Hello to all,
Few days ago, I shared videos in which I explained why I tought I had solved both Z13 and Z32 codes. As the video format may not be convenient for everyone, I wanted to share with you in detail the steps and reasoning, to solve them. What is striking about these two codes, is that they do not appear as being proper ciphers, but codes which require some specific approach to solve them, inspired by physics.
The very short length (13 and 32 characters) makes it impossible to find keys from these codes.
Logically, if these codes had a findable solution, then the key had to be obtained elsewhere. The resolution of the Z340 code provided a new key. My main assumption is that if the Z13 and Z32 codes could be resolved, then the Z340 key was the starting point for decoding them.
A. Resolution of Z13 code
A.1. Introducing the code
The code was contained in a letter from The Zodiac to the San Francisco Chronicle on April 20, 1970. The preamble to the code reads "My Name Is "
The code has a length of 13 characters, letters and symbols.
A.2. Method of resolution
The resolution method is a succession of 4 substitutions:
– Using the Z340 key
– Variation of the cipher A1Z26 (alphabetical rank) to convert letters into numbers
– Substitution of Zodiac signs by their number in the Zodiac dial
– Delastelle substitution (Trifid Alphabet)
The first step uses the key to the Z340 code, which leads to the following sequence:
The two signs of Zodiac Cancer and Aries are not deciphered by this key.
The second step is to use a variant of the A1Z26 alphabetical rank cipher that replaces a letter with its position in the alphabet. A variant indeed, because instead of taking into account the position in the alphabet, we consider only the unit corresponding to the position in the alphabet: so M in 13th position becomes 3, N becomes 4 etc.
Next, the third step is to replace the Zodiac symbols with their position in the Zodiac dial. The two unknown symbols are like the signs of Cancer and Aries:
Thus, we obtain a sequence of figures that is surprising by its lack of diversity: 1, 4, 5 and only one 8:
This may be reminiscent of a sequence of Trifid cipher, invented by Félix-Marie Delastelle in 1902. Except that the length of the code is not a multiple of 3, and it contains not 3 but 4 types of characters. The Trifid cipher is an encoding in base 3 of the letters of the alphabet, as is binary encoding in electronics, which consists of 0 and 1.
Several electronics protocols use not the value of voltage potential as an information element, but the variation of this potential between two states (NRZI: Non-Return to Zero Inverted, which existence I was able to verify before 1970). If we use this analogy, and translate this code by keeping the absolute gap between each number, we get:
At this point, we have a sequence of 12 digits, and 3 symbols: 1, 3 and 4. In fact, if we continue the analogy by applying the substitution of Delastelle (equivalent to a binary coding, but in base 3), with the following parameters: X – 3, Y – 4, Z – 1, we get the following sequence:
A.3. Interpreting the solution
The result of this sequence does not explicitly identify a suspect. Nevertheless, it immediately reminds of one of the suspects, Lawrence Kane, of whom two known aliases are:
– Lawrence Kaye
– Larry Kay
The assumption that the Zodiac made a mistake in encoding its message is plausible for two reasons:
– The first two Z408 and Z340 codes previously deciphered contain multiple errors, this helps to rule out the hypothesis that the Zodiac had an infallible encoding
– Although shorter than the other 2 codes, the Z13 code is the result of a more complex encoding because it is a succession of 4 substitutions, which increases the risk of error
The mistakes that the Zodiac could have made may have been as follows:
– An error on the antepenultimate character before Delastelle’s substitution: he would have put a Y instead of Z. This would result in the KAY result.
– A confusion in the association of numbers with symbols when substituting Delastelle: Y instead of X and Z instead of Y. What would lead to the KAYE result
The fact that this solution uses two encoding steps borrowed from electronics is plausible given that the suspect had followed a special training program in which he had the opportunity to learn such techniques.
