Search Results: Zodiac

An open question to the house, really: even though I have all manner of books and papers relating to other cipher mysteries, it struck me as odd a few days ago that I have next to nothing on the Zodiac Killer that I’d consider any sort of capsule library on the subject.

Despite his love of Americana, the section on the Zodiac Killer in Craig Bauer’s Unsolved is no more than a starting point (and that whole strand didn’t really end too well, in my cryptological opinion).

Conversely, I’m not sure I have enough pinches of salt to consume Robert Graysmith’s meisterwerken on the subject. Or is that just par for the whole Crazy Golf course, a necessary initiation of pain so you have been through the same awfulness as everyone else?

What I want is a Zodiac Killer book that sensibly describes each of the confirmed murders, the messages he definitely sent and all of the extant evidence (e.g. stamps, hairs, saliva, fingerprints, palmprints, DNA): and also discusses the murders that Zodiac claimed but didn’t carry out himself, and the messages attributed to him but which very probably weren’t by him.

But is this just too dreamily rational and sensible to hope for?

A few days ago, German cryptoblogger Klaus Schmeh mentioned a recent paper by Tom Juzek on the unsolved Z340 Zodiac Killer cipher. This first appeared in March/April 2018, but I was not aware of it before Klaus flagged it.

Juzek’s MSD metric

The metric Juzek uses to drive much of his argumentation is what he calls ‘MSD’ (“Mean Squared Distance”), which is simply the sum of the squares of the instance frequencies of bigrams (or trigrams), but then divided by the number of individual bigrams (or trigrams).

As an example, the 14-letter text “AAAAAAAAAABCD” is made up of thirteen bigram instances AA, AA, AA, AA, AA, AA, AA, AA, AA, AB, BC, and CD. Hence it contains 9 x AA, 1 x AB, 1 x BC, and 1 x CD: and so would have a bigram MSD of (9*9 + 1*1 + 1*1 + 1*1) / 13 = (84 / 13) = 6.46.

The same text contains twelve trigram instances AAA, AAA, AAA, AAA, AAA, AAA, AAA, AAA, AAB, ABC, and BCD. Hence it contains 8 x AAA, 1 x AAB, 1 x ABC, and 1 x BCD: and so would have a trigram MSD of (8*8 + 1*1 + 1*1 + 1*1) / 12 = 5.58.

However, Juzek quickly flags that this raw metric is not really good enough on its own:

The problem with the msd is that there are difficulties with comparing msd’s across data sets. This is because the length of a text influences the msd, as well as the length of a text’s character set. A 400 character cipher using 10 characters will see a different ngram distribution to a 100 character cipher using 40 characters.

Hence Juzek instead generates a “delta MSD”, which he defines as the difference between the ngram MSD of each ciphertext read horizontally (i.e. the generally presumed ‘correct’ symbol ordering) and the ngram MSD of its vertical transposition (i.e. every 17th character). This is to try to ‘normalize’ the raw MSD against a kind of statistically flattened version of the same.

Juzek then applies these two final metrics (bigram delta MSD and trigram delta MSD) to a number of real and fake ciphers, before concluding that the Z340 is quite unlike the Z408, and that it in fact presents more like fake ciphers than real ciphers.

What’s Wrong With This Picture?

Clearly, Juzek’s motivation for squaring ngram instance counts at all is to try to somehow ‘reward’ ngrams that are repeated in a given text being tested. Unfortunately, I think this is no more than a rather clunky and misleading way of looking at entropy / negentropy, which has a long-established and rigorous calculation procedure (and an enormous theoretical literature ranging across Computer Science and indeed Physics).

As a result, I think he may well have reinvented a perfectly round wheel in a somewhat square format: sorry, but I don’t think this is going to roll very far or very fast.

If the same calculations were repeated with different order ngram entropies, I think we might have something more interesting to work with here: but that’s already been done to death in the Zodiac Killer research world.

Moreover, the long-standing suggestion (which I think has a fair amount of evidential support) that the Z340 may well have been constructed in two distinct halves (Z170A and Z170B) would also mess with just about all of his arguments and conclusions. I’d much rather have seen that tested than Vigenere (it’s not a Vig, not even close).

Forward Context vs Backward Context?

