Experiment 187

“F10.1: Chaocipher with the left (cipher) wheel started from any keyword-mixed alphabet at any rotation and the right (plain) wheel free: exact”

F10.1, first family run. Counting checks first: in Chaocipher both wheels turn by the same amount, the place of the carved letter on the left wheel, and the left wheel's moves depend only on carved letters. So once the left wheel's start is fixed, the whole motion is fixed by the carved text, and each known letter says which letter stands at one place of the right wheel's start. The 24 known letters (13 different) then give 11 equalities plus distinctness on a right wheel that is otherwise free: a strong exact test. A free left wheel (26!, about 88 bits) cannot be searched; every keyword-mixed alphabet from the dictionary and the vocabulary (208,627 distinct alphabets) at all 26 rotations can: 5.4 million left wheels, K4 and 10 shuffled copies, compiled.

revertedstatus
a new rootparents
74 stime, all phases
0candidates
0/24known letters
unclocked
1

The experiment method

What the method does with the 24 known letters.

Chaocipher uses two alphabet wheels that are shuffled a little after every letter, so the same letter almost never turns into the same code letter twice. A neat property: how the wheels move depends only on the code letters, which we can all read on the copper. So if we guess how the cipher wheel started, 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. tell us exactly where letters must sit on the other wheel, and contradictions show at once. We try every starting cipher wheel made from an English word, at every turn.

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.

OBKRUOXOGHULBSOLIFBBWEASTNORTHEASTOTWTQSJQSSEKZZWATJKLUDIAWINFBBERLINCLOCKWGDKZXTJCDIGKUHUAUEKCARIN: THE COPPER, ALL 97 LETTERS, THE 24 KNOWN PLACES IN ACCENTfrom a guessed cipher wheel each known letter pins one place of the plain wheel's start: 13 different letters pin (filled), the 11 repeats must agree (outlined)EASTNORTHEASTBERLINCLOCKeach cell one text: does any of 208,651 word-mixed starting wheels (5,424,926 with their turns) fit?K410P1P2P3no starting wheel fitsits own wheel foundK4 0, copies 0; each plant 26 (its word at every turn)a cipher wheel in any order (26!, about 88 bits, against about 51 bits of checks) is too many to try: blockedOUT: NO READING; CHAOCIPHER WITH A WORD-MIXED CIPHER WHEEL DOES NOT FIT K4EASTNORTHEASTBERLINCLOCK
the idea

Chaocipher (Byrne, 1918; kept secret until 2010) shuffles both alphabet wheels after every letter. How they move depends only on the code letters, all of which are on the copper.

the check

Guess how the cipher wheel started; then every known letter says which letter stood where on the plain wheel at the start. Two Es must point to one place, two different letters to two places. Every wheel mixed from a dictionary word, on K4, ten scrambled copies and three planted texts.

the bound

No word-mixed starting wheel fits K4 or a copy; the planted texts' wheels are found. A wheel in any order at all is too many to try. F10.1 closed for word-mixed wheels, blocked otherwise.

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.

  1. Start the left wheel as the alphabet mixed from, say, BERLIN, turned 5 places.
  2. Find the carved O on it: its place i says how far both wheels turn; do the same for every carved letter in order.
  3. At place 22 the carved F sits at some place i on the left wheel; the known E must sit at place i of the right wheel at that moment, which traces back to one place of the right wheel's start.
  4. Every known letter fixes one place of the right wheel's start; two Es must trace back to the same place, two different letters to different places.
  5. One contradiction rules the starting wheel out.
the worksheet: the first steps by hand, on squared paper
WHY THE COPPER ALONE DRIVES THE WHEELSThe plain letter and its code letterstand at the same place on the twowheels. Both wheels then turn to bringthem to the top, so both turn by wherethe code letter stood: something we canread on the copper.So from a guessed start of the cipherwheel, every turn is known, and eachknown letter pins one place of the plainwheel's start. 13 different lettersamong 24 leave 11 checks.
4

Worked example, generated

The same steps run by the code on the real letters.

