The Zodiac ciphers

The ciphers are handwritten grids of letters, reversed letters, Greek-like signs and geometric symbols. Z408 is 24 rows of 17 symbols using 54 distinct symbols; Z340 is 20 rows of 17 using 63; Z13 is a single line of 13; Z32 two lines of 17 and 15, with 29 distinct symbols among its 32⁠[1]⁠[5]. Researchers work from ASCII transcriptions in which each drawn symbol is represented by one keyboard character; this project uses Oranchak's, which are the basis of the solvers' published work⁠[5].

Z408 was published in the Vallejo Times-Herald, the San Francisco Examiner and the San Francisco Chronicle in early August 1969 at the writer's demand. Z340 was published in the Chronicle on 12 and 13 November 1969⁠[1]. The originals are evidence in an open case; the FBI's released files include its 1969 cryptanalysis reports⁠[6].

Z408 decodes with a 54-symbol homophonic key into 390 letters of English with misspellings ("forrest", "anamal", "paradice") followed by 18 unread letters, EBEORIETEMETHHPITI⁠[1]. Its key rebuilt from this project's transcription is consistent except for one symbol that reads A five times and S three times, which is either an encoding slip or two drawn symbols merged in transcription.

Z340's solution has three parts. Rows 1 to 9 and rows 10 to 18 are each read by starting at the top left and stepping one row down and two columns right, wrapping at the edges; rows 19 and 20 are read in order with some words reversed. A symbol skipped on row 15 and an excluded fragment (LIFE IS) explain the garbles the solvers first met⁠[1]. The plaintext begins "I hope you are having lots of fun in trying to catch me that wasnt me on the TV show", a reference to a caller who claimed to be the Zodiac on Jim Dunbar's programme on 22 October 1969, and ends "my new life will be an easy one in paradice life is death"⁠[1]. Applying the derived key to the first nine transposed rows maps all 63 symbols with no conflicts, which this project confirmed with the data file.

Neither solved cipher names the writer. Z408 says "I will not give you my name"; Z340 continues the afterlife theme⁠[1].

Z340 was tried with the Z408 key within days, and by the FBI in a report of 18 December 1969 that found the Z408 key failed and suspected transposition⁠[1]⁠[6]. From 2006 onward, open software (ZKDecrypto, AZdecrypt) used hill-climbing on n-gram statistics to break homophonic ciphers automatically. Statistical work by the solvers' community found an excess of repeated symbol pairs at a spacing of 19, which pointed to a regular transposition. In 2020 Blake generated a batch of 655,088 transposition variants and Oranchak ran them through AZdecrypt; a (1,2)-decimation of the first nine rows produced readable fragments, which cribs then completed⁠[1].

Joachim von zur Gathen estimated the unicity distance of Z340's whole system, homophonic substitution plus sectioning, transposition and irregularities, at no more than 152 characters. Since the cipher has 340, a second readable decryption under the same system is very unlikely⁠[7].

For Z13 and Z32 no such argument exists. Thousands of plausible names fit Z13 under substitution, and Z32's 29 distinct symbols allow almost any 32-letter phrase⁠[8]⁠[1]. The last 18 letters of Z408 are in the same position: 15 of their 18 symbols are unique there⁠[1]. Published claims, such as a 2024 preprint reading Z32 as directions from Mount Diablo, have not been accepted by the cryptanalysts who solved Z340 or confirmed by investigators⁠[9].

For Z340 the competing readings were settled by the 2020 solution: earlier claimed solutions, including Gareth Penn's and Robert Graysmith's, relied on anagramming or free rearrangement and were rejected by the FBI, which says it reviewed many proposals over 51 years and found none with merit⁠[1]. The 2020 decryption is accepted because the transposition is regular, the plaintext was not forced, it refers to a datable event of October 1969, and its length is above the unicity distance⁠[1]⁠[7].

For Z13 the main readings are a name under substitution (many candidates), a non-name phrase, or a cipher with a further step like Z340's. For Z32 they are a location under substitution with the map's radian setting, a non-location taunt, or meaningless symbols. For the Z408 tail they are filler copied from above to square the third section, or a second message under another key⁠[1]. None of these can currently be tested to a conclusion.

For Z13 and Z32, the solvers name three routes: solid links between the solved ciphers' construction and the short ones; discovery that the short ciphers were copied from a source with a known solution; or the writer's worksheets. A confession or the identification of the writer by other means would also allow a candidate to be checked⁠[1]. A new statistical argument cannot overcome the length limit on its own.