As I was reading through Juzek’s paper, I was struck by a quite different question. If we are looking at an encrypted homophonic English ciphertext (a fairly reasonable assumption here), is there a notable difference between the left-context entropy (i.e. the information content of the text using the preceding letter as a context for predicting the next letter) with the right-context entropy?

That is, might encrypted homophonic English ciphertexts have a distinctly asymmetrical statistical “fingerprint” that would give us confidence that this is indeed what we are looking at in the Z340? Perhaps this has already been calculated: if so, it’s not work that I’m aware of, so please leave a comment here to help broaden my mind. 🙂

If you like cold case documentaries with only a mere frisson of cryptography, “Cold Case Files 1: The Zodiac” (which was recently uploaded to the TagTele site) could well be for you. While it’s an oldie (first released way back in 2003), it doesn’t try to impose any theories, but concentrates on interviewing people who were actually there… well, up to timecode 25:40, anyway, when it suddenly goes into ‘Arthur Leigh Allen = prime suspect’ mode (but then constantly bangs on about how he almost certainly wasn’t the Zodiac). Which is nice.

video since removed from TagTele site

What I wasn’t expecting was that – quite the opposite from what you might think from 2017’s documentary crop on the History Channel (which is an anagram, not many people know, of Clannish Theory, Shithole Cranny, and Horny Chatlines) – the police had actually worked through lots of the Zodiac DNA evidence by 2002. In the video, the specifically DNA-based angle (which starts at about timecode 33:25) shows that when DNA from Arthur Leigh Allen’s preserved brain was compared with the best reference samples derived from Zodiac primary evidence, it was enough to exclude him from being the Zodiac Killer.

Moreover, the documentary also discussed “writer’s palm” (from about 36:50 onwards), which is the imprint left by someone’s palm as they write a document. What it revealed (which I didn’t know) was that the palm prints police forensically recovered from Zodiac letters were good enough to compare with palm prints taken from Arthur Leigh Allen: all of which also proved that he was not the Zodiac Killer.

Of course, while it sounds ever so intriguing that Arthur Leigh Allen had a Zodiac watch, he was actually a scuba diver, and that was basically who Zodiac watches got marketed at. As an aside, I do wonder if the police ever looked at SF scuba clubs of the period: that may have been more of a productive avenue to explore than the American Cryptogram Association. Ah well. :-/

Incidentally, if you want to see a young-looking Tom Voigt, he’s in the documentary from about timecode 40:15, with the voiceover saying that his website gets a million hits per month (back in 2003). Goodness knows how much traffic it must get now, blimey. :-/

After The History Channel’s recent season of “The Hunt For The Zodiac Killer” programmes (episodes 1, 2, 3, 4 and 5), I thought it was time to get back to some non-fake-news codebreaking research.

In particular, I want to suggest an approach we might follow to try to solve the Z340 that (hopefully) won’t need a brain the size of a planet to run it. But first I’m going to talk about the Z13 cipher, because I think it tells us a lot about what is hidden inside the Z340 and indeed why the Z340 was written at all…

The Z13 Cipher

The text just above the Zodiac Killer’s Z13 cipher (20th April 1970) clearly and unambiguously refers back to a ‘name’ supposedly in the Z340 cipher (8th November 1969), though as far as I can see the “Dripping Pen” note that arrived with the Z340 didn’t mention a name at all:

An oft-repeated account for this is that the Z13 had been constructed in response to a kind of cryptographic ‘taunt’ that appeared six months previously in the Examiner newspaper on 22nd October 1969, as detailed here. In the Examiner piece, entitled “Cipher Expert Dares Zodiac To ‘Tell’ Name“, the President of the American Cryptogram Association issued a direct challenge to the Zodiac Killer to reveal his name in a cipher.

However, if you put all these pieces together, it seems highly likely to me that it was instead the Z340 cipher that had been constructed as a response to President Marsh’s taunt (it appeared a mere seventeen days later). Hence it seems entirely reasonable to conclude that the Z340 indeed contains a specific name for us to decrypt – though, as always, it seems highly unlikely that this will contain the Zodiac Killer’s actual name.

