Hill cipher with YAR-derived matrix parameters (width 9)

Every width-9 column order with any 2x2 Hill matrix (both layer orders) or any 3x3 Hill matrix (one layer order only). Also a 100,000-order sample at width 10 with a 2x2 Hill cipher, and 56 specific 2x2 matrices built from the raised YAR letters, tried directly and with every width-9 column order. No setting fits all 24 known letters. The script records only whether a setting fits all 24, so the 0 shown as Best Score is not a measured partial score.

In plain English: Every width-9 column order with any 2x2 Hill matrix (both layer orders) or any 3x3 Hill matrix (one layer order only), using a method that encrypts groups of letters using matrix multiplication (Hill cipher). Every combination within the stated scope was tested (43.3 million configurations); none produced a valid solution. This record is negative within the tested scope.

ELIMINATED 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: 43,282,720
Best Score: 0 / 24 known letters matched · low, no sign of a solution
Confidence: Tier 2: Exhaustive search under stated assumptions. Does not eliminate multi-layer variants.
Date Tested: 2026-02-18
Script: scripts/substitution/e_s_151_hill_w9_yart.py

Scope Limitations

This elimination does not rule out:

The 3x3 Hill cipher in the other layer order
Larger Hill matrices
Width-10 column orders outside the 100,000 sampled
Other widths and other transpositions

Assumptions

Hill cipher on the standard A-Z alphabet
Columnar transposition written in rows and read out by columns
For the YAR tests, matrices built from the raised letters (Y=24, A=0, R=17, with T=19 or D=3)

Reproduce

PYTHONPATH=src python3 -u scripts/substitution/e_s_151_hill_w9_yart.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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