In many situations, clients (e.g., researchers, companies, hospitals) need to outsource joint computations based on joint inputs to external cloud servers in order to provide useful results. Often clients want to guarantee that the results are correct and thus, an output that can be publicly verified is required. However, important security and privacy challenges are raised, since clients may hold sensitive information and the cloud servers can be untrusted. Our goal is to allow the clients to protect their secret data, while providing public verifiability i.e., everyone should be able to verify the correctness of the computed result. In this paper, we propose three concrete constructions of verifiable additive homomorphic secret sharing (VAHSS) to solve this problem. Our instantiations combine an additive homomorphic secret sharing (HSS) scheme, which relies on Shamir's secret sharing scheme over a finite field F, for computing the sum of the clients' secret inputs, and three different methods for achieving public verifiability. More precisely, we employ: (i) homomorphic collision-resistant hash functions; (ii) linear homomorphic signatures; as well as (iii) a threshold RSA signature scheme. In all three cases we provide a detailed correctness, security and verifiability analysis and discuss their efficiency.
Often service providers need to outsource computations on sensitive datasets and subsequently publish statistical results over a population of users. In this setting, service providers want guarantees about the correctness of the computations, while individuals want guarantees that their sensitive information will remain private. Encryption mechanisms are not sufficient to avoid any leakage of information, since querying a database about individuals or requesting summary statistics can lead to leakage of information. Differential privacy addresses the paradox of learning nothing about an individual, while learning useful information about a population. Verifiable computation addresses the challenge of proving the correctness of computations. Although verifiable computation and differential privacy are important tools in this context, their interconnection has received limited attention. In this paper, we address the following question: How can we design a protocol that provides both differential privacy and verifiable computation guarantees for outsourced computations? We formally define the notion of verifiable differentially private computation (VDPC) and what are the minimal requirements needed to achieve VDPC. Furthermore, we propose a protocol that provides verifiable differentially private computation guarantees and discuss its security and privacy properties.
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