A structural analytical approach to the Zodiac Z32 cipher based on sequence segmentation and the A=0 convention.
Hello everyone,
I’m from Italy and recently tried working on a possible solution to the Z32 cipher. I hope there are no translation mistakes, as the text was originally written in Italian.
If this is the correct section of the forum, I would like to share my proposed Z32 solution and hear your opinions.
Thank you!
Yes this is the correct place to post all work on codes.
I would love to see your work. Do I understand that your proposed solution results in “Hercules”?
MODERATOR
Eccomi!
I would like to share an analysis I have developed regarding the Zodiac Z32 cipher. I am not a professional cryptographer, but I approached this puzzle trying to apply a method that is as coherent and structured as possible.
In the attached document I propose an approach based on several main steps:
- dividing the Z32 sequence into subsequences separated by special characters;
- converting the letters into numerical values using the A = 0 system;
- interpreting mirrored letters with negative values, maintaining consistency with the graphical logic of the cipher;
- summing the values of each sequence and then converting the results back into letters.
Following this procedure, a series of letters emerges which, when properly rearranged, form the word HERCULES. This location actually exists in California and can be seen on the map associated with Zodiac’s July 26, 1970 letter, related to the so-called Mount Diablo code.
From the numerical values obtained in the sequences, I also interpret two parameters that appear consistent with the instructions given in the letter: 5 radians as the direction and 20 inches as the distance from Mount Diablo. Plotting these values on the map leads directly toward the city of Hercules.
In the final part of the document, I also analyze the last sequences of the cipher, from which possible initials of the author may emerge, for which I propose a few hypotheses.
As is now widely recognized, the structure of the Z32 cipher is too short to allow a unique solution through a simple substitution. For this reason, I deliberately chose not to approach the cipher using a classical homophonic substitution method, as was the case with Z408 and Z340.
In my opinion, it is possible that Zodiac intentionally constructed this cipher in a way that suggests a method similar to the earlier ciphers, leading those attempting to solve it down a path that produces ambiguous or non-unique results. In other words, the structure of Z32 itself may contain a kind of interpretative trap, encouraging solvers to think in terms of substitution when the underlying mechanism might actually be different.
For this reason, I tried exploring a more numerical and geometrical structure, organized in successive levels: first identifying the name of the city, then locating it through the map, and finally identifying the possible initials of the author. I interpret this process as a logical chain of steps leading to the resolution of the cipher.
I am sharing this work in the hope of receiving feedback, criticism, and observations from those who are more experienced than I am in the field of cryptography and the history of the Zodiac ciphers.
Thank you to anyone who takes the time to read and discuss it!
Perfect, I have posted my step-by-step solution in this post.
As soon as a moderator approves it, the link to the document will become visible.
Have a nice day!
The pages of the document should now be visible through the link. If anyone has questions or needs clarification, I will be happy to help.
I would also like to highlight a detail mentioned in the document: the number 32 coincides with the 32 segments that define the boundaries of the constellation Hercules in its modern astronomical definition.
I would also like to add an observation that I recently came across while watching a video by David Oranchak about the Z32.
In the video it is noted that, on the envelope associated with the July 26, 1970 letter, the abbreviation “Calif.” (California) appears to have been written in an unusual way, slightly rearranged as “Claif.”
A similar detail had already been observed on the envelopes associated with the Z340 cipher, where some of the writing was arranged diagonally; this feature was later interpreted as a possible graphical hint related to the method used to solve the cipher.
If a similar logic was used again in the case of the Z32, the anomaly “Claif” might be interpreted as an additional graphical hint from the author. In other words, it could suggest the need to alter or rotate the natural order of a sequence.
This becomes particularly interesting when compared with what I described in the document regarding the sequence associated with the omega symbol (Ω), which is the only sequence where the characteristic symbol appears at the beginning rather than at the end. In my analysis, I hypothesized that this sequence needs to be reordered and mirrored in order to become consistent with the structure of the other sequences.
From this perspective, the anomaly “Claif” could be interpreted as a possible meta-textual hint, through which the author indirectly suggests modifying the order of a sequence to obtain the correct reading of the cipher.
Of course, this is only an interpretative hypothesis, but I thought it was worth mentioning because it could represent another element consistent with the idea that Zodiac sometimes placed graphical or structural clues even outside the cipher itself, as in the case of the envelopes.
