The Voynich zodiac section – a block paradigm match…?

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Statistical and cryptanalytical analyses tend to assume that ciphers will fit one of a small number of well-known and well-researched pigeonholes (e.g. Vigenère, autokey, etc). Unfortunately, this kind of “backwards attack” can often be stopped dead if the encipherer includes one or more additional steps sideways, unless the backwards attacker happens to be cunning or lucky enough to reconstruct those tiny steps.

But as they knew in Bletchley Park, it is sometimes possible to “forwards attack” cryptograms. There, a “crib” was the name BP codebreakers used to describe where you already had the plaintext, typically obtained by decrypting the same message enciphered using a different cipher system: having this would help the code-breakers reconstruct daily settings for the second cipher etc. Just so you know, this is precisely why you should never forward a received (and deciphered) message word-for-word using a different cipher, a lesson many WW2 code bureaux stubbornly failed to learn.

Similarly, the idea behind my “block paradigm” methodology is that if we can use secondary historical clues to determine the plaintext from which a given section of ciphertext was derived, we stand a reasonably good chance (I think) of reconstructing the cipher forwards from there. You can therefore think of it as a high-level “historical crib”, where the plaintext is reconstructed via in-depth research rather than by breaking a parallel cipher.

At the very least, this whole process could very possibly yield a completely different class of problem to solve, which in the case of the Voynich Manuscript shouldn’t be a bad thing, given that a century’s worth of backwards attacks has been largely unproductive. 🙁

But what might the plaintext for the Voynich zodiac look like? Would we even recognize it if we had it in front of us?

The Voynich zodiac section

In the same way that many people have long suspected that the Voynich Manuscript’s “Herbal” section(s) probably contains plant and/or remedy descriptions (albeit secret, valuable or unexpected ones), there has long been a strong – yet untested – historical hypothesis about what the Voynich zodiac section might well contain, which is simply this: per-degree astrology. This is because each sign seems to be divided into 30 elements (29 in the case of Pisces, though this may possibly have simply been a slip of the quill), and there are 30 degrees in each zodiac sign (i.e. 12 x 30 = 360).

The modern history of per-degree astrology is something I covered here before: it moved back from Marc Edmund Jones (1925) to the nineteenth century astrologers “Charubel” (who claimed he channelled his per-degree symbols) and “Sephariel” (who claimed that he copied his from “La Volasfera”, supposedly a Renaissance book by Antonio Borelli / Bonelli [did he mean Guido Bonatti?], but this has never turned up).

It’s often written that Western medieval per-degree astrology arrived from Arabic sources via Pietro d’Abano (while he was in Spain during the 13th century). Heidelberg has a 15th century German translation of his work in MS Cod. Pal. Germ. 832 (“Regensburg, nach 1491”), which Rene Zandbergen mentioned in a comment here back in 2009. (If you look at fol. 36r onwards, you can see a few lines of text for each of the thirty degrees in each of the signs in turn, along with some rather jaunty miniatures.)

Prior to the Arabs, you can doubtless trace all this back to the original Indian sources (Diane O’Donovan pointed to the encyclopaedia-sized “Brihat-Samhita” by Varahamihira), but taking things back that far falls way beyond my paygrade, so I’m not going to attempt it in this post. 🙂

However, if you take the time to read Chapter XII of volume III of Lynn Thorndike’s “History of Magic and Experimental Science”, you’ll see that another medieval writer famously wrote on per-degree judicial astrology: and this is where my search began.

Andalò di Negro

Andalò di Negro (fl. first half of the 14th century) was a noble from Genoa. Boccaccio, who he famously taught “in the movements of the stars”, noted that “since [Andalò] had traversed nearly the whole world, and had profited by experience under every clime and every horizon, he knew as an eye-witness what we learn from hearsay” (De genealogia deorum, XV, 6, quoted in Thorndike, p.195).

andalo-and-boccaccio

One of Andalò’s works (“introductorium ad iudicia astrologie”) that discussed per-degree judidicial astrology was of particular interest to me. So, back in 2009, I managed to get some working photocopies of it courtesy of the Warburg Institute’s Photographic Collection: these were of the two known documents listed further below.

