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example, the letter in the ‘V’ position of the Japanese alphabet would be plugged
into the ‘B’ socket of the SIS analog). In this paper, we will use the SIS alphabet.
Figure 2 shows the input typewriter connected to Switch #3 while the output
typewriter is connected to Switch #1
3
. These are the correct connections for
deciphering a normal PURPLE message. The input and output connections
would be reversed when enciphering the message. However, messages could
also be enciphered in ‘reverse’ mode (i.e. enciphered in decipher mode and vice
versa).
Not shown in Figure 2 is the wiring of the switches, which required almost 2,000
wired connections. The sixes switch has six levels with 25 output contacts per
level. The wiring table for the sixes switch is shown in Figure 6, where the top row
denotes the input connection and each of the succeeding 25 rows denotes the
permutation output at that switch position. For each of the 25 output levels, all of
the “1” outputs of the switch must be connected together. The same rule applies
to outputs 2 through 6. Then each group of outputs at each level must be wired
together. With six levels and 25 contacts, this requires a total of 150 wires. Figure
4 shows the wiring of level 5 of the sixes switch and gives an example of the
wiring complexity. The remaining levels of the sixes switch would show similar
complexity. The twenties switches have 20 inputs and 25 positions, which
requires 500 wires for each of the three switches. The result was what has been
described as a “rat’s nest” of wiring surrounding each switch [2, p. 232].
To understand the operation of the PURPLE machine, consider the circuit of
Figure 4 with electric typewriters connected to the input and output. When a key
on the input typewriter is pressed, for example “K,” an electric current is applied
to the “K” input of the plugboard. Depending on the plugboard substitution, “K”
may be changed to one of the sixes, such as “U.” Since “U” is the fifth vowel, the
typewriter current will be applied to level 5 of the sixes switch. If the sixes switch
is in position 3, then Figure 6 tells us that input 5 is connected to output 2 (which
then connects to “E”). Next the output plugboard connects “E” to some other
letter, perhaps “S,” and finally the current causes an “S” to be printed on the
output typewriter.
3
The U.S. Army Signal Intelligence Service (SIS) cryptographers numbered the switches as #3,
#2, and #1, while the Japanese order was #1, #2, and #3. This would not have been obvious from
cryptanalysis, but was only discovered because the Japanese occasionally sent new switch
settings in messages, which were themselves enciphered, in the PURPLE system. Hereafter the
SIS numbering will be used.
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