Over the past couple of decades, I have from time to time “had a go” at solving the famous unsolved 340-symbol cipher sent by the Zodiac killer to the San Francsico Chronicle in November 1969:
340-symbol cipher sent by the Zodiac killer to the San Francisco Chronicle in November 1969
Needless to say, I never solved it. But it was fun to write computer programs to try.
On Christmas Day 2016 I sent an email to veteran code-breaker David Oranchak, after watching his 2015 Cryptologic History Symposium talk on Zodiac’s 340 cipher as a Christmas treat, with some ideas I had previously had about finding the letter frequency source that Zodiac had evidently used for his earlier (and solved at the time) 408-character substitution cipher. (In 2007 I had even scoured the State Library in Melbourne, Australia, and in 2016 the Public Library of my then-current city of San Francisco, California, to try to match the implied relative frequencies to any known table of English letter frequencies—with no success. I was hoping that San Francisco—the center of Zodiac’s attention—would be a better chance, but I still came away empty-handed.)
David was very gracious to reply, and briefly discuss my ideas, even though I clearly was infinitely less experienced in the field than he. He is a gentleman and a scholar.
On December 5, 2020, David, together with applied mathematician (and fellow Melburnian) Sam Blake and Belgian programmer Jarl Van Eycke solved the 340 cipher! David outlined their discovery in a YouTube video he posted on December 11, 2020—actually the fifth in a series of YouTube videos he had posted on the topic—following the FBI's confirmation of their solution.
David posted a comprehensive description of the 340 cipher, and how Zodiac likely created it (equivalent to what is described below, which I and likely others shared with him), in his sixth installment on January 29, 2021. Anyone interested in the 340 cipher should watch this video (and the later installments that have since followed, as promised at the end of this sixth installment).
Watch Oranchak’s video for a description of how they discovered the key (the most difficult part of the process!). The following, taken from his video, shows you which symbols (black) map to each original English letter (red):
The solution key to the 340 cipher, found by Oranchak, Blake, and Van Eycke
It is humbling that the final solution to a 50-year puzzle is so simply written down. Such is the mark of a true solution.
Even more humbling is the fact that my ideas about the letter frequency distribution implied by this solution can not be made to match that of the earlier 308 cipher—my hypothesis on this was completely wrong. How Zodiac decided on the number of symbols to use for each letter remains a mystery, and likely itself involves a degree of randomness—a characteristic of all of Zodiac’s communications: possibly genuine, but widely believed to be a deliberate ruse and obfuscation on his part.
As David explains, Zodiac broke the original message into three sections, with 9, 9, and 2 rows respectively. Within each of the first two sections, Zodiac wrote his message downwards, rather than across, and then rotated each row to the right by two, four, six … positions, with mistakes being made in the sixth row of the second section. Undoing those row rotations, after applying the above key, we can see the solution (I created this color-coded version to most easily show the words):
My color-coded illustration of the solution found by Oranchak, Blake, and Van Eycke
Reading down and across through the first two sections, then through the third section (with some words reversed), and finally the separate words in purple (and fixing some encoding mistakes), we see the Zodiac’s complete message:
I HOPE YOU ARE HAVING LOTS OF FUN IN TRYING TO CATCH ME
THAT WASN'T ME ON THE TV SHOW
WHICH BRINGS UP A POINT ABOUT ME
I AM NOT AFRAID OF THE GAS CHAMBER
BECAUSE IT WILL SEND ME TO PARADICE ALL THE SOONER
BECAUSE I NOW HAVE ENOUGH SLAVES TO WORK FOR ME
WHERE EVERYONE ELSE HAS NOTHING WHEN THEY REACH PARADICE
SO THEY ARE AFRAID OF DEATH
I AM NOT AFRAID BECAUSE I KNOW THAT MY NEW LIFE WILL BE AN EASY ONE IN
PARADICE
LIFE IS DEATH
It’s impossible to know for certain, but now that we have the solution to the 340, we can make a guess as to Zodiac's thought process in creating it.
Clearly, he was upset that his previous cipher was cracked so quickly, and wanted to make sure that this one wasn’t so easy. On the other hand, he seemed to understand that if he made it too difficult, then it would never be solved at all, which would prevent him from having a laugh when people realized that it, again, contained nothing useful for identifying him. So he stuck with the same simple method, of replacing each letter with a set of symbols (roughly chosen so that popular letters in English had more symbols assigned to them, to prevent it from being too easy to recognize, e.g., ‘E’ or ‘T’).
Here is where it becomes interesting. He clearly decided to make things more complicated by writing down the page, then across, rather than across and down. But he probably reasoned that that alone would not be enough to make the cipher difficult enough to crack. So he broke it into three sections, writing within the first before moving to the second.
He probably reasoned that that would still not be enough to prevent a rapid decryption. So he anchored “LIFE IS” at the end of the top row of the second section, in normal left-to-right text. He also switched to left-to-right in the third section, but reversed some of the words.
Had he stopped there, it may not have been 51 years before we had a solution to the 340. He probably realized that bigrams would still give a huge hint as to how he had encoded the message, and would point to his writing down the page rather than across. So he decided to cyclically rotate every row (i.e., rotate each row to the right, with the columns pushed off the right side pushing back in on the left side) by a linearly increasing number of columns each row. One extra column of rotation per row would not quite do it, because someone scanning through diagonals might still pick up the pattern. So he instead rotated by two extra columns per row, which would require someone to “jump through” the cipher like they were a knight on a chessboard.
That final decision is what made the 340 effectively unbreakable. Even though, in hindsight, we can see that he didn’t change his methods too much from the 408, that rotation was sufficient to make the space of possible methods enormous.
It is incredible that Oranchak, Blake, and Van Eycke did finally crack the uncrackable. It is difficult to know whether Zodiac was disappointed that he had made it just that much too difficult to crack in (likely) his lifetime, or whether he enjoyed the fact that, in hindsight, it was always so tantalizingly close. Maybe he intended to reveal the solution at some point in time, and died before doing it. We’ll likely never know.
© 2020–2024 John Costella