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

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

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.