Mathematica helps crack the code of Zodiac Killer

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The Zodiac’s 340-character message resisted decryption for 51 years

Cryptographic researchers have finally cracked a 51-year-old code left behind by Zodiac, a serial killer who terrorized Northern California in the late 1960s and early 1970s. Much of the code-cracking work was done in Mathematica, Wolfram’s statistics package.

According to Discover Magazine, which wrote about the effort in a story published in its January/February 2022 issue, three researchers successfully cracked one of the messages attributed to the Zodiac killer, who authorities believe killed at least five more than 50 years ago Killed people in the San Francisco Bay Area before.

The researchers – including David Orranchak, a computer programmer in Roanoke, Virginia; Sam Blake, an applied mathematician at the University of Melbourne; and Jarl van Eycke, a Belgian code-breaker and warehouse worker – had all tried unsuccessfully to crack the Zodiac’s 340-character code before joining forces in 2018, the company said Discover Magazine Story.

Over the years, many have attempted to unravel the 340-character message received from the Chronicle of San Francisco on October 14, 1969. This is believed to be the second cryptogram the killer sent to the newspaper, the first being a 408-character message sent in August of the same year and decrypted just a week later (the Murderer then sent two shorter messages, which have so far also resisted decryption).

But it wasn’t until the three started working in earnest during the downtime of the COVID-19 pandemic that they finally managed to decipher it. The major breakthrough, according to the magazine, was Blake’s idea that the cipher could simultaneously be a homophonic substitution cipher (where plaintext letters are matched to more than one ciphertext symbol) and a transposition cipher (where plaintext characters are shifted according to a regular system become) is. .

Visualizing the 1,2 decimation with the cipher split into three vertical segments, finally yielding the meaning of Z340 (courtesy Sam Blake)

With this theory in mind, Blake and Oranchak created thousands of possible solutions to the 340-character encrypted message (sometimes referred to as Z340) using Wolfram’s Mathematica statistics package and a pair of encryption solutions including AZdecrypt, developed by van Eycke, and zkdecrypto.

They tried different direct transposition methods with a direct offset of 18 or 19 characters. They looked for interesting patterns by transposing characters from the top-right corner, from the top-left corner, outside-in, and inside-out. Nothing at all. They tried single-level transpositions (down one row), two-level transpositions (down one row, then across two columns, etc.). Still nothing. They tried to count repeating bigrams or pairs of symbols. Nothing at all. Finally, they tried to combine all one- and two-step transpositions while repeating bigrams. nope

“Then we considered testing all 3-tuples of transpositions,” Blake wrote in a March 2021 blog post on the Wolfram website. However, this would require testing 155,929,364,660,224 candidate ciphers. One naive check per second would take over five million years. So we limited our experiments to decimations that could reasonably be written by hand, and then tested only high bigram candidates. Once again this search turned up nothing.”

The researchers then decided that perhaps the key was breaking the 340-character cipher. The 408-character cipher cracked in a week had been delivered on three sides, so researchers thought Z340 might have been engineered the same way. They split the cipher horizontally into two and three segments; vertically in two and three segments; and both horizontally and vertically into two and three segments. Then they used a “Reduce” function to compute all possible segments, resulting in correct two-dimensional decimations, Blake wrote. But it still didn’t bring an answer.

The plaintext behind the Z340 cryptogram, decrypted by the three researchers (courtesy of Sam Blake)

Finally, before beginning an exhaustive search that would use combinations of transpositions, the researchers went back and looked again at some of the 650,000 transpositions they had already tested. They found some interesting tidbits in plain language, including the words “the gas chamber.”

“Exploring this result further, David used our 9,9,2 vertical segment, 1,2 decimation transposition, and AZdecrypt to generate the phrases ‘HOPE YOU ARE’, ‘TRYING TO CATCH ME’ and ‘THE GAS ROOM ‘ to write off. ‘ Blake wrote. “Eureka! After 51 years we had deciphered part of the Z340.”

Finally, the rest of the message came into focus (though not without some additional cryptographic techniques, including good old word scrambling). Convinced they had solved the mystery, the researchers contacted the FBI in December 2020, who confirmed their work.

“Essentially all of my work on the Z340 was done in Mathematica,” Blake wrote. “I used Spartan’s high-performance computing cluster at the University of Melbourne to eliminate possible transpositions with zkdecrypto and David used AZdecrypt. Otherwise, all of the statistical analysis of the Z340 and the creation and analysis of the millions of candidate transpositions was done with Mathematica. The reason I use Mathematica is simple; It’s by far the most time-efficient language I could use for such a task.”

Considerable computing power was required to find the solution to the Zodiac Killer’s message, Orranchak said Discover Magazine. That would have made it almost impossible to use that kind of brute force approach to decryption in 1969, he said. However, that doesn’t mean that today’s supercomputers can crack today’s encryption, because today’s encryption methods are much stronger.

“They’re just not susceptible to these types of attacks,” Orranchak told the magazine. “The Zodiac cipher was almost certainly created with pencil and paper, but it was complex enough to survive attacks for 51 years.”

While the Zodiac’s message has been deciphered, the killer’s identity remains an unsolved mystery.

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