http://teddit.i2p/r/crypto/comments/tgvkf0/resources_for_multipower_rsa_using_modulus_of_the
Because Z/n is isomorphic to Z/p^k * Z/q, and exponentiating multiples of p to any power greater than 1 clearly isn ' t 1:1 in the left group. On the other hand, it ' s a negligibly rare failure case, and an attacker can ' t trigger it unless they ' ve already factored n. Also as I ' m sure you ' re aware, the point of multi-power RSA isn ' t to use d itself, but instead to use d mod p-1 and d mod q-1, and then Hensel lift to a solution mod p^k.