B. Z32 code resolution
B.1. Introducing the code
The code was contained in a letter from the Zodiac to the San Francisco Chronicle on June 26, 1970. In this letter, the Zodiac threatens to blow up a school bus. The Zodiac included in the letter a code that, coupled with a map he attached, would find the bomb before the students returned to school.
The code is 32 characters long, letters and symbols.
The map contains a handwritten indication: a dial positioned on Mount Diablo (clue 1) and the words “is to be set to Mag. N.” (clue 2).
The Zodiac sent another letter to the San Francisco Chronicle on July 26, 1970, with a postscript note: "The Mt Diablo Code concerns Radians and inches along the radians" (clue 3).
B.2. Principles of resolution
The resolution method is based on three principles:
– The Z340 key must be a resolution step to validate that the main hypothesis is correct: "Z340, Z13 and Z32 codes have the same key"
– All clues given by the Zodiac must be used and become understandable at the end of this solution
– The solution must be consistent with the context of the case: The Zodiac indicates that the code should allow to find a bomb aimed at a school bus. So it’s probably a location.
As with the Z13 code, the first step uses the key to the Z340 code, which leads to the following sequence:
As with the Z13 code, the signs of the Zodiac Aries and this time Libra, are not deciphered with the Z340 key.
B.3. Exploitation of clues
1. The first clue to exploit is the postscript (clue 3): "The Mt Diablo Code concerns Radians and inches along the radians." The Radian and inches are angle measurement units (1 inch – 0.001 Radian). Yet, the coordinates of Latitude and Longitude, which indicate a position, are angles, expressed in degrees.
2. The second clue to exploit is the dial, positioned on Mount Diablo (clue. 1). Mount Diablo is the landmark from which the "Principal Meridian" was defined in 1851, used by the Public Land Survey System.
3. The third clue is "Is to be set to Mag. N. (clue 2), which can be interpreted in light of previous indices as "Is to be set to Magnetic North". The Magnetic North is not aligned with the geographic north which serves as a reference for geographic coordinates. In addition, it moves annually, and its position is measured and standardized by the International Association of Geomagnetism and Aeronomy.
These 3 clues, Angle, Meridian and Magnetic North, suggest that the 32-character code contains position coordinates, not in the geographic referential, but geomagnetic.
I created a conversion tool to transpose geomagnetic coordinates into the geographic referential, and vice versa.
As with the Z13 code, the second step in deciphering is to use a variant of the A1Z26 alphabetical rank cipher that replaces a letter with its position in the alphabet. A variation indeed, because instead of taking into account the position in the alphabet, we consider only the unit corresponding to the position in the alphabet:
The result at this stage highlights a perfectly ordered sequence of numbers indicating the geomagnetic coordinates of a position close to South Tahoe Middle School. The probability to find a location in South Lake Tahoe given any random 32 digits sequence is of about 1/50000
Lake Tahoe holds a special place in the Zodiac case, for the following reasons:
– Lawrence Kane was suspected of being the Zodiac and lived in South Lake Tahoe
– An alleged Zodiac postcard sent to the San Francisco Chronicle in 1971 refers to the Lake Tahoe
– An alleged Victim of the Zodiac was working in South Lake Tahoe and disappeared on September 7, 1970
B.4. Finalizing the solution
The remaining characters of the code, after using the Z340 key, remain encrypted. However, it is striking to see the appearance of anagrammed NORT, WEST…
Given the letters in this sequence (one E, one I, while they are frequent letters in English), any attempt at an anagram using the letters failed to generate meaning. Similarly, by looking for various rules of transposition through a program that I developed, I could not achieve any sequence that could make sense despite hours of calculation.
In order to unblock the search, I hypothesized that the Zodiac had made a mistake, intentional or not. One of his most frequent mistakes concerns triangles, which he mixes. So I tested my program by replacing the full triangle with a point triangle:
This gave a result that suggested that this error was plausible, since it makes the word Diablo appear in anagram, reminiscent of the Map’s Mount Diablo clue (clue 1):
The starting point of my program is a 4x5matrix with the letters, removing the "nulls" and the coordinates already found:
The calculated transposition is a succession of circular permutations applied alternately on lines and columns (an analogy would be a search for a solution of a Rubik’s Cube by brute force).
