Cartographic mysteries of the second “La Buse” cryptogram…

The second “La Buse” cryptogram is a funny old thing: Emmanuel Mezino swears to its authenticity, but I’m really not as convinced as he is – given that a number of key elements (such as the cryptography, the dates, the drawing style, etc) seem jarringly incongruous to my eyes, there seems plenty of good reasons to infer that it is (at best) a later copy and/or an assemblage of earlier pieces, or (at worst) a modern fake.

Here’s Yannick Benaben’s image of it, the earliest that I’ve found on the web:-


And then there’s the cryptogram’s map to consider. Even though La Buse (Olivier Levasseur) ended his piratical career in the Indian Ocean, he seems to have begun it in the Caribbean, so it perhaps shouldn’t be at all surprising that this cryptogram should contain a very high-level map of the Florida / Caribbean area.


Many names on the map can be identified without difficulty:
* Florida – though because this area became ‘La Louisiane’ (named after Louis XIV of France, of which it was a colony) in 1682, it would seem that this map predates (or appears to predate) 1682.
* Virginie (= “Virginia”)
* Golfo Mexicano (= “Gulf of Mexico”)
* Tragillo (= “Trujillo”)
* Jamaica
* Cuba
* Tropicus Cancri (= “Tropic of Cancer”)
* Hispaniola – it looks to me as though the island of Hispaniola has been miscopied into two halves.
* S. Dominici (= “Santo Domingo”, Hispaniola’s capital city founded by Columbus’ brother Bartholemew in 1496, and also another name for Hispaniola).
* La Bermuda (= “Bermuda”, although on the map this is positioned way too close to the coast)

Curiously, the map has a snake design that wiggles – coincidentally or not, I can’t say – roughly up the path of the Mississippi. It’s far from historically obvious that the Mississippi River was only discovered (by Louis Jolliet and Jacques Marquette, says Wikipedia) in 1673: and hence it is tempting to suspect that this snake design was added simply to cover up a cartographic slip-up by a later forger or hoaxer (i.e. adding the 1673+ Mississippi River to a map supposed to be linked to La Buse, who died in 1730). But that’s just my speculation, please don’t read too much into it. :-)

The other map labels, though, are slightly less straightforward.

* Boriquen – this is clearly Boriken, the original Taino Indian name for Puerto Rico (although Columbus called it “San Juan Bautista”, i.e. St John the Baptist Island, which is presumably why the capital is called San Juan, and why the island’s motto is “Joannes est nomen eius”).

* Guanima was the original (pre-1520) name of the Bay of Marantzas on the north coast of Cuba, while “Guanahani” was the Taino Indian name for the first island to which Columbus came (the controversy over which island that actually was continues to the present day). And so it seems likely to me that the island on this map marked as “Guanima” was intended to be “Guanahani”, but got mangled in the copying.

* Boca Ioneque – I have no idea what this is. It’s next to “Guanima” and looks as though it is attached to an island, but I’m not sure if that’s helpful or not. All suggestions welcome!

* “Acalaia” / “Alcaldia” (town hall?), apparently on the Yucatan peninsula – though I did manage to work out what this (miscopied and mangled) label was late last year from some 16th century maps, I now cannot find my careful notes on it at all, bah. :-(

* R. Fuado – I have no idea what this is.

* C. de S. Marie – I have no idea what this is either.

* C. de S ???? – I can’t even read this, let alone guess what it is.

My Thoughts

This map is hugely odd. Not just the mix of languages (Spanish, French, Latin) or the miscopied labels (Guanima, Tragillo) or the suspicious snake tail (covering the Mississippi?) or the miscopied geography (Hispaniola), but the whole thing seems jarring to me. Manu may be convinced, but to my eyes this is all over the place.

But what do you think?

Can you help with Fred Pruszinski?

The more I think about poor old Fred Pruszinski and the suitcase he took from Broken Hill to Somerton Beach perched on the back of a stolen motorbike the weekend just before the Somerton Man died, the more I want to know the rest of what happened.

In my opinion, Pruszinski’s story could well turn out to form a parallel strand of the Somerton Man’s history: while I don’t yet know how these could be linked, I do now have a strong suspicion that I’m starting to ask the right kind of questions – and to me, that’s a really big deal.

