Zodiackiller.com Message Board: Ciphers: Welcome to Zodiac Cipher!

Thanks for the Cipher section, Tom. I'm sure we'll all have a lot of fun with it. I'll give a brief overview of the subject, just to get the ball rolling.

There were four ciphers sent by the Zodiac killer, only one of which has been partially solved. The ciphers were reviewed by government agencies with no firm results, and I believe the prevailing opinion of law enforcement to be that the remaining ciphers are hoaxes. (This is not an opinion I share.)

The text of the first cipher can be summed up as a rambling list of reasons Zodiac killed, along with some esoteric religious reasoning of why he would continue to kill.

This cipher was broken very quickly by G. and W. Harden, a couple of average citizens, just like you and me. This probably angered Zodiac, which is why the remaining ciphers are so difficult.

The best security for any cipher, no matter how complex, is its brevity of use. Zodiac gets high points for brevity.

The first cipher was 408 characters long, and all but the last 18 characters has been read.

The second cipher fell to 340 characters in length with extra symbols added and no subject mentioned. The last line of this cipher also demonstrates "random" statistics when compared to the rest of the cipher, and includes the word "Zodaik" (with a Greek delta for the d).

The third cipher was a mere 13 characters long, preceded by the words "My name is -". Presumably this cipher contains Zodiac's name. Graysmith notes in his book that a cryptologist from the American Cryptogram Association challenged Zodiac to give his name in cipher, and boasted that it would be broken. I can't find any references to the exact date that program aired, but it presumably aired before Zodiac said "My name is-". Z may well have risen to the radio challenge and given his actual name.

The fourth cipher was a whopping 32 characters long by comparison, and supposedly contained the location of a bomb which was set to destroy a school bus full of children. A Philips 66 map was sent along with the cipher. The map and the cipher can be viewed here on Tom's site. A later Zodiac letter indicated that this cipher pertained to "radians and inches along radians." If this cipher contains legible text, the bulk of it will most probably be numbers written out.

I'm very willing to discuss these ciphers in great detail, and I'm slowly updating a page of statistics that can be used for reference on each of the ciphers.

I will readily discuss any idea on cipher meaning or attempts at decryption of these ciphers, and I'm aware that just because I take a more scientific approach to the problem, one of you may have an insight that solves the problem once and for all. A lot of good cryptology is following a hunch in the right direction.

On the reverse side, I don't mind examining claims and presenting my findings on why that claim may or may not be valid. Any quid pro quo exchange of ideas has its practical purpose. I might be able to save you some time from going in the wrong direction, and you may be able to save me some time from going in the wrong direction.

Those of you who know me from past posts know that I have no favorite suspect and I frankly don't think we'll ever know for sure who the Zodiac was, but I do know that the only hard evidence in the case that has not been thoroughly examined and reexamined is the cipher evidence.

If there is a clue that will lead to the identification of the killer, it most likely resides in the cipher evidence, and to me that makes this section of Tom's board the most important section of all.

Good Hunting!!!

Glen,

Been following your posts for quite some time. I agree with the last part of your statement in particular, and that's why I think you could really be on to something. I find your explanations to be very interesting and do like to follow along. Even though I am licensed by the FCC with a 2nd class radiotelegraph license and can copy Morse at 25+ wpm ( it's a language ), I do not have the type of brain to actually DO this type of math/crypto work... so I'll leave that up to you. However, I'm rather curious as to what you actually intend to do with this. Are you going to make an attempt at solving these, or just discuss the theory? Do you have a timeline and a plan? I'm sure you do... just wondering what your game plan is.

All very good questions, and you do have the brain to do crypto work. All you need is a pencil and a piece of paper!

Presently I've been working on the 340-cipher, as time permits. It was necessary to establish a list of Zodiac letters to build a profile of Z language. This list generates statistics on character usage, word usage, and Z phraseology that can be useful. We found that while Z used the word THE as the most common word (we all do), his second most common word was the word "I"! That in itself has implications.

The next step was to determine whether the 340-cipher possibly contained meaningful text, or was it just a random fake sent by a hoaxter? Character placement and frequency are in line with the 408-cipher, there is a correction, and distant character spacing is in line with normal language. This leads me to believe that there is most probably intelligent information contained in this cipher. The single correction made on the page almost cinches it, making it worthwhile to continue the investigation.

The next step is a lengthy one, but it will save time later. It becomes necessary to determine just how the information is enciphered. Did Z used his old system with a twist, or did he do something entirely different? Is the system used forward, backward, up, down, diagonal, or is the information anagrammed in the body of the cipher?

I've tested for up, down, forward, backward, and diagonal, but the test for anagramming doesn't really exist, so I'm having to invent something that can give me meaningful insight into this particular aspect.

We are fortunate in this instance that we have an example of Z's cipher in the 408-cipher. What I've decided to do is to anagram Z's message from the 408-cipher using the three most common anagramming techniques, and then re-encipher the resulting text with his old system. This should generate some useful statistics on anagramming that can be used to compare with the 340-cipher.

Once all tests are completed, a rational estimate of methodology can be deduced, which will give direction to decipherment attempts. It's all pretty straight forward stuff.

I'm also presently compiling a list of possible equivalents for characters that can be used as tryouts on the cipher. By the process of logical elimination we can get the system down to a workable level and even have several interested people at a time working on one of the possible aspects of the cipher. Perhaps we can even get someone to write a program that can automate most of the paperwork for us.

While the brevity of the cipher works against us, we can certainly improve our chances by making some intelligent and informed observations.

The timeline for the project is quite another matter. Time for me is precious few minutes to work on projects presently, but I hope my schedule will improve. As I said before, the case is 30 years old, so I don't feel a great sense of urgency, but like you I wish to see this thing solved sometime soon!

I'm sure you own a pencil, so here's the piece of paper, located at:

http://www.geocities.com/cryptography_2000/z-340.html

Print this cipher out (several copies) and start taking some of your best guesses! As a starting point, a language run I did on the cipher last night came up with 18 possibles for the very beginning of the cipher. The two most possible beginnings are "I will,,," or "I kill..." for the first five characters of the cipher. Choose one or both and take your best shot at trying to figure out the rest of the cipher. If you assume a character is "I", fill in the letter "I" for all other occurrences of the character in the cipher body, and see if any other words come to mind. It's really a process of trial and error, based on intelligent assumptions.

An addendum on starting points -
please reference the below page to follow:

http://www.geocities.com/cryptography_2000/z-340.html

Characters 78 through 82, (O filled in, FP+P) is also a good tryout point. Language runs indicate that it's most probable equivalent is either "THERE" or "THESE".

This gives us the possibility of either an R or an S for the all important character "+".

(Don't forget that if the + character is an R, the word "WHERE" also becomes a third possible.)

Not sure what you mean by "anagraming"...

Anagramming is one form of character transposition, best demonstrated by the most common usage of the technique of repositioning the characters in each word:

The quick brown fox jumped over the fence.

het iuqkc rwnbo xfo updejm orev hte neecf.

Now we would remove all punctuation and run the characters together thus before replacing them with symbols:

hetiuqkcrwnboxfoupdejmorevhteneecf

Graysmith's solution is based on anagramming, but he fails to present any system by which the technique was carried out. Without a definite system of encryption, one can never be sure that the information extracted is correct, primarily because an astronomical amount of sentences can be constructed from this string, along with the right one, of course. A case in point are all the varied solutions sent to the newspapers from the last 18 characters of the 340-cipher.

I haven't found any evidence of anagramming in the 340-cipher, but since the issue has arisen in Graysmith's decipherment, it becomes necessary to run tests anyway so that when I say there isn't any anagramming, I have facts and statistics readily available to support my statement.

One correction, there is a simple method of testing for anagramming, though not always conclusive, and that is looking for most common word lengths, such as the length of the word "the" and seeing if there are any groups of three whose symbols appear in different positions.

Correction in the last post:

A case in point are all the varied solutions sent to the newspapers from the last 18 characters of the 408-cipher (3-part cipher).

For Glen Claston:
I don't know if Glen remembers my email to him when he came back on the Board after being away for a couple of months, but I told him that he held the key to solving this Z senario if it is ever to be solved. Maybe the law wouldn't agree but I'd sure like to see what he comes up with when(I KNOW HE WILL) he solves the ciphes
Bruce D..

Glen what is Graysmith's solution to the cipher? I have not seen it before.

