Privacy-Preserving Data-Oblivious Geometric Algorithms for Geographic Data - Computer Science > Computational GeometryReport as inadecuate




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Abstract: We give efficient data-oblivious algorithms for several fundamental geometricproblems that are relevant to geographic information systems, including planarconvex hulls and all-nearest neighbors. Our methods are -data-oblivious- inthat they don-t perform any data-dependent operations, with the exception ofoperations performed inside low-level blackbox circuits having a constantnumber of inputs and outputs. Thus, an adversary who observes the control flowof one of our algorithms, but who cannot see the inputs and outputs to theblackbox circuits, cannot learn anything about the input or output. Thisbehavior makes our methods applicable to secure multiparty computation SMCprotocols for geographic data used in location-based services. In SMCprotocols, multiple parties wish to perform a computation on their combineddata without revealing individual data to the other parties. For instance, ourmethods can be used to solve a problem posed by Du and Atallah, where Alice hasa set, A, of m private points in the plane, Bob has another set, B, of nprivate points in the plane, and Alice and Bob want to jointly compute theconvex hull of A u B without disclosing any more information than what can bederived from the answer. In particular, neither Alice nor Bob want to revealany of their respective points that are in the interior of the convex hull of Au B.



Author: David Eppstein, Michael T. Goodrich, Roberto Tamassia

Source: https://arxiv.org/



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