Interestingly (and unlike the Pietro d’Abano-derived Heidelberg manuscript), the key feature that seems to oddly parallel what we see in the Voynich Manuscript’s zodiac section is that these two documents contain only a small amount of data per degree (though admittedly arranged in columns of a table rather than in the form of nymphs, stars and labels).

The first document is at the British Library: I managed to get a look at this in person, kindly thanks (if I recall correctly) to a letter of introduction from Dr David Juste, who was then a historian of astrology at the Warburg Institute. One unusual feature was that a few key parts of the tables were highlighted in different colours, something that wasn’t at all apparent from the black-and-white photographs taken for the Warburg in the (I guess) 1920s or 1930s. (Sadly, the colour notes I took at the time have long since disappeared).

* BL Add. MS 23770 (BL: “14th century”, Warburg: “circa 1350”)
http://searcharchives.bl.uk/IAMS_VU2:IAMS032-002097417 – “Letter of introduction required to view this manuscript”
1. “INTRODUCTORIUS ad iudicia astrologie co[m]positus ab A[n]dalo de Nigro de Janua;” with paintings of the signs of the Zodiac, the planetary Gods, etc., ff. 1-44.
Aries (8r), Taurus (9v), Gemini (11r), Cancer (12v)
Leo (13v), Virgo (15r), Libra (16v), Scorpio (17v)
Sagittarius (18v), Capricorn (19v), Aquarius (20v), Pisces (21v)
You can see monochrome thumbnails of these twelve images on the Warburg Institute’s Photographic Collection.

In the case of the second document, since 2009 Cod. Fonds 7272 has been placed online and made downloadable by BNF. As a result, I can include links directly into the Gallica pages for you (which is nice).

* BNF Cod. Fonds Latin 7272
http://gallica.bnf.fr/ark:/12148/btv1b8452771j
Aries (112r), Taurus (114r), Gemini (115v), Cancer (116v)
Leo (118v), Virgo (119v), Libra (121r), Scorpio (122v)
Sagittarius (124v), Capricorn (126r), Aquarius (127v), Pisces (129r)

Here is the Aries table as it appears in BNF Cod. Fonds Latin 7272, courtesy of Bibliothèque nationale de France via Gallica:

7272-Aries-table

By way of a guide, fol. 22v of BL Add. MS 23770 explains (says Thorndike, p.192 n.5) Andalò di Negro’s “fivefold distinction of degrees within the signs: 1, masculine or feminine; 2, lucidus, tenebrosus, fumosi, or vacui; 3. putei; 4. azamena (like the putei, to be avoided); 5, augmentates fortunam.”

However, I have to mention at this point that according to Boncompagni’s (1875) “Un Catalogo dei Lavori di Andalò di Negro” (an offprint taken from “Bullettino di Bibliographia e di Storia delle Scienze, Matematiche E Fisiche”, Tomo VII – Luglio 1874, and for an original of which I paid a load of money several years ago but which is now available print-on-demand from Kessinger *sigh*), there might possibly be a third copy still floating around.

Boncompagni (pp.54-55) mentions that an 1834 alphabetical index of the Biblioteca Altieri di Roma published by Federico Blume lists: “de Nigro, Andali de Ianua, Introductorium ad iudicia astrologiae, Fogl. membr. V.E.5”. Moreover, Emilio Altieri’s index to the Biblioteca Altieri (car. 11a, recto, lin.2) reads: “Andalus de Nigro de Janua, de Astrologia, Pil. 13, Lett. A. Numo. 5”. Yet according to a 1690 index, “Il detto Altieri non possiede ora alcun esemplare manoscritto d’alcun lavoro di Andalo di Negro“, so it seems that it had already disappeared by then.

