Part of the World War II Cryptographic Simulation

Our spies abroad use a complicated and effective system to protect themselves. They first create a 'straddling checkerboard' using a keyword and then assign the most common letters the lowest numbers. Our radio operator for the Sorge net in Japan uses the keyword SUBWAY and, because he enciphers in English, the mnemonic ASINTOER(r) to remember the 8 most common letters in that language. First, the keyword is written out horizontally. Then, the remaining letters of the alphabet are filled in underneath it. Next, the spy goes through each column, assigning the most common letters a number starting with zero and the others a number starting with 80. Thus, using the SUBWAY example, the first step looks like this:

```S  U  B  W  A  Y
0  82 87 91 5  97

C  D  E  F  G  H
80 83 3  92 95 98

I  J  K  L  M  N
1  84 88 93 96 7

O  P  Q  R  T  V
2  85 89 4  6  99

X  Z  .  /
81 86 90 94
```

To make it easier to encode, the letters are placed into a straddling checkerboard:
```. 0 1 2 3 4 5 6 7 8 9
S I O E R A T N
8 C X U D J P Z B K Q
9 . W F L / G M Y H V
```
As can be seen above, the symbols '.' and '/' are tacked on to the end of the alphabet. The period is used as you would expect; however, the slash is used to denote that "real" numbers are being used instead of enciphered text. To encode a number slashes are first put around it and then each number is written twice. Thus, "Who commands 53rd army?" appears:

```W  H  O C  O  M  M A N D  S  /  5  3  /  A R M Y
91 98 2 80 2 96 96 5 7 83 0 94 55 33 94 5 4 96 97
```
The spy then takes an assigned book with a large number of statistics in it, such as an Almanac, chooses a page and line number at random, and uses those numbers as a one-time key. So if page 4, line 30, column 12 contained the numbers "564 7896 453 542 5412 72 456 967 702 943 10" the third number of the first group is taken and then the rest is written underneath the message. The numbers are then added using "non-carrying addition". This means that the tens digit is not carried (ie 7 + 7 = 4). So our previous message is further encoded like this.

```9 1 9 8 2 8 0 2 9 6 9 6 5 7 8 3 0 9 4 5 5 3 3 9 4 5 4 9 6 9 7
4 7 8 9 6 4 5 3 5 4 2 5 4 1 2 7 2 4 5 6 9 6 7 7 0 2 9 4 3 1 0
3 8 7 7 8 2 5 5 4 0 1 1 9 8 0 0 2 3 9 1 4 9 0 6 4 7 3 3 9 0 7
```

These are then divided into groups of five:
38778 25540 11980 02391 49064 73390 70000

A key is made by combining the page, line and column numbers and adding, by non-carrying addition, the 4th from the first and 4th from the last groups. Thus:

43012 KEY
02391 4th From First
02391 4th From Last
_____
47694 Indicator Group

This 'indicator group' is then placed at the front of the message and sent. This technique is highly effective because it takes a seemingly innocous book such as an Almanac and a sophisticated checkerboard scheme to produce an unbreakable cipher. Another important aspect is that making the most common letters the smallest and using non-carrying addition results in a relatively short message (averaging only 1.5 the size of the original) which reduces the time necessary to send.

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