The Z340 Cipher Reimagined: From 3D Surfaces to a Flattened Grid

The Zodiac’s 340 cipher is conventionally presented as a 17-column by 20-row grid. It was solved by David Oranchak, Sam Blake, and Jarl Van Eycke and the solution was announced on December 11, 2020. Their combined effort shows that the Z340 is a substitution cipher combined with a transposition that, when viewed in its solved form, can be read by following what resembles a knight’s move pattern: two characters to the right and one character down. While this reading pattern is commonly thought by many as a deliberate feature, the analysis that follows explores whether that pattern is instead an artifact of how the cipher was ultimately arranged into a rectangular grid.

When the solved cipher is examined, it appears to divide naturally into three parts: two sections that are each 17 columns by 9 rows, and a third section that is 17 columns by 2 rows.

In its conventional presentation, the first section has been previously proven to be read by starting at row 1, column 1, and following the knight-like movement through the first two diagonal paths. When the second diagonal path ends, the next readable letter is found at row 9, column 1, after which the reading resumes from row 1, column 3. This pattern continues through the section until the final diagonals, where an apparent irregularity occurs at row 1, column 18, before the reading resumes at row 2, column 2.

This description accurately reflects how the cipher must be read in its published 17×20 form, but it does not necessarily describe how the cipher was originally written. To explore this distinction, I color-coded the reading direction (in black), position changes (in blue), and apparent errors in the first section of the cipher (in red) as shown above. Several characters appearing in row 9 (in orange and purple) exhibit a distinctive pattern that later proves significant.

The second section of the cipher largely follows the same apparent reading path. However, it contains a five-letter phrase, “LIFE IS,” that remains horizontally oriented and does not participate in the diagonal transposition. This phrase does not disrupt the cipher but instead appears to be something the surrounding text was arranged around. At minimum, this suggests that “LIFE IS” was placed deliberately and treated differently from the rest of the section. As in the first section, there are clusters of characters that appear incorrect, particularly a long sequence in row 6, which becomes more suspicious due to its length and concentration.

The third section differs noticeably from the first two. It contains a mixture of forward-written and backward-written words. At the outset of this analysis, no clear explanation for this mixture was assumed. As the reconstruction progressed, however, it became increasingly plausible that the reversal of words is related to orientation rather than encryption technique, though this explanation remains incomplete on its own.

Attention then turned to the Zodiac’s envelope markings. On the face of the envelope, the phrase “PLEASE RUSH TO EDITOR” appears horizontally and consists of eighteen characters, excluding spaces. On the back of the envelope, the same phrase appears written diagonally. When the back of the envelope is visually aligned beneath the face, the offset between the two phrases loosely resembles the knight-like displacement seen in the cipher. However, this observation might not indicate a knight’s move instruction after all, but rather hint at a distinctive pattern that later proves significant.

Based on the eighteen-character length of the phrase, the cipher was re-examined using an 18-column format instead of the original 17 and then separated into the same three sections. First observable note is that the previously observed knight-like reading pattern no longer applied and that the text could now be read along straight diagonals from left to right. Working through the first section in this new format, readable diagonal text (in black) emerged without the need for a knight’s move. I offset a triangular block on the lower left side for easier readability. Characters that appeared incorrect were marked (in red), and at the ends of certain diagonals, letters were temporarily added to complete words (in blue). These added letters were placed into empty cells and marked distinctly.

              

After several diagonal passes, it became clear that the letters being added already existed elsewhere in the grid (highlighted in orange). This eight-character sequence matches the beginning of row 9 in the original 17×9 section. The remainder of that row can be seen at the base of the triangular portion on the left that had been separated earlier for clarity. This observation indicated that no letters were missing at all; instead, portions of the section in question, perhaps a triangle similar in shape to the left side, had been displaced when forced into the rectangular format.