So… rewind the time and place, if you will, back to November 1948 and Broken Hill. Pruszinski was just out of school, and was an avid miniature rifle shooter (he became Honorary Secretary of Silver City Miniature Rifle Club in 1949, and then shot for West Rifle Club), and went on to work for the local mines as an engine driver: so he must surely have had a reasonably wide network of friends and acquaintances.

Many of those people will have been at Pruszinski’s (sadly early) funeral in 1953. According to newspaper reports, his pall-bearers were J. Heslop, Don Hargreaves, Don Carlin, Kevin Cook, John Winkler, and Pat Fitzpatrick (along with Don Purcell, another close friend), while F. Anderson and Jack Brownett of West Broken Hill Rifle Club were there too, along with Pruszinski’s family and doubtless many more friends and workmates.

Some of those people must surely still be alive, right? I don’t honestly believe all trace of memory of Fred Pruszinski can already have been wiped from the world’s collective mental slate. And the unusual sequence of events that happened that weekend in November 1948 must surely have been the talk of Broken Hill for some time. People talk, that’s what they do: so why not listen? :-)

Unsurprisingly, what I want to do now is place a small advertisement in Broken Hill’s Barrier Daily Truth, saying something along the lines of:-

Can you help? I’m an historian trying to find people who knew Richard Frederick Arthur (‘Fred’) Pruszinski, formerly of 247 Williams Street, Broken Hill. He was the Honorary Secretary of Silver City Miniature Rifle Club, and then a member of West Broken Hill Rifle Club. At his funeral in 1953, his pall-bearers were Don Hargr[e]aves, Don Carlin, Kevin Cook, John Winkler, J. Heslop, and Pat Fitzpatrick, assisted by Don Purcell. Do you have any memories of Fred Pruszinski? If so, please email , thanks very much!

It’s a pretty good first attempt, but it has a fairly obvious shortcoming: people who knew Fred Pruszinski first-hand in 1948-1953 will be quite old now (85 or so, in fact), to the point that email may not be a good first way of asking for a response – so I think that including a telephone number as well could well yield much better results.

Hence here’s my request to you lovely people: would any Cipher Mysteries reader in Australia be kind enough to volunteer to help this by putting forward their phone number for me to add to this ad?

This many years after the event, I don’t realistically expect it to raise more than two or perhaps three telephone calls (in fact, zero or one may be closer to it), but I’d like to try all the same.

Someone out there must know what Fred Pruszinski was doing back then, surely?

Ina Harvey, the case, and the needle…

Gerry Feltus very helpfully included the text of Ina Harvey’s 1st December 1982 Adelaide News interview with Tom Loftus in “The Unknown Man” (pp.197-200). Harvey recalled a “strong and fit”, “professional” man with “an air of refinement” who had checked into the Strathmore Hotel close to Adelaide’s railway station for a few days before 1st December 1948.

She noted that “[He] had no baggage, except for a small black case – such as a doctor or musician who played the flute might carry”. Because she had suspicions about the man, she asked an employee to go into the man’s room (#21 or #23, she couldn’t recall) and have a look in the mysterious case – to her surprise, “the only item in the case was a needle”. Furthermore, “[from the employee’s] description I got the impression it could have been a hypodermic syringe.”

Pete Bowes now proposes that this flute case could well have been important: he suggests that it formed some kind of signal, a “covert [sign] of identification“, a chess move played out as part of a wider spy game unfolding on the streets of Adelaide in 1948.

Well… OK. But has Pete’s instinctual metal detector found the needle in a haystack we’ve all been grasping blindly for? In this instance, I don’t honestly think so. So if not a spy narrative, then what on earth was going on with the “needle” and the small black case?

And My Suggested Explanation Is…

What if… the small black case was actually a rifle case, for a takedown (easily dismantled) .22 rimfire rifle?

And what if the “needle” were a barrel cleaning rod, for (duh) cleaning the rifle barrel?

With Fred Pruszinski’s short life and indeed the whole rifle socks scenario, we have already seen how miniature (typically .22 calibre) rifles were popular in Australia in the years after WW2, mainly because of the difficulty of getting full-calibre shot.

