“Sanborn's triple matrixes: three grid stages in a row, sampled, then the tableau”
Three transposition stages instead of one or two. The space is too large to enumerate, so 200,000 triples are drawn at random from plain columnar widths 2-30, rotations, and keyed columnar from vocabulary words, each stage forward or inverse. The survival test and English scoring of experiments 6 and 16 are unchanged.
The artist said he sometimes scrambled the letters through three 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.. There are over a million ways to pick three grids from our set, too many to try with the slow English check, so we draw two hundred thousand at random. For each, we follow 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. through all three grids, ask whether a short secret word could 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. where they land, and whether the letters of that word look like English. Three grids in a row behave like a random shuffle, so the answer should look like the earlier grid experiments.
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
Three transposition stages in a row, drawn from 211 single stages (keyed column shuffles, rotations, grids), sampled 200,000 times, each followed by the table.
the scale
The best key run on the copper scores above every shuffled copper, but the shuffles were run with far fewer samples than the copper, so the comparison is unfair.
the lesson
Recorded as chance, and a rule added to the loop: every diagnostic needs at least ten shuffled controls run at full size, with the same number of trials as the copper.
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.
Pick three grids: rows of 7 read down, then a quarter turn of a 12-wide grid, then columns in the order of the letters of KRYPTOS.
Follow position 22, the E of EAST, through the first grid to its new place, then through the second, then the third.
Do this for all 24 known letters.
The carved letter at each final place, with the known letter, forces one key letter on the table.
Two final places a multiple of p apart share a key letter at period p; a disagreement kills p.
The smallest surviving p is this triple's score; write its 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.
stages: columnar 7, then rotate 12, then keyed columnar KRYPTOS; convention kry/kry/kry Vigenere
plain pos letter final place carved forced key letter
22 E 88 U D
23 A 62 F O
24 S 37 W L
64 B 26 Q F
65 E 97 R J
66 R 30 N M
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'. Experiments 6, 8, 16 and 26 covered single and double stages exhaustively for their route sets. Triples of 110 stage choices number about 1.3 million, beyond the budget with the English scoring, so this is a sample: 200,000 triples drawn uniformly, with a fixed seed, each stage one of plain columnar at widths 2-30 forward or inverse, a quarter-turn rotation at widths 2-30, or a keyed columnar from a vocabulary word forward or inverse. For each triple under the 8 distinct plain-cipher conventions the forced tableau key letters give the live periods by the divisor rule; the smallest live period is recorded, and the forced key at live periods up to 40 is scored as English on runs of five or more slots against ten shuffled controls. A triple with a live period under 20 or an English key above the controls would be a lead. Bounds: a 15 percent sample, not exhaustive; the smallest-period distribution says whether triples behave as random permutations.
6
Prediction
Written before the run; the result decides it.
The smallest live period over the sample is 22 or 23, as for single and double stages. The best forced key scores inside the range of ten shuffled controls. No candidate.
7
Method
Build the stage list.
Draw 200,000 triples with a fixed seed.
For each triple compose the three permutations and send the crib positions through.
For each of the 8 conventions force the key letters, find live periods by the divisor rule, and score the forced key at live periods up to 40.
Keep the twenty best keys and the smallest-period histogram.
Repeat on ten shuffles.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
Diagnostic, no candidates. 200000 triples x 8 conventions; smallest live period 20; best forced key -3.613 vs shuffled [-4.821, -4.937, -5.151, -4.484, -4.663, -4.922, -4.484, -4.857, -4.623, -4.478].
What was searched, as the harness recorded it.
family
three transposition stages (sampled) then periodic tableau
stages
211
triples sampled
200,000
conventions
8
keys scored
123,792
smallest live period
20
min live period histogram
20
1
23
32
24
492
25
211
26
1,001
27
1,412
28
3,483
29
1,643
30
5,053
31
3,371
32
9,537
33
8,251
best
score
-3.613
stages
keyed ABSCISSAE inv, keyed HILL, keyed VIRTUALLYINVISIBLE
convention
kry/kry/kry/beau
period
35
runs
INDERSH
score
-3.894
stages
keyed NORTH inv, rotate 11, rotate 5
convention
std/kry/kry/vig
period
39
runs
TWEREPA
score
-4.155
stages
keyed PALIMPSEST, columnar 18 inv, columnar 26
convention
kry/kry/kry/beau
period
36
runs
ORCESCO
score
-4.181
stages
keyed SHADOW inv, columnar 12, columnar 18 inv
convention
kry/kry/kry/vig
period
39
runs
DARTHTH
score
-4.251
stages
columnar 15, keyed BERLINWALL inv, keyed CARTER inv