Cryptanalytically, though, the Z13 couldn’t be further removed from the homophonic world of the (cracked) Z408 (and presumably the Z340), in that it has shape repeats and internal structure aplenty. In fact, if you colour all the Z13’s repeated cipher shapes (once again, using Dave Oranchak’s neat-o-rama Cipher Explorer), this is what you see:

Much as I love “Sarah The Horse” and “Clara Cataract” as elegant literary plaintexts for this, it’s important to note that these are homophonic solutions for something whose many repeats point to its actually being a monoalphabetic substitution cipher. Dave Oranchak’s “Laura Catapult”, and glurk’s “Gary Lyle Large” are fine examples of how it is possible to construct name-like phrases to fit: but these are relatively rare examples in a surprisingly sparse, errm, name-space.

In many ways, whereas the problem with the Z340 is that it has too many shapes, the problem with the Z13 is arguably that it has too few shapes. So there would seem to be something a little odd going on here, cryptanalytically speaking: something feels wrong.

In his 2017 book “Unsolved!”, Craig Bauer praised a possible crack of the Z13 cipher which I hadn’t previously heard of, and credits p.128 of Robert Graysmith’s (2002) “Zodiac Unmasked: The Identity of America’s Most Elusive Serial Killer Revealed” as the source (though Graysmith talks about it as if the suggestion were as old as the [Hollywood] Hills):

Now, even though this doesn’t quite fit the pattern (the N cipher shape shouldn’t be shared between plaintext F and M), I think Bauer was completely right to give this his imprimatur, because it seems exceptionally close. Giving MAD Magazine’s “Alfred E. Neuman” as his name feels like this exactly the kind of thing the Zodiac Killer would do, in that it is taunting, unhelpful, superior, nasty, satirical, self-centred, and narcissistic in all the right ways.

For ALFREDENEUMAN to be the Z13’s plaintext, the only concession you would need to make is that a single letter was misenciphered: and as starting points go for a ciphertext that already feels as though it has too few shapes, this is not half as big a step as almost all other solutions I’ve seen proposed. Even though I completely accept that this isn’t cast-iron proof, I do think it suggests that it is well worth considering as a conditional piece of evidence to work with.

And Now, The Z340 Cipher…

For me, the big (if not ‘huge’) question the above leads to is this: if this ALFREDENEUMAN Z13 decryption is actually correct, might the Zodiac Killer have included exactly the same name in his Z340 cipher? And if so, might we be able to use the name as a known-plaintext crib into the Z340? (AKA a block-paradigm match. 🙂 )

Assuming the Z340 does use some kind of homophonic cipher, there are (340 – 12) possible positions the Z13 crib could be positioned at: however, we should be able to eliminate any position containing a cipher shape repeat within the 13-shape stretch that does not match a repeat in the ALFREDENEUMAN crib, because that would mean that the same homophonic cipher shape would have been used to encipher two different plaintext letters.

For example, because Z340 line #4 begins “S99…”, the “99” part could not be any part of the Z13 crib because there are no doubled letters in “ALFREDENEUMAN”: this is also true for the “++” pairs in lines #4, #14, and #18. Similarly, the +..+ repeat on line #9 and the W..W repeat on line #18 both cannot be in the crib, because no plaintext letter is repeated three steps apart in “ALFREDENEUMAN”. If you run this against the most widely used Z340 transcription, there are – according to the vanilla C test I put together (below, which you can actually run for yourself by clicking on [Run]) – exactly 197 valid crib positions. So we can eliminate (340-12-197) = 131 candidate positions. Which is nice. 🙂

What I find interesting is that locking a set of fixed set of letters to an (albeit still hypothetical) crib should enable us to use a homophonic solver on far smaller subsections of the Z340 than we would normally be able to do. I’ve written before about how the top half and the bottom half of the Z340 have quite different (but subtly overlapping) properties: for example, how top-half ‘+’ characters seems to work differently to bottom-half ‘+’ characters. As a result, I think it would make sense to try to solve lines #1 to #9 separately from lines #11 to #19.

But there are other results, that point out how lines #1 to #3 seem to work quite differently from lines #4 to #6, and so on. So the ability to try to solve even smaller blocks of lines may well be a critically useful string for our cryptological bow.

