Cryptanalysis
Grids, squares, and alignments
Also found as grid analysis · alphabet square · position alignment
An arrangement is a test
A grid does not change the selected units unless you read them back in a different order. Its first job is to make positions and neighbours visible. Dimensions, fill direction, row or column order, offset, and window are all parts of the claim being tested.Friedman, Codes and CiphersHandbook of Applied Cryptography, chapter 7
Regular grids
A row fill places units across each row before moving down. A column read takes the first column from top to bottom, then the next. Reordering or reversing rows and columns produces another explicit arrangement while retaining each unit's source position.
- Row fill
ABCD / EFGH / IJKL- Column read
AEIBFJCGKDHL
An offset leaves earlier units outside the arrangement. A window limits the units included. An incomplete final row changes which columns are longer, so the dimensions must remain part of the result.
Alphabet squares
An alphabet square assigns one cell to each symbol in its inventory. Coordinates then name positions rather than values. This is the shared geometry behind Polybius coordinates and Playfair pairs, although the two ciphers use the square differently.
A complete Decipher square uses every inventory symbol exactly once. The current square arrangements include rows, columns, alternating rows or columns, and inward or outward spirals. They are named fill orders, not a search through arbitrary paths.
Align compatible units
Position-by-position comparison only makes sense after both sources use compatible units. Characters, Latin-letter slots, words, table cells, and coordinate pairs have different position spaces. An offset changes the pairs being compared and leaves the unmatched ends outside the overlap.
The aligned result can then support an ordered-pair count or a hypothesis. Alignment itself does not assert why the positions belong together.
Regular arrangements stop here
These operations cover regular rows, columns, named square fills, offsets, and windows. They do not define arbitrary geometric routes or claim to search every possible path through a shape.