Practical Differential Privacy for Location Data Aggregation using a Hadamard Matrix

Location data are very valuable personal information. These private data are frequently sent to servers to query relevant information to the users. Often aggregated location statistics are made publicly available for public resource planning, behavioral studies, or commercial usages. This raises privacy issues. Working under the differential privacy paradigm, Chen, Li, Qin, Kasiviswanathan, and Jin [ICDE'16] proposed a count estimation protocol called PCEP which ensures є-local differential privacy and provides good frequency approximation based on the private succinct histogram protocol by Bassily and Smith [STOC'15]. We observe that, while providing an excellent theoretical guarantee, one of the key steps which essentially reduces location dimension, based on the Johnson-Lindenstrauss Lemma is not very helpful in practice as the actual dimension is even larger than the original dimension. We replace this step with the usage of Hadamard matrix. This results in more communication-efficient protocol (because the Hadamard matrix can be computed efficiently by the users) with theoretically improved approximation guarantee.