Thus, after 2 days of calculation on two computers, my program gave a result that in 10 circular permutations, alternating lines and columns, made appear 3 words:
This sequence includes the words FIND, LABOR and DAY. What is surprising is:
– LABOR DAY is the day that marks the return of students to school: The first Monday in September, the 7th in 1970, which is consistent with the threat contained in the letter
– The remaining letters, anagrammed, form WEST and NORT (misspelled)
The meaning of the Z32 code could be, subject to the validity of hypotheses:
LABOR DAY FIND 45.609 NORT 58.719 WEST (geomagnetic coordinates)
So, the code referred to a school in South Lake Tahoe, and on the day when school year begins.
B.5. Interpreting the solution
Admittedly, the search for transposition is not perfect, it results in a partial result and it assumes an error (intentional or not) of the Zodiac. It would probably take more computational time to finally find by brute force the entire sequence that can also recompose the words NORT and WEST. Or simply there could be no transposition rule, but a very difficult to find anagram due to the lack of high frequency letters.
However, there are certain coincidences that are worth noticing:
– The solutions of the two codes are consistent one with the other: Lawrence Kane lived in South Lake Tahoe and the position found is in South Lake Tahoe.
– The location found also corresponds to a location consistent with the Zodiac letter, since it is 800 meters near a school
– The date of LABOR DAY (September 7, 1970), which coincides with the start of school, is consistent with the deadline given by the Zodiac in the threat letter of the code Z32
– The proposed solution exploits all the clues: the dial on Mount Diablo, the handwritten note on the map and the postscript
– The two proposed solutions use not one but two identical substitution stages: Z340 and the A1Z26 variant
CONCLUSION
The solutions of the first codes already resolved (Z408 and Z340) also include imperfections (substitution errors, transposition errors, uses of anagrams). But what made them valid was the general meaning that emerged: an intelligible text that could not be the only result of coincidences.
In our case, by imposing the initial hypothesis: "The Z340, Z13 and Z32 codes have the same key", we come up with proposals for solutions that are not perfect either, but are interconnected, and related to the real context. They designate a person, place and date consistent with a real threat.
The proposed solutions also allow a credible interpretation of clues 1, 2 and 3.
It seems that in order to solve these codes, the Zodiac wanted the investigators to use methods other than conventional cryptography techniques. The Zodiac uses telecommunication substitutions (NRZI and binary encoding) and geomagnetic coordinates.
Sharing an update on this solution. I was not very happy with the transposition approach (section B.4 of my previous post).
Having not been able to find a perfect transposition, I am proposing an alternative approach.
First, the coordinates are immediately followed by the letters W and N, which could stand for NORTH and WEST.
It could be intentional or not, but the random probability to have these letters at that place is of 0.3%. Therefore, it is plausible to think that they have been intentionally placed there in order to give a clue on the possible coordinates location in the sequence.
Secondly, the remaining letters allow anagrams of the words NORT (misspelled) and WEST, which are consistent with the fact that the code containes coordinates:
45.609 NORT 58.719 WEST
Thirdly, there are 12 letters remaining, which could form I wide variety of expressions, one could say.
Actually, I had a look at all the possible combinations.
Using a dictionary and a small program, I managed to find 3762 combinations (or “phrases”) possible to make with those 12 letters. Here is a summary:
As an example, here is an extract of the combinations:
Having been through all the 3762 sequences, or “phrases”, the only one providing a meaning was “LABOR DAY FIND”, which is the last piece of the Z32 solution:
LABOR DAY FIND 45.609 NORT 58.719 WEST
Given the nature of the Z32 code, it does not seem possible to have a 100% mathematical validation of the solution. This update however adds “likeliness” to the one proposed in this post.
