Caesar's cipher

In this cipher, the alphabet $ A$ is the usual alphabet of $ 26$ Roman letters. Punctuation, spaces and capitalizations are ignored. It is reported that Caesar used an encryption $ E:M\rightarrow M$ based on the substitution A $ \longmapsto$ d, ... , Z $ \longmapsto$ c, given by the table below.

A B C D E F G H I J K L M
d e f g h i j k l m n o p

N O P Q R S T U V W X Y Z
q r s t u v w x y z a b c

Example 1.7.22   ``Go Tigers'' is enciphered as ``jr wljhuv''.

If we identify each letter with its corresponding number via the labeling $ A$ is $ 1$, $ B$ is $ 2$, ..., $ Z$ is $ 26$, then Caesar's cipher is a cipher for which any letter $ \Lambda$ is related to its enciphered letter $ \lambda$ by

$\displaystyle \Lambda \equiv \lambda\ ({\rm mod}\ n), $

where in the example above $ n=3$. More generally, a substitution cipher is a cipher for which the alphabet $ A$ has been rearranged according to some fixed permutation. The Caesar cipher is a special case of this where the permutation is as indicated above.


David Joyner 2007-09-03