For this reason, many WW2-era weapons (such as the Martini Cadet training rifle) were recommissioned by companies such as Sportco as sports or competition rifles, and sold (for the most part) into rifle clubs. I’m not a rifle expert at all, but I do know that some rifles did definitely come apart into pieces: for example, the very rifle that Fred Pruszinski had in a suitcase that he took from Broken Hill to dump on Somerton Beach that very weekend was a takedown rifle – but only its stock was ever found (Pruszinski, who knew rifles well, insisted that he left both the barrel and the stock in the suitcase on the beach).

What, then, are the odds that the man staying at the Strathmore had come to town with a discreet little black carrying case for a takedown .22 calibre rifle? You know, the kind of case that a professional man would use to carry his rifle to Rifle Club meetings?

And – spookily enough – what are the odds that the rifle that Fred Pruszinski dumped on Somerton Beach was the same one that was meant to go in the Strathmore Hotel visitor’s little black case, and that was meant to be cleaned by the cleaning needle in it?

Might all these pieces, all moving around Adelaide on the same weekend, be parts of the same convoluted puzzle?

The Voynich Manuscript’s Three Crowns…

A recent comment to Cipher Mysteries by ‘Jimbo’ made me look again at the the various crowned nymphs in the Voynich Manuscript.

The Three Crowns

As far as I can see, there are three crowns in the Zodiac section, firstly in Cancer:-


There’s another in Leo:-


And another in Libra:-


There are also plenty of nymphs with a ‘tressed’ hairstyle in both the zodiac section and the water section, that some people (incorrectly, I suspect) think resembles some kind of crown. Here is a set of three examples from the Voynich’s Sagittarius page (rotated upright):-


Incidentally, one thing I can’t recall being mentioned elsewhere is that one particular nymph seems to directly link the zodiac pages to the water pages, by virtue of her standing in some kind of miniature bath or basin:-



To my eyes, there’s a big codicological (i.e. composition-layering) mystery about the whole way the nymphs were drawn. Not only were they originally all drawn with a single breast (and if there is some kind of long-standing graphical tradition of drawing one-breasted nymphs, it is something that decades of nymph-maniacal Voynicheros have apparently failed to uncover), but many specific details – most notably things such as these three crowns and the tressed head-dresses – were apparently added to the original drawing in a later ‘phase’ or composition pass.

And that begs the question: what was so wrong with the original unadorned ‘ugly duckling’ layer that the author felt compelled to dress it up with additional breasts, as well as crowns and tressed hairstyles? I don’t know, but I do wonder how far understanding that layering would carry us towards understanding the whole manuscript.

As far as the crowns go, the Cancer crown is somewhat dull, and was clearly added in a later pass; whereas the Leo crown was painted red and – crucially, I suspect – seems to have been part of the original layer, rather than an addition in a later construction phase.

The Libra crown is, like the Cancer crown, also clearly a later addition. Some people have speculated that this might have been modelled on a real crown that existed in the 15th Century, such as the Holy Crown of Hungary:-


…or perhaps something to do with Barbara of Cilli.

My Own Conclusions

Feel free to infer what you like from all the above.

For me, however, the Leo crown is the real deal, and the Cancer crown (added in almost the same place on the zodiac roundel preceding the Leo roundel) is a fake, designed to draw attention away from the Leo crown. Moreover, I strongly suspect that the Libra crown, for all its similarity to the Holy Crown of Hungary, is very probably a misdirection as well.

Yet… what was so telling about the red crown drawn in the original layer on the Leo zodiac roundel that the author wanted to distract our attention away from it? That, I think, is the right question to be asking here.

Edit: here’s what the Leo crown looks like, scaled up and overdrawn in Gimp. What does it mean? I don’t know but… I’m looking.


Westminster Under School Crypto Challenge

At a Westminster Under School Open Day not so long ago, I was delighted to find out from Miss Ellis (WUS’s Head of Mathematics) that after their final exams, Year 8 boys there spend time discovering the joys of cryptography and code-breaking: specifically, they go to Bletchley Park, find out about Enigma, and break some ciphers.

