In this work we present the concept of differential privacy as a rigorous mathematical definition of privacy, which is required for publishing private data. We define a general setting for numerical data and derive a lower bound for the required error of private mechanisms. Laplace mechanism, $K$-norm mechanism and recursive NIM mechanism are presented, each with an upper bound on its error. We conclude that NIM and $K$-norm mechanism are asimptotically optimal for specific classes of queries. Mechanisms are implemented and problems which arise during the implementation are addressed.
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