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In light of the recent development of multimedia and networking technologies, an exponentially increasing amount of content is available via various public services. That is why content identification attracts a lot of attention. One possible technology for content identification is based on digital fingerprinting. When trying to establish information-theoretic limits in this application, usually it is assumed that the codewords are of infinite length and that a jointly typical decoder is used in the analysis. These assumptions represent a certain over-generalization for the majority of practical applications. Consequently, the impact of the finite length on the mentioned limits remains an open and largely unexplored problem. Furthermore, leaking of privacy-related information to third parties due to storage, distribution and sharing of fingerprinting data represents an emerging research issue that should be addressed carefully. This paper contains an information-theoretic analysis of finite length digital fingerprinting under privacy constraints. A particular link between the considered setup and Forney's erasure/list decoding  is presented. Finally, complexity issues of reliable identification in large databases are addressed.