Cryptography Reference
In-Depth Information
as ACULCVUCMACUL:
TOBEORNO T TOBE
ACULCVUCMACUL
The repeated sequence ACUL is a giveaway. The repetition appears at
a distance 9; thus we can infer that possible values of N are 9 or 3 or 1. We
can then apply frequency analysis to the whole cryptogram, to every third
character and to every ninth character; one of them will reveal the plaintext.
This trial and error approach becomes more difficult for large values of N,
i.e., for very long keys.
In the 1920s, electromechanical technology transformed the original
Alberti's disks into rotor machines in which an encrypting sequence with
an extremely long period of substitutions could be generated, by rotating a
sequence of rotors. Probably the most famous of them is the Enigma machine,
patented by Arthur Scherbius in 1918.
A notable achievement of cryptanalysis was the breaking of the Enigma
in 1933. In the winter of 1932, Marian Rejewski, a 27-year-old cryptanalyst
working in the Cipher Bureau of the Polish Intelligence Service in Warsaw,
mathematically determined the wiring of the Enigma's first rotor. From then
on, Poland was able to read thousands of German messages encrypted by
the Enigma machine. In July 1939 Poles passed the Enigma secret to French
and British cryptanalysts. After Hitler invaded Poland and France, the effort
of breaking Enigma ciphers continued at Bletchley Park in England. A large
Victorian mansion in the center of the park (now a museum) housed the
Government Code and Cypher School and was the scene of many spectacular
advances in modern cryptanalysis.
1.4 Truly Unbreakable?
Despite its long history, cryptography only became part of mathematics and
information theory in the late 1940s, mainly as a result of the work of Claude
Shannon (1916-2001) of Bell Laboratories in New Jersey. Shannon showed
that truly unbreakable ciphers do exist and, in fact, they had been known
for over 30 years. They were devised in 1918 by an American Telephone
and Telegraph engineer Gilbert Vernam and Major Joseph Mauborgne of the
U.S. Army Signal Corps. They are called one-time pads or Vernam ciphers
(Figure 1.2).
Both the original design of the one-time pad and the modern version
of it are based on the binary alphabet. The plaintext is converted to a se-
quence of 0's and 1's, using some publicly known rule. The key is another
sequence of 0's and 1's of the same length. Each bit of the plaintext is then com-
bined with the respective bit of the key, according to the rules of addition in
base 2:
0
+
0
=
0
,
0
+
1
=
1
+
0
=
1
,
1
+
1
=
0
.
(1.2)
