“F6.14: the Nihilist transposition on a 10 x 10 square with three blank cells, one key of every order for rows and columns, then or before a repeating key on the table”
F6.14. The Nihilist transposition writes the text into a full square and reorders its rows and its columns by one key, then reads it off by rows (or by columns). 97 is prime, so the square is 10 x 10 with three blank cells, placed at each of F6.4's eight spots (end or start of the first or last row, top or bottom of the first or last column). Every one of the 10! = 3,628,800 key orders, both readings, forward and inverse: 116 million routes, compiled (the route builder checked against Python on 200 random settings), then a repeating key 1-26 on the standard or KRYPTOS table after or before. Ten scrambled coppers.
Write the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. into a 10 by 10 square (three squares left empty, since 97 is three short of 100), then rearrange the rows and the columns in the same order, given by a key, and copy the square out. We try every possible order of the ten rows and columns, every place for the empty squares and both ways of copying out, each 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., 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
The Nihilist transposition writes the text into a full square and reorders its rows and columns by one key. 97 is three short of 100, so a 10 by 10 square with three empty squares.
the check
Every one of the 10! orders, eight places for the empty squares, read by rows or by columns, both directions: 116,121,600 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 (copies 18, 17); 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 97 letters into a 10 x 10 square row by row, leaving the last three squares empty.
Take a key order of the ten rows and columns, say 3 7 0 9 1 5 2 8 4 6: row 3 becomes the first row, row 7 the second, and the columns likewise.
Copy the square out row by row, skipping the empty squares.
Note where each known letter lands; with a repeating key of length p on the table, two known letters landing a multiple of p apart must force the same key letter.
Repeat for every order, place of the empty squares and reading, 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.
10 x 10 square, last three cells empty; rows and columns reordered 3 7 0 9 1 5 2 8 4 6; read by rows
place letter square cell new cell lands at carved
22 E (2,1) (6,4) 62 F
23 A (2,2) (6,6) 64 N
24 S (2,3) (6,0) 58 A
64 B (6,3) (9,0) 88 U
65 E (6,4) (9,8) 96 A
74 K (7,3) (1,0) 11 U
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C1(a) ('matrix code'), C17(b) (padding); source: reports/Scheidt patents and field ciphers.md and foreign_agent_hand_systems.md (ACA's Nihilist transposition: one key for rows and columns of a complete square; attribution to Russian Nihilists doubtful). Model: cell (r, c) of message place i (row-wise, blanks skipped) moves to (pi^-1(r), pi^-1(c)); read row-wise (or column-wise) skipping blanks. Periodic key: order A or B, 8 classes, a period live if no slot holds two different forced letters; 0134's statistic.
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
Compile the builder and the periodic-key test; check the builder against Python.
For each blank place and each first key element (80 jobs): every remaining order (Heap's algorithm), both readings, forward and inverse.
Counts per order, period and text; 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
116,121,600 routes (80 of 80 jobs): shortest live K4 A 20 B 24 (coppers 18, 17); K4 above every copper in 0 of 52 cells, null 0-5
What was searched, as the harness recorded it.
family
Nihilist transposition, 10 x 10 square, three blanks at eight places, one key of every order for rows and columns, read by rows or columns, then or before a periodic key