We identify a new class of vulnerabilities in implementations of differential privacy. Specifically, they arise when computing basic statistics such as sums, thanks to discrepancies between the implemented arithmetic using finite data types (namely, ints or floats) and idealized arithmetic over the reals or integers. These discrepancies cause the sensitivity of the implemented statistics (i.e., how much one individual's data can affect the result) to be much larger than the sensitivity we expect. Consequently, essentially all differential privacy libraries fail to introduce enough noise to meet the requirements of differential privacy, and we show that this may be exploited in realistic attacks that can extract individual-level information from private query systems. In addition to presenting these vulnerabilities, we also provide a number of solutions, which modify or constrain the way in which the sum is implemented in order to recover the idealized or near-idealized bounds on sensitivity.
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