Unfortunately, I’m not (yet) a zkdecrypto-lite power-user, so I don’t know how to automate this kind of search Anyone who would like to collaborate on doing this, please feel free to step forward: or if you want to take the idea and do what you like with it, that’s fine by me too. Can you blame me if I want to see this solved before they start shooting Season #2? 😉

Just One Last Thing…

There is, of course, one other possibility that should be investigated… it’s just that those cold, creepy eyes in the famous Zodiac poster remind me of someone, can’t think who it is, but the name might come to me soon, who was it…?

C: Crib Matching Code

Without any further ado, here’s The History Channel’s “The Hunt for the Zodiac Killer” season #1 finale, wherein Craig Bauer, having immersed himself almost completely in Zodiac Killer arcana, conjures up a new solution of the Z340, whereupon everyone else falls (or seems to fall) in line:

video since removed from TagTele site

Well… OK, I guess. I suspect what most people would agree on about this ‘solution’ are:
* it’s primarily intuitive, and not really ‘cryptological’ in any useful sense of the word
* it’s either really brilliant or really foolish, and almost certainly nowhere inbetween

Craig’s Crack

Because the starting point for Craig Bauer’s decryption attempt was the idea that some letters might actually encipher themselves (to make the answer hide in plain sight), I’ve added a green background to those letters (or simply transformed letters) where the ciphertext and his decrypted text coincide, e.g. “HER……KI.L….” on the topmost line. You should be able to see 23 green-backgrounded letters.

However, for the sake of balance, I’ve also added a red background to those letters (or simply transformed letters) where the two do not coincide, e.g. “…PLVVP….TB.D” on the topmost line. You should be able to see 61 red-backgrounded letters (I think).

To make the following diagram, I used Dave Oranchak’s funky online Cipher Explorer tool:

It should be immediately obvious that a very high degree of selectivity is going on here: furthermore, seven letters are left out (on lines 2, 3, 5, 6 and 7), while three extra letters are inserted (lines 5 and 8). Finally, there is no consistent mapping of other shapes to plaintext letters as per the claimed decrypt, which is why I think it is safe to say that this is not a ‘cryptological’ decryption in any useful sense of the word.

The notion that a given historical ciphertext uses a handful of actual letters as themselves while the rest are somehow illusory or made up is an illusionary amateur cipher-breaking trope I have seen many dozens of times. In every case, it is a Pyrrhic victory of intense hopefulness over good sense, and achieves nothing bar wasting my time. If anyone can point my attention to anything about this particular decryption that varies from this rather self-defeating and useless template, I’d be fascinated to see it: but so far, this is just about as bad as it gets.

The motif of this antipattern is the codebreaker dreaming themselves an intense imaginary journey into the world of the codemaker, and bringing back as their prize a sampling of their vision, one that is every bit as hard to read as a book in a dream. All they have is the enduring conviction that they have solved it, a conviction that gets strengthened the brainier they are (and hence the more ingenious their post-rationalizing retro-fitting gets).

Total Immersion Delusion

If I were to give this kind of behaviour a “Pattern” name, I’d probably choose “Total Immersion Delusion“. Only someone who feels they have totally immersed themselves in their imagined world of the cipher maker would propose such a thing, and in almost every single case it is – sadly – a delusion that gets conjured up.

Here, you can see the seeds of the dream forming in the first line’s “HER…” and “KI.L” word-fragment patterns: but as the dream progressively fades away, the ability of the dreamer to fit the shape to the overselected letters reduces and reduces, until they’re left with only the sketchiest outlines of hope (a single green letter on lines 4, 5 and 7 demonstrates the degree to which it has triumphed over rationality here).

Sorry, but from what I can see, this Z340 ‘solution’ isn’t even close to being close: nobody’s going to come out of this particular dungheap smelling of roses, no matter how hard you hold your nose. Not huge, not a game-changer, sorry.

The new week brings a further episode of the History Channel’s “The Hunt for the Zodiac Killer”, not for the first time promising much but delivering little (Donna Lass car directions, really?) – the best part [37:25] was the interview with Zodiac Historian Misty Johansen (who wasn’t playing to CARMEL’s script). Even though it also partially revealed Craig Bauer’s much-trailed-and-supposedly-earth-shattering decryption of the Z340, that already looks to be more than a bit of a bust (sorry Craig), which I’ll discuss properly once the season finale has aired.

video since removed from TagTele site

Things must be particularly bad when it takes someone on Reddit to nail it, but according to ‘chickendance638’:

if you made a drinking game where you drank when somebody said “game-changer” or “huge” then one could forget about the incredibly shitty tv show that’s just been viewed.

