Cryptography Reference
In-Depth Information
Polyalphabetic methods are simple substitutions dependent on positions
. These
substitutions really depend only on the position in the text, while their inter-
relationships are determined
only
by the key and the method itself. Such a
method would be much harder to break if the substitution also depended on
the plaintext (naturally such that it could still be decrypted!) but that's not the
case here.
The advantage of this property is that methods can be easily synchronized,
which means that if some characters are garbled during a transmission then
only those few cannot be decrypted. Even if the length of the unclear part is
unknown, it is relatively easy to find the connection. We will see in Section 4.5
that there are methods allowing us to encrypt dependent on the plaintext and
synchronize at the same time.
2.4.2 Bitwise Vigenere Method: Vernam Cipher
A particularly simple variant of polyalphabetic ciphers is the bitwise Vigenere
method, representing the computer-friendly conversion of the characterwise
method. So far, we have looked at 26 letters and added modulo 26 (i.e., we
looked only at the remainders when dividing by 26). Nowadays we work with
bits and bytes. A bit is just a letter in a two-element alphabet (consisting of
'0s' and '1s', where '1' is written as 'L'). Adding modulo 2 in this alphabet
corresponds to the bitwise XOR (exclusive 'or', often written as
⊕
):
0+0=0
0+L=L+0=L
L+L=0
The Vigenere key can continue to remain a finite string, but instead of adding
characterwise, we now add bitwise (a string can actually be thought of as
a bit sequence). The decryption happens simply by re-encryption, since the
XOR operation is involutory (doing the XOR transformation twice generates
the output data again):
⊕
⊕
b=a
(a
b)
This different approach doesn't change anything in either the method or its
cryptanalysis. Schneier [SchnCr] calls this modified method the
simple XOR
method
, while Bauer [BauerMM] calls it the
Vernam cipher
. The latter name,
however, often refers to the bitwise one-time pad (see below).
