### Book Ciphers

Burton Rosenberg
Last Update: Tue Apr 1 01:44:21 EST 2003

Encryption is an old art. Here is perhaps the simplest encryption. I leave the reader to try her hand at breaking it:

```12,15,22,5;9,19;20,8,5;12,1,19,20;12,9,7,8,20;19,16,15,11,5,14;
```
A more interesting process is called the book cipher. Each letter is given by a row, column pair as it is found in an agreed upon text. So the cipher would read:
```row,column,row,column,row,column,...
```
Note all such ciphers would have an even number of numbers in them, which might be a hint that one is facing a book cipher. Here is the above text as a book cipher:
```1,1,3,10,5,6,1,16,2,5,2,6,1,14,4,7,1,10,3,7,2,4,3,5
```
and so on. Spaces, punctuation, etc., if the text is carefully numbered, can all be represented in a book cipher. For instance, you should be able to guess which pair of numbers represent the first space in the above cipher, if you have broken the easy cipher version of the same phrase.

This is a lot like taking a page from a book and circling letters to be read. The page to use, the page with the circled letters, must be shared ahead of time. This is often a weakness of a book cipher, since it leaves you the problem of distributing the page covertly but definitively.

In practice, people miscount, and that can lead to indecipherables. However, most errors seem to be in forgetting a comma, so it might be better to work with letters instead of numbers, where a=1, b=2, and so on. As long as you don't go past column x=24 there is no problem. (Else you have to work base 25, where A=25, B=50, C=75, etc., So that 27 would be Ab (25+2), 53 would be Bc (50+3). The letter z=0, so 75 is Cz (75+0). The letter y is unused.)

Squared paper is a great help to cryptographers. You can write a, b, c, etc., across the top, a, b, c, etc., down the left margin, and then write the book into the squares, so there is no further need to count.

```aebcbebrcdcecidwfqftfxgqiljljtjvkgkplbljnxokqprrswvjvuwewnwsyr
brcbevewoasbsctvujefeqetevfafufxgjglhshthuiyjlmlmunpnvokpxxp

pyqbqgqhqjbrcdcedcdidrfqfygcgegqiljljtlhncnqokoopxqgqprrrtrurvshsisj
spsqsrtstwuevovpvswewnxcxezdzrztbcbfbgbobqcaccdwevfafgfifugmgyhajbjpkbkjmx
```

Traditionally, once a letter is used from a text it is crossed off, so that no pattern of repeating integer pairs will aid the cryptanalysis. If, for instance, which ever letter is represented by 1,1 is always represented by 1,1, then the cipher degenerates to a so called simple substitution cipher, which is easy enough to break.