Over on the ZodiacKillerSite forums, pi is doing some interesting work investigating the use of route patterns in quadrants of the 340-character cipher.
His idea is to split the cipher text into four quadrants, and then rearrange the text in each quadrant based on all of the possible routes. He then measures the resulting cipher text to see if more repeating patterns emerge from the text, with the hope that the underlying rearrangement has more features of a real message.
What he found was that running this search on the 340 increases the repeating patterns in at least 15% of his tests. By contrast, doing the same search on the 408 only increases the patterns 0.0000076% of the time. I found a similar phenomenon when exploring quadrants with a slightly different approach (see here and here).
But this led to more questions: What would happen to other 340-character test ciphers? How hard is it to make a 340-character cipher that has very few repeated patterns, yet still contains a valid message?
To answer this, pi created a test cipher that contains very few repeated patterns.
This means the repeated pattern count alone is not enough to separate good and bad rearrangements. What can we use instead? Dan’s approach avoids measuring the candidate cipher text altogether by skipping directly to trying to solve the rearranged text via the zkdecrypto hillclimber. It is a slow approach, but methodical. But is there some measurement that we can apply as a short cut? I think this is still an open question, and that we still need to generate more test ciphers to answer it.
Does the 340 cipher contain simple manipulations that have confounded all attempts to crack it? Dan Umanovskis, the skilled programmer who hacked together zkdecrypto-lite, has created a new kind of attack to explore this possibility. Using a genetic programming approach, his new algorithm evolves manipulations of the cipher text, such as swapping rows, removing columns, and flipping the text. The algorithm then feeds the modified cipher text to zkdecrypto-lite which hunts for readable plain text. Candidate manipulations that result in higher zkdecrypto scores are kept (“survival of the fittest”) and “bred” (mixed together) to look for even better scores.
Hopefully his approach will bear fruit. Even if it doesn’t find a solution to the 340, it can be used to exclude certain possibilities. For instance, you can create many test ciphers that resemble the 340 and contain the types of manipulations that the algorithm searches for. If the algorithm can successfully crack all the test ciphers, and no solutions are appearing for the 340, then it’s likely the 340 uses some other method of encryption.
You can download and play with Dan’s algorithm here: https://github.com/umanovskis/lgp-decrypto, and read Dan’s description here: http://www.zodiackillerfacts.com/forum/viewtopic.php?f=50&t=1537.
Clicking the above logo will bring you to a Swedish thrash metal band, rather than mysterious cryptograms. Nevertheless, you may find yourself puzzling over their indecipherable lyrics.
Here is another quick (and pointless) diversion. As explored in the previous post, you can find words in the cryptograms without performing any substitutions. For example, in the 408-character cryptogram, the word “OUT” appears:
And the word “RIDE” can be discerned:
If we apply the solution key to those “words”, we get:
This led me to a question: Using the cipher symbols, can we create any “words” that turn into valid plain text words when deciphered using the 408’s solution key?
The tools I built for the previous post were still lying around, so they were useful in satisfying this nagging curiosity. Turns out that many words can be made this way. In the sampling below, each plaintext word is followed by its encipherment using the 408’s key. Then the interpretation of the encipherment is shown:
(If you really want to challenge your brain, try to find a word whose encipherment’s word can itself be enciphered into yet another valid word.)
One reason I was curious about these “word pairs” was because of the possibility that Zodiac “seeded” his solution key with a keyword. But even if he did, it seems impossible to discover the keyword, since too many words can be found by chance. Here’s another example of how easy it is to draw out ridiculous outcomes solely from chance:
Among the symbols of the 408-character cryptogram, Zodiac includes the normal looking letters A through Z, but excludes C. So, let’s write out those cipher letters, with the corresponding plain text substitutions underneath:
Now we can re-arrange the assignments to look for keywords:
Surely “the buffoon’s sweet genitalia” is not the message Zodiac was trying to convey…
Many people have noticed that words can be found among the symbols in the Zodiac killer’s cryptograms without performing any substitutions. Here are some examples from the 340:
HER 
TOM 
Looks a lot like “ZODIAC” 
FBI 
TOO 
GOD |
BOO is seen three times 
BOY is found twice |
Five occurrences of BY, resembling the Halloween card |
And here are some words easily found in the 408:
(more…)
Between 1956 and 1981, math and science writer Martin Gardner wrote the Mathematical Games
Some of Gardner’s wonderful puzzles, games, and curiosities.
He even wrote a book about codes and ciphers
I recently found an index to a collection of Martin Gardner’s correspondences and notes at Stanford University, and was surprised to discover that some of them pertain to the Zodiac ciphers. Naturally, I had to order photocopies and have a look.
Among the collection are letters that writer and amateur sleuth Gareth Penn wrote to Gardner in 1981 and 1984. Those who follow the Zodiac case have probably heard of Gareth Penn, a man who, for over twenty years, has obsessively written reams of material with bizarre theories linking UC Berkley professor Michael O’Hare to the Zodiac killings. Penn’s fixations have also drawn suspicions that he himself is the Zodiac killer. For a better background on this fascinating example of misplaced obsession, read “With Malice Aforethought” by Michael Martin, and Michael O’Hare’s own responses to the whole affair.
