The 340 cipher was the second cipher mailed on November 8th 1969, and the 13-Symbol cipher was the third cipher mailed on April 20th 1970, separated by just over five months. The Zodiac would refer to his 340 cipher at the beginning of the April 20th letter, stating "This is the Zodiac speaking. By the way have you cracked the last cipher I sent you. My name is...." This could be a simple clue leading into his new cipher, however, the author of the letter was highly unlikely to offer his real name. In addition, it is simply too short a code to be verifiable - and the Zodiac Killer must surely have known this if he had any rudimentary knowledge of code breaking. But with a clue or key affixed to the 13-Symbol code, then we may have a chance.
Up to this point in time, we only knew the murderer by the pseudonym Zodiac, so let us complete the introduction on the April 20th 1970 letter to "This is the Zodiac speaking. By the way have you cracked the last cipher I sent you. My name is Zodiac". However, this sounds a little flawed, so it is imperative we replace Zodiac with an alternative - something possibly embedded within the name of Zodiac itself.
The 340 cipher has been entered into every powerful computer known to man with no solution being found, leading many people to believe it has no solution at all and is just total gibberish. I don't know about the entirety of the 340 cipher, but the twentieth and final line of the cipher does contain perfect symmetry in six of the final eight characters. In addition, eight of the final nine characters are effectively carried forward from the 340 cipher to the 13-Symbol cipher, linking cipher two and cipher three together. In the 13-Symbol cipher he did refer to "My name is..", so we will look for his pseudonym in the 340 cipher and take this as the clue.
We already know that six symbols on the twentieth line of the 340 cipher look very similar to his pseudonym Zodiac, but was this unintentional or deliberate? To find this out we shall look at the symmetry of both ciphers. The 13-Symbol cipher from a character standpoint is extremely organized. It starts and ends with three alphabetical characters. The three circled 8's are symmetrically placed in positions 5, 7 and 9 of the code. The Zodiac symbol and 'upside down Aries' symbol are four in from either side. Either the Zodiac just happened upon this symmetry, or he designed it for purpose. Bearing this symmetry in mind, we will look for a symmetrical answer in both the 340 cipher and 13-Symbol cipher - and in addition - symmetry between the two.
The Zodiac Killer was undoubtedly an egotist, so it wouldn't be all that surprising if he used his own pseudonym in the clue, and embedded the answer within the name Zodiac itself. In the following examination I will be using the identical mathematical technique on both the 340 cipher and 13-Symbol cipher, to show perfect symmetry in both instances. It was this egotism that led me to believe the clue resided in the 'near' Zodiac on the twentieth line of the 340 cipher. So using a comparison technique, I placed the proper spelling of Zodiac under the 'near' Zodiac and simply counted the numerical alphabetical difference in the columns. But first let us take a look at the 13-Symbol cipher and note the bottom two lines in the diagram below.
Because of not only the existing symmetry within this cipher, but the fact it was thirteen characters in length, began with an A and ended with an M, along with Zodiac's penchant for word games, it seemed the obvious choice to place the first 13 letters of the alphabet under the cipher.
A to A = 0, B to E = 3, C to N = 11, F to K = 5, H to M = 5, K to N = 3, A to L = 11.
The above is achieved by staying within the alphabet and counting the numerical distance between the letters. Obviously, when we do not have two alphabetical characters there can be no difference, so a zero is attributed. You could attribute an X, but it actually makes no difference to the resulting symmetry.
How do we know if this is the technique that Zodiac employed? If we apply this technique to the 'near' Zodiac on the twentieth line of the 340 cipher using the correct spelling of Zodiac and it again produces perfect symmetry, then we have possibly bolstered our case. If, in addition, it produces something significant that relates to the 13-Symbol cipher, does it then become even more compelling? The most obvious choice this time is to place Zodiac underneath the six symbols on the twentieth line, like so:
Z to Z = 0, O to O = 0, D to triangle = 0, I to A = 8, A to I = 8, C to K = 8.
That is three 0's and three 8's, carried forward to the 13-Symbol cipher on April 20th 1970. But that is not all.
Either side of the 'near' Zodiac on the twentieth line of the 340 cipher we have the crosshairs and an 'inverted Aries' in part.
Both of which are situated on the 13-Symbol cipher, either side of the circled 8's (shown in the red rectangular boxes above).
This means that eight characters out of the last nine were effectively carried forward from the 340 cipher to the 13-Symbol cipher. It could be argued that the last eight characters of the 340 cipher were carried forward using the plus sign (+) at the end of the 340 cipher, signifying their addition to the 13-Symbol cipher.
Zodiac is now represented by the three circled 8's. 'In Christian numerology, the number 888 represents Jesus, or sometimes more specifically Christ the Redeemer. This representation may be justified either through gematria, by counting the letter values of the Greek transliteration of Jesus' name, or as an opposing value to 666, the number of the beast.' Wikipedia. This may be important when we consider the Zodiac's tendency to speak of "paradise" and the "afterlife" in many of his communications - in particular his 408 cipher. He would also cross "paradice" and "slaves" in the form of a crucifix on the Halloween card, as well as pasting a red crucifix on the 13-Hole postcard.
You can see in the above diagram that the letters K and M are embedded within the three 8's and therefore embedded in the name Zodiac. Were these his initials, and was he elevating himself to divine status? He certainly had the ego for it.
# There are some additional features of interest:
The 408 cipher was divided up into three sections of 8 lines and mailed to three different newspapers.
The final line of the 408 cipher contains an M and reversed K.
The final line of the 340 cipher contains an M and reversed K.
The 13-Symbol cipher contains the letter M and K.
The final character at the end of each of the three communications of the 408 cipher is either an M or reversed K.
The top line of the 32-Symbol cipher mailed on June 26th 1970 contains an M and reversed K.