Cryptography Reference
In-Depth Information
Enigma that was to enter history as the Nazi regime's cryptosystem of
choice to secure its military communications.
The essential component of these devices was the wired rotor wheel, a
mechanism that hardwired a single monoalphabetic substitution of 26
inputs to 26 outputs—for example,
a
to
m
,
p
to
z
, and so on. Two tech-
niques vastly multiplied the power of this simple mechanism: first, wheels
were placed alongside and connected to two or more additional rotors
wheels, each implementing distinct substitutions, so that the outputs of
one rotor fed the inputs of its neighbor; second, after the encryption of
each single letter, a stepping mechanism moved the first rotor forward one
position, while the second wheel moved forward one position after a com-
plete revolution of the first wheel, and so on with the third wheel—in the
manner of a car odometer. This resulted in each letter of the plaintext being
encoded with a completely different set of substitutions.
30
Using a different ciphering alphabet for each plaintext letter was a well-
established cryptographic technique, dating back as far as Trithemius's
1516
Six Topics of Polygraphy
. The longer the
period
—the number of different
cipher alphabets used before the same sequence of plaintext/ciphertext
alphabets is reused—the stronger the cipher and the more involved the
ciphering and deciphering process. The automation provided by rotor
machines enabled the period to grow to astronomical length (for the
Enigma, 26
3
or approximately 17,000) without loss of accuracy. Because
most military messages were of a much shorter length, Enigma-encrypted
ciphertexts thus rarely exhibited the kind of frequency patterns so crucial
to cryptanalysis. Brute force attacks were similarly difficult, as the total key
space exceeded 3 × 10
114
: 26
3
choices for the initial position of the rotors,
6 further choices for their ordering, and an additional 26! choices from a
plugboard that implemented a fixed but easily modified monoalphabetic
substitution.
The procedures for key agreement were sophisticated. Each organiza-
tional unit (groups of planes, U-boats, etc.) was issued a codebook listing
the original position of the rotors and plugboard for each day. After setting
up the machine with the codebook parameters, the operator would observe
the following procedure: for each new message, randomly select new rotor
positions, encrypt these using the codebook settings for the day, and trans-
mit the result as the first part of the message (the
indicator
); continue
encryption of the message using the random rotor positions. In order to
