Foundations
Transposition
Keep the characters, but change their order.
Also found as permutation cipher · route cipher
Move symbols without replacing them
A transposition keeps the same text units and changes their order. The prepared plaintext and ciphertext have exactly the same symbol counts. What changes is adjacency: plaintext neighbours may be pulled apart, and unrelated symbols may end up next to each other.Friedman, Codes and CiphersMilitary Cryptanalysis, Part IV
C[i] = P[σ(i)]P[i] = C[σ⁻¹(i)]Grids, routes, and Keys
Many transpositions put the text in a grid, then use one route to write it and another to read it. Keyed columnar transposition writes across rows and reads the columns in an order set by the Key. You also need rules for repeated letters in a keyword and for the longer columns in an incomplete final row.Friedman, Codes and CiphersACA Incomplete Columnar