“F1.10: Friedman's keyword-only key-advance schedules (run length by letter value, the CHRISTMAS expansion, EXTINGUISHER windows; ciphertext and plaintext interruptors; fraction-digit runs) on the sculpture's tables, exact, with scrambled copies”
F1.10. The report on Scheidt's patents and field ciphers ran scratch checks without controls showing no dictionary word fits the run-length and CHRISTMAS schedules on the standard or KRYPTOS tables, and no ciphertext-interruptor setting fits; the fraction-digit runs and the plaintext interruptor were untested, and TM 32-220 par. 126d's EXTINGUISHER windows were found later. Here all six, as an experiment with ten scrambled copies. Word schedules (each dictionary word gives one key): run length = the key letter's value (A = 1; and A = 0 with zero-length runs skipped), the CHRISTMAS expansion (sections ending at the letters numbered 1, 2, 3, ...), EXTINGUISHER windows of 2-5 letters. Free-letter schedules (key letters unknown, the 24 known letters force them): ciphertext interruptor (the key restarts after each occurrence of a chosen carved letter), plaintext interruptor (restarts after a chosen message letter; testable only inside the two known runs, each run starting at an unknown key place), fraction digits (each key letter used for as many letters as the next digit of 1/d, d 3-99, zeros dropped). Tables: plain and cipher alphabets standard or KRYPTOS, Vigenere, Beaufort or variant, key letters numbered on either alphabet.
A wartime US Army training text lists simple rules for when the secret wordthe secret word The word or string a cipher needs besides the method.'s next letter comes into use: each letter used for as many places as its position in the alphabet, the word expanded by a counting rule, the word restarted whenever a chosen letter appears, run lengths taken from the digits of a fraction, or overlapping three-letter windows of the word. Each needs only a word and a rule anyone can remember. We test every rule with every dictionary word (or with the word's letters left unknown) on the sculpture's tables, 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
US Army training texts give simple rules for when the next key letter comes into use: run lengths from letter values, a counting expansion, overlapping windows of the word, restarts at a chosen letter, digits of a fraction. Each needs only a word and a rule.
the check
Every rule with every dictionary word on the sculpture's tables, or with the word's letters left unknown, against the 24 known letters and ten scrambled copies.
the bound
No word fits any word rule; the restart and fraction rules fit K4 never, or no more often than the copies. Closed.
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.
Run length by value: with the word KEY, K (11th letter) is used for 11 places, E for 5, Y for 25, then K again.
Count along to place 22: which letter of the word is in use there, and at every other known place.
On the sculpture's table, the known letter and the carved letter at each place fix the key letter that must be in use.
The word fits only if it puts exactly those letters there, at all 24 places.
The other rules work the same way, with their own counting; for the interruptors and fractions the word's letters are left unknown and only need to agree with themselves.
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.
word KRYPTOS: the key letter in use at each known place, by schedule
runlen A=1 places 22-34: RRRRRRRRYYYYY 64-74: PPPPPPPTTTT
runlen A=0 places 22-34: RRRRRRYYYYYYY 64-74: PPPTTTTTTTT
christmas places 22-34: RYPTKRYKKRYPT 64-74: KRYPKRKRYPT
extinguisher 2 places 22-34: OSKRKRKRYPYPP 64-74: TOTOTOSOKRK
extinguisher 3 places 22-34: KRRYPRYYPTOPT 64-74: PRYPRYPTPTO
extinguisher 4 places 22-34: RYYPTOYPKRYPR 64-74: YPKRYRYPYPT
extinguisher 5 places 22-34: YPKRYPTRYPTOK 64-74: PTORYYPTKRY
sculpture's table (KRYPTOS alphabets, Vigenere): the key letters the known letters force
places 22-34: RDUMRIYWOYNKY 64-74: ELYOIECBAQK
CHRISTMAS expands to CHRISTMACCHCHRICHRISTMCHRCHRISCHRISTMASCHRIST (45 letters, as MC III §35c)
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C5(a) ('simple, can be remembered... with the correct key word/s', Scheidt 2011 via Bean), C20 (hand schedules), F1.4's list extended. Sources: Friedman, Military Cryptanalysis III §16b, §19, §21, §35c-d; TM 32-220 pars. 125-126 (126b plaintext interruptor, 126d EXTINGUISHER windows, 126e fraction 1/7), 89e (zeros dropped); reports/Scheidt patents and field ciphers.md and research_notes/Scheidt patents and field ciphers/addendum_downloaded_manuals.md. Note from the report: adjacent known pairs 26-27 (N, O under Q), 33-34 (T, S under S), 68-69 (I, N under T) can never share an alphabet. Word list kryptos/data/words.txt (234,428 words; lengths 3-20 used). EXTINGUISHER: windows W[t:t+m] cycled within a group whose length is the next number of W's alphabetical numbering (ties left to right), windows and numbers each cycling. Exact; statistic fixed before the run: per schedule, K4's count (word hits, or consistent free settings with at least one check) against ten coppers' range.
6
Prediction
Written before the run; the result decides it.
No dictionary word fits any word schedule on K4 (as the report's scratch checks found), coppers 0 as well; the free-letter schedules fit K4 only at the coppers' rate, the plaintext interruptor most often (few checks inside the runs). Zero candidates.
7
Method
For each word schedule and word: the key letter at each known place (positions 22-34, 64-74).
For each text, table and numbering: the forced key value at each known place; a word fits if its 24 values match exactly (hash lookup).
Free schedules: the slot of each known place per setting; a setting is consistent if no slot has two different forced values; count those with a check.
K4 against the coppers per schedule.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.