“Simulator, round two: which constructions reproduce the width-21 repeats, the width-7 doublet column and the closeness together?”
Generators chosen to share a key letter 21 or 7 positions apart: periodic systems at periods 7, 21 and 42 with free alphabets or the tableau, autokey at lag 21, progressive keys at period 21, Gromark with an even base, and transposition last at width 21. 5,000 samples each; the three unexplained statistics are the target.
Yesterday's workshop found three things about K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. that none of our fake K4sthe workshop An experiment that builds thousands of pretend K4s by each suspected method and measures them, to learn which methods produce text that looks like the real one. reproduced, all to do with letters 7 or 21 places apart behaving alike. So today we build fakes with methods that treat letters 7, 21 or 42 places apart alike: a secret word of that length, a number stream with that rhythm, a message keyed by itselfan 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. 21 letters back. Then we measure the fakes the same way and ask which method makes all three oddities look ordinary.
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 question
Experiment 18 found two marks in the copper that no simple method explains. This round tried methods built to make them: keys of length 7, 21 and 42, Gromark, progressive keys, column shuffles of width 21.
the dots
Each dot is the share of a method's simulated outputs that show the mark at least as strongly as K4. A method that made K4 would put both dots well to the right.
the result
All dots sit at the left, below 1 in 20 and mostly below 1 in 100. The marks remain unexplained; only Gromark with base 2 later reproduced the width-21 repeats.
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.
Take an English sentence of 97 letters and a key of 21 random letters repeated under it.
Encipher on the sculpture's table.
Write the result in rows of 21 and count how many vertical pairs, a letter and the one below it, occur twice or more; K4 has eleven.
Do this 5,000 times and see how often eleven or more appears.
Count the doublets and note which column of a width-7 layout they fall in; K4 has five of six in one column.
Repeat for the other methods.
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 period-21 free-alphabet generator against K4
plain ORMATIONWASGATHEREDANDTRANSMITTEDUNDERGRUUNDTOANUNKNOWNLOCATIONXDOESLANGLEYKNOWABOUTTHISTHEYSHOUL
cipher HVPMBRPGQPWHVTNBJBNNUODCGIUIUSXSEBSUKVLFZUHADEFSROVWHCBHHDOPYIFQTBSWPFUXNNZFYMGMRPSOMUOYMOXWMJPUN
statistic K4 sample
ic 0.0361 0.0397
distinct 26.0000 26.0000
doublets 6.0000 3.0000
width7_doublet_column 5.0000 1.0000
width21_vertical_repeats 11.0000 1.0000
repeated_bigrams 10.0000 8.0000
top_count 8.0000 8.0000
singletons 2.0000 3.0000
closeness_mean_distance 5.5833 7.0000
self_encryptions 2.0000 0.0000
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
0018 left three statistics unexplained by every generator: five of six doublets in one column at width 7, eleven vertical bigram repeats at width 21, and Bean's closeness of crib plaintext to ciphertext (knowledge/04-structure.md). Positions 21 apart that share a substitution alphabet make vertical pairs at width 21 repeat at English rather than flat rates, so periodic systems with period dividing 21 or 42, Gromark with an even base and a five-digit primer (Rogot, Deavours, Blackman), and autokey at lag 21 are the natural suspects; period 7 died under every alphabet (R and C both to P at 66 and 73), period 21 with vocabulary alphabets died in 0020, but a period-21 system with free alphabets did not. Each generator is scored as in 0018 on the three target statistics and the ten of 0018, with two-sided empirical p-values. A generator that gives all three targets p above 0.05 is a lead for a family. Bounds: 5,000 samples per generator; a ranking, not a verdict.
6
Prediction
Written before the run; the result decides it.
Periodic systems at period 21 and 42 with free alphabets reproduce the width-21 repeats (p above 0.2) but not the width-7 doublet column. No generator makes all three targets ordinary at once; the width-7 column stays below p 0.02 everywhere.