All the same, what with “The Imitation Game” and so forth, Nazi cryptography is at risk of becoming old hat (or do I mean alter Hut?). But what about Allied codes and ciphers? And – dare I ask it – what about that pesky WW2 cipher pigeon? Of course, once she found out that I knew about such wonderfully recondite (yet also historically and cryptologically rich) subjects, she set about trying to persuade me to give a presentation at the school.

What, me talk about Allied codes and ciphers, wartime pigeons, Typex machines, and D-Day history for two hours? (To be fair, I should perhaps say “for only two hours”.)

Needless to say, she didn’t have to twist my arm particularly hard. Or… at all, truth be told.

And so a few weeks ago, I pitched up at Westminster Under with a giant printout of the enciphered pigeon message, a 50-plus-slide Powerpoint presentation (heavy on nice photos, but light on text), and… a big empty space where I had originally hoped a Typex machine would be. (My cunning plan to borrow one from a friendly crypto collector fell through a few weeks beforehand, sadly. Oh well!)

To make the crypto side of the talk as ‘hands on’ as possible, I gave the boys a practical challenge using Double Transposition (The link is to a description I adapted from a genuine WW2 document Stu Rutter and I found at the National Archives in Kew.)

The boys divided into teams of three or four on a table, for each team to encipher secret messages for a different team to decipher (i.e. by supplying a pair of transposition keys with the message). Once they had got the hang of the technique, I set everyone the challenge of reliably enciphering the same short message at high speed: this was competitive and fun, yielding quite a nice balance of serotonin and adrenaline. 😉

In fact, there was a very specific Cipher Mysteries point to the exercise. Because we can tell that the cipher pigeon’s message was enciphered in only three minutes, we can deduce that it can only have been made using a machine cipher – nobody, I’m sure, could reliably encipher a message of that size in three minutes using Double Transposition, nor indeed with any of the other non-machine ciphers the Allies used in WW2. And Typex aside, the only other Allied machine cipher was the M-209, which had a ten-letter indicator (both the cipher pigeon message and Typex messages had five-letter indicators).

Incidentally, one nice crypto thing is that, having first gone through the history of the Typex machine, I decided to see how on the ball everyone was by throwing out a properly difficult crypto question to the audience:

Early in the war, German cryptanalysts noted that the probability of the letter ‘X’ appearing in the last 4 letters of a Typex message was extremely low. What did that tell them?

Naturally, when a boy (I didn’t get his name, sorry) at the far side called out the answer, I was hugely delighted, because many, many adults would not have reached that. (And so I leave it as an exercise for the reader, just as you’d expect).

As I’m sure will be no surprise, I thoroughly enjoyed myself – it was a great opportunity to give my cipher pigeon / Typex material a bit of a public airing – and I really hope that a fair few of the boys did too. They behaved in an exemplary manner, and were every bit as sharp, fast and engaged as I hoped they’d be. All credit to them for that, and a twenty-one gun salute to Miss Ellis not only for making it happen, but also for helping out on the tables for the Double Transposition exercise (which was very kind of her, and utterly necessary as it turned out).

Same again next year? I hope so! :-)

PS: right at the end, one of the teams very kindly handed me a nice Double Transposition cipher challenge they had devised, which I thought I’d share with you here (I hope that’s OK with them). I’ve kept their original keys ( 😉 ) but modified their cipher only very slightly:

Sender: Strawberries & Cream
Primary Transposition Key: 9, 1, 10, 4, 2, 7, 6, 8, 3, 5
Secondary Transposition Key: 3, 1, 4, 5, 9, 2, 6, 8, 7, 10
Cipher Message:

Can you decipher it? Enjoy! :-)

Voynich Talk in York with Rene Zandbergen & Bill Sherman

Many apologies, I thought I’d posted about this weeks ago but I obviously hadn’t, bah! :-(

At 11am to 12.15pm this Saturday (20th June 2015), the York Festival Of Ideas will be hosting Cracking the Code, a 75-minute panel discussion with Bill Sherman (currently of the V&A), John Clark (University of York), Rene Zandbergen, and Sir Dermot Turing (Trustee of the Bletchley Park Trust). It’s at the University of York, and it’s freeeeeeee.

