Cryptography Reference
In-Depth Information
will assume henceforth, that this has been done. Hence all of our keystreams
will be assumed to be generated by keystream generators that are CSPRNGs.
Now we are ready to look at the topic of this section. Before the formal
definition, think of a stream cipher as a cryptosystem where plaintext messages
are encrypted character by character, just before sending the cryptogram.
Stream Ciphers
Let
be a keystream.
A cryptosystem is called a
stream cipher
if encryption upon plaintext strings
m
1
m
2
···
K
be a keyspace for a cryptosystem and let
k
1
k
2
···∈
K
is achieved by repeated application of the enciphering transformation
for
j
≥
1,
E
k
j
(
m
j
)=
c
j
,
and deciphering occurs as repeated application of the deciphering transforma-
tion for
j
≥
1,
D
k
−
1
j
(
c
j
)=
m
j
.
If there exists an
∈
N
such that
k
j
+
=
k
j
for all
j
∈
N
, then we say that the
stream cipher is
periodic
with
period
.
Generally speaking, stream ciphers are faster than block ciphers, and are
easier to describe, since stream ciphers encrypt individual plaintext message
units, usually one bit at a time.
All keystream generators are periodic except for
one-time pads
. This is the
cryptosystem where the (randomly generated) key (used only once) is the size
of the plaintext. (Recall the discussion on pages 83 and 84).
The One-Time-Pad
The one-time-pad is a stream cipher with alphabet of definition
A
=
{
0
,
1
}
that enciphers in the following fashion.
Given a bitstring
m
1
m
2
···
m
∈
M
, and a keystream
k
1
k
2
···
k
∈
K
,
the enciphering transformation is given by
E
k
j
(
m
j
)=
m
j
⊕
k
j
=
c
j
∈
C
,
and the deciphering transformation is given by
D
k
j
(
c
j
)=
c
j
⊕
k
j
=
m
j
,
for all
j
=1
,
2
,...,
∈
N
. The keystream is randomly chosen and never used
again.
The one-time-pad is a stream cipher wherein the keystream does not repeat,
so it is not periodic. Moreover, it is an example of another notion we encountered
on page 83, namely, that of a running-key, a notion shared by a cipher we
described on page 56, namely, the Vigenere cipher (translated into arithmetic
modulo
n
). Recall that this is the cryptosystem where there is a keyphrase used
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