@lendor.77
Welcome to the forum, and thank you for sharing your work. I can see you put real effort into this, and I want to engage with it honestly.
I think there is a fundamental problem with the method, and I want to explain it as clearly as I can.
Z32 is a 32-character homophonic substitution cipher. We know this because the Zodiac used homophonic substitution in Z408 and Z340, both of which were solved, and because Z32 contains three pairs of repeated symbols at positions (0,25), (1,31), and (5,13) — the structural fingerprint of homophonic substitution. Any valid solution must satisfy these lock conditions: the plaintext letter at position 0 must equal position 25, position 1 must equal position 31, and position 5 must equal position 13. Your method does not check these constraints at all, which means it is solving a different puzzle than the one the Zodiac created.
Your procedure — segmenting by “special characters,” summing letter values, applying modulo 26 reduction, mirroring selected symbols with negative signs, then rearranging the output letters — introduces a large number of analyst choices at each step. Which symbols are “special”? Which letters get mirrored? Why does T get a negative value but O does not? Why is the omega sequence reordered when the others are not? Each of these decisions is a free parameter, and with enough free parameters, you can steer any 32-character sequence toward any short word. The result is not extracted from the cipher — it is constructed by the analyst.
A quick test: try applying your method to a random 32-character string. You will likely find that you can produce a California city name from that too, if you are free to choose which symbols are special, which values are negative, and which letters to rearrange. If a method works on random input, it does not demonstrate anything about the actual cipher.
I don’t say this to discourage you. The instinct to look for structural patterns beyond simple substitution is not unreasonable. But the method needs to be constrained enough that it can fail — otherwise it can’t succeed in any meaningful sense either.
Ciao coder1987!
Thank you for your detailed reply! I appreciate both the constructive tone and the time you put into your analysis. I would like to clarify a few points that I believe are central, both from a methodological perspective and regarding some specific technical aspects.
The first concerns the initial assumption: that Z32 must necessarily be a homophonic substitution cipher. In my view, this is not an established fact, but an inference based on Z408 and Z340. However, the fact that Zodiac used a certain method in those cases does not logically imply that he must have used the same method here, especially given that Z32 is much shorter and clearly tied to a map, angular directions, and a different operational context. The presence of repeated symbols is compatible with homophonic substitution, but it is not exclusive evidence of it — so there is a risk of treating an assumption as a conclusion.
As for the method I propose, it is not based on unconstrained choices, but on a sequence of defined steps: segmentation into sequences containing a single “special” symbol, A=0 conversion, treatment of symmetry through sign inversion, summation with modulo 26 reduction, and interpretation of the Greek symbols in angular terms, consistent with the map. From this process, the word HERCULES emerges — but more importantly, the result does not stop there. It also produces an angular value (5 radians) and a distance (20 units), which are consistent with the Mount Diablo map and align with the direction indicated by the crosshair in the July 26 letter . What emerges, therefore, is not just a linguistic result, but a convergence between text, numbers, and geometry.
Regarding the use of negative values, the rule is tied to symmetry: mirrored letters take negative values, and more generally, negative values never appear as initial elements but only as the result of a transformation . The letter T represents a boundary case, as it is inherently symmetrical. Within the omega sequence — which is already structurally anomalous — it can therefore be interpreted as a transformed element. It is also worth noting that if T were kept positive, the result would still yield an E, which remains compatible with HERCULES, but the S would be missing. This suggests that, in this specific sequence, the author may be pushing the rule to its limit — requiring a more refined application without actually breaking it. The letter O, by contrast, appears in initial position and is not derived from any transformation, and therefore remains consistently positive.
The same reasoning applies to the reordering of the omega sequence. This is not a freedom applied across the cipher, but a response to a specific structural anomaly: it is the only sequence where the “special” symbol appears at the beginning rather than at the end, thus breaking the pattern observed elsewhere . The reordering serves to realign it with the overall structure. Crucially, all such operations (reordering, sign inversion, etc.) are confined to this single sequence. If the method were arbitrary, one would expect similar interventions to be distributed throughout the text — not concentrated in one localized case.