left wheel starts as the BERLIN alphabet BERLINACDFGHJKMOPQSTUVWXYZ

place 1: carved O at left-wheel place 15: the left wheel turns by 15, the right by 16
place 2: carved B at left-wheel place 10: the left wheel turns by 10, the right by 11
place 3: carved K at left-wheel place 14: the left wheel turns by 14, the right by 15
place 4: carved R at left-wheel place 12: the left wheel turns by 12, the right by 13
place 5: carved U at left-wheel place 19: the left wheel turns by 19, the right by 20
place 6: carved O at left-wheel place 22: the left wheel turns by 22, the right by 23
place 7: carved X at left-wheel place 5: the left wheel turns by 5, the right by 6
place 8: carved O at left-wheel place 21: the left wheel turns by 21, the right by 22
place 9: carved G at left-wheel place 20: the left wheel turns by 20, the right by 21
place 10: carved H at left-wheel place 13: the left wheel turns by 13, the right by 14
place 11: carved U at left-wheel place 20: the left wheel turns by 20, the right by 21
place 12: carved L at left-wheel place 6: the left wheel turns by 6, the right by 7
place 13: carved B at left-wheel place 23: the left wheel turns by 23, the right by 24
place 14: carved S at left-wheel place 5: the left wheel turns by 5, the right by 6
place 15: carved O at left-wheel place 16: the left wheel turns by 16, the right by 17
place 16: carved L at left-wheel place 6: the left wheel turns by 6, the right by 7
place 17: carved I at left-wheel place 14: the left wheel turns by 14, the right by 15
place 18: carved F at left-wheel place 21: the left wheel turns by 21, the right by 22
place 19: carved B at left-wheel place 14: the left wheel turns by 14, the right by 15
place 20: carved B at left-wheel place 0: the left wheel turns by 0, the right by 1
place 21: carved W at left-wheel place 5: the left wheel turns by 5, the right by 6
place 22: carved F at left-wheel place 4: the left wheel turns by 4, the right by 5
place 23: carved L at left-wheel place 2: the left wheel turns by 2, the right by 3
place 24: carved R at left-wheel place 14: the left wheel turns by 14, the right by 15
5

Hypothesis, for a cryptanalyst

Family, key space, the constraint under test, and the clues it reads.

A10 (alphabets that change after every letter; knowledge/12-assumptions.md, for information); Chaocipher, J. F. Byrne 1918, offered to US agencies, method published 2010 (Rubin). Model: left wheel L (cipher), right wheel R (plain), zenith 0, nadir 13; encipher p as L[i] where R[i] = p; then L turned by i and its place-1 letter moved to the nadir, R turned by i + 1 and its place-2 letter moved to the nadir. Given L0, every i_t is fixed by the carved text, R_t[j] = R0[sigma_t(j)], and a known p_t requires R0[sigma_t(i_t)] = p_t. Statistic: consistent left wheels, K4 against 10 copies; plants as builder checks; implementation checked on Byrne's published test vector.

6

Prediction

Written before the run; the result decides it.

No keyword-started left wheel is consistent on K4 or on the copies (11 equalities each); plants are found. Zero candidates.

7

Method

  1. Check the implementation on Byrne's test vector (WELLDONEISBETTERTHANWELLSAID).
  2. Build every distinct keyword-mixed alphabet from the dictionary and the vocabulary.
  3. For each alphabet and rotation as the left wheel's start, run the wheels along each text to the last known place, collecting the right wheel's forced letters; stop at the first contradiction.
  4. Count consistent wheels on K4, 10 copies and 3 planted texts.
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

5,424,926 left wheels; consistent K4 0 (copies 0-0); plants [26, 26, 26]; Byrne's test vector reproduced

What was searched, as the harness recorded it.

family
Chaocipher, left wheel from any keyword-mixed alphabet (dictionary + vocabulary) at any rotation, right wheel free, exact
test vector ok
yes
alphabets
208,651
left wheels
5,424,926
consistent
k4
0
copies
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
plants
26, 26, 26
plants
  1. keyword
    SOCIOLOGIAN
    rotation
    0
  2. keyword
    STRADIVARI
    rotation
    10
  3. keyword
    TURBOEXCITER
    rotation
    5
k4 hits
none
checks
24 known letters, 13 different: 11 equalities on the right wheel's start, plus distinctness
free left wheel
26! starts (about 88 bits) against about 51 bits of checks: not searchable; blocked
copies
10 shuffled copies (seed 1870)
seconds
72
exhaustive
yes

How this experiment sits among the others is on the lineage page; its family's open hypotheses are on the families page.

Rendered from the record on 2026-10-18 12:26 UTC; updated after every experiment.
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