If you don’t know Bill Sherman, shame on you: he’s the person who curated the “Decoding the Renaissance: 500 Years of Codes and Ciphers” exhibition at the Folger Shakespeare Library from November 2014 to last March, that gave the Voynich Manuscript its first working holiday away from the Beinecke since Hans Kraus donated it to them. He’s also the author of “John Dee: The Politics of Reading and Writing in the English Renaissance” (on the shelf to my right), and numerous other books and articles.

The title of the session isn’t much help (nor indeed was the York Festival of Ideas PR), so I have honestly no idea what they plan to panelize (panelify?). When Rene and Bill did a talk at the Folger last November, it claimed to be a “conversation” that would “review what is known (and not known) and focus on new approaches to this old problem, including science and art history, Medieval and Renaissance history, codicology and conservation, and the history of collecting.

Hmmm… ohhh kayyyy, then. :-)

Anyhow, just in case they accidentally veer off into the marshy horrors of Baxland, I’ll bring a crate of rotten tomatoes: no pressure, people, but if you press that button, the stage will end up looking as if the red team won at Splatoon, I swear it.

But that aside, I’m looking forward to it. 😉

Declassified NSA documents…

Hans Jahr very kindly left a comment here on Cipher Mysteries recently, pointing me at a treasure trove of declassified NSA documents relating to William Friedman.

Some of these had already been declassified by different NSA mechanisms: but even so, there’s simply so much new material to go through here that it’s enough to make your head spin.

Of course, I’ve started trying to go through these (e.g. there’s not that much new on the Voynich Manuscript, but there’s a lot on the role of Typex II in the post-WW2 years), but it’s going to take a while. Please feel free to browse and search yourselves, and let me know if you stumble onto anything interesting. :-)

Incidentally, given that Friedman evaluated the Chaocipher in 1942, there may well be some Chaocipher-related correspondence in there somewhere for Moshe Rubin to find. (There’s a large Excel spreadsheet briefly listing out all the items).

Speaking of whom, Moshe Rubin also very kindly dropped me a email about an NSA page containing recently declassified Beale Papers documents.

As you’d expect, many have dated badly and many others are of little use, but that still leaves many other interesting things in the heap. Browse and enjoy; and if you do happen to find something about four miles from Buford’s Tavern… :-)

More generally, though, the NSA has posted up a list of declassified topics: this includes not only Friedman and Beale, but also VENONA, the death of John F. Kennedy, UFOs, etc etc.

Yet personally, I’m more interested by this unbelievably long list of declassified code/cipher stuff, which includes items relating to just about every country that ciphered anything in the first half of the 20th century. It took me half an hour to speed read through the titles alone!

I picked out a few choice items, firstly on Double Transposition (more on that in a few days’ time):-


Next, some documents on secret writing (at least one person here likes that :-) ):

NR 3464 CBQM37 4000A 19200000 SECRET INKS
NR 3468 CBQM37 863A 19431129 SECRET WRITING

There’s a report on the Zimmerman Telegram:-


A few pages I’ll try to get around to looking at before very long:-


And finally, a fair few photos:-


Unreadable books become hip literary phenomenon… (really?)

I just saw a nice little online article courtesy of Clara Chow of the Straits Times, riffing on a whole load of different unreadable books.

The trigger for her article is Iterating Grace, a short-story-sized illustrated bookette stunt clearly designed to mystify idiot tech startup thought leaders, particularly those with foolishly high opinions of themselves. (Errrm… that didn’t narrow it down half as much as I hoped. But never mind.)

Of course, this being the Internet and all, you only have to blink once before more stuff gets pulled unwillingly from the shadows into the light, in this case an alleged connection between “Iterating Grace” and an artist called Curtis Schreier, who long ago was part of a stunt-liking art collective called “Ant Farm”. And so it goes on.

Chow goes on to mention various vanity books (A. M. Monius’ philosophy book, a book by “Joe K” who is probably Swede Petter Nordlund), as well as Robin Sloan’s (2013) novel “Mr. Penumbra’s 24-Hour Bookstore”, which I haven’t yet read (but sounds entertaining).

