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We present Whisper, a system for privacy-preserving collection of aggregate statistics. Like prior systems, a Whisper deployment consists of a small set of non-colluding servers; these servers compute aggregate statistics over data from a large number of users without learning the data of any individual user. Whisper's main contribution is that its server-to-server communication cost and its server-side storage costs scale sublinearly with the total number of users. In particular, prior systems required the servers to exchange a few bits of information to verify the well-formedness of each client submission. In contrast, Whisper uses silently verifiable proofs, a new type of proof system on secret-shared data that allows the servers to verify an arbitrarily large batch of proofs by exchanging a single 128-bit string. This improvement comes with increased client-to-server communication, which, in cloud computing, is typically cheaper (or even free) than the cost of egress for server-to-server communication. To reduce server storage, Whisper approximates certain statistics using small-space sketching data structures. Applying randomized sketches in an environment with adversarial clients requires a careful and novel security analysis. In a deployment with two servers and 100,000 clients of which 1% are malicious, Whisper can improve server-to-server communication for vector sum by three orders of magnitude while each client's communication increases by only 10%.