To derive valuable insights from statistics, machine learning applications frequently analyze substantial amounts of data. In this work, we address the problem of designing efficient secure techniques to probe large datasets which allow a scientist to conduct large-scale medical studies over specific attributes of patients' records, while maintaining the privacy of his model. We introduce a set of composable homomorphic operations and show how to combine private functions evaluation with private thresholds via approximate fully homomorphic encryption. This allows us to design a new system named TETRIS, which solves the real-world use case of private functional exploration of large databases, where the statistical criteria remain private to the server owning the patients' records. Our experiments show that TETRIS achieves practical performance over a large dataset of patients even for the evaluation of elaborate statements composed of linear and nonlinear functions. It is possible to extract private insights from a database of hundreds of thousands of patient records within only a few minutes on a single thread, with an amortized time per database entry smaller than 2ms.

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