International Association
for Cryptologic Research

Abdalla et al. introduced a notion of ¥emph{identity-based inner-product functional encryption} (IBIPFE) that combines identity-based encryption (IBE) and inner-product functional encryption (IPFE). Thus far, several pairing-based and lattice-based IBIPFE schemes have been proposed. However, there are two open problems. First, there are no known IBIPFE schemes that satisfy the ¥emph{adaptive simulation-based security}. Second, known IBIPFE schemes that satisfy either the adaptive indistinguishability-based security or the selective simulation-based security do not have tight reductions. In this paper, we propose pairing-based and lattice-based IBIPFE schemes that satisfy the tight adaptive simulation-based security. At first, we propose a generic transformation from indistinguishability-based secure $(L + 1)$-dimensional (IB)IPFE} scheme to be simulation-based secure $L$-dimensional (IB)IPFE scheme. The proposed transformation improves Agrawal et al.'s transformation for plain IPFE (PKC 2020) that requires indistinguishability-based secure $2L$-dimensional scheme. Then, we construct a lattice-based IBIPFE scheme that satisfies the tight adaptive indistinguishability-based security under the LWE assumption in the quantum random oracle model. We apply the proposed transformation and obtain the first lattice-based IBIPFE scheme that satisfies adaptive simulation-based security. Finally, we construct a pairing-based IBIPFE scheme that satisfies the tight adaptive indistinguishability-based security under the DBDH assumption in the random oracle model. The pairing-based scheme does not use the proposed transformation towards the best efficiency.