Page:Red and Purple - A Story Retold.pdf/4

 CRYPTOLOGIC QUARTERLY

If there were 47 active teeth on a break wheel with a 26 long alphabet wheel, then there would be a cycle length of 26 ✕ 47 (1222), and coincidences would be observed more frequently on a width of 1222. In the case of a 6-wheel, a 20-wheel, and a break wheel with 47 effective teeth, the expected cycle length would be 20 ✕ 6 ✕ 47. Because of the common factor of 2, the cycle length would actually be 20 ✕ 3 ✕ 47.

The problem with measuring a cycle length of this size was that the messages were under 2000 characters long. The analysts therefore concentrated on the cycle of the 6-wheel. They considered counts for widths of 6 ✕ 31 through 6 ✕ 47. The highest count was for 6 ✕ 43, width 258. The hypothesis from this information, which was correct, was that there was a 47-long break wheel, with 43 effective teeth.

In order to locate the places on the wheel where there were skips (four skips in each cycle of 43), the message was written on a cycle of 43 letters. It was then possible to align the skips vertically. Adjacent columns could be matched to give the relative shift between the columns. 6

Further analysis led to a complete understanding of the Red machine and of the indicator system of the messages. It was possible to build an analog machine and to decrypt virtually all of the messages. Figure l is a photograph of an analog machine. It consists of a plug board, an interrupter wheel, a large alphabet wheel, a small alphabet wheel, a reversing gear, and an operating handle. The two alphabet wheels are under the plugboard. 7

There were 240 indicators for the settings of the three wheels of the machine. In addition, the sequences for the two alphabet wheels were set up on a plugboard which was changed daily. For key numbers starting with 0, 1, 2, or 3, the machine ran in ascending order, while for numbers 4, 5, 6, 7, 8, or 9 the machine ran in reverse order.

The following steps are instructions for deciphering the M-3A machine. Tables 1-A and 2 (mentioned below) had been generated by the analysts and were available to the decipherers.


 * 1. Obtain the message key number used in enciphering by subtracting from the transmitted key number the following numbers:


 * a. 1st to 10th of the month     - - 32210
 * b. 11th to 20th of the month    - - 23120
 * c. 21st to the end of the month - - 12320


 * 2. Enter table 1-A with the date and pick out the plugboard sequence. The sequences vary with message key number for any one date.


 * 3. With the key number (obtained by subtraction) enter table 2, pick out the initial settings for wheels B, C, and D, and set the wheels accordingly.


 * 6 Ibid., p. 9.
 * 7 R.I.P. 6, p. 1.