overexposed, here’s a link to a nice image of Z340 at a high-enough resolution to be useful. Thanks to this, I think you can see that the correction on row 6 is from a ‘right-facing K’ to a ‘left-facing K’, which could well be a copying error from an intermediate draft.

What’s more, it allows us to transcribe the ciphertext with a high degree of confidence that we’ve got it right: so here’s the transcription that Dave Oranchak and glurk use, which should be more than good enough for non-Zodiac experts wanting to play with it too:-

HER>pl^VPk|1LTG2d
Np+B(#O%DWY.<*Kf)
By:cM+UZGW()L#zHJ
Spp7^l8*V3pO++RK2
_9M+ztjd|5FP+&4k/
p8R^FlO-*dCkF>2D(
#5+Kq%;2UcXGV.zL|
(G2Jfj#O+_NYz+@L9
d<M+b+ZR2FBcyA64K
-zlUV+^J+Op7<FBy-
U+R/5tE|DYBpbTMKO
2<clRJ|*5T4M.+&BF
z69Sy#+N|5FBc(;8R
lGFN^f524b.cV4t++
yBX1*:49CE>VUZ5-+
|c.3zBK(Op^.fMqG2
RcT+L16C<+FlWB|)L
++)WCzWcPOSHT/()p
|FkdW<7tB_YOB*-Cc
>MDHNpkSzZO8A|K;+

OK, today’s thought follows on from my most recent Zodiac Killer post, which wondered to what degree cryptologists could make use of the likely presence in Z340 of broadly the same kind of homophone cycles present in the earlier Z408 ciphertext. Well blow me down if I didn’t just run into exactly that today, a paper by Håvard Raddum, Marek Sýs called “The zodiac killer ciphers” published in Tatra Mountains Maths Publ. 45 (2010), pp.75–91: the fulltext is freely downloadable here. There’s an earlier (slightly less formal) 2009 presentation here.

The two authors found evidence of low-level (i.e. length = 2 or 3) homophone cycle structure in the Z340 but not in its transposed version, which is a good indication that the cipher itself isn’t (diagonally) transposed. However, having myself written codes to look for homophone cycles in Z340, I think their assumption that it is a single homogenous cipher is not really justified: they would have got much more striking values had they divided it into two.

Really, the challenge with searching for homophone cycles in Z340 that they failed to address is that the statistical significance of the length 2 or length 3 homophone cycles they found is relatively low compared with the Z408 cipher. How many standard deviations are these actually away from the centre of the distribution? The biggest statistical problem with searching for best homophone cycles is that you have a lot to choose from, which I believe reduces the statistical significance of any you do happen to find. It’s a kind of statistical “darts paradox”: hitting the bullseye once in a million throws doesn’t suddenly make you a great darts player.

Still, they build up a lot of theoretical machinery (though I somehow doubt that you can reliably build n-cycles out of (n-1)-cycles given the many deviations from the cycle scheme the Zodiac Killer makes), which may well prove useful. Definitely something to ponder on.

Voynich fruitiness back in season…

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Go on, admit it: for all your research rationality and historical smarts, you secretly love nutty Voynich theories – the fruitier they are, the more in control of your own thoughts you feel. Of course, that feeling of superiority is merely the most fleeting of illusions: the only real difference is that you’re smart enough to keep your mouth shut. Better to remain silent and be thought a fool etc.

So here are some low-hanging Voynich fruits to help you feel better about yourself. Think of it as therapy you can actually afford!

(1) “Flanders”, a 50-post veteran on theforbiddentruth.net, shared his thoughts on “probable jew” Wilfrid Voynich’s conspiracy-fuelling pharmacological manuscript:-

These documents are called the Voynich Manuscripts, as they came into the possession and the estate of a probable jew, Wilfrid Michael Voynich, allegedly from the jesuits in Villa Mondragone.

Because of the jesuit, Vatican, jewish-communist connections as well as the mystery surrounding the documents, they may be of interest to those whose interests lie in those areas. Some of the information in the links ties in with activists in the pre-jewish/communist takeover of Russia. […]

One has to wonder is whether the documents have not actually been already translated while our present “wonderful jewish drug companies” are benefitting from “their research” into the “modern” pharmaceticals. Maybe someone else will have the key to knowledge which would remove some of their mystery.

Marvellous stuff, simply marvellous.