She has the Book of Soyga wrong, though: Jim Reeds famously worked out its algorithmic workings a decade ago. And as for a certain academic linguist’s I-can-read-nine-Voynich-words-all-of-them-‘meh’ self-asserted decryption… the less said the better.

Chow had fun joining all the dots together: but I don’t think she really understands that we are deep into the Freemium decade, and that blogs and social meedja posts are often just famebait, trying to dig over some virtual field-shaped community to plant a carefully crafted fame seed in. Ultimately, is “Iterating Grace” any less vain than the preening dotcom vanity it lightly satirizes? I don’t think so, but feel free to have your own opinion.

As for the poor old Voynich Manuscript, people deliberately misgrasp that at every turn to serve their own ends, to the point that their misgraspingness isn’t even funny any more. It’s hard not to conclude that His Royal Baxness and even Baron Ruggish have far less interest in the Voynich Manuscript itself than in what they think the Voynich Manuscript can do for their marvellous Middle England academic career vectors. In that respect, I think they both come across as just as shallow, despicable, meaningless, and indeed sickeningly modern as that most Freemium of casual games: Goat Evolution.

I kid you not.

The Z340 Cipher, a dissenting opinion…

The 408-symbol-long Zodiac Killer cipher (‘Z408′) was cracked by Donald and Bettye Harden in 1969 while the next 340-symbol-long Zodiac Killer cipher (‘Z340′) arrived not long after: ever since then, there has been a widespread presumption among researchers that the later cipher would just be a more complicated version of the earlier cipher (e.g. perhaps transposed in some way).

The Z340 certainly resembles Z408, insofar as the cipher shapes employed in both were very similar, and that certainly lends support to the widely-held presumption that Z340 uses the same kind of ‘pure’ homophonic cipher system. But is that the whole story? Personally, I’m not so sure…

Unusual Aspects of the Z340

It has long been pointed out that the Z340 cipher sports a number of idiosyncratic features that are not present in the earlier Z408 cipher. For example, the FBI’s Dan Olson pointed out a few years ago that:

* Statistical tests indicate a higher level of randomness by row, than by column. This indicates that the cipher is written horizontally and rules out any transposition patterns that are not strictly horizontal.

* Lines 1-3 and 11-13 contain a distinct higher level of randomness than lines 4-6 and 14-16. This appears to be intentional and indicates that lines 1-3 and 11-13 contain valid ciphertext whereas lines 4-6 and 14-16 may be fake.

* Because of the vertical symmetry of the statistical observations, the message may have been written, then split into two equal size parts and placed top over bottom.

These suggest that something odd might be going on though inside the cipher: in this respect, the Z340 cipher resembles the Voynich Manuscript’s frustrating ‘Voynichese’, which looks straightforward on the surface but which turns out to have many behavioural features which are not seen in other known ciphers.

I’d also add that row #10 starts and ends with ‘-‘, which looks somewhat artificial – though it could just be random, it may also have some kind of meta-significance for the interpretation of the overall cryptogram (e.g. “CUT HERE”).

Finally, I’d add that Z340’s final (20th) line looks very much as if it contains a mangled ZODIAK signature, which – if correct – would probably make sense as 50% crypto padding, and 50% flipping the bird at the FBI. 😉

Anyway, given that the message contains 20 lines of 17 symbols (20 x 17 = 340) and we can see similar artefacts in rows 1-3 and 11-13, then it seems likely to me that there was some kind of major coding break after row #10.

Consequently, I’ve long wondered whether the two halves of Z340 (let’s call them ‘Z170-A’ and ‘Z170-B’) used a different set of cipher-symbol-to-plaintext-letter assignments to each other: in which case, the sensible way to make progress would be to try to solve each half separately. Even so, we would still need to eke out some additional assistance (or meta-assistance) from the texts to make progress, because the odds are so heavily stacked against us.

