Fingerprint Codes Meet Geometry: Improved Lower Bounds for Secret Queries and Dynamic Data Analysis
Fingerprint codes are an important tool to prove the lower bounds on differential privacy. They have been used to prove strong bounds on several important questions, especially in the “low precision” regime. Unlike reconstruction/difference methods, but they are more suitable for proving very low bounds, on query sets that arise naturally in fingerprint coding. In this work, we propose a general framework for proving lower bounds for fingerprint type, which allows us to adapt the procedure to the geometry of the query set. Our approach allows us to show several new results.
First, we show that any (sample- and population-)accurate response algorithm Arbitrarily variable computation questions in the universe accuracy requirements samples. This shows that the methods based on privacy classification are good for this question, and they are better for lower bounds known in advance. again . Second, we show that anywhere -DP response algorithm to calculate the questions accurately requirements samples. Our framework allows to prove this directly and further by the bond was proved by Bun, Ullman and Vadhan (2013) using the formulation. Third, we show the sampling complexity of answering a set of 0-1 random questions under limited privacy variation. To achieve this, we provide new upper and lower bounds combined with existing bounds allowing us to complete the picture.