(2) Mark Russell added a comment to a Voynich-related post on the Government Book Talk website (which was, sensibly enough, actually discussing how to download Mary D’Imperio’s book “Elegant Enigma”)… but his thoughts memorably led off into the little-known world of the “fish/mammal”:-

4) In one of the [Voynich Manuscript’s] pictures they have a picture of a Pre Historic Fish/Mammal in the Middle of the page.
5) Recently they have found Two of these Fish/Manuals in the ocean—Must be over 100,000,000 years old in evolution.
6) They say that this species of fish/mammals was the evolution of Man going to Land.
[…]
17) The Scales on many of these pictures look like the scales from the Pre-Historic Fish/Mammal.
[…]
It is very interesting that this book has a Picture of a Fish/Mammal—We have only found (2) of these Fish/Mammals in the last 100 years. There is no way anyone should of been able to see one of these Fish/Mammals back in the 1400′s or the 1500′s.

Just in case you’re not quite connecting with Mark here, I’m pretty sure he’s trying to reach towards linking the fish-eating-a-nymph drawing in the Voynich Manuscript’s Q13 (the water / balneological quire) with the famous ‘Lazarus taxon’ – i.e. a species formerly thought to be extinct, but which subsequently turned out to be still alive – the coelacanth. So here’s the Voynich fish…

…and here’s a coelacanth caught in 1974 (courtesy of Wikipedia, bless ’em)…

Spooky, eh? 🙂

Harvard Professor nearly wades into Voynich swamp…

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Here’s an upcoming talk at Cambridge’s Sidney Sainsbury’s Sussex College on 12th October 2011 at 5pm which might be of interest to Voynich researchers. Harvard Professor George Grabowicz promises an interesting couple of hours with his lecture “The Eternal Return of National Mystifications: the Voynich Manuscript, the Book of Vles and the Igor Tale“. (It seems to be a follow-on to a talk he gave to the ASEES 42nd Annual National Convention in November 2010called Code and Message in Slavic Mystifications: the Book of Vles, the Voynich Manuscript and the Igor Tale.)

You’d be forgiven for not having heard about the other two named manuscripts: I’d only heard of the first one – the Book of V[e]les because it is generally believed (from its faked-up use of modern Slavic language) to be a literary forgery, and not the ancient Slavic battlefest written on mysterious planks as was originally claimed. Unless Grabowicz has some surprising new angle on this, I guess this part will be pretty straightforward.

But you’ll probably be unshocked to hear that there is a long-running debate over the authenticity of the final manuscript of the trio, “The Tale of Igor’s Campaign” (which, incidentally, Borodin used as the basis for his opera “Prince Igor”, historical trivia buffs). While Wikipedia would have us believe that the “current scholarly consensus” on the Ms is that it’s a genuine 12th century manuscript, there’s a vocal cadre of Harvard historians (led by [former?] Andrew W. Mellon Professor Emeritus Edward L. Keenan) who actually think it’s a goddamn fake. I can only presume, ummm, Harvard Professor Grabowicz has his own opinion on this matter. 🙂

“The Eternal Return” part of Grabowicz’s talk’s title, then, would seem to be about how some people would love these stories to be true almost in a religious way, so as to return to some mythically / nationalistically pure primordial state (following Mircea Eliade’s use of the term). But… what has all that got to do with the Voynich Manuscript?

Directly with the VMs itself, not a lot, I’d say: the claims that the Voynich is a fake or hoax remain extremely lightweight, and fail to sit comfortably with the radiocarbon dating, codicology, palaeography, and art history (all of which point fairly unequivocally to the 15th century). But then again, there is also a rich loam of faux historical retrospective storytelling that various people have projected back onto the VMs, most notably (in my opinion) John Stojko’s hilariously fruity “Letter to God’s Eye”.

It turns out that Grabowicz covered Stojko’s nonsense (admittedly tangentially on p.21, but it’s there none the less) way back when in a nice little article from 2001. What he also mentions – somewhat scarily – is that Stojko’s Voynich theory also appeared to be inching its way into nationalist accounts of Ukrainian history. It’s probably this that “Michael the friend of D” was talking about in 2007, that I mentioned somewhat cursorily here.

OK, it’s true that I tend to talk about these hallucinatory nationalist back-projections as if they’re high comedy, but the reality is that they’re desperately low tragedy, weapons of mass mystification used to trigger slow-motion car crashes between nations and factions. So, if Grabowicz can stoutly resist the postmodernist temptation to trashtalk the VMs’ authenticity (a swamp every sensible academic should actively avoid) and focus instead on the quasi-militant use of stupid theories in troubled times, it should be a great talk. 😉

Thoughts on the Zodiac Killer Z408 and Z340 ciphers..

