Computer Security and Cryptography

6.2 ROTOR SYSTEMS

A rotor system incorporates more than one rotor sharing the same axis of rotation. The rotor system shown in Figure 6.3 produces the polyalphabetic substitution, which is a composition of the r substitutions θ₀, θ₁, …, θ_r−1 (Fig. 6.4).

Figure 6.3 A straight-through rotor system.

Figure 6.4 An encipherment path in a straight-through rotor system.

If each of the r rotors are rotated counterclockwise k₀, k₁, …, k_r−1 positions (relative to their benchmarks), the substitution

is replaced by

It is intended that the position of at least one rotor changes after the encipherment of each plaintext letter in a rotor system. The position of the jth rotor for the encipherment of the ith plaintext letter is determined by a rotational displacement function k_j(i) so that

The simplest rotational displacement functions {k_j(i)} are (modulo m), with m = 26. This is analogous to an automobile's ...