In this context, I also find interesting an observation noted in a video by David Oranchak: on the envelope of the July 26 letter, “Calif.” appears to be written as “Claif.” In the case of Z340, similar graphical irregularities (such as diagonal writing) were later interpreted as operational hints. If a similar logic applies here, this could suggest the need to alter or reorder a sequence — consistent with what occurs in the omega sequence.
On the issue of “free parameters,” I agree with the principle that a method must be constrained enough to fail. However, testing this properly requires more than generating a word from random input. It would be necessary to show that a random sequence, processed through the same full procedure, can simultaneously produce a coherent word, consistent numerical values, a valid angular interpretation, and a real geographic target. Without that level of comparison, the objection remains largely theoretical.
Ultimately, the substitution model for Z32 has not, after decades, produced a widely accepted solution. The method I propose can certainly be debated, but it has the advantage of producing a coherent and testable chain (text, numbers, geometry, and map), which can be followed step by step.
At this point, I would simply pose one final consideration: what are the odds that a truly arbitrary method would lead, in a consistent way, to the identification of a Bay Area city that matches direction and distance, fits the Mount Diablo map, is thematically linked to explosives (Hercules), and is associated with a constellation — Hercules — that disappears in the fall at California latitudes, in possible alignment with “you have until next fall to dig it up”?
It is this convergence of geographic, numerical, symbolic, and temporal elements that, in my view, calls for a more detailed explanation than simple coincidence.
@lendor-77
Thank you for the thoughtful reply. Let me address the key points directly.
You ask what the odds are that an arbitrary method would produce a Bay Area city matching direction, distance, map, and thematic context. That’s the right question. But you should be asking it about your own method first, because the answer is: higher than you think.
The Phillips 66 map contains dozens of named cities and towns. The Bay Area is full of places with thematic connections to something — Hercules to explosives, Concord to harmony, Dublin to Irish history, Livermore to physics. If your method had produced CONCORD, you would have noted it sits on the map and connected it to the Zodiac’s desire for social compliance. If it had produced DUBLIN, you would have found an Irish connection. This is the Texas sharpshooter fallacy: you fire the bullet, then draw the target around wherever it lands, and marvel at the bullseye.
Now to the specific technical problems.
Your method requires rearranging the output letters to form HERCULES. The letters C, R, E, H, S, U, L emerge from your summation process, but they don’t spell HERCULES in order — you rearrange them. An anagram of seven letters from a 26-letter alphabet has a surprisingly high chance of matching some English word. The fact that you also get X and Y, which you set aside for a separate “initials” analysis rather than treating as failures, is a degree of freedom. If those letters had been H and E instead, you would have folded them into HERCULES. If they had been anything else, you would have found another use for them.
You say the omega sequence reordering is not arbitrary because it’s the only structurally anomalous sequence. But the reason it’s anomalous is that your own segmentation rules made it so. You defined the segmentation criterion, and when one segment didn’t fit the pattern, you reordered it. That’s not discovering a constraint — that’s creating an exception to rescue a result.
On the claim that Z32 might not be homophonic substitution: Z408 was homophonic substitution, solved in 1969. Z340 was homophonic substitution with transposition, solved in 2020. Z32 contains three pairs of repeated symbols at structurally significant positions — the signature of homophonic substitution. You are correct that this is an inference, not a proof. But it is an inference supported by every solved Zodiac cipher we have. Your alternative — that the Zodiac suddenly switched to a system involving A=0 numerical conversion, mirrored-letter sign inversion, modular arithmetic, sequence segmentation by special symbols, selective reordering, and anagram reassembly — has no precedent in any Zodiac cipher and no external support from any of his communications.
You ask what it would take to show the method fails on random input. I’ll tell you exactly: apply your full procedure to the Z32 ciphertext reversed, or to a random permutation of its symbols. If HERCULES or any comparably “coherent” result emerges, your method does not discriminate signal from noise. This is a test you can run today.
Now, you asked about convergence. My paper produces convergence too — but of a different kind. My solver tests 2,044,224 candidates across 12 template families, filters by three independent constraints (length, homophonic locks, map bounds), and produces 54 survivors. The top-ranked candidate, IN THREE AND THREE EIGHTHS RADIANS TEN, lands 254 meters from a 100-foot equilateral triangular depression near Lake Herman Road that wasn’t there in 1964 and was there by 1982. The cipher’s own lock structure forces 87% of survivors onto clock hours 8 and 10 — the two directions corresponding to the Zodiac’s known crime zones. The decoded coordinates fall 2.37 miles from the geometric centroid of the operational triangle formed by Mt. Diablo, Lake Berryessa, and Presidio Heights.