Few updates on the Z13 solution
1/ Trifid alphabet
Cragle shared a link to the Army cryptography manual Sam Blake was referring to in one of the interviews (thanks!):
https://www.nsa.gov/Portals/70/document … 078800.pdf
Page 72 describes the Trifid Alphabet, which I believe was used in the Z13 code. The Zodiac could have learned this cipher technique in this manual.
2/ Electronics protocole
Also, the Z13 code uses a variant of an electronics protocole called NRZI. While this protocole existed at the time, it was probably less common to be known by the general population than it is today.
We can read on Lawrence Kane:
Kane received training at the ‘Radio Materiel School’ in Chicago during this period. Admissions to the Electronics Training Program — an exclusive, highly classified military training program for which the radio material school served as hub — were approved on the basis of a rigorous classification and aptitude examination called the Eddy Test.
The fact that he passed the Eddy Test would also seem to suggest that Kane, despite receiving a meager formal education, had a fairly advanced understanding of mathematics and electronic componentry.
Many people have asked me to have this solution reviewed by cipher experts. So I did. It took a little bit of time, but I now have their feedback, which I wanted to share with you.
First, the cipher experts I contacted are mainly cipher researchers, working either for the government, or in education. All the contacts I have been in touch with have PhDs in cryptography. While they cannot validate 100% the solution due to the complex nature of the codes, they find it plausible.
Below some quotes:
it seems relatively probable to me, and articulated with the previous cryptograms, which is a good thing
I do not see it as a forced approach to find a solution at all costs
your solutions shed interesting light and can help progress towards the solution of the puzzle
a plausible and interesting interpretation of z13 and z32, which is certainly worth investigating, no longer from a cryptographic point of view, but from the point of view of the overall investigation
Whether in real life, Youtube, Reddit or in this forum, people have been asking "what do the Zodiac cipher experts think of these solutions ?". I hope they can also share with us their toughts.
Hello Fayzr,
It would be great to put some names with the quotes and their respective titles / jobs 
Hello themikado90,
It would be great to put some names with the quotes and their respective titles / jobs
They are research scientists in different organizations. One of them being the National Institute for Research in Digital Science and Technology ( https://inria.fr/en ).
But sorry I can’t share their personal info publicly without their consent.
I shared all my work in the previous posts because I think there are enough zodiac cipher experts around here who can easily confirm or contradict their conclusions.
I think the steps that you come up with it are interesting and very well thought out. However, there are a lot of steps and assumptions involved and in certain places you manipulate the cipher; for instance when setting the parameters for the Trifid (would you have set different parameters a completely different result would have come out). I think the danger in introducing so many steps is this: you can deduct many different "results" from the ciphers. Also, when looking at the solution for the Z340 the steps are actually quite straight forward and the results were clear. I think with such a small cipher the result should have also been ‘KAYE", not ‘KAYR’, it’s acceptable in larger cipher that are otherwise consistent and where the mistakes can be explained due to, say, skipping a symbol in the large cypher text.
Also, you state the following "Thus, we obtain a sequence of figures that is surprising by its lack of diversity: 1, 4, 5 and only one 8". This is not surprising at all because there is a lack of diversity in the very letters that you have derived those numbers for. Again, great work for diving in so deep but personally I think there are too many steps and assumptions to this proposed solution and is the result not clear enough (KAYR instead of KAYE) for this solution to be correct.
However, it would be interesting to see what more trained cryptologists than myself on this forum have to say about these proposed solutions.I think quotes without putting any names to them are a bit worthless, as for all we know you could’ve typed those things yourself (not saying that you did by the way).
Hello themikado90 and thanks for the feedback.
First, Z13 uses indeed multiple steps, but they are not totally arbitrary: the 2 major ones are actually the same as the ones used for the Z32.
Then, not any random number sequence can be eligible to Trifid deciphering (you need only 3 symbols and a length which is a multiple of 3). After the 3 first steps, the probability to have a sequence eligible to Trifid deciphering "by chance" was about 1/400.
