Consider a rotor with a hardwired permutation of {0,1,2,..., n — 1}. Denote this permutation as P = (ρο,ρι,... ,p n-i ), where P permutes i to pi. Let d i be the displacement of pi, that is, d i = pi...

Consider a rotor with a hardwired permutation of {0,1,2,..., n — 1}. Denote this permutation as P = (ρο,ρι,... ,p_n-i), where P permutes i to pi. Let d_i
be the displacement of pi, that is, d_i
= pi — i (mod n). Find a formula for the elements of the fcth rotor shift of P, which we denote P_k, where the shift is in the same direction as the rotors described in Section 6.2.3. Your formula must be in terms of pt and d_i.