Repeating-key cipher followed by a columnar transposition, widths 4 to 9, every column order

Every column order at widths 4 to 9 (409,104 orders), each with a repeating key of length 1 to 26 applied before the columnar step, checked directly against the 24 known letters without the Bean filter that was withdrawn on 2026-08-24. This re-run replaces earlier columnar results (E-FRAC-26, 27 and 35) that relied on that filter. The run's own count of 31.9 million settings includes Variant Beaufort, which here always gives the same result as Vigenere (the run's output also swaps the Beaufort and Variant Beaufort labels), so the count shown on this page, 21.3 million, counts distinct tests only.

In plain English: Tried a repeating-key cipher followed by a columnar transposition, at widths 4 to 9 in every column order and key lengths 1 to 26. No setting with a key of 24 letters or fewer fits all 24 known letters. Some settings with 25- or 26-letter keys fit, but a key that long can fit almost any text, and their number matches what chance predicts.

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: 21,273,408
Best Score: N/A
Confidence: Tier 2: Exhaustive search under stated assumptions. Does not eliminate multi-layer variants.
Truth Tag: [INTERNAL RESULT]
Script: scripts/campaigns/f_columnar_periodic_rederived_v1.py

Scope Limitations

This elimination does not rule out:

Widths above 9
The other layer order (letters rearranged before the key is applied)
Alphabets other than the standard A-Z
Keys that do not repeat

Assumptions

Repeating key applied first, then a standard columnar transposition (written in rows, read out by columns)
Standard A-Z alphabet
Known letters at their standard positions in the plaintext

Reproduce

PYTHONPATH=src python3 -u scripts/campaigns/f_columnar_periodic_rederived_v1.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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