Earlier I reported "interesting anomalies" and "peculiarities" existing in the 340-cipher. These are weaknesses that provide the best possible exploitation of the underlying system, and a list of them can be found at the following location for printout:

http://www.geocities.com/cryptography_2000/sequences.html

While it's more fun to attack the cipher as a whole, this list provides the most likely road into the true meaning of the cipher. Anyone who finds the proper letter correlations to the sequences posted will have essentially solved the cipher.

(the character numbers refer to character placement within the cipher, which can be referenced at
http://www.geocities.com/cryptography_2000/z-340.html )

Good Hunting!

For Bruce D.,

Thanks for the undeserved words, Bruce, and I did review your previous e-mail just for reference. (I'm pretty anal about saving things.)

I hope you notice that since I've only had time to do the boring statistical runs on this cipher and not much time to sit down with pencil and paper, I'm posting my findings in non-technical posts so whoever's interested can pick up a pencil and perhaps be the one to solve a Zodiac Cipher!

Despite everything I've looked at, there is no indication that this cipher differs much in structure from Z's original 3-part cipher, which is pretty good news. While it's obvious he did a much better job at frequency suppression and error checking, he still made mistakes.

The only check I've done that was inconclusive is whether or not this cipher is written left to right or right to left, since both directions generate the same stats. Other than that one little problem I haven't yet developed a good test for, everything else brings the cipher down to a level that just about anyone can work on and get lucky with.

As long as we keep in mind that it may be written right to left, we're down to identifying and exploiting the weaknesses and solving this thing.

We've probably got a couple of Hardens out there that have some time and like puzzles, so let's get started. It's 30 years overdue, don't you think?

If someone could get the NSA to toss the 340 on one of their Cray supers The code would be broken in min, if it is really a code and not just 340 symbols that mean nothing

Michael

If one believes everything Graysmith says, the 340-cipher was considered too short to produce meaningful statistics through computer runs. The FOIA files show that computer runs were made on the 340-cipher by the Army Security Agency (a onetime military arm of the NSA), and the Naval Academy, (also containing a military arm of the NSA). While their runs did not break the cipher, they did provide feedback on possible equivalents to certain cipher characters and groups.

By proxy, the NSA did feed this into their computers. So why wasn't it broken in minutes? Because machines are really good at breaking cipher written in machine language or generated by other machines, but machines have no advantage with cipher written by human beings because humans don't think like machines!

Until IBM's "Big Blue" that is...

I agree with kevin, Computers are far more powerful and complex now that they were even a few years ago. And do you really think that you can break a code with pencil and paper and the NSA super computers cant? In just the past few years they have built computers that can "think"

Michael

But can they think in an abstract manner like humans can? It's intuition or a hunch that often solves ciphers, and people have been plugging away at Z's other three ciphers for 30 years to no avail (unless you count Graysmith's solution to the 340-symbol cipher, and Penn's bizarre solutions as well). That's not to say that computers can't, because they probably can given enough time. But if the 340-symbol cipher is in fact a substitution-transposition cipher, I have to wonder how many other halfway coherent solutions can be derived from it?

The zodiac was an ego-maniac who craved attention. He wanted the public to believe he was more intelligent then the police force, probably because they had rejected him or mistreated him in some way. It probably made him furious that the first cipher was solved quickly.
What better way to look like a genius, then to next send unsolvable ciphers.Unsolvable because there is no solution. That way police and people like us would puzzle over them for decades to come. Is not that a possibility

Do I think a human can solve a cipher that a super-computer can't? No offense to super-computers, but when it comes to a cipher only 340 characters long created by a madman, the human mind is a vastly superior computing tool.

I also see Scott restating the "hoax" theory, to which I once again submit that in order for Z to have created a hoax of this caliber, he would have to have indeed been the genius he wanted everyone to think he was. That would force us to reevaluate our perception that he was an egomaniac, because if he was that good, every bit of his ego was well placed and well deserved!

I know nothing about ciphers. Its way over my head.I mean no offense to glen because you obviously have spent much time trying to decode them, which I think is very admirable. Puzzles are fun to try to solve. They are a challenge. Here it's a direct challenge from a serial killer. "You think your smarter then me, solve this"."Catch me." Remember though this challenge comes from a man with a very deranged mind. We know in his letter's he has misrepresented himself several times and exaggerated to great affect to make his crimes seem more grandiose. I would not use the word "hoax" to describe the zodiac unsolved ciphers. I just think they might be meant to mislead. To through the police "off the scent" so to speak.

To throw the police "off the scent"? I would have to say this belief may be justified with the "my name is" cipher and the "where's the bomb" cipher, as these would indeed have the desired effect. I don't believe this to be the case with the 340-cipher.

The 340-cipher came with no subject and offered no expectations when it was cracked, even though the first 3-part cipher offered expectations of the killer's identity. This cipher offered the police no scent at all, not even a boast.

The last two may yet prove to be hoaxes, they certainly have all the earmarks. But for all my previously stated reasons, as well as reasoning that goes beyond the obvious, I stand firm in my belief that the 340 cipher is no hoax.

I agree glen the 340 cipher was not a "hoax". It contained an actual message but in his letter Zodiac claimed that if it was solved it would contain his identity. It did not. In fact it could be argued that it contained no useful informations except to better understand Zodiac's motives. I believe the ciphers served two purposes to the Zodiac: 1. To waste police time, remember every homicide detective working on decoding the cipher was not out running down leads. 2. To broadcast to the world Zodiac intelligence. The two unsolved ciphers might have solutions. That they contain useful info that might unmask Zodiac is doubtful.

Determining whether the ciphers contain any new clues or information is precisely the purpose of this research, and we won't know either way until the ciphers have been solved.

We can only hope that Z's preoccupation with his own name led him to do something CRAZY (heh heh), like leave a clue to his identity. There is some indication in his letters that he was at least worried he had let something slip. Let's just hope so.

Glen,

When I tried to open your page, the second half of the cipher did not appear.

I just tried it and got both halves, but I've had problems in the past. It has to do with me using FrontPage extensions and file directories on Geocities. If you still have problems, maybe I can get Tom to post the two images on his site for easier access.

My master's thesis was titled, "The Complete Automated Cryptanalysis of Sequential Homophonic Ciphers". I got interested in the Zodiac ciphers at that time and am willing to dig out all of my research (finished and unfinished) for anyone who would want it. I have information regarding the following:

1) Z1 (the solved "long" Zodiac cipher), was solved after being published in the newspapers. It is a "random" homophonic cipher, but the Zodiac began it as a "sequential" homophonic cipher.

2) Z2 (the unsolved "long" Zodiac cipher) is not a sequential homophonic cipher. It could involve transposition.

3) William Friedman (the great) outlines the many different types of transposition ciphers. I stopped researching Z2 before writing a program to transpose Z2 by these methods. I believe this is the best way to try to solve it if no one has done this before.

4) Z2 has a "correction" that seems to indicate it does contain a message.

5) The ending of Z2, which contains Zodiac's name in ciphertext, is sure to be "padding", such as is the end of Z1 seems to be. The end of Z1 is most probably padding even though hundreds of people have proposed anagrammed solutions for it.

Some of the above was published under the same title in Cryptologia back in '93 or so. I'll have to give you the exact information or reprints if you want it (all of my six papers were inadvertently omitted from the multiyear
index).

John C. King
jkingqm@rectec.net

John, I'm interested in an elaboration of your post. I'd also be interested in the date(s) of the Cryptologia article(s): are they online?

--Jake
http://members.aol.com/Jakewark/index.html
"This is the Zodiac Speaking..."

I'm with Jake on this , let's check it out... J

John,

Thanks for the heads up. I have most back issues of cryptologia, and I probably read your papers at one time. I'll look them up again!

I look forward to any elaboration you might be willing to give on your studies of the 340 cipher. It has some very interesting features that clearly involve language.

Their are two papers, both touch on the Zodiac ciphers.

King, John C & Bahler. 1993. A Framework for the Study of Homophonic Ciphers in Classical Encryption and Genetic System. "Cryptologia" 17(1): 45-54.

King, John C. & Bahler. 1993. An Algorithmic Solution of Sequential Homophonic Ciphers. "Cryptologia" 17(2): 148-165.

John C. King
jkingqm@rectec.net

Since John King brought up the possibility of transposition in the 340-cipher, I’ll present some notes on the subject for general review. Transposition is one of the possible aspects of the 340-cipher that has drawn the most attention, and definitely something I’ve been concerned with in the course of this investigation.

We already know that Zodiac used two types of frequency suppression – multiple characters for high frequency characters, and intentional misspelling of words. Anagramming/transposition would be another form of frequency suppression, and most certainly must be looked at and tested for because the method of solution would then be quite different.

