In many problems such as biometrics, multimedia search, retrieval, recommendation systems requiring privacy-preserving 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 amplification is used. In the most cases, the privacy amplification is uniformly applied to all binary features resulting in the data degradation and corresponding loss of performance. To avoid this undesirable effect we propose a new privacy amplification technique that benefits from side information about bit reliability. In this paper, we investigate the identification rate-privacy leak trade-off. The analysis is performed for the case of perfect match between the side information shared between the encoder and decoder as well as for the case of imperfect side information.