Repetitions and periods

Record positions before interpreting gaps

A repeated sequence is the same run of selected units appearing more than once. Decipher reports one-based start positions and the gap from each occurrence to the next. Overlapping occurrences count.

A repeated ciphertext group can occur because the same plaintext met the same key phase, but it can also occur by accident. Several gaps sharing a factor are more useful than one isolated repeat.Gaines, CryptanalysisMilitary Cryptanalysis, Part II

A candidate period is not necessarily the period

The Kasiski method takes factors of repetition gaps as period candidates. Multiples can work too: columns split at period 6 also respect a true period 3, but each column contains fewer units. A written key such as ABCABC has length 6 and fundamental period 3.Gaines, CryptanalysisMilitary Cryptanalysis, Part II

Split the text by phase

For candidate period m, phase r contains positions whose index has the same remainder r modulo m. Decipher's periodic columns use the Latin-letter stream in order, fold it to uppercase, and distribute it into the selected number of columns.

If the candidate fits a repeating-key substitution, each phase may behave more like a monoalphabetic sample. Check that idea with frequency evidence or a phase-by-phase statistic, while remembering that every phase is shorter than the whole text.