Cryptography Reference
In-Depth Information
produced for each message is a monumental task, especially since each one has
to be the size of the plaintext, which is the second problem. To have keys the
size of the plaintext creates unwieldy key management problems. Yet, it is a
completely provable secure cryptosystem. Thus, it is used by those who need it
for absolute secrecy, such as, for instance, the protection of missile launch codes.
Then it is practicable, but for low-level security such as e-mail messages between
government oQcials for the day-to-day running of business, other means must
be used.
It is part of the folklore that Soviet spies used one-time pads to send mes-
sages, and that they were also used in German diplomatic systems starting in
the late 1920s.
In our modern computer age, one can translate all plaintext and ciphertext
into numerical data, in particular, into binary.
2.7
Since we have a sequence of
zeros and ones now, we can perform addition modulo 2, so we again end up
with zeros and ones, ideal for transmission. This is how the one-time pad was
used in the legendary
hot line
between Washington and Moscow, inspired by the
Cuban missile crisis of the 1960s. They used what was called the
one-time tape
,
which was a physical manifestation of the Vernam cipher. At the American end,
this took the form of the ETCRRM II or
Electronic Teleprinter Cryptographic
Regenerative Repeater Mixer II
. The manner in which the one-time tape worked
was that there existed two magnetic tapes, one at the enciphering source, and
one at the deciphering end, both having the same running key on them. To
encipher, one performs addition modulo 2 with the plaintext and the bits on the
tape. To decipher, the receiver performs addition modulo 2 with the ciphertext
and the bits on the (identical) tape at the other end.
2.8
Thus, they had instant
deciphering and perfect secrecy if they used truly random keys, each used only
once, and the tapes were burned after each use. The same keys cannot be used
twice since the one-time pad would then be open to an attack since the key
k
can be computed by addition modulo 2 of the plaintext with the ciphertext.
2.9
Thus, we see that today one-time pads are most practicable for military and
diplomatic purposes when unconditional security is of the utmost importance.
Vernam is known for other discoveries. A patent was filed in September of
1918 (and granted with issuance in July 1919) for a cipher that Vernam invented,
which was the first polyalphabetic cipher automated using electrical impulses.
For this, he has earned the title of the
Father of Automated Cryptography
.
+2
t
a
t
where
a
j
∈{
0
,
1
}
and
t
is a nonnegative integer. The
a
j
s are called
bits
, which is a contraction
of
bi
nary digi
ts
. Typically, we will use the notation throughout for this binary representation
as:
n
10
=(
a
t
a
t
−
1
...a
1
a
0
)
2
to denote that our base 10 integer
n
has a binary representation
as given. For instance, the binary representation of 100 is: (100)
10
= (1100100)
2
since
100 = 2
6
2.7
Recall that any
n
can be represented in the form
n
=
a
0
+2
a
1
+2
2
a
2
+
∈
N
···
·
1+2
5
·
1+2
4
·
0+2
3
·
0+2
2
·
1+2
1
·
0+2
0
·
0. See Appendix A for more information
on basic mathematical facts.
2.8
This process is often called
XORing
since it is use of
exclusive or
, which we will denote
later in the text by
(see page 116).
2.9
Thisisanexampleofwhatiscalleda
known-plaintext attack
,whichmeansanattackwhere
a cryptanalyst has both some plaintext and its corresponding ciphertext from an intercepted
cryptogram from which to deduce the plaintext in general, or the key.
⊕
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