In his first letter to Gardner, Penn writes about how much he enjoys Gardner’s column on mathematical puzzles, and encloses copies of his various articles and writings about the Zodiac Killer:
(more…)
(photo credit: Elonka Dunin)
Thanks to Doc for informing me about this story. Above is CIA analyst David Stein, the first person to crack encrypted messages in the Kryptos sculpture at the CIA, leaving only one message unsolved. Twenty-three years after the sculpture was created, the last message still remains unsolved.
Wired.com posted this story recently, triggered by the NSA widely distributing Stein’s declassified and fascinating account of how he tackled Kryptos for over seven years using only pen and paper. Although Stein was first, his work was only known to CIA colleagues. Cryptographer and computer scientist Jim Gillogly was the first to publicly announce the correct solutions, but he was unaware of Stein’s work. Gillogly is also known for identifying a strange sequence in one of the Beale cryptograms, which he explains is evidence that the Beale papers are a hoax.
Read more about how Stein cracked Kryptos here. And be sure to read Elonka Dunin’s nicely organized breakdown of the entire Stein article. Those of us working on the 340 might find some insight and new ideas in such details.
Mike Morford recently relaunched his Zodiac Killer discussion forum:
His forum was formerly available by invitation only, but is now open to everyone. It is filled with lively conversations on a wide variety of topics, including news, suspects, the killer’s correspondences, evidence, analysis, theories, and non-Zodiac crimes. My favorite topics, of course, are the cipher-related ones, in which forum members present their ideas, observations, and theories about the various cryptograms attributed to the killer.
Join the conversation at ZodiacKillerSite.com!
On October 23, 1969, the San Francisco Examiner published an article about the ongoing hunt for the Zodiac killer. This enciphered “message to Zodiac” appeared in the article:
The article was published after the 408-character cryptogram was solved, and before the 340-character cryptogram was mailed.
Using a simple observation, you can easily solve the Examiner’s cryptogram (if you want to skip ahead to the solution, click here). The cryptogram has only 44 characters, and 33 of them are unique. With so few repeated characters, many possible plain texts can fit. For example, if you feed the cryptogram to zkdecrypto, it yields this plaintext:
ERSWILLYOURAGESTOFTHECANAMEDTHEPRESANDBEINTE
This solution looks a lot like English text, but is the wrong solution. This cryptogram would have been very difficult to solve without applying the simple observation. Do you know of a way to solve it without knowing the trick?
(Thanks to Deb for uncovering the article)
UPDATE Apr 24, 2013: Here is an excerpt from the book The Cases That Haunt Us
Updated April 17, 2013: In light of recent events, I’ve decided to remove the ricin recipe plaintext from this post. The FBI, however, continues to display the encrypted ricin recipe on their website.
Cryptographer Klaus Schmeh recently posted about a cryptogram that appears in an FBI article about how their Cryptanalysis and Racketeering Records Unit (CRRU) breaks codes and ciphers to solve crimes.
The FBI article says the cryptogram contains “enciphered instructions for making ricin poison found in the notebook of a lone bomber in Virginia.” I couldn’t find any decryptions of the cipher text, so I transcribed it, and fed it into zkdecrypto lite, which very quickly found a rough approximation of the plaintext. A little bit of extra work yielded the full solution, which really does contain a recipe for ricin poison, encrypted using simple homophonic substitution.
At first I was hesitant to post the solution. Is it irresponsible to reveal a dangerous recipe to the public? But I’ve decided to post it for these reasons:
- The FBI already posted the cryptogram in full view of the public.
- The cryptogram is very easy to solve.
- Ricin recipes are already very easy to come by via Google searches.
- The enciphered recipe is very crude, producing only a mash form that is not further purified for dangerous potential. Similar recipes in terrorist “cookbooks” are “deemed incapable of achieving a good product for causing a large number of casualties by any exposure route, mainly because of the low content of toxin of the final extracts” [1]
- Only one death has been attributed to ricin poisoning. Every other ricin-related incident seems to involve dumbasses stockpiling the stuff for its claimed deadly potential.
Here’s the decoded plaintext:
[redacted]
And here is the full analysis of the solution, including the solution key, symbol cycles, and symbol frequencies.
The cryptogram bears some interesting similarities to the Zodiac’s ciphers: It is 354 characters long (to Zodiac’s 340), has 65 distinct symbols (to Zodiac’s 64 in the 408-character cipher), uses homophonic substitution (like Zodiac’s 408), and uses some of the same symbols. The ricin bomber, however, did not do a good job of concealing the letter frequencies of the plaintext. In fact, if you look at the symbol frequencies, the most common symbols correspond directly to the most common letters in English: E, T, A, O, N, etc. This is because the lone bomber did not correctly flatten the frequencies with the proper number of symbol assignments per plain text letter.
The FBI says this cryptogram is just one small part of 24 pages of enciphered messages. It would be interesting to see what else was in the notebook, and to know more about the bomber. I can’t find any news sources that mention the Virginia lone bomber. Does anyone have any ideas?
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