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Motivated by the recent widespread emergence of Location-Based Services (LBS) over mobile devices, the authors explore efficient protocols for proximity-testing. Such protocols allow a group of friends to discover if they are all close to each other in some physical location, without revealing their individual locations to each other. They focus on hand-held devices and aim at protocols with very small communication complexity and a small number of rounds. The proximity-testing problem can be reduced to the Private Equality Testing (PET) problem, in which parties find out whether or not they hold the same input (drawn from a low-entropy distribution) without revealing any other information about their inputs to each other.
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