“The message written into a grid along one path and read out along another (snake, spiral, diagonal), with a repeating key before or after”
0023, 0057 and 0074 masked the message without moving letters across a grid. 0080-0083 moved them by K3's rule, quarter turns and column reading only. Here the message is written into a grid of width 2-96 along one of 30 hand paths (rows, snake rows, columns, snake columns, spirals from each corner either way, diagonals, snake diagonals, each forwards or backwards) and read out along another, 900 path pairs per width.
One way to hide the shape of English is to write the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. into a grida grid Writing the message into rows of some width and reading it out in another order, column by column for instance, which shuffles the letters without changing them. in an odd order, snaking back and forth, spiralling in from a corner, or along the diagonals, and then copy it out in another order. After that the letters go through the tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. with a short secret word. We try 30 such paths for writing and 30 for reading at every grid width, with secret words of up to 26 letters, and check each against the 24 known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK..
Words in the margin are defined on the glossary page.
1.1
The method at work
The carved letters go in at the top; the reading comes out at the bottom.
the paths
Write the message into a grid in an odd order, snaking, spiralling in from a corner or along the diagonals, then copy it out in another: 30 paths each way at every width from 2 to 96, then a short secret word on the table.
the check
After the move, known letters that fall in the same slot of the secret word must agree. No route keeps a word shorter than 21 letters alive, on the copper or on the scrambled coppers.
measured after the run
Periods 22 and 23 looked high: 47 and 405 live settings against a scrambled-copper maximum of 32 and 339. Counted as distinct sets of checks they are 13 and 88, inside the scrambled coppers' 8-15 and 74-98: look-alike routes repeat the same checks.
2
Best candidate against the known letters
This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.
3
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Write the message into rows of 10 letters, snaking: row 1 left to right, row 2 right to left, and so on.
Read it out by columns, top to bottom.
Each known letter, say E at place 22, now sits at a new place j.
With a secret word of length p after the move, the key letter at j is letter j mod p of the word; it must turn E into the carved letter at j.
Known letters landing on the same key letter must agree.
Repeat for every pair of paths, width, word length up to 26 and table rule, and with the key used before the move.
the worksheet: the first steps by hand, on squared paper
4
Worked example, generated
The same steps run by the code on the real letters.
write in snake rows of 10, read by columns: where the first known letters land
place letter grid cell (row, col) lands at copper there
22 E (3, 2) 13 B
23 A (3, 3) 23 L
24 S (3, 4) 33 S
25 T (3, 5) 43 S
64 B (7, 4) 37 W
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Type 4 of directions.md, open item 'plaintext written in boustrophedon, spiral or columns'. Scheidt: he 'masked the English language' before the keyed step (C2, C3); Sanborn: 'double matrixes... then went back to this table' (C1), visual systems (family 4). Grid of width w = 2-96 filled to 97 cells in row order, the last row short; a path is an order of its cells: rows, snake rows, columns, snake columns, spirals inward from each corner clockwise or anticlockwise, anti-diagonals and snake anti-diagonals, main diagonals, and each of these reversed (30 paths). Route: write along path X, read along path Y, X != Y; deduplicated with inverses. Key: one repeating key, period 1-26, after the move (slot = carved place mod p) or before it (slot = message place mod p), 8 consistency classes of the tableau (plain and cipher alphabets standard or KRYPTOS, Beaufort or not). Exact by slot agreement; ten shuffled coppers set the chance level per period.
6
Prediction
Written before the run; the result decides it.
No route makes a repeating key of length 20 or less consistent; at every period the count of consistent (route, class) settings on K4 lies inside the range of the ten shuffled coppers, give or take one period by chance. Zero candidates.
7
Method
For each width, build the grid's cells and the 30 paths.
For each pair of paths, compute where each message letter lands; drop repeats and inverses.
For each route and class, compute the key value forced at each known letter and test, for each period, whether known letters sharing a key slot agree, both orders.
Repeat on ten shuffled coppers.
List K4's settings consistent below period 20.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
0candidates returned
0passed every gate
0/24known letters, best
–lowest loss
nonechampion before
43,579 distinct path-pair routes (121,721 repeats skipped) x 8 classes x 2 orders, periods 1-26. K4 live below period 20: 0. Periods where K4 is outside the control range: {'A': [22, 23], 'B': []}.
What was searched, as the harness recorded it.
family
write along one of 30 grid paths, read along another, widths 2-96, then or before a periodic tableau key