That is convergence between cryptographic structure, geographic reality, physical ground evidence, and crime scene geometry — all derived from a method with published code, explicit assumptions, and a clear falsification path (GPR at the site). Every step is reproducible. Every claim is auditable.
Your method produces a city name through a chain of analyst choices. My method produces coordinates, a ground feature, and a testable prediction through constrained computation. I think the distinction speaks for itself.
Thank you for the detailed reply! I’ll respond directly to the main points.
On the “post-hoc selection” concern
I understand the objection, but I think it is being applied in an overly simplified way here. The process does not start from a result and then adapt it to the context. Instead, letters and values emerge from an internal structure of the cipher, and are then tested against external constraints (map, direction, distance). For the objection to hold, it would be necessary to show that multiple alternative results satisfy the same set of constraints simultaneously. It is not enough to note that many cities exist in the Bay Area; one would need to demonstrate that other locations match, at the same time:
- the same constrained set of letters derived from the process;
- the same consistency with direction and distance;
- the same alignment with the crosshair;
- and a non-generic contextual coherence.
Without that, comparisons with other place names remain hypothetical.
On the anagram
I agree that, taken in isolation, an anagram has limited evidentiary value. But here the target is not an arbitrary word. The cipher is explicitly tied to a map, so the relevant search space is not the dictionary, but plausible locations within that cartographic context. In that sense, the rearrangement of letters does not occur in a free space, but in one that is already strongly constrained. Moreover, the letters themselves are not arbitrary: they emerge from a constrained process. The fact that they are not already ordered is a valid point, but not sufficient, on its own, to make the result arbitrary.
On X and Y
Regarding X and Y, I understand the concern about “degrees of freedom,” but I think the issue should be framed differently. X and Y are not introduced or reinterpreted after the fact: they are part of the raw output of the procedure. For that reason, they are neither discarded nor forced into the primary word. The fact that they do not directly enter the sequence that leads to HERCULES suggests that they may have a distinct role, rather than being errors to eliminate. In other words, the method produces a multi-layered output, not a single linear result. Treating them as errors would itself introduce arbitrariness, just as much as forcing them into the main result would. A more cautious position is to acknowledge that the method yields more than one piece of information, not all of which necessarily operate on the same level. Any additional interpretations (such as those related to initials) should be considered separate hypotheses. If, in the future, a concrete and verifiable correspondence with a real individual were to emerge, it could represent an additional point of interest, but it is not required to support the main result. In that sense, the situation is analogous to yours: the presence of a physical ground confirmation strengthens the hypothesis, but is not what the method initially relies on.
On the omega sequence
The anomaly does not arise from the segmentation rules; it is observable beforehand. It is the only sequence in which the “special” symbol appears at the beginning rather than at the end. The reordering does not introduce an exception, but attempts to reconcile this sequence with the overall pattern. It is also significant that:
- no other sequence is modified;
- all transformations are confined to this single case.
If this were an arbitrary adjustment, one would expect interventions to be distributed across the cipher, not localized precisely where a structural deviation is present.
On the homophonic substitution assumption
I agree that it is the most natural hypothesis and is supported by the solved ciphers. However, it remains an inference, not a proof. In the case of Z32, it has not yet produced a widely accepted solution. This does not invalidate it, but it leaves open the possibility that the structure may include additional or different elements.
On testing with random input
I understand the proposal, but I’m not convinced it is an appropriate test in this context. The method is not designed to operate on arbitrary strings, but on a structure that includes:
- symbol distribution;
- positional patterns;
- and an explicit linkage to a map.
Randomizing the input removes exactly the features the method is meant to interpret.
Final point
The key issue, in my view, is not the individual result, but the fact that multiple independent elements remain consistent with each other:
- internal cipher structure;
- alphabetic output;
- numerical values;
- geometric interpretation;
- and cartographic alignment.
It is this overall convergence, rather than any single step, that I find difficult to attribute to coincidence alone.