I’ve run several different sets looking for transposition, and all would appear to indicate that transposition is not present. Language structure appears to be intact and contiguously written in the standard left-to-right manner.

Any consideration of transposition must take into account the several methods that could have been employed, but each of these methods has the same desired effect-the disruption of word structure. A comparison of the ciphertext of both the 3-part and 340-ciphers does not demonstrate any significant shift between the two ciphers in digraph and trigraph transposition or distribution.

A common form of transposition/anagramming is the transposition of each character in a word, performed on each word in turn. In this simple method, we must consider the total number of ways the letters in a word can be transposed. Since we know that Z’s average word length is between 3 and 4 words, this means that many of his words will fall in this grouping. Below are the 6 possibles for a three letter word and the 24 possibles for a 4 letter word.

3 letters – abc, acb, bca, bac, cab, cba


4 letters – abcd, abdc, acbd, acdb, adbc, adcb, bacd, badc, bcda, bcad, bdac, bdca, cabd, cadb, cbda, cbad, cdab, cdba, dabc, dacb, dbca, dbac, dcab, dcba.

If we consider the most common word "the" as our sample, we find expected occurrences of digraphs for "the" would be th-2 te-2 he-2 ht-2 et-2 eh-2, or otherwise stated as an equal number of digraphs present for each transposition of the word "the" in a homophonic substitution cipher. As you read on, you'll see this does not present itself in the 340 cipher.

The 340-cipher contains 21 recurring digraphs, making up 46 characters, or around 13.5% of the total character count. While is just half of the 26% reflected in the 3-part cipher, the 340-cipher has more characters and is shorter than the 3-part cipher. Transposition would be expected to increase the number of digraphs possible in the 340-cipher, which contains 314 unique digraphs. This is a factor of .923, which admittedly seems high until we look at the 3-part cipher, which has no transposition present but still maintains an extremely high digraph factor of .855, not out of bounds with observations of the 340-cipher. Had Zodiac not deviated from his initial system in the 3-part cipher, the ratio would have been even higher.

Using the 3-part cipher as a model for comparison, entropy levels of each of the two ciphers can be compared. Single word transposition can be carried out on the 3-part cipher and entropy compared to the 340-cipher. Methods beyond single-word transposition would yield even higher entropy than this common method of character transposition, becoming much more apparent as the transposition algorithm becomes more complex.

With that in mind for further tests, a look at the progression of digraphs and trigraphs might give some clues as to the presence of transposition. No matter what the plaintext value of the character, it would be transposed to many different positions if transposition were present. Digraph statistics are similar for all characters, so the best illustration would be the high volume character “+”, which appears 24 times in the 340 cipher.

Since I can’t use the Zodiac font on the message board, my character references pertain to my computerized version of the cipher, found at:

http://www.geocities.com/cryptography_2000/340.txt

-The “+” character -

+ doubles 3 times, preceeds 18 unique characters, and preceeds P and R twice each. + follows P once, but never follows R, even though R is followed by 8 unique characters.

Of the 18 characters preceeded by +, B is the most interesting. B is followed by 10 unique characters, the c and y characters twice each, but is never followed by +.

FB occurs 3 times, and the BF combination appears only once, similar to the TE or TH digraphs in the English language. FB or BF never coincide with +.

Of each character preceded by the + character:

F is followed by 6 unique characters, but is never followed by +.
I is followed by 9 unique characters, but is never followed by +.
K is followed by 7 unique characters, but is never followed by +.
L is preceded and followed by + one time each.
N is followed by 4 unique characters, but is never followed by +.
O is preceded and followed by + one time each.
P is preceded by + twice, and followed by + once.
R is preceded by + twice, but never followed by +.
U is preceded and followed by + one time each.
Z is followed by 4 unique characters, but is never followed by +.
^ is followed by 6 unique characters, but is never followed by +.
a is followed by 4 unique characters, but is never followed by +.
b is preceded and followed by + one time each.
u (the zodiac symbol) is followed by 9 unique characters, but is followed only once by the +.
y is followed by 5 unique characters, but is never followed by +.

On transposition of the digraphs that occur more than once:

FB –3 Bf -1
Gh –3 hG -0
M+ -3 +M -0
+P –2 P+ -1
+R –2 R+ -0
0F –2 F0 -0
0t –2 t0 -0
3R –2 R3 –0
6O –2 O6 –0
Bc –2 cB -0
By –2 yB –1
Fl –2 lF -0
I0 –2 OI -0
Np –2 pN -0
O+ -2 +O -1
Op –2 pO -1
UZ –2 ZU -0
P2 –2 2P -0
Z6 –2 6Z -0
ab –2 ba -0

On transposition of the two trigraphs that occur more than once:

I0F –2
IF0 -0
FI0 -0
F0I -0
0FI -0
0IF –0

FBc –2
FcB –0
BcF –0
BFc –0
cBF –0
cFB –0

Another check for transposition is to check character displacement at distances of two, three, or four apart. Results yield about the same as digraphs, but with an interesting side note. Characters tend to “cluster” in regular language, and since such a short cipher would not be expected to have a wide variance of topics in its body, this means that some words or forms of the same word should be repeated. While there are a few more less noticeable sequences, I’ve already provided a partial list of some of these at:

http://www.geocities.com/cryptography_2000/sequences.html

These sequences generally appear to be directional, much like language, and there does appear to be too many of them to contemplate the presence of transposition.

Any insight on this, John?

Before getting into word transposition I would take a look at _all_ of the transpositions described by Friedman. There are many many types.

In order to see if any of these transpositions of Z2, or Z2 itself, have the expected number of digraphs, etc., one must know what to expect. One way to do this is to encrypt several plaintexts of length N=340 as random homophonic ciphers with the same multiplicity level and get an average count of the language statistics.

I may have done the latter. See my first paper on how to do it. I would have to look at my old research stashed in a closet to see if I did it for a cipher of length N=340. I might could even see if I could find C code on old 5 1/4" disks I have. I could also dig out a copy of the many types of transpositions from Friedman. Let me know if you want any of this.

I can also try to find my version of Z2 on disk where it is transcribed into numerical ciphertext symbols. Some of the original ciphertext symbols are a little ambiguous, for example, some characters look like either circles completely filled in or circles halfway filled in. Hard to tell with that felt-tip marker of Zodiac's. The SFPD sent me a copy of Z2 but it is not as good as a copy someone had sent me years before.

In a nutshell, rule out all of the simple explanations first.

John C. King
jkinqm@rectec.net

The transcription I posted, along with the matching Zodiac font

transcription: http://www.geocities.com/cryptography_2000/340.txt

font: http://www.geocities.com/cryptography_2000/zodiac.zip

are the best representations I've been able to come up with after examining everything in print and on the internet. I beleive it's pretty accurate, with the possible exception of one character that may possibly be two characters, but the copies are too hard to read to be absolutely sure.

As far as starting from simple and working upward, this is also my philosophy.

My language statistics and other comparisons are drawn from a database of all the words and phrases Zodiac himself wrote. Since he wasn't any William Shakespeare, it's a better language sample than random passages from some other source and is more likely to provide reliable data than say, a cookbook.

Using the "simple first" approach, we must consider that a homophonic cipher is very old and not all that sophisticated (over 600 years old). Being a classical cipher in the truest sense, it makes me consider that any changes Z would have made would also draw on information obtained from a book on classical cryptography. I've examined these first and looked for evidence of the simple forms. I am familiar with Friedman's work on the subject, as was probably every government cryptanalyst that examined this cipher, and I (possibly incorrectly) reached the same conclusion they did - that the length of this cipher falls below the threshold of unambiguous solution by modern cryptanalytic means. I've fallen back on tried-and-true (albeit more time consuming) classical methods of examination to draw meaning from this passage.

Just a FYI for consideration - During my examination something came to light which I still haven't made sense of, so I've kept it in the back of my mind until I can quantify the effect - Z "divided" the cipher at the 10th line by using a dash character at the beginning and end of the line. These could simply be artifacts of the cipher itself, but when I consider that digraph and separated pairs of characters tend to reverse themselves in the second half of the cipher, I'm inclined to watch for some sort of system reversal in the second half. I've yet to do the counts necessary to back up this observation, but I'll get to it pretty soon.

In the meantime I'm rereading your papers. Doesn't a 340 character sample seem a bit small to gain more than just general information from this type of analysis? Even though the cipher falls above the "solveable" threshhold of 189 to 270 characters as observed by Shannon for this type of cipher, it falls well below the threshold of unambiguous solution by purely mathematical/automated means.

