CRYPTOLOGIC QUARTERLY
stepped, and then continued to pause as the medium wheel stepped.15 The following chart depicts what happens when the slow wheel turns.
| Fast Wheel | Delayed Fast | Medium | Slow | (1-2-3 motion) |
| 23 | 1 | 25 | 1 | |
| 24 | 2 | 25 | 1 | |
| 25 | 2 | 25 | 2 | |
| 1 | 2 | 1 | 2 | |
| 2 | 3 | 1 | 2 | |
| 3 | 4 | 1 | 2 | |
| . | . | . | . 16 |
Of the 120 indicators, 20 were used for each type of motion. The differences within each type .of motion were determined by the starting point of the wheels. The starting points had been carefully selected by the Japanese to reduce the possibility of overlaps and to avoid messages in depth.17
There were three cryptographic elements of Purple which had to be recovered if every Purple message were to be read.
- 1. The basic wiring of the switches.
- 2. The setting of the switches.
- 3. The plugboard sequence used for enciphering the message.
The first element, the basic wiring of the switches, was determined in the solution of the first few messages. This fundamental part of the system did not change. The setting of the respective switches was determined by the key (transmitted in the first group of the message). This remained constant, once determined for any one message, and was then known for all messages with the same key. The third element, the sequence used for any particular message, changed from day to day. In order to read all messages enciphered by means of this system (once the basic wiring of the rotary switches had been recovered and the settings for the switches for each of the 120 keys determined), only the third of the basic elements had to be recovered cryptanalytically. Since this was a function of the date, the problem became a matter of solving a new sequence for each day's traffic.18
Once the initial success was achieved, the analysts set out to create an analog machine. Figures 2 and 3 show this machine, which may be viewed at the NSA archives. As of 1 April 1941 it was possible to read 99 percent of the intercepted traffic. In addition, it had become possible to determine the route
- 6 R.I.P 77, p. 2-20.
- 16 Ibid.
- 17 Friedman., p. 7.
- 18 Ibid., p. 2-3.
