This paper considers the problem of transmitting digital data from a source reliably to a legitimate user, subjected to a wiretap at a receiver that employs a fixed decoding strategy. Specifically, we assume that the wiretapper views the same channel output as the legitimate user, but decodes the message using some fixed decoding strategy which might be mismatched with respect to the channel. This model aims to capture the natural situation in privacy where knowledge of the privacy mapping at the source can me modeled as channel statistics. In that case, all observers receive the same data, but have different levels of knowledge, or familiarity, regarding the observed user who uses a privacy mapping. We analyze two different security metrics; probability of error at the eavesdropper and semantic-security, and provide achievable rates under both criteria.