Yet there’s another feature of the Z340 cipher which struck me a while back but which I haven’t got round to blogging about until now. It’s all to do with doubled shapes, and the story starts with the Z408 ciphertext…

Z408’s doubled letters

To construct Z408, the Zodiac Killer used 7 shapes for { E }, 4 shapes each for { T, A, O, I, N, S }, 3 shapes each for { R, L }, 2 shapes each for { D, F, H }, and 1 shape each for the rest (probably): this yields a grand total of 54-ish cipher shapes to encipher 26 plaintext letters.

Given that the instance count curve for the English alphabet is often described as “ETAOINSHRDLU…”, this tiered arrangement makes sense (as I recall, various researchers have tried to use the homophone allocation to infer which popular cryptography manual the Zodiac Killer specifically relied upon, but I don’t remember if there was a definitive answer to that question).

However, one particular letter caused him a lot of practical problems for Z408: the letter L. Even though this has a relatively small frequency count (compared to, say, the letter E), the particular text he enciphered included numerous ‘LL’ pairs. That is kind of what you get if you want to say the word ‘KILL’ all the time: the words with a double-L are KILLING, KILLING, ALL, KILL, THRILLING, WILL, ALL, KILLED, WILL, WILL, WILL, and COLLECTING.

(As an aside, I’ve often wondered whether the multiple repetitions of the word “WILL” might possibly imply that the Zodiac Killer’s first name was indeed “WILL” / William. The subconscious is a funny ‘wild animal’ in that way.)

Anyway, as a direct result of this, the letter L is used here more often than its normal English stats would suggest: and so the Zodiac Killer had to encipher ‘LL’ 12 times with only three shapes in its tier. To avoid pattern repetitions, he ended up doubling up the enciphered L-shapes a few times, and so the final Z408 ciphertext included a number of doubled L shapes.

The only other doubled letter was ‘G’, which only had a single shape allocated to it, and which appeared doubled only once.

Z340’s Problem With ‘+’

If Z340 (which uses 63 distinct shapes) uses a similar kind of homophonic cipher to the one used in the Z408 cipher (which uses 54 distinct shapes), then I would say it has a very specific problem with whatever is being enciphered by the shape ‘+’.

‘+’ occurs 24 times (7% of the total number of characters, and exactly double that of ‘B’, the second most frequent shape), which by itself largely makes a nonsense of the suggestion that Z340 is a homophonic cipher: anything with that high a frequency count should surely have a whole set of homophones to represent it.

You might wonder whther ‘+’ enciphers a frequent word or syllable, such as ‘THE’ or ‘ING’. However, it appears three times immediately doubled with itself, i.e. ‘++’ (the only other letter that appears doubled is the sequence ‘pp’ that occurs once near the start of row #4).

Even if, as Dave Oranchak did, you do a brute force search for homophone cycles (don’t get me started on what they are, or we’ll be here all night), you don’t find anything that accounts for Z340’s ‘+’ shape.

And yet, as Dave Oranchak points out, Z340 has some strong-looking homophone cycles, such as [l*M] [l*M] [l*M] lM [l*M] [l*M] [l*M], which would seem to imply that Z340 is at heart a homophonic cipher. There are plenty of other measures (many noted by my late friend Glen Claston) that point in the same direction,

Moreover, because the number of shapes used is greater than for the Z408 cipher, you would naturally expect to see more tiers or wider tiers (though 7 shapes for E was already quite a wide tier). So you would naturally expect to see a consequent flattening of the statistics. And yet ‘+’ bucks that trend completely.

How Can We Reconcile These Two?

As a starting point, you might note that ‘M+’ occurs three times in the top half, but not at all in the bottom half. In fact, M is always followed by + in the top half, and never followed by + in the bottom half (where it occurs four times).

It seems to me that the ‘+’ shape makes the top half (Z170-A) easy and the bottom half (Z-170-B) difficult all at the same time. And that’s not something that I personally can comfortably reconcile with the kind of one-size-fits-all pure homophonic solutions most people seem to be looking for, even with confounding transposition stages thrown in: the behaviour of the ‘M+’ pattern would seem to point away from almost all of the transposition variants previously proposed.

Having really, really thought about it, my tentative conclusion is that ‘+’ seems to operate more as a kind of meta-token rather than as a pure token. I mean this in the same general way that certain Voynichese letters seem to me to encipher 15th century shorthand tokens (‘contractio’, etc).