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As I mentioned here and indeed here a few days ago, my usually-Early-Renaissance-focused thoughts have of late been turning slowly to the Zodiac Killer Ciphers, in particular to the unsolved 340-character cipher known as “Z340”. Unusually as cipher mysteries go, we also have an earlier cipher called “Z408” (no prizes for guessing its length) by the same person, one that was quickly cracked (using the crib “KILL”). Z408 turned out to be a homophonic simple substitution cipher (but with spelling mistakes, copying mistakes, and a few subtly odd features); and there are plenty of good reasons to think that Z340 will share many of these same basic aspects (but made somewhat harder to crack).

Even though it was originally a crib which helped to crack it, Z408 has other weaknesses, most notably the way it sequentially cycles through homophones (“multiple ciphertext shapes for the same plaintext character”). For example, plaintext ‘t’ maps to the four ciphertext homophones HI5L, and appears in the text as the sequence HI5LHI5ILHI5LHI5LHI5LHI5LI5LHL5IIHI. If you count each successful letter-to-letter transition matching the modulo-4 sequence [HI5L] as a 0.25 success event (=26) and each non-match (=8) as a 0.75 failure event, I believe you get a raw probability of less than 1 in a billion (i.e. of at least 26 successes from 34 events). Please check my maths, though – I used this online binomial calculator with N = 35-1, k = 26, p = 0.25, q = 0.75. For more on these homophone sequences, Zodiac ciphermeister Dave Oranchak kindly pointed me at a full list of Z408 homophone sequences.

Incidentally, the top few match counts are:-
e -> ZpW+6NE – N = 54-1, k = 38
t -> HI5L – N = 35-1, k = 26
s -> F@K7 – N = 20-1, k = 15
o -> X!Td – N = 27-1, k = 13
n -> O^D( – N = 23-1, k = 20
i -> 9PUk – N = 44-1, k = 35
a -> GSl8 – N = 26-1, k = 10

It would be great to tell you how statistically significant these sequences are, but I know enough stats to know that it’s not quite as easy as it looks (for a start, we’re preselecting the best order of letters to use) – any passing statisticians, please feel free to leave a comment. I’m also quite surprised that nobody has apparently tried to use this weakness as a direct way to find the Z340 cipher’s homophones (in fact, John Graham-Cumming also blogged about this in June this year), but – as I’ll show shortly – I suspect trying just that on its own wouldn’t be enough.

Taking a brief step sideways, I’m always intrigued by mistakes in ciphers, because these often point to how the cipher was constructed. One interesting feature (but which I’m still trying to understand to my own satisfaction) is the solid triangle cipher shape in Z408, and how it appears to encipher different letters at different times. The view often put forward elsewhere is that this varied due to copying errors, perhaps arising because the Zodiac Killer’s pen was too thick, causing him to misread his draft version. As for me, I’m not so sure, because the solid triangle decrypts to a curious sequence:-
* “A” in “bec-A-use”
* “S” in “mo-S-t dangerous”
* “A” in “an-A-mal”
* “S” in “mo-S-t thrilling”
* “A” in “with -A- girl”
* “S” in “if it i-S-”
* “E” in “my slav-E-s”
* “A” in “my -A-fterlife”

Of these, only the “A” in “an-A-mal” is possibly a copying error (“I” is enciphered by an empty triangle shape) as compared to just a spelling mistake (the Zodiac Killer has plenty of those). But even that seems a little unlikely when the whole ASASAS[E]A pattern that emerges – so very similar to the homophonic sequences discussed above – is pointed out. I haven’t yet figured out what this implies, but it’s pretty interesting, right?

Moving on to the uncracked Z340 cipher, I have to say that what strikes me most is the difference between its top half (lines 1-10) and its bottom half (lines 11-20). It turns out that back in 2009, FBI codebreaker Dan Olson pointed out to Tom at zodiackiller.com that lines 1-3 and 11-13 contained very few repeats: other people have wondered whether this points to some kind of block-level transposition going on. Me, I suspect there’s a far stronger inference to be made: that even though they share nearly all the same character shapes, I’m pretty sure that the top and bottom halves of Z340 use completely different cipher letter assignments, and hence may well need to be cracked independently. Further, I suspect that the Zodiac may well have intended to send them out separately (Z408 was sent as three independent sections), but (for some reason) ended up sending them both as a single cipher.

[Incidentally, I also don’t believe that the last few letters of the bottom half of Z340 are genuinely part of the ciphertext to be cracked: they seem to spell “ZODAIK”, which is just a touch too coincidental for me. 🙂 ]

Right now, I think that a constructive first big step would be to search for statistically significant homophone sequences in the top and bottom halves of Z340, because we can be reasonably sure that the most frequent letters will probably have four or more homophones, just as with the Z408 cipher: trying this out may well yield some surprisingly revealing results. Any takers at the FBI? 😉