Computer Security and Cryptography

7.8 THE PURPLE KEYS

There are seven elements comprising the PURPLE key:

PK1.	The plugboard connections
PK2.	The VOW-stepper implementing 25 permutations of the six-letter input/output pairs – #PK2 = (6!)25;
PK3.	The initial position i0 VOW of the vowel stepper – #PK3 = 25;
PK4.	The 25 permutations in each of the four consonant-stepper banks – #PK4 = (20!25)3;
PK5.	The initial positions (i0(C(0)), i0(C(1)), i0(C(2)) of the consonant steppers – #PK5 = 253;
PK6.	The interconnection permutations Π0, 1 and Π1, 2 betwecn Banks i and i + 1 for i = 0, 1 – #PK6 = 20!2; and
PK7.	The motions of the consonant steppers – #PK7 = 6.

Of course, not all of these #PK ≡ #PK1 × #PK2 × #PK3 × #PK4 × #PK5 × #PK6 × #PK7 keys are independent; for example, the composition of a consonant-stepper CS and the interconnection permutation Π to the next bank is equivalent to just another consonant-stepper. Even so, the PURPLE had a substantial key space.

The Ko codebook listed basic operating instructions for PURPLE; the Otsu codebook listed plugboard settings, which were prescribed in advance and used throughout the Japanese network. Some papers on PURPLE suggest initial wheel settings might have been chosen randomly by the sender and included (in plaintext) in the message indicator. Later, the Otsu codebook listed a set of values whose labels were included in the message indicator.

Why did ...