That sums up the known versions of this work tolerably well: but what might these tell us about the Voynich zodiac? Obviously, that’s a good question something I’ll have to leave for a follow-on post…

Posted in: Voynich Manuscript

Swedish Zodiac Killer Z32 theory…

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A few days ago, I had a nice email from two Swedish engineers called Henrik (Henke) Sundberg and David Thelin: surprisingly, they claimed that they had worked out the details of the Zodiac Killer’s 32-character “map cipher” (also known as “Z32”).

The first thing I did was to put up a new page describing the Z32 cipher, something I’ve been meaning to do for a few years: as normal, I tried to cover the raw factuality and basic observations rather than out-and-out theories and speculation.

The short version is that the letter-shapes in the Z32 cipher look nearly exactly the same as the (famously solved) Z408 cipher, which makes it seem very much as though it too is a homophonic cipher, though with different letter assignments (deciphering it using the Z408 key doesn’t seem to yield anything sensible). Unfortunately, 32 characters (made up of 29 different shapes, i.e. only three appear more than once) wouldn’t normally be anywhere near large enough for a homophonic cryptogram to be cracked, unless you had some significant additional information to work with. (Hint: a cipher key would be a good start. 🙂 )

However, in this case there was some other extra information: a roadmap of the San Francisco Bay Area with a “Zodiac Killer” shape centred on Mount Diablo, and a note saying “The Map coupled with this code will tell you where the bomb is set. You have untill next Fall to dig it up“. A second “little list” letter (posted a month later) give a further clue: “PS. The Mt. Diablo code concerns Radians 4#inches along the radians“.

Sundberg and Thelin’s theory (described in this PDF file) is that it’s in fact a very scientific cipher, as much a stegotext as a cryptogram.

Z32-cipher

From this, they extract the phrases “C3H3”, “Octane”, and “North of West”, while “HCEL(Zodiac)PW(triangle)” reminds them of how the molecule HClO3 looks, centred around the Zodiac symbol. From which they deduce that they need to look 1 inch (i.e. 6.4 miles) along a vector due West from magnetic North.

Guys, guys… I’m really sorry, but I think you’ve got it wrong. Nobody in their right (or indeed wrong) mind would concoct a chain of reasoning based around a vague resemblance to a particular molecule in order to encode a unit vector. Even dear old Jessica Lee wouldn’t do that, much as she likes chemistry and ciphers.

Look: the Zodiac Killer wasn’t some evil scientific genius, he was a sick, unhappy man with a grudge against the SFPD (probably a surrogate for his sick unhappy relationship with his abusive, distant father) on a gun-powered external power trip, a (literally) vain attempt to right the perceived wrongs in his personal life. I don’t even think he knew properly what a “radian” is, because he doesn’t use the term correctly in his note.

Posted in: Zodiac Killer Ciphers

Zodiac Killer Ciphers

The Zodiac Killer was a serial killer active in California in the late 1960s and early 1970s. He was never formally identified or charged, though a number of people have since written books and articles claiming to have named him.

There are four main Zodiac Killer Ciphers / cryptograms that are widely believed to have been sent by him:
* Z408 – 31 Jul 1969 – (solved)
* Z340 – 08 Nov 1969 – cipher (unsolved)
* Z13 – 20 Apr 1970 – “my name is” cipher (unsolved)
* Z32 – 26 Jun 1970 – the “map code” cipher (unsolved)

There are also several other ciphers which have been attributed to him (but which seem rather more likely to be hoaxes and/or copycats), most notably:-

* Z148
* Z63

Zodiac Killer Z32

The “Z32” cipher (i.e. the Zodiac Killer’s 32-character-long cipher, also known as the “map code” cipher, or the “Phillips roadmap cipher”) was sent to the San Francisco Chronicle on 26th Jun 1970. It was part of a letter that ended in this way:-

map-letter-cropped

This cipher was accompanied by a section of a map: made by the Phillips 66 company, this was a roadmap of California that at that time was widely available at service stations. (There’s a huge version here.) The Zodiac Killer had placed his signature symbol on top of Mount Diablo, together with what seem to be instructions as to how to link the map with the contents of the cipher.

