Computer Security and Cryptography

7.10 CRIBBING PURPLE: FINDING THE C-STEPPERS

Recovery of the C-steppers is considerably more complicated, because the consonant substitution has the very large period of 25³. Rowlett [1998, p. 151] describes the excitement when Genevieve Feinstein (née Grotjan) discovered the characteristic property of the C-stepper alphabets that was crucial in the success of Magic, the United States codename for intelligence derived from the cryptanalysis of PURPLE.

Table 7.52 lists the positions of the three banks of C-steppers for 0 ≤ i < 78.

7.10.1 First Characteristic Property of C-Steppers

If

• The speed of the C-stepper banks is (S, M, F).
• The permutations Π (i, i + 1) (i = 0, 1) are factored into the C-stepper substitutions, and
• The initial positions of the V-stepper and all C-steppers are 0, then

the ciphertext alphabets in positions [0, 23] and [26, 49] are related as follows:

Table 7.52 shows

If x₂, x₂ ∈ CON and

implies

for 0 ≤ i ≤ 23. That is, when

• the consonant x₁ is enciphered in position ...