The Zodiac Killer Ciphers: Breaking Down Z408 and Z340

Between 1969 and 1970, the Zodiac Killer sent four encrypted messages to San Francisco Bay Area newspapers, taunting police and the public to decode them. These ciphers became among the most studied in cryptographic history — analyzed by the FBI, the NSA, amateur codebreakers, and computer scientists for decades. One was cracked in a week. Another took 51 years. Two remain unsolved.

The Zodiac ciphers are a masterclass in how cipher design, message length, and sheer luck determine whether a code can be broken.

The Z408 Cipher: Cracked in One Week

The first Zodiac cipher, known as Z408, was a 408-character message sent in three parts to three different newspapers in July 1969. The Zodiac demanded the papers publish the cipher on their front pages, threatening to go on a killing spree if they refused.

Structure: Homophonic Substitution

Z408 uses a homophonic substitution cipher — a type of substitution cipher where common letters are represented by multiple different symbols. In a simple substitution, E is always replaced by the same symbol, making frequency analysis straightforward. In homophonic substitution, E might be represented by any of four or five different symbols, flattening the frequency distribution and making analysis much harder.

Z408 used 54 different symbols to represent 26 letters, with common letters like E, T, and A getting multiple symbols each.

How the Hardens Cracked It

Donald and Bettye Harden, a high school teacher and his wife from Salinas, California, cracked Z408 in about a week using a combination of frequency analysis and word guessing.

Their breakthrough came from a simple assumption: the Zodiac was probably ego-driven and would use the word "I" and the phrase "KILL" or "KILLING" in his message. They searched for repeated patterns consistent with these words.

Once they identified a few letter-symbol mappings from these guesses, the substitutions cascaded. Each confirmed letter revealed more context, which suggested more words, which confirmed more letters. Within days, they had the complete solution.

The Decoded Z408 Message

The decoded message was a rambling statement about the thrill of killing. It claimed that victims would become the killer's slaves in the afterlife. Notably, it did not contain the killer's identity — despite the Zodiac's claim that his name was hidden in the cipher.

The last 18 characters of Z408 appeared to be garbled or nonsensical, possibly due to encoding errors by the Zodiac himself. Whether these final characters contain meaningful content or are simply mistakes remains debated.

The Z340 Cipher: 51 Years of Failure

The second cipher, Z340, was a 340-character message sent to the San Francisco Chronicle on November 8, 1969. It appeared to use a similar homophonic substitution system as Z408 — but nobody could crack it.

Why Z340 Resisted for So Long

Z340 wasn't just a harder version of Z408. It used a fundamentally different and more complex encryption scheme that combined multiple techniques:

Homophonic substitution (like Z408) — multiple symbols per letter, flattening frequencies.

Transposition — the order of the symbols was scrambled after substitution. This meant that even if you figured out the correct substitution mappings, reading the symbols left-to-right, top-to-bottom wouldn't produce the plaintext.

Unusual reading order — the symbols needed to be read in a specific diagonal pattern, not in the standard left-to-right rows. This was the crucial obstacle that defeated decades of analysis.

Every attack assumed the message was read in rows. Nobody considered that the reading direction itself was part of the cipher.

The 2020 Breakthrough

In December 2020, a team of three amateur cryptanalysts finally cracked Z340:

David Oranchak, an American software developer who had been working on Z340 for over 14 years. Jarl Van Eycke, a Belgian programmer who wrote custom cipher-solving software called AZdecrypt. Sam Blake, an Australian mathematician who contributed to the search algorithm.

Their approach was systematic: they programmed their software to test thousands of different reading orders (diagonal, spiral, skip patterns) combined with millions of possible homophonic substitution mappings. When the software tested a specific diagonal transposition pattern, the decrypted text scored dramatically higher on English-language statistical tests than any previous candidate.

The key insight was the transposition scheme. The 340 characters were arranged in a 17×20 grid, and the plaintext was read off in a specific two-region diagonal pattern that split the grid. Without trying that particular reading order, the correct substitution mappings were invisible.

The Decoded Z340 Message

The decoded message was characteristically taunting. The Zodiac mocked efforts to catch him and expressed a lack of fear about being identified. Like Z408, it did not reveal his identity.

