  Cloud computing has garnered attention as a platform of query processing
systems. However, data privacy leakage is a critical problem. Chowdhury et al.
proposed Crypt(epsilon), which executes differential privacy (DP) over
encrypted data on two non-colluding semi-honest servers. Further, the DP index
proposed by these authors summarizes a dataset to prevent information leakage
while improving the performance. However, two problems persist: 1) the original
data are decrypted to apply sorting via a garbled circuit, and 2) the added
noise becomes large because the sorted data are partitioned with equal width,
regardless of the data distribution. To solve these problems, we propose a new
method called DP-summary that summarizes a dataset into differentially private
data over a homomorphic encryption without decryption, thereby enhancing data
security. Furthermore, our scheme adopts Li et al.'s data-aware and
workload-aware (DAWA) algorithm for the encrypted data, thereby minimizing the
noise caused by DP and reducing the errors of query responses. An experimental
evaluation using torus fully homomorphic encryption (TFHE), a bit-wise fully
homomorphic encryption library, confirms the applicability of the proposed
method, which summarized eight 16-bit data in 12.5 h. We also confirmed that
there was no accuracy degradation even after adopting TFHE along with the DAWA
algorithm.
