“Two and three matrix stages in mixed readings (turn either way, Sanborn's rows-then-columns-down, and its reverse), then or before a repeating key on the table”
F6.3 (mixed three-stage routes), exhaustive at small widths. 0083 closed three clockwise quarter turns at every width 2-96; 0099 two turns in mixed senses; 0037 only sampled mixed triples. Here each stage writes the text in rows of w (last row short) and reads the columns in one of four ways: left column first bottom-up (clockwise turn), right column first top-down (anticlockwise turn), left column first top-down (Sanborn's own description of a matrix code, plain columnar) or right column first bottom-up. Every ordered pair of readings at widths 2-96, and every ordered triple at widths 2-24 (the all-clockwise triples are 0083's and skipped), forward and inverse, then or before a periodic key 1-26 on the standard or KRYPTOS tables (8 classes).
Sanborn described his 'matrix codes': write the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. in rows on paper, then copy it out going down the columns; and he said he sometimes did this two or three times 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 four natural ways to copy out the columns (left or right column first, going down or up). We try every combination of two such steps at every grid width, and of three steps at widths up to 24, each followed or preceded by a repeating secret wordthe secret word The word or string a cipher needs besides the method. on the sculpture's tables, and check them 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 against scrambled copies of the carved textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page..
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
Sanborn's matrix code: write the message in rows, copy it out down the columns, sometimes twice or three times, then use the table. Four ways to copy out the columns, every pair at widths 2-96 and every triple at widths 2-24.
the check
For each of 1,762,597 routes and 8 ways of using the sculpture's tables, a key length is dead if two known letters sharing a key letter need different ones.
the bound
No route allows a key shorter than 20 on K4; the coppers manage the same. K4 is above every copper in 2 of 52 cells, a copper 0-2 against the rest.
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 on squared paper.
Copy it out column by column, left column first, top to bottom (Sanborn's matrix code).
Write that result in rows of 9 and copy it out right column first, bottom to top.
Write that in rows of 5 and copy it out left column first, bottom to top (a quarter turn).
Note where each of the 24 known letters has landed and the carved letter there.
With a repeating key of length p on the table, each known letter forces one key letter in its slot (landing place mod p); two that share a slot must agree, or p is dead.
Repeat for every combination of readings and widths, 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.
three matrix stages: rows of 7 read down the columns left first; rows of 9 read up, right first; rows of 5 read up, left first
place letter after 1 after 2 after 3 copper there
22 E 4 64 66 P
23 A 18 9 77 D
24 S 32 50 88 U
64 B 10 96 1 O
65 E 24 40 90 U
74 K 53 15 95 C
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C1(a) (Sanborn, CNN 2005, knowledge/sources/cnn-2005-sanborn-interview-transcript.txt: matrix codes are 'a very specific type of encoding system, in which you basically take a piece of paper, and you write a line of plain text out, right, in successive rows. And then basically you write it going from top to bottom instead of left to right... sometimes I used double matrixes and triple matrixes... and then went back to this table'), C2(a) (the K3 matrix and 'all the possible shifts'). Route space: stage(w, r) for w = 2-96 and r in {cw, ccw, col, colr}; doubles: 16 reading pairs x 95^2 widths; triples: 63 reading triples (all-cw excluded) x 23^3 widths 2-24; forward and inverse; duplicates removed within each worker's share (first stage), so a few cross-share duplicates count twice on K4 and coppers alike. Key: periodic tableau 1-26 after the move (slot = landing place, order A) or before (slot = message place, order B), plain and cipher alphabets standard or KRYPTOS, Vigenere/variant or Beaufort (8 distinct classes, as 0006 showed). A period is live if no two known letters in one slot force different key letters. Exact. Research note combined_methods_and_sevens.md: every public search stops at two stages. The research note's per-stage padding is F6.4, not here.
6
Prediction
Written before the run; the result decides it.
As for one, two and three clockwise turns (0008, 0083, 0099): nothing live below period 20 beyond the coppers' rate, and K4 above every copper in no more (order, period) cells than the most any single copper manages against the rest. A K4 count beyond that null stops the queue for a replication. Zero candidates.
7
Method
Compute the where-map of every stage (width 2-96, four readings).
Compose every pair, and every triple at widths 2-24, forward and inverse; skip repeats.
For each route, class and text, the key letter each known letter forces at its slot.
Period p (1-26) is live in an order if no slot holds two different forced letters.
Count live settings per period on K4 and ten scrambled coppers; compare cell by cell; list K4's live settings below 20.
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
1,762,597 routes (380 of 380 first stages) x 8 classes x 2 orders, periods 1-26. K4 settings live below 20: 0 (A), 0 (B); coppers A 0-0, B 0-1. K4 above every copper in 2 of 52 cells; null 0-2. Stop queue: False.
What was searched, as the harness recorded it.
family
two or three matrix stages (rows of w, columns read in one of four ways), then or before a periodic tableau key
readings
cw
left column first, bottom up
ccw
right first, top down
col
left first, top down
colr
right first, bottom up
doubles
16 reading pairs x widths 2-96 each
triples
63 reading triples (all-cw skipped, 0083) x widths 2-24 each