# Double box key

The double box key (also double cassette key , English two-square cipher or double playfair ) was a manual key method used by the German Wehrmacht between 1941 and 1944 during the Second World War .

## history

The double box key is based on the Playfair method invented by Sir Charles Wheatstone in 1854 , which arranges the capital letters of the Latin alphabet in a square matrix of 5 × 5 letters, the "key square" , for encryption and decryption . Since this only offers 25 spaces, but there are 26 capital letters (without umlauts), the letter J has been omitted and replaced by I or II if necessary. This method was used by the British as early as the Crimean War (1853–1856) and used by both sides, the British and the Germans, and by each other in the First World War broken . In order to increase cryptographic security, the German authorities expanded the process from one to two key squares during World War II. This increases the combinatorial complexity of the method and the key space considerably. The key length is almost doubled, which contributes to improved security. In contrast to the "classic" Playfair method, which mostly uses a password to generate the key square and fills in the remaining letters in alphabetical order - with the cryptographic disadvantage that it often ends in WXYZ - with the double box key, completely irregularly filled "boxes" (Key squares) used, which were changed daily, sometimes even every three hours. This also contributed to the cryptographic strengthening.

## Procedure

The encryption method is basically a monoalphabetic, bigraphic, bipartite substitution. This means that the plain text to be encrypted is broken down into bigrams , which are individually replaced by secret bigrams . To do this, the first letter of a bigram is searched for in the first (left) box and the second letter of a bigram in the second (right) box. There are two possible cases to be distinguished.

First, both letters are on the same line. Then the secret digram is formed by the two letters to the right of the plain letters (shifting step). Second, the two letters are on different lines. Then a rectangle is formed, in the two corners of which the two plain letters lie and in the two remaining corners the secret letters are read (cross-over step).

There have been variations of this encryption rule in the form of the order in which the two secret letters are read. Usually the first secret letter was read in the right box and the second in the left box. Cascading of the encryption step described is also described. The two result letters were then interpreted as an intermediate result and encrypted a second time according to the same procedural rule.

It was customary to also seriate the plaintext. For this purpose, it was written in lines of (for example) 21 letters and then not the letters adjacent to one line were encrypted, but the letters in two lines vertically below each other.

## example

Based on two "random" key boxes that were presented to all participants in a key network anew every day, the following plain text should be encrypted: This is only an example text and it is used here on our Wikipedia to illustrate the double box key method . After replacing the umlauts ü with ue, the text consists of 107 letters. An even number of letters is required for the bigraphic procedure, which can easily be achieved by adding an X at the end. The plain text prepared in this way for encryption is written (without spaces between words) in an even number of lines with 21 letters each and the last two lines in such a way that they are of the same length, i.e.:

Plain text:

```DIESISTNUREINBEISPIEL
TEXTUNDERDIENTHIERINU
NSERERWIKIPEDIAZURILL
USTRATIONDESDOPPELKAS
TENSCHLUESSE
LVERFAHRENSX
```

Key boxes:

```OSQWD   BRYME
EPKUZ   OHCGL
FCGLM   TAQZF
IRHTN   SUWDP
AXBVY   XNIVK
```

Starting with the first bigram DT (the two letters directly below each other in the first column in the first two lines) the plain text is now encrypted. IE, EX, ST, IU and so on follow as further clear big charts. The first letter of a bigram, such as D for the first, is searched for in the left box and the second letter, here T, is searched for in the right box and encrypted using the method explained above. DT becomes BM (crossover step). IE becomes PO, EX becomes OA, ST becomes BC (also cross steps). With the fifth bigram IU, a shift step occurs for the first time and it becomes WR. Overall, you get the following ciphertext, which was usually transmitted in Morse code as groups of five by radio .

Ciphertext:

```BMPOO ABCWR RXPNP DHWPH
CAPOU YXGCP WABQH SWAHA
ATWIB ROFUS HFSCY VSEHB
PRLSO IMNSE KILNL WPPPA
QMTTP UGAPD YQTGU GAUHW
LORXB ROA
```

The recipient of this secret message writes the text in double lines of 21 letters each, alternating in the upper and lower lines, thus reversing the seriation. Then he uses the two key boxes available to him and decrypts by reversing the process steps. After decoding, the original plain text results: this is just an example text that is used in our wikipedia to illustrate the double-box key methodx

## literature

• Friedrich L. Bauer : Deciphered Secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin et al. 2000, ISBN 3-540-67931-6 , p. 68.
• Charles David: A World War II German Army Field Cipher and How We Broke It . Cryptologia , Vol 20 (1), January 1996, pp 55-76.
• Rudolf Kippenhahn : Encrypted messages, secret writing, Enigma and chip card . Rowohlt, Reinbek bei Hamburg 1999, p. 134. ISBN 3-499-60807-3 .