Cryptology I.8 Transpositions

a7Hzq .#5r< kÜ\as TâÆK$ ûj(Ö2 ñw%h: Úk{4R f~`z8 ¤˜Æ+Ô „&¢Dø

Contents

1. Transpositions and their Properties
2. Examples [mathematical version]: Geometric Transpositions, Grilles, Block Transpositions, Perl Program
3. Cryptanalysis of a Columnar Transposition (Example)
4. Cryptanalytic Approaches [mathematical version]
5. Bigram Frequencies in English, German, and French
6. The Values of Bigram Scores [mathematical version], Empirical Values for English, German, and French
7. A More Systematic Approach, Example
8. The Similarity of Columnar and Block Transpositions [mathematical version]

Here is the complete mathematical part as PDF.

Idea

All the cryptographic procedures that we considered up to now worked by replacing each plaintext letter by another one, letter per letter. In this chapter we follow a complementary approach: Don't change the letters but instead change their order. This approach also goes back to anitiquity.