Efficient Function-Hiding Inner Product Functional Encryption and Its Application to Fine-Grained Data Sharing

In a function-hiding inner product functional encryption (FH-IPFE) scheme, both secret keys and ciphertexts are associated with vectors. Given a secret key for an $n$-dimensional vector $\mathit{x}$, and a ciphertext for an $n$-dimensional vector $\mathit{y}$, a decryptor learns the inner product value $⟨\mathit{x},\mathit{y}⟩$ and nothing else about both $\mathit{x}$ and $\mathit{y}$. FH-IPFE has been shown to be very useful in privacy-preserving computation. In this paper, we first propose a new (secret-key) FH-IPFE scheme and prove it the secure in the generic group model. Compared with the state-of-the-art scheme of Kim et al., the proposed scheme has comparable performance in decryption and reduces 1) the size of master key from $n^2$ to $3n-1$, 2) the setup complexity from $O\left(n^3\right)$ to $O\left(n\right)$, and 3) the encryption and key generation complexities from $O(n^2)$ to $O(n\log n)$. To the best of our knowledge, this is the most efficient construction based on pairings to date. Moreover, we apply our FH-IPFE scheme to build a fine-grained data sharing system, where data owners store their encrypted data on an untrusted server. Our design supports not only basic database operations but also statistical analyses on encrypted data. To achieve this goal, we also introduce a new security notion, partial-key exposure-resilient simulation-based security (PK-ER-SIM), for FH-IPFE, which enables lightweight clients to securely delegate heavy computations to a powerful server and may be independent of interest.