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              <p>Recent years have witnessed a significant development for functional encryption (FE) inthe multi-user setting, particularly with multi-client functional encryption (MCFE). The challengebecomes more important when combined with access control, such as attribute-based encryption(ABE), which was actually not covered syntactically by the public-key FE nor semantically by thesecret-key MCFE frameworks. On the other hand, as for complex primitives, many works havestudied the admissibility of adversaries to ensure that the security model encompasses all realthreats of attacks.1. At a conceptual level, by adding a public input to FE/MCFE, we cover many previous primitives,notably attribute-based function classes. Furthermore, with the strongest admissibility forinner-product functionality, our framework is quite versatile, as it encrypts multiple sub-vectors,allows repetitions and corruptions, and eventually also encompasses public-key FE and classicalABE, bridging the private setting of MCFE with the public setting of FE and ABE.2. Finally, we propose an MCFE with public inputs with the class of functions that combinesinner-products (on private inputs) and attribute-based access-control (on public inputs) forLSSS policies. We achieve the first AB-MCFE for inner products with strong admissibility(from Nguyen et al., ACNS’23) and with adaptive security.In the end, our concrete MCFE leads to MIFE for inner products, public-key single-input inner-product FE with LSSS key-policy, and KP-ABE for LSSS, with adaptive security. Previous AB-MCFEconstructions are either restricted in terms of weaker admissibility (Nguyen et al., ASIACRYPT’22)or considers a slightly larger functionality of attribute-weighted sum but with only selective security (Agrawal et al., CRYPTO’23).</p>
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