Page:Red and Purple - A Story Retold.pdf/9

 RED AND PURPLE

cyclic repetition and to solve the system. There were never more than two messages that met this condition. A second possibility was to convert several messages with the same indicator but on different days to the same base. In a thousand or more messages, a mere six were found which met this second condition. These six messages, with indicator 59173, were the key to the breaking of the system.

The analysts discovered repeated sequences within these six messages on 20 September 1940 at 2 p.m. The first complete solution came one week later, on 27 September, the same day that Germany, Italy, and Japan signed the Tripartite Agreement. Two of the six messages were completely deciphered, and the other four were partially deciphered. More important, from this solution the analysts were able to build distribution tables which could be used to solve any message with indicator 59173. Since there were 120 indicators, only 119 were left to be solved.13

One reason that the solution of Purple was so difficult was that the analysts assumed that Purple was a rotor machine, like Red. In fact Purple was a uni-selector machine (see Appendix B). With Red, the sixes and the twenties were enciphered by a commutator whose stepping was controlled by a break wheel of 47 positions with certain skips in the cycle. With Purple, the sixes were enciphered by means of a single uniselector. The encipherment of the twenties was performed by three uniselectors in series.

In more detail the machine consisted of 13 switches, each of 25 points. These switches were of the type used in automated telephony. One of the 13 switches controlled the encipherment of the sixes. This switch went through the same 25-point cycle over and over, as many times as necessary to encipher the message. The twenty-five different alphabets used in the encipherment were a carefully selected set of 25 of the possible 720 permutations of six elements. The remaining 12 switches enciphered the twenties. There were three banks of four switches each. Each bank contained 25 points which yielded 25 cubed or 15,625 different sequences for enciphering the 20-long alphabet.14

The motion of Purple - difficult to describe - can be thought of as four wheels. The single switch that controlled the encipherment of the sixes will be called the fast wheel. The banks of switches that controlled the enciphering of the twenties can be thought of as three wheels: a delayed fast wheel, a medium wheel, and a slow wheel. These three wheels could be changed to any of six possible orders of motion: 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2, and 3-2-1, where 1 represents the delayed fast wheel, 2 the medium wheel, and 3 the slow wheel. The fast wheel moved every time. The delayed fast wheel moved except when the medium or slow wheel moved. Thus the delayed fast wheel moved for 25 steps, and then paused as the medium wheel moved. When the medium wheel reached 25, and the fast wheel reached 24, the delayed fast wheel paused as the slow wheel


 * 13 Ibid., p. 6.
 * 14 R.I.P. 77, p. 1B-1.