This led to the removal of the added letters and the repositioning of the lower-right triangular block. The triangular block on the right was selected to mirror the shape of the lower-left triangle and was moved down one row and left one column, very much like the wording we see on the envelope used for mailing. This adjustment restored the section to a 17-column width and preserved diagonal readability.

            

Reworking the first section from the beginning after this move showed that the same small number of apparent errors remained, but the diagonal text now flowed continuously. At one point, the word “ME” required the letter “M,” with no empty spaces remaining. This indicated that the lower-left triangular block also needed to be repositioned. Moving it to the top-right of the section resolved the issue and completed the first section’s diagonal reading.

The same process was then applied to the second section. After adjusting the column count and repositioning the triangular blocks, the text again read diagonally without a knight-like movement. Notably, the number of apparent errors in this section remained the same as before, but their distribution changed. A previously continuous string of errors was broken apart and redistributed due to the reconfiguration, suggesting that the perceived errors are not caused by the diagonal reading itself but by how the text was forced into the grid.

After completing the second stage, seeing again the partial string of errors above that was also apparent in the original 17x9 grid, I immediately realized that it was at this point that Jarl Van Eycke had suggested years earlier to remove the H at the end of the 7-character string above and move it to just before the RA. I applied that logic and reworked the second section. The result reduced all perceived errors down to 4 as shown:

At this stage, the first two sections both took on a chevron-like appearance. These chevrons are not interpreted by me as intentional symbols but as the visible result of flattening a continuous surface that originally extended across edges or corners. The straight diagonal readability observed after these adjustments suggests that diagonal writing was the original orientation of the text.

Crucially, changing the cipher from 17 columns to 18 disrupted the knight-like reading entirely, while restoring diagonal continuity through triangular repositioning. This demonstrates that the knight’s move depends strictly on the imposed 17x20 rectangular constraint. Because the knight-like pattern is fragile and disappears when that constraint is relaxed, it is unlikely to have been an intentional writing method. Instead, it is better understood as an artifact created when a diagonally written, continuous surface was flattened and forced into a rectangular grid.

This interpretation aligns with a physical analogy such as a cigarette box.

           

A cigarette box is born from a single continuous surface before it is folded and glued into a three-dimensional object.

When flattened, text that might have originally crossed edges may appear separated, offset, or reversed. Corners would produce triangular regions, and opposite faces would appear mirrored. In this context, the chevrons produced from the first and second sections would represent orthographic projections of adjacent faces. The backward words in the third section may correspond to text that originated on an opposite or inverted face of the same continuous surface.

Under this framework, the knight’s move is not a cipher instruction but a projection artifact. The original construction likely involved diagonal writing on a continuous surface, much like the cigarette box, which was later flattened and rearranged to fit the 17x20 format. The triangular relocations performed during reconstruction are therefore not arbitrary manipulations but attempts to rejoin surface regions that were originally adjacent before being forced into a 17x20 construct.

The third part of the 340-cipher differs from the first two sections. While parts 1 and 2 are read diagonally across the chevron-shaped projections, part 3 is written horizontally and contains a mixture of forward and backward words. At the start of part 3, the word “LIFE” appears reversed, which may relate to the horizontal phrase “LIFE IS” in the second section. This suggests that part 3 represents a different surface of the same overall construction, with the backward words corresponding to a face viewed from an opposite or perpendicular angle, while the forward words correspond to faces maintaining the original orientation.

Unlike the first two sections, part 3 does not require triangle manipulations or additional adjustments to be read. Its layout follows naturally from the physical relationship of the surfaces, and the mixed directions can be seen as a projection effect rather than an intentional cipher trick. Taken together, the three parts indicate that the cipher text was written across multiple connected surfaces - either a single continuous strip or the faces of a small three-dimensional object - which was then flattened or adjusted to fit the 17x20 grid. This process created the final layout of the cipher and explains why the diagonals, chevrons, and backward words appear as they do, while also suggesting that the knights move reading was not an intentional feature but a byproduct of the grid constraint.