Columnar Transposition

cryptography

Definition

Columnar Transposition

Columnar transposition is a transposition cipher in which the plaintext is entered line by line into a matrix. The ciphertext is obtained by reading the matrix column by column in an order determined by a key.

Operation

The key is a list of numbers (of length $k$, the number of columns) containing each number from $1$ to $k$ exactly once. Each column is assigned one key element, and the columns are read in the order specified by those elements.

Example

Encrypting with key 3, 1, 2, 5, 4

Plaintext: THIS IS A TRANSPOSITION

The plaintext is written row-wise into a 5-column matrix, and columns are read in the order determined by the key:

Key	3	1	2	5	4
	T	H	I	S
	I	S		A
	T	R	A	N	S
	P	O	S	I	T
	I	O	N

Reading columns in key order (1, 2, 3, 4, 5) gives the ciphertext:

HSROOI ASNTITPI STSANI

Security

Brute-Force and Heuristic Attacks

Brute-force attacks are effective only for short keys, since the number of possible keys is $k!$. For larger keys, heuristic optimisation methods (e.g. hill climbing) can be applied. Decryption with partially correct keys produces partially correct text, which guides the search.