We address the problem of replicating a Voronoi diagram @math of a planar point set @math by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in @math ; 2. the distance to and label(s) of the nearest site(s) in @math ; 3. a unique label for every nearest site in @math . We provide algorithms showing how queries of Type 1 and Type 2 allow an exact cloning of @math with @math queries and @math processing time. We also prove that queries of Type 3 can never exactly clone @math , but we show that with @math queries we can construct an @math -approximate cloning of @math . In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.
There has been less prior related work that takes the black hat'' perspective of this paper, which asks the question of how quickly a data set can be discovered from seemingly minimalistic responses to queries on that object. For example, Goodrich @cite_8 studies the problem of discovering a DNA string from genomic comparison queries and Nohl and Evans @cite_38 study quantitative measures on the global system information that is leaked from learning the contents of multiple RFID tags that are generated by that system.
@cite_38 @cite_8
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Radio Frequency Identification (RFID) systems promise large scale, automated tracking solutions but also pose a threat to customer privacy. The tree-based hash protocol proposed by Molnar and Wagner presents a scalable, privacy-preserving solution. Previous analyses of this protocol concluded that an attacker who can extract secrets from a large number of tags can compromise privacy of other tags. We propose a new metric for information leakage in RFID protocols along with a threat model that more realistically captures the goals and capabilities of potential attackers. Using this metric, we measure the information leakage in the tree-based hash protocol and estimate an attacker’s probability of success in tracking targeted individuals, considering scenarios in which multiple information sources can be combined to track an individual. We conclude that an attacker has a reasonable chance of tracking tags when the tree-based hash protocol is used. In this paper, we study the degree to which a genomic string, @math ,leaks details about itself any time it engages in comparison protocolswith a genomic querier, Bob, even if those protocols arecryptographically guaranteed to produce no additional information otherthan the scores that assess the degree to which @math matches stringsoffered by Bob. We show that such scenarios allow Bob to play variantsof the game of Mastermind with @math so as to learn the complete identityof @math . We show that there are a number of efficient implementationsfor Bob to employ in these Mastermind attacks, depending on knowledgehe has about the structure of @math , which show how quickly he candetermine @math . Indeed, we show that Bob can discover @math using anumber of rounds of test comparisons that is much smaller than thelength of @math , under various assumptions regarding the types of scoresthat are returned by the cryptographic protocols and whether he can useknowledge about the distribution that @math comes from, e.g., usingpublic knowledge about the properties of human DNA. We also providethe results of an experimental study we performed on a database ofmitochondrial DNA, showing the vulnerability of existing real-world DNAdata to the Mastermind attack.