  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 \emph{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
\emph{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.
