Posted by: @shaqmeister

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One final question for this afternoon, as I’m needing to get off to work soon…

Have you ever given consideration to the thought that The Zodiac’s “My name is ______” might, in fact, be complete in itself, as in:

“My name is [I’m not going to give you my name].”

and that the cipher below this starts a completely new idea and doesn’t have anything to do with names?

After the cipher, the letter itself just goes on to talk about bombs.

At the very least, I have always wanted to make sure that I never ruled this out as a possibility. (Indeed, it has always been my preference to view it in this way.)

Personally, I’m more inclined to think that Zodiac did actually include his name somewhere within one of his ciphers. Beyond my own Z13 solution, I have this impression that serial killers often live on a kind of razor’s edge: on one side, the urge to “shout” their name to the world and claim their actions, and on the other, the need to avoid being caught.

That said, of course anything is possible. For example, some time ago I saw an interesting interpretation of the Z32 online: with a bit of imagination, by rotating the cipher you could read “WANT MY NAME.” It was quite a fun idea, even if clearly more suggestive than provable.

Buongiorno, @lendor-77!

I have two final questions that I would like to ask if I may, just to make sure I now fully understand the totality of your proposal.

Firstly, as to the four candidate initials that you have evaluated in this post, was it intentional that for 2) and 2.2) you took the ‘H’ to be positive? Being on the first line and therefore also under the reversed reading order, I might have expected this to be negative also (e.g. −H − E − R − C + X = −7 − 4 − 17 − 2 + 23 + 26 = 19 → T).

Secondly, as to the markers ‘X’ and ‘Y’ in the sequence ordering ‘HERCXUYLES’, are you assuming that although these are ‘X’ and ‘Y’, they could have been any letters (which would need to be the case in order to propose that the author had the freedom to be able to insert random initials here, e.g. ‘HERCQUDLES’)?

Grazie

@shaqmeister buondì!

Sì, anche la tua interpretazione è corretta. Avevo ipotizzato che, essendo la H una lettera simmetrica, il suo valore non cambiasse leggendola in senso antiorario, a differenza delle altre lettere. Nel tuo caso, leggendola in senso orario, ha senso considerare tutte le lettere dell’alfabeto HERC come negative, il che naturalmente porta a iniziali diverse.

Per quanto riguarda la lettura delle lettere, anche ipotizzando iniziali come QD , non credo che l’approccio corretto sia quello di leggere una sequenza lineare come HERC Q U D LES . Non credo che l’autore intendesse una lettura così diretta.

L’idea, invece, è che le lettere di HERCULES debbano essere utilizzate come base per ricavare le iniziali attraverso una sequenza di passaggi logici:

• identificare le sequenze;
• riconoscere la stringa HERCULE insieme a due caratteri sconosciuti ( X e Y );
• cerca la S , che può essere derivata solo dalla sequenza “gamma”. Questo passaggio non è banale: richiede di “giocare” con una delle regole del sistema, ovvero che T , essendo simmetrica, può essere trattata come positiva o negativa. Inoltre, è improbabile che la lettera S compaia solo in questa sequenza sia una coincidenza;
• aggiornare la sequenza gamma introducendo la S ;
• Si noti che la sequenza gamma è fuori posto e deve essere riordinata (richiamando anche l’idea “calif / claif”). Tuttavia, il semplice scambio dei simboli non cambierebbe il risultato. Cambia solo se applichiamo nuovamente la logica del sistema, cioè specchiando i caratteri, il che produce una S negativa ;
• Una volta allineata la sequenza gamma con le altre, è possibile ricavare i due caratteri mancanti.

Scritto in questo modo può sembrare un po’ contorto, ma in pratica è più semplice di quanto sembri. Abbiamo già visto come, nella sequenza gamma, Zodiac sembri “giocare” con le proprie regole. L’idea è che potrebbe aver fatto la stessa cosa anche nel possibile riordino della sequenza.

@shaqmeister good morning!

Yes, your interpretation is also correct. I had assumed that, since H is a symmetrical letter, its value wouldn’t change when read counterclockwise, unlike the other letters. In your case, reading it clockwise, it makes sense to consider all the letters in HERC as negative, which naturally leads to different initials.