That is not to say that extremely useful information cannot be identified and exploited on ciphers this short. Monalphabetics have been solved at below their threshold of 27 characters by careful observation of frequency and character placement, and Z's 3-part cipher fell easily because of his "LL" redundancy in both language and cipher symbol. Good analysis can reveal a lot about even a short section of cipher.

I have your papers in hand, and I for one am interested in anything you have to offer in the line of research or observations that may help in solving this cipher.

Glen ,
I follow your writings everyday and I hope in the long run some of it absorbs. I wanted to say
your doing one heck of a good job at trying to figure these ciphers out- what true dedication to something so complex . Most pleased to see John King has joined the group & crossing my fingers if you work as a pair we will see solutions... Can you recommend a good book as a starting point for me (basic) on ciphers & cyrptography ... I'd like to help but I must understand the task first ...
Thanks , J
Thanks , J

Thanks J, and I too look forward to any insight John King wishes to share with us.

The field I dabble in for liesure is generally described as "classical cryptography", a study of older systems (human derived systems) of cryptography. I only mention this because most books published today are directed toward computer encryption algorithms and algorithms designed to detect and crack computer encryption algorithms. As John King mentioned, William Friedman and others defined the mathematics of cryptography during the first half of this century and set the stage for the computer generation of cryptography.

I'm a big fan of William Friedman and others involved in this process, and fully recommend that anyone interested in cryptography read "The Codebreakers", by David Kahn and available at Amazon.com. Kahn's book gives a very good history and overview of the field of cryptography. Kahn also touches on some of the "classical" techniques that I employ.

Jan Van Der Lubbe has a book out called "Basic Methods of Cryptography", which I've reviewed and find acceptable. Amazon.com lists several others that I haven't reviewed and therefore cannot attest to the quality of their subject matter.

There are also some very good FAQs available on the internet on each of the types of ciphers we've discussed here, and also discussions of basic cryptanalytic techniques for each of these systems. I've yet to find a FAQ that tells anyone how to identify an unknown system however!

The American Cryptogram Association (ACA) publishes a list of books and periodicals for their members, some of which I own. There are also books published by members of the ACA that can be found in this list that describe basic techniques of decipherment for many cipher systems, along with textbook examples. I point out that in real life, I've never run into a "textbook" example of a particular cipher system, which makes this field so much fun.

One of the best sources of information on cryptography and deciphering techniques I can think of right now is a university library. I first researched certain types of systems in a university library which had books going back some 150 years on the subject. My advice would be to take the time to search through the stacks and find the books that best speak to you. If you find one you like, go out and buy it. I found one from 1906 and spent 2 1/2 years sending letters to booksellers before I ran across a copy - a deal at $75.00, some 15 years ago!

If you have a good understanding of mathematics and statistics, I highly recommend William Friedman's books and papers, which I believe are still available in reprint from Amazon.com or some other bookseller.

As to the task we're trying to accomplish here, I think I'll set out the basics in a separate thread.

Glen mentioned a couple of things, one being whether their is enough redundancy for an unambiguous automated solution. I can think of two automated methods. Probablistic relaxation works great for monoalphabetic substitution ciphers. See my later (1995?) paper in Cryptologia where I extended it to solve polyalphabetic substitution ciphers. Unfortunately I don't know of anyone who has extended it successfully to homophonic substitution such as Zodiac's. I know people have tried, particularly people working on the Beale treasure ciphers. I've talked with several but no one ever got too far with it, but the Beale Ciphers are much harder than Zodiac's.

Another automated method would be heuristic search techniques. These have also been tried by many people working on the Beale ciphers.

Glen is right in that the cipher is short enough to make automated cryptanalysis very difficult. However it should be long enough to be able to tell that a solution is "the" solution.

That is the fun part about using computer for automated cryptanalysis. You can get them to do the grunt work but they don't have the "insight" a human would, such as the solvers of Zodiac's first cipher where they figured, "This Zodiac guy is an egomaniac. He probably talks about himself in the cipher." Sure enough the message started out, "This is the Zodiac speaking."

Glen is also right that all the basic approaches have probably been tried. Dr. Carl Hammer told me about a meeting the NSA (National Security Agency had) had regarding the Zodiac's ciphers. They came to the conclusion that Z2 most likely did have some kind of message, that is, it most likely wasn't just random symbols written down by Zodiac to frustrate us all.

What I would really like to see is a psychological profile of the Zodiac and an idea of what me might expect to see in a solution of Z2. I was talking to Jake about John Douglas's books on criminal profiling. Has anyone seen anything like this on Zodiac. I'm sure Z2 does _not_ contain Zodiac's real name. He's way to smart for that. It probably contains something similar to Z1. Glen has a good idea of studying the language statistics of Zodia'c writing such as common words. Even though Zodiac went through the trouble of enciphering Z1, it had mistakes in it, perhaps both pre-encryption (spelling, grammar) and encryption. Z2 probably does also.

I think Z2 does have a message. Zodiac went though a lot of effort in both encrypting a message _and_ the physical act of writing down the odd ciphertext symbols in a neat grid. He probably proofread his cipher then made his correction after finishing it. After all that work in his messed up state of mind he probably wasn't going to rewite the entire thing. See Graysmith for some notes on his state of mind when writing his messages. He mentions possible drug use and, uh, autoerotic activities.

Glen, offline could you let me see all of the transpositions you've tried? Since Z2 is written in a block then each of the four corners could be a starting point for each transposition method. I'll dig out Friedman's outline on transpositions in the meantime (he was a great guy wasn't he?). If Friedman was alive he would have solved this one no doubt! :-) All of us put together just might do it.

I'm real sleepy and zoned out now, just enough to think, "Hmm. What would I do if I were the Zodiac encrypting this message." All we need is one little insight to try out to get a solution. It's probably simple. Trying out word transposition such as Glen is doing is certainly worth looking into. I have a really good set of trigram language statistics on disk "somewhere". In, yes another paper, 1992 or '93 Cryptogia I tell how to use an adjustment formula by Shannon to get trigram statistics where there are no word boundaries (spaces) such as in Zodiac's messages. Using these and altering them to skew a little bit towards Zodiac's writing style would be good for any attempt at automated cryptanalysis.

John C. King

For any email replies please use the following email address. I'm writing from someone else's computer: jkingqm@rectec.net

John,

As far as testing for any given transposition method, beyond Index of Coincidence, Chi-2 tests and entropy comparisons for Z plaintext and known ciphertext, I haven’t done anything major. (That's a sad statement - 6 months and I haven't even sharpened a pencil yet!)

Most of my work to date has been involved in trying to identify the type of cipher used. Any actual attempts at decipherment would be futile without a pretty clear understanding of what we’re dealing with. It’s been a few months since I ran these tests, but it’s simple enough to run the cipher through the programs again and provide you with the output for examination. I ruled out polyalphabeticity and keyed/sequential/progressive transposition on the basis of these tests (along with other circumstantial information.) If nothing peaks in the IoC test or the Chi-2 test, I can only consider that the passage is below the threshold and any specific testing for sequential and progressive systems of transposition on a passage this short would yield inconclusive data. Like you said though, the tests I’ve run have already been run by people with a lot more umpa’s in their band than I have, and they probably didn’t have your information at the time, so it’s worth a try.

Funny you should mention Probabilistic Relaxation, because I was just reading a section on that tonight in Cryptologia with homophonic substitution in mind. Strange coincidence. I might drop that idea, but it has its merits. Let’s not forget that monalphabetic substitution has an unambiguous solution threshold of 27, and that’s why the calculators all over the net solve these things with ease. There are also some very good calculators out there for Vigenere’ and other types of progressively keyed polyalphabetics and their variants. (I’m sure they are based on the principles outlined in your work.) Homophonics, even random systems, are really nothing more than multiple alphabets with a whole lot of nulls. I was considering your paper and how to factor out nulls based on frequency.

Beale Ciphers? I thought they were keyed to written text, such as the Declaration of Independence. I read a paper about a year ago from someone who went to great lengths to prove the remaining Beale Ciphers were hoaxes. We all know in cryptography that it is next to impossible to prove something a hoax without solving it first, but this guy (I can’t remember his name right now) certainly offered enough statistical evidence to make you think 1,457 times before trying to solve the remaining Beale Ciphers!

As far as starting at the four corners of the block to look for transposition, it has occurred to me. Two things throw me off that scent, but it should be tried nonetheless. The first is the fact that “Zodaik” appears in the last line, which signifies to me that the last line may be garbage. The second is the “division” of the text at line 10, and the fact that the two halves differ statistically.

