We study the interference channel with one-sided generalized feedback and secrecy requirement. In our model Message 1 that is known just to Encoder 1 should be decoded by both receivers. Message 2—known only to Encoder 2—should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an outer bound on the capacity-equivocation region for this model that is valid for the ”noisy cribbing” regime. The gap between this upper bound and the inner bound reported before is just in the Markov conditions satisfied by one of the auxiliary random variables. Furthermore, we consider a simplified causal cognitive interference model: the interference channel with a cribbing encoder. We show that when, conditioned on the input of Encoder 1, the interference channel is degraded our outer bound is tight thereby establishing the capacity-equivocation region for this case.