Though I’m pleased to say that the same commenter then proved sufficiently wise to the dangers of expressing even mild exasperated sarcasm on the Interweb by noting:

Gotta be careful, if it catches on I could be responsible for more deaths than Zodiac himself

Anyhoo, the Zodiac-Killer-associated cipher this week’s episode highlighted was a short ciphertext included in a letter sent to the Times Union in Albany, NY and postmarked August 1st 1973 (which Karga Seven’s handwriting expert duly affirmed was by the Zodiac Killer). So let’s do our collective codebreaking thing on the “Albany Cipher”…

The Albany Cipher

As always with everything Zodiac related, it’s important to say that the Albany Cipher had been discussed and debated by Zodiac researchers for many years before it appeared on the show. The clearest image we currently have to work with is…

…though this image of its cipher scanned from Lyndon Lafferty’s (2012) “The Zodiac Killer Cover-Up: The Silenced Badge” (p.427) may possibly be slightly clearer, but it’s hard to be sure because of the screening…

Incidentally, I emailed the Times Union’s archive people to see if they happen to have a photo of the letter in their files. They kindly replied that:

We do not have the letter and nobody here has any information on its whereabouts, the actual receipt of the letter and what happened to it.

Which is a shame, but it is what it is.

Cracking the Albany Cipher

As was made clear during Hunt Ep.4, the Albany Cipher was originally cracked by the FBI many years ago, though the version they released to the public had the very first part of the plaintext – presumably containing the non-victim’s name – heavily redacted. So far, this was a basically correct account, i.e. the programme makers didn’t yet again claim that the decryption was puked out by CARMEL.

What we have of the plaintext runs: xxxxxxxxxxxxALBANYMEDICALCENTRETHISONLYTHEBEGINNING. Even though it would normally be the case that having this many plaintext letters would force the rest of the ciphertext to be one of only a small number of possibilities, a number of things conspire to make this difficult here. For a start, a number of cipher letter shapes are very similar: moreover, the quality of the reproductions we have are not good enough to definitively tell them apart; while a third difficulty is that people’s names tend to be more variable and hard to pin down than ‘pure’ dictionary words. And so on.

From the letters we have, the cipher alphabet mapping looks something like this:

Using these, some of the letters in the name section seem quite solid: CONxxExxENLY. The closest single word (with a couple of ciphering slips) would be CONSEQUENTLY, but because that’s not a name, it doesn’t make sense in context. If you like Mexican food, you can also try to start it CON QUESA: but this also seems unlikely in context.

Which is why, back in 2013, Zodiac crypto-meister Dave Oranchak floated the idea that the name might possibly be CONNIExHENLY. (This is of course the same name that CARMEL supposedly suggested in 2017, *sigh*.)

But cryptologically, I’m not so sure that Dave was on the money here: given that there seems no obvious reason to think that the message contains homophones, we should surely not begin by accepting ‘N’ as the fourth plaintext letter, and, rather, should instead directly reject it. However, because most of the plaintext alphabet has already been allocated, the unique shape at position four must surely be an otherwise unused plaintext letter.

Moreover, there are patterns within the mapping layout: for example, I’ve marked up R/S/T with the same proxy cipher shape in the table because (frankly) I can’t tell them apart in the ciphertext, so they look to be part of the same shape family. Hence I wouldn’t be at all surprised if the same pattern was also used for adjacent letters Q or U. And finally, the closest visual match to the unknown fourth shape of the ciphertext is the shape used for Y: so I would be unsurprised if this letter stood in for an adjacent letter e.g. X or Z.

Put all this together: and if this is a name, my own best guess is that the first six letters are in fact “CONZUE” (short for “CONZUELA”). I’m sure Spaniards will be happy to tell me which part of Spain or South America “Conzuela” is typical of (or whatever).

Fans of Family Guy will (of course) know the name Consuela well:

Yes, it’s the famous “I clean toilet” sketch. 🙂

What would Consuela say about the Albany Cipher – does she think it was made by the Zodiac Killer? Only one possible answer: “No, no“. Well… either that, or “More Lemon Pledge“, you choose (and you pay). 😉