Cryptography Reference
In-Depth Information
In other words, the ciphertext can be computed by adding the plaintext
P
and the
key
K
and then reducing the summodulo 26. In a similar way, decryption consists
of subtracting the key
K
from the ciphertext
C
and then reducing modulo 26. In
other words, the decryption algorithm can be described as:
P
=
C
−
K
mod 26
.
INSECURITY OF THE CAESAR CIPHER
Hopefully it should already be evident that a bank should not adopt the Caesar
Cipher to protect its financial records! It is useful, however, to be able to
articulate the problems with the Caesar Cipher precisely, using cryptographic
terminology.
There are several reasons why the Caesar Cipher is not a secure cryptosystem,
some of which we will discuss with respect to later cryptosystems. By far the most
obvious, and serious, is the size of the keyspace. With only 26 possible keys to try
out, an exhaustive key search is well within the means of an attacker armed with a
pencil, a scrap of paper, and five minutes to spare! The attacker simply tries each
of the 26 keys to obtain 26 candidate plaintexts. If the plaintext is recognisable
(for example, it is in English) then the correct one should be obvious.
Note that if the plaintext does not contain identifiable redundancy (suppose it
consists of randomly chosen letters) then an exhaustive key search is still highly
effective as it reduces the number of candidate plaintexts to 26. Even if the original
plaintext was just five letters long, without any knowledge of the ciphertext all we
know is that the plaintext is one of
26
5
=
26
×
26
×
26
×
26
×
26
=
11881376
possible plaintexts consisting of five letters. Once we have seen the ciphertext, we
can reduce this to just 26 candidates, which is dramatic progress.
In Section 3.1.3 we will discuss the only very special (and impractical)
circumstance when the Caesar Cipher
is
a secure cryptosystem.
2.1.2
Simple Substitution Cipher
Our next example is the
Simple Substitution Cipher
, which is a considerable
improvement on the Caesar Cipher. Like the Caesar Cipher, however, we will
see that this cryptosystem is also fundamentally flawed. We start with a useful
definition.
PERMUTATIONS
A
permutation
of a set of objects is an arrangement of the objects in some order.
For example, (
A
,
B
,
C
), (
B
,
C
,
A
) and (
C
,
A
,
B
) are all permutations of the letters
A
,
B
and
C
. The total number of possible permutations of
A
,
B
and
C
is:
3
×
2
×
1
=
6
.
