THE MECHANICS OF THE Z38 CODE

On December 7th 1969 the Zodiac Killer mailed a letter and code from Fairfield just hours before he phoned the Oklahoma radio station KTOK, both times imitating the caller to the Jim Dunbar TV show on October 22nd 1969. The person who mailed the letter provided crucial information in the Z38 code that showed intrinsic knowledge regarding the mechanics of the 340 cipher and its use of the knight's move in chess. In other words, the person who mailed the December 7th 1969 letter knew how to solve the 340 cipher. They knew this because they were the Zodiac Killer. The following will show how I arrived at the plausible solution of  "TRYING TIMES. SO I NEED APPOINTMENT TO GET HELP". 

Bearing in mind that the phone call to Oklahoma and the letter mailed on December 7th 1969 to the San Francisco Chronicle, were both continuing the theme of the Jim Dunbar TV show and Melvin Belli fiasco, in which the hoax caller was pleading for help, there is a strong probability that the Z38 code may contain a message along the same lines. If it did, it would almost certainly have been something the Zodiac Killer read in the newspapers on this topic, such as the article in the Los Angeles Times newspaper on October 23rd 1969, the day after the television show.
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In the 340 cipher message, decoded by David Oranchak, Sam Blake and Jarl Van Eycke on December 5th 2020, the Zodiac Killer used the headlines from the San Francisco Chronicle newspaper on October 24th 1969, which was titled over two pages, reading both "That Wasn't Zodiac, Say 3 Who Know" and "It Wasn't Zodiac, Say 3 Who Know". In his 340 message he stated "That Wasn't Me on the TV Show". The numerous references in the newspapers immediately after October 22nd 1969 about the caller saying "I don't want to go to the gas chamber", was replied to by Zodiac, who encoded "I am not afraid of the gas chamber". The Zodiac Killer would emphasize these two points in the first seven lines of the deciphered message.   ​

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The news was abound with the failed meeting between the "Zodiac Killer" (Sam) and Melvin Belli at the Vincent de Paul thrift store in Daly City, later that day. The Los Angeles Times newspaper on October 23rd 1969 read "Attorney Melvin Belli in a phone booth at a San Francisco television station talking to caller who said he was the Zodiac Killer. Caller made an appointment but didn't keep it". This was the sort of the thing the Zodiac Killer may have mocked, after writing "I just need help" on December 7th 1969. There were two plus signs (+) together in the Z38 code, so I knew they had to represent the same plaintext letter, and gambled on the word "appointment". This would not only fill up a significant portion of the Z38 code, but would mean that the code ended with the plaintext letter "P". That was likely the last letter of "help", which also featured prominently in the Los Angeles Times newspaper and others. In fact, the title of the article was "I Want Help, Zodiac Caller Tells Attorney on Telephone". After placing "appointment" and "help" in the Z38 code, it allows us to form the word "to" immediately after "appointment" because of the double character (dotted circles). The phrase "appointment to get help" was then easy to work out. 

THE "H" AND "+" CIPHERTEXT CHARACTERS BEGIN THE 340 CIPHER AFTER THE PERIOD 19 SHIFT (KNIGHT'S MOVE)

The first 18 ciphertext characters could then be filled in somewhat, with the dotted circle represented by the plaintext letter "T",  the circle with the single vertical line through it represented by the plaintext letter "I", the plain circle ​represented by the plaintext letter "E", the square represented by the plaintext letter "G", the triangle represented by the plaintext letter "O", and the slanted line​ represented by the plaintext letter "N". We were left with this.

The plaintext letters in blue on the top line looked like it could spell "times", followed by the word "so", thereby satisfying the double "L" ciphertext. So I took a gamble and placed the words into the message like so. 

The rest was pretty simple. After the word "so" I added the personal pronoun of "I", and "need" was the obvious next choice. The final part was filling in the blanks for the starting five plaintext letters ending in "G". Trying times" is a well-known phrase that one might experience, and necessitates the need for an "appointment to get help". This completed the Z38 code. Whether it is the correct solution I can't say for certain, but it satisfies the workings of a substitution cipher and has relevance to the contemporary events the Zodiac Killer was reading in the newspapers at the time, just like the message in the 340 cipher.

THE DECEMBER 7TH 1969 "FAIRFIELD" LETTER AND Z38 CODE

THE Z38 KEY

In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key, there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key completely, assuming the underlying message has redundancy. For a simple substitution cipher, the number of possible keys is 26! = 4.0329 × 1026 = 288.4, the number of ways in which the alphabet can be permuted. Assuming all keys are equally likely, H(k) = log2(26!) = 88.4 bits. For English text D = 3.2, thus U = 88.4/3.2 = 28. So given 28 characters of ciphertext it should be theoretically possible to work out an English plaintext and hence the key. Wikipedia. 

• Simple Monoalphabetic Substitution Cipher: The theoretical unicity distance is about 28 characters. In practice, cryptanalysts typically need around 50 characters to perform reliable frequency analysis and achieve a definite solve.

FURTHER READING: "IRON" AND "DEATH" FEATURED IN TWO CIPHERS