I’ve stated many other reasons I’m not keen on transposition in this cipher, but that doesn’t mean it does not exist. If it were sequential perhaps, characters in line 1 and line 11 alternating, that could possibly still match some of the evidence I’ve been able to extract from this cipher. It will match some, but not all the evidence, that’s the problem.

I’m still stuck in the “Sequential Homophonic Cipher” mode for many reasons. Digraph counts and progression give clues, as well as the old “leader/follower” chart. There is some evidence of lower frequency characters grouping. The G, O, and R for instance group around the backward L and the Z character. Granted 340 characters is not a lot to expect to see many of these types of patterns, so the fact that I do see quite a few is surprising and still points toward a sequential homophonic cipher at the core. In the case of the G, O, and R, one or more may be different plaintext characters, but their relationship indicates that backward L and the Z character are identical in meaning.

My avenue of approach at this moment is to find out as much as I can about each character and eliminate as many possibilities as to their meaning as I can. Once I have a reduced set, I can work from that angle to postulate a much more informed attack.

I think your idea of testing for transposition is a good one, if you can come up with an automated scheme to test for all the various types. Many are clearly out of bounds because of the entropy they impart with their use versus the entropy present here, so we are considering much more mundane systems in this cipher than we would normally test for in, shall we say, more legitimate cipher.

As I stated previously, I doubt what we’ll come up with will be a textbook example of the system employed, so any computer model has to take into account the vast number of errors encountered in Zodiac’s first cipher before attempting to solve the puzzle. Many of the words may be so badly misspelled that they will more closely resemble a “soundex” dictionary than a real one.

On the subject of errors – with one or two exceptions, no properly used homophonic cipher can produce the groups of ++ and pp we have in this cipher. No homophonic cipher can produce strings such as 0T0M either. We also wouldn’t have two FBc and I0F groups using such high frequency characters (One of these groups is actually I0FBc)! These are either artifacts of transposition as YOU suspect, or artifacts of a “pseudo” random construction, which I suspect. If I am right, it’s no wonder this thing hasn’t fallen to a machine, because the only machine that can intuit the construction is a human brain. If you are right, the solution may be much easier, so I’m putting my money on you! :-)

-My opinion for what its worth: Zodiac’s house may look fine from a distance, but the walls are three bubbles short of a level and a pie slice short of a square-

In a letter to Dave Toschi,Dave Peterson wrote:"The source of Zodiac's cipher symbols appears to be the book, "A History of Secret Societies," by Arkon Daraul,[wonder if his parents would have liked him enough to give him a name like John!]1961,The Citadel Press,New York.As per enclosed, he[Z[ used identically ,the reverse F for the D, and the triangle for the I and the T for the O. Some 11 symbols from the book ,he simply switched to different letters of his cipher alphabet. And 13 of his symbols appear to be minor variations of the book's symbols (in his first 3 part cipher of August ,1969). In Zodiac's later cipher of Nov. 9, 1969, he added the symbols ,from the book ,of the dot and the dash,along with some other variations of the book's symbols. The above may indicate that Zodiac is not necessarily as informed in different fields as his symbols seemed to show."Glen- what do you think? I have not searched for the book yet as I just dug up the letter. Can anyone get a copy?FYI-Peterson worked military Intelligence during WWII.

As made known to attendees of the 7/4/02 task force meeting, it's my belief the last 18 characters of the 7-31-69 cipher--the EBEORIETEMETHHPITI -- are to be unscrambled as follows: TIME I HIT THE BEER. The remaining three spell out: POE. If a crossword puzzle answer, the question for it might be: "Author Allen?"

Arthur Leigh Allen was known to drink beer, and even was said to have brewed his own at home.

He said in the Cheri Bates letter: "It's about TIME..."

His cipher tells of a day of the "greatest pleasures" (at least for a maniac): hunting "anamals," getting his rocks off, collecting slaves for paradice. What better way to end the day than by getting drunk?

Note that while there have been some interesting ways to unscramble the 18 characters using the Hardens' letters (Robert Emmett The Hippie etc.), Zodiac's cipher seems to follow a direct one-letter-for-one-character translation, which this answer includes.

Actually "Beoriete Methhpiti" can easily be read as Theodore Kaczynski. The larger question is why The Zodiac mailed in codes in the first place. I believe it is explained in The Manifesto. Kaczynski writes: "A person is said to be well socialized if he believes in and obeys the moral code of his society and fits in well as a functioning part of that society.".... "violence is a form of "liberation". In other words, committing violence, they break through the psychological restraints that have been trained into them."......."the thought and behavoir of THE OVERSOCIALIZED person.."....."The moral code of our society is so demanding that no one can think, feel, and act in a completely moral way."....."We suggest that oversocialization is among the more serious cruelties that human beings inflict on one another."....The summary on this is: The Socialized live by their moral code, The Zodiac has his own code..."I like killing people because it is so much fun." I think that I have nailed this one! It's supported by what he writes. The code is the exact opposite of "the moral code of society". Kaczynskis job-quitting would represent a rejection of the socialized mold. Notice how that parallels with The Zodiac breaking loose. The terrorist equation is: Theodore Kaczynski versus The socialized and their moral code, as The Zodiac with his own code. Keep in mind, that anger and disaffection are the foundation mainly for his publicity-seeking killer spree. I think we should assume that this guy is serious, seriously angry and wanting to make a point. I would look away from such motivations as a watch-inspired name and beer-drinking games. I would view the game-playing nature of The Zodiac as a layer and not foundational as some appear to be suggesting.

I thought it stood for "San Benito Mental Hospital."

I've been working on deciphering the 340 cipher for about a week now, and have tried everything from establishing the frequency of each symbol used to color-coding each symbol to establish a "visual" pattern. I've tried starting with "this is the Zodiac speaking" right to left, left to right, spiral down, sideways, upways, turning it over and using a light to look through it's backside...and I've almost employed the use of a mirror, all to no avail. Maybe someone else can try these methods and come up with results? One thing, though, is that the cipher uses the symbol of a square with a dot in it ONCE. I thought that it could be an X (or Q, J, or Y) and that it could be used to spell the following: experience(d), exit, exhale(d), fix or affixiated, mix (as in bomb components), six or sixth, x-mass, Super-X or explode. The circle with the dot was used only twice, and the backwards "B" used only three times. I did a probability chart a while ago from Z's first, 3-part cipher, establishing how many alternates were used for each alphabetical letter. The lesser used letters (K,G,P,B,C,U,M,V,W,X,Y) used only 1 alternate each, where as the more commonly used letters had more (E of course having 7). Maybe this can help anyone...

"Actually Beoriete Methhpiti can easily be read as Theodore Kaczynski". How Zander?

By using the Zodiac symbol. The points are like a clock 0,3,6,9. Give letters their number value. You'll find that Theodore Kaczynski=Tehimioh Erttpebei(Beoriete Methhpiti scrambled) with the number differences as 03369633 69969960. Notice how Kaczynski's repeating letters equal the same letter OO=II, EE=HH, and KK=EE. The only zeroes are the beginning and end of Theodore Kaczynski. His name has gone full circle, so to speak. In the code they are presented as the last letter in each name. Look at the number pattern. Thats not something that appears to be something that has surfaced at random. The math on this is extremely tight if you fully analyze this.

That's very interesting Zander. I don't dispute what you have found, however it is unfortunate that it is a subjective solution, i.e. it relies on first scrambling the final letters into a particular order prior to applying the numerical aspects. Given the astronomical number of possible letter combinations here, there is only one believable scenario, that being that you deliberately attempted to fashion Kaczynski's name from the letters. You succeeded, but like others before you who have come up with other solutions for this section, you show no proof that this was the intented solution. Any solution deliberately intended would have to have proof, Zodiac would not have neglected to provide it being the cryptographer that he was. It's possible that such proof exists, but you have not provided it.

Regardless, that's still admirable work on your part.

Ray

That is truly remarkable work, Mr. Kite.

