“Construction simulator: which cipher families produce texts with K4's statistical fingerprint?”
New root in family 7. Not a solver: fourteen generators encrypt English windows with random keys, and K4's statistics are placed in each family's distribution.
revertedstatus
a new rootparents
15 mintime, all phases
0candidates
0/24known letters
1
The experiment method
What the method does with the 24 known letters.
Instead of trying to break the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered., we build a workshop. We take ordinary English text, scramble it with each kind of cipher we suspect, using random keys, thousands of times, and measure the results: how evenly the letters are spreadthe index of coincidence The chance that two letters picked at random from the text are the same., how often a letter repeats its neighbour, how letters line up in columns. Then we ask which kind of cipher most often produces text that measures like K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.. The method that solved another famous cipher, the Zodiac killer's, worked this way. It will not tell us the message, but it tells us where to dig.
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 fingerprints
Ten numbers describe the copper: how evenly letters are used, doubled letters, and two oddities. Five of the six doubled letters line up in one column when the copper is written in rows of 7, and eleven vertical pairs repeat in rows of 21.
the simulator
Each candidate method was run 5,000 times on English messages, and its outputs measured the same way. The closest method is the one whose outputs look most like K4.
the result
Hill ciphers and transposition with a table come closest overall, but none of them makes the width-7 column or the width-21 repeats often. Those two marks are still unexplained.
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.
Count each letter in K4: K appears 8 times, M and Y once.
The index of coincidence is the chance two letters drawn at random match: add n(n-1) over the 26 counts and divide by 97 times 96; K4 gives 0.0361.
Now take an English sentence of 97 letters and encipher it with a repeating key of 28 random letters on the sculpture's table.
Count its letters the same way and compute its index.
Do this 5,000 times and see where 0.0361 falls among the results.
Repeat for the other statistics and the other ciphers.
A cipher that rarely produces K4's numbers is unlikely; one that often does stays on the list.
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.
one sample from the periodic-Vigenere generator against K4
plain ORMATIONWASGATHEREDANDTRANSMITTEDUNDERGRUUNDTOANUNKNOWNLOCATIONXDOESLANGLEYKNOWABOUTTHISTHEYSHOUL
cipher QEUCCMKEVQJJHVAIPGLTXZYKUZJAZASJGJECXEJBGHWFSFTXDLZAEABRBEFADWMEQBMXDEUIXBAILTEGMQOASNMRVGXFCUWHU
statistic K4 sample
ic 0.0361 0.0395
distinct 26.0000 26.0000
doublets 6.0000 2.0000
width7_doublet_column 5.0000 2.0000
width21_vertical_repeats 11.0000 1.0000
repeated_bigrams 10.0000 7.0000
top_count 8.0000 9.0000
singletons 2.0000 4.0000
closeness_mean_distance 5.5833 7.2083
self_encryptions 2.0000 0.0000
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Oranchak, Blake and Van Eycke solved Zodiac 340 by simulating constructions until one reproduced the ciphertext's fingerprint (knowledge/07-people.md). K4's fingerprint (knowledge/04-structure.md): index of coincidence 0.0361; all 26 letters present; six doublets, five of them in one column at width 7; eleven repeated vertical bigrams at width 21; top frequency 8; and Bean's closeness, the crib plaintext letters sitting near their ciphertext letters on the standard alphabet. Each generator takes a random 97-letter window of the K1-K3 plaintexts and a random key: periodic Vigenere on the KRYPTOS alphabet at periods 27-30, Quagmire with random alphabets, progressive key, plaintext autokey, running key, columnar then Vigenere, Vigenere then columnar, Hill 2x2 and 3x3, Gromark base 10, plus three calibration generators (random letters, pure transposition, monoalphabetic). For each statistic and generator we record the two-sided empirical p-value of K4's value and a combined distance. The result ranks families by plausibility; it decides none. Bounds: 5,000 samples per generator, these twelve statistics.
6
Prediction
Written before the run; the result decides it.
K4's flat letter distribution sits comfortably inside every polyalphabetic family and outside the monoalphabetic and pure-transposition calibrations. The width-7 doublet column and the width-21 repeats are unusual under every generator, with p-values near 0.01 to 0.1, so no family is singled out by them. Bean's closeness statistic separates families: letter-for-letter systems on a near-standard alphabet reproduce it more often than transposed or Hill systems.
7
Method
Define the statistics on a 97-letter text, with the plaintext available for the closeness statistic at the 24 crib positions.
Build fourteen generators.
Draw 5,000 samples each.
For each statistic, compute K4's two-sided empirical p-value under each generator and a z-score.
Combine the z-scores into a distance and rank the generators.
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
Diagnostic, no candidates. Ranking nearest first: Hill 2x2 (6.02); Hill 3x3 (6.32); columnar transposition then Vigenere (6.44); Vigenere then columnar transposition (6.44); Quagmire, random alphabets, period 27-30 (6.46).