Indeed the results of Trifid deciphering can give various results depending on:
– The base 3 alphabet encoding convention. In our case, the result obtained uses the conventional encoding (A = XXX, B = XXY … Z = ZZY), it has not been "forced"
– The association between the numbers 1, 3 and 4 of the code and the letters X, Y Z. 6 combinations are possible, and they give the following results:
3=X,1=Y,4=Z UAMW
3=X,4=Y,1=Z KAYR
1=X,3=Y,4=Z XNBS
4=X,3=Y,1=Z DNZI
4=X,1=Y,3=Z G OE
1=X,4=Y,3=Z Q CJ
What were the ods that one of this 6 results, not only looked a lot like a Zodiac case suspect name, but a suspect which leaved in the area found in the other cipher, using the same two first substitutions ? (I don’t know 
but I would say very low)
Finally, a word about KAYR vs KAYE: as I mentioned in the 1st post, it could be the result of a mistake. Or, it could just not be a mistake, but "KAY" + a filler ("R"). KAY is not just "like" KAYE, it IS actually one of Lawrence Kane aliases (Larry Kay).
However, it would be interesting to see what more trained cryptologists than myself on this forum have to say about these proposed solutions.I think quotes without putting any names to them are a bit worthless, as for all we know you could’ve typed those things yourself (not saying that you did by the way).
I agree ! This is why I’m sharing, and I appreciate you take time to look at it.
Hi Fayzr,
Thanks for your reply.
I never said the steps were arbitrary (but I will get back to this point later), I am saying that because you have introduced so many steps you are somewhat forcing certain results. I do indeed know that for Trifids you need 3 symbols and a length which is a multiple of 3; however, you have forced this in the cipher by introducing what you seem to refer to as a non-return-to-zero, but isn’t, an NRZ is a method of encoding used for asynchronous and slow speed synchronous transmission interfaces where the binary low and high states are represented by the numbers 1 and 0 and are transmitted by specific and constant DC. I don’t exactly know what you are referring to in this context.
You are right in saying there are 6 different options within the different configurations of the Trifid; one of them matches the first 3 letters of a Zodiac suspect, but only after:
– applying the Z340 key
– converting letters into numbers corresponding to their alphabetical ranking number in the alphabet
– replacing the remaining unknown symbols with their position in the Zodiac dial
– create a new number sequence by calculating the respective absolute gap between each number
– applying a Trifid with your favoured configuration (X – 3, Y – 4, Z – 1)
and only then can you come to the result KAYR, statistically not very significant considering how many steps you have made to get there. To get back to the point of arbitrary, most of them are arbitrary to a great degree (except for the applying of the Z340 key). I could come up with other manipulations of those numbers and add many layers and potentially get some interesting results also.
You introduce a similar level of randomness in your proposed solution of the Z32 when you select the numbers that you think indicate the geomagnetic coordinates; why those numbers? Number which only take on relevance when, in fact, you consider Larry Kane as being Zodiac and Donna Lass a Zodiac crime (both have not been proven) and out of that context those locations are not relevant to the Zodiac case at all.
I have to say I really like your creative and "out of the box" approach!
Hello themikado90
Thanks, all interresting questions.
To answer your question regarding the NRZI (not to be confused with NRZ), there are actually multiple variants of an RZ protocole:
Now to explain the NRZI in the context of the Z13, I made the following chart:
I hope this helps clarify the topic.
One final word on NRZI. NRZI is used with binary encoding. Trifid alphabet is just like a binary encoding in electronics. So I think the fact that the code uses those two operations together makes somewhat sens if we consider them equivalent to an electronics encoding (one could add on top of that the electronics training background of the suspect).