Ray and Alan: Thanks. But Ray I challenge you to take a closer look at the math involved and how this works. For example the "T" possibilities are K,N,Q,T,W,Z,C (9,6,3,0,3,6,9). The only possibility for a match to "BEORIETE METHHPITI" is T=T or T=TTT. Now look at the "D"=UXADGJM. So D=M which means without that one "M" in "BEORIETE METHHPITI", Theodore Kaczynski is unworkable. So much for endless possibilities, you see what I mean? In fact, look at "A"=RUXADGJ. Guess what that means. A=R only. Which means any name with 2 A's is unworkable. Arthur Leigh Allen, Larry Kane, Michael Ohare etc. Another example: Bruce Mcgregor Davis: "D"=UXADGJM which means "D"="M" only: also meaning two D's is unworkable. G=XADJMP meaning G=MP making Bruce Davis unworkable because DGG cant equal MP. I'm just giving 16 to 17 letter names as comparisons, not that there is any importance to establishing other suspects as unworkable. Also, these are superficial stoppages, so to speak. For example, there is at least one other way to forfeit Allens name, by 6/5 ratio. I'm trying to say that this is a mathematical tightrope. I can list a lot of 2 and 3 and 4 letters combos that automatically cancel a name such as AA and DD I've already mentioned. If the shorter ones don't disqualify, the deeper ones will.
But don't take my word for it: I challenge anyone to fit a 17 letter name(not a bogus one either) into this math system. If you are lucky enough to find one, then I doubt it will be as good as Theodore Kaczynski: because it appears to be designed: all of Ted's 3 double letters equal the same letter and the numbers involved appear designed: 0 33 6 9 6 33 6 99 6 999 6 0. (corrected other post). This makes it look like as Kaczynski went down his name, he decided to use larger numbers more and more, while going thru the alphabet near the end. I did not make up this number system either. It is taken from the Zodiac symbol. Zodiac ,himself, has given the numbers 0,3,6,9 to the north,east,south, and west points of his symbol. Of course, I needed the name Theodore Kaczynski first to realize it was even hidden in there, but that's not fabrication. Anyway, I've got pages of analysis on this that I wont list. But if you study this tightrope math system, you'll end up face to face with the fact that Theodore Kaczynski is the only name that reasonably works here.

Zander,

I agree that it's interesting, possibly even mathematically tight. But without some way to verify or prove the solution, it's no more likely this is the intended solution than "It's time to hit the beer," or for that matter, no more likely than that the letters are only gibberish. In other words, that it produces a name is not enough. Also, I have to say that maybe you did invent the 0,3,6,9 thing, because nowhere did Zodiac say that the crossed circle represented a clock face. In fact, if anything, he described it as a unit circle (radians reference). In this case, 0 would be at the 3 o'clock position, travelling counter-clockwise would indicate intervals of PI/2: 0, PI/2, PI, 3PI/2, and 2PI. So while your solution is impressive, you still need to show evidence that the 0,3,6,9 was intended to compute the solution.

Ray

The 0,3,6,9 Zodiac symbol can be found: opening page Zodiackiller.com:to Zodiac letters:to Zodiac-button letter,cipher...Map Hit Map!... Ray, I accept your position here. If you're not necessarily intrigued by this, then that's the way it goes. The Zodiac chose the odd number of 17 as his code lines. I'm guessing it's because that's how many letters are in his name. This was his first code, and I believe he designed it this way, in order to leave the last 17 as his signature in code. I would guess that he erred and had an extra, so he doubled the "E" in afterlife. This 17 letter signature works well with his openings This is (The Zodiac speaking)(17 letters).
So I think that we are working with a signature, somehow coded,anagrammed for the last 17. I would surmise that if he wanted an 18 letter signature, that he would have fashioned his code in eighteens. Anyway, it is popular belief that The Zodiac has somehow signed his code.

Zander... Very interesting solution to the unsolved ending of the three part cipher. It seems to work well, but I can see where it would be hard to confirm; however, if it could be found that Ted, either as himself or the Unabomber, used a similar type code and/or anagramming, I think that would be great confirmation of a solid solution.

I don't believe that the code key to TK's coded diary has ever been released. Much of his diary was written in numeric code and it was said that the key to the code was also found. I tried once, through an FOIA request, to obtain the key; however, was unsuccessful.

In the VPD report one citizen offered this suggestion as to the word scramble at the end of the three part cipher:"This is the tip-Robert E. Lee."Of course ,there is Robert Emmit(no hint of Emmit being a middle name!).And "Or be with me in the pit".There are lots more- all ingenious in their own way."I will NOT give you my NAME"!
Actually,it is endless and can never be proven one way or the other unless some hard evidence surfaces.All combinations,like Zanders,for example, should be looked at and encouraged-ideas are the name of the game-Zs game that is!

The "M" is the middle the alphabet and the middle of the last line of the code: 8 letters:"M":8 letters. Going the next letter after "M" right then left,ETC. You get: Meet the hip riot EIB. Who or what is EIB????

Please excuse me if this has been asked before and I missed it. How many, if any, local, state or federal departments, agencies or universities are officially examining the Zodiac ciphers?

I imagine the Defense Dept has super-computers programmed to crunch all manner of cryptographs. I wonder if anyone has approached our best code breakers with the Zodiac ciphers as a challenge. Just thinking out loud. Thanks in advance for your response...Fascinating stuff.

I approached the Israeli guy who broke Edgar Allen Poe's crypto about a year ago. He was "somewhat" interested, but not enough to follow through.

I believe a master cryptographer who used to post here tried his hand at it and failed, although he gave a fascinating analysis of what the cipher was and what it wasn't.

BFree,

Unfortunately, no one is working on the codes except amatuers. The police, government agencies, FBI do have some resources in this direction, but have neither the time nor the inclination to put them to work on a 30+ year old murder case. This is especially true because every last man Jack of them believes that the codes are already basically solved and there is no identification of the Zodiac within them. At one time, the NSA and FBI were involved with decryption efforts on Zodiac ciphers. Neither agency actually solved anything. The FBI however did authenticate the Harden solution for the first cipher. The cold war was on and national security was simply the priority. In my view, this does not mean that Zodiac defeated the best cryptographic minds the way Graysmith so dramatically claims. I think the best cryptographic minds just had better things to do with their time. It's hard to get qualified people to spend time working on things already deemed pretty much solved.

Still, I wonder if someday somebody will discover that Zodiac really did tell us who he was. Wouldn't that be a shocker?

Ray

Zander,

I have been on hiatus from this group for a while due to travels & work, but
I caught your intriguing post regarding the "Unexplained" letters at the
end of the 3 part cipher:

http://www.zodiackiller.com/ExaminerCipher.html

Indeed if a clean, robust mathematical algorithm can be found to
translate these letters into a name or other English text, it would be
a huge lead. Since you suggested you had a "mathematically tight"
method to translate these letters into a name, I decided to
investigate in detail. Perhaps I'm daft, but I took me some time to
grasp exactly what you did. At risk of misreprenting your work I'd
like to lay out this algorithm as clearly as possible & add in some of
my own thoughts. Please correct me if I haven't got it right.


The Zander Algorithm for the
Unexplained Letters in the 3-Part Cipher


The last 18 letters of the 3 Part Cipher, following "AFTERLIFE", do
not spell anything, ( see,
eg. http://www.sfgate.com/offbeat/zodiac.html )

STEP 0.: Remove the E after "AFTERLIFE", giving the Original Text:

BEORIETEMETHHPITI

STEP 1.: Anagram This Text Into:

TEHIMIOHERTTPEBEI

(we must admit that this choice of anagram is arbitrary, right?
See below for a different choice)

STEP 2:

Decrypt Anagrammed Text by replacing each letter with a choice of 7
letters, all of which are either 0, 3, 6, or 9 letters away from the
original letter. For example A would be replaceable by D (=A+3), G
(=A+6), J, (=A+9) OR: X (=A-3), U (A-6), R(A-9) or by A itsself (A+0).

I will call these offsets "Shift Factors". For Shift Factors of:
[-9,6,3,0,3,6,9], A would be represented by: [R,U,X,A,D,G,J] Using a
small computer program I made a table which shows us all the possible
decryptions of "TEHIMIOHERTTPEBEI". Just read left to right, choosing
a different shift factor (row) as you go.


T E H I M I O H E R T T P E B E I Shift Factor
--------------------------------- ------------
K V Y Z D Z F Y V I K K G V S V Z -9
N Y B C G C I B Y L N N J Y V Y C -6
Q B E F J F L E B O Q Q M B Y B F -3
T E H I M I O H E R T T P E B E I 0
W H K L P L R K H U W W S H E H L 3
Z K N O S O U N K X Z Z V K H K O 6
C N Q R V R X Q N A C C Y N K N R 9
--------------------------------- ------------

Reading across, if we choose Shift factors of:

0 3 -3 6 -9 6 3 -3 6 9 9 6 9 9 -9 9 0

We Get:

T H E O D O R E K A C Z Y N S K I

Just as you said. On the other hand a different choice of shift
factors gives some other words, if not names. With out much effort
I came up with:

Z E N I S F U N B O O K S B E E R

We should also add that the initial choice of anagrams was
"arbitrary." However, I think I see why you settled upon that one. I
tried some other possible, simpler, anagrams, for example ones
beginning with "THEOMORE" [0,0,0,0,-9,0,0,0]. But getting the
remaining letters to map to KACZYNSKI proved impossible, suggesting
the uniqueness of this choice of anagrams (assuming of course that they
are intended to spell TK's name.)