As for how the letters should be read, even if we assume initials like QD, I don’t think the correct approach is to read a linear sequence such as HERC Q U D LES. I don’t believe the author intended such a direct reading.

The idea, instead, is that the letters of HERCULES should be used as a base to derive the initials through a sequence of logical steps:

– identify the sequences;

– recognize the string HERCULE along with two unknown characters (X and Y);

– find the S, which can only be derived from the “gamma” sequence. This step is not trivial: it requires “playing” with one of the system’s rules, namely that T, being symmetrical, can be treated as either positive or negative. Also, it’s unlikely that the letter S appearing only in this sequence is a coincidence;

– update the gamma sequence by introducing the S;

Note that the gamma sequence is out of place and must be reordered (also recalling the “calif / claif” idea). However, simply swapping the symbols would not change the result. It only changes if we apply the system’s logic again—by mirroring the characters—which produces a negative S.

– Once the gamma sequence is aligned with the others, it becomes possible to derive the two missing characters.

Written this way, it may seem a bit convoluted, but in practice it’s simpler than it sounds. We’ve already seen how, in the gamma sequence, Zodiac seems to “play” with its own rules. The idea is that he may have done the same thing in the possible reordering of the sequence.

Posted by: @lendor-77

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As for the reading of the letters, even assuming initials like QD , I don’t think the correct approach is to read a linear sequence like HERC Q U D LES . I don’t think the author intended such a direct reading.

Your explanation is clear and I think I just about understand it now, except for perhaps this last point.

It was not my intention to suggest that if he had produced ‘HERQUDLES’ his initials would be QD from a direct reading. My question was more about the ‘freedoms’ and ‘constraints’ that we have talked a lot about.

In this example, I would be working from an assumption that his initials were UD and asking, if that were the case, would the author have had the freedom to use the following according to your method:

H + E + R + C + Q = 7 + 4 + 17 + 2 + 16 = 46 → 46 – 26 = 20 → U

U + D = 20 + 3 = 23 → X

or does your method require the two ‘unknowns’ to be precisely ‘X’ and ‘Y’, which would be a further constraint?

Posted by: @shaqmeister

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In this example, I would be working from an assumption that his initials were UD and asking

Apologies, that should have been “UX.”

I think I understand your request. As soon as I have a moment during the day or later this evening, I’ll reply. Sorry, I didn’t realize earlier that I had posted the response in Italian instead of translating it.

Just to simplify (hopefully) my question here, and taking the left-hand sides of the following to be a kind of mathematical variable representing your markers here…

Does you method require that the author was constrained by:

x = 'X'; y = 'Y'

or could he have used:

x = 'Q'; y = 'D'

if that brought him to the result he was looking for—his actual initials (here, assumed to be UX)?

Posted by: @shaqmeister

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La tua spiegazione è chiara e credo di averla capita quasi del tutto, fatta eccezione forse per quest’ultimo punto.

Non era mia intenzione suggerire che, se avesse scritto “HER Q U D LES”, le sue iniziali, leggendole letteralmente, sarebbero state QD. La mia domanda riguardava piuttosto le “libertà” e i “vincoli” di cui abbiamo parlato a lungo.

In questo esempio, partirei dal presupposto che le sue iniziali fossero UD e mi chiederei, se così fosse , se l’autore avrebbe avuto la libertà di usare quanto segue secondo il tuo metodo:

H + E + R + C + Q = 7 + 4 + 17 + 2 + 16 = 46 → 46 – 26 = 20 → U

U + D = 20 + 3 = 23 → X

Oppure il tuo metodo richiede che le due “incognite” siano precisamente “X” e “Y”, il che costituirebbe un ulteriore vincolo ?

Alright, let me try to explain this more clearly and see if I’ve understood it correctly, especially regarding the role of X and Y.

Since X and Y are not part of the word HERCULES, they suggest that the two sequences they belong to represent unknown letters. At the same time, however, they are not just placeholders: they seem to have an active role in the process.

