1) Understand what Transposition Ciphers are and how they work.

2) Encrypt using the Reverse and the Rail Rence Cipher and Fractionation Systems. 

3) Learn how to break Transposition Ciphers.

Notice that MEETMEATNOON becomes NOONTAEMTEEM. I am sure you saw that the letters were simply reversed. Notice that no letter was replaced, they were simply rearranged. This cipher is called the "Reverse Cipher". Reversing the letters is the simplest example of a transposition cipher: 

1) How can Transposition Ciphers be broken? 

In order to encrypt a message using the Transposition Cipher, the letters can be shuffled without any system. Otherwise, the recipient has no idea how to decrypt the message. However, by choosing a system to rearrange the letters it allows an eavesdropper to be successful with his work. Testing many conceivable rearrangement will eventually the original message. 

Step 1: (Realization that the ciphertext was encrypted using a transposition cipher.) Computing the relative frequencies of the cipher letters reveals that cipher letters occur with the same frequency as plain letters. An eavesdropper realizes that plain letters were simply rearranged. 

Step 2: Transposition ciphers are broken by testing possible rearrangements. First, try to read the cipher text backwards. If that does not yield the plain text then try the rail fence of depth two, then of depth three, then of depth four, etc. If that does not yield the plain text check if two consecutive letters were switched. With today's computer power possible transpositions can be checked quickly. In conclusion: the transposition ciphers don't offer any security.    

2) How can the Security of Transposition Ciphers be increased? 

The Rail Fence is the simplest example of a class of transposition ciphers called "Route Ciphers". These were quite popular in the early history of cryptography. Generally, in Route Ciphers the elements of the plaintext (here single letters) are written on a pre-arranged route into a matrix agreed upon by the sender and the receiver. The introductory example uses a 2 (rows) by 19 (columns) matrix in which the plaintext is entered sequentially by columns, the encryption route is therefore to read the top row and then the lower.

To gain an acceptable level of security, the route would have to be more complicated than the one in this example. One form of transposition that has enjoyed widespread use relies on identifying the route by means of an easily remembered keyword. Say we choose the keyword "cat" a matrix can be written out like the one below. We choose the letter "x" to fill the remaining spots in the matrix.

The order in which the rows are read out to form the ciphertext is determined by the alphabetical order of the letters in the keyword "cat".

This matrix therefore yields the ciphertext: 
        "rssichsnbkeixtnotnpraeonsyapioiecbrealx"

To decode, the recipient simply fills 3 rows evenly with the ciphertext according to the alphabetical order of the letters in the shared keyword "cat". 

The security of transposition ciphers can be further improved by re-encrypting the resulting cipher using another transposition. Because the product of the two transpositions is also a transposition, the effect of multiple transpositions is to further increase the complexity of the route through the matrix. However, although the plaintext gets more and more shuffled the plaintext letters are still part of the ciphertext and sufficient patience and experience in cryptoanalysis will eventually yield the original plaintext. 

In modern cryptography transposition cipher systems serve mainly as one of several methods used as a step in forming a product cipher.

3) Fractionation Systems: Further Improving the Security Level 

In fractionation systems, letters are both substituted (which we will study in detail in the next lesson) and transposed yielding a superencryption. First, the plain letters are substituted by selected letters (commonly pairs of letters are used, in which case the cipher is called a "biliteral cipher"). Secondly, such letters are then super-encrypted by a transposition. Let's study an example of a Fractionation System.

 

A D F G V X A o r a n g e D b c d f h i F j k l m p q G s t u v w x V y z 0 1 2 3 X 4 5 6 7 8 9

Example1: (ADFGVX Cipher) One of the most famous field ciphers ever was a fractionation system - the ADFGVX Cipher which was employed by the German Army during the first world war. This system was so named because it used a 6 by 6 matrix to substitution-encrypt the 26 letters of the alphabet and 10 digits into pairs of the symbols A, D, F, G, V and X. The variable setup of the matrix is guaranteed through the choice of a keyword (here orange) that precedes the remaining letters and digits. The resulting bi-literal cipher is only an intermediate cipher, it is then written into a rectangular matrix and transposed to produce the final cipher which is the one which was transmitted.

For instance, let's encrypt "cryptography" using the key word "orange". The first letter "c" becomes "DD" as the starting letters of the row and the column in which "c" appears. Similarly, the next letter "r" turns into "AD", etc. 

This intermediate ciphertext then fills the columns (left to right) of a transposition matrix using the keyword "water". Since "water" consists of 5 letters the matrix contains 5 rows. Note that the matrix is filled up with AA at the bottom right.  

The final cipher is read as rows based on the alphabetical order of the letters of the key "water": 

                "DFAAVDGVFAVDAVAAVAFVDAADD".

To decode, the recipient sets up the two matrices based on the two keywords to first undo the transposition and to finally undo the ADFGVX-substitution. Although this superencryption offers more security, it can be broken in steps. First, the ADFGVX - Substitution Cipher has to be deciphered - I will show you how on the following  "Substitution Cipher" page. Secondly, the remaining transpositions can be undone by testing many possible transpositions. 

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