So I would say great job at finding TK's name in the code here, & congrats
on your work. The only unclear aspect here is how many possible names could
be spelled out of the letters arising from one of the numerous possible
anagrams. These kind of probability questions are hard to answer but I'm
working on a possible answer in regards to the 340 cipher.

Obiwan

Welcome back Obiwan and thanks once again for laying things out for us.It is much appreciated.
Good work Zander! It's a find, it's there and should be looked into further.In and of itself the Math is tight,however I would have reservations about the assumptions you have made in putting it together.
Let me ask both of you a something; Kaczynski's name or a close match has now been found in four places.Zander has it here and in the bottom line of the 340.Doug has an excellent interpretation of the 13 code and also has a close match from the introduction "this is the Zodiac speaking.
I do like the latter most of all because I agree with Doug that this statement is very important.
Is there anyway to compute the statistical odds against chance of a suspects name showing up more than once in these communications?
We have approx. 20 written communications, how do the odds work for once ,twice ,three, four?

Even considering the arbitrary nature of the initial anagramming, I think it's amazing that this particular suspect's name just happens to conveniently (and accurately) pop up in a variety of places. In addition to Zander's solution, see my solution of the 13-symbol cipher at http://home.att.net/~mignarda/sets.pdf. Kaczynski, of course, was a highly skilled mathematician who would have been perfectly capable of encrypting his name using any of a number of advanced functions that would have been inscrutable to anyone not trained like himself.

Obiwan, what do think the chances are that Kaczynski used his name as the basis for his encryption?

Lapumo, for some reason I didn't see your post above mine, which makes essentially the same point as my post directly below it. I don't want you to think I was ignoring your point. I think it's a valid one, and it would be very nice to know the probabilities involved.

Correction to my previous post: The 2nd to last shift factor should be 6 not 9. Here is the grid again, with Bold to lead your eye:


T E H I M I O H E R T T P E B E I Shift Factor
--------------------------------- ------------
K V Y Z D Z F Y V I K K G V S V Z -9
N Y B C G C I B Y L N N J Y V Y C -6
Q B E F J F L E B O Q Q M B Y B F -3
T E H I M I O H E R T T P E B E I 0
W H K L P L R K H U W W S H E H L 3
Z K N O S O U N K X Z Z V K H K O 6
C N Q R V R X Q N A C C Y N K N R 9
--------------------------------- ------------


This is the simplest demonstration of Zander's finding I could think of:


T E H I M I O H E R T T P E B E I
0+3-3+6-9+6+3-3+6+9+9+6+9+9-9+6+0
T H E O D O R E K A C Z Y N S K I

The letters on top are an anagram of BEORIETEMETHHPITI (17 of the 18 Unexplained letters from the 3-part cipher). The numbers are how much you need to shift the anagram to get the name. Of course any string of letters can be mapped into any other string by sufficient shifting. What is unusual here is that all the shifts are multiples of 3, and that Zodiac later wrote 0,3,6,9 on the map as a clue.

Is there anyway to compute the statistical odds against chance of a suspects name showing up more than once in these communications?

The odds of two things happening, unrelated are the product of each of the things happening individually. (Ie the odds of Coin=HEADS and die = 6 are 1/2 * 1/6 = 1/12) The problem here is computing the odds of the individual events. To compute the odds that the Zander Algorithm leads to a name RANDOMLY, we would have to: First look at all possible anagrams of BEORIETEMETHHPITI (STEP 1). For each anagram, draw up a table like the one I showed above (STEP2). Then for all these tables find out how many have names hidden in them. There are 17! = 355 Trillion ways to anagram a 17 character string (minus a correction for repeated letters). How many of these tables would you like to look at Lapumo? I could make some up for you. I'm also interested in these probability questions...more on that later.

Obiwan, what do think the chances are that Kaczynski used his name as the basis for his encryption?

What you are talking about, Doug, is using KACZYNSKI is the key which enables the code to be broken. That is different from what we have here where, according to ZK, KACZYNSKI is the plaintext which has been encoded into ciphertext using a certain algorithm.

If TK is the Zodiac, then I think yes, there is a fair chance he might use his name as an encryption key. TK must have tried anagramming his name at some point and he clearly would have known that you can find ZODIAC in his name. I take it you are thinking about the TK diaries which were in a code that the FBI has not yet revealed?

I've been working on deciphering the 340 cipher for about a week now.

Hi Kendra, Your frequency work sounds good, I like the color coding. It probably duplicates work some of us have done previously. Just so you know here's a summary of my freqency analysis of the 340 Cipher:

http://www.ciw.edu/chris/z/z2stats.html

But first see this page:

http://www.ciw.edu/chris/z/340explain.html

Which lays out my computer-readable ASCII version of the cipher symbols. The main challenge of the 340 is that the length of ciphertext is small compared to the number of symbols used.

Hopefully you've checked out the previous discussions on the 340-cipher at:

http://www.zodiackiller.com/messageboard/messages/14/584.html?1013792066

Where I noted that solving just the 10 most frequent letters in the 340-cipher gives you 1/3 of the whole cipher... Good luck!

The big draw on the solution is: That Teds double letters all equal the same letter. That sends the odds into orbit, if all names must follow that standard. I find it interesting that the number 6 is used for the letters KOKO Z. The number pattern appears designed. Kaczynski uses a string of numbers in his diaries. The letters add up to: Beoriete=79 Theodore=90 Methhpiti=108 Kaczynski=119. Both are 11 difference. My experience with my solution is this: 90% of names are disqualified within a minute. The rest basically fail at some point after that. The easiest way to showcase the difficulty here is to draw out 2 3 and 4 letter combos that automatically disqualify a name such as AA and DD. I see Kaczynski's name in: "The Zodiac" itself, which is an abbreviated form of his name. Beoriete Methhpiti. Doug's 13-code solution. And the 340 code where THEODOR and KAZINSKI are on the first and last lines. That's well against the odds there, when you study the frequency of symbols used and so forth. Also "THEO" appears hidden in the beginning of the code.

In an FBI computer report on the 13 character cipher they came up with Adam Shanahan,Adam Flanagan,and Adam Granahan plus Gemini.
It is endless and dozens of ingenious( and not so bright)combinations arise,with those that have suspects finding- by either computation or word manipulations,etc.-their suspects name in the midst.As I have said-let it continue as this is the spirit of research.
Zodiac wrote he would NOT give his real name.
He was into PEN NAMES and symbols though Zodiac(Z and the cross/circle)being the most prominent with rh,BY ---,Robert Emmit,RP or Red Phantom,A Friend,Yours truly,A citizen,etc.,all following.Some are questionable like Robert Emmit,but others were clearly used by ZODIAC.

In another code section, the question is asked: "Scrabble tiles equal 187, does that number mean anything to anyone?" When I gave out the (Beoriete Methhpiti-Theodore Kaczynski) figures, I was hoping someone would notice and take it from there and realize my 0,3,6,9 solution wasn't just picked out of thin air. The numbers for letters on Scrabble= 187 and numbers for letters BEORIETE METHHPITI also equals 187. Which makes the average 187/17= 11 or "K". beorieteMethhpiti=kkkkkkkkkkkkkkkkk. So we have Theodore Kaczynski matched to Beoriete Methhpiti at +11,+11(Beoriete(79)Theodore(90):Methhpiti(108)Kaczynski(119)), where the average or base number is also 11. At this point, any mathematician, worth his IQ, will say there must be a number system in place around the name "Theodore Kaczynski" centered on the number 11. Not to mention, that the only matches are the "E" and the "I"(perfect name word breaks) and that "K" is the letter chosen.

"Scrabble tiles equal 187, does that number mean anything to anyone?"

Actually that number doesn't mean anything to me. At least it didn't before I started reading this board....from which I have picked up that this is a number used by police to refer to murders? Is that right? I'm not sure that police code is commonly known, except in crime-fighting circles.

187 as 11x17 on the otherhand, might be quite significant. 17 is obviously significant from the ciphers. The fact that both 11 and 17 are prime, given Z's math background, should not be overlooked. Good observation ZK. You mention "base number" of 11. This makes me wonder if using base-17 numbering could get us anywhere...oh so many possibilites so little time.

