Cryptography Reference
In-Depth Information
A permutation of all the letters of the alphabet is the 26 letters of the alphabet
arranged in some order. The most natural permutation is (
A
,
B
,
C
,...,
Z
),
but (
Z
,
Y
,
X
,...,
A
) is also a permutation, and so is any arrangement such as
(
G
,
Y
,
L
,...,
X
,
B
,
N
). The total number of such permutations is:
26
×
25
×
24
×···×
3
×
2
×
1
,
which is such a big number that we normally write it using the notation 26
(which
is read as 26
factorial
). In general, if we have
n
objects then the total number of
possible permutations is:
!
n
!=
n
×
(
n
−
1)
×
(
n
−
2)
×···×
3
×
2
×
1
.
DESCRIPTION OF THE SIMPLE SUBSTITUTION CIPHER
The Simple Substitution Cipher can be described as follows:
1. Write the letters
A
,
B
,
C
,...,
Z
in their natural order.
2. Alice and Bob agree on a randomly selected permutation of the letters of the
alphabet.
3. Underneath the letters
A
,
B
,
C
,...,
Z
, write out the chosen permutation of the
letters of the alphabet.
Alice encrypts plaintext letters by replacing them (
substituting
them) with the
permutation letter that is directly beneath them in the table.
This process is depicted in Figure 2.2. In the example shown, the chosen
permutation is
D
G
. The plaintext
EAGLE
is encrypted to
TDZOT
.
On receiving the ciphertext, Bob, who also knows the randomly chosen
permutation, just replaces each ciphertext letter on the bottom row with the
,
I
,
Q
,...,
ABCDEFGHI JKLM
DI QMTBZSYKVOF
NOPQRSTUVWXYZ
ERJAUWPXHLCNG
Figure 2.2.
Encryption using the Simple Substitution Cipher
