Local differential privacy (LDP) is an efficient solution for providing privacy to client's sensitive data while simultaneously releasing aggregate statistics without relying on a trusted central server (aggregator) as in the central model of differential privacy. The shuffle model with LDP provides an additional layer of privacy, by disconnecting the link between clients and the aggregator, further improving the utility of LDP. However, LDP has been shown to be vulnerable to malicious clients who can perform both input and output manipulation attacks, i.e., before and after applying the LDP mechanism, to skew the aggregator's results. In this work, we show how to prevent malicious clients from compromising LDP schemes. Specifically, we give efficient constructions to prevent both input \ánd output manipulation attacks from malicious clients for generic LDP algorithms. Our proposed schemes for verifiable LDP (VLDP), completely protect from output manipulation attacks, and prevent input attacks using signed data, requiring only one-time interaction between client and server, unlike existing alternatives [28, 33]. Most importantly, we are the first to provide an efficient scheme for VLDP in the shuffle model. We describe and prove secure, two schemes for VLDP in the regular model, and one in the shuffle model. We show that all schemes are highly practical, with client runtimes of < 2 seconds, and server runtimes of 5-7 milliseconds per client.
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