Double Columnar Transposition
The encryption and decryption can be performed by hand, using a piece of paper and a simple matrix, in a similar way as it is done for the Columnar Transposition.
The Double Columnar Transposition was introduced to make cryptanalysis of messages encrypted by the Columnar Transposition more difficult. It was supposed to prevent anagrams of the plaintext words appearing in the analysed ciphertext.
The main idea behind the Double Columnar Transposition is to encrypt the message twice, by using the original Columnar Transposition, with identical or different secret keys. The output from the first encryption would be the input to the second encryption.
The matrices used in both steps may have different sizes, if the two keywords of different lengths have been used.
All the operation performed during encryption and decryption, and all the parameters that have to be defined, remain the same, as in the Columnar Transposition.
Security of the Double Columnar Transposition
Breaking the Double Columnar Transposition is more difficult than breaking its simpler version, due to the fact that anagrams will not appear when trying to apply different sizes of matrices to the intercepted ciphertext.
An attacker has to try many different combinations of keywords in order to find patterns in the ciphertext. The cipher is more likely to be broken if multiple messages of the same length and encrypted with the same keys were intercepted. They can be anagrammed simultaneously, which makes the cryptanalysis much more effective.
It may be estimated that having a few messages of the same length, encrypted with identical keys, would allow the attacker to determine both the plaintexts and the secret keys. This technique was widely using by the French for breaking German messages at the beginning of World War I, until the Germans improved their system.
The Double Columnar Transposition remains one of the strongest ciphers that can by used manually, without the need of having electronic equipment. Another cipher that is considered to be as strong as it is the VIC cipher.