“Two keyed columnar transpositions from the puzzle's words, then the tableau”
Route set: every ordered pair of vocabulary words as two keyed columnar transpositions, each forward or inverse, instead of plain widths. Sanborn's 'double matrixes' with the matrices keyed by words.
The artist said he sometimes scrambled the letters through two grids before using 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.. The third messagethe earlier messages The three solved parts of the sculpture. was scrambled through 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. whose columns were ordered by a key wordthe secret word The word or string a cipher needs besides the method.. So we try two such grids in a row, each ordered by a word the puzzle knows, in every combination, and ask the usual question: where do 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. land, and could a short secret word on the table then produce the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. there?
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 routes
The message is written in rows, its columns shuffled by one puzzle word, and again by a second, then enciphered on the table with a repeating key: 15,376 routes.
the histogram
For each route, the shortest key length the known letters allow. The floor is 23, lower than with one shuffle, but the key fragments there read as noise.
the scale
The best key run on the copper scores below the best on one of the ten shuffled coppers. Double shuffles of this kind are chance.
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.
Take the words KRYPTOS and ABSCISSA.
Write the message in rows of 7 under KRYPTOS, number the columns by alphabetical order of the letters (K=1, O=2, P=3, R=4, S=5, T=6, Y=7), and read the columns out in that order.
Write the result in rows of 8 under ABSCISSA and read it out the same way.
The E at position 22 of the message is now at some position j; the carved letter at j and E force a key letter on the sculpture's table.
Do this for all 24 known letters.
Two landing spots a multiple of p apart share a key letter at period p; a disagreement kills p.
For the periods that survive, write the forced letters into their slots and read them.
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.
route: keyed columnar KRYPTOS then keyed columnar ABSCISSA; convention kry/kry/kry Vigenere
column order under KRYPTOS: [0, 3, 6, 2, 5, 1, 4]; under ABSCISSA: [0, 1, 4, 2, 3]
plain pos letter lands at carved forced key letter
22 E 79 Z H
23 A 74 K N
24 S 49 W L
25 T 63 B T
64 B 42 Q F
65 E 94 K I
66 R 11 U Q
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Sanborn, CNN 2005 (C1): 'double matrixes and triple matrixes... then went back to this table'. The NSA's K3 reading was a keyed columnar with key KRYPTOS; 0006 and 0016 used plain widths and single vocabulary keys. Here both stages are keyed by words from the vocabulary (C7 reading a, C8): 61 x 61 ordered pairs x 4 direction combinations, 14,884 routes, each followed by a periodic tableau under 24 conventions. For each route the cribs land at known positions, the divisor rule gives the live periods, and for live periods up to 40 the forced key is scored as English on runs of five or more slots, with vocabulary matching and ten shuffled controls. Bounds: complete for this route set.
6
Prediction
Written before the run; the result decides it.
No route lets the cribs force a tableau key shorter than 22, and the forced keys at periods up to 40 score inside the range of ten shuffled controls. No vocabulary match; zero candidates pass.
7
Method
Build the routes from ordered pairs of vocabulary words, each stage forward or inverse.
For each route send the crib positions to their intermediate positions.
For each convention force the key letters and find live periods by the divisor rule.
Score the forced key at live periods up to 40 on runs of five or more slots; match against the vocabulary.
Repeat on ten shuffles.
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
Diagnostic, no candidates. 15376 routes; smallest live period 23; best forced key -3.797 vs shuffled [-4.315, -4.088, -4.057, -4.118, -3.819, -3.579, -3.993, -4.23, -3.713, -4.077].
What was searched, as the harness recorded it.
family
double keyed columnar (vocabulary words) then periodic tableau