In particular, they can be seen both as endpoints of the calculation and as sum correctors, meaning elements that allow the total to reach exactly the value needed to produce the intended letter.

In my initial example, the mechanism works like this:

C + R + E + H − S + X = 2 + 17 + 4 + 7 − 18 + 23 = 35 → 35 − 26 = 9 → J
C + R + E + H − S + X + U + Y = 35 + 20 + 24 = 79 → 79 − 78 = 1 → B

Once we reach the point where the unknown letters X and Y come into play, we obtain the final result, which allows us to derive the initials.

Within this framework, the S also seems to play a specific role: it acts almost like a key, something that needs to be adjusted in order for the whole mechanism to work properly, since it initially appears in a position that requires reordering, as suggested by the calif / claif clue. So it’s not just a letter to be found, but a necessary step to make the entire system consistent.

Of course, as I’ve already said, this remains my hypothesis. I can support it and argue in its favor, but I can’t claim that it is objectively better than other possible solutions we’ve discussed, at least within the context of the Z32.

All is clear to me now, lendor. Thank you for providing this detailed explanation.

So, as placeholders only, you would say that the author intentionally chose these to be ‘X’ and ‘Y’, and any other letters he may have thought to use instead, for any other reason, would not have been possible. On top of this, however, you also have ‘X’ and ‘Y’ function as a term in each of the sums producing your ultimate result, in which case we must regard their functioning as a term in this sense as being fixed (fully constrained)—they can only contribute +23 and +24 to their respective totals without any flexibility to contribute a different value.

On top of this, we must also notice that all the remaining terms in both the sums are likewise constrained, here by the fact that they are required to be so to give us ‘HERCULES’ in the first place. Therefore, the solution idea overall is almost totally constrained to produce JB, with the only slight freedom having been left to the author here being the actual placement of the X and Y blocks.

Ultimately, then, we have here another example whereby the author could only have found the initials JB in the already existing cipher. He had no means of being able to change anything to put them there if they were not already present.

And that’s fine. Only, compared to the simple process of merely “seeing” (finding) ‘UL’ already present, in the more straightforward example, here we cannot get around the fact that even the author would have had some significant work to do before he would, himself, have “found” ‘JB’.

Everything is perfect, and I completely agree!

In analytical terms, the problem that your method faces in relation to being fully constrained arises from the fact that, in your evaluations, you require:

x = ‘C’ + ‘R’ + ‘E’ + ‘H’ − ‘S’ + ‘X’
y = ‘C’ + ‘R’ + ‘E’ + ‘H’ − ‘S’ + ‘X’ + ‘U’ + ‘Y’ 

with all terms in the right-hand sides constants—hence x and y are already fixed—and not:

x = ‘C’ + ‘R’ + ‘E’ + ‘H’ − ‘S’ + a
y = ‘C’ + ‘R’ + ‘E’ + ‘H’ − ‘S’ + a + ‘U’ + b

where a and b are free for the author to set at will.

Basically, having X, Y be both the identifier for unknowns and a value term in how these are used to derive the initials, your method thereafter is, as we have said, fully constrained to give JB.

For myself, I now have your method for the Z32 very clear in my mind, and I can only hope that one day I might get to see your other work on the Z13. Thank you.

Hello to everyone reading this message! I could use your help, but let me start from the beginning.

A few days ago, I read an interesting post by @Marclean in the thread “Symbols and Letters 340 Key.” One of his observations particularly caught my attention, so I would like to thank him for giving me this insight.

Marclean pointed out that the Z18 sequence:

EBEORIETEMETHHPITI

has a rather unusual structure: it consists of 9 vowels and 9 consonants. Furthermore, if repeated letters are removed while preserving the order of their first occurrence, exactly 9 distinct letters remain:

EBORITMHP

This observation led me to two considerations.

The first may be somewhat marginal to the main subject of this thread, but it is still intriguing: the number 9 also recurs in some analyses of the dates associated with the Monster of Florence murders. I therefore brought this feature of Z18 to the attention of a researcher who is investigating the possible recurrence of this number.