map2

A follow-up note from the Zodiac Killer (on page 5 of the “little list” letter, postmarked 26th July 1970) added: “PS. The Mt. Diablo code concerns Radians &#inches along the radians“.

list-letter-page5-cropped

Cipher Facts

Only three shapes (the ‘C’-shape, the ‘O’-shape, and the hollow triangle shape) within the ciphertext appear twice: everything else appears exactly once. This seems to imply that we are looking at a homophonic cipher, the same cipher technique that the Zodiac Killer used in his Z408 cipher. As a result, it would be impossible to solve such a small homophonic ciphertext unambiguously without a large amount of extra information, or without knowing the cipher key.

Interestingly, because nearly all of the cipher shapes used in the (solved) Z408 cipher key reappear in this cipher, it seems possible that this might do the trick. Unfortunately, applying the Z408 homophonic cipher key to it yields nothing that makes any obvious sense:-

(C) I F E L N I O W H D A (Ω) N G O A
O E S N B X (shaded box) T (C) E T D I E I

Furthermore, solving this (slightly more language-like) cipher as if it were a newspaper cryptogram again seems to yield nonsense, e.g. “dsbelishourtwichthekingmadearses“.

Geography Facts

The Phillips 66 California roadmap scale for “San Francisco And Vicinity” is 1 inch to about 6.4 miles: so the plaintext should presumably contain both a number (for the direction) and a number in inches (i.e. to be multiplied by 6.4 to give a physical distance in miles along that direction).

The reference to magnetic north seems to imply that the bearing was calculated not from the map, but by eye from the peak of Mount Diablo. (Here’s a video panorama taken from the top platform area, and diagrammatic views facing North and facing South.)

People will always have different opinions on anything to do with the Zodiac Killer, but it seems most likely to me that at the top of Mount Diablo he turned his watch round (or rotated an external bezel) so that 12 o’clock faced magnetic North; and then read off the time (or bezel value) that would point to his bomb target of choice. Hence the plaintext part indicating ‘direction’ could easily be something like a time, though some people have concluded that it would be measured in radians.

In 1970, magnetic North for this area fell 15 degrees clockwise of true North: so for example San Francisco (at 256 degrees round from true North) would have been at about 241 degrees clockwise relative to magnetic North, i.e. extremely close to “eight o’clock”. Similarly, San Mateo sits 227 degrees from true North, i.e. 212 degrees from magnetic North, i.e. extremely close to “seven o’clock”.

Claimed Solutions

The most famous claimed solution to the Z32 cipher was by Gareth Penn, who was convinced that the word “radians” held the key, and that the locations of various killings (relative to Mt Diablo) were determined by some kind of mathematical or geometric scheme. However, it seems fairly unlikely that this was correct, and few now believe that the Zodiac Killer followed the precise scheme suggested by Penn.

“I want to report a murder” – Otto Kinzel rocks the Zodiac…

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If you happen to like both technical-minded heavy metal and cipher mysteries, I might possibly have a hot tip for you (thanks to Phil Strahl’s blog). Otto Kinzel has released an album on Bluntface Records called “I want to report a murder”, where every track is based on features or events in the Zodiac Killer cipher case.

Kinzel has even done a 7-minute video of the title track “I want to report a murder”: but you might want to to skip past the first atmospheric 1 minute 28 secs of video intro and get with the metal…

PS: if you’re reading this as an email & the video didn’t get embedded, here’s the direct link to the video on YouTube. Enjoy!

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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?

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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.

Posted in: Zodiac Killer Ciphers

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? 😉

Posted in: Zodiac Killer Ciphers ⋅ Tagged:

Zodiac Killer 340 cipher cracked (…errrm, no, not really, sorry!)

