  In this paper we compare the performance of various homomorphic encryption
methods on a private search scheme that can achieve $k$-anonymity privacy. To
make our benchmarking fair, we use open sourced cryptographic libraries which
are written by experts and well scrutinized. We find that Goldwasser-Micali
encryption achieves good enough performance for practical use, whereas fully
homomorphic encryptions are much slower than partial ones like
Goldwasser-Micali and Paillier.
