III. Transposition Cipher

First Transposition Cipher in History

It was firstly used by Greeks and Spartans for military secrecy, 15th Century B.C. as Scytale Cipher.

A Scytale Cipher is simply a wooden stick around which a strip of leather is wrapped. Sender writes the message along the length of the stick and unwinds the strip, where letters are transposed in some order.

What is a Transposition Cipher ?

Transposition Cipher idea relies on re-arranging the order or positions of the alphabets – fixed by a given rule – without modifying their values, where the fixed rule is the key.

Rail-Fence Cipher

One of the important application of the Transposition Cipher is Rail-Fence Cipher. Rail-Fence Cipher lists the plaintext alphabets diagonally over a number of rows and retrieve alphabets row by row. For instance;

Permutation Cipher

Another application of the Transposition Cipher is Permutation Cipher. Permutation Cipher, lists the plaintext alphabets row by row and retrieves the ciphertext alphabets row by row or column by column. Here, key is a permutation of a set of size n and determines the row or column order where key length (n) corresponds to n rows or columns. If the key is n alphabets long, there are n! possible keys. Transposition ciphers can be also generalized by a permutation cipher with a key of length equal to the plaintext.

Permutation Cipher Example

I. Row by Row (Horizontal)

Plaintext: WHEREAREYOU, Permutation Key: 4231.

WHER EARE YOUX ( Here, X stands for padding ) => Horizontal Order.

W-1; H-2; E-3; R-4 stands for initial status. Applying Permutation Key yields: R(4)H(2)E(3)W(1). Hence, WHER becomes RHEW.

E-1; A-2; R-3; E-4 stands for initial status. Applying Permutation Key yields: E(4)A(2)R(3)E(1). Hence, EARE becomes EARE.

Y-1; O-2; U-3; X-4 stands for initial status. Applying Permutation Key yields: X(4)O(2)U(3)Y(1). Hence, YOUX becomes XOUY.

Finally we get ciphertext: RHEWEAREXOUY from plaintext: WHEREAREYOU.

II. Column by Column (Vertical)

Plaintext: WHEREAREYOU, Permutation Key: 4231.

WHER

EARE

YOUX => ( Here, X stands for padding ), Vertical Order.

Applying Permutation Key yields: REX(4)HAO(2)ERU(3)WEY(1). Hence, Plaintext: WHEREAREYOU becomes Ciphertext: REXHAOERUWEY.

Transposition Cipher Security

Since the alphabet values do not change, frequency distribution remains the same, it’s vulnerable to cryptanalysis (for known or chosen plaintext attack).

Product Cipher

Product Cipher is the combinations of substitution ciphers and transposition ciphers, where improves security compare to substitution and transposition ciphers respectively. Mostly, modern ciphers use Product Ciphers.

O.S. Tapsin

Resources: https://www.nku.edu/~christensen/1402%20permutation%20ciphers.pdf — http://www.cs.toronto.edu/~sgorbunov/347f13/lectures/crypto/IntroToCrypto.pdf — https://d3c33hcgiwev3.cloudfront.net/_fc8b94e4198a6b65f784a188875c1e76_slides_classical_cipher_transposition.pdf?Expires=1567468800&Signature=QZJ6BhS3XhjrcZVeIJmdSDsdKa8YPQoSchJchh44-iQLY1xS7xWvOQT1NyO1h7xrDm0mRMzX4vpJUyID0ZvcsmmmLeADNYBxjXmpSNpz7ElPoN6L26no4E72WIVEg0qdIGszhgDm9wxYJrKCVZHNuDHNTOQjYPWSfjEn7mauFUo_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A by Sang-Yoon Chang, Ph.D. —