The second consideration, which is more relevant to this thread, concerns the sequence EBORITMHP. Out of curiosity, I applied every possible Caesar shift to these nine letters and obtained the following results:

Shift  0: EBORITMHP

Shift  1: FCPSJUNIQ

Shift  2: GDQTKVOJR

Shift  3: HERULWPKS

Shift  4: IFSVMXQLT

Shift  5: JGTWNYRMU

Shift  6: KHUXOZSNV

Shift  7: LIVYPATOW

Shift  8: MJWZQBUPX

Shift  9: NKXARCVQY

Shift 10: OLYBSDWRZ

Shift 11: PMZCTEXSA

Shift 12: QNADUFYTB

Shift 13: ROBEVGZUC

Shift 14: SPCFWHAVD

Shift 15: TQDGXIBWE

Shift 16: UREHYJCXF

Shift 17: VSFIZKDYG

Shift 18: WTGJALEZH

Shift 19: XUHKBMFAI

Shift 20: YVILCNGBJ

Shift 21: ZWJMDOHCK

Shift 22: AXKNEPIDL

Shift 23: BYLOFQJEM

Shift 24: CZMPGRKFN

Shift 25: DANQHSLGO

It was precisely at this point that I noticed a curious feature connected to the solution I proposed for Z32.

If you read through this thread and follow how my analysis developed, you will see that I divided Z32 into 9 sequences. For each sequence, I added together the alphabetical values of its symbols using an A=0 system, obtaining the following nine-character sequence:

CREHƧXUYL

Let us now compare it with shift 16 derived from EBORITMHP:

Z32: CREHƧXUYL
Z18: UREHYJCXF

The two sequences share no fewer than 7 out of 9 characters:

C – R – E – H – X – U – Y

But this peculiarity is not limited to the number of characters they share. When the two sequences are divided as follows, a very interesting structure emerges:

Z32: C | REH | ƧX | U | YL
Z18: U | REH | YJ | C | XF

The sequence REH appears in exactly the same position in both cases, from the second to the fourth character. Furthermore, the letters C and U occupy the same two positions in reverse order: in Z32, C appears at the beginning and U in the seventh position, whereas in Z18 the opposite occurs, with U at the beginning and C in the seventh position.

These two letters therefore seem to “mark out” both sequences according to the same structure:

Z32: C | REH | __ | U | __
Z18: U | REH | __ | C | __

Finally, two pairs of characters remain in each sequence:

Z32: ƧX | YL
Z18: YJ | XF

Here, too, another curious feature emerges: the letters X and Y appear in both sequences, but they are distributed across the two pairs in a crossed arrangement. In Z32, X belongs to the first pair and Y to the second; in Z18, the opposite occurs, with Y in the first pair and X in the second.

This creates a pattern somewhat similar to the interchange observed between C and U, although in this case the correspondence is not as immediate: to align X and Y in the same column within their respective pairs, the ƧX pair would need to be rearranged.

Z32: ƧX | YL
Z18: YJ | XF

At this point, however, I will stop because I would like to ask you two questions.

My first question is: how can I determine whether the similarities between the sequence produced by my proposed Z32 solution and shift 16 of Z18 are genuinely significant or simply due to chance?

The two sequences share seven out of nine characters, contain REH in exactly the same position, and display the C–U interchange as well as, less directly, the X–Y interchange. What kind of test could I perform to determine how likely it would be to obtain a similar result by chance when comparing the Z32 sequence with all possible Caesar shifts of a nine-letter sequence?

My second question is more general and concerns the procedure I followed.

At the end of this reasoning, I arrived at a possible interpretation based on comparing two sequences. Through two separate processes, I obtain two very similar results. I then superimpose the sequences, identify the matching elements, and use the differences between them in an attempt to derive the final message.

I have applied a similar procedure to some anonymous letters associated with the Monster of Florence case. I would therefore like to know whether this method has a specific name and whether it can be related to an established cryptological technique, such as comparison with known plaintext, subtraction between sequences, or some form of differential analysis.

Or is it simply my own interpretive method, without a formally recognized equivalent in cryptology?

I would especially like to understand this so that I can describe my procedure accurately, without incorrectly assigning a technical name to it.