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A certain Corey Starliper of Tewksbury, Mass claimed last month (July 2011) to have finally solved the famous-but-uncracked “340” (i.e. 340-glyph long) message sent in 1969 to the San Francisco Chronicle by the Zodiac Killer. Bless ‘im, but his so-called solution boils down to opportunistically choosing between multiple Caesar shifts, while modifying words and adding in extra ones where it all goes a bit Pete Tong.

Hence it should be no great surprise to most Cipher Mysteries readers that, however sincerely Mr Starliper believes his solution to be correct, I’m sure it’s basically a crock. However, the best thing about it is that it inspired Dave Oranchuk to post up a nice page demolishing it (though I personally wouldn’t call it a “hoax”, but rather a fairly typical example of the kind of self-convincing non-cryptology we’ve all seen countless times).

I don’t normally post on the Zodiac Killer ciphers (I’m more of a Renaissance guy myself), but plenty of people do find it interesting: to me, it has a home-grown 2d transposition feel to it, a bit like a lo-tech d’Agapeyeff cipher. Incidentally, I rather like Dave Oranchuk’s Zodiac webtoy, which lets you try out all kinds of crypto toolbox stuff on it (and indeed on various other ciphers). Enjoy! 🙂

Posted in: Zodiac Killer Ciphers

German zodiac woodcuts…?

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My last post on Elmar Vogt’s new blog received a comment from infinitii, asking me for the source for the suggestion that the zodiac motifs may have been copied from a (possibly 14th century) German woodcut calendar. I had long forgotten the story’s origin, but a quick grep through the VMs mailing list archives (the ones before 2002 that aren’t yet on the web) turned up what seems to be the key thread.

Jorge Stolfi began (29Dec2000):-

In the meantime, I remembered I had seen something like the VMS Sagittarius somewhere in the astrological books. And I have found it on the Web – have a look at:

  http://www.englib.cornell.edu/mhh4/planets/jupiter.html

This is from an early (15th c.) German “Planets’ Children” blockbooks (the planets’ children theme was also found in some of the Books of Hours – eg. the most beautiful one of Duc de Berry). The crossbow man looks *very much* like the VMS Sagittarius to me. Also note that the actual Sagittarius in a small circle at the feet of Jupiter above is represented as a man – not a traditional centaur (even though he holds a standard bow).

I think this confirms the 15th c. German origin as stated by Panofsky (a great authority, after all) – at least until a better argument is put forward (I am not convinced by the humanist hand argument and still less by the other Italian origin arguments recently presented by Dana – people were coming to study in Italy from all over Europe and thus
were heavily influenced by Renaissance culture and art).

Rene Zandbergen then replied (30Dec2000) to the last two paragraphs:-

Yes, very ‘block book’ and very German. In Saxl’s ‘Verzeichniss’ other nice examples can be seen.

I’m not yet ready to decide. Is the theme German and the execution Italian? Or in the block book, where the execution is German, the theme of the planets’ children was widespread. The profusely illustrated but otherwise only moderately useful book ‘Alchemie & Mystik’ by Alexander Roob gives a lot of nice examples.

Jorge Stolfi continued (30Dec2000):-

What I meant is that the crossbow man really looks like the VMS Sagittarius and that I have not seen that sign represented by a man rather than a centaur elsewhere. Are there any examples of non-German non-centaur Sagittarius?

Rene Zandbergen responded (30Dec2000):-

He does indeed. I found out I have copies of some illustrations from the same block book (in German) but these are not including Sagittarius.

Certainly, there are German Sagitarii which _are_ centaurs, but that doesn’t really help. I’ll scan a few nice images from a book called ‘Flores Albumasaris’ printed in Augsburg around 1480. They’re woodcuts but allow a nice comparison with some of the VMs images. Sagittarius is a Centaur here.

