Paper 2025/398

Tight Adaptive Simulation Security for Identity-based Inner-Product FE in the (Quantum) Random Oracle Model

Abstract

Abdalla et al. (ASIACRYPT 2020) introduced a notion of identity-based inner-product functional encryption (IBIPFE) that combines identity-based encryption 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 adaptive simulation-based security. Second, known IBIPFE schemes that satisfy the adaptive indistinguishability-based security or the selective simulation-based security do not have tight reductions. In this paper, we propose lattice-based and pairing-based IBIPFE schemes that satisfy the tight adaptive simulation-based security. At first, we propose a generic transformation from an indistinguishability-based secure $(L + 1)$-dimensional (IB)IPFE scheme to a simulation-based secure $L$-dimensional (IB)IPFE scheme. The proposed transformation improves Agrawal et al.'s transformation for plain IPFE (PKC 2020) that requires an 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 simulation-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.