Therefore the solution to Z13 could be viewed as:
– Z340 (like for Z32)
– Alpha to digits (like for Z32)
– Zodiac dial
– Electronics encoding
Regarding Z32, although in my post I present it secondly, it’s actually the first code I worked on. Believe me or not, I didn’t know much about Kane, and like many people I was thinking that ALA was a very compelling suspect…
You introduce a similar level of randomness in your proposed solution of the Z32 when you select the numbers that you think indicate the geomagnetic coordinates; why those numbers?
So why those numbers ? First, all the clues indicated geomagnetic coordinates. And secondly, I assumed that those coordinates pointed a location in Northern California (not much arbitrary given the confirmed crimes locations). So there had to be a sequence of coordinates in the code, close to 44._ _ _ , 60. _ _ _ (+/- 3 degrees, Norther California), and there were two*:
The first one points on a location in the mountains (around Sonora Junction in Eastern Sierra), the second on South Lake Tahoe. There is a link between the Zodiac case and Lake Tahoe due to the Pines Card (wether authenticated or not).
Now what makes that location even more plausible is that the rest of the code forms the words LABOR DAY FIND _________ NORT _______ WEST, which are meaningful in the context of the letter.
I have to say I really like your creative and "out of the box" approach!
Thank you very much, and I appreciate your challenge. I am aware this is not pure cryptography, and this is also why the research scientists could not validate the solution from a mathematical perspective. But they tend to think that it is plausible and it deserves attention from the investigators to be studied further. Don’t you think so?
*if we exclude the sequence from the bottom right to left which we already discussed in another thread
Hi
Just sharing interesting observation from a Youtube viewer on the Z13 ( https://youtu.be/_OSEseQdUqc in the comments section):
Regarding the "mistake" at the end, the Aries character is translated into 1, which gives the 4 after the distance with the next digit has been computed.
The thing is the Aries sign is upside down in the original text, and slightly slanted. If you consider that a rotation has been applied to the Aries sign, and map that rotation to the zodiac circle, you end up with a 6 instead of a 1. After the distance calculation and the trifid alphabet, you end up with 111 for the last letter, which is the _ letter and would solve the inconsistency.I don’t know maybe it’s just too far fetched, but it could explain the inconsistency with the last letter.
I find it very interresting. However, if you do so, you end-up with 112 for the 3rd letter, and no longer a sequence we can decipher with trifid alphabet. This "side effects" introduced by the "distance calculation" explains why this cipher is likely to have errors, even if it’s too short.
It yet again points to a different way of interpreting the cipher. I am still not convinced this solution is correct. However, if you feel confident about it maybe reach out to David Oranchak and team to see if they can put you in touch with the FBI cryptology unit?
It yet again points to a different way of interpreting the cipher. I am still not convinced this solution is correct. However, if you feel confident about it maybe reach out to David Oranchak and team to see if they can put you in touch with the FBI cryptology unit?
I’m assuming that they already have done as they are claiming that both are solved.???
Just a note on decimal degrees coordinates, 3 decimal degrees is accurate with in a 111 meter or 364 foot radius. So the position on the map displayed on page one should be considered in this context.
That’s a level of accuracy not readily available in 1970’s (3 decimals), unless you have a giant waypoint like Mt Diablo.
Hi
This post to clarify my point on the connection between the ciphers:
The 3 ciphers, Z340, Z32 and Z13 seem to share common ciphering techniques, and their results are consistent between them.
Connections in their resolution
The ciphers use techniques borrowed from each other:
– Z340, Z32 and Z13 all use the same substitution key
– Z32 and Z13 use the same A1Z26 variant to convert letters to numbers
The relative constancy in the utilization of those ciphering technique would have been unlikely if we had looked to force the solution. And this is due to one simple point: the codes are from the same author.
Connections in their results
Not only do the Z13 and Z32 have some common ciphering techniques, but their results are also consistent. Larry Kay lived close to South Lake Tahoe, which is the place found in the Z32 cipher.
On top of that, I also propose a solution to the Pines Card, which also points near South Lake Tahoe. Speculation has been on-going for years on its link with the abduction of Donna Lass, who disapeared on… Labor Day (a result of Z32).
