Location data are widely used in mobile apps, ranging from location-based
recommendations, to social media and navigation. A specific type of interaction
is that of location-based alerts, where mobile users subscribe to a service
provider (SP) in order to be notified when a certain event occurs nearby.
Consider, for instance, the ongoing COVID-19 pandemic, where contact tracing
has been singled out as an effective means to control the virus spread. Users
wish to be notified if they came in proximity to an infected individual.
However, serious privacy concerns arise if the users share their location
history with the SP in plaintext. To address privacy, recent work proposed
several protocols that can securely implement location-based alerts. The users
upload their encrypted locations to the SP, and the evaluation of location
predicates is done directly on ciphertexts. When a certain individual is
reported as infected, all matching ciphertexts are found (e.g., according to a
predicate such as “10 feet proximity to any of the locations visited by the
infected patient in the last week”), and the corresponding users notified.
However, there are significant performance issues associated with existing
protocols. The underlying searchable encryption primitives required to perform
the matching on ciphertexts are expensive, and without a proper encoding of
locations and search predicates, the performance can degrade a lot. In this
paper, we propose a novel method for variable-length location encoding based on
Huffman codes. By controlling the length required to represent encrypted
locations and the corresponding matching predicates, we are able to
significantly speed up performance. We provide a theoretical analysis of the
gain achieved by using Huffman codes, and we show through extensive experiments
that the improvement compared with fixed-length encoding methods is
substantial.

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