You say the test of applying your method to random input is inappropriate because it would remove the structural features the method is designed to interpret. That is exactly the point. A method that can only be applied to the one string it was designed around, and which cannot be tested against any control, is by definition unfalsifiable — it cannot fail, and therefore it cannot succeed in any meaningful sense. You have described a closed system: the cipher has structure, your method interprets that structure, and the result is declared meaningful because it came from that structure. But every 32-character string has symbol distributions, positional patterns, and internal regularities. If you refuse to test whether your procedure extracts equally “coherent” results from other strings, you are not protecting the method’s integrity — you are protecting it from evaluation. My method, by contrast, invites exactly this test: anyone can modify the lexicon, swap the templates, change the ranking algorithm, or scramble the input, and check whether the result holds. Six of my twelve template families produce zero survivors — the method fails where it should fail. That is what distinguishes a constrained methodology from a narrative one. You have built an elegant story. I have built a machine that breaks when the input is wrong and works when it isn’t. That is the difference, and no amount of thematic resonance between Hercules and explosives changes it.
Thank you, the point of disagreement is now much clearer.
I agree that a method must be able to fail. Where I disagree is on the type of test you propose. Testing on random input works well for methods designed to operate over large datasets or generic search spaces (like yours). My approach, on the other hand, is not a general-purpose decoder, but an interpretative hypothesis applied to a specific object, which has both an internal structure and an explicit link to a map. Applying it to random strings removes exactly the conditions the method is meant to interpret. This, however, does not make it unfalsifiable.
The method can fail, for example:
- if the structure is not stable;
- if alternative interpretations produce equally coherent but incompatible results;
- if the derived values do not lead to a consistent geometry;
- or if the result does not integrate with the cartographic reference.
So yes, it can fail. But not through randomization of the input, rather through loss of coherence across the different levels of the result. I think this is the real difference: your method tests validity by making the system “break” under varied input; mine tests validity through coherence between structure, numbers, geometry, and map. If that coherence does not hold, the method loses value.
I would just add one final observation, which I consider secondary but verifiable. The constellation Hercules, in its official IAU (1930) definition, is bounded by a polygon composed of 32 segments. This has no symbolic meaning in astronomy, but it is a geometric property of its formal definition. I simply find it interesting that this number matches the 32-character length of the Z32 cipher. I do not consider this as evidence, but as a possible structural consistency that may be worth noting within the broader framework.
@lendor.77
Hi again, I am enjoying our discussion regarding our competing proposed solutions.
You’ve just defined your method’s falsification criteria as “loss of coherence” — but you are the sole judge of what counts as coherent. When your omega sequence broke the pattern, you declared it a structural anomaly and reordered it, preserving coherence. When X and Y didn’t fit HERCULES, you declared them a separate layer, preserving coherence. When T’s symmetry created an ambiguity, you assigned it negative to get the letter you needed, preserving coherence. At every point where the method threatened to fail by your own criteria, you made an interpretive choice that rescued it. A falsification framework where the analyst decides in real time whether coherence has been lost is not falsification — it is editorial discretion.
And on the 32 segments of the Hercules constellation boundary: the official constellation boundaries, as set by Eugène Delporte in 1930, are defined by a polygon of 32 segments for Hercules, yes. But the edges of each constellation boundary are segments of meridians of right ascension and parallels of declination in the equatorial coordinate system relative to the equinox B1875.0 — these segment counts are artifacts of how many turns each boundary polygon needs to navigate around neighboring constellations. the International Astronomical Union designates 88 constellations of stars, and their boundary polygons span a wide range of segment counts. Orion’s boundary has 26 segments. Draco has 40. Serpens has 44. If Z32 had been 26 characters long, you would have noted Orion the Hunter. If it had been 40, Draco the Dragon. The number 32 matches Hercules because with 88 constellations spanning a broad range of polygon complexities, some constellation was always going to match. This is not structural consistency. It is a coincidence given a large enough pool of candidates — which is the same issue that underlies the entire method. You have built an elegant story. I have built a machine that breaks when the input is wrong and works when it isn’t, and utilizes every hint that Zodiac provided.