Careful, gentlemen, you're starting to write and think like Gareth Penn...

Or perhaps we're starting to write and think like Zodiac? Ed, If there is going to be a big solution to this case based upon the evidence we have before us then that solution will very likely come from understanding the hidden, probably mathematical meaning in one or more of the existing Z letters/ciphers. True, they may be meaningless and this may be a dead end, but barring the revelation of new physical evidence (ie P.S. keys turning up in somebody's house), the best hope for a "solution" to the case IMHO is via a (possibly mathematical) decipherment of Z's writings.

I happen to think that Penn started off on the right track, but may have wandered far afield with his morse code soutions, etc. But I have not read his books, so to be fair, I can't really criticize. ps. Since everybody seems to be so anti-penn, anybody want to send/sell me a copy of his book(s), which apperently are pure rubbish?

Tony,

In response to your reply over on the TK 340 Odds thread:

You are right. There haven't been any conclusive solutions in 34 years. That sounds pretty impressive on it's face. But the way you frame it, it sounds like there's been a bunch of guys with pocket protectors and thick glasses sitting in a basement office of the Pentagon staring at a computer screen, crunching numbers for 34 years straight. It's a fallacy to assume that "the top codebreakers in the world" are stumped by the Zodiac ciphers. The fact is they aren't even working on this. Nor have they been for about the past 33.9 years! The NSA and FBI and the Navy looked briefly at the ciphers without success. The FBI verified the Harden key for the first cipher. And that was pretty much it. To repeat what I said on an earlier post (July 18 in this thread), the cold war was in full swing back then, and government agencies such as NSA didn't have the time or the motivation to dedicate much effort to working on something like this. National security was simply the priority.

Additionally, Zodiac was not a cryptography expert. He was himself an amatuer, and his codes are the result of amatuer cryptography. Therefore, it must be understood that they will be broken/solved definitively (unless everyone adopts a "blow it off" attitude). When the break occurs, I predict it will be due exclusively to the work of dedicated amatuers who refused to give up. Therefore, the fact that the experts "failed" to solve the ciphers means absolutely nothing to me. It's easy to fail when you don't do anything.

I'd say the reason there hasn't yet been a conclusive solution identifying Zodiac is that the focus has always been in the wrong places. Even when provided with numerous clues by Z, there was not much effort expended in that direction, especially after the phrase, "I will not give you my name" was discovered. To my way of thinking, this would be a very good way to get people off his trail if in fact he had encoded his identity.

Of course, the other possibility for the 340 is that it is just unsolvable junk. There are those on here (and they know who they are) who find this a particularly pleasant option, because they can then have yet another reason for not getting constructively involved. All that is required is a hasty application of "Occam's Principle of Limited Imagination".

Don't get me wrong, I wasn't getting hot under the collar when I wrote my reply to your post. Actually, I was laughing my head off. Now ask yourself this, why would I think that was funny?

This is most definitely an amazing case.

Ray

I have taken the advice of the project team and have forwarded a packet of info on BEORIETE METHHPITI to a math professor by way of a 3rd year Clemson student who is some variation of a math major. The solution works by giving the letter its number ((A=1 B=2, Z=26 etc.)). The solution works with the Zodiac symbol itself, as an encoding wheel if you will. Zodiac, on several occasions, used the symbol like a clock, on the map he placed 0,3,6,9 at the points. Those points can be argued as being 2 elevens, so you have 0,3,6,9 placed on 2 11's. Here's some more info from the packet: 1. Zodiacs 13-code is well structured, balanced if you will, a sequence of 8K8M8 appears, suggesting it was designed 8,8,8=KM. 2. Theodore Kaczynski=209=19x11 3. Beoriete Methhpiti=187=17x11 4. Placing Theodore Kaczynski under Beoriete Methhpiti you find that the only matches are E and I, the last letter of each name, name breaks. 5. The 22 difference is perfectly balanced with 11 for each side. (T)90 (B)79...(K)119 (M)108 NOTES: A. 17x11 and 19x11 are prime numbers. B. Scrabble is a number for letter game, the pieces add up to 187(Ted was very good at Scrabble from a young age). C. 187 is the murder number. D. the letter K equals 11. E. Hurkos predicted the importance of 2 elevens in the Zodiac case(LOL-that's not included).
The solution continues with the second stage, if you will, that is 0,3,6,9. Of course that's posted, see above up some. Anyway the notes on that are: THEODORE KACZYNSKI=TEHIMIOH ERTTPEBEI(all 0,3,6,9 difference)= scrambled to BEORIETE METHHPITI. A. The name runs full circle of the Z symbol from zero to zero. B. Those only matches are the first and last of Ted's entire name, when scrambled, the matches move to the last letter of each name. C. The string of numbers going down Ted's name keeps getting higher in use, suggesting as Ted went down his name, he tried to make it more difficult. Look>> 0,3,3,6,9,6,3,3,6,9,9,6,9,9,9,6,0. Ted waits till his last name to go thru the alphabet or look at actual difference in letters>> 0,3,3,6,9,6,3,3,6,17,17,6,9,9,17,6,0 D. ALL of Ted's double letters equal the very same number, suggesting design. E. The 6(sixes) uses the letters KOKO-Z. (compare to Theodore (J. KAC-Z)ynski(that's just for fun)). F. The 3 is HERE and 9 CANDYS. G. ZY=HH is of interest.
Further, Kaczynski uses a code that involves a string of numbers mixed with words. I have requested a percentage. That is something like: 51% TK's name is placed there by design, 49% coicidence. I put it at 85/15. I have some more detailed math work I'm holding back for now, but I believe that is enough to draw a similar 85/15 or plus reply. Also, it appears that only less than 1 % of all 17 letter names are workable thru the 0,3,6,9 Z-wheel. Also, I'm looking for an estimate on the number of names that will work if it is required as a standard that the double letters in the name must equal the same number. I place that at 20,000 to 1 at the moment.

2 X ?!

Just before we get into the detail of this ,please explain/clarify the following points.
1."These points can be argued as being 2 elevens".
2."suggesting it was designed 8,8,8 =KM
3."Kaczynski uses a code that involves a string of numbers mixed with words" The 13 code?
4. What is it exactly you have requested the % on?

1.The Zodiac symbol broken down is a wheel(circle) and 4 points, the straight lines equal 2 elevens(it's a visual thing). So you have 0,3,6,9 off 2 elevens on the map. 2. The 13-code is very orderly. It reads letter,letter,letter,symbol,(8,leter,8,letter,8)symbol,letter,letter,letter. Same forward as backward, balanced. Even the 8K8M8 is balanced because 888=KM 8+8+8=24, K(11)+M(13)=24. 3. That code is a Unabomber one that Doug posted on "Code Challenge". It involves words and strings of numbers. If I'm right about how I believe it works, it would support this BM solution. Usually when words are slipped into a number code, it's because the code-creator is using a number system based on the letter before it. Also suggesting to confirm this is the tedious nature of figuring out the exact number over and over again. It's like this: (Z,53,13,42,1,91.) So you work off the Z(26)+53=79=26+26+26+1=A. A(1)+13=14=N. N(14)+42=56=26+26+4=D. D(4)+1=5=E. E(5)+91=96=26+26+26+18=R. ZANDER. But that's in simple form and solvable. Imagine now a plus or minus is assigned to 13 letters and 13. Imagine there are simple rules like words that automatically send the decoder back to the previous word. Imagine certain combos of letters send the decoder back also. Imagine the code-creator assigns a few numbers to mean nothing(like the backward c in the 340). I can't say for sure, that it is similar to this, but including words from time to time suggests that like a domino-builder, the code writer is using safeguards against tripwiring his code into oblivion. So with only a page for a key, that code is realistically impossible to decipher. 4. The opinion of the professor(or any others) is requested to answer what is the most reasonable explanation for the numbers being what they are. He might side with this anagram theory but only by a 51/49 ratio. 51 being for the solution, 49 for coincidence. I have it at 85/15(not to be confused with the 99.99 % assumption that Ted is Z.) Or even the opinion might be that it doesn't even qualify as coincidence, though I would find such a reply unrealistic. *Warren, clarify your question, if you have one. Lapumo (and Ray) I will say this. I am interested in all cryptic options, but honestly I haven't seen any non-Kaczynski cryptics that I feel are solid. The only reason I dogged your work is that a claim of solving the case accompanied it(at least by Ray) and even I with my massive ego, make no claims of solving the case thru Beoriete Methhpiti. I look forward to reading your solution when it's the right time to put it out.