The decoded message also contained deliberate misspellings and errors — whether from the Zodiac's own mistakes or intentional obfuscation is unclear. Some portions remain slightly ambiguous due to the interaction between substitution errors and the transposition scheme.

The Z13 Cipher: Still Unsolved

Alongside a letter mailed on April 20, 1970, the Zodiac included a 13-character cipher string preceded by the text "My name is—" followed by a cross-hair symbol and the 13 enciphered characters.

Why Z13 May Be Unsolvable

Thirteen characters of a homophonic substitution cipher provide almost no leverage for cryptanalysis. There are far too many possible plaintext solutions that fit the available symbols. Without additional constraints (a known cipher method, a confirmed plaintext fragment, or more ciphertext), the cipher is deeply ambiguous.

If the Z13 encodes a name, the number of possible names that fit the symbol pattern is enormous. Even if the correct substitution mappings were somehow found, verifying the solution without corroborating evidence would be nearly impossible.

The FBI and NSA have analyzed Z13 without publishing a solution. The cipher may remain permanently ambiguous — not because it's complex, but because it's too short.

The Z32 Cipher: Still Unsolved

The Zodiac's fourth cipher, Z32, consists of 32 characters embedded in a letter that accompanied a map of the San Francisco Bay Area. The letter claimed the map and cipher together would reveal the location of a bomb.

At 32 characters, Z32 has more material to work with than Z13 but still far less than the hundreds of characters typically needed for reliable homophonic substitution analysis. No accepted solution has been published.

Cryptanalysis Techniques Used

The Zodiac ciphers showcase several important cryptanalysis concepts:

Frequency analysis — counting symbol frequencies and matching them to expected English letter frequencies. This worked for Z408 (with homophonic adjustments) but failed for Z340 due to the transposition layer.

Crib dragging — guessing likely plaintext words (I, KILL, THE, BECAUSE) and testing whether they're consistent with the symbol patterns at various positions. The Hardens used this approach to crack Z408.

Hillclimbing algorithms — computer programs that start with a random substitution key, make small changes, and keep changes that improve the "English-likeness" score. Oranchak's team used this technique extensively for Z340.

Transposition analysis — testing different reading orders for the ciphertext. This was the missing piece for Z340 and required brute-forcing thousands of possible patterns.

The Citizen Codebreaking Community

The Zodiac ciphers demonstrate the power of persistent amateur analysis. The FBI and NSA — with their massive resources — couldn't crack Z340. Three independent hobbyists, working in their spare time with custom software, succeeded after decades of effort.

Online communities dedicated to the Zodiac ciphers continue to work on Z13 and Z32. Forums, Reddit threads, and dedicated websites share analysis, propose solutions, and debate methodology. Modern computing power makes it feasible for individuals to run attacks that would have been impossible even a decade ago.

For more on famous ciphers that have (and haven't) been broken, see our article on famous unsolved ciphers. To practice the techniques used to break the Zodiac ciphers, try our substitution cipher solver and cipher identifier.

Frequently Asked Questions

Did cracking Z340 reveal the Zodiac Killer's identity?

No. Like Z408, the decoded Z340 message contained taunting and boasting but no identifying information. Despite claiming his name was hidden in the ciphers, no decoded message has revealed a name.

Is the Zodiac Killer case still open?

The case remains officially open with the San Francisco Police Department and the FBI, though no new suspects have been publicly identified based on the cipher solutions. The Zodiac Killer has never been definitively identified.

What type of cipher did the Zodiac use?

The Zodiac primarily used homophonic substitution — a type of substitution cipher where common letters map to multiple different symbols. Z340 additionally used transposition (rearranging symbol order after substitution).

Could modern AI solve the remaining Zodiac ciphers?

AI could potentially help with Z32 (32 characters provides some statistical leverage). Z13 is likely too short for any analytical method — 13 characters simply doesn't constrain the solution enough. The fundamental problem isn't computing power; it's insufficient data.

How did the Zodiac create his ciphers?

Based on analysis of Z408 and Z340, the Zodiac likely created his ciphers by hand using a substitution table (possibly written on paper), then applying any transposition steps manually. Errors in both ciphers suggest hand-encoding rather than machine-assisted encryption.