Then there’s a brief lull, until Rafal Prinke continues the thread (09 Jan 2001) with a number of closely related art historical bombshells:-

I have received a very kind and informative reply from Prof. Ewa Sniezynska-Stolot of the Jagiellonian University in Cracow (my repeated apologies to the list I had not written to her earlier). Below is a translation/summary of her letter.

——————————–

I have inspected the VMS at Beinecke. The signs of the Zodiac do not present problems – they are simply not of the Arateia type but were modernized. As I wrote in my books, because of linguistic mistakes and changes in artistic styles, human figures were represented in contemporary garments (viz. Gemini, Virgo, Sagittarius). Attributes were changed in the same way, eg. Sagittarius’ bow developed into a crossbow in the 15th c.

The genre scenes, eg. Aries eating a bush, suggest that the signs were redrawn from a calendar. Garments: the jopulas [?] of men with a belt suggest the 14th/15th c. but headdresses of men (Gemini, Sagittarius) definitively indicate the 15th c. This was common fashion in Europe at that time. The Sagittarius’ cap with fox tail points to Germany – but they were also worn in Poland. I believe that the manuscript can be dated
to mid-15th c. From the astrological iconography point of view, the Taurus at a well is somewhat strange – unless an image of donkeys was a basis for it and then it would refer
to Cancer – but that is certainly going too far.

In my opinion it is a notebook of a liberal arts student. Similar notebooks are Beinecke 225 and 226. The former belonged to Paul de Worczin who studied in Cracow in 1422
(according to the Beinecke catalogue Cracow is in Bohemia!). The latter is also from Cracow.

In our Institute we have a database with descriptions of most of existing medieval zodiacal iconography. I am now preparing a similar database of the iconography of
individual degrees of the Zodiac.

————————————–

Thus she confirms the opinion of Panofsky (and my own amateurish feeling) that the VMS should be dated to mid-15th Germany/Poland/Bohemia.

The suggestion that it is a student’s notebook is a bit of a revelation to me! Drawing naked ladies and fantastic pipelines during boring lectures is perhaps what they were doing from the dawn of time.

Prof. Sniezynska-Stolot has not addressed the VMS script but I hope to keep in contact with her. Maybe that was some kind of a medieval “beta-kappa” students’ corporation fun popular in Cracow and there are loads of similar manuscripts at the Jagiellonian Library?

Here’s a picture of a [modern] jopula (no, I didn’t know what it was either): basically, it’s a 14th/15th century outer garment made of four pieces plus sleeves, something like a doublet. Looks quite snug! 🙂

Rene Zandbergen picked up on the Sagittarius crossbowman’s hat’s fox tails (11Jan2001):-

Brumbaugh always made a point of stressing that this was a Florentine archer’s hat. Guess in whose opinion I put more trust.

Rafal Prinke then made a related calendaric aside (13Jan2001):

There were 3 styles of beginning the year in March:

1) Venetian – 1st March
2) Florentine and Pisan – 25th March (with a year’s difference)
3) Gallic – Easter Sunday (ie. not always in March)

The Venetian style was also used in Ruthenia (but not in Poland, which used exclusively Christmas and 1st January, along with Germany, Bohemia and Sweden). Russia changed to the Byzantine style in 1492 (1st September), also used in other Orthodox countries and in southern Italy.

The Florentine style was used in England, while the Gallic style – in France and the Netherlands.

So – if we accept the calendaric basis for the VMS Zodiac, it points either to Venice (and thus Northern Italy, which is the favoured hypothesis now) or pre-1492 Ruthenia, which might suggest further possibilities of a connection with Cyrillic, Greek, Georgian, Armenian or Turkish influences on the VMS script and content.

Incidentally, I should also flag this as a good example of how a single small thread in the VMs mailing circa 2000 typically contained more effort, historical research, genuine collaboration and reflective thought than entire months of postings there do now. People sometimes think that I’m perhaps being nostalgic or unrealistic when I talk of the decline of the list: but sadly it’s a very real phenomenon.

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