“Two column shuffles, one of them seven columns wide in any of its 5,040 orders, with a repeating key before or after”
The public double-columnar searches stop at widths 2-6 or skip every pair with a 7 (Zekios, KryptosBot), and keithadler lists keyed double columnar as unsearched. Here one stage is a width-7 column shuffle in every one of its 5,040 orders and the other is a plain column shuffle at widths 2-30 or a column shuffle keyed by a puzzle word (repeated letters dropped, or kept with ties read left to right), in either order, with the exact crib test for a repeating key of length 1-26 on either side.
A column shufflea column shuffle Writing the text in rows under a key word and reading the columns in the alphabetical order of the key's letters. writes the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. in rows under a key and reads the columns out in the keythe secret word The word or string a cipher needs besides the method.'s order. Doing it twice with two keys is the classic double transposition. Five of K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.'s six doubled lettersthe doublets Places where a carved letter is immediately followed by the same letter. line up in one column when it is written in rows of seven, and the sculpture's name has seven letters, so one of the two shuffles may well be seven columns wide. Nobody has tried that combination in full. We take every possible order of seven columns, pair it with a second shuffle from the puzzle's wordsthe puzzle's words A list of 62 words tied to the sculpture: the earlier secret words, place names, the names of the people involved, the words in the Morse code, and the themes Sanborn has named. or a plain one, and ask whether a repeating secret worda repeating secret word A secret word written under the message again and again. on the table could then give the copper's known letters.
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 shuffle
A column shuffle writes the message in rows under a key and reads the columns in the key's alphabetical order. Done twice, with one key seven letters long, it is the double transposition nobody had run with a 7.
the check
After both shuffles, a repeating secret word on the table must give the copper's letters where the known letters landed; two known letters in one slot of the word must agree.
the bound
All 5,040 orders of seven columns with 253 second shuffles, either first: no word of 1 to 20 letters fits, and 21-26 fit as often as on scrambled coppers.
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. Read the columns in the alphabetical order of the key letters, K O P R S T Y, which is columns 0, 5, 3, 1, 6, 4,
Place 22, the E of EAST, is in row 3 of column 0, the column read first, so it becomes letter 4.
Write that text in rows of 5 under ABSCI (ABSCISSA with its repeated letters dropped) and read columns A B C I S, that is 0, 1, 3, 4, 2. Letter 4 is in row 0, column 3; columns 0 and 1 hold 20 letters each, so it becomes letter 41.
The copper at 41 is J: a repeating key on the table must turn E into J there. Work out that key letter for all 24 known letters.
For a key of length p, two known letters whose landing places differ by a multiple of p share a key letter; if they need different ones, p is dead.
Repeat for all 5,040 orders of seven columns, every second shuffle, both stage orders, the key before or after, and ten scrambled coppers.
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.
first shuffle: rows of 7 under KRYPTOS, columns read K O P R S T Y (sequence 0 5 3 1 6 4 2);
second shuffle: rows of 5 under ABSCI (ABSCISSA, repeats dropped), columns read A B C I S (0 1 3 4 2)
place letter column after KRYPTOS after ABSCISSA copper there
22 E 0 4 41 J
23 A 1 46 10 H
24 S 2 87 38 T
64 B 0 10 61 N
65 E 1 52 31 G
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Type 2 of directions.md, the first open item of the prior-work database's seven-based gaps ('keyed double columnar transposition with one width of 7... KryptosBot's double-columnar run skipped every pair involving 5 or 7, its register marks width 9 x width 7 NOT covered, Zekios stopped at 6 x 6, keithadler lists keyed double columnar as unsearched'). Evidence: the width-7 doublet column (0056; about p 0.02 after conditioning on six doublets, prior-work report) and KRYPTOS's seven letters (C8(a): KRYPTOS as a transposition key for K4, as for K3); C1(a) 'double matrixes'. Route: columnar encryption (write rows, read columns in sequence) twice, one stage of width 7 in all 5,040 reading sequences, the other a plain sequence at widths 2-30 read left-to-right or right-to-left (58) or a keyword sequence from data/vocabulary.txt, K1-K3 words of 3-20 letters and the C13/C14 words, read as true keywords (columns in alphabetical order of the key letters; issue #26 found 0006-0081 read the rank list as the sequence), once with repeated letters dropped and once on the whole word with ties left to right, deduplicated; the width-7 stage first or second. Key: periodic tableau key of period 1-26 after the moves (slot = landing place mod p) or before them (slot = place mod p), 8 classes of plain and cipher alphabet and Beaufort-or-not; live if no slot holds two different forced letters. Exact; ten shuffled coppers through the identical search. Left open: both stages with free orders above width 7 (9 x 7 has 1.8 billion pairs), autokey keys with these routes.
6
Prediction
Written before the run; the result decides it.
No setting is live below period 20 beyond the rate on the shuffled coppers, and the count of live settings at each period 1-26 lies inside the control range, give or take the spread at 24-26. Zero candidates.
7
Method
List the 5,040 reading sequences of seven columns and the second-stage sequences (plain 2-30, word keys both ways).
For each pair and each stage order, compose the two moves and skip repeats.
For each route, class and text, compute the key letter each known letter forces at its landing place.
For each period 1-26 and each key order, the period is live if no slot holds two different forced letters.
Count live settings per period on K4 and ten shuffled coppers.
List K4's live settings below period 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
2,548,223 distinct double-columnar routes (253 of 253 second stages x 5,040 x 2 stage orders; 2,017 repeats) x 8 classes x 2 key orders, periods 1-26. K4 live below 20: 0; controls: {'A': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'B': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]}. Outside the control range: {'A': [21], 'B': [24]}.
What was searched, as the harness recorded it.
family
double columnar, one stage width 7 in all 5,040 orders, the other plain 2-30 or word-keyed; periodic key 1-26 before or after