“F6.8: three-stage routes with at least one keyword columnar stage (puzzle and K1-K3 words), the others any of the four column readings at widths 2-24, then or before a repeating key on the table”
F6.8 (pivot audit, issue #55, D6). 0037 sampled three-stage routes with keyed columnar stages (15 percent); 0083 and 0134 enumerated triples of plain readings only. Here every triple of stages in which at least one stage is a keyword columnar transposition (true key order, columns read top to bottom, 0085's reading) keyed by a puzzle word or a K1-K3 plaintext word, and the other stages are keyword stages or any of the four column readings at widths 2-24: about 24 million triples, forward and inverse, deduplicated, compiled; then a repeating key 1-26 on the standard or KRYPTOS table after or before. Ten scrambled coppers.
Sanborn spoke of double and triple matrixes, and K3the earlier messages The three solved parts of the sculpture. was moved by 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. keyed by the word KRYPTOS. Here the letters go through three grids, at least one of them keyed by a word from the puzzle or the earlier messages, the others read in any of the four plain ways, then 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., tested 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. and scrambled copies.
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
K3 was moved through a grid keyed by KRYPTOS. Here three grids in a row, at least one keyed by a word from the puzzle or the earlier messages, the others read in any of four plain ways, then the table.
the check
131 keyword grids and 92 plain ones: every triple with a keyword grid, both directions, 20,370,476 routes, each with a repeating key on the sculpture's tables, after or before.
the bound
Shortest key that fits K4: 20 after, 24 before, as on the copies; K4 leads the copies in 0 of 52 cells.
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 in rows of 7 under KRYPTOS and read the columns in the order of its letters: K, O, P, R, S, T, Y.
Write the result in rows of 11 and read the columns left to right, top to bottom.
Write that in rows of 9 and read up the columns (a quarter turn).
Note where each known letter lands; with a repeating key of length p on the table, known letters a multiple of p apart must force the same key letter.
Repeat for every word, reading and width, the key before or after, and on scrambled copies.
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.
KRYPTOS-keyed columnar (columns K O P R S T Y), then rows of 11 read down, then rows of 9 turned
place letter after 1 after 2 after 3 carved
22 E 4 28 8 O
23 A 46 14 54 L
24 S 87 89 78 K
64 B 10 82 2 B
65 E 52 68 48 Z
74 K 39 49 39 Q
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C1(a) ('double matrixes and triple matrixes', CNN 2005, knowledge/sources/cnn-2005-sanborn-interview-transcript.txt), C8(a) (KRYPTOS as K3's column key), C7(a) (K1-K3 words as keys). Keyword columnar: write in rows of len(word), number the columns by the word's letters in alphabetical order (ties left to right), read the columns in that order top to bottom. Words: 0115's puzzle list (vocabulary, K1-K3 plaintext words, theme words) of length 2-24 with at least two distinct letters. Plain readings: cw, ccw, col, colr at widths 2-24 (0134's). Periodic key: order A (after) or B (before), 8 classes, period live if no slot holds two different forced key letters. Statistic fixed before the run (0134's).
6
Prediction
Written before the run; the result decides it.
Nothing live below key length 20 beyond the coppers' rate; K4 above every copper in no more cells than the null's maximum. Zero candidates.
7
Method
Stage maps: 92 plain readings (four readings x widths 2-24) and one keyword columnar per word.
Compiled: every triple with at least one keyword stage, composed, forward and inverse, deduplicated within each first stage.
Live periods 1-26 per order, class and text; counts; the fixed statistic.
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
20,370,476 routes (223 of 223 first stages): shortest live K4 A 20, B 24 (coppers 20, 24); K4 above every copper in 0 of 52 cells, null 0-2
What was searched, as the harness recorded it.
family
three stages with at least one keyword columnar (puzzle and K1-K3 words), others plain readings at widths 2-24, then or before a periodic key