Here’s a new hypothesis I am proposing: the zodiac wrote the last 18 characters of the z408 as a clue on the nature of the z340 he would send out 3 months later.

By slightly shuffling EBEORIETEMETHHPITI without adding, replacing or removing any letters, we can obtain a meaningful and error-free 3-word phrase. Only 5 letters have to be moved to obtain that phrase, which means that 13 of the 18 letters are actually already in the proper sequence. Here is that phrase:

EERIEBEHEMOTHPITTI or, with spaces: EERIE BEHEMOTH PITTI

The following diagram illustrates how this phrase can be scrambled to obtain the original EBEORIETEMETHHPITI by moving only 5 letters:

Here is another diagram that helps visualize how this phrase is so similar to the original 18 letters. 13 characters (shown in black) remain in exactly the same order; only 5 characters (shown in green) are shuffled around:

Now, what is a pitti?? Here is what I think this complete phrase could refer to:

The Palazzo Pitti, in English sometimes called the Pitti Palace, is a vast mainly Renaissance palace in Florence, Italy. It is situated on the south side of the River Arno, a short distance from the Ponte Vecchio. The core of the present palazzo dates from 1458 and was originally the town residence of Luca Pitti, an ambitious Florentine banker.
[…]
In the late 18th century, the palazzo was used as a power base by Napoleon, and later served for a brief period as the principal royal palace of the newly united Italy.

Here are some pertinent descriptions of the Pitti palace from books that would have been available at the time the z408 was written:

…severe and forbidding building…

The rusticated stonework gives the palazzo a severe and powerful atmosphere…

Here are definitions of some key words mentioned above:
eerie: Strange and frightening, mysterious
behemoth: Something enormous in size or power
forbidding: Unfriendly or threatening in appearance

Given these definitions, "eerie behemoth" can be an apt description of the Pitti palace.

This is all well and good but how can this possibly relate to the z340?

Some have hypothesized the zodiac found inspiration in the book The Codebreakers – The Story of Secret Writing, by David Kahn, to create his ciphers. In this book, there is a long section about Leon Battista Alberti. Here are some interesting excerpts:

…Alberti, a man who, perhaps better than anyone except Leonardo da Vinci, epitomizes the Renaissance ideal of the universal man.

Alberti’s three remarkable firsts – the earliest Western exposition of cryptanalysis, the invention of polyalphabetic substitution, and the invention of enciphered code – make him the Father of Western Cryptology.

And then, there is this:

As an architect, he completed the Pitti Palace…

In short, the architect who worked on the Pitti Palace is also the inventor of the polyalphabetic substitution. Hence, the hypothesis is that the z408 contains an indirect reference to polyalphabetic ciphers, presumably a hint regarding the nature of the z340.

Alberti’s polyalphabetic invention consists in a wheel with 2 concentric discs. The outer disc contains the plaintext letters, and the inner disc contains the cipher letters. The cipher is written in lower-case letters. Each time the cipher author chooses to change the alphabet (i.e. rotating the inner disc) he will write a letter in upper-case to indicate that the alphabet has now shifted (using the upper-case letter as the new reference point).

I think this basic principle could have been used in the z340. For example, the "+" symbol might be used to indicate a shift in the alphabet. The added complexity in the z340 is that if it is a polyalphabetic cipher, it would be homophonic as well.

An interesting coincidence is that Alberti’s concentric discs are split in 24 segments which means that 24 alphabets can be used in his system. The z340 has 24 "+" symbols meaning that if "+" was an alphabet-switching indicator, 24 alphabets could have been used (since the last "+" is at the very end of the cipher).

There is another amusing coincidence. Alberti’s system uses enciphered codes, numbers written in the plaintext. These numbers are indexes in a dictionary of pre-defined words where each word is associated to a number. Since Alberti’s system only allows the digits 1 to 4 and a maximum of 4 digits per number, the theoretical maximum number of entries in that dictionary is:

However, according to the book, Alberti used a minimum of 2 digits per number so the actual limit would have been 336.

If the zodiac did consult The Codebreakers book, he wouldn’t have had to look too far to find a reference to Alberti’s polyalphabetic system. Alberti’s polyalphabetic cipher disk is printed right on the title page of the book, just after the front page.

A final note regarding the last 18 symbols of the z408. While it is of course possible that it is only filler, I have some doubts about that.

I find the "pull-down" theory very compelling, but I don’t subscribe to its final conclusion. This theory demonstrates that it is statistically unlikely to be a coincidence that so many symbols in the last line of the z408 are "pulled down" from another line of the cryptogram, especially considering that a whole tetragram is copied in that manner. While this theory shows the author of the cipher likely grabbed parts of the z408 to construct the last line, to me, it does not demonstrate that the intent was to create filler.

The z408’s last line exhibits other statistical properties that make it quite unique:

• 82% of the symbols on the z408’s last line are composed of repeating n-grams. That’s 14 symbols, compared to an average of 7.1 symbols per line in all the other 23 lines.[/*:m:2fw4gw4x]
• The last line has the highest repeating n-gram count.[/*:m:2fw4gw4x]
• The last line has 4 repeating n-grams longer than 2. The average of other lines is 0.9.[/*:m:2fw4gw4x]
• The last line has 0 symbols of frequency 6 or lower. The average of all other lines is 4.4.[/*:m:2fw4gw4x][/list:u:2fw4gw4x]

What this tells me is that there probably was an intent to make the last line very stable by not using low frequency symbols and by re-using so many portions of the cipher. If the last 18 character segment is indeed meaningful but is further scrambled or enciphered, it becomes necessary to ensure its stability by using means other than relying on its underlying plaintext intrinsic textual structure to guarantee a proper intermediary decipherment which can then be used for a secondary decipherment.

_pi