Construction of Differentially Private Summaries over Fully Homomorphic Encryption

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.