In many problems such as biometrics, multimedia search, retrieval, recommendation systems requiring privacypreserving similarity computations and identification, some binary features are stored in the public domain or outsourced to third parties that might raise certain privacy concerns about the original data. To avoid this privacy leak, privacy protection is used. In most cases, privacy protection is uniformly applied to all binary features resulting in data degradation and corresponding loss of performance. To avoid this undesirable effect we propose a new privacy amplification technique that is based on data hiding principles and beneffts from sideinformation about bit reliability a.k.a. soft fingerprinting. In this paper, we investigate the identification-rate vs privacy-leak trade-off. The analysis is performed for the case of a perfect match between side information shared between the encoder and decoder as well as for the case of partial side information.