James McDonald
Cryptography
Dr. Buchanan
9/15/04
ADFGVX Cipher
The German Army began using the ADFGVX cipher as a communication tool during the First World War. It is closely related to the ADFGX cipher, which later evolved into the ADFGVX cipher. The ADFGX cipher was the original version and the ADGGVX was a latter version. The original inventor of the ADFGX cipher was a German colonel by the name of Fritz Nebel. He first used the ADFGX cipher on March 5, 1918, later expanding it to the ADFGVX cipher in June of that same year. The German Army used this cipher in order to communicate amongst their ranks. The ADFGVX cipher uses a Polybius Square as well as a transformation in encoding its messages.
The progression from the ADFGX cipher to the ADFGVX cipher consisted of the use of a 6 x 6 grid instead of the original 5 x 5 grid used with the ADFGX cipher. These grids were used with a device known as a Polybius Square. The 5 x 5 grid originally applied to the 24-letter Greek Alphabet. This grid used all twenty-five spaces to express a traditional 26-letter alphabet, combining both “I” and “J” on the same grid space. It is said that this was done because of the easiness with which “I” and “J” were confused in the Morse code system. Being that these messages were mostly transmitted during the First World War, this explanation seems feasible. The 6 x 6 grid provided thirty-six spaces, giving its users the capability to express all twenty-six letters as well as the numbers from zero to nine in their messages. The following is an example of a Polybius Square applied to the 26-letter alphabet:
This Polybius Square would represent the letter “a” with the coded number 11, the letter f with 21, and so on. First, the row would be written followed by the column. An example of the familiar computer science message “Hello World” would look as follows, 23 15 31 31 34 52 34 42 31 14. Now we have an example of the Polybius Square as it was used with the ADFGX cipher:
Notice that the “I” and “J” both correspond with FA, just as they corresponded with 24 in the first example. The previous message would be written as follows, GF AG DX DX FD GG FD AF DX DD. Lastly, we have an example of the Polybius Square as it was used with the ADFGVX cipher:
Once again, we would obtain the following “Hello World” message by the following, DF VF GA GA AG FF AG GX GA AX. It is also worth noting that the various letters used in this cipher were chosen because of their distinct differences in representation when translated into Morse code. Because most of the messages transmitted through this cipher were of a high level of importance and secrecy, it was important that no misinterpretations occur. These messages can also be considered fractionated. The Polybius Square along with its corresponding alphabet is called a fractionated key. The Germans changed their fractionated keys daily during World War I.
When the sender and receiver of a message have corresponding Polybius Squares, messages can obviously be transmitted back and forth rather easily. Because security and secrecy was such a high priority during the war, and additional element was added in encoding the ciphers. This element is called a transposition, making the ADFGVX cipher a transposition cipher. This type of cipher encodes a message by reordering the plaintext, or the text that makes up the enciphered message, according to a specific set of rules defined by its users. A person who receives a message would know the specific rules and reorder the message before applying the key, which would be a 6 x 6 Polybius Square in the case of the ADFGVX cipher. In using a transposition, a “keyword” would be used at the top of any message. Messages were usually sent in rectangular form where there would be the same amount of elements in each row and in each column. Filler letters would be used at the end of a message in order to make the final row complete. Most “keywords” consisted of up to two-dozen letters and were changed daily just as the in the case of fractionated keys. The following example uses a four-letter “keyword”:
D F V F
G A G A
A G F F
A G G X
G A A X
The “keyword”, MATH in this case, would then be put into alphabetical order:
F F D V
A A G G
G F A F
G X A G
A X G A
The message would read as follows, FFDVA AGGGF AFGXA GAXGA, and would usually be transmitted in five-letter “words” as shown. Messages could also be received in the following form, FAGGA FAFXX DGAAG VGFGA, reading each column at a time, rather than each row. In researching this topic, it was unclear as to which method of arrangement was used by the German Army, although one could hypothesis that it probably changed on a regular basis. The receiver of a message would have to know the “keyword” and the correct order of arrangement in order to translate the message in the correct manner. They would then apply the message to the correct fractionated key and translate the cipher into normal text.
The ADFGVX cipher was cryptanalised shortly after its implementation by the German Army, by a Frenchman named Georges Painvin. Painvin decoded the general idea of how the cipher worked just nine days after its origination on June 9, 1918. Although Painvin was not able to fully solve the cipher, he did solve enough of it to stop Germany's spring offensive in France. Painvin's accomplishment was remarkable at the time, being one of the biggest uses of cryptanalysis at that point in history. He used the fact that some of the messages would begin with similar, stereotypical beginnings as well as statistical analysis in breaking the cipher.
Resources:
http://www.webster-dictionary.org/definition/ADFGVX%20cipher