Column and route rearrangements plus a repeating key, on 73 letters left by a column-band filler model

A repeating-key Vigenere, Beaufort or Variant Beaufort cipher (key lengths 1 to 13) combined with column, rail-fence and route rearrangements, on the 73 letters left by a column-band filler model. Rearrangements: every column order at widths 7, 8 and 9 (408,240 orders), rail fence with 2 to 15 rails, and serpentine, spiral and column-by-column routes at widths 7 to 14, with the key lined up with either the carved or the rearranged order. The 73 letters are what remains after treating 24 K4 letters in columns 8 to 16 of a 28-by-31 layout of the cipher text as filler. 31.8 million settings. The best, 18 of 24 known letters at width 9 with an 11-letter key, is noise: a random-order check suggests about 3 or 4 settings that good are expected by chance in the full width-9 search.

In plain English: A repeating-key Vigenere, Beaufort or Variant Beaufort cipher (key lengths 1 to 13) combined with column, rail-fence and route rearrangements, on the 73 letters left by a column-band filler model, using a combined approach: scramble the letter order AND replace each letter. Every combination within the stated scope was tested (31.8 million configurations); none produced a valid solution. Best match: 18/24 known letters. That is not a real signal: searches of this kind can reach scores this high without the right key. This record is negative within the tested scope.

NOISE Tier 2

How to read this record

Verdict – ELIMINATED (ruled out within the tested scope), NOISE (nothing beyond what chance produces for a search of this size; also shown when a record stored no verdict of its own), INCONCLUSIVE (the test left candidates or options standing, or could not decide, so it does not rule the method out), INTERESTING (slightly above random, almost certainly coincidence), SIGNAL (statistically unusual, warrants investigation), or FULL MATCH (all 24 known letters correct).
Confidence Tier – Tier 1 = mathematical proof, valid while its stated assumptions hold. Tier 2 = every possibility within the stated scope tested. Tier 3 = partially tested or sampled. Tier 4 = not yet properly tested.
Configs Tested – How many different key/parameter combinations were tried.
Best Score – How many of the 24 known plaintext letters the best attempt matched (out of 24). N/A means no such score could be read from this record.
Keystream Consistency (Bean) – Whether the key values at different positions are mathematically consistent with each other. The check only holds when the known letters stay in their carved positions (no letters rearranged or removed), and the full set used here assumes the standard A to Z alphabet.
Scope Limitations – What this elimination does not rule out.

Configs Tested: 31,800,000
Best Score: 18 / 24 known letters matched · high, but judged chance for this search
Confidence: Tier 2: Exhaustive search under stated assumptions. Does not eliminate multi-layer variants.
Truth Tag: [INTERNAL RESULT]
Date Tested: 2026-03-12

Scope Limitations

This elimination does not rule out:

Other rearrangements (for example double columnar, Myszkowski or turning grille)
Column orders at widths other than 7 to 9
Key lengths above 13
Other ways of choosing the 24 filler letters

Assumptions

Filler letters are the K4 letters in columns 8 to 16 of a 28-by-31 layout of the cipher text, minus one kept column
Known letters move to positions 13-25 and 47-57 of the 73 (counting from 0)
Repeating key of length 1 to 13

Reproduce

PYTHONPATH=src python3 -u scripts/grille/e_mitm_trans_sub_73_01.py

Requires the kryptos repo, Python 3.11+, PYTHONPATH=src. Some recent scripts may not be in the public repository yet.

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