Tightly CCA-secure inner product functional encryption scheme

Inner product functional encryption (IPFE) is a modern public key paradigm where the master key can derive a secret key sky for a vector y, which can then be used to decrypt a ciphertext of x to get the inner product (x, y) as output. In ASIACRYPT 2019, Tomida proposed the first tightly secure IPFE scheme in the multi-user and multi-challenge setting based on the matrix decisional Diffie-Hellman (MDDH) assumption. However, the construction achieves CPA security only. Up to now, there is no IPFE scheme with tight CCA security available. In this paper, we construct the first tightly CCA-secure IPFE scheme in the multi-user and multi-challenge setting. The security reduction to the MDDH assumption (including SXDH, k-LIN, etc.) loses only a factor O(log lambda) with lambda the security parameter. Moreover, our scheme enjoys full compactness. To support inner product function of dimension m, our SXDH-based IPFE has (m(2) + 8m + 14) and (3m + 14) group elements in the master public key and ciphertext respectively. This is comparable to the tightly CPA-secure IPFE proposed by Tomida based on the DDH assumption, whose master public key and ciphertext contain (m(2) + 2) and 3m group elements, respectively. Furthermore, we construct the first IPFE with both tight CCA-security and function-hiding property, based on our CCA-secure IPFE. The tight function-hiding CCA security is obtained by adapting the techniques in Lin (CRYPTO 2017) and Gay (PKC 2020) to the multi-user and multi-challenge setting. (C) 2021 Elsevier B.V. All rights reserved.