Transmission, identification and common randomness capacities for wire-tape channels with secure feedback from the decoder

We analyze wire-tape channels with secure feedback from the legitimate receiver. We present a lower bound on the transmission capacity, which we conjecture to be tight and which is proved to be tight for Wyner's original (degraded) wire-tape channel and also for the reversely degraded wire-tape channel for which the legitimate receiver gets a degraded version from the enemy. Somewhat surprisingly we completely determine the capacities of secure common randomness and secure identification. Unlike for the DMC, these quantities are different here, because identification is linked to non-secure common randomness.