Ptolemaic Indexing

This paper discusses a new family of bounds for use in similarity search, related to those used in metric indexing, but based on Ptolemy's inequality, rather than the metric axioms. Ptolemy's inequality holds for the well-known Euclidean distance, but is also shown here to hold for quadratic form metrics in general, with Mahalanobis distance as an important special case. The inequality is examined empirically on both synthetic and real-world data sets and is also found to hold approximately, with a very low degree of error, for important distances such as the angular pseudometric and several Lp norms. Indexing experiments demonstrate a highly increased filtering power compared to existing, triangular methods. It is also shown that combining the Ptolemaic and triangular filtering can lead to better results than using either approach on its own

On the Measurement of Privacy as an Attacker's Estimation Error

A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and systematic approach to measuring privacy, as well as to assist systems designers in selecting the most appropriate metric for a given application. In this work we propose a theoretical framework for privacy-preserving systems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims to disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and comparing a number of well-known metrics under a common perspective. The arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.Comment: This paper has 18 pages and 17 figure

Anonymizing continuous queries with delay-tolerant mix-zones over road networks

This paper presents a delay-tolerant mix-zone framework for protecting the location privacy of mobile users against continuous query correlation attacks. First, we describe and analyze the continuous query correlation attacks (CQ-attacks) that perform query correlation based inference to break the anonymity of road network-aware mix-zones. We formally study the privacy strengths of the mix-zone anonymization under the CQ-attack model and argue that spatial cloaking or temporal cloaking over road network mix-zones is ineffective and susceptible to attacks that carry out inference by combining query correlation with timing correlation (CQ-timing attack) and transition correlation (CQ-transition attack) information. Next, we introduce three types of delay-tolerant road network mix-zones (i.e.; temporal, spatial and spatio-temporal) that are free from CQ-timing and CQ-transition attacks and in contrast to conventional mix-zones, perform a combination of both location mixing and identity mixing of spatially and temporally perturbed user locations to achieve stronger anonymity under the CQ-attack model. We show that by combining temporal and spatial delay-tolerant mix-zones, we can obtain the strongest anonymity for continuous queries while making acceptable tradeoff between anonymous query processing cost and temporal delay incurred in anonymous query processing. We evaluate the proposed techniques through extensive experiments conducted on realistic traces produced by GTMobiSim on different scales of geographic maps. Our experiments show that the proposed techniques offer high level of anonymity and attack resilience to continuous queries. © 2013 Springer Science+Business Media New York