The Zodiac explicitly stated that The Mount Diablo Code, as he called it, concerns “‘radians’ & # inches along the ‘radians'”. My proposed plaintext is IN THREE AND THREE EIGHTHS RADIANS TEN, and utilizes the clock hour angles that Zodiac drew around Mt. Diablo on the Phillips 66 map, and points to a physical landmark that is visible from satellite imagery by the same road as the Zodiac’s first crime scene. A landmark that can be scanned with ground penetrating radar, to determine, without guessing, whether something is buried within it or not.
Thank you, this is a valid and important objection, and it helps clarify the core issue.
You are right that if “coherence” were left entirely to the analyst’s discretion, the method would become unfalsifiable and reduce to a narrative. The point, however, is that the choices you mention are not free adjustments made to preserve a result, but responses to specific structural constraints, and importantly, limited in scope.
In particular, these transformations are concentrated within a well-defined sequence that is already visibly anomalous compared to the others, as if the author had intentionally distinguished it.
For example: the omega sequence is the only one in which the “special” symbol appears at the beginning rather than at the end; X and Y are not removed or altered, but left as unresolved outputs; the sign assignment follows symmetry conditions and is not applied freely.
In other words, the method does not allow continuous adjustment: the transformations are localized in a specific point that is already anomalous and are not freely applicable across the entire cipher. This is the key distinction: if similar interventions were required in multiple places, or if different choices produced equally coherent but incompatible results, then the method would lose value.
So the question is not whether interpretation exists, because it does, but whether it is limited or potentially uncontrolled.
If instead the transformations remain limited and concentrated in a single already anomalous point, while still maintaining consistency with the underlying rules of the method and without introducing ad hoc criteria, then the question becomes whether this level of structure is sufficient to merit attention.
On the constellation point, I agree with your clarification. The number of segments depends on how the boundaries are defined and varies across constellations; I do not consider it evidence or a unique correspondence. The observation only makes sense because Hercules already emerges from the internal process: in that context, the numerical match is at most a secondary alignment, and taken on its own it has no evidentiary value.
More generally, I think the difference between our approaches also lies in the objective. Your method is designed to produce a verifiable result and to fail under controlled variation, and that is a strong criterion. Mine is trying to determine whether multiple independent constraints, structural, numerical, geometric, and cartographic, can align without requiring continuous correction.
If that alignment required repeated intervention, then your criticism would be entirely valid. If instead the transformations remain limited and constrained, then the question becomes whether that level of structure is sufficient to justify further consideration.
I think this is ultimately the key point: not whether interpretation is present, but whether it is sufficiently controlled to be meaningful.
Good night!
Thank you this is genuinely one of the most gracious and well reasoned exchanges I’ve had on this forum. I mean that sincerely.
I want to accept your framing and work within it, because I think it actually reveals the problem more clearly than my previous responses did.
You say the transformations are “concentrated in a single already anomalous point.” But consider what that single point is doing. The omega sequence is where your angular value comes from. It’s where the reordering happens, where the sign inversion of T is applied, and where the mirrored S produces the letter needed to complete HERCULES. If you remove or change any one of those decisions, HERCULES disappears and the angular value changes. The single point where all your interventions are concentrated is also the single point that produces most of your result. That’s not a localized exception — it’s the load-bearing wall of the entire structure. A method where the most consequential output depends on the most heavily interpreted input is not constrained by that concentration. It is vulnerable to it.
You also say that X and Y are “left as unresolved outputs,” and that this is more honest than forcing them into the result. I appreciate the intellectual honesty there, truly. But an unresolved output in a 32-character cipher is not a minor footnote — it means your method does not fully account for 2 of the 8 letters it produces. A method that explains 75% of its own output and leaves the rest as “possibly operating on a different level” has not yet demonstrated the convergence it claims.
I think you’re a careful thinker, and I respect that you’re engaging with these objections rather than dismissing them. If you’re interested, I’d genuinely encourage you to try one thing: apply your full procedure to the Z32 ciphertext with the two rows swapped (row 1 becomes row 2 and vice versa). Same symbols, same distribution, different positional structure. If HERCULES or any comparably coherent city name does not emerge, that would actually strengthen your case considerably. And if something does emerge — well, that’s important to know too. Either way, you learn something. That’s all any of us can ask of a method.
Sleep well, and thanks again for the exchange.
