“F6.20, part 1: a 10x10 turning grille (Fleissner) copied out by rows, before or after a repeating key on the table; free keys of 1-6 letters and every key word of 7 or more, every card, exact, with planted grilles in the same run”
F6.20 (issue #78), a move never tested: the turning grille. A 10x10 card with one hole in each of its 25 rotation orbits (4^25, about 10^15 cards); the message is written through the holes row by row, the card turned a quarter, four times; 97 letters leave three cells empty, skipped when the grid is copied out row by row (Fleissner's read-off). Four procedures: turned clockwise or anticlockwise, the empty cells at the end of the writing or at its start (writing and reading by columns is the transpose, the same set of moves). Then a repeating key on the standard or KRYPTOS table after the grille (A) or before it (B). Two arms, both exact over every card: any key of 1-6 letters (8 table classes), and every dictionary or puzzle word of 7 letters or more as the key (24 conventions). A depth-first search walks the top half of the grid, fixing a cell's turn and its 180-degree partner's at once and checking each known letter as it lands. Copied out by columns is a different set of moves and far costlier; it follows as part 2. The F7 standing step rides along.
A turning grillea turning grille A square card with holes cut so that, turned a quarter at a time through four positions, it uncovers every square of a grid exactly once. is a square card with holes in it. Lay it on a 10 by 10 grid and write the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. through the holes; turn the card a quarter and write on; after four turns every square holds a letter (here three stay empty, since the message has 97). Copy the grid out row by row and the letters are scrambled. We ask whether such a card, with a repeating secret wordthe secret word The word or string a cipher needs besides the method. on the sculpture's tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS., could have made K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.. There are a thousand million million cards, too many to try one by one, but the known words rule most of them out a few squares in, so a careful search can check every card.
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 idea
A turning grille: a card with 25 holes laid on a 10 x 10 grid, the message written through the holes, the card turned a quarter four times, the grid copied out row by row. Then, or first, a repeating key on the sculpture's table.
the check
Every one of the 4^25 cards, by a search that drops a card as soon as two known letters disagree: any key of 1-6 letters, and each of 200,563 words as the key, on K4, ten scrambled copies and four planted texts.
the bound
No card fits K4 or any copy; every planted card is found. Free keys of 7-26 letters cost too much to settle (blocked); copying out by columns is 0200.
2
Experiment lineage
What this experiment was built on, from the lineage page: 7 experiments before it, back to the root of its line. Its number is in bold.
keptreverted, in its family's colour×error or timeoutreverted under today's rulesbuilt on a parent in the same familybuilt on a parent in another family
3
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 under Result and bounds below.
4
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Cut 25 holes in a 10 by 10 card so that turning it four times uncovers every square once.
Lay it on the grid and write the first 25 letters through the holes, row by row.
Turn the card a quarter clockwise and write the next 25; and twice more. The last three holes stay empty.
Copy the grid out row by row, skipping the empty squares: 97 letters.
Encipher those 97 on the table with a repeating key word (or encipher first, then use the card).
To test a card against K4: follow each known letter to its square, read the carved letter there, and see whether the key letters it demands repeat with the key's length or spell the key word.
the worksheet: the first steps by hand, on squared paper
5
Worked example, generated
The same steps run by the code on the real letters.
a card: the turn on which each square is written (0-3), clockwise, copied out by rows
1 0 3 2 1 2 3 0 1 2
0 3 2 1 0 1 2 3 0 1
3 2 1 0 3 0 1 2 3 0
2 1 0 3 2 3 0 1 2 3
1 0 3 2 1 2 3 0 1 2
0 3 2 1 0 3 0 1 2 3
1 0 3 2 1 0 1 2 3 0
2 1 0 3 2 1 2 3 0 1
3 2 1 0 3 2 3 0 1 2
0 3 2 1 0 3 0 1 2 3
the holes of the first position are the 0s; the 97 letters fill the 0s row by row, then the 1s, 2s, 3s;
the last three 3s stay empty
place known lands at carved
22 E 88 U
26 N 1 O
34 T 32 K
64 B 53 K
74 K 92 U
6
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C1(a) (a matrix stage, then the table), C3 (Sanborn's 'spatial systems... pattern, light and shadow': a grille is a card held to the light), C5 (a hand system keyed by 'key word/s'). Source: reports/agent-memorized-hand-ciphers.md (Fleissner 1881; German army 1916; Abwehr and RS44 stencils, Lewis, German Agent Systems). Model: c = T(sigma(p)) (order A) or sigma(T(p)) (order B), sigma the grille's permutation, T a periodic tableau key. Search: the top half of the grid in row order; a cell's rank in its turn is the count of earlier top cells of that turn, its 180-degree partner (turn + 2) has rank 24 minus that count, so both message places are known at once. Free key: each slot's value is set by its first known letter and checked by the rest; key words: every letter is a check (24 checks against about 50 bits of card). Count: distinct landing maps (the carved squares of the 24 known letters), since cards that differ only where unknown letters go are one reading of the known ones. Statistic fixed before the run: free key, per procedure and order, the shortest length with a landing map that fits and the cells (order, length) where K4's count exceeds every copy's; key words, the number of (word, convention, order, procedure) settings with a map, K4 against each copy. Measured cost: a free key of 7 letters takes 10^8-10^9 nodes per setting, 12 letters over 2 x 10^9: lengths 7-26 with a free key are blocked by cost. Not tested: stencils with arbitrary holes, the Abwehr's 13x19 card (no remembered rule for its holes in the source).
7
Prediction
Written before the run; the result decides it.
No card fits K4 with any key of 1-6 letters or any key word, in either order and any procedure; the scrambled copies the same. Each planted grille is found, on its own landing map. The grille plus a key makes the two fingerprints together at the random-letter rate (zero in 2,000). Zero candidates.
8
Method
Orbits: the 25 cells of the top-left quarter; a card is one turn (0-3) per orbit.
Walk the top half in row order; at a cell whose orbit is new, branch over its four turns; place the message letter there (turn, rank) and at the 180-degree partner (turn + 2, rank 24 minus).
Mark the three empty cells (last three of turn 3, or first three of turn 0); a carved place is the row position less the empty cells before it.
Each known letter landed: key slot = carved place (A) or message place (B) mod the length; free key: set or check the slot; key word: compare with the word's letter. Prune on a clash; stop a branch once all 24 landed.
Every procedure, order, class and length 1-6, then every key word on 24 conventions, on K4, ten copies and four plants; compiled, checked against a literal Python builder on 25,600 cards and 32 plants.
9
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
Plants: free key cw, out by rows, empty cells at the start A: found True; free key ccw, out by rows, empty cells at the end B: found True; key word ccw, out by rows, empty cells at the start B: found True; key word cw, out by rows, empty cells at the end A: found True. Free keys 1-6: K4 fits 0 settings; K4 above every copy in 0 cells, copies 0-0. Key words (200,563): settings with a card K4 0, copies 0-0.
What was searched, as the harness recorded it.
family
10x10 turning grille (25 holes, three empty cells), then or before a repeating key on the standard/KRYPTOS tables; exact constraint search
cards per procedure
1,125,899,906,842,624
procedures
cw, out by rows, empty cells at the end, cw, out by rows, empty cells at the start, ccw, out by rows, empty cells at the end, ccw, out by rows, empty cells at the start