Constant-weight PIR: Single-round Keyword PIR via Constant-weight Equality Operators


Rasoul Akhavan Mahdavi and Florian Kerschbaum, University of Waterloo


Equality operators are an essential building block in tasks over secure computation such as private information retrieval. In private information retrieval (PIR), a user queries a database such that the server does not learn which element is queried. In this work, we propose equality operators for constant-weight codewords. A constant-weight code is a collection of codewords that share the same Hamming weight. Constant-weight equality operators have a multiplicative depth that depends only on the Hamming weight of the code, not the bit-length of the elements. In our experiments, we show how these equality operators are up to 10 times faster than existing equality operators. Furthermore, we propose PIR using the constant-weight equality operator or constant-weight PIR, which is a PIR protocol using an approach previously deemed impractical. We show that for private retrieval of large, streaming data, constant-weight PIR has a smaller communication complexity and lower runtime compared to SEALPIR and MulPIR, respectively, which are two state-of-the-art solutions for PIR. Moreover, we show how constant-weight PIR can be extended to keyword PIR. In keyword PIR, the desired element is retrieved by a unique identifier pertaining to the sought item, e.g., the name of a file. Previous solutions to keyword PIR require one or multiple rounds of communication to reduce the problem to normal PIR. We show that constant-weight PIR is the first practical single-round solution to single-server keyword PIR.

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@inproceedings {279988,
author = {Rasoul Akhavan Mahdavi and Florian Kerschbaum},
title = {Constant-weight {PIR}: Single-round Keyword {PIR} via Constant-weight Equality Operators},
booktitle = {31st USENIX Security Symposium (USENIX Security 22)},
year = {2022},
isbn = {978-1-939133-31-1},
address = {Boston, MA},
pages = {1723--1740},
url = {},
publisher = {USENIX Association},
month = aug,

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