“Column shuffles keyed by the puzzle's words, read the right way round this time: once or twice, with a repeating key or an autokey”
Issue #26: ten records (0006-0081) passed a keyword's rank list as the reading sequence, so their keyed column shuffles read the columns in the inverse order. This reruns keyed columnar with the true keyword reading (columns in the alphabetical order of the key letters), with repeated letters dropped and on the whole word with ties left to right, once (both directions) or twice (every ordered pair), against a repeating key of length 1-26 before or after, and against the plaintext and ciphertext autokeys at every lag in both orders.
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. keyed by a word writes the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. in rows under the word and reads the columns in the alphabetical order of its letters. Our earlier experiments made a slip: they read the columns in a related but different order, so the true keyed shuffles were never tested. This experiment repeats the tests with the right order: every puzzle word as the keythe secret word The word or string a cipher needs besides the method., used once or twice, followed or preceded by a repeating secret worda repeating secret word A secret word written under the message again and again. on 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., or by an autokeyan autokey cipher A cipher that uses the message itself, or the scrambled text itself, as the secret word, each letter enciphered with the letter a fixed distance before it., where the message feeds its own key.
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 slip
A keyword shuffle reads the columns in the alphabetical order of the key's letters. Ten earlier experiments read them in the order of the ranks themselves, a different shuffle (issue #26).
the rerun
Every puzzle word as the key, once or twice (40,771 shuffles), read the right way, with a repeating secret word or an autokey on either side.
the bound
Nothing fits beyond what scrambled coppers show, so the earlier conclusions stand for both readings.
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. The key letters rank K 0, R 3, Y 6, P 2, T 5, O 1, S 4.
Read the columns in rank order: column 0 (K), then 5 (O), 3 (P), 1 (R), 6 (S), 4 (T), 2 (Y). The earlier records read 0, 3, 6, 2, 5, 1, 4 instead, the ranks themselves.
Place 23, the A of EAST, is in row 3 of column 1. Columns 0, 5 and 3 hold 14 letters each, so it becomes letter 46; the earlier reading put it at 73.
Under a repeating key on the table, the known letter and the copper letter at its new place force one key letter; two known letters whose new places differ by a multiple of the key length must force the same one.
Under an autokey, two known letters one lag apart are tied through the copper letters between them.
Repeat for every word key, once or twice, every key length and lag, both orders, 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.
KRYPTOS as a column key: K R Y P T O S ranks 0 3 6 2 5 1 4, so the columns are read 0 5 3 1 6 4 2
(the earlier records read 0 3 6 2 5 1 4, the ranks themselves)
place letter column lands at (true) lands at (earlier)
22 E 0 4 4
23 A 1 46 73
24 S 2 87 45
25 T 3 32 18
64 B 0 10 10
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Correction run for issue #26, filed during type 2 of directions.md. The bounds it restores: keyed columnar then tableau (0006, 0016), tableau then keyed columnar (0007, 0058), keyed double columnar (0026), keyed columnar with ciphertext autokey (0063), and the keyed-columnar subsets of 0080 and 0081. Clues C1(a) (02-sanborn-said.md, CNN 2005, 'double matrixes'), C8(a) (KRYPTOS as a transposition key for K4, as the NSA read it for K3), C7(a) (K1-K3 words as keys). Key words: data/vocabulary.txt, the K1-K3 plaintext words of 3-20 letters, and the C13/C14 words; each gives up to two sequences (repeats dropped, as kryptos.alphabets.numeric_order does; or the whole word with ties left to right), deduplicated. Routes: each sequence once, columnar encryption or its inverse; every ordered pair of sequences, encryption twice. Keys: (i) periodic tableau key 1-26 after the move (slot = landing place mod p) or before it (slot = place mod p), 8 classes, live if no slot holds two different forced letters; (ii) plaintext autokey and (iii) ciphertext autokey at lags 1-96, one alphabet throughout (standard or KRYPTOS), three modes, autokey after the move (order A) or before it (order B), checked exactly as in 0081. Ten shuffled coppers through the identical search.
6
Prediction
Written before the run; the result decides it.
As for the inverse readings: nothing live below period 22 for the repeating key beyond the shuffled-copper rate; no autokey setting passes five checks; counts at every level inside the control range, give or take the spread at the lowest levels. Zero candidates.
7
Method
Build the keyword sequences and the single and double routes; skip repeats.
For each route, test a repeating key of length 1-26 on either side by the forced-letter slots.
For each route, test the plaintext and ciphertext autokeys at every lag on either side by walking the chains between known letters.
Count survivors by period or number of checks on K4 and ten shuffled coppers.
List K4's survivors below period 20 or with four or more checks.
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
40,771 distinct routes from 201 keyword sequences. Periodic: 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]}; periods outside the control range {'A': [], 'B': [26]}. Autokey: ptak order A: K4 >=1..6 [114744, 4018, 135, 3, 0, 0], controls max [118127, 4110, 149, 12, 1, 0]; ptak order B: K4 >=1..6 [31166, 585, 37, 0, 0, 0], controls max [32560, 695, 63, 2, 1, 0]; ctak order A: K4 >=1..6 [31451, 1132, 50, 0, 0, 0], controls max [37509, 2109, 76, 4, 1, 0]; ctak order B: K4 >=1..6 [9627, 369, 11, 0, 0, 0], controls max [10091, 446, 23, 4, 0, 0]. Outside: ['ctak A: [2]', 'ctak B: [3]']. K4 autokey settings with 4+ checks: 3.
What was searched, as the harness recorded it.
family
true keyword columnar (issue #26), once or twice, with a periodic key 1-26 or plaintext/ciphertext autokey, both orders