A Suggestion

As I recall, the Hardens found their crib by guessing that the first letter was “I” and then looking for the word “KILL”: the ease of which doubtless made an already angry psychopath even angrier than he already was.

Hence to my mind, the thing he would most likely have been looking to solve when moving from his Z408 cipher system to his Z340 cipher system was how to make that new system impervious to that specific kind of an attack. And the key letter that let him down first time round was the letter ‘L’, specifically in its doubled form.

Consequently, I propose that this was the single technical challenge that spurred the internal changes from Z408 to Z340. And there was one obvious – but admittedly very old-fashioned – trick that he could have used to make doubled letters harder to see.

So here’s my suggestion. Could it be that the Zodiac Killer used ‘+’ as a meta-token to mean “REPEAT THE LAST LETTER“? (‘++’ would then mean a tripled letter, or perhaps something else entirely).

If that’s correct, I would further expect that ‘M’ was one of the homophones for ‘L’, and the [l*M] cycle could very well have been the 3-long homophone loop for ‘L’.

Do you really believe that the Zodiac could write a taunting message to the police without using the four-letter sequence “KILL”? In many ways, that was kind of the whole point.

Some Scorpion S5 probability calculations…

I mentioned in a previous post that I thought that the Scorpion S5 cipher’s numerous shape families might offer a backdoor into its cipher system, if they just happened to be elegantly arranged on downward diagonals. I pointed out that if this were correct, the “dice” shape family that appears in columns 1, 3, 4, 8 (twice), 9, 12, 14, 15 would be most likely to have been arranged such that A was 1, C was 3, D was 4 (and so forth).

However, I didn’t actually get so far as calculating the precise probabilities in that post: but now I have (I think).

In my Scorpion spreadsheet, the total probability that a specific family was enciphered as a specific sequential set of letters is calculated as the product of each individual letter’s likelihood. By ‘likelihood’ here, I mean not the probability of that letter occurring randomly (i.e. P, its raw instance probability), but the chances of that occurring exactly N times within a column of letters of height H. And in Excel, you calculate this function using the in-built function ‘BINOMDIST(N, H, P, false)‘. (Note that instead using ‘BINOMDIST(N, H, P, true)’ would calculate the cumulative likelihood of that happening, i.e. the chances of that probability P event happening 0 times up to N times out of a maximum of H times.)

For the raw instance probability values, I used the Scorpion encipherer’s plaintext as a reasonable approximation of the text we are likely to find encrypted inside the S5 cipher. I think there’s a pretty good chance that it will be good enough.

As for the height H: once you have rearranged the message according to the 16 apparent columns of the ciphertext, columns 1 to 4 contain 12 instances each, while for columns 5 to 16, each on contains 11 instances. All of which means that the binomial probability table for N out of 11 looks like this:


For example, even though the raw instance probability for ‘E’ is 11.35%, the chance that a given 11-high column of letters will contain exactly one ‘E’ is 37.4271% (or so my spreadsheet says, anyway).

But rather than limit the calculation only to length-16 families, I added a trick whereby shorter families can be checked against other diagonals in the cipher table. If you use the number 99 as the count for an individual family’s column, the spreadsheet works around it in the calculation, by allowing the shifted alphabet to start not at ‘A’ but at ‘z’ (i.e. ‘A – 1′).

I’ve included 11 shape families from the S5 cipher: if you copy a row from any one of these across to row #33, the spreadsheet will calculate a composite ranking value for each of 28 different offsets in column U (the ‘Result’ column). This is equal to the final probability times a million (or else the numbers would be too small to be practical).

For example, the relative rankings for the dice family are:-

2.737265 A
0.013655 B
0.000000 C
0.000046 D
0.293415 E
0.018483 F
0.093272 G
0.000451 H
0.000078 I
0.000000 J
0.009360 K
0.074230 L

Here, the ranking for ‘A’ (2.7372765) is nearly 10x the ranking for second placed ‘E’ (0.293415), which is essentially what my initial imprecise guess was (thank goodness). :-)

It’ll take a while to figure out what this all means, but I thought I’d post the basic spreadsheet sooner rather than later. :-)

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