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Secure computations on non-integer values

In this paper we present for the first time a framework that allows secure two-party computations on approximations of real valued signals. In our solution, we use a quantized logarithmic representation of the signal samples, which enables to represent both very small and very large numbers with bounded relative error. We show that numbers represented in this way can be encrypted using standard homomorphic encryption schemes; furthermore we give protocols that allow to perform all arithmetic operations on such encrypted values. Finally we demonstrate the practicality of our framework by applying it to the problem of filtering encrypted signals.