“F13.4b: a periodic key on 2.08 million dictionary keyword tables, key lengths 1-26, from the ciphertext alone: an exact per-column frequency screen of every table, then quadgram climbs and MIX8m on the best 50 per length”

1. Build a table from a word, say HYDRAULIC: HYDRAULICBEFGJKMNOPQSTVWXZ.
2. Guess a key length and write the carved letters in that many columns.
3. For each column, try all 26 shifts and keep the one whose letters are most like English (many E, T, A; few Q, Z).
4. Do this for every word in the dictionary and keep the 50 tables that look best.
5. For those, improve the shifts by how well the whole text reads, and compare K4's best with what shuffles of K4 reach.

The screen's first step on a planted message: plain alphabet HYDRAULIC-mixed, key SHADOW (6), standard cipher alphabet:

  plain alphabet  HYDRAULICBEFGJKMNOPQSTVWXZ
  carved          NHKDFRWODNIEWZHTAHVYPYOGAHESXGVPEIIGUCANZCWWKYFHYOIRYZ
  key, true       SHADOW
  key, by letter counts per column alone: SHADOW
  reading         THEHOTAIRESCAPINGFROMTHECHAMBERCAUSEDTHEFLAMETOFLICKER

Every one of 2.08 million tables gets this step at every key length; the 50 best per length are then climbed.

F1 on dictionary keyword tables (0109: exact with the known letters, nothing below 26) read without them: the hedge for A1 and A2 on the table family Sanborn's K1-K2 belong to, with C27(c) (his chart 'slightly different from the one on Kryptos') and C5 (key word/s) read as a keyword-mixed alphabet. F13.1 puts the cell at 143 bits at length 26 (122 for the key, 20.3 for the 2.08 million tables), under MIX8m's 189. The frequency screen is the hand method's first step (each column's shift by letter counts; Friedman, Military Cryptanalysis I) and is exact per column; it loses the true table when columns are short, which the plants measure. Pre-registered: one statistic per text, S = max over L of the z-score of the best MIX8m log-probability at L against the shuffles; K4 flags at p < 0.05 against 100 shuffles; a planted length is decided when at least 6 of its 8 plants are above all 10 own shuffles. The item closes for the decided lengths and is blocked above them.

Plants found 8 of 8 at length 5, most at 10, few at 15-26: the frequency screen needs columns of 7 letters or more to keep the true table among 2 million, so decided to about 10. K4 inside its shuffles (p above 0.05); its 26 readings put at most 4-5 known letters in place. F13.4b closes for the short lengths and is blocked above.

1. Tables: 0109's 208,062 alphabets x 5 pairings (W/W, W/standard, standard/W, W/KRYPTOS, KRYPTOS/W) x 2 forms.
2. Screen (C): per text, table and length 1-26, the sum over columns of the best shift's English letter log-frequency; the 50 best tables per length kept.
3. Climb: for each kept table, coordinate ascent on the shifts by quadgrams from the screen's shifts and from 9 random starts; the best reading per table rescored by MIX8m (0233's weight 0.55); per length the best.
4. S = max over lengths of the z-score against K4's 100 shuffles; K4 ranked; each plant against its 10 own shuffles.
5. K4's best reading at each length submitted (key: the two alphabets, the form, the shifts); gate 4's controls are the shuffles' best readings scored as the harness scores.

All 26 candidates, lowest loss first.

K4 statistic 1.80 at length 5, p 0.663 against 100 shuffles; plant power L5 8/8, L10 4/8, L15 2/8, L20 0/8, L26 2/8; decided lengths [5]

What was searched, as the harness recorded it.

item

F13.4b

search reads known letters

no

alphabets

208,062

tables

2,080,620

pairings

W/W, W/STD, STD/W, W/KRY, KRY/W

forms

added, Beaufort

key lengths

1, 26

screen

per column best shift by English letter frequency, exact; best 50 tables per length

climb

coordinate ascent on quadgrams from the screen's shifts and 9 random starts; MIX8m rescoring

texts

541

k4 copies

100

k4 statistic

1.804

k4 best length

5

k4 p

0.663

copies statistic max

4.639

copies statistic median

2.052

k4 rank per length copies at or above

1

17

2

48

3

95

4

42

5

4

6

70

7

45

8

99

9

61

10

37

11

48

12

67

13

69

14

83

15

30

16

40

17

19

18

81

19

83

20

75

21

52

22

37

23

88

24

53

25

9

26

31

plant power

5

8, 8

10

4, 8

15

2, 8

20

0, 8

26

2, 8

plant exact recovery

5

7, 8

10

2, 8

15

0, 8

20

0, 8

26

0, 8

plant true table best

5

7, 8

10

2, 8

15

0, 8

20

0, 8

26

0, 8

decided lengths at 6 of 8

5

k4 best readings

5

reading

NTTAENDCWNYLANTDOYZRWRSADAIEAHIMONTOEDOFFIONWEBIKYONTREKOHKMBRAPAPFDCITRESCISTHBONGYMIMNVESGFSXSU

word

ACCEPTOR

10

reading

LCONTOAFTEDICTEMIURAFEINOURREOROTTEWSTDYPMTTFBCDISCHOITTIMITVECABQOTFHIELOSIDIMVCHDRIIHOONWUPONEY

word

DOESKIN

expected total time

541 texts x about 70 s = about 10.5 core-hours

exhaustive

no

compute seconds

12,997